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https://physics.stackexchange.com/questions/477278/b-violation-and-electric-charge | 1,563,880,694,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195529276.65/warc/CC-MAIN-20190723105707-20190723131707-00181.warc.gz | 500,666,487 | 34,940 | # B violation and electric charge
Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as
$$\Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum}) \tag1$$
So, I've been thinking: if $$B$$ is violated, is this implying that electric charge isn't conserved? And I have a technical question on this $$B$$: is it defined as
$$B = \frac{N_q - N_{\bar{q}}}{3}, \quad {\rm or}\quad B = N_q - N_{\bar{q}}\ ?$$
At tree level, Feynman diagrams grant conservation but I can imagine a triangle diagram with a loop made with a fermion, $$f$$, that produces a $$Z^0$$, goes on the loop and destroys with its antipaticle given as a result another $$Z^0$$ boson (see image below). Since this vertices contain left and right projectors, then they give an anomaly such as the chiral anomaly.
In the picture,
$$\sum_f = \sum_{all\ quarks\\within\ SM}$$
• I'm not sure how your triangle diagram is relevant to your question, since neither of $\gamma, Z^0$ are electrically charged. – ACuriousMind May 1 at 23:41
• @ACuriousMind What should I use? – Vicky May 2 at 0:07 | 353 | 1,202 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2019-30 | longest | en | 0.897581 |
https://goprep.co/write-the-names-of-the-following-compounds-and-deduce-their-i-1nkbm5 | 1,603,704,192,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107891203.69/warc/CC-MAIN-20201026090458-20201026120458-00140.warc.gz | 350,129,931 | 28,794 | # Write the names of the following compounds and deduce their molecular masses.Na2SO4, K2CO3, CO2, NaOH, MgCl2, AlPO4, NaHCO3
i. Na2SO4 : Sodium Sulphate
Steps for finding the molecular mass:
Molecular mass of Na2SO4 = 2(Atomic mass of Na) + 1(Atomic mass of S) + 4(Atomic mass of O)
Molecular Mass = 2(23) + 1(32) + 4(16)
= 46 + 32 + 64
= 142 g/mol
ii.K2CO3: Potassium Carbonate
Steps for finding the molecular mass:
Molecular mass of K2CO3 = 2× (Atomic mass of K) + 1× (Atomic mass of C) + 3× (Atomic mass of O)
Molecular Mass = 2× (39) + 1× (12) + 3× (16)
= 78 + 12 + 48
= 138 g/mol
iii.CO2:- Carbondioxide
Molecular mass of CO2 = 1× (Atomic mass of C) + 2× (Atomic mass of O)
Molecular Mass = 1× (12) + 2× (16)
= 12 + 32
= 44 g/mol
iv.NaOH:Sodium Hydroxide
Molecular mass of NaOH = 1× (Atomic mass of Na) + 1× (Atomic mass of O) + 1× (Atomic mass of H)
Molecular Mass = 1× (23) + 1× (16) + 1× (1)
= 23 + 16 + 1
= 40 g/mol
v.MgCl2:Magnesium Chloride
Molecular mass of MgCl2 = 1× (Atomic mass of Mg) + 2× (Atomic mass of Cl)
Molecular Mass = 1× (24) + 2× (35.5)
= 24 + 70
= 94 g/mol
vi.AlPO4:-Aluminium Phosphate
Molecular mass of AlPO4 = 1× (Atomic mass of Al) + 1× (Atomic mass of P) + 4× (Atomic mass of O)
Molecular Mass = 1× (27) + 1× (31) + 4× (16)
= 27 + 31 + 64
= 122 g/mol
vii.NaHCO3: Sodium Bicarbonate
Molecular mass of NaHCO3 = 1× (Atomic mass of Na) + 1× (Atomic mass of H) + 1× (Atomic mass of C) + 3× (Atomic mass of O)
Molecular Mass = 1× (23) + 1× (1) + 1× (12) + 3× (16)
= 23 + 1 + 12 + 48
= 84 g/mol
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view all courses | 844 | 2,386 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2020-45 | longest | en | 0.6943 |
https://numbas.mathcentre.ac.uk/question/38046/j-richard-s-copy-of-extract-common-factors-of-polynomials.exam | 1,582,700,479,000,000,000 | text/plain | crawl-data/CC-MAIN-2020-10/segments/1581875146187.93/warc/CC-MAIN-20200226054316-20200226084316-00169.warc.gz | 477,704,948 | 3,780 | // Numbas version: exam_results_page_options {"name": "J. Richard's copy of Extract common factors of polynomials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "
Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.
"}, "variables": {"x7": {"definition": "random(1..5)", "description": "", "name": "x7", "group": "Ungrouped variables", "templateType": "anything"}, "x2": {"definition": "random(1..5)", "description": "", "name": "x2", "group": "Ungrouped variables", "templateType": "anything"}, "x1": {"definition": "random(1..5)", "description": "", "name": "x1", "group": "Ungrouped variables", "templateType": "anything"}, "x6": {"definition": "random(1..5)", "description": "", "name": "x6", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"definition": "repeat(random([3, 11, 17, 29, 37, 43] except b),50)", "description": "
Vector of every other random prime number
", "name": "a", "group": "Ungrouped variables", "templateType": "anything"}, "x4": {"definition": "random(-5..-1)\n\n", "description": "", "name": "x4", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "repeat(random([ 5, 19, 47] ),50)", "description": "
extra primes for when you need a third constant
", "name": "c", "group": "Ungrouped variables", "templateType": "anything"}, "x5": {"definition": "random(1..5)", "description": "", "name": "x5", "group": "Ungrouped variables", "templateType": "anything"}, "x3": {"definition": "random(1..5 except [x2])", "description": "", "name": "x3", "group": "Ungrouped variables", "templateType": "anything"}, "b": {"definition": "repeat(random(2, 7, 13, 23, 31, 41, 53),50)", "description": "
Vector of the other every other random prime number
", "name": "b", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "gaps": [{"type": "jme", "vsetRangePoints": 5, "showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "marks": 1, "checkVariableNames": false, "variableReplacements": [], "scripts": {"mark": {"script": "question.mark_factorised(this);", "order": "after"}}, "showPreview": true, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "answer": "2({a[0]}x+{b[0]})", "showFeedbackIcon": true, "failureRate": 1, "unitTests": [], "expectedVariableNames": []}], "scripts": {}, "sortAnswers": false, "prompt": "
$\\simplify{{2*a[0]}x+{2*b[0]}}=$ [[0]]
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$\\simplify{6{a[1]}y+6{b[1]}y^2}=$ [[0]]
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$\\simplify{{a[2]}x*y*z+{b[2]}x^2y^2z^2}=$ [[0]]
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$\\simplify{5{a[3]}d+5{b[3]}r+5m}=$ [[0]]
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$\\simplify{6{a[4]}c*d^2+6{b[4]}c^2d+6{c[1]}c^2d^2}=$ [[0]]
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An expression can be factorised by finding common factors of each term in the expression.
\n
Completely factorise the following expressions by finding their common factors.
\n
Make sure that you include a multiplication symbol * between each algebraic variable, and before brackets, e.g. a*b*(x+1) instead of ab(x+1). Otherwise, the system might not accept your answer.
", "tags": ["common factors", "common factors of linear algebraic equations", "common factors of quadratic equations", "finding common factors", "Linear equations", "linear equations", "quadratic equations", "Quadratic Equations", "Quadratic equations", "taxonomy"], "extensions": [], "advice": "
In order to factorise the expressions, the factors that make up each term in the expression need to be identified and, where these factors are the same for all terms in the expression, those factors can be taken outside the brackets. Stop when the remaining terms have no more common factors.
\n
#### a)
\n
Both terms have a common factor of $2$.
\n
\\begin{align}
\\simplify{2{a[0]}x+2{b[0]}}&=
(\\simplify[]{2{a[0]}})x+2\\times\\var{b[0]}\\\\
&=\\simplify[]{2({a[0]}x+{b[0]})}
\\end{align}
\n
#### b)
\n
Both terms have common factors of $6$ and $y$.
\n
\\begin{align}
\\simplify{6{a[1]}y+6{b[1]}y^2}&= 6 \\times \\var{a[1]} y + 6 \\times \\var{b[1]} y^2 \\\\
&= 6 \\times (\\simplify{{a[1]}y + {b[1]}y^2}) \\\\
&=6y(\\simplify[]{{a[1]}+{b[1]}y})
\\end{align}
\n
#### c)
\n
Both terms have common factors of $x$, $y$ and $z$.
\n
\\begin{align}
\\simplify{{a[2]}x*y*z+{b[2]}x^2y^2z^2}&=\\var{a[2]} \\times xyz + \\var{b[2]} \\times xyz \\times xyz\\\\
&=xyz(\\var{a[2]} + \\var{b[2]} xyz)
\\end{align}
\n
#### d)
\n
All three terms have a common factor of $5$.
\n
\\begin{align}
\\simplify{5{a[3]}d+5{b[3]}r+5m}&= 5 \\times \\var{a[3]} d+5 \\times \\var{b[3]} r + 5 m \\\\
&=\\simplify[]{5({a[3]}d+{b[3]}r+m)}
\\end{align}
\n
#### e)
\n
All the terms have common factors of $6$, $c$ and $d$.
\n
\\begin{align}
\\simplify{6{a[4]}cd^2+6{b[4]}c^2d+6{c[1]}c^2d^2} &= 6 \\times \\var{a[4]} c d^2 \\;+\\; 6 \\times \\var{b[4]} c^2 d \\;+\\; 6 \\times \\var{c[1]} c^2 d^2 \\\\
&= 6(\\var{a[4]} c d^2 + \\var{b[4]} c^2 d + \\var{c[1]} c^2 d^2) \\\\
&=6cd(\\var{a[4]}d+\\var{b[4]}c+\\var{c[1]}cd)
\\end{align}
\n", "name": "J. Richard's copy of Extract common factors of polynomials", "functions": {}, "ungrouped_variables": ["a", "b", "c", "x1", "x2", "x3", "x4", "x5", "x6", "x7"], "preamble": {"js": "question.mark_factorised = function(part) {\n var match = Numbas.jme.display.matchExpression;\n var unwrap = Numbas.jme.unwrapValue;\n var getCommutingTerms = Numbas.jme.display.getCommutingTerms;\n var matchTree = Numbas.jme.display.matchTree;\n\n var expr = part.studentAnswer;\n\n // is the student's answer in the form factors*(terms)?\n var m = match('m_all(m_any(m_number,m_type(name),m_type(name)^m_number))*(m_all(??)+m_nothing);rest', expr, true);\n if(!m) {\n part.multCredit(0,\"You don't seem to have extracted a common factor.\");\n return;\n }\n \n var terms = getCommutingTerms(m.rest,'+').terms;\n \n var gcd; // greatest common divisor of the coefficients of each term\n var min_degrees = {}; // minimum degree of each variable across the terms - if greater than 0, that variable is a common factor\n \n // for each term, collect the scalar part and the degree of each of the variables\n terms.map(function(t,i) { \n var factors = getCommutingTerms(t,'*').terms;\n var degrees = {};\n var n = 1;\n factors.forEach(function(f) {\n var tok = f.tok;\n var scalar = 1;\n var name = null;\n var degree = 0;\n var m = Numbas.jme.display.matchTree(Numbas.jme.compile('m_any(m_number;n, m_type(name);name, m_number;n*m_type(name);name, m_type(name);name^(m_number;degree), m_number;n*m_type(name);name^m_number;degree )'),f,true)\n\n console.log(Numbas.jme.display.treeToJME(f));\n\n if(!m) {\n console.log(' no match');\n return;\n }\n console.log(' match',m.n,m.name,m.degree);\n if(m.n) {\n n *= unwrap(m.n.tok);\n }\n if(m.name) {\n name = m.name.tok.name;\n if(m.degree) {\n degree = unwrap(m.degree.tok);\n } else {\n degree = 1;\n }\n degrees[name] = (degrees[name] || 0) + degree;\n }\n });\n console.log(Numbas.jme.display.treeToJME(t), degrees, n);\n \n if(i==0) {\n gcd = n;\n } else {\n gcd = Numbas.math.gcd(gcd,n);\n }\n \n Object.keys(degrees).forEach(function(k) {\n if(i==0) {\n min_degrees[k] = degrees[k];\n } else {\n min_degrees[k] = Math.min(min_degrees[k] || 0, degrees[k]);\n }\n });\n Object.keys(min_degrees).forEach(function(k) {\n if(degrees[k]===undefined) {\n min_degrees[k] = 0;\n }\n });\n \n });\n \n var common_factors = [];\n if(gcd>1) {\n common_factors.push(gcd);\n }\n Object.keys(min_degrees).filter(function(k){return min_degrees[k]>0}).forEach(function(k) {\n common_factors.push(k+'^'+min_degrees[k])\n });\n \n if(common_factors.length==0) {\n return true;\n } else {\n part.multCredit(0,\"Your terms still have a common factor of $\"+Numbas.jme.display.exprToLaTeX(common_factors.join('*'),'all',Numbas.jme.builtinScope)+\"$.\");\n }\n};", "css": ""}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}, {"name": "J. Richard Snape", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1700/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}, {"name": "J. Richard Snape", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1700/"}]} | 4,105 | 12,827 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2020-10 | latest | en | 0.499606 |
https://gerardnico.com/data_mining/walk | 1,586,045,373,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370526982.53/warc/CC-MAIN-20200404231315-20200405021315-00201.warc.gz | 485,600,532 | 25,973 | # Statistics - Random Walk
## 1 - Walk
A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the price of a fluctuating stock can be modelled as random walks. Half the time it goes up, half the time it goes down.
## 3 - Example
width=600;
height=300;
randomWalk = ( function() {
let y = height/2, values = [y];
for (let x = 0; x < width; ++x) values.push(y = y + (Math.random() - 0.5) * 40 + (height/2 - y) * 0.1);
return values;
})()
canvas = document.getElementById("graph");
context = canvas.getContext("2d");
context.beginPath();
context.moveTo(0, randomWalk[0]);
for (let x = 0; x < width; ++x) context.lineTo(x, randomWalk[x]);
context.lineJoin = context.lineCap = "round";
context.strokeStyle = "black";
context.stroke();
<canvas id="graph" width="600" height="300"></canvas> | 238 | 850 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-16 | latest | en | 0.559661 |
http://machinedesign.com/archive/sizing-pneumatic-cyclinders-and-iso-valves?page=3 | 1,485,156,597,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560282140.72/warc/CC-MAIN-20170116095122-00047-ip-10-171-10-70.ec2.internal.warc.gz | 173,726,415 | 17,900 | GT
22.48
(P1-P2)P2
and list values for varying inlet gage pressures in the accompanying Basic Data table.
This reduces the flow-coefficient equation to Cv = QA. In terms of cylinder volume and time,
Q= VP1 28.8tPa
where atmospheric pressure, Pa, is assumed to be 14.7 psi.
Next, calculate values for compression ratio, Cr = P1/Pa, for various inlet pressures and also list values in the Basic Data table.
Restating the volumetric flowrate equation in terms of compression ratio results in
Q= VCr 28t
Now examine the impact of cylinder volume and stroke time for known Cv values of ISO valves. Given that Cv = QA; and V = (π/4)d2l, we can restate the equation as:
Cv=
( » | 180 | 681 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-04 | latest | en | 0.811734 |
https://numbermatics.com/n/427168739084290624/ | 1,709,577,743,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476464.74/warc/CC-MAIN-20240304165127-20240304195127-00896.warc.gz | 417,229,014 | 7,108 | # 427168739084290624
## 427,168,739,084,290,624 is an even composite number composed of two prime numbers multiplied together.
What does the number 427168739084290624 look like?
This visualization shows the relationship between its 2 prime factors (large circles) and 21 divisors.
427168739084290624 is an even composite number. It is composed of two distinct prime numbers multiplied together. It has a total of twenty-one divisors.
## Prime factorization of 427168739084290624:
### 26 × 1882812
(2 × 2 × 2 × 2 × 2 × 2 × 188281 × 188281)
See below for interesting mathematical facts about the number 427168739084290624 from the Numbermatics database.
### Names of 427168739084290624
• Cardinal: 427168739084290624 can be written as Four hundred twenty-seven quadrillion, one hundred sixty-eight trillion, seven hundred thirty-nine billion, eighty-four million, two hundred ninety thousand, six hundred twenty-four.
### Scientific notation
• Scientific notation: 4.27168739084290624 × 1017
### Factors of 427168739084290624
• Number of distinct prime factors ω(n): 2
• Total number of prime factors Ω(n): 8
• Sum of prime factors: 188283
### Divisors of 427168739084290624
• Number of divisors d(n): 21
• Complete list of divisors:
• Sum of all divisors σ(n): 427170972441504981
• Sum of proper divisors (its aliquot sum) s(n): 2233357214357
• 427168739084290624 is a deficient number, because the sum of its proper divisors (2233357214357) is less than itself. Its deficiency is 427166505727076267
### Bases of 427168739084290624
• Binary: 101111011011001101110110100011110000100010101001010010000002
• Hexadecimal: 0x5ED9BB478454A40
• Base-36: 38U2OHMOS5DS
### Squares and roots of 427168739084290624
• 427168739084290624 squared (4271687390842906242) is 182473131650862760134311181294309376
• 427168739084290624 cubed (4271687390842906243) is 77946817564060807638718550137173937303271328952090624
• The square root of 427168739084290624 is 653581470.8850692503
• 427168739084290624 is a perfect cube number. Its cube root is 753124
### Scales and comparisons
How big is 427168739084290624?
• 427,168,739,084,290,624 seconds is equal to 13,582,644,583 years, 11 weeks, 1 day, 9 hours, 37 minutes, 4 seconds.
• To count from 1 to 427,168,739,084,290,624 would take you about forty billion, seven hundred forty-seven million, nine hundred thirty-three thousand, seven hundred forty-nine years!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
• A cube with a volume of 427168739084290624 cubic inches would be around 62760.3 feet tall.
### Recreational maths with 427168739084290624
• 427168739084290624 backwards is 426092480937861724
• The number of decimal digits it has is: 18
• The sum of 427168739084290624's digits is 82
• More coming soon!
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## Cite this page
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"Number 427168739084290624 - Facts about the integer". Numbermatics.com. 2024. Web. 4 March 2024.
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Numbermatics. (2024). Number 427168739084290624 - Facts about the integer. Retrieved 4 March 2024, from https://numbermatics.com/n/427168739084290624/
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The information we have on file for 427168739084290624 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 427168739084290624, math, Factors of 427168739084290624, curriculum, school, college, exams, university, Prime factorization of 427168739084290624, STEM, science, technology, engineering, physics, economics, calculator, four hundred twenty-seven quadrillion, one hundred sixty-eight trillion, seven hundred thirty-nine billion, eighty-four million, two hundred ninety thousand, six hundred twenty-four.
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Some bits of this website may not work unless you switch it on. | 1,271 | 4,676 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2024-10 | latest | en | 0.724959 |
https://homework.cpm.org/category/CC/textbook/cca2/chapter/10/lesson/10.1.2/problem/10-35 | 1,723,619,790,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641104812.87/warc/CC-MAIN-20240814061604-20240814091604-00090.warc.gz | 226,711,120 | 15,591 | ### Home > CCA2 > Chapter 10 > Lesson 10.1.2 > Problem10-35
10-35.
Consider the series $21+17+13+\dots+-99$ as you answer the questions in parts (a) through (c) below.
1. Write an expression for the $n$th term.
Use a system of equations or look at the difference between terms and the value of the first term.
2. How many terms are in the series? How can you tell?
Set the equation you found in part (a) equal to $-99$ and solve for $n$.
3. What is the sum of this series?
Use the rectangle method or Antonio's method.
$-1209$ | 154 | 535 | {"found_math": true, "script_math_tex": 5, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-33 | latest | en | 0.896138 |
https://www.hackmath.net/en/example/491?tag_id=5,64 | 1,553,432,207,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203448.17/warc/CC-MAIN-20190324124545-20190324150545-00548.warc.gz | 774,371,844 | 6,601 | # Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
Result
V1-V2 = 503.6 cm3
#### Solution:
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Math student
What do all those symbols mean? Is there a more simple format...that you could put this in?
Petr
S - surface area of cube
V - volume of cube(s)
#### To solve this example are needed these knowledge from mathematics:
Tip: Our volume units converter will help you with converion of volume units. Pythagorean theorem is the base for the right triangle calculator.
## Next similar examples:
1. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
2. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
3. Spherical cap
From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
4. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
5. Tetrahedral pyramid
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The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
7. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
8. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
9. Cone
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
10. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
11. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
12. 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
13. Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
14. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
15. Cut and cone
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16. Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long? | 751 | 3,016 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2019-13 | latest | en | 0.865519 |
https://people.maths.bris.ac.uk/~matyd/GroupNames/321/Dic3xC3xC9.html | 1,716,654,451,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058830.51/warc/CC-MAIN-20240525161720-20240525191720-00634.warc.gz | 376,680,864 | 6,518 | Copied to
clipboard
## G = Dic3×C3×C9order 324 = 22·34
### Direct product of C3×C9 and Dic3
Series: Derived Chief Lower central Upper central
Derived series C1 — C3 — Dic3×C3×C9
Chief series C1 — C3 — C32 — C3×C6 — C3×C18 — C32×C18 — Dic3×C3×C9
Lower central C3 — Dic3×C3×C9
Upper central C1 — C3×C18
Generators and relations for Dic3×C3×C9
G = < a,b,c,d | a3=b9=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 140 in 90 conjugacy classes, 50 normal (20 characteristic)
C1, C2, C3, C3, C3, C4, C6, C6, C6, C9, C9, C32, C32, C32, Dic3, C12, C18, C18, C3×C6, C3×C6, C3×C6, C3×C9, C3×C9, C3×C9, C33, C36, C3×Dic3, C3×Dic3, C3×C12, C3×C18, C3×C18, C3×C18, C32×C6, C32×C9, C9×Dic3, C3×C36, C32×Dic3, C32×C18, Dic3×C3×C9
Quotients: C1, C2, C3, C4, S3, C6, C9, C32, Dic3, C12, C18, C3×S3, C3×C6, C3×C9, C36, C3×Dic3, C3×C12, S3×C9, C3×C18, S3×C32, C9×Dic3, C3×C36, C32×Dic3, S3×C3×C9, Dic3×C3×C9
Smallest permutation representation of Dic3×C3×C9
On 108 points
Generators in S108
(1 53 62)(2 54 63)(3 46 55)(4 47 56)(5 48 57)(6 49 58)(7 50 59)(8 51 60)(9 52 61)(10 31 77)(11 32 78)(12 33 79)(13 34 80)(14 35 81)(15 36 73)(16 28 74)(17 29 75)(18 30 76)(19 95 102)(20 96 103)(21 97 104)(22 98 105)(23 99 106)(24 91 107)(25 92 108)(26 93 100)(27 94 101)(37 71 83)(38 72 84)(39 64 85)(40 65 86)(41 66 87)(42 67 88)(43 68 89)(44 69 90)(45 70 82)
(1 2 3 4 5 6 7 8 9)(10 11 12 13 14 15 16 17 18)(19 20 21 22 23 24 25 26 27)(28 29 30 31 32 33 34 35 36)(37 38 39 40 41 42 43 44 45)(46 47 48 49 50 51 52 53 54)(55 56 57 58 59 60 61 62 63)(64 65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80 81)(82 83 84 85 86 87 88 89 90)(91 92 93 94 95 96 97 98 99)(100 101 102 103 104 105 106 107 108)
(1 80 53 13 62 34)(2 81 54 14 63 35)(3 73 46 15 55 36)(4 74 47 16 56 28)(5 75 48 17 57 29)(6 76 49 18 58 30)(7 77 50 10 59 31)(8 78 51 11 60 32)(9 79 52 12 61 33)(19 71 102 37 95 83)(20 72 103 38 96 84)(21 64 104 39 97 85)(22 65 105 40 98 86)(23 66 106 41 99 87)(24 67 107 42 91 88)(25 68 108 43 92 89)(26 69 100 44 93 90)(27 70 101 45 94 82)
(1 67 13 91)(2 68 14 92)(3 69 15 93)(4 70 16 94)(5 71 17 95)(6 72 18 96)(7 64 10 97)(8 65 11 98)(9 66 12 99)(19 57 37 75)(20 58 38 76)(21 59 39 77)(22 60 40 78)(23 61 41 79)(24 62 42 80)(25 63 43 81)(26 55 44 73)(27 56 45 74)(28 101 47 82)(29 102 48 83)(30 103 49 84)(31 104 50 85)(32 105 51 86)(33 106 52 87)(34 107 53 88)(35 108 54 89)(36 100 46 90)
G:=sub<Sym(108)| (1,53,62)(2,54,63)(3,46,55)(4,47,56)(5,48,57)(6,49,58)(7,50,59)(8,51,60)(9,52,61)(10,31,77)(11,32,78)(12,33,79)(13,34,80)(14,35,81)(15,36,73)(16,28,74)(17,29,75)(18,30,76)(19,95,102)(20,96,103)(21,97,104)(22,98,105)(23,99,106)(24,91,107)(25,92,108)(26,93,100)(27,94,101)(37,71,83)(38,72,84)(39,64,85)(40,65,86)(41,66,87)(42,67,88)(43,68,89)(44,69,90)(45,70,82), (1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45)(46,47,48,49,50,51,52,53,54)(55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81)(82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108), (1,80,53,13,62,34)(2,81,54,14,63,35)(3,73,46,15,55,36)(4,74,47,16,56,28)(5,75,48,17,57,29)(6,76,49,18,58,30)(7,77,50,10,59,31)(8,78,51,11,60,32)(9,79,52,12,61,33)(19,71,102,37,95,83)(20,72,103,38,96,84)(21,64,104,39,97,85)(22,65,105,40,98,86)(23,66,106,41,99,87)(24,67,107,42,91,88)(25,68,108,43,92,89)(26,69,100,44,93,90)(27,70,101,45,94,82), (1,67,13,91)(2,68,14,92)(3,69,15,93)(4,70,16,94)(5,71,17,95)(6,72,18,96)(7,64,10,97)(8,65,11,98)(9,66,12,99)(19,57,37,75)(20,58,38,76)(21,59,39,77)(22,60,40,78)(23,61,41,79)(24,62,42,80)(25,63,43,81)(26,55,44,73)(27,56,45,74)(28,101,47,82)(29,102,48,83)(30,103,49,84)(31,104,50,85)(32,105,51,86)(33,106,52,87)(34,107,53,88)(35,108,54,89)(36,100,46,90)>;
G:=Group( (1,53,62)(2,54,63)(3,46,55)(4,47,56)(5,48,57)(6,49,58)(7,50,59)(8,51,60)(9,52,61)(10,31,77)(11,32,78)(12,33,79)(13,34,80)(14,35,81)(15,36,73)(16,28,74)(17,29,75)(18,30,76)(19,95,102)(20,96,103)(21,97,104)(22,98,105)(23,99,106)(24,91,107)(25,92,108)(26,93,100)(27,94,101)(37,71,83)(38,72,84)(39,64,85)(40,65,86)(41,66,87)(42,67,88)(43,68,89)(44,69,90)(45,70,82), (1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45)(46,47,48,49,50,51,52,53,54)(55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81)(82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108), (1,80,53,13,62,34)(2,81,54,14,63,35)(3,73,46,15,55,36)(4,74,47,16,56,28)(5,75,48,17,57,29)(6,76,49,18,58,30)(7,77,50,10,59,31)(8,78,51,11,60,32)(9,79,52,12,61,33)(19,71,102,37,95,83)(20,72,103,38,96,84)(21,64,104,39,97,85)(22,65,105,40,98,86)(23,66,106,41,99,87)(24,67,107,42,91,88)(25,68,108,43,92,89)(26,69,100,44,93,90)(27,70,101,45,94,82), (1,67,13,91)(2,68,14,92)(3,69,15,93)(4,70,16,94)(5,71,17,95)(6,72,18,96)(7,64,10,97)(8,65,11,98)(9,66,12,99)(19,57,37,75)(20,58,38,76)(21,59,39,77)(22,60,40,78)(23,61,41,79)(24,62,42,80)(25,63,43,81)(26,55,44,73)(27,56,45,74)(28,101,47,82)(29,102,48,83)(30,103,49,84)(31,104,50,85)(32,105,51,86)(33,106,52,87)(34,107,53,88)(35,108,54,89)(36,100,46,90) );
G=PermutationGroup([[(1,53,62),(2,54,63),(3,46,55),(4,47,56),(5,48,57),(6,49,58),(7,50,59),(8,51,60),(9,52,61),(10,31,77),(11,32,78),(12,33,79),(13,34,80),(14,35,81),(15,36,73),(16,28,74),(17,29,75),(18,30,76),(19,95,102),(20,96,103),(21,97,104),(22,98,105),(23,99,106),(24,91,107),(25,92,108),(26,93,100),(27,94,101),(37,71,83),(38,72,84),(39,64,85),(40,65,86),(41,66,87),(42,67,88),(43,68,89),(44,69,90),(45,70,82)], [(1,2,3,4,5,6,7,8,9),(10,11,12,13,14,15,16,17,18),(19,20,21,22,23,24,25,26,27),(28,29,30,31,32,33,34,35,36),(37,38,39,40,41,42,43,44,45),(46,47,48,49,50,51,52,53,54),(55,56,57,58,59,60,61,62,63),(64,65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80,81),(82,83,84,85,86,87,88,89,90),(91,92,93,94,95,96,97,98,99),(100,101,102,103,104,105,106,107,108)], [(1,80,53,13,62,34),(2,81,54,14,63,35),(3,73,46,15,55,36),(4,74,47,16,56,28),(5,75,48,17,57,29),(6,76,49,18,58,30),(7,77,50,10,59,31),(8,78,51,11,60,32),(9,79,52,12,61,33),(19,71,102,37,95,83),(20,72,103,38,96,84),(21,64,104,39,97,85),(22,65,105,40,98,86),(23,66,106,41,99,87),(24,67,107,42,91,88),(25,68,108,43,92,89),(26,69,100,44,93,90),(27,70,101,45,94,82)], [(1,67,13,91),(2,68,14,92),(3,69,15,93),(4,70,16,94),(5,71,17,95),(6,72,18,96),(7,64,10,97),(8,65,11,98),(9,66,12,99),(19,57,37,75),(20,58,38,76),(21,59,39,77),(22,60,40,78),(23,61,41,79),(24,62,42,80),(25,63,43,81),(26,55,44,73),(27,56,45,74),(28,101,47,82),(29,102,48,83),(30,103,49,84),(31,104,50,85),(32,105,51,86),(33,106,52,87),(34,107,53,88),(35,108,54,89),(36,100,46,90)]])
162 conjugacy classes
class 1 2 3A ··· 3H 3I ··· 3Q 4A 4B 6A ··· 6H 6I ··· 6Q 9A ··· 9R 9S ··· 9AJ 12A ··· 12P 18A ··· 18R 18S ··· 18AJ 36A ··· 36AJ order 1 2 3 ··· 3 3 ··· 3 4 4 6 ··· 6 6 ··· 6 9 ··· 9 9 ··· 9 12 ··· 12 18 ··· 18 18 ··· 18 36 ··· 36 size 1 1 1 ··· 1 2 ··· 2 3 3 1 ··· 1 2 ··· 2 1 ··· 1 2 ··· 2 3 ··· 3 1 ··· 1 2 ··· 2 3 ··· 3
162 irreducible representations
dim 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 type + + + - image C1 C2 C3 C3 C4 C6 C6 C9 C12 C12 C18 C36 S3 Dic3 C3×S3 C3×S3 C3×Dic3 C3×Dic3 S3×C9 C9×Dic3 kernel Dic3×C3×C9 C32×C18 C9×Dic3 C32×Dic3 C32×C9 C3×C18 C32×C6 C3×Dic3 C3×C9 C33 C3×C6 C32 C3×C18 C3×C9 C18 C3×C6 C9 C32 C6 C3 # reps 1 1 6 2 2 6 2 18 12 4 18 36 1 1 6 2 6 2 18 18
Matrix representation of Dic3×C3×C9 in GL3(𝔽37) generated by
10 0 0 0 10 0 0 0 10
,
16 0 0 0 1 0 0 0 1
,
36 0 0 0 11 0 0 28 27
,
6 0 0 0 16 25 0 6 21
G:=sub<GL(3,GF(37))| [10,0,0,0,10,0,0,0,10],[16,0,0,0,1,0,0,0,1],[36,0,0,0,11,28,0,0,27],[6,0,0,0,16,6,0,25,21] >;
Dic3×C3×C9 in GAP, Magma, Sage, TeX
{\rm Dic}_3\times C_3\times C_9
% in TeX
G:=Group("Dic3xC3xC9");
// GroupNames label
G:=SmallGroup(324,91);
// by ID
G=gap.SmallGroup(324,91);
# by ID
G:=PCGroup([6,-2,-3,-3,-2,-3,-3,108,122,7781]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^9=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
×
𝔽 | 4,888 | 8,109 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-22 | latest | en | 0.391717 |
https://idoabramsohn.com/doing-trigonometry-987 | 1,675,511,219,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00209.warc.gz | 329,383,787 | 6,902 | # How to solve exponential equations
This can be a great way to check your work or to see How to solve exponential equations. Our website can help me with math work.
## How can we solve exponential equations
Do you need help with your math homework? Are you struggling to understand concepts How to solve exponential equations? Precalculus is a course that students take in high school to prepare for calculus. It builds on concepts from algebra and geometry, and introduces new concepts such as limits, derivatives, and integrals. Because of the broad range of topics covered in precalculus, many students find it to be a challenging course. If you are struggling with precalculus, there are a number of resources that can help you. One option is to use a precalculus problem solver. These online tools can quickly generate solutions to specific problems, and they can also provide step-by-step explanations of how the solutions were derived. This can be a valuable resource for understanding difficult concept. In addition, there are a number of websites and books that offer general guidance on solving precalculus problems. These resources can help you to develop your problem-solving skills and confidence. With some practice, you will be able to tackle even the most challenging precalculus problems.
It is important to be able to solve expressions. This is because solving expressions is a fundamental skill in algebra. Algebra is the branch of mathematics that deals with equations and variables, and it is frequently used in physics and engineering. Many word problems can be translated into algebraic expressions, and being able to solve these expressions will allow you to solve the problem. In order to solve an expression, you need to use the order of operations. The order of operations is a set of rules that tells you the order in which to solve an equation. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Using the order of operations, you can solve any expression.
Linear algebra is a critical tool for solving mathematical problems. Linear algebra solvers are specially designed to solve linear algebra problems. There are many different types of linear algebra solvers, each with its own advantages and disadvantages. The most popular type of linear algebra solver is the Gaussian elimination method. This method is very efficient for solving large systems of linear equations. However, it can be slow for smaller systems of equations. Another popular type of linear algebra solver is the LU decomposition method. This method is more versatile than the Gaussian elimination method and can be used to solve both large and small systems of linear equations. Linear algebra solvers are an essential tool for mathematicians and engineers alike. | 540 | 2,867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2023-06 | latest | en | 0.955116 |
http://www.federica.unina.it/agraria/equipment-and-industrial-plants-for-food-industries/heat-exchangers-ii/ | 1,659,918,824,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570741.21/warc/CC-MAIN-20220808001418-20220808031418-00563.warc.gz | 78,792,003 | 7,996 | # Fabrizio Sarghini » 25.Heat Exchangers - II Part
### Heat Exchangers
If the heat exchanger has a complex structure, for example multiple passage of tubes in multiple shells, the method requires altering LMDT for an appropriate correction factor F
$\Delta T_{eff}=F\cdot \Delta T_{LMDT}$
which is computed as a function of the 2 parameters
$P=\frac{t_2-t_1}{T_1-t_1}$
$R=\frac{T_1-T_2}{t_2-t_1}$
### Heat Exchangers – NTU Effectiveness Method
The Number of Transfer Units (NTU) method is used to calculate the rate of heat transfer in heat exchangers (especially counter current exchangers) when there is insufficient information to calculate the Log-Mean Temperature Difference (LMTD).
When the fluid inlet and outlet temperatures are specified or can be determined by simple mass balance, then the LMTD method can be used, whereas when this information is not available the NTU or the effectiveness method is used.
### Heat Exchangers – NTU Effectiveness Method
The maximum possible heat transfer which can be hypothetically achieved in a counter flow heat exchanger of infinite length is given by the product of the maximum possible temperature difference
$\Delta T_{max}=T_{HI}-T_{CI}$
multiplied by the smaller heat capacity rate
$C_{\min}=\min(c_{PH}\cdot m_h, c_{PC}\cdot m_C)=\min(C_H, C_c)$
### Heat Exchangers – NTU Effectiveness Method
The quantity
$W_{\max}=C_{\min}(T_{HI}-T_{CI})$
is the maximum heat which could be transferred between the fluids.
The effectiveness ε
$\epsilon=\frac W{W_{\max}},\epsilon \in [0,1]$
is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate where
$W=C_H(T_{HI}-T_{HO})=C_C(T_{CO}-T_{CI})$
### Heat Exchangers
The knowledge of e for a particular heat exchanger together with the inlet conditions of the enables us to calculate the amount of heat transferred between the fluids by using
$W=\epsilon \cdot W_{\max}$
For any heat exchanger it can be shown that
$\epsilon =f\Biggl(NTU, \frac {C_{\min}}{C_{\max}}\Biggr)$
For given geometries, e can be computed using correlations in terms of the heat capacity ratio
$C=\frac{C_{\min}}{C_{\max}}$
and the number of transfer units,
$NTU=\frac{UA}{C_{\min}}$
where U is the overall heat transfer coefficient and A is the heat transfer area.
### Heat Exchangers – NTU Effectiveness Method
The specific equation for the effectiveness of a parallel flow heat exchanger can be written as
$\epsilon =\frac{1-e^{[-NTU(1+C)]}}{1+C}$
while in the special case of condensation or vaporisation C=0 and therefore the effectiveness is given by
$\epsilon =1-e^{-NTU}$
### Plate and Fin Heat Exchangers
Single Plate Heat Exchanger.
### Shell and Tube Heat Exchangers
Progetto "Campus Virtuale" dell'Università degli Studi di Napoli Federico II, realizzato con il cofinanziamento dell'Unione europea. Asse V - Società dell'informazione - Obiettivo Operativo 5.1 e-Government ed e-Inclusion
Fatal error: Call to undefined function federicaDebug() in /usr/local/apache/htdocs/html/footer.php on line 93 | 815 | 3,054 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2022-33 | latest | en | 0.748791 |
https://web.vu.lt/mif/s.jukna/boolean/tilling-gaps.html | 1,719,303,011,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865694.2/warc/CC-MAIN-20240625072502-20240625102502-00059.warc.gz | 519,869,494 | 7,403 | ## Tilling matrices and their complements
Recall that the tiling number of a boolean matrix $A$ is $\dec{A}=\Dec{A}{0}+\Dec{A}{1}$, where $\Dec{A}{\sigma}$ for $\sigma\in\{0,1\}$ is the minimum number of pairwise disjoint all-$\sigma$ submatrices of $A$ covering all its $\sigma$-entries. It is clear that if $A$ is an $n\times n$ matrix, then $\Dec{A}{0}\leq n$ and $\Dec{A}{1}\leq n$: single rows give us disjoint monochromatic submatrices. The logarithm $\log\dec{A}$ of the tiling number of matrices $A$ is a trivial lower bound on their the deterministic communication complexity $\cc{A}$. We also know that $$\label{eq:1} \cc{A}\Leq \log^2\dec{A}\qquad\mbox{ and even }\qquad \cc{A}\Leq \log^2\Dec{A}{1}\,,$$ where the former upper bound is due to Aho, Ullman and Yannakakis (1983), and the latter is due to Yannakakis (1991).
An old problem was: how well does the tiling number captures the deterministic communication complexity? Kushilevitz, Linial, and Ostrovsky (1999) have shown (via a rather nontrivial argument) that $\cc{A}\geq 2\cdot \log\dec{A}$ holds for some matrices $A$. Göös, Pitassi, and Watson (2018) have substantially improved this lower bound to $\cc{A}\Geq \log^{1.5-o(1)}\dec{A}\qquad\mbox{ and }\qquad \cc{A}\Geq \log^{2-o(1)}\Dec{A}{1}\,.$ Note that the latter lower bound is essentially tight since $\cc{A}\Leq \log^2\Dec{A}{1}$.
But what about the relation between the combinatorial measures $\Dec{A}{0}$ and $\Dec{A}{1}$ themselves?
Question: Can $\Dec{A}{0}$ be much larger than $\Dec{A}{1}$?
By the second inequality in \eqref{eq:1}, we have $$\label{eq:2} \log\Dec{A}{0}\leq \log \dec{A}\leq \cc{A}\Leq \log^2\Dec{A}{1}\,.$$
Note that $\Dec{A}{0}=\Dec{\co{A}}{1}$, where $\co{A}$ is the complement of the matrix $A$. Hence, the question actually is: can the ones of a matrix be decomposed into much smaller number of rectangles (all-$1$ matrices) than those of the complement matrix?
Below we show that recent results concerning biclique coverings and the clique vs. independent set problem answer the above question affirmatively.
Remark: Combinatorial measures of matrices corresponding to their nondeterministic communication complexity are the cover numbers $\cov{A}{0}$ and $\cov{A}{1}$, where $\cov{A}{\sigma}$ is the minimum number of not necessarily disjoint all-$\sigma$ submatrices of $A$ covering all its $\sigma$-entries. Then $\log\cov{A}{1}$ is exactly the nondeterministic communication complexity of the matrix $A$. These two measures can exponentially differ on already very simple matrices. For example, if $A=\overline{I_n}$ is the complement of the $n\times n$ identity matrix $I_n$, then $\cov{A}{0}\geq 2^{\cov{A}{1}/2}\,.$ The lower bound $\cov{I_n}{1}\geq n$ is trivial: no two $1$-entries of $I_n$ can belong to the same all-$1$ submatrix. The upper bound $\cov{\overline{I_n}}{0}\leq 2\log n$ is also easy to see by labeling the rows and columns by binary vectors of length $\log n$, and considering rectangles differing in one bit of the labels.
### Biclique coverings of graphs
Fix some set of vertices, say $V=\{1,\ldots,n\}$. A biclique $B(X,Y)$ is specified by an ordered pair $(X,Y)$ of disjoint subsets of vertices (color classes), and consists of all edges $\{u,v\}$ with $u\in X$ and $v\in Y$, or $u\in Y$ and $v\in X$. A biclique $k$-covering of a graph $G=(V,E)$ is a collection $B(X_1,Y_1),\ldots,B(X_t,Y_t)$ of bicliques lying in $E$ such that every edge $e\in E$ belongs to at least one and to at most $k$ of these bicliques. Let $\bp{G}{k}$ denote the minimum number $t$ of bicliques in such a covering of $G$.
A classical result of Graham and Pollak (1971) is that $\bp{K_n}{1}=n-1$ holds for the complete $n$-vertex graph $K_n$. Alon (1997) substantially extended this result by showing that $\bp{K_n}{k}=\Theta(k n^{1/k})$ holds for every $k\geq 1$.
A biclique $1.5$-covering of a graph $G$ is a biclique $2$-covering $B(X_1,Y_1),\ldots,B(X_t,Y_t)$ of $G$ such that $(X_i\times Y_i)\cap (X_j\cap Y_j)=\emptyset$ for all $i\neq j$. That is, we now consider disjoint rectangles $X_i\times Y_i$ ("directed" versions of bicliques $B(X_i,Y_i)$), and the requirement is that for every edge $\{u,v\}$ of $G$, either $(u,v)$ or $(v,u)$ belongs to at least one of the rectangles $X_i\times Y_i$.
It is clear that $\bp{G}{2}\leq \bp{G}{1.5}\leq \bp{G}{1}$ holds for every graph $G$. For the complete graph, Alon's result yields $\bp{G}{1.5}\geq \bp{G}{2}\Geq n^{1/2}$. By improving a previous result of Amano (2014), where an upper bound $\bp{K_n}{1.5}\Leq n^{2/3}$ was proved, Shigeta and Amano (2015) proved an almost optimal upper bound $\bp{K_n}{1.5}\leq n^{1/2+o(1)}$.
### Partial partitions of matrices
The adjacency matrix of $K_n$ is the complement $\overline{I_n}$ of the identity matrix $_n$. So, in terms of Boolean matrices, the upper bound $\bp{K_n}{1.5}\leq n^{1/2+o(1)}$ of Shigeta and Amano (2015) result translates to the claim that the matrix $\overline{I_n}$ has a "partial decomposition" into at most $n^{1/2+o(1)}$ rectangles. Here, a partial decomposition of a symmetric matrix $A$ as a collection of pairwise disjoint rectangles in (all-$1$ submatrices of) $A$ with the following property: for every $1$-entry $(i,j)$ of $A$, either $(i,j)$ or $(j,i)$ is a $1$-entry in at least one of the rectangles. That is, the rectangles now do not need to cover all $1$-entries of $A$, but for every $1$-entry either this entry or its "symmetric copy" (w.r.t. to the diagonal) must be covered.
We thus have the following
Theorem 1 (Shigeta and Amano): The complement $\overline{I_m}$ of the identity $m\times m$ matrix $I_m$ has a partial decomposition $R_1,\ldots,R_t$ into $t\leq m^{1/2+o(1)}$ rectangles.
Using Theorem 1, it is easy to construct matrices $A$ with $\Dec{A}{0}\gg \Dec{A}{1}$.
Theorem 2: There exist $n\times n$ matrices $A$ such that $\Dec{A}{1}\leq n^{1/2+o(1)}$ but $\Dec{A}{0}=n$. Hence, $\Dec{A}{0}\geq \Dec{A}{1}^{2-o(1)}\,.$
Proof: Let $R_1,\ldots,R_t$ be a partial decomposition of $\overline{I_n}$ into $t\leq n^{1/2+o(1)}$ rectangles, and consider the $n\times n$ matrix $A$ with $A[i,j]=1$ iff $R_\ell[i,j]=1$ for some $\ell\in\{1,\ldots,t\}$. Thus, $A$ is obtained from the matrix $\overline{I_n}$ by switching to $0$ some its $1$-entries (those not covered by the rectangles). Below is an example of a partial decomposition of $\overline{I_6}$ into $4$ rectangles $R_1=\{1,2\}\times\{4,6\}$ ($\bullet$), $R_2=\{1,3\}\times\{2,5\}$ ($\ast$), $R_3=\{3,6\}\times\{1,4\}$ ($\Box$) and $R_4=\{2,4,6\}\times\{3,5\}$ ($\diamond$), and the resulting matrix $A$:
$\mathrm{Rectangles} = \begin{bmatrix} {\bf 0} & \ast & . & \bullet & \ast & \bullet\\ . & {\bf 0} & \diamond & \bullet & \diamond & \bullet\\ \Box & \ast & {\bf 0} & \Box & \ast & . \\ . & . & \diamond & {\bf 0} & \diamond & . \\ . & . & . & . & {\bf 0} & . \\ \Box & . & \diamond & \Box & \diamond & {\bf 0} \end{bmatrix}\qquad A=\begin{bmatrix} {\bf 0} & 1 & 0 & 1 & 1 & 1\\ 0 & {\bf 0} & 1 & 1 & 1 & 1\\ 1 & 1 & {\bf 0} & 1 & 1 & 0 \\ 0 & 0 & 1 & {\bf 0} & 1 & 0 \\ 0 & 0 & 0 & 0 & {\bf 0} & 0 \\ 1& 0 & 1 & 1 & 1 & {\bf 0} \end{bmatrix}$
The partial decomposition $R_1,\ldots,R_t$ into $t\leq n^{1/2+o(1)}$ rectangles of $\overline{I_n}$ gives us a partition of all $1$-entries of $A$ into $t\leq n^{1/2+o(1)}$ pairwise disjoint rectangles; so, $\Dec{A}{1}\leq n^{1/2+o(1)}$.
On the other hand, the matrix $A$ has the following property: for every two distinct $0$-entries $(i,i)$ and $(j,j)$ on the diagonal, at least one of $(i,j)$ or $(j,i)$ is a $1$-entry of $A$. Thus, the complement matrix $\oA$ has a fooling set of size $m$: no two $1$-entries of the diagonal of $\oA$ can belong to the same all-$1$ matrix. Thus, $\Dec{A}{0}=\Dec{\oA}{1}=n$. $\Box$
Remark: The SUM-complexity of a Boolean matrix $A$ is the minimum number of fanin-two addition $(+)$ gates sufficient to compute the the operator $f(x)=Ax$ over the semigroup $(\NN,+)$. In this comment the matrix from Theorem 2 is used to show that the SUM-complexity of an $n\times n$ matrix can be by a factor of $n^{1/4-o(1)}$ larger than the SUM-complexity of its complement.
### A super-polynomial gap
By Theorem 2, partitioning $0$-entries of some matrices may be quadratically more expensive than partitioning their $1$-entries, and the result of Alon (1997) implies that no larger gaps can be achieved using partial decompositions. Much larger gaps follow from the recent lower bounds on the nondeterministic communication complexity of the CIS (clique vs independent set) problem.
For a given graph $G$ on $v$ vertices, a CIS-intersection matrix $A_G$ is constructed in the following way. The rows are labeled by cliques, and columns by independent sets of $G$, and $A_G[a,b]=|a\cap b|$. That is, the $0$s of $A_G$ correspond to disjoint pairs $(a,b)$, and $1$s to pairs $(a,b)$ sharing a common vertex.
Clearly, $\Dec{A_G}{1} \leq v$, since all $1$s of $A_G$ may be partition into $v$ rectangles $R_1,\ldots,R_v$ with $R_i=\{(a,b)\colon i\in a\cap b\}$. By \eqref{eq:2}, we have $\log \Dec{A_G}{0}\Leq \log^2 v$. But it was long unknown whether $\log \Dec{A_G}{0}$ can be much larger than $\log v$. In a series of works, existence of $v$-vertex graphs $G$ with $\log \Dec{A_G}{0}\Geq \log^{2-c} v$ for smaller and smaller values of $c$ where shown: $c=0.872$ (Göös 2015), $c=0.5+o(1)$ (Ben-David et al. 2021) and $c=o(1)$ (Balodis 2021).
These results imply that the gap between $\Dec{A}{0}$ and $\Dec{A}{1}$ can be even super-polynomial.
Theorem 3: There exist matrices $A$ such that $\log \Dec{A}{0}\Geq \log^{2-o(1)}\Dec{A}{1}\,.$
By \eqref{eq:2}, this lower bound is essentially tight (in terms of $\Dec{A}{1}$).
Proof: Take a graph $G=(V,E)$ whose existence is is shown by Balodis (2021), and let $v=|V|$. For the corresponding clique-independent set matrix $A_G$, we then have $\log \Dec{A_G}{1} \leq \log v$ and $\Dec{A_G}{0} \Geq \log^{1+c} v$ with $c=1-o(1)$. Cliques and independent set of $G$ are subsets of $V$. So, $A_G$ is a $2^r\times 2^s$ matrix with $r,s\leq v$. Turn the matrix $A_G$ into a square $n \times n$ matrix $A$ with $n=2^v$ by duplicating some rows or columns: this affects neither $\Dec{A}{0}$ nor $\Dec{A}{1}$. Thus, $\log \Dec{A}{1}= \log\Dec{A_G}{1}\leq \log v$ but $\log \Dec{A}{0}=\log \Dec{A_G}{0}\Geq \log^{2-o(1)}\Dec{A}{1}$. $\Box$
In terms of the dimension $n$ of $n\times n$ matrices $A$, the gaps given by Theorems 2 and 3 are as follows:
• Theorem 2: $\Dec{A}{0}/\Dec{A}{1}\Geq n^{1/2-o(1)}$; matrix $A$ explicit.
• Theorem 3: $\Dec{A}{0}/\Dec{A}{1}\Geq (\log n)^{\alpha}$ for $\alpha=(\log\log n)^{2-o(1)}-1$; matrix $A$ not explicit (existence only).
References:
1. A.V. Aho, J.D. Ullman, M. Yannakakis (1983). On notions of information transfer in VLSI circuits. Proc. 15th STOC, 133-139. local copy
2. Alon N. (1997), Neighborly Families of Boxes and Bipartite Coverings. In: Graham R.L., Nešetril J. (eds) The Mathematics of Paul Erdős II. Algorithms and Combinatorics, vol 14. Springer, Berlin, Heidelberg. doi: 10.1007/978-3-642-60406-5_3. Manuscript
3. K. Amano (2014), Some improved bounds on communication complexity via new decomposition of cliques. Discrete Appl. Math., Vol. 166, 249-254. doi: 10.1016/j.dam.2013.09.015
4. K. Balodis (2021), Several separations based on a partial Boolean function. arXiv:2103.05593 [added March 2021]
5. S. Ben-David, M. Göös, S. Jain and R. Kothari (2021), Unambiguous DNF from Hex. arXiv:2102.08348
6. M. Göös (2015). Lower bounds for clique vs. independent set. Proc. 56th FOCS, 1066-1076.
7. M. Göös, T. Pitassi and T. Watson (2018). Deterministic Communication vs. Partition Number. SIAM J. Comput. 47(6), 2435-2450. ECCC report.
8. R. L. Graham and H. O. Pollak (1971): On the addressing problem for loop switching, Bell Syst. Tech. J. 50, 2495-2519. See here for a linear algebra proof by Trevberg.
9. E. Kushilevitz, N. Linial and R. Ostrovsky (1999). The linear-array conjecture in communication complexity is false. Combinatorica, 19(2):241-254. doi: 10.1007/s004930050054.
10. M. Shigeta and K. Amano (2015), Ordered biclique partitions and communication complexity problems. Discrete Appl. Math., Vol. 184, 248-252. doi: 10.1016/j.dam.2014.10.029.
11. M. Yannakakis (1991): Expressing combinatorial optimization problems by linear programs, J. Comput. Syst. Sci. 43, 441-466. local copy.
S. Jukna
February 5, 2021 | 4,301 | 12,390 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-26 | latest | en | 0.856004 |
https://www.physicsforums.com/threads/any-hope-for-this-pde-diffusion-in-population-genetics.383508/ | 1,510,943,230,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934803848.60/warc/CC-MAIN-20171117170336-20171117190336-00307.warc.gz | 849,692,605 | 15,181 | # Any hope for this PDE? Diffusion in population genetics
1. Mar 3, 2010
### Schraiber
I'm working on a problem in multi-allele diffusion in population genetics and I have come to this PDE:
$$0 = (tp_1(1-p_1)-sp_2)\frac{\partial u}{\partial p_1}+(sp_2(1-p_2)-tp_1)\frac{\partial u}{\partial p_2} + \frac{p_1(1-p_1)}{2}\frac{\partial^2 u}{\partial p_1^2} + \frac{p_2(1-p_2)}{2}\frac{\partial^2 u}{\partial p_2^2} - p_1p_2 \frac{\partial^2 u}{\partial p_1 \partial p_2}$$
The boundary conditions are u(0,p2) = 0 (for all p2), u(1,0) = 1
I'm not entirely sure it's possible to solve, though it's highly symmetric so I thought I'd give it a shot and see if anyone has any ideas. I tried separating which obviously doesn't work (unless I'm a failure) and I've spent some time searching for clever transformations that might work, but it seems to be of no use :(
Thanks! | 299 | 871 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2017-47 | longest | en | 0.922577 |
https://study.com/academy/practice/quiz-worksheet-practice-finding-the-area-of-a-sector.html | 1,571,638,950,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987756350.80/warc/CC-MAIN-20191021043233-20191021070733-00264.warc.gz | 704,672,007 | 26,425 | # Finding the Area of a Sector: Formula & Practice Problems Video
Instructions:
question 1 of 3
### What is the area of the following sector? (approximate pi to 3.14)
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### 2. If a clock's face measures 14 inches across, how much area is between the minute and hour hands at 5 o' clock? (approximate pi to 3.14)
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In this quiz, you will practice finding the area of a sector and finding the angle of a sector through various word problems.
## Quiz & Worksheet Goals
This quiz will test your abilities in:
• Finding the area of a sector given a diagram
• Using information about a sector's area to find the angle
## Skills Practiced
• Making connections- use your understanding of circle diagrams to find the area of a sector in a circle
• Problem solving - use acquired knowledge to solve multiple sector area word problems
If you need more information on this topic, refer to the lesson titled Finding the Area of a Sector: Formula & Practice Problems. This lesson was designed to cover these objectives:
• Define what a sector is
• Understand where a sector originates within a circle
• Describe how to find the area of a sector
• Identify the formula when the angle is provided in degrees
• Know the formula using radians for angles
Final Exam
Chapter Exam
Support | 374 | 1,708 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2019-43 | longest | en | 0.895935 |
http://mathhelpforum.com/calculus/56244-total-cost.html | 1,480,820,817,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541170.58/warc/CC-MAIN-20161202170901-00375-ip-10-31-129-80.ec2.internal.warc.gz | 177,275,686 | 9,972 | 1. Total cost ??
The average cost per item to produce q items is given by a(q) = 0.5q2 – 2q + 3 for q > 0. What is the total cost C(q) for producing q items? What is the MC of producing q items? At what production level does MC = average cost? What is the significance of this point?
2. Originally Posted by ab32
The average cost per item to produce q items is given by a(q) = 0.5q2 – 2q + 3 for q > 0. What is the total cost C(q) for producing q items? What is the MC of producing q items? At what production level does MC = average cost? What is the significance of this point?
$C(q)=q a(q)$
$MC(q)=\frac{dC}{dq}$
The point at which the marginal cost equals the average cost is the point beyond which each additional unit increases the average cost of production (at least if the average cost drops with each additional unit initially).
CB | 227 | 846 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2016-50 | longest | en | 0.918441 |
https://engineering.stackexchange.com/questions/56277/design-forces-for-a-home-built-trailer-structure-tiny-home-or-camper | 1,718,347,053,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861521.12/warc/CC-MAIN-20240614043851-20240614073851-00200.warc.gz | 215,926,271 | 39,790 | # Design forces for a home built trailer structure (tiny home or camper)?
I am going to purchase a steel trailer frame, and then I want to build a camper on top of that. This will be full height teardrop which is likely wood framed but I am also considering aluminum framing. So some of the questions I have relate to choosing the right size of aluminum tubing.
Most small teardrops I have seen use plywood framed sides, and some use wood framing which looks similar to how you might frame a stationary structure. Likewise for tiny homes, most of the designs I have seen use what looks like traditional house framing. One of the concerns that I have is that I have sufficient strength in the structure to keep it safe but also keep it in tact while driving. For example, in a car accident, I do not want the camper to disintegrate and become an additional safety hazard. But more typically, the structure also needs to withstand rapid acceleration, braking, cornering, etc.
Load I think the structure will want to sheer against the steel trailer frame (for example, as the trailer comes to a stop). So I want to know the lateral force so that I have the right number and size of connectors. I also want to determine a lateral design force to keep the structure from collapsing over.
Method My thinking was that if I fix the weight of the structure, and I have a design value for acceleration, then I can calculate the sheer and lateral forces on the structure using F = m x a. For example, my initial estimate is 1000 lbs of framing and wall coverings, and if the acceleration is 20g, then the force would be 20,000 lb. I can then use that to calculate the correct connectors and size of the vertical framing.
Acceleration I think typical braking would produce something like 1g of acceleration, and some car accident references I found put the g's in 100+ range. My suspicion is that this car accident values reflect hitting a stationary object, but is that really what I should be designing around?
Many one off car designs have been built to 3-2-1 loading, but I'd prefer 5-3-2 for road use. That is, if the weight on one wheel is 1000 lbf, design the suspension and mounting points for 5000 lbf vertical, 3000 lbf longitudinal (potholes) and 2000 lbf laterally into curbs etc. Your bodywork does not need to be as heavily designed as that if the suspension is doing its job, after all you don't experience 5g in a car other than in a crash.
The formula F = ma is an over-kill or an oversimplification for designing a vehicle/vehicle parts to endure wind pressure at speed. The correct equation to use is "$$F_D = C_DA(\rho U^2/2)$$". In which,
$$F_D =$$ Drag Force
$$C_D =$$ Drag Coefficient
$$A =$$ The effective (exposing) body area
$$\rho =$$ Air Density
$$U =$$ Relative Speed (The flow velocity relative to the object)
See this article for the introduction and estimate of the "drag coefficient" for various types of vehicles. | 670 | 2,948 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2024-26 | latest | en | 0.955302 |
https://www.urionlinejudge.com.br/judge/en/profile/76434?direction=asc&sort=Ranks.runtime | 1,603,533,712,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107882103.34/warc/CC-MAIN-20201024080855-20201024110855-00159.warc.gz | 955,842,562 | 6,363 | # PROFILE
Check out all the problems this user has already solved.
Problem Problem Name Ranking Submission Language Runtime Submission Date
1015 Distance Between Two Points 07798º 4399170 C 0.000 5/16/16, 10:45:25 PM
1035 Selection Test 1 06056º 4399477 C 0.000 5/16/16, 11:23:19 PM
1016 Distance 07108º 4399310 C 0.000 5/16/16, 11:08:09 PM
1017 Fuel Spent 07481º 4399317 C 0.000 5/16/16, 11:08:37 PM
1018 Banknotes 06142º 4399319 C 0.000 5/16/16, 11:09:01 PM
1019 Time Conversion 06672º 4399455 C 0.000 5/16/16, 11:09:21 PM
1020 Age in Days 06898º 4399459 C 0.000 5/16/16, 11:22:19 PM
1021 Banknotes and Coins 03739º 4399463 C 0.000 5/16/16, 11:22:41 PM
1036 Bhaskara's Formula 05654º 4399520 C 0.000 5/16/16, 11:27:03 PM
1037 Interval 05600º 4399528 C 0.000 5/16/16, 11:27:29 PM
1049 Animal 03724º 6283939 C 0.000 3/11/17, 6:33:36 PM
1038 Snack 06010º 4399542 C 0.000 5/16/16, 11:28:05 PM
1040 Average 3 04335º 4399544 C 0.000 5/16/16, 11:28:25 PM
1041 Coordinates of a Point 05141º 4399582 C 0.000 5/16/16, 11:30:56 PM
1042 Simple Sort 04606º 4399587 C 0.000 5/16/16, 11:31:31 PM
1048 Salary Increase 05287º 5520510 C 0.000 10/26/16, 10:39:05 AM
1043 Triangle 04718º 4399593 C 0.000 5/16/16, 11:31:59 PM
1044 Multiples 05011º 4399598 C 0.000 5/16/16, 11:32:18 PM
1045 Triangle Types 03121º 4399677 C 0.000 5/16/16, 11:37:25 PM
1046 Game Time 03962º 4399688 C 0.000 5/16/16, 11:38:02 PM
1047 Game Time with Minutes 02621º 4399693 C 0.000 5/16/16, 11:38:19 PM
1118 Several Scores with Validation 02292º 6488887 C 0.000 3/29/17, 4:03:29 PM
1050 DDD 07611º 6284116 C 0.000 3/11/17, 6:49:29 PM
1052 Month 06682º 6441094 C 0.000 3/25/17, 2:52:03 PM
1059 Even Numbers 07940º 6359190 C 0.000 3/18/17, 6:40:18 PM
1060 Positive Numbers 07261º 6441127 C 0.000 3/25/17, 2:55:48 PM
1064 Positives and Average 06324º 6460071 C 0.000 3/27/17, 4:54:07 AM
1065 Even Between five Numbers 06342º 6460082 C 0.000 3/27/17, 4:58:05 AM
1066 Even, Odd, Positive and... 06099º 6460162 C 0.000 3/27/17, 5:22:40 AM
1014 Consumption 07966º 4399167 C 0.000 5/16/16, 10:44:57 PM
1 of 6 | 1,010 | 2,060 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2020-45 | latest | en | 0.361097 |
https://codereview.stackexchange.com/questions/124518/classification-tree-in-swift | 1,656,826,378,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00205.warc.gz | 226,235,679 | 68,962 | Classification tree in Swift
As an effort to teach myself Swift as well as to get familiar with machine learning algorithms, I've been trying to implement common algorithms, starting with a Random Forest. This is, for the moment just one of the tree, but I have been trying to implement it just from the theory, without looking at pseudo-code, in order to really understand the process.
It was harder than I thought, due to the lack of convenience statistical and data-related functions and methods that are common in R or Python. This code seems to work and builds correct trees, although some of the methods I use, (lots of mapping...) sometimes seem a bit convoluted.
First, a node to store the splits:
import Foundation
class Node: CustomStringConvertible
{
let isTerminal:Bool
var value:Double? = nil
var leftChild:Node? = nil
var rightChild:Node? = nil
var variable:Int? = nil
var description: String
var result:Int? = nil
init(value:Double, variable:Int)
{
//Split node
self.value = value
self.isTerminal = false
self.variable = variable
self.description = "\(variable): \(value)"
}
init(result: Int)
{
//Terminal node
self.result = result
self.isTerminal = true
self.description = "Terminal node: \(result)\n"
}
{
self.leftChild = child
self.description += " L -> \(child)\n"
}
{
self.rightChild = child
self.description += " R -> \(child)\n"
}
//For prediction
func getChild(x:Double) -> Node
{
if x < value
{
return leftChild!
}
else
{
return rightChild!
}
}
}
Some data taken from the famous Iris dataset:
let x = [[6.8,6.2,5.9,5.9,5.7,7.7,4.5,5.8,5,6.3,5.1,4.3,5.7,4.9,7],
[3,3.4,3.2,3,2.6,3,2.3,2.7,2.3,2.5,3.8,3,3.8,3,3.2],
[5.5,5.4,4.8,5.1,3.5,6.1,1.3,4.1,3.3,4.9,1.9,1.1,1.7,1.4,4.7],
[2.1,2.3,1.8,1.8,1,2.3,0.3,1,1,1.5,0.4,0.1,0.3,0.2,1.4]]
let y = [3,3,2,3,2,3,1,2,2,2,1,1,1,1,2]
The impurity criterion (gini) function:
func giniImpurity(y:[Int]) -> Double
{
let len = Double(y.count)
let countedSet = NSCountedSet(array: y)
let squaredProbs = countedSet.map { (c) -> Double in
let cnt = Double(countedSet.countForObject(c)) / len
return cnt * cnt
}
return 1 - squaredProbs.reduce(0, combine: +)
}
Iterating through X to find the best split. I am not certain of the way to sort and iterate through the values...
func findBestSplit(x:[Double], y:[Int]) -> (bestVal: Double, maxDelta: Double)
{
// Find the indices that sort x
let xSortedIndices = x.indices.sort { x[$0] > x[$1] }
let xSorted = xSortedIndices.map { x[$0] } //Sort y according to those let ySorted = xSortedIndices.map { y[$0] }
var bestGin:Double = 0
let origini = giniImpurity(y)
var bestSplit = 0
//Iterate through all values of x to find the best split
for i in 0..<ySorted.count
{
let left = Array(ySorted[0..<i])
let right = Array(ySorted[i..<ySorted.count])
let gini = (giniImpurity(left) * Double(left.count) + giniImpurity(right) * Double(right.count)) / Double(y.count)
let deltaGini = origini - gini
if deltaGini > bestGin
{
bestGin = deltaGini
bestSplit = i
}
}
return (bestVal: xSorted[bestSplit], maxDelta: bestGin)
}
And finally the tree building:
func buildTree(x: [[Double]], y:[Int]) -> Node
{
var bestVar:Int = 0
var bestGini:Double = 0
var bestVal:Double = 0
// Apply the findBestSplit on all columns to find the best split among those
for col in 0..<x.count
{
let res = findBestSplit(x[col], y: y)
if res.maxDelta > bestGini
{
bestVar = col
bestGini = res.maxDelta
bestVal = res.bestVal
}
}
let node = Node(value: bestVal, variable: bestVar)
//Split X & Y according to the split found
let rightIndices = x[bestVar].indices.filter { x[bestVar][$0] > bestVal} let leftIndices = x[bestVar].indices.filter { x[bestVar][$0] <= bestVal}
let rightX = x.map { (col) -> [Double] in
return rightIndices.map {col[$0]} } let leftX = x.map { (col) -> [Double] in return leftIndices.map {col[$0]}
}
let rightY = rightIndices.map {y[$0]} let leftY = leftIndices.map {y[$0]}
// If pure enough, add terminal node, else recurse
if giniImpurity(leftY) < 0.1
{
let countedSet = NSCountedSet(array: leftY)
let counts = countedSet.map { countedSet.countForObject($0) } let result = Array(countedSet)[counts.indexOf(counts.maxElement()!)!] as! Int node.addLeftChild(Node(result: result)) } else { node.addLeftChild(buildTree(leftX, y: leftY)) } if giniImpurity(rightY) < 0.1 { let countedSet = NSCountedSet(array: rightY) let counts = countedSet.map { countedSet.countForObject($0) }
let result = Array(countedSet)[counts.indexOf(counts.maxElement()!)!] as! Int
}
else
{
}
return node
}
let root = buildTree(x, y: y)
I would love to have feedback on this, either on the Swift style or on the correctness of the algorithm.
• Welcome to Code Review! Good job on your first question. Apr 2, 2016 at 2:25
So, let's focus on your Node class at the top. I started off, without looking at anything else, and just swiftlinting it.
You have a 55 line file with 20 violations.
Fortunately, 19 of them are autocorrectable. Seven of the violations are for opening brace placement. In Swift, we prefer our opening brace to be on the same line rather than new line. Another twelve of the violations are for your colon spacing. When declaring variables or parameters, the colon should appear next to the variable name without a space, followed by a space, and then the type.
Running
\$ swiftlint autocorrect
Results in a file which looks like this:
import Foundation
class Node: CustomStringConvertible {
let isTerminal: Bool
var value: Double? = nil
var leftChild: Node? = nil
var rightChild: Node? = nil
var variable: Int? = nil
var description: String
var result: Int? = nil
init(value: Double, variable: Int) {
//Split node
self.value = value
self.isTerminal = false
self.variable = variable
self.description = "\(variable): \(value)"
}
init(result: Int) {
//Terminal node
self.result = result
self.isTerminal = true
self.description = "Terminal node: \(result)\n"
}
func addLeftChild(child: Node) {
self.leftChild = child
self.description += " L -> \(child)\n"
}
func addRightChild(child: Node) {
self.rightChild = child
self.description += " R -> \(child)\n"
}
//For prediction
func getChild(x: Double) -> Node {
if x < value {
return leftChild!
}
else {
return rightChild!
}
}
}
But swiftlint still identifies one major error.
Node.swift:39:19: error: Variable Name Violation: Variable name should be between 3 and 40 characters long: 'x' (variable_name)
The parameter name to your getChild function is unacceptably short. x does not serve as a descriptive variable name, and it makes the code hard to read.
But... this linting was with swiftlint's default configuration, which is FAR too lax in my opinion, and egregiously, it lets you get away with force unwrapping!
If I pull in the configuration file that I use*, swiftlint finds six new serious violations.
Node.swift:14:1: error: Space After Comment Violation: There should be a space after // (comments_space)
Node.swift:22:1: error: Space After Comment Violation: There should be a space after // (comments_space)
Node.swift:38:1: error: Space After Comment Violation: There should be a space after // (comments_space)
Node.swift:3:1: error: Empty First Line Violation: There should be an empty line after a declaration (empty_first_line)
Node.swift:41:29: error: Force Unwrapping Violation: Force unwrapping should be avoided. (force_unwrapping)
Node.swift:44:30: error: Force Unwrapping Violation: Force unwrapping should be avoided. (force_unwrapping)
The first four violations here, I believe, are pretty self explanatory.
The last two are also pretty explanatory I believe... but it probably requires a lot more thinking on your part in terms of how you're going to handle your child nodes.
And that's where we can start getting into an actual discussion on the logic here.
First, let's handle the simplest problem you have...
var description: String
Anyone can edit this property. Its setter has the same scope as its getter, and really, it shouldn't be writable at all. In fact, it should simply be a computed property which is calculated when it is called.
var description: String {
return "" // build description of the object
}
Some of your comments make it clear that you're thinking of two different sorts of objects...
init(value: Double, variable: Int) {
//Split node
init(result: Int) {
//Terminal node
Importantly, the getChild method doesn't even make sense to call on a terminal node. And the isTerminal property becomes completely obsolete if we just make these two different nodes into two different types.
It also allows us to get rid of all of the optional values (unless it makes sense for a split node to have just one child).
So, I'd propose something approximately looking like this...
protocol Node: CustomStringConvertible {}
class TerminalNode: Node {
let result: Int
var description: String {
// build & return description
}
init(result: Int) {
self.result = result
}
}
class SplitNode: Node {
let value: Double
let variable: Int
let leftChild: Node
let rightChild: Node
var description: String {
// build and return description string
}
init(value: Double, variable: Int, leftChild: Node, rightChild: Node) {
self.value = value
self.variable = variable
self.leftChild = leftChild
self.rightChild = rightChild
}
func childForValue(value: Double) -> Node {
return value < self.value ? leftChild : rightChild
}
}
• Very informative answer, thank you. I should have indeed spent more time thinking about the design of the node... For the position of the braces, I thought it was a matter of taste. As I get confused when I don't see my opening brace on the same column... I thought indeed that "x" and "y" as names were too short, but I wasn't sure what to call them. Most machine learning libraries refer to predictor and response variables as x and y, and I didn't want to breaks style. Apr 2, 2016 at 8:03
• Even if we consider brace style to be a matter of taste, what is not a matter of taste is that it should be done consistently, which you have not done. Consider your line let rightX = x.map { (col) -> [Double] in, you've broken the consistency. But it's when you get to the functional bits of Swift like this that we realize that the only way to be consistent and look good in all cases is with same line braces. Apr 2, 2016 at 14:10 | 2,796 | 10,288 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2022-27 | longest | en | 0.785458 |
https://www.answerexplanations.com/act/answer-explanations/answer-explanations-for-act-june-2013-form-71c/ | 1,548,252,216,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547584332824.92/warc/CC-MAIN-20190123130602-20190123152602-00170.warc.gz | 702,848,045 | 15,331 | Home » ACT » ACT Answer Explanations » Answer Explanations for: ACT June 2013, Form 71C
# Answer Explanations for: ACT June 2013, Form 71C
This document contains detailed answer explanations to every question from the June 8, 2013 ACT, Form 71C. Many Mathematics and English explanations also link to content pages that explain the relevant grammatical and mathematical concepts in greater detail. Please note that this document contains the explanations only, and does not provide the test questions themselves; it is a tool intended for use with a copy of your test that you purchased from the ACT via the Test Information Release (TIR). The following are sample explanations:
English
3) D) Answer choice A is incorrect because it creates a sentence with two independent clauses joined only by a comma without a conjunction. B and C are incorrect for the same reason. D is correct because it turns the second part of the sentence into a phrase, which is correctly linked to the preceding independent clause by a comma.
Mathematics
1) A) The total decrease is equal to \$26,200 – \$17,500 = \$8,700. Now you can find the average yearly decrease over the four years: \$8,700/4 = \$2,175. Remember that “per” indicates division, so you know that to find the decrease per year, you must divide the total decrease by the number of years. See averages. | 302 | 1,352 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-04 | latest | en | 0.925206 |
https://www.scribd.com/doc/223961247/9-Regresi-Log-reg-Cox-2012 | 1,540,233,776,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583515375.86/warc/CC-MAIN-20181022180558-20181022202058-00228.warc.gz | 1,086,547,760 | 64,374 | # R E G R E S I L O G I S T I K
Dalam statistika
Logistic regression:
a model used
for prediction of
the probability of
occurrence of an
event by fitting
data to a logistic
curve
(Logistic regression/logistic model/logit model)
Logistic curve
(“S”/”Sigmoid”)
t
(waktu)
P
(Prob.)
Linear regression
Logistic regression
Logistic regression
Log.reg.
Probabilitas (P) seseorang memp.
gejala artritis, sebagai fungsi umur (t)
Logit Transformation
logit)
Logit: log p/(1-p) (disebut juga log odds)
Odds: p/(1-p)
Logistic regression: maps probabilities onto the
scale of the linear predictor in logistic regression
Log odds: logarithm of the odds of probabilities
Fungsi LOG. REG.: to assess the likelihood of a
disease or health condition as a
function of a risk factor (and covariates)
P
logRF
ODDS ?
ODDS RATIO ?
ODDS suatu outcome (merupakan ukuran asosiasi) :
perkiraan berapa besar kemungkinan (likely) terjadinya (p)
atau tidak terjadinya (unlikely: 1-p) suatu outcome (event,
ODDS RATIO (OR):
(1). Ratio of the probality of occurrence over the probability of
nonoccurrence (p/(1-p) satu kelompok (mis. diberi terapi)
dengan kelompok lain (tidak diberi terapi).
kanker paru pada perokok dan nonperokok: OR=2
OR = 2, artinya perokok kemungkinan menderita kanker paru
2x dibanding nonperokok.
(2). Merupakan perkiraan indikator lain, yaitu risiko relatif (RR)
ODDS suatu event:
Odds = p/(1-p) p: probabilitas event terjadi
(mis. event: sembuh; jika tidak diberi obat:
probabilitas sembuh 0,66
Odds: 0,6667/0,3333 = 2
Jika diberi obat baru: prob. sembuh 80% atau 0,8
Seberapa lebih baik obat baru tsb. jika
dibandingkan dengan obat lama?
ODDS dan ODDS RATIO
Dengan obat baru:
Odds sembuh: 0,080/0,20 = 4
Odds ratio: 4/2 = 2
Odds obat baru: 2x lebih tinggi
Odds in the no treatment group
ODDS RATIO =
Odds in the treatment group
probability of the event p
Odds = =
1 – probability of event 1 – p
Atau Odds
Probability: p =
1 + Odds
* ODDS RATIO (OR) vs RELATIVE RISK (RR)
Probability of occurrence p
OR: =
probability of nonoccurrence 1-p
OR dipakai untuk mengestimasi risiko relatif (relative risk): RR
RR: risiko suatu kondisi tertentu vs kondisi lain.
(mis. RR 3: 3 x lebih tinggi pada wanita tanpa prenatal
care (PNC) (dibandingkan dengan wanita dengan PNC)
Low Birth Weight (LBW)
Yes (LBW) No (normal) Row totals
Prenatal Care
No 75 175 250
Yes 20 180 200
95 355 450
Tab. of Probabilities
LBW 75
Prob. of LBW with no PNC: = = 0.3
No PNC 250
Normal Weight 175
Prob. of Normal BW with N PNC: = = 0.7
No PNC 250
(Tab. of Prob. Cont.)
LBW 20
Prob. of LBW with PNC: = = 0.1
PNC 200
Normal Weight 180
Prob. of Normal BW with PNC: = = 0.9
PNC 200
Tab. of ODDS
Prob. of occur. 03
Odds of LBW infant, when no PNC: = = 0.43
Prob. of non-occur. 07
Prob. of occur. 0.3
Odds of LBW infant, when PNC: = = 0.11
Prob. of non-occur. 0.9
ODDS RATIO (OR)
probabilitas (odds) lain:
0,43/0,11 = 3,91
Risiko LBW:
- Tanpa PNC: 75/250 = 0,3
- Dengan PNC: 20/200 = 0,1
RISIKO RELATIF (RR): 0,3/0,1 = 3,0
Regresi logistik banyak dipakai untuk memprediksi
event di bidang kedokteran & sosial
-KEDOKTERAN: prediksi probabilitas mengalami
serangan jantung (penyakit/kondisi)
berdasarkan pengetahuan tentang faktor
risiko (umur, seks, body mass index/BMI)
Var. bebas (FAKTOR RISIKO): umur, seks, BMI
Var.terikat (OUTCOME): prob. serangan jantung
- SOSIAL, mis. marketing/pemasaran:
prediksi kecenderungan pembeli
membeli/tidak produk atau
menghentikan/tidak berlangganan
KEGUNAAN REGRESI LOGISTIK
1. Memprediksi var. terikat (dependen);
skala: dikotomik (binomial) berdasarkan var.
bebas (independen; skala: kontinu dan/atau
kategorik/ordinal
2. Menentukan % varian var. terikat yang
diterangkan oleh var. bebas
3. Me-ranking relative importance of independents
4. Menilai efek interaksi (antarvar. bebas/kovariat)
5. Memahami dampak variabel
prediktor/kovariat/faktor
(Dampak var. kovariat biasanya dijelaskan oleh
OR (odds ratio)
REGRESI LOGISTIK
• Mencapai aplikasi maksimumnya untuk
mengestimasi suatu kemungkinan (likelihood)*
setelah mentransformasi var. terikat menjadi var.
logit (the natural log of the odds of the dependent
occurring or not)
• Dengan cara ini: regresi logistik bisa mengestimasi
* Maximum Likelihood Estimation (MLE):
metode dipakai untuk menghitung coefficient logit
(Berbeda dengan penggunaan Ordinary Least
Square (OLS): estimasi coefficient in regression line)
REGRESI LOGISTIK (RL)
(LOGISTIC REGRESSION/LR)
RL dipakai untuk memprediksi/
menilai kemungkinan/probabilitas
(likelihood) suatu outcome
(penyakit, kondisi kes.) (Y) sebagai
fungsi faktor risiko (FR) dan
kovariat (X)
REGRESI LOGISTIK (RL)
(LOGISTIC REGRESSION/LR)
Dipakai untuk memprediksi atau menilai
kemungkinan (likelihood) suatu outcome –
penyakit atau kondisi kes. (Y) – sebagai
fungsi faktor risiko (dan kovariat) (X)
1. Simple LR:
menilai asosiasi antara 1 var. bebas (X:
exposure atau predictor var., faktor
risiko (skala: nominal – kontinu) dan 1
var. terikat (Y): outcome, response var.;
skala: nominal dikotomik)
2. Multiple LR: menilai asosiasi antara
> 1 var. bebas (X
i
) (nominal, kontinu) dan
1 var. terikat (Y) (nominal dikotomik)
Analisis RL: seberapa besar peningkatan
(increment) var. paparan (eksposure)
mempengaruhi odds of the outcome
(Odds: p/1-p: probabilitas suatu event terjadi
dibagi probabilitas suatu event tidak terjadi)
FAKTOR (“Design Variable”): prediktor (nominal
atau ordinal, yang level-nya dimasukkan
sebagai dummy variable
(Satu faktor bisa mempunyai beberapa level)
KOVARIAT: Var. Bebas (independen)(skala: interval)
INTERAKSI: bisa ditambahkan dalam model (mis.
interaksi umur-pendapatan: age income
Untuk kovariat kontinu: membuat satu var.
yang merupakan produk dua var. yang ada
Untuk var. kategorik: multiplikasi dua kode
kategorik.
Mis. Ras (1)* agama (2)
Definition Example: getting heads Example: getting a 1
in a 1 flip of a coin in a single roll of a dice
# of times something happens
Odds = 1/1 = 1 (or 1:1) 1/5 = 0,2
(or 1:5)
# of times it does NOT happen
# of times something happens
Prob. = 1/2 = 0,5 (or 50%) 1/6 = 0.16
(or 16%)
# of times it could happen
VARIABEL2 DALAM REGRESI LOGISTIK
VARIABEL BEBAS (X) VARIABEL TERIKAT (Y)
(independent/input/ ISTILAH (dependent/output/
predictor/exposure/ LAIN event/outcome)
risk factor)
numerik atau kategorik SKALA nominal dikotomik
Contoh:
X Y
umur, seks, BMI serangan jantung
(body mass index) (ya/tidak)
faktor risiko event/outcome
LOGISTIC REGRESSION (LR)
SIMPLE LR MULTIPLE LR
Mengeksplorasi asosiasi
antara satu (skala:
dikotomik) outcome variable
dan satu exposure variable
(skala: kontinu/ordinal/
kategorik)
Mengeksplorasi asosiasi antara satu
(dikotomik) outcome variable dan dua/>
exposure variable (kontinu/ordinal/kategorik)
Bagaimana mengisolasi hubungan antara
exposure variable dan outcome variable dari
efek satu atau lebih var. lain (disebut
kovariat atau confounders) setelah
mengeluarkan) pengaruh var. independen
(umur, penghasilan dll.).?
Bagaimana seks mempengaruhi prob.
menderita hipertensi setelah mengontrol FR
lainnya (covariats/confounders: umur,
kolesterol dll.)
Bagaimana seks (jenis kelamin)
mempengaruhi probabilitas
menderita hipertensi?
FUNGSI LOGISTIK
(logistic function):
1
f(z) =
1 + e
-z
z: input ( - infinity + infinity ) e: exponent=2,7
(besarnya paparan (exposure) berupa beberapa
faktor risiko/FR)
(besarnya kontribusi total semua FR dipakai
dalam model ini: dikenal sebagai logit)
f(z): output atau outcome (0 or 1)/binomial (dikotomik)
(probabilitas outcome tertentu untuk sejumlah FR)
Fungsi logistik (logistic function): f(z)
0,5
1
f(z) =
1 + e
-z
f(z)
z
- tak terhingga
+ tak terhingga
Regresi logistik membentuk
var. prediktor yang merupakan
kombinasi linier var.
eksplanatoris. Nilai2 var.
prediktor kemudian di-
oleh fungsi logistik (bentuk S)
Aksis horisontal: nilai2
prediktor
Aksis vertikal: probabilitas.
sesuai dengan prob. 0,12
(nilai -1 0,27)
Prediktor
Prob.
MODEL REGRESI
LOGISTIK
z = β
0
+ β
1
x
1
+ β
2
x
2
+ β
3
x
3
………. β
k
x
k
β
0
= intercept, jika nilai2 semua FR = 0
(artinya: nilai z seseorang jika tidak memp. FR)
β
1
……... β
k
: koefisien regresi
- Pos.(+): FR meningkatkan probabilitas outcome;
- Neg. (-): FR menurunkan probabilitas outcome
- Mendekati 0: FR berpengaruh kecil terhadap prob. outcome
LOGISTIC FUNCTION
Input Output
(z) f(z)
Age, sex, BMI Prob. heart attack
(FR) (Event)
Contoh fiktif reg. log.
Tiga FR (umur, seks, kadar kolesterol darah)
dipakai untuk memprediksi dalam 10 tahun risiko
kematian karena serangan jantung
β
0
= -5,0 (intercept); β
1
= +2,0; ß
2
=-1,0; β
3
= +1,2
X
1
2
= seks (0: laki2; 1: peremp.);
X
3
1
Risiko kematian = dimana z = -5,0 + 2,0 X
1
– 1,0 X
2
1 + e
-z
+ 1,2 X
3
Dalam model ini:
- Peningkatan umur berasosiasi dengan
peningkatan risiko kematian karena serangan
jantung (z naik sampai 2,0 setiap 10 th.
di atas umur 50)
- Jenis kelamin peremp. berasosiasi dengan
penurunan risiko kematian karena serangan
jantung ( z turun 1,0 jika pasien peremp.)
- Peningkatan kolest. berasosiasi dengan
penigkatan risiko kematian (z naik 1,2
untuk setiap peningkatan 1 mmol/L kolest.
di atas 5mmol/L)
LOGIT FUNCTION
(FUNGSI LOGIT)
Mencoba mengetahui asosiasi antara faktor2
risiko dan satu kondisi.
Diperlukan rumus yang memungkinkan
menghubungkan var.2 tsb. : logit function
menghubungkan beberapa nilai var. bebas
LOGIT MODEL
Logit {E(Y
i
)} = Log (p
i
/1-p
i
) = Intercept + β
1
X
1
+ β
2
X
2
+ ….. + β
i
X
i
(log : natural log)
Logit: log p/(1-p)
E: exponential= 2,7
Model logistik memberikan probabilitas bahwa
outcome (enuresis) terjadi sebagai fungsi var.2
independen (3 var.: stres psikol., jenis kel., umur)
1
p
x
=
1 + exp[-(b
0
+ b
1
x
1
+ b
2
x
2
+ b
3
x
3
)]
b
0
: intercept; b
1
, b
2
, b
3
: koef. regresi;
exp: the base of the natural logarithm (2.718) is
taken the power shown in parentheses.
1
p
x
=
1 + e
-z
fungsi eksponensial var. bebas
Contoh (Presenting Problem 4):
3 VAR. BEBAS 1 VAR. TERIKAT
1. stres psikologis enuresis (wet/ngompol)
2. seks (L/P) (ya/tidak)
3. umur
Dalam Pres. Probl. 4 ini var. bebas (stres, seks,
(event: enuresis)
Contoh Aplikasi Reg. Log.
Kematian karena penyakit jantung
Tiga FR (umur, jenis kel., kadar kolesterol darah) dipakai
untuk memprediksi risiko kematian dalam 10 tahun)
Β
0
= -5,0 (intersep); β
1
= +2,0; β
2
= -1,0; β
3
= +1.2
X
1
= umur (dalam dekade) : <5,0
X
2
= seks (0: laki2; 1: peremp.)
X
3
1
RISIKO KEMATIAN:
1 + e
-z
z = - 0,5 + 2,0 x
1
– 1,0 x
2
- 1,2 x
3
z = - 0,5 + 2,0 x
1
– 1,0 x
2
+ 1,2 x
3
Meningkatnya umur berasosiasi dengan
meningkatnya risiko kematian (z naik dengan 2,0
setiap 10 tahun di atas umur 50 tahun)(+2,0 X
1)
Perempuan berasosiasi dengan penurunan risiko
kematian karena penyakit jantung (z menurun
dengan 1,0 jika pasien tsb. perempuan)(-1,0 X
2
)
Peningkatan kolesterol berasosiasi dengan
meningkatnya risiko kematian (z naik 1,2 setiap
kenaikan kolesterol 1 mmol/L diatas 5 mmol/L)
Model tsb. bisa dipakai memprediksi risiko kematian
pasien karena penyakit jantung:
Mis. Pasien berumur 50 tahun dan kadar kolesterolnya
7,0 mmol/L RISIKO KEMATIAN-nya:
1
1 + e
-z
z = -5,0 + (+2,0)(5,0 – 5,0) + (-1,0) + (1,2)(7,0-5,0)
Ini berarti dengan model ini risiko kematian pasien
tsb. karena penyakit jantung 10 tahun yang akan
Contoh Reg.Log.
Prosedur reg.log. memerlukan tiga tabel:
(1). Tabel rangkuman analisis
(2). Tabel koefisien
(3). Deviance table
Var.I: lamanya (hari) radioterapi (var. eksplanatoris);
Var. II: absence (0) dan presence (1) penyakit
setelah 3 th terapi (var. respon)
Reg.log. menunjukkan: intercept = 3,81944; koef. untuk
menurunkan odds absence of disease = 8%.
Summary of Statistical Analysis:
Number of observations 24
Observations with Missing values 0
Response variable desease
Tables
1. Table labeled parameters give parameter estimates with
asymptotic standard errors
2. Wald tests
3. p-values
Coefficient Stand. Error Wald test Chi sq.>p
Intercept 3.81944 1.83516 4.33163 0.03741
Therapy -0.08648 0.04322 4.00424 0.04539
The deviance table decomposes the deviance into
two components: 1. a residual and 2. a model
component
Because only one var. is used in the model, the
hypotesis tested by the deviance statistic is the
same as for the Wald test. The p-values of the
two test statistics are very similar:
Deviance df p-value
Model 4.81306 1 0.02824
Residual 27.78822 22 0.18281
OUTPUT LOGISTIC REGRESSION
Statistik yang penting dalam log. reg.: koef. regresi
(koef. β: β
1
, β
2
, β
3
….), SE (standard error), nilai-p.
Interpretasi koef. β untuk berbagai var. independen:
Jika X
j
: var. dikotomik (nilai 1 atau 0)
Koef. β = log odds bahwa individu akan memp.
event untuk orang dengan X
j
=1 vs orang dengan X
j
=0
Dalam model multivariat: koef. β adalah efek
independen var. X
j
i
semua kovariat lainnya di dalam model
Jika X
j
: var. kontinu e
β
merupakan odds
bahwa individu akan memp. event untuk orang
dengan X
j
= m
Artinya: untuk setiap kenaikan 1 unit X
j
Odds seseorang memp. event dengan
X
j
=m+1 vs seseorang dengan X
j
=m
Dengan kata2 lain: untuk setiap kenaikan 1 unit
dalam X
j
Odds memp. event Y
i
berubah
dengan e
β
, dengan adjusting semua kovariat lain
dalam model multivariat
Apa arti koef. β?
Tipe var. bebas Contoh var. Koef.β dalam Koef. Β dalam
simple LR multiple LR
Kontinu TB, BB, LDL Perub. Log odds perub. log odds var.
var. terikat per 1 terikat per 1 unit perub.
unit perub. Var. var. bebas setelah
bebas mengontrol efek
perancu kovariat dalam model
Kategorik Seks (2 subgroup: Perbedaan dlm. Perbedaan dalam log
laki2 dan peremp. Log odds VT odds VT per 1 unit
perub.
Di sini: laki2 sebagai unt. 1 nilai var. var. kategorik vs kel. re-
kelomp. referensi kategorik vs kel. refensi (mis. antara pe-
referensi (mis. remp.dan laki2, setelah
antara peremp dan laki2 mengontr. efek konfound.
kovariat dalam model
• Banyak bidang kedokteran menggunakan parameter sasaran
utama/primernya:
• Mis.:
-waktu mulai dari diagnosis kanker paru sampai mati
(event/outcome)
- waktu mulai dari pemberian terapi sampai sembuh/berhasil
(event/outcome)
“EVENT” bisa berupa: sukses/sembuh atau gagal/mati
(Penting untuk mendefinisikan dengan baik:
1. awal periode waktu
Waktu antara 1 dan 2: SURVIVAL TIME;
meskipun event tsb. tidak harus berupa mati)
( Contoh: apakah terapi memperpanjang survival time?)
VARIABEL2
DALAM REGRESI COX
(VB) (VT)
(t)
EXPLANATORY VAR. EVENT/OUTCOME
(RISK FACTORS/
COVARIATES)
(Terapi sukses/sembuh
Diagnosis gagal/mati)
( t )
(survival time)
t
• CENSORING (berkaitan dengan SURVIVAL TIME)
1.
- Alasan etis (Clinical Trial:
t harus singkat)
- event yang diharapkan
tidak sampai akhir trial
2. Subjek meninggalkan trial:
- tidak berpartisipasi lebih lanjut
- meninggal (yang tidak ada kaitannya
dengan trial)
CENSORED: tidak diikutsertakan
REGRESI COX
(PROPORTIONAL HAZARDS REGRESSION)
• REGRESI COX: Metode untuk meneliti efek beberapa
variabel (risk factors) terhadap waktu yang
diperlukan untuk terjadinya event (mis. survival
time).
(Khusus: jika outcome berupa kematian dikenal
sebagai: Cox regression for survival
analysis)
• Metode ini tidak berasumsi mengenai “survival
model” tertentu, tetapi tidak sepenuhnya benar non-
parametrik (karena: tidak berasumsi bahwa efek
(Saran: jangan menggunakan regresi Cox tanpa
bimbingan ahli statistik)
REGRESI COX
• Efek simultan beberapa variabel terhadap waktu
survival bisa diteliti.
A. Parameter2 yang diuji:
1.Terapi;
2. seks;
3. derajat reseksi;
4. status metastasis
B. Efek umur (var. kontinu) pada waktu operasi
Dalam kedua hal tsb. (A dan B) regresi Cox bisa
dipakai untuk memperolah estimator besarnya efek.
Estimasi ini berupa rasio hazard.
Hazard dan rasio hazard
1. HAZARD (risiko): probability of end point*
• Kumulatif hazard pada waktu t:
risiko meninggal antara waktu 0 - t.
• Fungsi survival pada waktu t atau H(t) disebut hazard
model:
probability of surviving sampai waktu t.
• Koefisien regresi Cox berhubungan dengan hazard:
- Koefisien positif: menunjukkan prognosis lebih
buruk
- Koefisien negatif: menunjukkan efek protektif
(lebih baik) variabel yang berkaitan
* End point (death, other event of interest e.g.
recurrence of disease)
2. HAZARD RATIO: H(t)/H
0
(t)
- berkaitan dengan variabel prediktor
ditunjukkan oleh eksponen
koefisiennya (exp): b
1
..... b
k
- dianggap sebagai angka kematian
relatif (relative death rate)
- interpretasi rasio hazard tergantung
prediktor (x
1
..... x
k
) yang dikaji.
• Hazard model: H(t)
H(t) = H
0
(t) x exp(b
1
x
1
+ b
2
x
2
+
b
3
x
3
+ .... b
k
x
k
)
• Hazard ratio: H(t)/H
0
(t)
• exp: exponent: 2,7
Time-dependent & fixed covariates
• Dalam penelitian prospektif: jika individu2 diikuti
- TIME-DEPENDENT COVARIATES
- FIXED COVARIATES
• Kovariat dikatakan time-dependent:
perbedaan antara nilai2 untuk dua subjek
mis. kolesterol serum
• Kovariat dikatakan tetap (fixed) jika:
mis. seks atau ras.
• Analisis Model dan Deviance
• Tes kemaknaan statistis suatu model termasuk
dalam topik “analisis model”:
• - the likelihood chi-square statistic dihitung
dengan membandingkan deviance (-2 log
likelihood) model yang dipilih dengan
semua kovariat model tsb. dengan kovariat2
yang di-drop.
• Kontribusi individual kovariat2 model yang
dipakai bisa dinilai dari tes signifikansi.
(perhitungan2 statistis bisa menggunakan
paket2 yang ada: SPSS, STATS. STATA dll.)
• Contoh Regresi Cox
Table 2. Results of Cox regression for overall survival in 280 children
with medulloblastoma (M)
n HR 95% CI p
Metastasis status on diagnosis
MO 114
M1 33 2.11 1.13-3.94 0.001
M2/3 40 3.06 1.76-5.33
Unknown 93 1.54 0.94-2.52
Treatment
Maintenance chemotherapy 127 0.006
Sandwich chemotherapy 153 1.76 1.17-2.67
Operation diagnosis 280 0.93 0.00-0.98 0.005
n: no. of cases; HR: hazard ratio; 95% CI (CI for hazard
ratio); p: p value of lielihood ratio test control group for
categorical varables
REGRESI COX (RC)
Menerapkan proportional hazard model
(duration model)
(Disebut juga: Cox’s proportional
hazards model for survival-time
(time-to-event) outcomes on one or
more predictors
Didesain untuk menganalisis waktu (time
atau waktu antara events (time-to-
event)
Satu atau lebih var. (kovariat) dipakai
untuk memprediksi satu var. status
(event)
Contoh klasik univariat:
analisis waktu mulai dari diagnosis
penyakit terminal sampai kematian
(event) disebut:
SURVIVAL ANALYSIS
VARIABEL
1.VAR. STATUS (EVENT VAR. atau
CENSORING VAR.):
dianalisis dalam kaitannya dengan var. waktu
Contoh var. status: kematian (dalam
kajian medis): mati=0, hidup=1
2. VAR. WAKTU (TIME VAR.):
Var. waktu merupakan durasi event, seperti
yang didefinisikan oleh var. status (awal studi
sampai akhir studi atau sampai terjadinya
event, mis. mati)
3. KOVARIAT (COVARIATES):
var.prediktor (var. bebas/independen)
dalam model Cox bisa bersifat:
(1). Kategoris atau Kontinu:
(a).Kategoris (mis. seks, ras)
atau
(b). Kontinu (mis. umur, penghasilan)
(2). Bisa bersifat fixed atau time-dependent:
(a). FIXED COVARIATE:
Mis. jenis kelamin/seks, umur
(b). TIME-DEPENDENT COVARIATE;
(mis. gaya hidup, pengukuran fisiologis:
tekanan darah; cummulative exposure (mis.
merokok)
COX MODEL: a well recognized statistical
technique for exploring the
relationship between the survival
(death, recurrence of a disease) of
a patient and several explanatory
(IV) variables
- Provides an estimate of the
treatment effect on survival after
variables.
- It allows us to estimate the hazard
(or risk) of death, or other event of
interest, for individuals, given their
prognosis variables
ANALYSIS TIME (WAKTU ANALISIS) ( t ): adalah var. waktu,
dimana t = 0 merupakan waktu awitan (onset) risiko.
ONSET OF RISK:
artinya ketika kegagalan (atau event) terjadi pertama kali
SURVIVAL ANALYSIS: mengkaji/menganalisis waktu antara ikut
dalam penelitian (entry the study) sampai terjadinya event
(mis. kematian).
CENSORED SURVIVAL TIME:
selama periode kajian/studi
Info. dari subjek2 yang tersensor, yaitu mereka yang tidak
mengalami event yang diteliti selama waktu observasi,
biasanya memberi kontribusi terhadap estimasi model tsb.
• Contoh kajian dimana beberapa subjek tidak
mengalami event selama kajian (tersensor):
- Apakah laki-laki dan perempuan memp. risiko
paru akibat merokok?
• Dibuat model regresi Cox: mmerokok erokok
merokok (batang/hari) dan jenis kelamin
sebagai kovariat bisa diuji hipotesis
mengenai efek jenis kelamin terhadap time-
to-onset kanker paru
INTERPRETASI MODEL COX
Melibatkan pengujian koefisien setiap
var. eksplanatoris:
- Koef. regresi positif untuk var.
eksplanatoris: hazard tinggi ;
jika nilainya besar (tinggi):
prognosis lebih buruk
- Koef. regresi negatif:
prognosis lebih baik jika nilai
negatifnya lebih tinggi/besar
KEGUNAAN MODEL COX
Menganalisis survival data:
- Mengisolasi efek perlakuan (terapi) dari efek var. lain
- Menggunakan a priori jika diketahui bahwa ada var.2
lain disamping terapi yang mempengaruhi
survival pasien, dan var.2 ini tidak mudah
dikontrol dalam clinical trial): meningkatkan
efek perlakuan (terapi) dengan memperkecil
confidence interval)
- Secara simultan mengeksplorasi efek beberapa
SURVIVAL TIMES: perkembangan gejala tertentu atau
terjadinya relapse (kambuh) setelah penyakit tersebut remisi
(berkurang), dan juga sampai saat meninggal
MENGAPA SURVIVAL TIMES (ST) DISENSOR?
(Censored Survival Times)
Gambaran penting ST: event yang dikaji sangat jarang
Mis. suatu kajian yang membandingkan survival pasien
yang mengalami macam operasi yang berbeda untuk
kanker hati
beberapa pasien yang di-follow up selama beberapa
tahun, masih mungkin ada beberapa pasien yang tetap
masih hidup sampai akhir studi.
Survival times ini disebut: Censored Survival Times
(CST), untuk menunjukkan bahwa periode observasi di-
cut off sebelum event yang dipelajari terjadi (mis.
meninggal)
Metode Kaplan-Meier
Berdasarkan ST (termasuk yang CST)
dalam sampel individu2: bisa diestimasi proporsi pop.
seperti orang2 yang akan dapat survive jika periode
waktunya diperpanjang di bawah kondisi yang sama
Metode ini disebut: Kaplan-Meier Method (K-MM)
K-MM: memungkinkan dibuat tabel (Life Table)
atau gambar (Survival Curve)
K-MM: menggunakan logrank test, bisa dipakai untuk
mengeksplorasi (and adjust for) efek beberapa
variabel, seperti umur dan durasi penyakit,
yang diketahui mempengaruhi survival.
KAPLAN-MEIER
METHOD (K-MM)
• Metode untuk mengestimasi proporsi
pop. orang2 yang survived selama
waktu dibawah kondisi yang sama
• Metode ini disebut juga PRODUCT
LIMIT atau KAPLAN-MEIER METHOD
(K-MM):
Memungkinkan dihasilkannya tabel dan
grafik: life table dan survival curve
• Table 1. Calculation of K-M estimate of survivor function
A B C D E F
Survival Number at Number of Number Proportion Cummu-
time (yrs.) risk at start death censored surviving lative pro-
of study until end portion
of interval surviving
0.909 10 1 0 1-1/10=0.900 0.900
1.112 9 1 0 1-1/9=0.889 0.800
1.322* 8 0 1 1-0/8=1.000 0.800
1.328 7 1 0 1-1/7=0.857 0.686
1.536 6 1 0 1-1/6=0.8333 0.571
2.713 5 1 0 1-1/5=0.800 0.457
• Table 1 (cont.)
A B C D E F
2.741* 4 0 1 1-0/4=1.000 0.457
2.743 3 1 0 1-1/3=0.667 0.305
3.524* 2 0 1 1-0/2=1.000 0.305
4.079 1 0 1 1-0/1=1.000 0.305
* Indicates a censored survival time
Cumm.
proport.
surv.
1.0
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4
5
Overall survival (yrs. from surgery)
Fig.1 Kaplan-Meier estimate of the survival function
diketahui mempengaruhi survival bisa
memperbaiki presisi estimasi efek terapi.
Metode regresi yang diperkenalkan oleh Cox
dipakai untuk mempelajari beberapa variabel
bersamaan sekaligus:
Proportional Hazards Regression Analysis
(Cox’s Regression Analysis/Method)
( Metode untuk mempelajari efek beberapa var.
event: mis. mati)
HAZARD ?
HAZARD RATIO ?
Hazard (or Risk): the probability of the end point
(death, or any other event of interest, eg.
recurrence of disease)
Hazard model:
H(t) = H
0
(t) x exp(b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ … + b
k
X
k
X
1
… X
k
: var.2 prediktor; H
0
waktu t (merupakan hazard seseorang dengan 0 untuk
semua nilai var. prediktor) (exp: exponent)
Hazard model:
l
n
[H(t)/H
0
(t)] = b
1
X
1
+ b
2
X
2
+ b
3
X
3
+ … b
k
X
k
Hazard ratio: H(t)/H
0
(t)
Koef. b
1
… b
k
diestimasi oleh
regresi Cox
(diinterpretasi dengan cara yang sama
seperti multiple logistic regression)
Jika mis. kovariat (faktor risiko)
1
)
diinterpretasi sebagai instantaneous
relative risk suatu event.
Mis. kovariat: kontinu exp(b
1
):
instantaneous* relative risk suatu
event, setiap saat peningkatan 1 nilai
kovariat dibandingkan dengan individu
lain, asal kedua individu tsb.
memp.kovariat yang sama.
(* saat itu juga)
Grafik menunjukkan kurva survival untuk semua semua var. kategorik
Mult (1: multiple previous gallstones, 0: single previous gallstone), dan
untuk semua nilai rerata semua kovariat dalam model.
KAPLAN-MEIER METHOD
Kaplan-Meier curve
Survival times of 5 children with brain tumors
Kaplan-Meier curve for 33 children and adolescents
with medulloblastoma and metastasis status M1 | 8,692 | 24,804 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2018-43 | latest | en | 0.310953 |
https://calculationcalculator.com/biswa-to-square-kilometer | 1,726,112,468,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651420.25/warc/CC-MAIN-20240912011254-20240912041254-00230.warc.gz | 125,095,953 | 22,652 | # Biswa to Square Kilometer Conversion
## 1 Biswa is equal to how many Square Kilometer?
### 0.000125465 Square Kilometer
##### Reference This Converter:
Biswa and Square Kilometer both are the Land measurement unit. Compare values between unit Biswa with other Land measurement units. You can also calculate other Land conversion units that are available on the select box, having on this same page.
Biswa to Square Kilometer conversion allows you to convert value between Biswa to Square Kilometer easily. Just enter the Biswa value into the input box, the system will automatically calculate Square Kilometer value. 1 Biswa in Square Kilometer? In mathematical terms, 1 Biswa = 0.000125465 Square Kilometer.
To conversion value between Biswa to Square Kilometer, just multiply the value by the conversion ratio. One Biswa is equal to 0.000125465 Square Kilometer, so use this simple formula to convert -
The value in Square Kilometer is equal to the value of Biswa multiplied by 0.000125465.
Square Kilometer = Biswa * 0.000125465;
For calculation, here's how to convert 10 Biswa to Square Kilometer using the formula above -
10 Biswa = (10 * 0.000125465) = 0.00125465 Square Kilometer
Biswa Square Kilometer (sq km) Conversion
1 0.000125465 1 Biswa = 0.000125465 Square Kilometer
2 0.00025093 2 Biswa = 0.00025093 Square Kilometer
3 0.000376395 3 Biswa = 0.000376395 Square Kilometer
4 0.00050186 4 Biswa = 0.00050186 Square Kilometer
5 0.000627325 5 Biswa = 0.000627325 Square Kilometer
6 0.00075279 6 Biswa = 0.00075279 Square Kilometer
7 0.000878255 7 Biswa = 0.000878255 Square Kilometer
8 0.00100372 8 Biswa = 0.00100372 Square Kilometer
9 0.001129185 9 Biswa = 0.001129185 Square Kilometer
10 0.00125465 10 Biswa = 0.00125465 Square Kilometer
11 0.001380115 11 Biswa = 0.001380115 Square Kilometer
12 0.00150558 12 Biswa = 0.00150558 Square Kilometer
13 0.001631045 13 Biswa = 0.001631045 Square Kilometer
14 0.00175651 14 Biswa = 0.00175651 Square Kilometer
15 0.001881975 15 Biswa = 0.001881975 Square Kilometer
16 0.00200744 16 Biswa = 0.00200744 Square Kilometer
17 0.002132905 17 Biswa = 0.002132905 Square Kilometer
18 0.00225837 18 Biswa = 0.00225837 Square Kilometer
19 0.002383835 19 Biswa = 0.002383835 Square Kilometer
20 0.0025093 20 Biswa = 0.0025093 Square Kilometer
21 0.002634765 21 Biswa = 0.002634765 Square Kilometer
22 0.00276023 22 Biswa = 0.00276023 Square Kilometer
23 0.002885695 23 Biswa = 0.002885695 Square Kilometer
24 0.00301116 24 Biswa = 0.00301116 Square Kilometer
25 0.003136625 25 Biswa = 0.003136625 Square Kilometer
26 0.00326209 26 Biswa = 0.00326209 Square Kilometer
27 0.003387555 27 Biswa = 0.003387555 Square Kilometer
28 0.00351302 28 Biswa = 0.00351302 Square Kilometer
29 0.003638485 29 Biswa = 0.003638485 Square Kilometer
30 0.00376395 30 Biswa = 0.00376395 Square Kilometer
31 0.003889415 31 Biswa = 0.003889415 Square Kilometer
32 0.00401488 32 Biswa = 0.00401488 Square Kilometer
33 0.004140345 33 Biswa = 0.004140345 Square Kilometer
34 0.00426581 34 Biswa = 0.00426581 Square Kilometer
35 0.004391275 35 Biswa = 0.004391275 Square Kilometer
36 0.00451674 36 Biswa = 0.00451674 Square Kilometer
37 0.004642205 37 Biswa = 0.004642205 Square Kilometer
38 0.00476767 38 Biswa = 0.00476767 Square Kilometer
39 0.004893135 39 Biswa = 0.004893135 Square Kilometer
40 0.0050186 40 Biswa = 0.0050186 Square Kilometer
41 0.005144065 41 Biswa = 0.005144065 Square Kilometer
42 0.00526953 42 Biswa = 0.00526953 Square Kilometer
43 0.005394995 43 Biswa = 0.005394995 Square Kilometer
44 0.00552046 44 Biswa = 0.00552046 Square Kilometer
45 0.005645925 45 Biswa = 0.005645925 Square Kilometer
46 0.00577139 46 Biswa = 0.00577139 Square Kilometer
47 0.005896855 47 Biswa = 0.005896855 Square Kilometer
48 0.00602232 48 Biswa = 0.00602232 Square Kilometer
49 0.006147785 49 Biswa = 0.006147785 Square Kilometer
50 0.00627325 50 Biswa = 0.00627325 Square Kilometer
51 0.006398715 51 Biswa = 0.006398715 Square Kilometer
52 0.00652418 52 Biswa = 0.00652418 Square Kilometer
53 0.006649645 53 Biswa = 0.006649645 Square Kilometer
54 0.00677511 54 Biswa = 0.00677511 Square Kilometer
55 0.006900575 55 Biswa = 0.006900575 Square Kilometer
56 0.00702604 56 Biswa = 0.00702604 Square Kilometer
57 0.007151505 57 Biswa = 0.007151505 Square Kilometer
58 0.00727697 58 Biswa = 0.00727697 Square Kilometer
59 0.007402435 59 Biswa = 0.007402435 Square Kilometer
60 0.0075279 60 Biswa = 0.0075279 Square Kilometer
61 0.007653365 61 Biswa = 0.007653365 Square Kilometer
62 0.00777883 62 Biswa = 0.00777883 Square Kilometer
63 0.007904295 63 Biswa = 0.007904295 Square Kilometer
64 0.00802976 64 Biswa = 0.00802976 Square Kilometer
65 0.008155225 65 Biswa = 0.008155225 Square Kilometer
66 0.00828069 66 Biswa = 0.00828069 Square Kilometer
67 0.008406155 67 Biswa = 0.008406155 Square Kilometer
68 0.00853162 68 Biswa = 0.00853162 Square Kilometer
69 0.008657085 69 Biswa = 0.008657085 Square Kilometer
70 0.00878255 70 Biswa = 0.00878255 Square Kilometer
71 0.008908015 71 Biswa = 0.008908015 Square Kilometer
72 0.00903348 72 Biswa = 0.00903348 Square Kilometer
73 0.009158945 73 Biswa = 0.009158945 Square Kilometer
74 0.00928441 74 Biswa = 0.00928441 Square Kilometer
75 0.009409875 75 Biswa = 0.009409875 Square Kilometer
76 0.00953534 76 Biswa = 0.00953534 Square Kilometer
77 0.009660805 77 Biswa = 0.009660805 Square Kilometer
78 0.00978627 78 Biswa = 0.00978627 Square Kilometer
79 0.009911735 79 Biswa = 0.009911735 Square Kilometer
80 0.0100372 80 Biswa = 0.0100372 Square Kilometer
81 0.010162665 81 Biswa = 0.010162665 Square Kilometer
82 0.01028813 82 Biswa = 0.01028813 Square Kilometer
83 0.010413595 83 Biswa = 0.010413595 Square Kilometer
84 0.01053906 84 Biswa = 0.01053906 Square Kilometer
85 0.010664525 85 Biswa = 0.010664525 Square Kilometer
86 0.01078999 86 Biswa = 0.01078999 Square Kilometer
87 0.010915455 87 Biswa = 0.010915455 Square Kilometer
88 0.01104092 88 Biswa = 0.01104092 Square Kilometer
89 0.011166385 89 Biswa = 0.011166385 Square Kilometer
90 0.01129185 90 Biswa = 0.01129185 Square Kilometer
91 0.011417315 91 Biswa = 0.011417315 Square Kilometer
92 0.01154278 92 Biswa = 0.01154278 Square Kilometer
93 0.011668245 93 Biswa = 0.011668245 Square Kilometer
94 0.01179371 94 Biswa = 0.01179371 Square Kilometer
95 0.011919175 95 Biswa = 0.011919175 Square Kilometer
96 0.01204464 96 Biswa = 0.01204464 Square Kilometer
97 0.012170105 97 Biswa = 0.012170105 Square Kilometer
98 0.01229557 98 Biswa = 0.01229557 Square Kilometer
99 0.012421035 99 Biswa = 0.012421035 Square Kilometer
100 0.0125465 100 Biswa = 0.0125465 Square Kilometer
200 0.025093 200 Biswa = 0.025093 Square Kilometer
300 0.0376395 300 Biswa = 0.0376395 Square Kilometer
400 0.050186 400 Biswa = 0.050186 Square Kilometer
500 0.0627325 500 Biswa = 0.0627325 Square Kilometer
600 0.075279 600 Biswa = 0.075279 Square Kilometer
700 0.0878255 700 Biswa = 0.0878255 Square Kilometer
800 0.100372 800 Biswa = 0.100372 Square Kilometer
900 0.1129185 900 Biswa = 0.1129185 Square Kilometer
1000 0.125465 1000 Biswa = 0.125465 Square Kilometer
2000 0.25093 2000 Biswa = 0.25093 Square Kilometer
3000 0.376395 3000 Biswa = 0.376395 Square Kilometer
4000 0.50186 4000 Biswa = 0.50186 Square Kilometer
5000 0.627325 5000 Biswa = 0.627325 Square Kilometer
6000 0.75279 6000 Biswa = 0.75279 Square Kilometer
7000 0.878255 7000 Biswa = 0.878255 Square Kilometer
8000 1.00372 8000 Biswa = 1.00372 Square Kilometer
9000 1.129185 9000 Biswa = 1.129185 Square Kilometer
10000 1.25465 10000 Biswa = 1.25465 Square Kilometer
Biswa is a land measurement unit, It is mainly used in rural area of India. 1 Biswa is equal to 150 Gaj. Biswa is medium area measurement unit.
Square Kilometer is a multiple of the square meter (sq mt), the SI unit of area or surface area. The abbreviation for Square Kilometer is "km2". 1 Square Kilometer is approximately equal to 1000000 square meters (sq mt) or 100 Hectare (ha).
The value in Square Kilometer is equal to the value of Biswa multiplied by 0.000125465.
Square Kilometer = Biswa * 0.000125465;
1 Biswa is equal to 0.000125465 Square Kilometer.
1 Biswa = 0.000125465 Square Kilometer.
• biswa to sq km
• 1 biswa = square kilometer
• biswa into square kilometer
• biswas to square kilometers
• convert biswa to square kilometer
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→ | 3,126 | 8,335 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2024-38 | latest | en | 0.560725 |
https://www.netlib.org/lapack/explore-html/d0/d50/group__complex16_o_t_h_e_rauxiliary_gac02e898b96584c2453f8b0f698259ff6.html | 1,695,455,155,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506480.35/warc/CC-MAIN-20230923062631-20230923092631-00092.warc.gz | 1,016,358,614 | 6,562 | LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlahrd()
subroutine zlahrd ( integer N, integer K, integer NB, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( nb ) TAU, complex*16, dimension( ldt, nb ) T, integer LDT, complex*16, dimension( ldy, nb ) Y, integer LDY )
ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
Purpose:
This routine is deprecated and has been replaced by routine ZLAHR2.
ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
matrix A so that elements below the k-th subdiagonal are zero. The
reduction is performed by a unitary similarity transformation
Q**H * A * Q. The routine returns the matrices V and T which determine
Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
Parameters
[in] N N is INTEGER The order of the matrix A. [in] K K is INTEGER The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. [in] NB NB is INTEGER The number of columns to be reduced. [in,out] A A is COMPLEX*16 array, dimension (LDA,N-K+1) On entry, the n-by-(n-k+1) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details. [in] LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). [out] TAU TAU is COMPLEX*16 array, dimension (NB) The scalar factors of the elementary reflectors. See Further Details. [out] T T is COMPLEX*16 array, dimension (LDT,NB) The upper triangular matrix T. [in] LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. [out] Y Y is COMPLEX*16 array, dimension (LDY,NB) The n-by-nb matrix Y. [in] LDY LDY is INTEGER The leading dimension of the array Y. LDY >= max(1,N).
Further Details:
The matrix Q is represented as a product of nb elementary reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
A(i+k+1:n,i), and tau in TAU(i).
The elements of the vectors v together form the (n-k+1)-by-nb matrix
V which is needed, with T and Y, to apply the transformation to the
unreduced part of the matrix, using an update of the form:
A := (I - V*T*V**H) * (A - Y*V**H).
The contents of A on exit are illustrated by the following example
with n = 7, k = 3 and nb = 2:
( a h a a a )
( a h a a a )
( a h a a a )
( h h a a a )
( v1 h a a a )
( v1 v2 a a a )
( v1 v2 a a a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
Definition at line 166 of file zlahrd.f.
167*
168* -- LAPACK auxiliary routine --
169* -- LAPACK is a software package provided by Univ. of Tennessee, --
170* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172* .. Scalar Arguments ..
173 INTEGER K, LDA, LDT, LDY, N, NB
174* ..
175* .. Array Arguments ..
176 COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ),
177 \$ Y( LDY, NB )
178* ..
179*
180* =====================================================================
181*
182* .. Parameters ..
183 COMPLEX*16 ZERO, ONE
184 parameter( zero = ( 0.0d+0, 0.0d+0 ),
185 \$ one = ( 1.0d+0, 0.0d+0 ) )
186* ..
187* .. Local Scalars ..
188 INTEGER I
189 COMPLEX*16 EI
190* ..
191* .. External Subroutines ..
192 EXTERNAL zaxpy, zcopy, zgemv, zlacgv, zlarfg, zscal,
193 \$ ztrmv
194* ..
195* .. Intrinsic Functions ..
196 INTRINSIC min
197* ..
198* .. Executable Statements ..
199*
200* Quick return if possible
201*
202 IF( n.LE.1 )
203 \$ RETURN
204*
205 DO 10 i = 1, nb
206 IF( i.GT.1 ) THEN
207*
208* Update A(1:n,i)
209*
210* Compute i-th column of A - Y * V**H
211*
212 CALL zlacgv( i-1, a( k+i-1, 1 ), lda )
213 CALL zgemv( 'No transpose', n, i-1, -one, y, ldy,
214 \$ a( k+i-1, 1 ), lda, one, a( 1, i ), 1 )
215 CALL zlacgv( i-1, a( k+i-1, 1 ), lda )
216*
217* Apply I - V * T**H * V**H to this column (call it b) from the
218* left, using the last column of T as workspace
219*
220* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows)
221* ( V2 ) ( b2 )
222*
223* where V1 is unit lower triangular
224*
225* w := V1**H * b1
226*
227 CALL zcopy( i-1, a( k+1, i ), 1, t( 1, nb ), 1 )
228 CALL ztrmv( 'Lower', 'Conjugate transpose', 'Unit', i-1,
229 \$ a( k+1, 1 ), lda, t( 1, nb ), 1 )
230*
231* w := w + V2**H *b2
232*
233 CALL zgemv( 'Conjugate transpose', n-k-i+1, i-1, one,
234 \$ a( k+i, 1 ), lda, a( k+i, i ), 1, one,
235 \$ t( 1, nb ), 1 )
236*
237* w := T**H *w
238*
239 CALL ztrmv( 'Upper', 'Conjugate transpose', 'Non-unit', i-1,
240 \$ t, ldt, t( 1, nb ), 1 )
241*
242* b2 := b2 - V2*w
243*
244 CALL zgemv( 'No transpose', n-k-i+1, i-1, -one, a( k+i, 1 ),
245 \$ lda, t( 1, nb ), 1, one, a( k+i, i ), 1 )
246*
247* b1 := b1 - V1*w
248*
249 CALL ztrmv( 'Lower', 'No transpose', 'Unit', i-1,
250 \$ a( k+1, 1 ), lda, t( 1, nb ), 1 )
251 CALL zaxpy( i-1, -one, t( 1, nb ), 1, a( k+1, i ), 1 )
252*
253 a( k+i-1, i-1 ) = ei
254 END IF
255*
256* Generate the elementary reflector H(i) to annihilate
257* A(k+i+1:n,i)
258*
259 ei = a( k+i, i )
260 CALL zlarfg( n-k-i+1, ei, a( min( k+i+1, n ), i ), 1,
261 \$ tau( i ) )
262 a( k+i, i ) = one
263*
264* Compute Y(1:n,i)
265*
266 CALL zgemv( 'No transpose', n, n-k-i+1, one, a( 1, i+1 ), lda,
267 \$ a( k+i, i ), 1, zero, y( 1, i ), 1 )
268 CALL zgemv( 'Conjugate transpose', n-k-i+1, i-1, one,
269 \$ a( k+i, 1 ), lda, a( k+i, i ), 1, zero, t( 1, i ),
270 \$ 1 )
271 CALL zgemv( 'No transpose', n, i-1, -one, y, ldy, t( 1, i ), 1,
272 \$ one, y( 1, i ), 1 )
273 CALL zscal( n, tau( i ), y( 1, i ), 1 )
274*
275* Compute T(1:i,i)
276*
277 CALL zscal( i-1, -tau( i ), t( 1, i ), 1 )
278 CALL ztrmv( 'Upper', 'No transpose', 'Non-unit', i-1, t, ldt,
279 \$ t( 1, i ), 1 )
280 t( i, i ) = tau( i )
281*
282 10 CONTINUE
283 a( k+nb, nb ) = ei
284*
285 RETURN
286*
287* End of ZLAHRD
288*
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
subroutine zlarfg(N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).
Definition: zlarfg.f:106
Here is the call graph for this function: | 2,534 | 7,050 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2023-40 | latest | en | 0.775975 |
https://namibiahub.com/interest-rate-calculations-at-iob/ | 1,716,661,820,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058830.51/warc/CC-MAIN-20240525161720-20240525191720-00566.warc.gz | 371,027,128 | 11,904 | # INTEREST RATE CALCULATIONS at IOB
## INTEREST RATE CALCULATIONS at IOB
What is INTEREST RATE CALCULATIONS?
The interest rate for a given amount on simple interest can be calculated by the following formula, Interest Rate = (Simple Interest × 100)/(Principal × Time) The interest rate for a given amount on compound interest can be calculated by the following formula, Compound Interest Rate = P (1+i) t – P.
# 2022 Intakes in Namibia [Universities, Colleges, VTC Intake]
Overview
Interest rates are one of the most important aspects of the American economic system. They influence the cost of borrowing, the return on savings, and are an important component of the total return of many investments. Moreover, certain interest rates provide insight into future economic and financial market activity.
Frequently Asked Questions
What is interest rate rate?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).
How do interest calculations work?
Divide your interest rate by the number of payments you’ll make that year. If you have a 6 percent interest rate and you make monthly payments, you would divide 0.06 by 12 to get 0.005. Multiply that number by your remaining loan balance to find out how much you’ll pay in interest that month.
What is the difference between interest and interest rate?
When you put your money in a savings account, interest is the return you receive on your savings from the bank. Interest rates indicate this cost or return as a percentage of the amount you are borrowing or lending (since you are “lending” your savings to the bank).
What are the types of interest rate?
There are essentially three main types of interest rates: the nominal interest rate, the effective rate, and the real interest rate. The nominal interest of an investment or loan is simply the stated rate on which interest payments are calculated.
What is rate of interest in math?
How much is paid for the use of money, as a percent. Example: Alex invests \$1000 at a 6% yearly interest rate, and so receives \$60 in interest after a year. Because \$1000 × 6% = \$60.
What is the formula of rate?
We can solve these problems using proportions and cross products. However, it’s easier to use a handy formula: rate equals distance divided by time: r = d/t.
How do interest rates work?
In the case of money you own, such as a savings account, interest is the amount you earn when you let someone else use or hold your funds. For example, if you borrow \$5,000 at a simple interest rate of 3% for five years, you’ll pay a total of \$750 in interest. The formula for simple interest is A = P (1 + rt).
Is a 2.75 interest rate good?
Yes, 2.875 percent is an excellent mortgage rate. It’s just a fraction of a percentage point higher than the lowest–ever recorded mortgage rate on a 30-year fixed-rate loan.
Is a 3.5 interest rate good?
That said, yes, 3.5% is a good interest rate for most car loan borrowers. In general, people with average to above-average credit scores can find interest rates from 3% to 4.5% on 36-month car loans.
Is high interest rate good?
Bottom line: A rate increase or decrease is neither good nor bad. It’s more like an indication of the overall U.S. economy. Instead of panicking when it changes, focus on fulfilling your long-term saving and debt payoff goals one at a time.
What happens when interest rates fall?
Lowering rates makes borrowing money cheaper. This encourages consumer and business spending and investment, and can boost asset prices. Lowering rates, however, can also lead to problems such as inflation and liquidity traps, which undermine the effectiveness of low rates.
Do interest rates matter?
One way that interest rates matter is they influence borrowing costs. If interest rates are lower, that will encourage more people to take out a mortgage and purchase a house, purchase an automobile, or take out a loan for home improvement, those kinds of things.
Is 2.99 a good car loan rate?
If you’re buying a new car at an interest rate of 2.9% APR, you may be getting a bad deal. However, whether or not this is the best rate possible will depend on factors like market conditions, your credit background, and what type of manufacturer car incentives there are at a given point in time on the car you want.
Will interest rates go up in 2022?
Most experts expect mortgage rates to continue rising throughout 2022, so the window to lock in a lower rate could be closing. If you’re looking to buy a home, you might also want to lock a rate sooner rather than later.
What is a good interest rate for a savings account?
The best savings account interest rates are around 0.50%. At a brick-and-mortar bank, you’ll often find savings rates closer to the national average, which is currently 0.07%. | 1,093 | 4,946 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-22 | latest | en | 0.958373 |
http://en.kakprosto.ru/how-127160-how-to-define-the-work-in-an-isothermal-process | 1,487,704,187,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170823.55/warc/CC-MAIN-20170219104610-00068-ip-10-171-10-108.ec2.internal.warc.gz | 78,770,985 | 14,344 | You will need
• - sealed container with a piston;
• - scales;
• thermometer;
• - the range.
Instruction
1
Calculate work of gas at a constant temperature. This will determine which gas performs work, and calculate its molar mass. Using the periodic table to find molecular mass, which is numerically equal to molar mass, measured in g/mol.
2
Find the mass of gas. To do this, vent the air from the sealed container and weigh it on the scale. After that extract the gas, which is determined, and again weigh the container. The difference between the masses of the empty and filled vessel and is equal to the mass of gas. Measure it in grams.
3
Measure with a thermometer the temperature of the gas. In isothermal process it will be permanent. If the measurement is performed at room temperature, it is sufficient to measure the temperature of the surrounding air. Measurements are produced in Kelvins. For this, the temperature measured in degrees Celsius, add 273 to the number.
4
Determine the initial and final gas volume in operation. To do this, take a vessel with a movable piston, and computing the level of his ascent, calculate the primary and secondary volume of geometric methods. To do this, use the formula for volume of a cylinder V=π•R2•h, where π≈3,14, R is the radius of the cylinder, h its height.
5
Calculate work of gas in an isothermal process. To do this, divide the mass of gas m its molar mass M. Polecany multiply the result by the universal gas constant R=8.31 and the temperature T in Kelvin. The result multiply by the natural logarithm of the ratio of final and initial volumes V2 and V1, A = m/M•R•T•ln(V2/V1).
6
In the case where the known quantity of heat Q, which received the body in an isothermal process, use the second law of thermodynamics Q = ∆U + A. Where A is the working gas, ΔU is the change in its internal energy. Since the change in internal energy depends on temperature, and at isothermal process remains constant, then ΔU=0. In this case, the working gas is equal to the heat transferred to it Q = A. | 481 | 2,048 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2017-09 | latest | en | 0.917308 |
https://mail.openjdk.java.net/pipermail/hotspot-runtime-dev/2016-August/020848.html | 1,653,687,045,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00760.warc.gz | 424,771,688 | 3,466 | # RFR (XS) 8161280 - assert failed: reference count underflow for symbol
Ioi Lam ioi.lam at oracle.com
Fri Aug 26 13:34:01 UTC 2016
```
On 8/25/16 10:37 AM, Kim Barrett wrote:
>> On Aug 25, 2016, at 4:26 AM, Ioi Lam <ioi.lam at oracle.com> wrote:
>>
>> On 8/24/16 11:52 PM, Kim Barrett wrote:
>>>> On Aug 24, 2016, at 8:46 PM, Ioi Lam <ioi.lam at oracle.com> wrote:
>>>>
>>>> Hi Kim,
>>>>
>>>> Thanks for pointing out the problems with the shift operators. I never knew that!
>>>>
>>>> Since I am shifting only by 16, can change the expressions to these?
>>>>
>>> Yes. I remembered that technique shortly after hitting send.
>>> Multiplying a signed value doesn't work (is UB) in the general case
>>> because of overflow, but we know the value ranges here are safe from
>>> that.
>>>
>>>> jshort(new_value / 0x10000)
>>> No, because under 2s complement arithmetic, arithmetic right shift of
>>> a negative number is not necessarily equivalent to division by the
>>> corresponding power of 2. [See, for example, "Arithmetic shifting
>>> considered harmful", Guy Steele, ACM SIGPLAN Notices, 11/1977.]
>>>
>>> Consider the 32bit value with all 1s in the upper 16 bits, and a
>>> non-zero value in the lower 16 bits. If division is truncate, which
>>> it is defined to be for C99/C++11 (*), that value / 0x10000 == 0,
>>> rather than the desired -1. Clear the low 16bits first and then
>>> divide, and I think it works for the case at hand, though I haven't
>>> proved it. But pragmatically we’re probably better off assuming
>>> right shift works as expected, though perhaps in a wrapper to
>>> help indicate we’ve actually thought about the issue.
>>>
>>> (*) For C89/C++98 the rounding of division involving negative operands
>>> is implementation defined, perhaps in part to allow the "optimization"
>>> of division by a power of 2 to arithmetic right shift.
>>>
>>>> Does C/C++ preserve signs when multiplying/dividing with a positive constant?
>> Hi Kim,
>>
>> I looked for the use of >> in our source code:
>>
>> globalDefinitions.hpp:
>> inline jint high(jlong value) { return jint(value >> 32); }
>>
>> sharedRuntimeTrans.cpp:
>> static double __ieee754_log(double x) {
>> double hfsq,f,s,z,R,w,t1,t2,dk;
>> int k,hx,i,j;
>> ...
>> k += (hx>>20)-1023;
>>
>> So maybe we already assume that >> "does the right thing" for us?
> Yes, that's what I expected to see.
>
>> -------------------------------
>>
>> Since I am doing something very specific (setting/extracting the top 16 bits of a jint), I am a bit hesitant to add routines for general shifting. globalDefinitions.hpp has these:
> The suggestion of using a wrapper was a "perhaps", and not really
> intended for you to deal with while addressing the problem at hand.
> Sorry I was confusing about that.
>
> If we do something along that line (as a separate project), I suggest
> we keep with the names we've already got for similar operations,
> e.g. use java_shift_{left,right} to be consistent with java_add and
> friends.
Hi Kim,
Thanks for the clarification.
My RBT tests passed, so I will check in the code as is in my last webrev
using the >> and << operators. I'll leave the general problem of
java_shift_left/right as a future improvement.
Thanks
- Ioi
>> inline int extract_low_short_from_int(jint x) {
>> return x & 0xffff;
>> }
>> inline int extract_high_short_from_int(jint x) {
>> return (x >> 16) & 0xffff;
>> }
>> inline int build_int_from_shorts( jushort low, jushort high ) {
>> return ((int)((unsigned int)high << 16) | (unsigned int)low);
>> }
>>
>> I am thinking of adding:
>>
>> inline int extract_signed_high_short_from_int(jint x) {
>> if (x >= 0) {
>> return (x >> 16) & 0xffff;
>> } else {
>> return int((unsigned int)x >> 16) | 0xffff0000);
>> }
>> }
>>
>> inline int build_int_from_shorts(jshort low, jshort high) {
>> return build_int_from_shorts(jushort(low) & 0xffff, jushort(high) & 0xffff);
>> }
>>
>> What do you think?
>> - Ioi
>
``` | 1,096 | 3,995 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2022-21 | latest | en | 0.911536 |
https://zbmath.org/?q=an:1131.76012 | 1,696,458,392,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511424.48/warc/CC-MAIN-20231004220037-20231005010037-00169.warc.gz | 1,208,263,697 | 14,046 | ## Large time existence for 3D water waves and asymptotics.(English)Zbl 1131.76012
Summary: We rigorously justify in three dimensions the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a nondimensionalized version of water wave equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep water, from small to large surface and bottom variations, and from fully to weakly transverse waves.
The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.
### MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 35Q35 PDEs in connection with fluid mechanics
### Keywords:
asymptotic models; well-posedness; energy bounds
Full Text:
### References:
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Notes Math., vol. 503, 426–437 (1976) [42] Paumond, L.: A rigorous link between KP and a Benney-Luke equation. Differ. Integral Equ. 16, 1039–1064 (2003) · Zbl 1056.76014 [43] Schneider, G., Wayne, C.E.: The long-wave limit for the water wave problem. I: The case of zero surface tension. Commun. Pure Appl. Math. 53, 1475–1535 (2000) · Zbl 1034.76011 [44] Serre, F.: Contribution à l’étude des écoulements permanents et variables dans les canaux. La Houille Blanche 3, 374–388 (1953) [45] Shatah, J., Zeng, C.: Geometry and a priori estimates for free boundary problems of the Euler’s equation. Preprint (http://arxiv.org/abs/math.AP/0608428), Comm. Pure Appl. Math. (to appear) · Zbl 1174.76001 [46] Su, C.-H., Gardner, C.S.: Korteweg–de Vries equation and generalizations. III: Derivation of the Korteweg–de Vries equation and Burgers’ equation. J. Math. Phys. 10, 536–539 (1969) · Zbl 0283.35020 [47] Wright, J.D.: Corrections to the KdV approximation for water waves. SIAM J. Math. Anal. 37, 1161–1206 (2005) · Zbl 1093.76010 [48] Wu, S.: Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130, 39–72 (1997) · Zbl 0892.76009 [49] Wu, S.: Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 12, 445–495 (1999) · Zbl 0921.76017 [50] Yosihara, H.: Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. Res. Inst. Math. Sci. 18, 49–96 (1982) · Zbl 0493.76018 [51] Yosihara, H.: Capillary-gravity waves for an incompressible ideal fluid. J. Math. Kyoto Univ. 23, 649–694 (1983) · Zbl 0548.76018 [52] Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194 (1968)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 3,281 | 10,149 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2023-40 | latest | en | 0.846982 |
https://richardvigilantebooks.com/is-2-a-lucky-house-number/ | 1,709,323,618,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475701.61/warc/CC-MAIN-20240301193300-20240301223300-00694.warc.gz | 474,929,123 | 10,619 | # Is 2 a lucky house number?
## Is 2 a lucky house number?
Is number 2 lucky in Feng Shui? The number 2 represents balance, as in yin and yang. It symbolises relationships. It is an auspicious number in Chinese culture, as they believe that ‘good things come in pairs’.
For example, if you live at 724 Main Street, you’ll take your address number (“724”) and add the digits together:
1. 7 + 2 + 4 = 13. Then, if you get a double-digit number as a result, add again:
2. 1 + 3 = 4. Your house number is 4!
3. 1 – A, J, S.
4. 2 – B, K, T.
5. 3 – C, L, U.
6. 4 – D, M, V.
7. 5 – E, N, W.
8. 6 – F, O, X.
### What Does a number 2 house mean in numerology?
While a 1-House is great for individuation, a 2-House has a dualistic nature and is perfect for partnerships. The energy of harmony and a yinyang balance is the predominant energy of the number 2. For a single person living in a 2-house, the home will naturally attract a partner for the occupant.
How do I find out my feng shui house number?
If your birth year is 1989 and you identify as female:
1. Add all the digits of your year: 1 + 9 + 8 + 9 = 27.
2. Reduce to a single digit: 2 + 7 = 9.
3. For females, add 4 to that number: 9 + 4 = 13.
4. Reduce to a single digit: 1 + 3 = 4.
5. Your feng shui kua number is 4.
#### Is 5 a good number for a house?
A house number that totals to 5 is great for those looking for immediate financial gains. Investors go for this number as this brings in best possible returns. It is the right fit for interior decorators who are always looking for something new and have to design new trends every season.
How did Kensington Olympia railway station get its name?
The station’s name is drawn from its location in Kensington and the adjacent Olympia exhibition centre. The station was originally opened in 1844 by the West London Railway but closed shortly afterwards. It reopened in 1862 and began catering for Great Western services the following year.
## Where is the London Overground at Kensington Olympia?
London Overground Class 378 at Kensington Olympia. The station is on the West London line of the London Overground network, which is signed by Transport for London as the “Willesden Junction – Clapham Junction” line. The line lies entirely in zone 2, and can be used to bypass central London.
What is the name of the tube station in Kensington?
On London Underground and London Overground maps, station signage and the London Rail & Tube Services map, it is labelled Kensington (Olympia). On the automated announcements and the dot matrix indicators on District line trains, the station is shown as simply Olympia. | 683 | 2,631 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-10 | latest | en | 0.918188 |
https://numberworld.info/3064546097 | 1,624,549,659,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488556133.92/warc/CC-MAIN-20210624141035-20210624171035-00318.warc.gz | 391,171,641 | 3,882 | # Number 3064546097
### Properties of number 3064546097
Cross Sum:
Factorization:
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
b6a94331
Base 32:
2raigph
sin(3064546097)
-0.87789094737821
cos(3064546097)
-0.4788606107328
tan(3064546097)
1.8332912077165
ln(3064546097)
21.843165303035
lg(3064546097)
9.4863661584087
sqrt(3064546097)
55358.34261428
Square(3064546097)
9.3914427806379E+18
### Number Look Up
Look Up
3064546097 which is pronounced (three billion sixty-four million five hundred forty-six thousand ninety-seven) is a very unique number. The cross sum of 3064546097 is 44. If you factorisate the number 3064546097 you will get these result 251 * 12209347. The figure 3064546097 has 4 divisors ( 1, 251, 12209347, 3064546097 ) whith a sum of 3076755696. The number 3064546097 is not a prime number. 3064546097 is not a fibonacci number. 3064546097 is not a Bell Number. The number 3064546097 is not a Catalan Number. The convertion of 3064546097 to base 2 (Binary) is 10110110101010010100001100110001. The convertion of 3064546097 to base 3 (Ternary) is 21220120111001221022. The convertion of 3064546097 to base 4 (Quaternary) is 2312222110030301. The convertion of 3064546097 to base 5 (Quintal) is 22234010433342. The convertion of 3064546097 to base 8 (Octal) is 26652241461. The convertion of 3064546097 to base 16 (Hexadecimal) is b6a94331. The convertion of 3064546097 to base 32 is 2raigph. The sine of 3064546097 is -0.87789094737821. The cosine of the figure 3064546097 is -0.4788606107328. The tangent of the number 3064546097 is 1.8332912077165. The root of 3064546097 is 55358.34261428.
If you square 3064546097 you will get the following result 9.3914427806379E+18. The natural logarithm of 3064546097 is 21.843165303035 and the decimal logarithm is 9.4863661584087. I hope that you now know that 3064546097 is amazing figure! | 705 | 2,001 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2021-25 | latest | en | 0.648255 |
http://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.172328.html | 1,368,959,099,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368697380733/warc/CC-MAIN-20130516094300-00057-ip-10-60-113-184.ec2.internal.warc.gz | 320,212,299 | 4,493 | # SOLUTION: Write equations in slope-intercept form for two lines that contain (-1, -5).
Algebra -> Algebra -> Length-and-distance -> SOLUTION: Write equations in slope-intercept form for two lines that contain (-1, -5). Log On
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Geometry: Length, distance, coordinates, metric length Solvers Lessons Answers archive Quiz In Depth
Click here to see ALL problems on Length-and-distance Question 172328This question is from textbook Geometry : Write equations in slope-intercept form for two lines that contain (-1, -5). This question is from textbook Geometry Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!x=-1 could be one line another line could contain the origin (0,0) so slope would be -5-0/-1-0=5 y-0=5(x-0 : y=5x+0 | 233 | 951 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2013-20 | latest | en | 0.855597 |
https://jp.mathworks.com/matlabcentral/answers/428912-plotting-trajectories-for-each-time-step | 1,610,822,853,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703506832.21/warc/CC-MAIN-20210116165621-20210116195621-00032.warc.gz | 409,249,563 | 24,590 | # Plotting trajectories for each time step
36 ビュー (過去 30 日間)
Hari krishnan 2018 年 11 月 9 日
コメント済み: Hari krishnan 2018 年 11 月 9 日
I have the trajectory of an object moving in a plane with the time of detection, X and Y coordinates of the object. I am able to plot the coordinates and the final trajectory of the object as shown in the figure. What should i do, if i need to see each step in the movement trajectory of the object rather than the final trajectory (like sort of an animation)? The mat file is attached with this, the first column corresponds to the time, second and third column corresponds to X and Y coordinates respectively. Any help to solve this will be appreciated.
time_of_detections = finaL_plot_matrix_cell{1,4}(2:end,1);
X_coordinate_ant13 = finaL_plot_matrix_cell{1,4}(2:end,2);
Y_coordinate_ant13 = finaL_plot_matrix_cell{1,4}(2:end,3);
plot(X_coordinate_ant13,Y_coordinate_ant13,'r');
サインインしてコメントする。
### 採用された回答
KSSV 2018 年 11 月 9 日
t = data(:,1) ;
x = data(:,2) ;
y = data(:,3) ;
idx = t>=220.20 ;
t = t(idx) ;
x = x(idx) ;
y = y(idx) ;
h = plot3(t(1),x(1),y(1)) ;
axis([min(t) max(t) min(x) max(x) min(y) max(y)])
for i = 1:length(t)
set(h,'Xdata',t(1:i),'Ydata',x(1:i),'Zdata',y(1:i)) ;
drawnow
end
#### 3 件のコメント
Hari krishnan 2018 年 11 月 9 日
@KSSV thank you very much, this is what exactly was looking for. I would like to ask one more question. If i want to search for a specific time (say 220.20) and just to start plotting trajectories from that specific time, is there a way to proceed?
KSSV 2018 年 11 月 9 日
Hari krishnan 2018 年 11 月 9 日
Thank you very much.
サインインしてコメントする。
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Translated by | 547 | 1,758 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-04 | latest | en | 0.433966 |
https://mathpoint.net/mathproblem/least-common-denominator/easy-steps-to-learn-algebra.html | 1,611,515,796,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703550617.50/warc/CC-MAIN-20210124173052-20210124203052-00450.warc.gz | 441,503,295 | 12,944 | Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
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Equ. #7:
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Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
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Solve for:
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easy steps to learn algebra
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Author Message
monkjxds
Registered: 14.08.2004
From: Pennsylvania
Posted: Sunday 19th of Aug 18:44 Hi math lovers , I heard that there are various programs that can help with us studying ,like a tutor substitute. Is this really true? Is there a program that can aid me with math? I have never tried one until now, but they shouldn't be hard to use I suppose . If anyone tried such a program, I would really appreciate some more detail about it. I'm in Algebra 1 now, so I've been studying things like easy steps to learn algebra and it's not easy at all.
IlbendF
Registered: 11.03.2004
From: Netherlands
Posted: Monday 20th of Aug 08:12 You can find many links on the internet if you google the keyword easy steps to learn algebra. Most of the content is however designed for the people who already have some know how about this subject. If you are a complete novice, you should use Algebrator. Is it easy to understand and very useful too.
Registered: 10.07.2002
From: NW AR, USA
Posted: Wednesday 22nd of Aug 09:04 I agree. Algebrator not only gets your homework done faster, it actually improves your understanding of the subject by providing very useful information on how to solve similar problems . It is a very popular product among students so you should try it out.
Gog
Registered: 07.11.2001
From: Austin, TX
Posted: Wednesday 22nd of Aug 17:45 Algebrator is the program that I have used through several math classes - Pre Algebra, Pre Algebra and Algebra 2. It is a really a great piece of algebra software. I remember of going through problems with solving inequalities, sum of cubes and graphing inequalities. I would simply type in a problem homework, click on Solve – and step by step solution to my math homework. I highly recommend the program. | 683 | 2,704 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2021-04 | latest | en | 0.917246 |
http://mc.flibnet.org/UnrealWiki/semisolid.html | 1,638,480,974,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362297.22/warc/CC-MAIN-20211202205828-20211202235828-00258.warc.gz | 49,352,426 | 5,149 | # Semisolid
Semisolid brushes are a type of additive brush. They are coloured pink in UnrealEd. They can only be additive, never subtractive.
They don't cut up the BSP so they can't cause BSP errors in solid geometry but they have problems of their own.
There are two methods of inserting a semi solid brush into a map:
• With the red builder brush molded into shape, use the Add Special button
• Any brush can be converted into a semisolid by :
1. Select the brush
2. Do Brush Context Menu → Solidity → Semisolid. The brush turns pink (using default colors), indicating it is a semisolid.
## Usage
Semisolids are useful for decorative geometry, usually things that the player probably won't touch, such as:
• beams
• light fixtures on walls
• pillars
Some topics that mention using semisolids:
## Technical
Semisolids dont cut up the BSP world; they cut up only themselves. They are good for keeping BSP node counts low. Low node counts make a map run faster. Since semis don't cut up the BSP world, they cannot cause [BSP error]?s such as HOM or cratering.
### Limitations
Semisolids can sometimes cause errors:
• missing polygons (you can see through it to the subtractive surface behind it)
• missing collision: the surfaces look right, but the player falls through them.
If you get these errors, change your map so the problem brush doesn't touch other semisolids, nonsolids or zone portals. If your semi geometry touches another semi, intersect the touching brushes to make them one brush.
### How Semisolids reduce node count
Here's a simple example of a situation where you'd use a semisolid & why it's good.
Let's say you want to round off a corner. You could:
1. make a specially-shaped brush and subract it, like the yellow crescent-type shape top left in the diagram. (this would be done by intersection? or with the 2D Shape Editor.)
2. subtract a small cube and add into it a quarter cylinder. (again, make the quarter-cylinder by intersection or use the tarquin brushbuilders.)
3. same as above, but add the cylinder as a semisolid brush.
Methods one and two give the same result. Indeed, the simplest way of doing method 1 is to do method 2, re-make the cube and de-intersect to make the crescent shape. Both of these will produce cuts like the bottom left picture in the BSP. These diagonal cuts (in green) will probably extend into the rest of the area you're working in and maybe further. Diagonal cuts like these that don't lie on whole grid points are a prime cause of BSP holes, and raise the map's node count.
The picture in the bottom right shows what happens with method 3. The original cube isn't filled in: the area shaded in grey is still part of the map. You could walk into the curved wall and see it if you type ghost into the UT console. The engine sees the floor of that cube as a full square, just as if you hadn't added the semisolid. The curved walls (in pink) are placed in front of this, like a fake wall. The engine knows to block players and projectiles on this.
The net result is that the off-grid shapes are kept localised to a small portion of the BSP tree. The BSP at large is still based on cubes with integer points.
## Related Topics
Sudsyman73: so, if making semisolids is easy and doesn't tax the engine as much why would anybody ever use the add button? Should all of the pillars and statues and decorations and whatnot be in semisolid form?
inio: Semisolids are sorta equivalent to static meshes, only they don't get the on-card geometry caching and such. You can't use them to seal off zones (I don't think), and they create overdraw (because they don't cut the polygons they intersect). They're good for pillars and stairs and such. There's lots of semisolids in my CTF-Peach original UT map (availble here) for stars and such. There's still plenty of adds though.
Tarquin: Exactly. You still use adds for all sorts of neat CSG stuff. Also for things players walk on, since semisolids can sometimes be unreliable for this.
Sudsyman73: so use them for surfaces that players/bots will not walk on and pillars and things? What's CSG stuff?
Sobiwan: CSG is added or subtracted brushes that cut up the BSP world.
Sudsyman73: actually, inio, i think you can use semisolids to zone off areas. unless of course once again i have made some obvious mistake...
Tarquin: I'm pretty sure they can't.
inio: He might be right to some extent. If a node is completely contained within a semisolid, it gets put into zone 0, so I think there may be some zoning going on with semisolids.
Category Mapping | 1,068 | 4,568 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2021-49 | latest | en | 0.911677 |
https://www.scribd.com/presentation/70853936/Lecture-2-Relaxing-the-Assumptions-of-CLRM-0 | 1,566,668,214,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027321160.93/warc/CC-MAIN-20190824152236-20190824174236-00258.warc.gz | 977,817,550 | 71,901 | You are on page 1of 17
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)
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x
)
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)
3
i
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i
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if
_ =
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(
)
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(
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)
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i
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=
2
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2
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x
+
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x
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X X
x x
2
3 i
3
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2
3
2
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i
+
2
2
2
n
x
x
(
x x
)
2 i
3
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3
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var( ˆ ) =
2
2
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x
(1
r
)
x
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r
)
2
i
2,3
3
i
2,3
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r
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)
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2
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i
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2
2
i
0
120
100
80
60
40
20
0.8
Correlation
0.6
0.4
0.2
1.2
0
1
2
2
j
2
j
2
2
2
j
j
2
j
2
j
# CONFIDENCE INTERVALS AND T- STATISTICS
±1.96
se
(
)
VIF
k
k
k
k 0
t =
se
(
)
VIF
Due to low t-stats we can not reject our
Null Hypothesis
k
H
:
=
=
...
=
=
0
0
2
3
k
# H a: Not all slope coefficients are simultaneously zero
2
2
n k ESS
n
k
R
R /( k 1)
F =
=
=
2
2
k
1
11 R
(1
R
)/(
n
k
)
ue to high R square the F-value will be very high and rejection of Ho will be easy
X
1
i
2
/( k 2)
x x
,
,
x
...
x
i
2
3
k
2
) /( n k
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,
,
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i
2
3
k | 1,159 | 1,763 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2019-35 | latest | en | 0.375191 |
https://civilengineering.blog/2017/11/06/plane-truss/?shared=email&msg=fail | 1,576,443,218,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541310866.82/warc/CC-MAIN-20191215201305-20191215225305-00124.warc.gz | 315,177,716 | 32,910 | ## Truss
A truss is an articulated structure composed of straight members arranged and connected in such a way that they transmit primarily axial force. If all the members lie in one plane it is called a plane truss. A three-dimensional truss is called a space truss.
### PLANE TRUSS
The basic form of a truss is a triangle formed by three members joined together at their common ends forming three joints. Such a triangle is clearly rigid. Another two members connected to two of the joints with their far ends connected to form another joint forms a stable system of two triangles. If the whole structure is built up in this way it must be internally rigid. Such a truss if supported suitably will be stable.
For example,
The truss has to be supported in general by three reaction components, all of which are neither parallel nor concurrent. Such a truss is called a simple truss. Various combinations of basic triangular elements produce general truss structures shown in Fig. 3.1. These trusses are stable and statically determinate.
Several common types of trusses are shown in Fig. 3.2. Trusses given in Fig. 3.2a, b and c are roof trusses and are used up to 30 m span. The other type of trusses are commonly used in bridges.
#### GEOMETRIC STABILITY AND STATIC DETERMINACY OF TRUSSES
A truss which possesses just sufficient number of members or bars to maintain its stability and equilibrium under any system of forces applied at joints is called a statically determinate and stable truss.
A planner truss may be thought of as a structural device having j joints in a plane. The forces that act on the joint are the member forces, the external loads and the reactions. Since all the joints are in equilibrium, we can write two equilibrium equations, and for each joint. Thus, for the entire truss we can write 2j equations. The unknowns are the member forces and the reaction components. Therefore, if the structure is statically determinate, we can write the relation.
2j = m + r
where m = number of members
r = number of components.
The following general statements can be made concerning the relation between j, m and r.
2j < m + r. There are more unknowns than the number of equilibrium equations. The structure is statically indeterminate. The degree of indeterminacy is n = m + r – 2j. Only inspection can be used to study geometric instability. The truss may be redundant either internally or externally or both. To analyses statically indeterminate trusses we need additional relationships, such as compatibility of displacements.
2j = m + r. The structure is statically determinate and the unknowns can be obtained from 2 j equations. The degree of indeterminacy n=0 ). Apart from inspection there are several ways of detecting instability.
2j > m + r. There are not enough unknowns. The structure is a mechanism and always unstable.
In the light of the above statements consider the trusses in Fig. 3.3. The truss in Fig. 3.3a has six joints, eleven members and three reaction components; hence it is indeterminate by two degree. On inspection it is seen that the truss is stable but it has two additional diagonal members, one in each panel, that are redundant. The removal of these redundant members cause no instability to the truss. Thus, the truss is internally redundant by two degree. The truss in Fig. 3.3.b is stable but there is an additional roller support which is not necessary for its stability. Hence the truss is statically indeterminate by one degree and the indeterminacy is external.
The truss in Fig. 3.3c is unstable. From inspection as well as from a count of members it is clear that the truss is deficient and one diagonal member is necessary to make the truss rigid and stable. Consider the truss in Fig. 3.3d. It has more members than just required. But on inspection it is clear that the end panels are made over rigid by providing diagonal members both ways and the central panel is deficient thereby making the truss unstable. It may be noted that the truss is unstable due to improper distribution of members.
Save
Save
Save
Save
Save | 904 | 4,107 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2019-51 | latest | en | 0.952422 |
https://metanumbers.com/1027067 | 1,643,231,582,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304961.89/warc/CC-MAIN-20220126192506-20220126222506-00406.warc.gz | 449,394,667 | 7,345 | # 1027067 (number)
1,027,067 (one million twenty-seven thousand sixty-seven) is an odd seven-digits prime number following 1027066 and preceding 1027068. In scientific notation, it is written as 1.027067 × 106. The sum of its digits is 23. It has a total of 1 prime factor and 2 positive divisors. There are 1,027,066 positive integers (up to 1027067) that are relatively prime to 1027067.
## Basic properties
• Is Prime? Yes
• Number parity Odd
• Number length 7
• Sum of Digits 23
• Digital Root 5
## Name
Short name 1 million 27 thousand 67 one million twenty-seven thousand sixty-seven
## Notation
Scientific notation 1.027067 × 106 1.027067 × 106
## Prime Factorization of 1027067
Prime Factorization 1027067
Prime number
Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 1.02707e+06 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 13.8422 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 1,027,067 is 1027067. Since it has a total of 1 prime factor, 1,027,067 is a prime number.
## Divisors of 1027067
2 divisors
Even divisors 0 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 1.02707e+06 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 513534 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 1013.44 Returns the nth root of the product of n divisors H(n) 2 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 1,027,067 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 1,027,067) is 1,027,068, the average is 513,534.
## Other Arithmetic Functions (n = 1027067)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 1027066 Total number of positive integers not greater than n that are coprime to n λ(n) 1027066 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 80297 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 1,027,066 positive integers (less than 1,027,067) that are coprime with 1,027,067. And there are approximately 80,297 prime numbers less than or equal to 1,027,067.
## Divisibility of 1027067
m n mod m 2 3 4 5 6 7 8 9 1 2 3 2 5 6 3 5
1,027,067 is not divisible by any number less than or equal to 9.
## Classification of 1027067
• Arithmetic
• Prime
• Deficient
### Expressible via specific sums
• Polite
• Non-hypotenuse
• Prime Power
• Square Free
## Base conversion (1027067)
Base System Value
2 Binary 11111010101111111011
3 Ternary 1221011212112
4 Quaternary 3322233323
5 Quinary 230331232
6 Senary 34002535
8 Octal 3725773
10 Decimal 1027067
12 Duodecimal 41644b
20 Vigesimal 687d7
36 Base36 m0hn
## Basic calculations (n = 1027067)
### Multiplication
n×y
n×2 2054134 3081201 4108268 5135335
### Division
n÷y
n÷2 513534 342356 256767 205413
### Exponentiation
ny
n2 1054866622489 1083418697359909763 1112743591241350440555121 1142862222025480072929626460107
### Nth Root
y√n
2√n 1013.44 100.894 31.8346 15.9338
## 1027067 as geometric shapes
### Circle
Diameter 2.05413e+06 6.45325e+06 3.31396e+12
### Sphere
Volume 4.53821e+18 1.32558e+13 6.45325e+06
### Square
Length = n
Perimeter 4.10827e+06 1.05487e+12 1.45249e+06
### Cube
Length = n
Surface area 6.3292e+12 1.08342e+18 1.77893e+06
### Equilateral Triangle
Length = n
Perimeter 3.0812e+06 4.56771e+11 889466
### Triangular Pyramid
Length = n
Surface area 1.82708e+12 1.27682e+17 838597 | 1,353 | 3,985 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2022-05 | latest | en | 0.817805 |
https://www.math10.com/en/algebra/derivative-function.html | 1,720,792,863,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514404.71/warc/CC-MAIN-20240712125648-20240712155648-00314.warc.gz | 644,081,611 | 7,612 | First Derivative Formulas
y is a function y = y(x)
C = constant, the derivative(y') of a constant is 0
y = C => y' = 0
Example: y = 5, y' = 0
If y is a function of type y = xn the derivative formula is:
y = xn => y' = nxn-1
Example: y = x3 y' = 3x3-1 = 3x2
y = x-3 y' = -3x-4
From the upper formula we can say for derivative y' of a function y = x = x1 that:
if y = x then y'=1
y = f1(x) + f2(x) + f3(x) ...=>
y' = f'1(x) + f'2(x) + f'3(x) ...
This formula represents the derivative of a function that is sum of functions.
Example: If we have two functions f(x) = x2 + x + 1 and g(x) = x5 + 7 and y = f(x) + g(x) then y' = f'(x) + g'(x) =>
y' = (x2 + x + 1)' + (x5 + 7)' = 2x1 + 1 + 0 + 5x4 + 0 = 5x4 + 2x + 1
If a function is a multiple of two functions the derivate is given by:
y = f(x).g(x) => y' = f'(x)g(x) + f(x)g'(x)
If f(x) = C(C is a contstant), and y = f(x)g(x)
y = Cg(x) y'=C'.g(x) + C.g'(x) = 0 + C.g'(x) = C.g'(x)
y = Cf(x) => y' = C.f'(x)
There are examples of the following formulas in the task section.
y =
f(x) g(x)
y' =
f'(x)g(x) - f(x)g'(x) g2(x)
y = ln x => y' = 1/x
y = ex => y' = ex
y = sin x => y' = cos x
y = cos x => y' = -sin x
y = tan x => y' = 1/cos2x
y = cot x => y' = -1/sin2x
y = arcsin x => y' =
1 √1 - x⋅x
y = arccos x => y' =
-1 √1 - x⋅x
y = arctan x => y' =
1 1 + x2
y = arccot x => y' =
-1 1 + x2
When a function is a function of function: u = u(x)
y = f(u) => y' = f'(u).u'
Example: let's given y = sin(x2)
Here u = x2, f(u) = sin(u), the derivatives are f'(u) = cos(u), u' = 2x
y' = (sin(u))'⋅u' = cos(x2)⋅2x = 2⋅x⋅cos(x2)
Problems involving derivatives
1) f(x) = 10x + 4y, What is the first derivative f'(x) = ?
Solution: We can use the formula for the derivate of function that is the sum of functions
f(x) = f1(x) + f2(x), f1(x) = 10x, f2(x) = 4y for the function f2(x) = 4y, y is a constant because the argument of f2(x) is x so f'2(x) = (4y)' = 0. Therefore, the derivative function of f(x) is: f'(x) = 10 + 0 = 10.
2) Calculate the derivative of f(x) =
x10 4.15 + cosx
Solution: We have two functions h(x) = x10 and g(x) = 4.15 + cos x
the function f(x) is h(x) divided by g(x). h'(x) = 10x9 g'(x) = 0 - sin x = -sin x
f'(x) =
h'(x).g(x) - h(x).g'(x) (g(x))2
f'(x) =
10x9(4.15 + cos x) - x10(-sin x) (4.15 + cosx)2
=
x10sin x + 10(60 + cos x)x9 (60 + cosx)2
3) f(x) = ln(sinx). what is the derivative of the function f(x)?
Solution: To solve the task we have to use the last formula. As we can see f(x) is a function of function of function f(x) = h(g(x)) where h = ln, and g = sin x
f'(x) =
1 g(x)
g'(x) =
1 sin x
cos x =
cos x sin x
More about derivatives in the maths forum
Feedback Contact email: | 1,150 | 2,695 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2024-30 | latest | en | 0.70409 |
https://mocktestpro.in/mcq/mechanical-operations-mcqs-optimum-time-cycle/ | 1,686,152,153,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224653930.47/warc/CC-MAIN-20230607143116-20230607173116-00266.warc.gz | 448,789,420 | 22,990 | Engineering Questions with Answers - Multiple Choice Questions
# Mechanical Operations MCQ’s – Optimum Time Cycle
1 - Question
What does the following equation represents?
Q= K1 ND3
a) Flow of impellor
b) Discharge
c) Velocity
d) Density
Explanation: The quantity of flow is defined as the amount of fluid which moves axially or radially away from the impellor at the surface area of rotation.
2 - Question
What does the following equation represents?
P=QρH
a) Density
b) Discharge
c) Velocity
d) Power
Explanation: The power requirements cannot always be calculated for a system with great degree of reliability, thus the following equation can be used.
3 - Question
What does the below equation represent?
a) Schmidt number of mixing
b) Froude number of mixing
c) Reynold’s number of mixing
d) Dom number of mixing
Explanation: The following represents the Reynold’s number for mixing, where N is the impellor rotational speed and D is the impellor diameter.
4 - Question
What does the following represents?
a) Schmidt number of mixing
b) Froude number of mixing
c) Reynold’s number of mixing
d) Dom number of mixing
Explanation: The following represents the Froude number for mixing, where N is the impellor rotational speed and g is the gravitational constant 32.2 ft/sec2.
5 - Question
What does the below equation represent?
a) Schmidt number
b) Froude number
c) Reynold’s number
d) Power number
Explanation: The power number PO is used in most of the correlations to represent the relationship to system performance.
6 - Question
What does the following represents?
a) Entrainment
b) Flow rate
c) Discharge
d) Throttle
Explanation: From a propeller, the entrainment by the circular jet is given by the above equation, where X is the distance from impellor source not to exceed 100 jet diameters.
7 - Question
The maximum Q/p1/3 for a circular jet is at X= _________
a) 1.71D0
b) 2.5D0
c) 7D0
d) 8.5D0
Explanation: The maximum Q/p1/3 for a circular jet is at X=1.71D0 or in other word the optimum jet origin diameter is 1/17.1 of the distance desired for effective entrainment.
8 - Question
What does the below equation represent?
b) Gravity
c) Centrifugal force
d) Exhaust force
Explanation: The above equation represents the velocity gradient, where P is the power dissipated and other terms are dynamic viscosity and volume.
9 - Question
As the velocity gradient increases, the shear force _______
a) Decreases
b) Increases
c) Remains same
d) Constant
Explanation: We know that the rate of particulate collision the rate is directly proportional to the velocity gradient, G must be sufficient to furnish desired rate.
10 - Question
Calculate G, if two mercury particles are moving at 2 m/sec to each other at a distance of 10 m?
a) 0.2
b) 5
c) 0.5
d) 2 | 710 | 2,796 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2023-23 | latest | en | 0.861316 |
https://www.puzzlesbrain.com/tag/riddles-and-puzzles/page/11/ | 1,718,710,709,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861752.43/warc/CC-MAIN-20240618105506-20240618135506-00046.warc.gz | 842,628,788 | 56,060 | Categories
## Trapped room doors dragon sun glass riddle
Trapped room doors dragon sun magnifying glass riddle You are trapped in a room. There are two doors. If you go in one door, a dragon is going to breath fire on you. If you go into the other door, there is a room made of magnifying glass. And the sun is reflecting off of […]
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## Fruit Crime Animal Vowel Riddle
Fruit Crime Animal Vowel Riddle This is a fruit. You cross off the first letter it is a crime. Cross of the second letter its an animal. Cross off the next two letters it is a vowel. What is it? Answer: Answer is Grape Grape – You cross off the first letter then Rape is […]
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## Why is daughter happy?
Why is daughter happy? Father goes to prison and the mother will have to sell her hotel, but their young daughter is happy. Why is this and what situation are they in? Answer:
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## Are you genius Solve this brainteaser
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## Which clock is odd one out
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## Can you find the hidden bird in the picture below?
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## How many brownies for friend brainteaser
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## What does Rob wish to win the fight?
What does Rob wish to win the fight? Rob and Bob are arch enemies. They decide to have a fight to the death one day when a fairy appears. The fairy says it will give them both one wish. Bob wishes, “I wish for twice whatever Rob asks for.” What can Rob ask for […]
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## Chemistry riddle who are the killers
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## Why cannot cat jump through window fun riddle
Why cannot cat jump through window? If a cat can jump 5 feet high, then why can’t it jump through a window which is 3 feet high? Answer: | 706 | 2,935 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-26 | latest | en | 0.947972 |
https://edbodmer.com/carrying-charges-effect-of-economic-life-and-degradation/ | 1,722,656,129,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640356078.1/warc/CC-MAIN-20240803025153-20240803055153-00588.warc.gz | 178,568,657 | 29,080 | # Degradation in Levelised Cost Calculation
.
.
.
.
Step 1: Compute Real Rate as (1-Nominal Rate)/(1+Inflation Rate) – 1
Step 2: Compute Real Rate with overall degradation effect:
This adjusted rate is applied to the PMT function and to the O&M function for overall degradation.
#### Step 3: Factor for O&M to increase O&M (Real rate with adjustment is higher):
Factor for Real O&M = PV(Real Rate Adjusted, Life,-1)/PV(Real Rate,Life,-1)
Real O&M = Initial Real O&M x Factor
.
#### Part 2: Adjustments to Nominal LCOE for Overall Output Degradation as with Solar Project
Lets start with the case of computing the carrying charge for the case where nominal levelized cost is computed. In this case the PMT formula should be adjusted in a similar manner as it is in the real case for inflation. Remember that you can conisder degradation as negative inflation. If degradation occurs, then you must recover more money in nominal terms the account for the reduction in output over time.
This is a bit more confusing. The O&M goes up because it should inflate and it goes up further because of degradation. So there are two adjustments to the O&M for nominal levelization. You compute a PV factor adjustment and use the real rate in the numerator and the nominal rate adjusted for degradation in the denominator. To begin the discussion, recall the inflation rate adjustment for O&M in the nominal case.
On another page I have explained how to make adjustments for inflation in operation and maintenance when computing the levelized cost on a nominal basis. The adjustment is necessary because the reported operating and maintenance is generally stated in current dollars or euros etc. — on a real basis. If you are computing the nominal LCOE and you have the real O&M expense, then you can increase the O&M Expense using the PV (not the NPV) formula in excel. You can think about the basic fact that if you use the PV formula with the life of the project, then the PV gives you a higher number when you have a lower discount rate.
Step 2: Apply the Adjusted Nominal Rate in the PMT function
Step 3: Adjust the Initial O&M.
You can use a factor as follows:
Nominal Case: Factor = PV(Real Rate, Life, -1)/PV(Nominal Rate, Life, -1)
This factor will be above 1.0 if the inflation rate is positive and the real rate is below the nominal rate.
Now to the degradation adjustment. To begin, you can compute the real O&M cost using the PV formula. You can do this in two steps.
O&M for Nominal = Current O&M x Adjustment Factor2
.
.
.
## Inclusion of Degradation in the Levelised Cost using adjustments to both Carrying Charges and O&M Costs
The formulas below evaluate levelised cost when the quantity of the units change. Different amount of units affects the weighting of the levelised price. For example, if the number of units is half of the units when the units start and if the price changes, then weighted average price changes. Without discounting, the screenshot below is 13.33. The price is not the average of 15.00 because you should give less weight to the price when there is less generation.
You should make changes to both nominal and real LCOE and you should make operating expense adjustments. The adjustments are represented by the following equations:
O&M Factor Nominal = PV(Real IRR,Life,-1)/PV(Adjusted Nominal IRR,life,-1)
O&M Factor Real = PV(Adjusted Real IRR,Life,-1)/PV(Real IRR,life,-1)
When you think about things, the levelised nominal cost is a silly number. Think about a hydro plant than may last 80 years. The nominal levelised cost is the flat value over 80 (with a minor adjustment for inflation in O&M expenses discussed below). With even a minor rate of inflation like 2%, the real value in 80 years is a very small percent of the value in the first year (divide by 1.02^80) — 4.9 times. It would be much better to compute the current value that, when inflated, gives you the target return. In simple terms this involves using a real cost of capital as described below.
## Degradation with for a Single Expense Rather than the Entire Project (Hydrogen Case)
As stated above, for an electrolyzer the degradation can be for the quantity of electricity purchased rather than for the entire project.
PV(Real, Life,-1)/PV(Nominal,Life,-1)
Adusted Nominal = (1+Nominal)/(1-Real) – 1 | 1,000 | 4,338 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2024-33 | latest | en | 0.894744 |
http://stackoverflow.com/questions/12722970/xnpv-calculation-in-c-sharp-or-vb-without-using-excel/12724398 | 1,419,600,311,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1419447549109.94/warc/CC-MAIN-20141224185909-00097-ip-10-231-17-201.ec2.internal.warc.gz | 90,587,836 | 16,263 | # XNPV calculation in C# or VB without using excel
Has anyone developed a financial function XNPV? I am looking for code that will calculate this value. I am not looking to call excel to calculate the value.
Any help would be great, thanks
-
I believe this is the correct implementation in c#:
``````public double XNPV(decimal[] receipts,DateTime[] dates, double dRate, DateTime issueDate, decimal cf, int x)
{
double sum;
for(int i =0;i<dates.Length;i++)
{
TimeSpan ts = dates[i].Subtract(issuedate);
sum +=receipts[i] / ((1 + dRate / cf) ^ ((ts.TotalDays / 360) * cf));
}
return sum;
}
``````
and this is the equivalent in VB:
``````Public Function XNPV(ByVal Receipts() As Decimal, ByVal Dates() As Date, ByVal dRate As Double, ByVal IssueDate As Date, ByVal CF As Decimal, ByVal x As Integer) As Double
Dim i As Integer
Dim sum As Double
For i = 0 To UBound(Dates)
sum = sum + Receipts(i) / ((1 + dRate / CF) ^ ((DateDiff / 360) * CF))
XNPV = sum
End Function
``````
-
I adapted the code above and included an example of how to call it. It should be easy to adapt to use a variable discount rate instead of .1
``````Public Function XNPV(ByVal Receipts() As Decimal, ByVal Dates() As Date, ByVal dRate As Double, ByVal StartDate As Date) As Double
Dim i As Integer = 0
Dim dXNPV As Double = 0
Dim dXRate As Double = 1 + dRate
Dim dDayOfCF As Long = 0
Dim dAdj As Double = 0
Dim dResult As Double = 0
For i = 0 To UBound(Dates)
dDayOfCF = (DateDiff(DateInterval.Day, StartDate, Dates(i)))
dXNPV = Receipts(i) / (dXRate ^ dAdj)
dResult += dXNPV
Next
XNPV = dResult
End Function
Private Sub SimpleButton2_Click(sender As System.Object, e As System.EventArgs) Handles SimpleButton2.Click
Dim tblReceipts(2) As Decimal
Dim tblDates(2) As DateTime
Dim dtStartDate As DateTime = "1/1/13"
Dim XNPVResult As Decimal = 0
tblReceipts(0) = -100000
tblReceipts(1) = 500000
tblReceipts(2) = 2000000
tblDates(0) = "1/1/13"
tblDates(1) = "1/7/13"
tblDates(2) = "1/1/15"
'xCF = 1 + DateDiff(DateInterval.Day, dtIssueDate, tblDates(2))
XNPVResult = XNPV(tblReceipts, tblDates, 0.1, dtStartDate)
MsgBox(XNPVResult)
End Sub
``````
- | 672 | 2,134 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2014-52 | latest | en | 0.606861 |
http://mathhelpforum.com/calculus/14987-limit-problem.html | 1,480,791,823,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541066.79/warc/CC-MAIN-20161202170901-00468-ip-10-31-129-80.ec2.internal.warc.gz | 176,620,729 | 9,713 | 1. ## a limit problem
lim (1-cos 2x) / 3x
x->0
i think the answer is 0, can someone explain how to solve this?
2. Originally Posted by viet
lim (1-cos 2x) / 3x
x->0
i think the answer is 0, can someone explain how to solve this?
Rewrite as,
(1-cos 2x) / (2x) * (2/3)
Now the first factor is zero because of the famous limit,
lim (x-->0) (1-cos 2x)/2x =0 | 136 | 360 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2016-50 | longest | en | 0.904984 |
https://www.freezingblue.com/flashcards/print_preview.cgi?cardsetID=227972 | 1,516,089,189,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886237.6/warc/CC-MAIN-20180116070444-20180116090444-00660.warc.gz | 914,374,416 | 3,798 | Home > Preview
The flashcards below were created by user wamplord on FreezingBlue Flashcards.
1. 1+0=
1
2. 1+1=
2
3. 1+2=
3
4. 1+3=
4
5. 1+4=
5
6. 1+5=
6
7. 1+6=
7
8. 1+7=
8
9. 1+8=
9
10. 1+9=
10
11. 1+10=
11
## Card Set Information
Author: wamplord ID: 227972 Filename: Simple Addition Updated: 2013-07-23 23:48:04 Tags: math addition Folders: Description: Beginner math Show Answers:
Home > Flashcards > Print Preview | 180 | 425 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2018-05 | longest | en | 0.673181 |
https://bartlesvilleschools.org/is-90-minutes-the-same-as-an-hour-and-a-half | 1,642,633,584,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301592.29/warc/CC-MAIN-20220119215632-20220120005632-00450.warc.gz | 178,464,992 | 12,675 | # Is 90 minutes the same as an hour and a half?
An hour is made up of 60 minutes. So, 90 minutes equals between one and two hours (2 x 60 = 120 minutes). It is precisely halfway between 1 and 12 hours, therefore 90 minutes is 1 and 12 hours (or less formally, 1 and a half hours).
## What is the ratio of 1 hour to minutes?
Divide the amount of minutes by 60 to convert from minutes to hours. 120 minutes, for example, equals 2 hours since 120/60 =2.
## How long is 180 minutes in an hour?
It may also be stated as: 180 minutes = 1 0.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 An estimated numerical conclusion would be: one hundred and eighty minutes equals about zero hours, or an hour equals approximately zero point three hundred and eighty minutes. A minute is a time or angle unit. It is the name of several different units of measurement for frequency of motion, including the standard minute defined by the rate at which a pendulum swings once around its bob. A second is the duration of a single rotation of a body, such as a planet or moon. It is equal to sixty minutes per day. The word "minute" comes from the Latin minimus, meaning "little." Thus, a minute is a small amount of time.
An hour is the length of time it takes for the earth to rotate on its axis, making only one complete revolution. Because day is used as the basic unit of measure in most countries, an hour is divided into 60 minues, which are in turn divided into 6 seconds. There are 24 hours in a day. If we divide this number by 60 we get one hour. So, one hour equals 60 minutes.
In mathematics and physics, an hourglass is a vessel with two bulbous ends, each filled with sand that slowly drains through an opening at the bottom. The amount of time that has elapsed since the last full hourglass was turned over is called an hour.
## How many hours and minutes does 90 minutes last?
One hour and thirty minutes is equivalent to ninety minutes. This is a simple way for you to keep track of time when you have several tasks to complete in a single hour window.
An easy way to remember this formula is that there are 60 minutes in an hour and 90 minutes make one hour. You can also think that there are \$90\$ minutes or that one hour consists of \$90\$ minutes.
You should know that there are actually 86,400 seconds in a day but since we use the clock to measure time it is better if you assume that there are 60 minutes per hour instead. That's why we say that an hour lasts for 90 minutes.
We can calculate how many hours something will take if we know how long it takes to do one task. For example, it will take you about an hour to write a book from start to finish so writing a book would take 90 minutes per hour or 2 hours 30 minutes per day. A week would then consist of two days of writing followed by one day of rest.
Writing a book is not a straight forward process and depending on what you want to publish your book may require some extra effort.
## Which is correct, 60 min or 1 HR?
[60 min/1 hour] = 1 is written mathematically as a value of 1. The opposite is also true: [1 hour/60 minutes] = 1 Divide the minutes by 60 to convert them to hours.
## Is 60 seconds the same as 1 minute?
A minute is made up of 60 seconds. In other terms, a second is one-hundredth of a minute. So, yes, a minute is exactly one thousand seconds long.
## What is 75 seconds when expressed in minutes and seconds?
One minute is equivalent to 6 x 101 seconds every second. One minute is equal to one second (60 seconds divided by one second). A second is made up of 0.0166666666667 minutes... Seconds to Minutes Conversion Table
SecondsMinutes
75 sec1.25 min
90 sec1.5 min
105 sec1.75 min
120 sec2 min
## What if a minute was 100 seconds?
As a result, if we changed one minute to 100 seconds and one hour to 100 minutes, there would be 8.64 hours in a day.
#### About Article Author
##### Carrie Simon
Carrie Simon has been an educator for over 10 years. She loves helping people discover their passions and helping them take steps towards fulfilling those passions. Carrie also enjoys coaching sports with kids in her free time.
#### Disclaimer
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# Fp3 Help
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1. https://2d31ca6ec4f6115572728c3a9168...%20Numbers.pdf
q1ii?
How am I supposed to draw it?
Like I don't know what 1+w is, if someone can explain how to work that out.
2. So
Use De Moivres Theorem such that
Then you just draw a nice spiral.
(Original post by Super199)
https://2d31ca6ec4f6115572728c3a9168...%20Numbers.pdf
q1ii?
How am I supposed to draw it?
Like I don't know what 1+w is, if someone can explain how to work that out.
3. (Original post by Cryptokyo)
So
Use De Moivres Theorem such that
Forget the n preceding the isin
Then you just draw a nice spiral.
What happens to the one after the De Moivre's bit?
4. So
Use De Moivres Theorem such that
(Original post by Super199)
What happens to the one after the De Moivre's bit?
5. is so good to use....
6. (Original post by Cryptokyo)
So
Use De Moivres Theorem such that
No I get that bit. Thats what part 1 was asking. The bit I don't understand is how you draw 1+w.
7. (Original post by Super199)
What happens to the one after the De Moivre's bit?
Yeah, dunno what the other user is doing... just think of them as vectors. So you move 1 unit along the real plane to the right and then tack on the vector w and move in that direction, for w^2 you just move from your previous position along the direction of w^2. You should dint that you end up at the origin again once you've drawn the one with w^4. (think back to roots of unity and how they form vertices of special geometric shapes)
8. (Original post by Zacken)
Yeah, dunno what the other user is doing... just think of them as vectors. So you move 1 unit along the real plane to the right and then tack on the vector w and move in that direction, for w^2 you just move from your previous position along the direction of w^2. You should dint that you end up at the origin again once you've drawn the one with w^4. (think back to roots of unity and how they form vertices of special geometric shapes)
How do you know that 1+w causes the point to move to the right of 1 and that 1+w+w^2 causes it to move to the left of 1+w? I'm looking at the ms atm. I don't quite get how you work out the direction
9. (Original post by Super199)
How do you know that 1+w causes the point to move to the right of 1 and that 1+w+w^2 causes it to move to the left of 1+w? I'm looking at the ms atm. I don't quite get how you work out the direction
Angle of 2pi/5, that's obviously to the right. Angle of 4pi/5 is obviously to the left, etc...
10. The points you need to point are:
Essentially you are plotting the behaviour of the sine and cosine functions as the angle varies. That is the idea they want and not exact plotting but here are the points anyway.
11. I think I am going crazy
12. (Original post by Zacken)
Angle of 2pi/5, that's obviously to the right. Angle of 4pi/5 is obviously to the left, etc...
Damn, yh got it cheers man.
Although how do you know the last one has to go to the origin?
13. (Original post by Cryptokyo)
Then you just draw a nice spiral.
It's not a spiral, it's a polygon.
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https://www.indiabix.com/placement-papers/ericsson/763 | 1,601,088,463,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400232211.54/warc/CC-MAIN-20200926004805-20200926034805-00560.warc.gz | 858,956,452 | 8,281 | # Placement Papers - ERICSSON
## Why ERICSSON Placement Papers?
Learn and practice the placement papers of ERICSSON and find out how much you score before you appear for your next interview and written test.
## Where can I get ERICSSON Placement Papers with Answers?
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### ERICSSON PAPER - 12 FEB 2006 - GURGAON
Posted By : Anirudh Rating : +33, -11
I gave test on 12 Feb 2006 in Gurgoan
There were two round
1 aptitude (60 questions 60 mins)
2 c or Java test (15 questions 30 mins)
first one has 2 clear the aptitude test then only u can give the C or java test
Aptitude
1. first 10 questions where of data interpretation
they will give u some figures based on that u have to answer
2. 5 questions of data sufficency.
3. 20 questions of quantitive aptitude
mainly from rs aggrawal (solved examples)
topics like profit and loss
time and work
percentage average clock time boats work and distance
4. 10 questions of analytical reasoning
a. one questions of similar puzzle given in rs agrawal verbal and nonverbal reasoning
5 5 questions of verbal reasoning
synonyms + some verbal reasoning question based on passage
6.10 technical questions
3 questions on unix
1 question which is not a universal gate
2 more question of Electronics
www.Friends
C paper
questions not in correcr order
---------
1 i don't remember exactly but something on function ptr.
2 is char a[] and char *ptr same ? Ans no
3 can we use void fun(char *ptr) in place of void fun( char a[])? Ans Yes
4. what is the o/p of printf("%d",i++*++i); Ans no o/p error
5. in a 64 bit os what is the o/p of sizeof(a)= ? char a[10]; Ans 10
6 what is the o/p of
for(i=0;i<10;i++);
{
printf("%d",i);
} Ans no o/p
7.can a structure point to itself ? Ans Yes
8-12. 5 questions on command line arguments (simple one from test ur c skills from yashwant kanetakar)
13 will this work strcpy(string,'a'); Ans Yes
14. char *a="abcd";
char *b="fgeh";
strcpy(a,b) will it work
is no what is the error?
Ans it will not work as what is beyond abcd in a is not known
15. i don't remember | 687 | 2,375 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2020-40 | latest | en | 0.802975 |
http://www.pitsco.com/Clearance/Grades_9-12 | 1,498,534,828,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320915.38/warc/CC-MAIN-20170627032130-20170627052130-00597.warc.gz | 612,860,106 | 69,416 | Items 1 to 16 of 66
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From \$29.96 | 1,316 | 5,646 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2017-26 | latest | en | 0.912396 |
https://www.teacherspayteachers.com/Product/Linear-Equations-Complete-Supplementary-Pack-Word-Wall-4215765 | 1,623,649,595,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487611445.13/warc/CC-MAIN-20210614043833-20210614073833-00287.warc.gz | 936,073,841 | 34,277 | DID YOU KNOW:
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# Linear Equations - Complete Supplementary Pack & Word Wall
7th - 10th
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1. Need extra practice for students throughout the year? Or maybe you are looking for guided notes so students can follow your lessons. Save SO MUCH time with this year long bundle! It includes Exponents & Scientific Notation, Congruence & Similarity, Linear Equations, Functions, and Irration
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### Description
Students work with proportional relationships and rates to write, use, and solve equations in one and two variables.
This complete pack includes the following individual resources:
Bundle A: Writing and Solving Linear Equations Worksheet Bundle
Bundle B: Linear Equations and Their Graphs in Two Variables Worksheet Bundle
Bundle C: Slope and Equations of Lines Worksheet Bundle
Bundle D: Systems of Equations Worksheet Bundle
Linear Equations Word Wall
30 topics covered!
**If you only need ONE topic, each is sold individually! Click on any link above for a more detailed description and preview of each.
What is covered:
Bundle A - Students practice writing and solving linear equations.
Bundle B - Students practice writing, using and graphing equations in two variables.
Bundle C - Students practice using equations in slope-intercept and standard form to solve a variety of problems on slope and constant rate.
Bundle D - Students solve systems of equations by graphing, substitution method and elimination method; word problems included.
Method of delivery:
- Fill in the blank vocabulary and key ideas
- Practice Problems
- True or False
- Matching
- Challenge Word Problems
Possible uses:
- Homework
- Math stations/centers
- Extra help for struggling students
- End-of-topic cumulative review guide
- Extra practice for struggling students
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You might be interested in:
- these FREEBIES
- the unit on Congruence
- the unit on Percents & Proportional Relationships
or my store for other material to supplement the 7th & 8th grade curriculum!
**If you have any requests and/or updates for my work, please message me!
Total Pages
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### Standards
to see state-specific standards (only available in the US).
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3𝘹 + 2𝘺 = 5 and 3𝘹 + 2𝘺 = 6 have no solution because 3𝘹 + 2𝘺 cannot simultaneously be 5 and 6.
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Analyze and solve pairs of simultaneous linear equations.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. | 795 | 3,748 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2021-25 | latest | en | 0.854748 |
http://curious.astro.cornell.edu/our-solar-system/42-our-solar-system/the-earth/gravity/94-does-your-weight-change-between-the-poles-and-the-equator-intermediate | 1,545,017,264,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376828056.99/warc/CC-MAIN-20181217020710-20181217042710-00519.warc.gz | 70,464,123 | 14,454 | ## Does your weight change between the poles and the equator? (Intermediate)
Hi, I'm a seventh grade student in Washington. I had this question: The Earth is spinning, so there is more centrifugal force near the Equator of the earth than near the North Pole, because the Equator is spinning faster. So if you lived on the Equator wouldn't you weigh less than someone who lived on the North Pole, beacause there is more force trying to pull you away from earth? Thanks for your time and effort. I really appreciate it.
You are right, that because of centrifugal force you will weigh a tiny amount less at the Equator than at the poles. Try not to think of centrifugal force as a force though; what's really going on is that objects which are in motion like to go in a straight line and so it takes some force to make them go round in a circle. (Centrifugal force is a fictitious force that shows up in the equations of motion for an object in a rotating reference frame - such as on Earth's Equator.)
So some of the force of gravity (centripetal force) is being used to make you go around in a circle at the Equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the Equator is given by four times pi squared times the radius of the Earth divided by the period of rotation squared (4×π2×R/T2). Earth's period of rotation is a sidereal day (86164.1 seconds, slightly less than 24 hours), and the equatorial radius of the Earth is about 6378 km. This means that the centripetal acceleration at the Equator is about 0.03 m/s2 (metres per second squared). Compare this to the acceleration due to gravity which is about 9.8 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles!
There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere (technically, an oblate spheroid), with the radius at the Equator slightly larger than the radius at the poles. (This shape can be explained by the effect of centrifugal acceleration on the material that makes up the Earth, exactly as described above.) This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator.
Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator.
Here are some other pages which discuss this phenomenon:
This page was last updated by Sean Marshall on September 20, 2015.
### About the Author
#### Karen Masters
Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.
Website: http://icg.port.ac.uk/~mastersk/ | 741 | 3,229 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2018-51 | longest | en | 0.960166 |
https://kr.mathworks.com/matlabcentral/cody/problems/764-soccer-toto/solutions/98354 | 1,582,609,456,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146033.50/warc/CC-MAIN-20200225045438-20200225075438-00260.warc.gz | 446,813,914 | 15,642 | Cody
# Problem 764. Soccer - TOTO
Solution 98354
Submitted on 13 Jun 2012 by Richard Zapor
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
2 Pass
%% n = 5; y_correct = 243; assert(isequal(your_fcn_name(n),y_correct))
3 Pass
%% n = 9; y_correct = 19683; assert(isequal(your_fcn_name(n),y_correct))
4 Pass
%% n = 12; y_correct = 531441; assert(isequal(your_fcn_name(n),y_correct))
5 Pass
%% n = 3; y_correct = 27; assert(isequal(your_fcn_name(n),y_correct)) | 192 | 590 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-10 | latest | en | 0.562289 |
https://se.mathworks.com/matlabcentral/answers/590746-generate-n-samples-of-random-variables-based-on-a-given-discrete-uniform-distributions-can-anyone-t | 1,603,648,439,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107889574.66/warc/CC-MAIN-20201025154704-20201025184704-00285.warc.gz | 516,574,685 | 192,281 | # Generate n samples of random variables based on a given discrete uniform distributions. Can anyone tell me what is the difference between the codes I wrote?
15 views (last 30 days)
DDD on 8 Sep 2020
Commented: Rena Berman on 9 Oct 2020 at 16:39
Question: Write a MATLAB program to sample K values from the probability mass function Pi=i/55, i=1, 2, ….10. Plot the histogram of generated values for K=50, 500, and 5000.
Version 1:
Version 2:
I am new to Matlab. I don't know the difference, but both codes get the same results.
Rik on 11 Sep 2020
Why did you delete your question? That is very rude.
Rena Berman on 9 Oct 2020 at 16:39
Walter Roberson on 8 Sep 2020
The first code generates one new random number each time through the loop, for a total of sampleK random numbers generated out of which sampleK random numbers are used.
The second code generates sampleK random numbers each time through the loop, and uses the i'th of them, ignorning the others, for a total of sampleK * sampleK random numbers generated out of which sampleK random numbers are used.
If you were to move the
u = rand(sampleK,1);
to before the for loop, then you would be making one call that generated sampleK random numbers all at one time, and then used one at a time. That would be more efficient than generating one random number sampleK times.
Show 1 older comment
James Tursa on 8 Sep 2020
You might want to look at the result of cumsum(prob) instead of doing all the sum(prob(1:2)) etc. calculations individually.
Walter Roberson on 8 Sep 2020
DDD on 8 Sep 2020
Honestly, when I saw this question, my first instinct was to solve it using randsample().
The following is what I did, but I am required to solve this question using a uniform random number generator.
Deleted | 451 | 1,762 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2020-45 | latest | en | 0.914786 |
https://us.metamath.org/mpeuni/itsclc0xyqsolb.html | 1,718,299,534,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861480.87/warc/CC-MAIN-20240613154645-20240613184645-00224.warc.gz | 525,687,517 | 6,492 | Mathbox for Alexander van der Vekens < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > Mathboxes > itsclc0xyqsolb Structured version Visualization version GIF version
Theorem itsclc0xyqsolb 45110
Description: Lemma for itsclc0 45111. Solutions of the quadratic equations for the coordinates of the intersection points of a (nondegenerate) line and a circle. (Contributed by AV, 2-May-2023.) (Revised by AV, 14-May-2023.)
Hypotheses
Ref Expression
itsclc0xyqsolr.q 𝑄 = ((𝐴↑2) + (𝐵↑2))
itsclc0xyqsolr.d 𝐷 = (((𝑅↑2) · 𝑄) − (𝐶↑2))
Assertion
Ref Expression
itsclc0xyqsolb ((((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) ∧ ((𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ))) → ((((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶) ↔ ((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄)))))
Proof of Theorem itsclc0xyqsolb
StepHypRef Expression
1 itsclc0xyqsolr.q . . . 4 𝑄 = ((𝐴↑2) + (𝐵↑2))
2 itsclc0xyqsolr.d . . . 4 𝐷 = (((𝑅↑2) · 𝑄) − (𝐶↑2))
31, 2itsclc0xyqsol 45108 . . 3 ((((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) ∧ (𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ)) → ((((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶) → ((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄)))))
433expb 1117 . 2 ((((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) ∧ ((𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ))) → ((((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶) → ((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄)))))
5 simpl 486 . . 3 (((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) → (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ))
6 simpr 488 . . 3 (((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) → (𝐴 ≠ 0 ∨ 𝐵 ≠ 0))
7 simpl 486 . . 3 (((𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ)) → (𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷))
81, 2itsclc0xyqsolr 45109 . . 3 (((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0) ∧ (𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷)) → (((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄))) → (((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶)))
95, 6, 7, 8syl2an3an 1419 . 2 ((((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) ∧ ((𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ))) → (((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄))) → (((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶)))
104, 9impbid 215 1 ((((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐶 ∈ ℝ) ∧ (𝐴 ≠ 0 ∨ 𝐵 ≠ 0)) ∧ ((𝑅 ∈ ℝ+ ∧ 0 ≤ 𝐷) ∧ (𝑋 ∈ ℝ ∧ 𝑌 ∈ ℝ))) → ((((𝑋↑2) + (𝑌↑2)) = (𝑅↑2) ∧ ((𝐴 · 𝑋) + (𝐵 · 𝑌)) = 𝐶) ↔ ((𝑋 = (((𝐴 · 𝐶) + (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) − (𝐴 · (√‘𝐷))) / 𝑄)) ∨ (𝑋 = (((𝐴 · 𝐶) − (𝐵 · (√‘𝐷))) / 𝑄) ∧ 𝑌 = (((𝐵 · 𝐶) + (𝐴 · (√‘𝐷))) / 𝑄)))))
Colors of variables: wff setvar class Syntax hints: → wi 4 ↔ wb 209 ∧ wa 399 ∨ wo 844 ∧ w3a 1084 = wceq 1538 ∈ wcel 2115 ≠ wne 3014 class class class wbr 5052 ‘cfv 6343 (class class class)co 7149 ℝcr 10534 0cc0 10535 + caddc 10538 · cmul 10540 ≤ cle 10674 − cmin 10868 / cdiv 11295 2c2 11689 ℝ+crp 12386 ↑cexp 13434 √csqrt 14592 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1912 ax-6 1971 ax-7 2016 ax-8 2117 ax-9 2125 ax-10 2146 ax-11 2162 ax-12 2179 ax-ext 2796 ax-sep 5189 ax-nul 5196 ax-pow 5253 ax-pr 5317 ax-un 7455 ax-cnex 10591 ax-resscn 10592 ax-1cn 10593 ax-icn 10594 ax-addcl 10595 ax-addrcl 10596 ax-mulcl 10597 ax-mulrcl 10598 ax-mulcom 10599 ax-addass 10600 ax-mulass 10601 ax-distr 10602 ax-i2m1 10603 ax-1ne0 10604 ax-1rid 10605 ax-rnegex 10606 ax-rrecex 10607 ax-cnre 10608 ax-pre-lttri 10609 ax-pre-lttrn 10610 ax-pre-ltadd 10611 ax-pre-mulgt0 10612 ax-pre-sup 10613 This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2071 df-mo 2624 df-eu 2655 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2964 df-ne 3015 df-nel 3119 df-ral 3138 df-rex 3139 df-reu 3140 df-rmo 3141 df-rab 3142 df-v 3482 df-sbc 3759 df-csb 3867 df-dif 3922 df-un 3924 df-in 3926 df-ss 3936 df-pss 3938 df-nul 4277 df-if 4451 df-pw 4524 df-sn 4551 df-pr 4553 df-tp 4555 df-op 4557 df-uni 4825 df-iun 4907 df-br 5053 df-opab 5115 df-mpt 5133 df-tr 5159 df-id 5447 df-eprel 5452 df-po 5461 df-so 5462 df-fr 5501 df-we 5503 df-xp 5548 df-rel 5549 df-cnv 5550 df-co 5551 df-dm 5552 df-rn 5553 df-res 5554 df-ima 5555 df-pred 6135 df-ord 6181 df-on 6182 df-lim 6183 df-suc 6184 df-iota 6302 df-fun 6345 df-fn 6346 df-f 6347 df-f1 6348 df-fo 6349 df-f1o 6350 df-fv 6351 df-riota 7107 df-ov 7152 df-oprab 7153 df-mpo 7154 df-om 7575 df-2nd 7685 df-wrecs 7943 df-recs 8004 df-rdg 8042 df-er 8285 df-en 8506 df-dom 8507 df-sdom 8508 df-sup 8903 df-pnf 10675 df-mnf 10676 df-xr 10677 df-ltxr 10678 df-le 10679 df-sub 10870 df-neg 10871 df-div 11296 df-nn 11635 df-2 11697 df-3 11698 df-4 11699 df-n0 11895 df-z 11979 df-uz 12241 df-rp 12387 df-seq 13374 df-exp 13435 df-cj 14458 df-re 14459 df-im 14460 df-sqrt 14594 df-abs 14595 This theorem is referenced by: itsclc0b 45112
Copyright terms: Public domain W3C validator | 3,420 | 5,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-26 | latest | en | 0.120593 |
https://socratic.org/questions/how-do-you-write-y-2-1-1-4-x-5-in-standard-form | 1,721,342,325,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514860.36/warc/CC-MAIN-20240718222251-20240719012251-00695.warc.gz | 474,905,775 | 6,294 | # How do you write y+2.1=1.4(x-5) in standard form?
Feb 11, 2017
$\textcolor{red}{14} x - \textcolor{b l u e}{10} y = \textcolor{g r e e n}{91}$
#### Explanation:
The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$
where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
To transform, first, multiply each term in parenthesis on the right side of the equation by $\textcolor{red}{1.4}$
$y + 2.1 = \left(\textcolor{red}{1.4} \times x\right) - \left(\textcolor{red}{1.4} \times 5\right)$
$y + 2.1 = 1.4 x - 7$
Next, subtract $\textcolor{red}{2.1}$ and $\textcolor{b l u e}{1.4 x}$ from each side of the equation:
$- \textcolor{b l u e}{1.4 x} + y + 2.1 - \textcolor{red}{2.1} = - \textcolor{b l u e}{1.4 x} + 1.4 x - 7 - \textcolor{red}{2.1}$
$- 1.4 x + y + 0 = 0 - 9.1$
$- 1.4 x + y = - 9.1$
Now, multiply each side of the equation by $\textcolor{red}{- 10}$ to complete the transformation:
$\textcolor{red}{- 10} \left(- 1.4 x + y\right) = \textcolor{red}{- 10} \times - 9.1$
$\left(\textcolor{red}{- 10} \times - 1.4 x\right) + \left(\textcolor{red}{- 10} \times y\right) = 91$
$14 x - 10 y = 91$ | 541 | 1,320 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.84375 | 5 | CC-MAIN-2024-30 | latest | en | 0.585582 |
https://ncsforum.movidius.com/discussion/comment/1112/ | 1,560,775,545,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998475.92/warc/CC-MAIN-20190617123027-20190617145027-00144.warc.gz | 528,226,658 | 8,097 | #### Howdy, Stranger!
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# Incorrect output with simple custom tensorflow network (tf.add bug?)
Hi,
To test the running of a custom tensorflow network on the NCS, I've created a small "hello world" type example (see below). Unfortunately, the NCS gives the incorrect output when running this example.
This example network aims to take an input value, multiply it by itself and add 10.
The following script generates a tensorflow graph (tf_maths.meta file). The script also prints the output values for inputs 0 to 10.
``````import tensorflow as tf
tf.reset_default_graph()
# Name of the graph
name = 'tf_maths'
# Tensorflow graph that multiplies an input number by itself and adds 10
x = tf.get_variable("input", shape=[1,1], initializer = tf.zeros_initializer, dtype = tf.float16)
x1 = tf.matmul(x, x, name = 'multiply')
v1 = tf.Variable(10.0, name = 'variable1', dtype = tf.float16)
v2 = tf.Variable(0.0, name = 'variable2', dtype = tf.float16)
with tf.Session() as sess:
# Initialise variables
init_op = tf.global_variables_initializer()
sess.run(init_op)
# Test with inputs 0 to 10
for i in range(0,11):
assign_op = x.assign([[i]])
sess.run(assign_op)
print('%i, %s' %(i,sess.run(y2)))
# Save the graph
saver = tf.train.Saver(tf.global_variables())
saver.save(sess, './' + name)
``````
I then run the following command to compile the graph, ready for loading on to the NCS.
``````mvNCCompile tf_maths.meta -in input -on output -s 12 -is 1 1
``````
Finally, I run the following script to load the graph on to the NCS and test the output values with input values 0 to 10.
``````from mvnc import mvncapi as mvnc
import numpy as np
# get input parameters
graph_path = './graph'
devices = mvnc.EnumerateDevices()
if len(devices) == 0:
print('No devices found')
quit()
device = mvnc.Device(devices[0])
device.OpenDevice()
with open(graph_path, mode='rb') as f:
graph = device.AllocateGraph(graphfile)
# Testing numbers 0 to 10
for i in range(0,11):
a = np.array([[i]])
output, userobj = graph.GetResult()
print('%i, %s' %(i,output))
else:
print('deallocate graph')
graph.DeallocateGraph()
device.CloseDevice()
print('Finished')
``````
Unfortunately, the output values aren't correct. As shown below:
input expected output NCS output
0.0 10.0 0.0
1.0 11.0 12.0
2.0 14.0 24.0
3.0 19.0 36.0
4.0 26.0 48.0
5.0 35.0 60.0
6.0 46.0 72.0
7.0 59.0 84.0
8.0 74.0 96.0
9.0 91.0 108.0
10.0 110.0 120.0
As you can see, the NCS looks to be multiplying the input by 12.0, rather than performing the intended operation. If I create a similar tensorflow graph in which I only do matrix multiplications (no add operations) I do get the correct output.
Is there possibly a bug in the compiler when interpreting a tf.add layer? I'd be very grateful if you could confirm the approach that I am taking to run a custom tensorflow network on the NCS is correct, and if so, the cause of the problem when performing add operations
• Any comments on this issue would be very much appreciated.
• I am also facing same issue. I am getting wrong output when I run in Movidius stick.
• Bump for comment
• @tf_movidius If you remove the tf.add layer you also will not get correct results, the problem is elsewhere. The mvNCCompile is working properly with 3 channels input (RGB images) when making graph from tensorflow model. Can you try reworking your TF model to be using 3 channels and test if the TF results match the NCS results then. | 1,057 | 3,844 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2019-26 | latest | en | 0.724579 |
https://math.stackexchange.com/questions/2549891/drunk-mail-man-n-letters-to-n-addresses | 1,723,585,621,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641085898.84/warc/CC-MAIN-20240813204036-20240813234036-00192.warc.gz | 301,898,818 | 37,621 | # Drunk Mail Man N letters to N Addresses
Suppose that $n$ different letters are sent to $n$ different addresses on the same street, one to each address. A drunk mailman randomly delivers the letters to the $n$ addresses on the street, one to each address. What is the expected number of letters that were received at correct addresses? Find the probability that at least one letter is put in a correctly addressed envelope.
I have no clue for the expected value but I know the answer for the second question is approaching $\frac{e-1}{e}$ as $n \to \infty$ by using inclusion exclusion.
The number of correctly delivered letters is $X = \sum_{i=1}^n X_i$, where $X_i = 1$ if letter number $i$ is delivered correctly, $0$ otherwise. Then $\mathbb E[X_i] = \mathbb P(X_i = 1) = 1/n$, and $\mathbb E[X] = \sum_{i=1}^n \mathbb E[X_i] = 1$.
The expected value is 1 for any $n$. We use induction on $n$ to prove this.
The base cases are straightforward. Now suppose the assertion is true for $n \leq k$, and we need to see the case $n = k+1$.
Case 1: The first letter is correctly sent. The chance is $\frac{1}{k+1}$. For the rest $k$ letters, in average there are 1 letter being correctly sent, so in this case, there are $1+1=2$ letters sent correctly in average.
Case 2: The first letter is sent incorrectly. Then we start to tract the relations. Suppose letter 1 is sent to address $a_1$, and letter $a_1$ is sent to address $a_2$, and we continue the process until we find a loop, that is, until we get to the address 1. We separate into two cases by the size of the loop, $\ell$.
Case 2-1: $\ell < k+1$. In this case the $\ell$ letters in the loop are messed up, while in the rest $k+1 - \ell$ letters, in average there is 1 letter being sent correctly.
Case 2-2: $\ell = k+1$. The chance that this happens is $\frac{1}{k+1}$. And if this happens, none of the letters is sent correctly.
By combining all cases, the expected value of letters sent correctly is $$\frac{1}{k+1}\times 2 + \frac{k-1}{k+1}\times 1 + \frac{1}{k+1}\times 0 = 1.$$ This ends our induction process. | 596 | 2,083 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2024-33 | latest | en | 0.907231 |
https://homeofengineers.com/please-show-all-steps-and-work-used-to-derive-the-answer-im-more-interested-in-making-sure-that-i-understand-how-to-use-formulas-and-correct/ | 1,712,989,990,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816586.79/warc/CC-MAIN-20240413051941-20240413081941-00002.warc.gz | 282,488,366 | 19,074 | Please show all steps and work used to derive the answer. I’m more interested in making sure that I understand how to use formulas and correct processes properly, rather than just the right answer.
According to creditcard.com, 29% of adults do not own a credit card.
a. Suppose a random sample of 500 adults is asked, “Do you own a credit card?” describe the sampling distribution of p̂, the proportion of adults who own a credit card?
b. What is the probability that in a sample of 500 adults, more than 30% do not own a credit card
c. What is the probability that in a random sample of 500 adults, between 25% and 30% do not own a credit card?
Thank you! | 157 | 661 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-18 | latest | en | 0.950062 |
https://www.chess.com/nl/forum/view/general/solving-mate-in-two-problems?page=1 | 1,492,955,656,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917118707.23/warc/CC-MAIN-20170423031158-00531-ip-10-145-167-34.ec2.internal.warc.gz | 899,927,427 | 18,460 | x
Schaken - Speel & Leer
Chess.com
GRATIS - in Win Phone Store
# solving mate in two problems
• #1
Some are easy, while some are hard (not so obvious). What is the best way to solve mate in two? Other than knowing tactics, is there a certain strategy?
• #2
anyone?
• #3
Well, composed puzzle are not so much about tactics as about "themes".
You probabl have to approach them differently from regular positions. Many have very little basis in reality. I always say puzzles are not chess, but a seperate discipline using the rules of chess.
I guess if ou understand all or some of the themes, you might spot the patterns easier
http://en.wikipedia.org/wiki/Glossary_of_chess_problems
• #4
rooperi wrote:
Well, composed puzzle are not so much about tactics as about "themes".
You probabl have to approach them differently from regular positions. Many have very little basis in reality. I always say puzzles are not chess, but a seperate discipline using the rules of chess.
I guess if ou understand all or some of the themes, you might spot the patterns easier
I practice mate puzzles to help my tactical vision without moving pieces. How differently?
• #5
Lemme give ou an example. This puzzle, (like many others) is more about the composer trying to accomplish a task, and not setting a problem for a solver.
This is a theme called starflights. The black king is on e2 (the centre of the star) d1, f1, d3, f3 are the points of the stars. If the king escapes to any of these squares, there is a seperate and different mate for each square.
• #6
chessplayer19987 wrote:
Some are easy, while some are hard (not so obvious). What is the best way to solve mate in two? Other than knowing tactics, is there a certain strategy?
Well, mate is when you give check and the opponent can't evade it.
So - the second move has to be a check. Now what has to happen in the first move to get a mate for your check? -> Make sure the checking piece can't be taken or blocked and the king can't run away, either ...
• #7
andreasweber wrote:
chessplayer19987 wrote:
Some are easy, while some are hard (not so obvious). What is the best way to solve mate in two? Other than knowing tactics, is there a certain strategy?
Well, mate is when you give check and the opponent can't evade it.
So - the second move has to be a check. Now what has to happen in the first move to get a mate for your check? -> Make sure the checking piece can't be taken or blocked and the king can't run away, either ...
Not that simple. Some mates are forced, meaning you have to check your opponent on the first move then give mate. But alot are not so obvious.
of
Nu online | 633 | 2,663 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2017-17 | latest | en | 0.955839 |
http://mathhelpforum.com/math-topics/164059-maximum-frequency.html | 1,481,113,147,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542060.60/warc/CC-MAIN-20161202170902-00439-ip-10-31-129-80.ec2.internal.warc.gz | 170,466,431 | 10,755 | 1. ## maximum Frequency
1. The problem statement, all variables and given/known data
Hi
I am solving the june 2009 Physics 1 paper (Syllabus A). The mark scheme answer has got me slightly confused on 2 questions:
1. Calculate the maximum frequency of the photon emitted when the 9.0 ev
electron collides with an atom.
2.Calculate the specific charge of an isotope with 143 neutrons and 92 protons
2. Relevant equations
1) E= hf
2) Specific charge= charge/mass
3. The attempt at a solution
1)f= E/H
Therefore
f= 9 x 1.6x 10^-19/6.63 x 10^-34
But the schemes answer is very different to mine.
2)In the schemes answer, the mass was calculated as both 143 and 92. I presumed that the nucleon number constituted the mass, while the electrons (or number of protons) constituted the charge. (Multiplied by 92 in this case).
Anybody? Thanks.
2. 1) Well, you have to take into account the work function...
$E = hf_o + hf$
$9.0 \times 1.6\times10^{-19} = Work\ function + hf$
2) The total mass of an atom is given by the sum of relative mass of neutrons and protons, that is 143+92 = 235. The charge is given by the sum of the relative charges of all the protons, that is +92
Hm... you're dealing with Uranium-235!
3. Hi
Thanks for the usual prompt reply. Okay, lets go!
Question 1
So, the specific charge will be
92 x 1.6 x 10^-19/235 x 1.67 x 10^-27. Please confirm this
Question 2
I cant seem to work out the work function. How can I do this?
And yes I am dealing with Uranium! I have 8 modules in January. Sso maybe one of its higher isotopes??
4. 1. Yes
2. It's normally given in the question as the threshold frequency, or worked out by using other values before. I can't give you the answer here, because different metals have different work functions.
5. Thanks once again. | 502 | 1,786 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2016-50 | longest | en | 0.908383 |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-1-equations-and-inequalities-exercise-set-1-2-page-119/68 | 1,537,732,108,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159744.52/warc/CC-MAIN-20180923193039-20180923213439-00227.warc.gz | 756,996,743 | 12,974 | # Chapter 1 - Equations and Inequalities - Exercise Set 1.2 - Page 119: 68
$x=3$ conditional equation
#### Work Step by Step
$\frac{3}{x-3}=\frac{x}{x-3}+3$ $\frac{3}{x-3}=\frac{x}{x-3}+3(\frac{x-3}{x-3})$ $\frac{3}{x-3}=\frac{x+3(x-3)}{x-3}$ $3=x+3(x-3)$ $3=x+3x-9$ $3=4x-9$ $4x=12$ $x=3$
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# Scientific notation. What is scientific notation? Numbers are written in the form M × 10 ^n, Where the factor M is a number greater than or equal to.
## Presentation on theme: "Scientific notation. What is scientific notation? Numbers are written in the form M × 10 ^n, Where the factor M is a number greater than or equal to."— Presentation transcript:
Scientific notation
What is scientific notation? Numbers are written in the form M × 10 ^n, Where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number. Ex. 6.5 × 10⁴ km Ex. 9.8 × 10¯³ g
How to determine scientific notation
Convert numbers into scientific notation 89000 68.65 .00087 .000000000453 222.22
Adding and subtracting scientific notation Can be performed only if the values have the same exponent (n factor). Ex. 4.2 × 10² − 2.2 × 10² = 2 × 10² If they do not have the same number, adjustments must be made so the exponent values are equal. Ex. 7.001 × 10³ + 9.3 × 10⁴ =.7001 × 10⁴ + 9.3 × 10⁴ = 10.0001 × 10⁴ = 1.00001 × 10⁵
Add or subtract 6.09 × 10¯¹ + 9.2 × 10¯¹ 7.968 × 10⁴ - 9.68 × 10³ 5900 + 7.8 × 10³ 2.31 × 10¯³ + 6.12 × 10¯⁵ 1.22 × 10¹² + 1.22 × 10¹⁴ 2.34 × 10² + 1.8 × 10¯¹
Multiplication of scientific notation The M factors are multiplied, and the exponents are added algebraically. Ex. 1.2 × 10⁵ × 5.45 × 10² = 6.54 × 10⁷
Multiply scientific notations
Dividing scientific notation
Divide scientific notations
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MAE 20 Homework_1_summer_2010
# MAE 20 Homework_1_summer_2010 - (h Indicate all the...
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MAE 20 June 30, 2010 Homework 1 Due on Wednesday (July 7), at the beginning of class Clearly show the detailed steps in your solutions. (a) Even though the bonding energies for a ceramic, say MgO, ~ 1000 kJ/mole is larger than that of diamond (~ 700 kJ/mole) why are ceramics more brittle? (b) Give two examples where secondary bonding (van der Waals bonding) is observed? (c) What is the bonding type in diamond? Discuss a property that is commensurate with its bonding? (d) What type(s) of bonding would be expected for: (i) brass, (ii) rubber, (iii) GaAs, (iv) solid xenon, (v) bronze, (vi) Nylon. (e) Would you expect MgO or Mg to have higher strength? Why? (f) Sketch the following directions in a cubic unit cell: (i) [101] (ii) [0 , (iii) [ 2 , (iv) [301] (g) Determine the Miller indices for the four planes shown in the following unit cells:
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Unformatted text preview: (h) Indicate all the directions of the form &lt;110&gt; that lie in the ( 1 plane, of a cubic unit cell. (i) What is the atomic packing fraction? Show that the atomic packing fraction for a body-centered cubic (bcc) crystal is 0.68 (or 68%) (j) Fe has a bcc crystal structure, with an atomic radius of 0.124 nm and an atomic weight of 55.85 g/mole. Compute the value of its theoretical density. (k) Determine the planar density and packing fraction for Nickel (Ni) in the (100), (110), and (111) planes. On which plane is deformation most likely to happen? Why? (l) Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 600 K. Assume an energy for vacancy formation of 0.55 eV/atom....
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• Dec 21st 2005, 03:23 AM
Greg E
velocity of falling object
If you drop a 1.36 kg weight and it falls .1524 meters, what is its velocity when it hits the ground and how is this calculated. Ultimately I am trying to decide how much energy is released.
Thanks,
Greg
• Dec 21st 2005, 12:45 PM
CaptainBlack
Quote:
Originally Posted by Greg E
If you drop a 1.36 kg weight and it falls .1524 meters, what is its velocity when it hits the ground and how is this calculated. Ultimately I am trying to decide how much energy is released.
Thanks,
Greg
An object dropped near the surface of the earth experiences an approximately
constant acceleration of $-g$ the minus sign is conventional as
up is normally taken as positive, and so downward accelleration is negative.
So $v=-g\cdot t+c$, and if the initial speed is $0$ then $c=0$.
Integrating again gives:
$x=-\frac{g\cdot t^2}{2}+x_0$,
where $x_0$ is the initial height of the weight, for convenience we will
take this to be $0$.
Now we are interested in what is happening when the weight has fallen
$0.1524m$. This occurs when:
$0.1524=-\frac{g\cdot t^2}{2}$,
or:
$t=\sqrt{\frac{2\cdot 0.1524}{g}}$.
Putting this back into the equation for vertical velocity:
$v=-g \cdot \left( \sqrt {\frac{2 \cdot 0.1524}{g}} \right)=-\sqrt{g \cdot 2 \cdot 0.1524}$.
At the earth surface $g \sim 9.81 m/s$.
We could have short circuited this calculation by knowing that the change
in potential energy when the weight drops through a height $h$is
$PE=m \cdot g \cdot h$,
which will equal the kinetic energy of the weight when it has fallen from rest
through a distance $h$:
$KE= \frac{1}{2}m \cdot v^2$
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# The Effect of Pressure on Rate of Reaction
This page describes and explains the way that changing the pressure of a gas changes the rate of a reaction.
### The facts
Increasing the pressure on a reaction involving reacting gases increases the rate of reaction. Changing the pressure on a reaction which involves only solids or liquids has no effect on the rate.
Example 1
In the manufacture of ammonia by the Haber Process, the rate of reaction between the hydrogen and the nitrogen is increased by the use of very high pressures.
$N_2(g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)$
In fact, the main reason for using high pressures is to improve the percentage of ammonia in the equilibrium mixture, but there is a useful effect on rate of reaction as well.
### The explanation
#### The relationship between pressure and concentration
Increasing the pressure of a gas is exactly the same as increasing its concentration. If you have a given mass of gas, the way you increase its pressure is to squeeze it into a smaller volume. If you have the same mass in a smaller volume, then its concentration is higher. You can also show this relationship mathematically if you have come across the ideal gas equation:
Rearranging this gives:
Because "RT" is constant as long as the temperature is constant, this shows that the pressure is directly proportional to the concentration. If you double one, you will also double the other.
### The effect of increasing the pressure on the rate of reaction
#### Collisions involving two particles
The same argument applies whether the reaction involves collision between two different particles or two of the same particle. In order for any reaction to happen, those particles must first collide. This is true whether both particles are in the gas state, or whether one is a gas and the other a solid. If the pressure is higher, the chances of collision are greater.
### Reactions involving only one particle
If a reaction only involves a single particle splitting up in some way, then the number of collisions is irrelevant. What matters now is how many of the particles have enough energy to react at any one time.
Suppose that at any one time 1 in a million particles have enough energy to equal or exceed the activation energy. If you had 100 million particles, 100 of them would react. If you had 200 million particles in the same volume, 200 of them would now react. The rate of reaction has doubled by doubling the pressure.
### Contributors
Jim Clark (Chemguide.co.uk) | 528 | 2,551 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2017-04 | latest | en | 0.933665 |
http://www.hextobinary.com/unit/linearcurrent/from/megaamppyd/to/kamppmicrom | 1,591,438,795,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348513230.90/warc/CC-MAIN-20200606093706-20200606123706-00126.warc.gz | 173,033,950 | 6,644 | #### Megaampere/Yard Kiloampere/Micrometer
##### How many Kiloampere/Micrometer are in a Megaampere/Yard?
The answer is one Megaampere/Yard is equal to 0.0010936132983377 Kiloampere/Micrometer. Feel free to use our online unit conversion calculator to convert the unit from Megaampere/Yard to Kiloampere/Micrometer. Just simply, enter value 1 in Megaampere/Yard and see the result in Kiloampere/Micrometer.
##### How to Convert Megaampere/Yard to Kiloampere/Micrometer (MA/yd to kA/μm)
By using our Megaampere/Yard to Kiloampere/Micrometer conversion tool, you know that one Megaampere/Yard is equivalent to 0.0010936132983377 Kiloampere/Micrometer. Hence, to convert Megaampere/Yard to Kiloampere/Micrometer, we just need to multiply the number by 0.0010936132983377. We are going to use very simple Megaampere/Yard to Kiloampere/Micrometer conversion formula for that. Pleas see the calculation example given below.
Convert 1 Megaampere/Yard to Kiloampere/Micrometer 1 Megaampere/Yard = 1 × 0.0010936132983377 = 0.0010936132983377 Kiloampere/Micrometer
##### What is Megaampere/Yard Unit of Measure?
Megaampere per yard is a unit of measurement for linear current density. It is defined as flow of current in megaampere through a conductor which is one yard wide.
##### What is the symbol of Megaampere/Yard?
The symbol of Megaampere/Yard is MA/yd which means you can also write it as 1 MA/yd.
##### What is Kiloampere/Micrometer Unit of Measure?
Kiloampere per micrometer is a unit of measurement for linear current density. It is defined as flow of current in kiloampere through a conductor which is one micrometer wide.
##### What is the symbol of Kiloampere/Micrometer?
The symbol of Kiloampere/Micrometer is kA/μm which means you can also write it as 1 kA/μm.
##### Megaampere/Yard to Kiloampere/Micrometer Conversion Table
Megaampere/Yard [MA/yd] Kiloampere/Micrometer [kA/μm] 1 0.0010936132983377 2 0.0021872265966754 3 0.0032808398950131 4 0.0043744531933508 5 0.0054680664916885 6 0.0065616797900262 7 0.007655293088364 8 0.0087489063867017 9 0.0098425196850394 10 0.010936132983377 100 0.10936132983377 1000 1.0936132983377
##### Megaampere/Yard to Other Units Conversion Chart
Megaampere/Yard [MA/yd] Output 1 Megaampere/Yard in Abampere/Centimeter equals to 1093.61 1 Megaampere/Yard in Abampere/Foot equals to 33333.33 1 Megaampere/Yard in Abampere/Inch equals to 2777.78 1 Megaampere/Yard in Abampere/Meter equals to 109361.33 1 Megaampere/Yard in Abampere/Micrometer equals to 0.10936132983377 1 Megaampere/Yard in Abampere/Millimeter equals to 109.36 1 Megaampere/Yard in Abampere/Nanometer equals to 0.00010936132983377 1 Megaampere/Yard in Abampere/Yard equals to 100000 1 Megaampere/Yard in Ampere/Centimeter equals to 10936.13 1 Megaampere/Yard in Ampere/Foot equals to 333333.33 1 Megaampere/Yard in Ampere/Inch equals to 27777.78 1 Megaampere/Yard in Ampere/Meter equals to 1093613.3 1 Megaampere/Yard in Ampere/Micrometer equals to 1.09 1 Megaampere/Yard in Ampere/Millimeter equals to 1093.61 1 Megaampere/Yard in Ampere/Nanometer equals to 0.0010936132983377 1 Megaampere/Yard in Ampere/Yard equals to 1000000 1 Megaampere/Yard in Biot/Centimeter equals to 1093.61 1 Megaampere/Yard in Biot/Foot equals to 33333.33 1 Megaampere/Yard in Biot/Inch equals to 2777.78 1 Megaampere/Yard in Biot/Meter equals to 109361.33 1 Megaampere/Yard in Biot/Micrometer equals to 0.10936132983377 1 Megaampere/Yard in Biot/Millimeter equals to 109.36 1 Megaampere/Yard in Biot/Nanometer equals to 0.00010936132983377 1 Megaampere/Yard in Biot/Yard equals to 100000 1 Megaampere/Yard in Kiloampere/Centimeter equals to 10.94 1 Megaampere/Yard in Kiloampere/Foot equals to 333.33 1 Megaampere/Yard in Kiloampere/Inch equals to 27.78 1 Megaampere/Yard in Kiloampere/Meter equals to 1093.61 1 Megaampere/Yard in Kiloampere/Micrometer equals to 0.0010936132983377 1 Megaampere/Yard in Kiloampere/Millimeter equals to 1.09 1 Megaampere/Yard in Kiloampere/Nanometer equals to 0.0000010936132983377 1 Megaampere/Yard in Kiloampere/Yard equals to 1000 1 Megaampere/Yard in Megaampere/Centimeter equals to 0.010936132983377 1 Megaampere/Yard in Megaampere/Foot equals to 0.33333333333333 1 Megaampere/Yard in Megaampere/Inch equals to 0.027777777777778 1 Megaampere/Yard in Megaampere/Meter equals to 1.09 1 Megaampere/Yard in Megaampere/Micrometer equals to 0.0000010936132983377 1 Megaampere/Yard in Megaampere/Millimeter equals to 0.0010936132983377 1 Megaampere/Yard in Megaampere/Nanometer equals to 1.0936132983377e-9 1 Megaampere/Yard in Microampere/Centimeter equals to 10936132983.38 1 Megaampere/Yard in Microampere/Foot equals to 333333333333.33 1 Megaampere/Yard in Microampere/Inch equals to 27777777777.78 1 Megaampere/Yard in Microampere/Meter equals to 1093613298337.7 1 Megaampere/Yard in Microampere/Micrometer equals to 1093613.3 1 Megaampere/Yard in Microampere/Millimeter equals to 1093613298.34 1 Megaampere/Yard in Microampere/Nanometer equals to 1093.61 1 Megaampere/Yard in Microampere/Yard equals to 1000000000000 1 Megaampere/Yard in Milliampere/Centimeter equals to 10936132.98 1 Megaampere/Yard in Milliampere/Foot equals to 333333333.33 1 Megaampere/Yard in Milliampere/Inch equals to 27777777.78 1 Megaampere/Yard in Milliampere/Meter equals to 1093613298.34 1 Megaampere/Yard in Milliampere/Micrometer equals to 1093.61 1 Megaampere/Yard in Milliampere/Millimeter equals to 1093613.3 1 Megaampere/Yard in Milliampere/Nanometer equals to 1.09 1 Megaampere/Yard in Milliampere/Yard equals to 1000000000 1 Megaampere/Yard in Statampere/Centimeter equals to 32785701409046 1 Megaampere/Yard in Statampere/Foot equals to 999308178947710 1 Megaampere/Yard in Statampere/Inch equals to 83275681578976 1 Megaampere/Yard in Statampere/Meter equals to 3278570140904600 1 Megaampere/Yard in Statampere/Micrometer equals to 3278570140.9 1 Megaampere/Yard in Statampere/Millimeter equals to 3278570140904.6 1 Megaampere/Yard in Statampere/Nanometer equals to 3278570.14 1 Megaampere/Yard in Statampere/Yard equals to 2997924536843100
##### Other Units to Megaampere/Yard Conversion Chart
Output Megaampere/Yard [MA/yd] 1 Abampere/Centimeter in Megaampere/Yard equals to 0.0009144 1 Abampere/Foot in Megaampere/Yard equals to 0.00003 1 Abampere/Inch in Megaampere/Yard equals to 0.00036 1 Abampere/Meter in Megaampere/Yard equals to 0.000009144 1 Abampere/Micrometer in Megaampere/Yard equals to 9.14 1 Abampere/Millimeter in Megaampere/Yard equals to 0.009144 1 Abampere/Nanometer in Megaampere/Yard equals to 9144 1 Abampere/Yard in Megaampere/Yard equals to 0.00001 1 Ampere/Centimeter in Megaampere/Yard equals to 0.00009144 1 Ampere/Foot in Megaampere/Yard equals to 0.000003 1 Ampere/Inch in Megaampere/Yard equals to 0.000036 1 Ampere/Meter in Megaampere/Yard equals to 9.144e-7 1 Ampere/Micrometer in Megaampere/Yard equals to 0.9144 1 Ampere/Millimeter in Megaampere/Yard equals to 0.0009144 1 Ampere/Nanometer in Megaampere/Yard equals to 914.4 1 Ampere/Yard in Megaampere/Yard equals to 0.000001 1 Biot/Centimeter in Megaampere/Yard equals to 0.0009144 1 Biot/Foot in Megaampere/Yard equals to 0.00003 1 Biot/Inch in Megaampere/Yard equals to 0.00036 1 Biot/Meter in Megaampere/Yard equals to 0.000009144 1 Biot/Micrometer in Megaampere/Yard equals to 9.14 1 Biot/Millimeter in Megaampere/Yard equals to 0.009144 1 Biot/Nanometer in Megaampere/Yard equals to 9144 1 Biot/Yard in Megaampere/Yard equals to 0.00001 1 Kiloampere/Centimeter in Megaampere/Yard equals to 0.09144 1 Kiloampere/Foot in Megaampere/Yard equals to 0.003 1 Kiloampere/Inch in Megaampere/Yard equals to 0.036 1 Kiloampere/Meter in Megaampere/Yard equals to 0.0009144 1 Kiloampere/Micrometer in Megaampere/Yard equals to 914.4 1 Kiloampere/Millimeter in Megaampere/Yard equals to 0.9144 1 Kiloampere/Nanometer in Megaampere/Yard equals to 914400 1 Kiloampere/Yard in Megaampere/Yard equals to 0.001 1 Megaampere/Centimeter in Megaampere/Yard equals to 91.44 1 Megaampere/Foot in Megaampere/Yard equals to 3 1 Megaampere/Inch in Megaampere/Yard equals to 36 1 Megaampere/Meter in Megaampere/Yard equals to 0.9144 1 Megaampere/Micrometer in Megaampere/Yard equals to 914400 1 Megaampere/Millimeter in Megaampere/Yard equals to 914.4 1 Megaampere/Nanometer in Megaampere/Yard equals to 914400000 1 Microampere/Centimeter in Megaampere/Yard equals to 9.144e-11 1 Microampere/Foot in Megaampere/Yard equals to 3e-12 1 Microampere/Inch in Megaampere/Yard equals to 3.6e-11 1 Microampere/Meter in Megaampere/Yard equals to 9.144e-13 1 Microampere/Micrometer in Megaampere/Yard equals to 9.144e-7 1 Microampere/Millimeter in Megaampere/Yard equals to 9.144e-10 1 Microampere/Nanometer in Megaampere/Yard equals to 0.0009144 1 Microampere/Yard in Megaampere/Yard equals to 1e-12 1 Milliampere/Centimeter in Megaampere/Yard equals to 9.144e-8 1 Milliampere/Foot in Megaampere/Yard equals to 3e-9 1 Milliampere/Inch in Megaampere/Yard equals to 3.6e-8 1 Milliampere/Meter in Megaampere/Yard equals to 9.144e-10 1 Milliampere/Micrometer in Megaampere/Yard equals to 0.0009144 1 Milliampere/Millimeter in Megaampere/Yard equals to 9.144e-7 1 Milliampere/Nanometer in Megaampere/Yard equals to 0.9144 1 Milliampere/Yard in Megaampere/Yard equals to 1e-9 1 Statampere/Centimeter in Megaampere/Yard equals to 3.0501101304e-14 1 Statampere/Foot in Megaampere/Yard equals to 1.0006923e-15 1 Statampere/Inch in Megaampere/Yard equals to 1.20083076e-14 1 Statampere/Meter in Megaampere/Yard equals to 3.0501101304e-16 1 Statampere/Micrometer in Megaampere/Yard equals to 3.0501101304e-10 1 Statampere/Millimeter in Megaampere/Yard equals to 3.0501101304e-13 1 Statampere/Nanometer in Megaampere/Yard equals to 3.0501101304e-7 1 Statampere/Yard in Megaampere/Yard equals to 3.335641e-16 | 3,413 | 9,781 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2020-24 | latest | en | 0.841366 |
http://mathhelpforum.com/advanced-statistics/198943-estimator-parameters-print.html | 1,527,127,772,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865884.49/warc/CC-MAIN-20180524014502-20180524034502-00531.warc.gz | 183,971,572 | 2,886 | # Estimator of parameters
• May 17th 2012, 09:49 PM
Lunzyboy
Estimator of parameters
I've got an uni assignment to do and I can't figure out one of the questions.
We have to consider 2 models, the first being Y = Beta1 + Beta2(X) + u
Then the second being Y = Alpha1 + Alpha2(X/100) + u
We've been given a dataset:
82.1 41.3 29.2 18.5 -25.2 -29.3 27 16 57.1 61.9 29.3 45.5 -31.2 -35.8 30 14 50.3 35.3 61.9 31
Y-value X-value
I've worked out Beta1 = 10.698 and Beta2 = 1.026 ,using the formulas described below for the first model, which is correct, but I'm not too sure on the 2nd model:
For the 2nd model, we have to derive the estimators of the parameters (alpha1 + alpha2).
I know Alpha2 would equal Beta2Hat, which = Summation(xiyi)/Summation(xi^2)
Alpha1 would also equal Beta1Hat?, which = YHat - Beta2Hat*XHat
The thing that has confused me is the (X/100).
How would the (X/100) change the estimators of the parameters? | 320 | 934 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2018-22 | latest | en | 0.913388 |
https://thebestassignmenthelp.com/sbm1108-accounts-assignment-accounts/ | 1,550,316,999,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247480272.15/warc/CC-MAIN-20190216105514-20190216131514-00064.warc.gz | 719,530,990 | 16,430 | # SBM1108 | ACCOUNTS ASSIGNMENT | ACCOUNTS
### SBM1108 | ACCOUNTS ASSIGNMENT | ACCOUNTS
You are required to analyse the following problems and discuss an appropriate decision making or modelling approach for your proposed solution.
Q5. Lars Van Hoek is about to install a new machine for making parts for domestic appliances. Three suppliers have made bids to supply the machine. The first supplier offers the Basic or machine, which automatically produces parts of acceptable, but not outstanding, quality.
The output from the machine varies (depending on the materials used and a variety of settings) and might be 1,000 a week (with probability 0.1), 2,000 a week (with probability 0.7) or 3,000 a week. The net profit for the machine is \$4 a unit. The second supplier offers a Supertramp machine, which makes higher quality parts. The output from this might be 700 a week (with probability 0.4) or 1,000 a week, with a net profit of \$10 a unit. The third supplier offers the Switchover machine, which managers can set to produce either 1,300 high-quality parts a week at a profit of \$6 a unit, or 1,600 medium-quality parts a week with a profit of \$5 a unit. If the machine produces 2,000 or more units a week, Lars can export all production as a single bulk order. Then there is a 60% chance of selling this order for 50% more profit and a 40% chance of selling for 50% less profit. What should Lars do to maximize the expected profit?
Q6. Sunseed industries produce different types of raw materials and it is interesting is using simulation to estimate the profit per unit for its new product x. the selling price for the product will be \$40 per unit. Probability distributions for the raw material cost, the production cost, and the marketing cost are estimated as follows:
Raw material cost(\$) Probability Production Cost(\$) Probability Marketing Cost(\$) Probability 16 0.20 10 0.25 5 0.40 18 0.30 11 0.45 6 0.60 20 0.35 12 0.30 22 0.15
a.compute profit per unit for the base case, worst case, and best case.
b.construct a simulation model to estimate the mean profit per unit.
1. management believes the project may not be sustainable if the profit per unit is less than \$2. Use simulation to estimate the probability the profit per unit will be less than \$2.
You are required to analyse the following problems and discuss an appropriate decision making or modelling approach for your proposed solution.
The proposed decision making must then be presented to an audience with full justification of your assumptions and constraints. It should be clear to the audience exactly how and what type of modelling approach you have selected for the business problem.
Q7. An electronics store sells two models of television. The sales of these two models, X and Y, are dependent, that is, if the price of one increases, the demand for the other increases. A study is made to find the relationship between the demand (D) and the price (P) in order to maximize the revenue from these products. The result of the study is shown below:
Dx = 476 – 0.54 Px + 0.22 Py
Dy = 601 + 0.12 Px – 0.54 Py
1. Construct a model for that total revenue and implement it on a spreadsheet.
2. Develop a two-way data table to estimate the optimal pieces of each of the two products in order to maximize the total revenue. Vary price of each product from \$600 to \$900 in increments of \$50.
Show your workings in excel and save your file as Q6#IDSBM1108.xls (20 marks)
Q8. Bob Jane tyres, Inc. makes two types of tyres, for suvs and Hatchbacks. The firm has 500 hours of production time, 250 hours available for shipping. The production time required per type is given in the following table:
Product Hours Type Production Packaging Shipping Profit/Tyre SUV tyres 2 1.5 1 \$22 Hatchbacks tyres 1.5 1 0.5 \$12
Assuming that the company is interested in maximizing the total profit contribution, find the optimal solution using Excel Solver and answer the following using the sensitivity analysis report:
1. How many hours of production time will be scheduled in each department?
2. What is the slack time in each department?
3. If one more hour is available for packaging, what is the change in profit?
4. What is the change in profit if one more hour is available for shipping? | 1,009 | 4,308 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-09 | longest | en | 0.873306 |
https://www.airmilescalculator.com/distance/lsh-to-cei/ | 1,709,538,448,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476432.11/warc/CC-MAIN-20240304065639-20240304095639-00471.warc.gz | 637,728,884 | 48,096 | # How far is Chiang Rai from Lashio?
The distance between Lashio (Lashio Airport) and Chiang Rai (Chiang Rai International Airport) is 249 miles / 401 kilometers / 217 nautical miles.
The driving distance from Lashio (LSH) to Chiang Rai (CEI) is 428 miles / 688 kilometers, and travel time by car is about 10 hours 31 minutes.
249
Miles
401
Kilometers
217
Nautical miles
## Distance from Lashio to Chiang Rai
There are several ways to calculate the distance from Lashio to Chiang Rai. Here are two standard methods:
Vincenty's formula (applied above)
• 249.308 miles
• 401.222 kilometers
• 216.643 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 249.931 miles
• 402.225 kilometers
• 217.184 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Lashio to Chiang Rai?
The estimated flight time from Lashio Airport to Chiang Rai International Airport is 58 minutes.
## Flight carbon footprint between Lashio Airport (LSH) and Chiang Rai International Airport (CEI)
On average, flying from Lashio to Chiang Rai generates about 62 kg of CO2 per passenger, and 62 kilograms equals 136 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Lashio to Chiang Rai
See the map of the shortest flight path between Lashio Airport (LSH) and Chiang Rai International Airport (CEI).
## Airport information
Origin Lashio Airport
City: Lashio
Country: Burma
IATA Code: LSH
ICAO Code: VYLS
Coordinates: 22°58′40″N, 97°45′7″E
Destination Chiang Rai International Airport
City: Chiang Rai
Country: Thailand
IATA Code: CEI
ICAO Code: VTCT
Coordinates: 19°57′8″N, 99°52′58″E | 517 | 1,963 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-10 | latest | en | 0.81774 |
https://math.stackexchange.com/questions/1487418/initial-category-having-all-limits-and-colimits | 1,701,402,088,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100264.9/warc/CC-MAIN-20231201021234-20231201051234-00258.warc.gz | 434,825,719 | 37,669 | Initial category having all limits and colimits?
Is there a 'smallest' category having all finite limits and colimits? (In the sense of initial object in the category of categories with this property).
(For a few moments, I thought it would simply be the category of finite sets and ordinary maps, but that can't be, because in that category, sum distributes over product but not vice versa.)
Edit: the functors in the category are to preserve all these finite limits and colimits, and the empty category is excluded.
• Perhaps you want functors in this category to preserve limits and colimits. Oct 19, 2015 at 13:18
• If I didn't make a mistake, the discrete category on one object has all finite limits and colimits. Of course it's not an initial category like that, but it's definitely the smallest. Oct 19, 2015 at 13:19
• Of course, of course (to both comments). Obviously I mean the initial object, and obviously in the category with limit- and colimit-preserving functors. Oct 19, 2015 at 13:28
• @Najib Idrissi BTW, your example is actually the terminal object, me thinks? Oct 19, 2015 at 13:29
We need to be precise here. Consider the following category $\mathcal{M}$:
• The objects are small categories with chosen initial object, binary coproducts, coequalisers, terminal object, binary products, and equalisers.
• The morphisms are functors that strictly preserve the chosen colimits and limits.
With a bit of work one can verify that $\mathcal{M}$ is a locally presentable category – specifically, it is clear that $\mathcal{M}$ has colimits of small filtered diagrams, limits of small diagrams, and has a small generating set. (In fact, $\mathcal{M}$ is locally finitely presentable – for this, one can check that it is the category of models for a finitary essentially algebraic theory.)
In particular, $\mathcal{M}$ has an initial object, which may be constructed using Freyd's initial object lemma.
Of course, you might object that $\mathcal{M}$ is not really the category you had in mind. Indeed, it seems more likely that you are interested in the following 2-category $\mathfrak{K}$:
• The objects are small categories with limits and colimits of finite diagrams.
• The morphisms are functors that preserve limits and colimits of finite diagrams (up to isomorphism).
• The 2-cells are natural transformations.
There is an evident forgetful functor $\mathcal{M} \to \mathfrak{K}$, and it is straightforward to check that it preserves initial objects in the following sense: if $M$ is an initial object in $\mathcal{M}$ and $K$ is an object in $\mathfrak{K}$, then the hom-category $\mathfrak{K} (U M, K)$ is equivalent to $\mathbf{1}$.
In particular, $\mathfrak{K}$ has an initial object in the sense of bicategories. However, $\mathfrak{K}$ does not have an initial object in the sense of ordinary categories.
• Ok. This 'initial bicategory', is it equivalent to something that we are very familiar with from 'ordinary' mathematics? (And is there a reference for the results that you mention, so that I can spend a bit more time on it?) Oct 19, 2015 at 15:09
• I do not have an explicit description of the initial object of $\mathcal{M}$. The results I mention are covered in any textbook account of locally presentable categories – for instance, Locally presentable and accessible categories. Oct 19, 2015 at 16:12
There can't be such a category, because if there were then it would have a unique limit/colimit preserving functor $F$ to any category with all finite limits and colimits. But such a category can have an automorphism $G$ that fixes no object, and so $GF$ is a different limit/colimit preserving functor to that category.
• This argument shows that there isn't a initial object in the sense of ordinary categories. But there are other ways to interpret the question... Oct 19, 2015 at 14:42 | 933 | 3,841 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2023-50 | latest | en | 0.944201 |
https://numberworld.info/27301 | 1,582,788,289,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146665.7/warc/CC-MAIN-20200227063824-20200227093824-00355.warc.gz | 470,795,581 | 3,764 | # Number 27301
### Properties of number 27301
Cross Sum:
Factorization:
Divisors:
1, 23, 1187, 27301
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
6aa5
Base 32:
ql5
sin(27301)
0.53105088848627
cos(27301)
0.84733992815041
tan(27301)
0.62672709126957
ln(27301)
10.214678610539
lg(27301)
4.4361785549722
sqrt(27301)
165.23014252854
Square(27301)
### Number Look Up
Look Up
27301 (twenty-seven thousand three hundred one) is a amazing number. The cross sum of 27301 is 13. If you factorisate the figure 27301 you will get these result 23 * 1187. 27301 has 4 divisors ( 1, 23, 1187, 27301 ) whith a sum of 28512. 27301 is not a prime number. The number 27301 is not a fibonacci number. 27301 is not a Bell Number. 27301 is not a Catalan Number. The convertion of 27301 to base 2 (Binary) is 110101010100101. The convertion of 27301 to base 3 (Ternary) is 1101110011. The convertion of 27301 to base 4 (Quaternary) is 12222211. The convertion of 27301 to base 5 (Quintal) is 1333201. The convertion of 27301 to base 8 (Octal) is 65245. The convertion of 27301 to base 16 (Hexadecimal) is 6aa5. The convertion of 27301 to base 32 is ql5. The sine of the number 27301 is 0.53105088848627. The cosine of 27301 is 0.84733992815041. The tangent of 27301 is 0.62672709126957. The square root of 27301 is 165.23014252854.
If you square 27301 you will get the following result 745344601. The natural logarithm of 27301 is 10.214678610539 and the decimal logarithm is 4.4361785549722. that 27301 is great figure! | 593 | 1,655 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2020-10 | latest | en | 0.753246 |
https://tsfa.co/omni-compound-interest-calculator-40 | 1,679,983,625,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00273.warc.gz | 661,271,079 | 5,841 | # Omni compound interest calculator
n = m × t where n is the total number of compounding intervals i = r / m where i is the periodic interest rate (rate over the compounding intervals) For the matter of simplicity, in
## Compound Interest Calculator
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x (t) = x_0 \cdot \left (1 + \frac {r} {100}\right)^t x(t) = x0 ⋅ (1 + 100r)t is used when there is a quantity with an initial value, x_0 x0, that changes over time, t, with a constant rate of
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Math can be tough, but with a little practice, anyone can master it! | 435 | 1,861 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2023-14 | latest | en | 0.901806 |
https://learn.careers360.com/school/question-please-solve-r-d-sharma-class-12-chapter-differentiation-exercise-10-point-3-question-1-maths-textbook-solution/?question_number=1.0 | 1,716,296,017,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058484.54/warc/CC-MAIN-20240521122022-20240521152022-00466.warc.gz | 305,232,916 | 40,116 | #### Please solve R.D.Sharma class 12 chapter Differentiation exercise 10.3 question 1 maths textbook solution.
Answer $\frac{d y}{d x}=\frac{2}{\sqrt{1-x^{2}}}$
Hint:
$\begin {array} {l}\cos ^{-1}(\cos \theta)=\theta\ \ if \ \ \theta \varepsilon[0, \pi]\\\\ \cos ^{-1}(\cos \theta)=-\theta \ \ if \ \ \theta \varepsilon[-\pi, 0] \end{array}$
Given:
$\cos ^{-1}\left\{2 x \sqrt{1-x^{2}}\right\}, \frac{1}{\sqrt{2}}
Solution:
$\begin {array}{ll} Lets\: y=\cos ^{-1}\left\{2 x \sqrt{1-x^{2}}\right\} \\\\ Lets \: \mathrm{x}=\cos \theta \Rightarrow \theta=\cos ^{-1} \mathrm{x} \\\\ Now \ \ y=\cos ^{-1}\left\{2 \cos \theta \sqrt{1-\cos ^{2} \theta}\right\}\end{array}$
$\begin {array}{ll} Using \therefore \cos ^{2} \theta+\sin ^{2} \theta=1,2 \sin \theta \cos \theta=\sin 2 \theta\\\\ \mathrm{y}=\cos ^{-1}\left\{2 \cos \theta \sqrt{\sin ^{2} \theta}\right\}\\\\ \end{array}$
$\begin {array}{ll} y=\cos ^{-1}(2 \cos \theta \sin \theta]\\\\ y=\cos ^{-1}(\sin 2 \theta)\\\\ \therefore \cos \left(\frac{\pi}{2}-\theta\right) \Rightarrow \sin \theta\\\\ y=\cos ^{-1}\left(\cos \left(\frac{\pi}{2}-2 \theta\right)\right)\\\\ \end{array}$
Now by considering the limits,
$\begin{array}{l} \frac{1}{\sqrt{2}}-2 \theta>-\frac{\pi}{2}\\\\ \Rightarrow \frac{\pi}{2}>\frac{\pi}{2}-2 \theta>\frac{\pi}{2}-\frac{\pi}{2} \end{array}$
Therefore,
$\begin{array}{l} y=\cos ^{-1}\left(\cos \left(\frac{\pi}{2}-2 \theta\right)\right)\\\\ y=\cos ^{-1}\left(\cos \left(\frac{\pi}{2}-2 \theta\right)\right)\\\\ y=\left(\frac{\pi}{2}-2 \theta\right) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{array}$ $\left\{\cos ^{-1}(\cos \theta)=\theta\right\}$
$y=\frac{\pi}{2}-2 \cos ^{-1} x$
$\text { if } \theta \varepsilon[0, \pi]$
Differentiating with Respect to x, we get
$\begin{array}{l} \frac{d y}{d x}=\frac{d}{d x}\left(\frac{\pi}{2}-2 \cos ^{-1} x\right)\\\\ \therefore \frac{d}{d x}\left(\cos ^{-1} x\right) \Rightarrow \frac{-1}{\sqrt{1-x^{2}}}\\\\ \therefore \frac{\mathrm{d}}{\mathrm{dx}} \text { (constant) }=0\\\\ \frac{d y}{d x}=0-2\left(\frac{-1}{\sqrt{1-x^{2}}}\right)\\\\ \frac{d y}{d x}=\frac{2}{\sqrt{1-x^{2}}} \end{array}$ | 860 | 2,213 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2024-22 | latest | en | 0.299984 |
http://www.akyildizinsaat.org/what-is-actually-a-projectile-physics-what-if-the-laws-of-physics-have-been-unique/ | 1,603,614,334,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107888402.81/warc/CC-MAIN-20201025070924-20201025100924-00497.warc.gz | 108,486,188 | 8,220 | # What is often a projectile physics? What in the event the laws of physics have been different?
What if the laws of physics have been the identical as what we know, that is all we need to have to understand to turn buy essay online out to be an engineer or to turn into a medical doctor.
Let us get started by describing what we are discussing here. A projectile is definitely an object that is definitely fired with the intent of striking a target. The laws of physics can’t be changed to have an effect on these projectiles simply because their motions, once they hit a target, have a non-linear acceleration as a result of gravity and air resistance. So, regardless of what law of physics you use to analyze these events, there will often be an equation to become applied to calculate the force necessary to move these objects.
Laws may be described in several ways. For instance, we can say that the force expected to move an object with the laws of physics might be proportional to the square on the distance traveled and towards the time it requires the object to travel the distance. Considering that these laws are constants, however, we are able to apply Newton’s second law for the events and calculate the force to complete so.
buy buy essay online essay online
However, we need to keep in mind that this is only an approximation of your laws of motion. There are many regions where Newton’s second law doesn’t hold correct.
It is true that kinetic power systems, for instance those discovered in stars, starships, and satellites usually are not governed by the identical laws as human beings. So, this equation is only valuable for figuring out the force that has to be exerted on a target to result in it to move. But, because the forces needed to accelerate a physique inside a particular direction (known as the instantaneous force) would be different to get a human physique and to get a rocket or satellite, the equations can still be employed to calculate the force needed to accelerate a human physique.
These equations are often generally known as “First-Order Equations”. buy essay online They may be made use of to calculate the force needed to move objects, which include a person, in 1 distinct path when it comes to the initial order linear equations. So long as the needed values are identified for the acceleration, the resulting force have to be determined.
But what when the laws of physics were distinct? If the laws of physics have been various, then you could calculate the force required to accelerate a rocket towards the speed of light. This is a aim of lots of scientists, due to the fact this would give us the answer to the query, what’s a projectile physics? What in the event the laws of physics were the same as what we know, that is all we need to understand to turn into an engineer or to turn out to be a doctor.
For instance, suppose that the laws of physics did not contain a force that is certainly proportional towards the square with the distance traveled. Instead, suppose that the equations expected to describe the motion of a bullet in flight necessary that the initial velocity is around exactly the same as the speed of light. This would imply that the speed of a bullet for the duration of a quick pursuit could be a great deal more rapidly than light, producing the projectile substantially much easier to intercept.
The power required to accelerate a projectile will be a function of the air resistance brought on by friction. If there have been no air resistance, then it would be feasible to calculate the power needed to accelerate a rocket towards the speed of light.
Assuming the particles accelerated at the identical speeds, there will be some further velocity, permitting for the extra power and time that would be required to achieve exactly the same acceleration. This would also be correct if the laws of physics didn’t include the linear acceleration aspect that applies to human bodies.
So, what exactly is a projectile physics? What in the event the laws of physics had been distinctive?What when the laws of physics had been the same as what we know, that may be all we have to have to know to turn into an engineer or to come to be a medical professional. | 835 | 4,242 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2020-45 | latest | en | 0.965684 |
https://www.includehelp.com/c/sum-of-an-array-using-multithreading-in-c-cpp.aspx?ref=rp | 1,722,859,606,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640447331.19/warc/CC-MAIN-20240805114033-20240805144033-00287.warc.gz | 634,638,097 | 51,865 | # Sum of an array using Multithreading in C/C++
In this tutorial, we will learn how we can use multithreading while summing up an array in C/C++? By Radib Kar Last updated : April 20, 2023
In my last article, we saw details about why we need multithreading and how can we use multithreading in C/C++? Here, is a live example for you which will show you the application of multithreading, a real-world program with the proper implementation and also analysis if we had any improvements.
## Problem Statement
The problem statement is pretty simple.
Sum up an array of 10000000 elements where are elements are consecutive natural numbers
That means it's basically finding the sum of 1 to 1,00,00,000
## 1. Naïve approach to find sum of an array
Firstly we see the naïve program without threading
```#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define MAX_NO_OF_ELEMENTS 10000000
static long long int sum;
static int arr[MAX_NO_OF_ELEMENTS];
int main()
{
for (int i = 0; i < MAX_NO_OF_ELEMENTS; i++)
arr[i] = i + 1;
clock_t start, end;
double cpu_time_taken;
start = clock();
//summing
for (int i = 0; i < MAX_NO_OF_ELEMENTS; i++)
sum += arr[i];
end = clock();
cpu_time_taken = ((double)(end - start)) / CLOCKS_PER_SEC;
printf("Total sum: %lld\n", sum);
printf("Time taken to sum all the numbers are %lf\n", cpu_time_taken);
return 0;
}
```
Output:
## 2. Multithreading approach to find sum of an array
Now here we go with the multithreading implementation. Let us first see the code then we will discuss.
```#include <stdio.h>
#include <stdlib.h>
#define MAX_NO_OF_ELEMENTS 10000000
typedef struct arg_data {
} arg_data;
//shared data on which threads will work concurrently
//array which will be summed
static int arr[MAX_NO_OF_ELEMENTS];
//sum variable that will store the total sum
static long long int sum;
void* worker_sum(void* arg)
{
int startpart = endpart - (MAX_NO_OF_ELEMENTS / MAX_NO_OF_THREADS);
printf("Here we will sum %d to %d\n", arr[startpart], arr[endpart - 1]);
long long int current_thread_sum = 0;
for (int i = startpart; i < endpart; i++) {
}
return NULL;
}
int main()
{
//let the array consists of first MAX_NO_OF_ELEMENTS integers,
//1 to MAX_NO_OF_ELEMENTS
for (int i = 0; i < MAX_NO_OF_ELEMENTS; i++)
arr[i] = i + 1;
//argument data to send in worker functions
//total number of threads we will create
clock_t start, end;
double cpu_time_taken;
start = clock();
}
//joining the threads one by one
for (int i = 1; i <= MAX_NO_OF_THREADS; i++)
end = clock();
cpu_time_taken = ((double)(end - start)) / CLOCKS_PER_SEC;
printf("All child threads has finished their works...\n");
printf("Total sum: %lld\n", sum);
printf("Time taken to sum all the numbers are %lf\n", cpu_time_taken);
return 0;
}
```
Since we covered the threading part in our pre-requisite article, I am not bringing those staffs again like how to create a thread, what is thread join and all.
So what we have done here is we created a thread pool with a suitable number of threads. I have created a thread pool with 4 threads. If you have more number of CPU cores, you can increase the number, but in that case, be sure to change the worker function to(to adjust what part a thread is supposed to read)
Now we want that each thread will find the sum of a particular part only.
Since we have 4 threads and total array size is 10000000,
We want that
1st thread will sum 1 to 2500000
2nd thread will sum 2500001 to 5000000
3rd thread will sum 5000001 to 7500000
4th thread will sum 7500001 to 10000000
That's why we have passed the thread number as an argument to the worker function with help of a struct and the range of numbers to sum for a thread is
```endpart=(thread_number)*(MAX_NO_OF_ELEMENTS/MAX_NO_OF_THREADS);
```
This ensures that, though the threads will run concurrently, it will never break the data integrity, as it will never sum the same number multiple times. This has ensured that though the thread work on a shared data resource, they are independent of each other.
Finally, we have joined all the child threads before printing the final sum(total sum)
Below is the output for multiple runs. Now why I have run multiple times that I will cover on the conclusion part of this article.
## Comparison Between the naïve implementation & multithreading implementation
Below is the output of two runs where the first one is the naïve one and the second one is the multithreaded implementation one.
While comparing I have commented out the printing additional statements in the worker function as that would take extra time otherwise.
Now, you can see that the naïve run has taken lesser time. So it seems that multithreading is not at all useful as it has taken more time. But that's not the case. Multithreading has additional timing because of the worker function call, thread creation, thread joining etc. Since, here the program was pretty simple and didn't require high computation, function calls, that's why the naïve implementation has taken less time here. But it won't be the case if you do high computations, such as operating on any large data where you don't need execution to happen sequentially. In such cases, multithreading is extremely useful as you can utilize your CPU properly.
Now let's come to the conclusion. Why I have made multiple runs? I have made multiple runs to show you the concurrency. If you see all three outputs minutely, you will find that the order of the printed statements are different which proves that the execution of threads has been different every time. It depends on your OS, how it manages thread execution. But one thing is common is the final result. That is because we have made sure that all child thread will finish their executions before printing the final sum. We are not bothered about the order of thread execution and they are independent, we just want all threads to finish their execution before we print our sum.
The output of run1:
Here, thread 2 has been started first, then 1, then 3 and then 4
The output of run2:
Here the thread starting order is 1, 2, 3, 4
The output of run 3:
Here, you can see that thread 2, 3, 4 has started all together, that's what we say concurrency.
Student's Section
Subscribe | 1,509 | 6,253 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-33 | latest | en | 0.694909 |
https://quizgecko.com/learn/exploring-the-wonders-of-algebra-a-deep-dive-zyajgx | 1,725,708,193,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650826.4/warc/CC-MAIN-20240907095856-20240907125856-00727.warc.gz | 466,863,084 | 45,637 | 12 Questions
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# Exploring the Wonders of Algebra: A Deep Dive into Mathematical Symbols and Equations
Created by
@DeliciousSaturn
mathematics
equations
operations
### Variables in algebra are represented by ______
<p>letters</p> Signup and view all the answers
### The rules of algebra allow us to simplify, combine, and solve algebraic expressions and ______
<p>equations</p> Signup and view all the answers
### The distributive property states that the product of a sum is equal to the sum of the ______
<p>products</p> Signup and view all the answers
### Systems of linear equations consist of two or more equations with the same ______
<p>variables</p> Signup and view all the answers
### Algebraic methods such as substitution, elimination, and ______ are used to solve these systems
<p>graphing</p> Signup and view all the answers
### Substitution involves replacing one variable with an expression derived from another ______
<p>equation</p> Signup and view all the answers
### Algebra is a foundational tool in mathematics and has numerous applications in ______, engineering, and technology
<p>science</p> Signup and view all the answers
### Algebra is used in economics to model market behavior and analyze demand and supply ______
<p>curves</p> Signup and view all the answers
### Higher-level courses in algebra, such as abstract algebra, linear algebra, and number theory, build upon the foundation established in elementary ______
<p>algebra</p> Signup and view all the answers
## Exploring the Wonders of Math: A Deep Dive into Algebra
Algebra, a branch of mathematics that deals with symbols and their relationships, is a powerful tool for understanding and solving problems. In this article, we'll delve into the beauty and importance of algebra, revealing its role in shaping our mathematical worldview and its applications in everyday life.
### The Essence of Algebra
Algebra began as a means to solve systems of linear equations, which involve two or more equations that must be satisfied simultaneously. Algebraic expressions are built from numbers, variables, and operations such as addition, subtraction, multiplication, and division. These expressions are manipulated using rules of algebra to solve for unknown variables.
### The Language of Algebra
As in any language, algebra has a vocabulary and grammar. The fundamental elements of algebra are numbers, variables, and operations. Variables are represented by letters, such as x, y, or z, and are used to represent unknown values. Algebraic equations and inequalities are constructed using variables, constants, and operations.
### The Rules of Algebra
Algebraic manipulations follow a set of rules. These rules allow us to simplify, combine, and solve algebraic expressions and equations. For example, the order of operations dictates the order in which we perform operations within an expression. The distributive property states that the product of a sum is equal to the sum of the products.
### Solving Systems of Linear Equations
Systems of linear equations consist of two or more equations with the same variables. Algebraic methods such as substitution, elimination, and graphing are used to solve these systems. Substitution involves replacing one variable with an expression derived from another equation, while elimination methods involve manipulating equations to remove one variable. Graphing methods involve plotting points to find the intersection of lines.
### Applications of Algebra
Algebra is a foundational tool in mathematics, and it has numerous applications in science, engineering, and technology. For instance, algebra is used in economics to model market behavior and analyze demand and supply curves. It also plays a crucial role in biology to describe the relationships between variables, such as population growth or chemical reactions. In physics, algebraic equations are used to analyze motion, energy, and forces.
### Algebra in Higher Levels of Mathematics
Algebraic concepts and methods are not confined to elementary algebra. Higher-level courses in algebra, such as abstract algebra, linear algebra, and number theory, build upon the foundation established in elementary algebra. Abstract algebra, for example, deals with the properties and behavior of algebraic structures such as groups, rings, and fields. Linear algebra, on the other hand, focuses on systems of linear equations and the properties of vectors and matrices.
### Conclusion
Algebra is a powerful tool for understanding and solving problems. It is a foundational subject in mathematics that has numerous applications in science, engineering, technology, and higher-level mathematics courses. With its set of rules, symbols, and operations, algebra allows us to simplify and manipulate complex expressions and equations, making it a vital tool in our mathematical toolbox.
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## Description
Delve into the beauty and importance of algebra, its role in shaping our mathematical worldview, and its applications in everyday life. Learn about algebraic expressions, equations, rules, and methods for solving systems of linear equations. Explore the diverse applications of algebra in various fields and its significance in higher levels of mathematics.
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· 阅读 15948
## 什么是组合
function compose(...fns){
//忽略
}
// compose(f,g)(x) === f(g(x))
// compose(f,g,m)(x) === f(g(m(x)))
// compose(f,g,m)(x) === f(g(m(x)))
// compose(f,g,m,n)(x) === f(g(m(n(x))))
//···
## 应用 compose 函数
let n = '3.56';
let data = parseFloat(n);
let result = Math.round(data); // =>4 最终结果
compose函数改写：
let n = '3.56';
let number = compose(Math.round,parseFloat);
let result = number(n); // =>4 最终结果
let splitIntoSpaces = str => str.split(' ');
let count = array => array.length;
let countWords = compose(count,splitIntoSpaces);
let result = countWords('hello your reading about composition'); // => 5
## 开发中组合的用处
let str = 'jspool'
//先转成大写，然后逆序
function fn(str) {
let upperStr = str.toUpperCase()
return upperStr.split('').reverse().join('')
}
fn(str) // => "LOOPSJ"
"jspool" => ["J","S","P","O","O","L"]
let str = 'jspool'
function stringToUpper(str) {
return str.toUpperCase()
}
function stringReverse(str) {
return str.split('').reverse().join('')
}
let toUpperAndReverse = compose(stringReverse, stringToUpper)
let result = toUpperAndReverse(str) // "LOOPSJ"
let str = 'jspool'
function stringToUpper(str) {
return str.toUpperCase()
}
function stringReverse(str) {
return str.split('').reverse().join('')
}
function stringToArray(str) {
return str.split('')
}
let toUpperAndArray = compose(stringToArray, stringToUpper)
let result = toUpperAndArray(str) // => ["J","S","P","O","O","L"]
let str = 'jspool'
function stringToUpper(str) {
return str.toUpperCase()
}
function stringReverse(str) {
return str.split('').reverse().join('')
}
function getThreeCharacters(str){
return str.substring(0,3)
}
function stringToArray(str) {
return str.split('')
}
let toUpperAndGetThreeAndArray = compose(stringToArray, getThreeCharacters,stringToUpper)
let result = toUpperAndGetThreeAndArray(str) // => ["J","S","P"]
## 实现组合
// compose(f,g)(x) === f(g(x))
// compose(f,g,m)(x) === f(g(m(x)))
// compose(f,g,m)(x) === f(g(m(x)))
// compose(f,g,m,n)(x) === f(g(m(n(x))))
//···
function compose(f,g){
return function(x){
return f(g(x));
}
}
function compose(f,g,m){
return function(x){
return f(g(m(x)));
}
}
function compose(...fns){
return function(x){
//···
}
}
function compose(...fns){
return function(x){
return fns.reduceRight(function(arg,fn){
return fn(arg);
},x)
}
}
## 实现管道
compose的数据流是从右至左的，因为最右侧的函数首先执行，最左侧的函数最后执行！
function pipe(...fns){
return function(x){
return fns.reduce(function(arg,fn){
return fn(arg);
},x)
}
}
## 写在最后
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http://metamath.tirix.org/mpests/funcringcsetcALTV2lem6.html | 1,713,778,191,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818105.48/warc/CC-MAIN-20240422082202-20240422112202-00880.warc.gz | 18,264,507 | 2,670 | Metamath Proof Explorer
Theorem funcringcsetcALTV2lem6
Description: Lemma 6 for funcringcsetcALTV2 . (Contributed by AV, 15-Feb-2020) (New usage is discouraged.)
Ref Expression
Hypotheses funcringcsetcALTV2.r ${⊢}{R}=\mathrm{RingCat}\left({U}\right)$
funcringcsetcALTV2.s ${⊢}{S}=\mathrm{SetCat}\left({U}\right)$
funcringcsetcALTV2.b ${⊢}{B}={\mathrm{Base}}_{{R}}$
funcringcsetcALTV2.c ${⊢}{C}={\mathrm{Base}}_{{S}}$
funcringcsetcALTV2.u ${⊢}{\phi }\to {U}\in \mathrm{WUni}$
funcringcsetcALTV2.f ${⊢}{\phi }\to {F}=\left({x}\in {B}⟼{\mathrm{Base}}_{{x}}\right)$
funcringcsetcALTV2.g ${⊢}{\phi }\to {G}=\left({x}\in {B},{y}\in {B}⟼{\mathrm{I}↾}_{\left({x}\mathrm{RingHom}{y}\right)}\right)$
Assertion funcringcsetcALTV2lem6 ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\wedge {H}\in \left({X}\mathrm{RingHom}{Y}\right)\right)\to \left({X}{G}{Y}\right)\left({H}\right)={H}$
Proof
Step Hyp Ref Expression
1 funcringcsetcALTV2.r ${⊢}{R}=\mathrm{RingCat}\left({U}\right)$
2 funcringcsetcALTV2.s ${⊢}{S}=\mathrm{SetCat}\left({U}\right)$
3 funcringcsetcALTV2.b ${⊢}{B}={\mathrm{Base}}_{{R}}$
4 funcringcsetcALTV2.c ${⊢}{C}={\mathrm{Base}}_{{S}}$
5 funcringcsetcALTV2.u ${⊢}{\phi }\to {U}\in \mathrm{WUni}$
6 funcringcsetcALTV2.f ${⊢}{\phi }\to {F}=\left({x}\in {B}⟼{\mathrm{Base}}_{{x}}\right)$
7 funcringcsetcALTV2.g ${⊢}{\phi }\to {G}=\left({x}\in {B},{y}\in {B}⟼{\mathrm{I}↾}_{\left({x}\mathrm{RingHom}{y}\right)}\right)$
8 1 2 3 4 5 6 7 funcringcsetcALTV2lem5 ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\right)\to {X}{G}{Y}={\mathrm{I}↾}_{\left({X}\mathrm{RingHom}{Y}\right)}$
9 8 3adant3 ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\wedge {H}\in \left({X}\mathrm{RingHom}{Y}\right)\right)\to {X}{G}{Y}={\mathrm{I}↾}_{\left({X}\mathrm{RingHom}{Y}\right)}$
10 9 fveq1d ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\wedge {H}\in \left({X}\mathrm{RingHom}{Y}\right)\right)\to \left({X}{G}{Y}\right)\left({H}\right)=\left({\mathrm{I}↾}_{\left({X}\mathrm{RingHom}{Y}\right)}\right)\left({H}\right)$
11 fvresi ${⊢}{H}\in \left({X}\mathrm{RingHom}{Y}\right)\to \left({\mathrm{I}↾}_{\left({X}\mathrm{RingHom}{Y}\right)}\right)\left({H}\right)={H}$
12 11 3ad2ant3 ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\wedge {H}\in \left({X}\mathrm{RingHom}{Y}\right)\right)\to \left({\mathrm{I}↾}_{\left({X}\mathrm{RingHom}{Y}\right)}\right)\left({H}\right)={H}$
13 10 12 eqtrd ${⊢}\left({\phi }\wedge \left({X}\in {B}\wedge {Y}\in {B}\right)\wedge {H}\in \left({X}\mathrm{RingHom}{Y}\right)\right)\to \left({X}{G}{Y}\right)\left({H}\right)={H}$ | 1,189 | 2,628 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-18 | latest | en | 0.353637 |
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Unformatted text preview: . . . , 0, where k = index (λ). T H • Construct a basis B for N (A − λI). Starting with any basis Sk−1 for Mk−1 (see p. 211), sequentially extend Sk−1 with sets Sk−2 , Sk−3 , . . . , S0 such that Sk−1 is a basis for Mk−1 , Sk−1 ∪ Sk−2 is a basis for Mk−2 , Sk−1 ∪ Sk−2 ∪ Sk−3 is a basis for Mk−3 , IG R etc., until a basis B = Sk−1 ∪ Sk−2 ∪ · · · ∪ S0 = {b1 , b2 , . . . , bt } for M0 = N (A − λI) is obtained (see Example 7.7.3 on p. 582). • Y P Build a Jordan chain on top of each eigenvector b ∈ B. i For each eigenvector b ∈ Si , solve (A − λI) x = b (a necessarily consistent system) for x , and construct a Jordan chain on top of b by setting O C i P = (A − λI) x i−1 (A − λI) x · · · (A − λI) x x (i+1)×n . Each such P corresponds to one Jordan block J (λ) in the Jordan segment J(λ) associated with λ. The first column in P is an eigenvector, and subsequent columns are generalized eigenvectors of increasing order. • Copyright c 2000 SIAM If all such P ’s for a given λj ∈ σ (A) = {λ1 , λ2 , . . . , λs } are put in a matrix Pj , and if P = P1 | P2 | · · · | Ps , then P is a nonsingular matrix such that P−1 AP = J = diag (J(λ1 ), J(λ2 ), . . . , J(λs )) is in Jordan form as described on p. 590. Buy online from SIAM http://www.ec-securehost.com/SIAM/ot71.html Buy from AMAZON.com 7.8 Jordan Form http://www.amazon.com/exec/obidos/ASIN/0898714540 595 Example 7.8.3 Caution! Not every basis for N (A − λI) can be used to build Jordan chains associated with an eigenvalue λ ∈ σ (A) . For example, the Jordan form of ⎛ It is illegal to print, duplicate, or distribute this material Please report violations to [email protected] 3 A = ⎝ −4 −4 0 1 0 ⎞ 1 −2 ⎠ −1 ⎛ is 11 ⎝0 1 J= 0 0 ⎞ 0 0⎠ 1 because σ (A) = {1} and index (1) = 2. Consequently, if P = [ x1 | x2 | x3 ] is a nonsingular matrix such that P−1 AP = J, then the derivation beginning on p. 593 leading to (7.8.5) shows that {x1 , x2...
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http://weather.org/singer/5more12.htm | 1,513,183,756,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948529738.38/warc/CC-MAIN-20171213162804-20171213182804-00545.warc.gz | 309,265,400 | 2,075 | The two rays with the dotted lines hit the center points accurately and set the basis for the 12 cu The other rays were drawn with dashed lines, since they are not close hits. The dashed and dotted lines will be used in the remainder of the circumferential charts to distinguish between good hits and fair hits.
The approximate points indicated by the dashed lines on this chart seem to detract from its quality, but before you jump to any hasty conclusions, let us take another look at the phenomenon of longitudinal glide reflection. By careful inspection, you will see that #58 and #88 are on opposite sides of the ray line. Likewise, #26 and #42 lie on opposite sides of their common ray. And the same can be said for #12 and the obscure #14, and for the two obscure points #7 and #8. These dashed lines that are approximate hits, really represent average positions between two or more points. This then gives added significance to this symmetry pattern since it also uses some average positions. The preceding charts were examples of simple symmetry, whereas now, I have introduced a clear cut example of complexity which involves glide symmetry. You can now go back to the previous charts and find many other examples of glide reflection which I have not pointed out specifically.
### 155
This chart demonstrates two different rings. The inner ring is based on the fundamental units of 11 cu and 6 cu, while 12 cu and 18 cu are multiples of 6 cu. The outer ring, made up of the points #46, #37, #60, and #79, has been drawn to show that it has the fundamental of 11 cu, which is a continuation of 11 cu in the inner ring.
### 156
All the angles are divisible by the main symmetry element of 4. There is a balance left and right of bilateral symmetry around the 16 cu between #72 and #39.
### 157
The main symmetry element is 13 cu, followed by 5 cu and its multiples, plus one 14 cu. The hard core of this chart was established with #79, #80, #76, #40, and #51. The rest of the rays were drawn as a matter of interest. Point #48 seems to fit.
### 158
Here, again, we have bilateral symmetry with the 4 cu between #76 and #63 as the center piece.
### 159
This pattern involves the symmetry elements of 8 cu and 10 cu. | 511 | 2,233 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2017-51 | latest | en | 0.959503 |
https://metanumbers.com/26647 | 1,601,413,157,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402088830.87/warc/CC-MAIN-20200929190110-20200929220110-00622.warc.gz | 502,211,466 | 7,423 | ## 26647
26,647 (twenty-six thousand six hundred forty-seven) is an odd five-digits prime number following 26646 and preceding 26648. In scientific notation, it is written as 2.6647 × 104. The sum of its digits is 25. It has a total of 1 prime factor and 2 positive divisors. There are 26,646 positive integers (up to 26647) that are relatively prime to 26647.
## Basic properties
• Is Prime? Yes
• Number parity Odd
• Number length 5
• Sum of Digits 25
• Digital Root 7
## Name
Short name 26 thousand 647 twenty-six thousand six hundred forty-seven
## Notation
Scientific notation 2.6647 × 104 26.647 × 103
## Prime Factorization of 26647
Prime Factorization 26647
Prime number
Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 26647 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 10.1904 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 26,647 is 26647. Since it has a total of 1 prime factor, 26,647 is a prime number.
## Divisors of 26647
2 divisors
Even divisors 0 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 26648 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 13324 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 163.239 Returns the nth root of the product of n divisors H(n) 1.99992 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 26,647 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 26,647) is 26,648, the average is 13,324.
## Other Arithmetic Functions (n = 26647)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 26646 Total number of positive integers not greater than n that are coprime to n λ(n) 26646 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2924 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 26,646 positive integers (less than 26,647) that are coprime with 26,647. And there are approximately 2,924 prime numbers less than or equal to 26,647.
## Divisibility of 26647
m n mod m 2 3 4 5 6 7 8 9 1 1 3 2 1 5 7 7
26,647 is not divisible by any number less than or equal to 9.
## Classification of 26647
• Arithmetic
• Prime
• Deficient
### Expressible via specific sums
• Polite
• Non-hypotenuse
• Prime Power
• Square Free
## Base conversion (26647)
Base System Value
2 Binary 110100000010111
3 Ternary 1100112221
4 Quaternary 12200113
5 Quinary 1323042
6 Senary 323211
8 Octal 64027
10 Decimal 26647
12 Duodecimal 13507
20 Vigesimal 36c7
36 Base36 kk7
## Basic calculations (n = 26647)
### Multiplication
n×i
n×2 53294 79941 106588 133235
### Division
ni
n⁄2 13323.5 8882.33 6661.75 5329.4
### Exponentiation
ni
n2 710062609 18921038342023 504188908699886881 13435121850125885718007
### Nth Root
i√n
2√n 163.239 29.8687 12.7765 7.67591
## 26647 as geometric shapes
### Circle
Diameter 53294 167428 2.23073e+09
### Sphere
Volume 7.92563e+13 8.92291e+09 167428
### Square
Length = n
Perimeter 106588 7.10063e+08 37684.5
### Cube
Length = n
Surface area 4.26038e+09 1.8921e+13 46154
### Equilateral Triangle
Length = n
Perimeter 79941 3.07466e+08 23077
### Triangular Pyramid
Length = n
Surface area 1.22986e+09 2.22987e+12 21757.2
## Cryptographic Hash Functions
md5 cc65a7dd40f9de3463468921203d2177 fe51b61830043fa0ff272078bd20ab73bb81b481 c9794c6f1e88987c53933b72e6892299a3cbf5d37cc401c35f74e2ae162841d0 d8d8a11b006a79449e4637fc2c5e012c592d776d3208a50fe95a887a36fa66fcc187433f96b60fc8d81f146f4f998dccb054ed444db51791dbf17c712a272530 3cee6727ce36a977dff3b66e3ab0254cf56fc9fd | 1,428 | 4,139 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2020-40 | longest | en | 0.82624 |
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Week 2 Lecture Notes
# Week 2 Lecture Notes - Announcements Finish Reading Chapter...
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Announcements - Finish Reading Chapter 6 (if you have not done so), Begin reading Ch.7, sections 7.1 - 7.3 - Finish the Ch. 6 assigned problems: 1, 5, 10, 13, 17, 23, 27, 29, 32, 38, 46, 50, 61, 65, 72, 73, 80, 85, 103, 114 - Attend SECTION today & tomorrow! Sections D09 and C09 are open for enrollment (currently half-filled). Helproom opens at 4 pm today! Prof. Crowell’s Office Hours: Mon 1-3 PM, Tues 12-2 PM (3221 Urey Hall) - Continue to visit the Course Website on WebCT for updates (e.g. all of Ch.6 handouts available). - Buy a Remote Transmitter from the UCSD Bookstore if you do not already have one. We will be using the old style “IR” clickers. We will begin using them in class on Wednesday. Ro-vibrational Spectroscopy E total = E rot + E vib The rotational levels are closely spaced compared to the vibrational levels (with a separation of 2 hcB(J+1) ). For CO, the rotational constant B = 1.93 cm -1 , E/hc = BJ(J+1), and kT = 69.4 cm -1 at 100K. Hence, several rotational levels are populated even at 100K, and increasingly more as the temperature is raised.
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Δ U (I 2 ) = Δ U translation + Δ U rotation + … Δ U vibration Δ U (I 2 ) = 3/2 nR Δ T + nR Δ T + … nR Δ T C V = Δ U / Δ T C V,m = Δ U / (n Δ T) C V,m = C V,m (trans) + C V,m (rot) + … C V,m (vib) C V,m = 3/2 R + R + … R C V,m (2 I atoms) = 2 C V,m (translation, I atom) = 2 (3/2 R) = 3 R Heat Capacity for Atoms and Molecules N = # of atoms
Types of Processes Isothermal = Constant Temperature with corresponding changes in Pressure, Volume, and with Heat added or removed. Isobaric = Constant Pressure with corresponding changes in Volume, Temperature, and with Heat added or removed.
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SurfaceAreaOfPyramidUsingNet_Module.docx
# Finding the Surface Area of Pyramids Using Nets
Unit 6: Geometry
Lesson 24 of 37
## Big Idea: No made up numbers! (At least during the heart of the lesson).
Print Lesson
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Standards:
Subject(s):
Math, volume (3-D Geom), Geometry, surface area, circumference (Determining Measurements), measuring with rulers, pyramid, pi, circles, 7th grade
55 minutes
### Grant Harris
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https://www.neetprep.com/question/42747-force-FKyixj-K-positive-constant-acts-particle-movingin-xyplane-Starting-origin-particle-taken-along-thepositive-xaxis-point--parallel-yaxis-pointa-total-work-done-force-F-particles-Ka-Ka-Ka-Ka/55-Physics--WorkEnergy-Power/680-WorkEnergy-Power | 1,596,738,203,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439737019.4/warc/CC-MAIN-20200806180859-20200806210859-00490.warc.gz | 704,339,404 | 73,608 | A force $\mathbit{F}=-K\left(y\mathbit{i}+x\mathbit{j}\right)$ (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is
(1) $-2K{a}^{2}$
(2) $2K{a}^{2}$
(3) $-K{a}^{2}$
(4) $K{a}^{2}$
Concept Questions :-
Work done by variable force
High Yielding Test Series + Question Bank - NEET 2020
Difficulty Level:
If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is
(1) $\frac{1}{2}mgR$
(2) 2 mgR
(3) mgR
(4) $\frac{1}{4}mgR$
Concept Questions :-
Gravitational Potential energy
High Yielding Test Series + Question Bank - NEET 2020
Difficulty Level:
A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then
(1) Lorry will come to rest in a shorter distance
(2) Car will come to rest in a shorter distance
(3) Both come to rest in a same distance
(4) None of the above
Concept Questions :-
Concept of work
High Yielding Test Series + Question Bank - NEET 2020
Difficulty Level:
A particle free to move along the x-axis has potential energy given by $U\left(x\right)=k\left[1-{e}^{-{x}^{2}}\right]$ for $-\infty \le x\le +\infty$, where k is a positive constant of appropriate dimensions. Then
(1) At point away from the origin, the particle is in unstable equilibrium
(2) For any finite non-zero value of x, there is a force directed away from the origin
(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin
(4) For small displacements from x = 0, the motion is simple harmonic
Concept Questions :-
Potential energy: Relation with force
High Yielding Test Series + Question Bank - NEET 2020
Difficulty Level:
The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to
(1) $\sqrt{m}$
(2) Independent of m
(3) $1/\sqrt{m}$
(4) m
Concept Questions :-
Concept of work
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An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is
(1) mg
(2) $mg\left(1-\frac{h}{d}\right)$
(3) $mg\left(1+\frac{h}{d}\right)$
(4) $mg{\left(1+\frac{h}{d}\right)}^{2}$
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Gravitational Potential energy
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A body is moving along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
(1) t1/2
(2) t3/4
(3) t3/2
(4) t2
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Power
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A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time t1 as it hits the bat and time t2 when it touches the ground
(1)
(2)
(3)
(4)
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Work-Energy theorem
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The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is -
(1) 20 ergs
(2) 60 ergs
(3) 70 ergs
(4) 700 ergs
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The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is-
(1) 0.1 N/cm
(2) 5 N/cm
(3) 0.3 N/cm
(4) 1 N/cm
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how to set air infiltration under 50 pa pressure
I am doing a passive house model, the required airtightness is less than 0.6 ACH at 50 pa difference. In Opensutdio, in space infiltration design flow rate rates, i can set 0.6 air changes per hour but the question is how to set 50 Pascal pressure difference?
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You will need to convert the 0.6ACH50 value to a value at "natural pressure" conditions.
There are several ways to do this, of varying speed and accuracy.
What is typically done in residential calculations is to use a correction factor, known as an "n-factor" or "LBL factor" (after Lawerence Berkeley Lab, where it was developed) to convert your air change rate at 50 pascals (ACH50) to an air change rate at natural pressure (ACHnat).
ACHnat = ACH50/n
The n-factor comes from a series of corrections, based on climate zone (temperature influence), the number of stories (stack effect influence), and how exposed the building is (wind influence). Here is a table for looking up the n-factor for U.S. locations:
If you would like a more rigorous approach, you can derive the factor for your application by doing an hourly calculation with local weather data, similar to how the n-factors were determined above, or do a full airflow-network model in CONTAM or related pressure-network software. Consult the ASHRAE Handbook of Fundamentals chapter on Infiltration and Ventilation for equations on residential infiltration (16.24 in ASHRAE HOF 2017).
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Thanks for your comment! So if the n-factor is 10, then the air infiltration rate is 0.06 ACHnat?
( 2017-09-12 07:28:48 -0500 )edit
That is correct. If you have multiple spaces in the model, I would suggest calculating the total infiltration rate (cfm or m3/s), then dividing that by the exterior facade area (walls+roof) and assigning that in your model as a flow rate per exterior facade area. That way, infiltration is modeled in spaces proportional to their exterior surface area.
( 2017-09-12 12:27:47 -0500 )edit
Matt - what is the source for your table of n-Factors above? Thanks!
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2020-11-03, 09:06 #1 sweety439 Nov 2016 26×3×13 Posts Type of primes in various bases 1. Permutable prime 1.1. Largest permutable prime in base n (repunit primes excluded) written in base 10 for 3<=n<=36: (since no such primes exist for base 2) (conjectured) 7, 53, 3121, 211, 1999, 3803, 6469, 991, 161047, 19793, 16477, 24907, 683437, 3547, 67853, 80273, 94109, 72421, 148639, 182537, 228953, 9967, 358069, 17467, 99929, 21943, 369319, 26981, 23580569, 1048571, 1037657, 1012369, 1271117, 1367687 1.2. Largest permutable prime in base n (repunit primes excluded) written in base n for 3<=n<=36: (since no such primes exist for base 2) (conjectured) 21, 311, 44441, 551, 5554, 7333, 8777, 991, AAAA7, B555, 7666, 9111, D7777, DDB, DDD6, DDDB, DDD2, 9111, G111, H333, IIIB, H77, MMMJ, PLL, 5222, RRJ, F444, TTB, PGGGG, VVVR, SSS5, PPPJ, TMMM, TBBB 1.3. Length of largest permutable prime in base n (repunit primes excluded) for 3<=n<=36: (since no such primes exist for base 2) (conjectured) 2, 3, 5, 3, 4, 4, 4, 3, 5, 4, 4, 4, 5, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 5, 4, 4, 4, 4, 4 1.4. Number of permutable primes in base n (repunit primes excluded) for 2<=n<=36: (conjectured) 2. Left-truncatable prime 2.1. Largest left-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for base 2) 23, 4091, 7817, 4836525320399, 817337, 14005650767869, 1676456897, 357686312646216567629137, 2276005673, 13092430647736190817303130065827539, 812751503, 615419590422100474355767356763, 34068645705927662447286191, 1088303707153521644968345559987, 13563641583101, 571933398724668544269594979167602382822769202133808087, 546207129080421139, 1073289911449776273800623217566610940096241078373, 391461911766647707547123429659688417, 33389741556593821170176571348673618833349516314271, 116516557991412919458949, 10594160686143126162708955915379656211582267119948391137176997290182218433, 8211352191239976819943978913, 12399758424125504545829668298375903748028704243943878467, 10681632250257028944950166363832301357693, 720639908748666454129676051084863753107043032053999738835994276213, 4300289072819254369986567661, ?, 645157007060845985903112107793191, 1131569863270120248974817136287838489359936416046975582122661310411, 924039815258046855588818237912726885772934968646554431, 982498935397824993800810311994840611581693708091339679644860318739434026149, 448739985000415097566502155600731235704288431019152509, ? 2.2. Largest left-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist for base 2) 212, 333323, 222232, 14141511414451435, 6642623, 313636165537775, 4284484465, 357686312646216567629137, A68822827, 471A34A164259BA16B324AB8A32B7817, CC4C8C65, D967CCD63388522619883A7D23, 6C6C2CE2CEEEA4826E642B, DBC7FBA24FE6AEC462ABF63B3, 6C66CC4CC83, AF93E41A586HE75A7HHAAB7HE12FG79992GA7741B3D, CIEG86GCEA2C6H, FC777G3CG1FIDI9I31IE5FFB379C7A3F6EFID, G8AGG2GCA8CAK4K68GEA4G2K22H, FFHALC8JFB9JKA2AH9FAB4I9L5I9L3GF8D5L5, IMMGM6C6IMCI66A4H, HMJEJFA3A71DID9MFMNFE3D3KJHA61KH92IFCA3LB8GF444FBB7AH, ME6OM6OECGCC24C6EG6D, L2K853AC9IC628859L93F7FLAM7L25EN3C3PC27, O2AKK6EKG844KAIA4MACK6C2ECAB, 5C9126C3PN6IRP5FPBMKA5LGBMO387R5IJLO54OFBFJL85, KCG66AGSCKEIASMCKKJ, ?, UUAUIKUC4UI6OCECI642SD, LFLHKUDGSP39SAAPAD9I9OLIOUOH6GV68OR8UMJ6LRUB, 6ISWQOIMIWC8OKQAIMKUQ24KO86WK2ASCEC5, U9WSWU4T672RCMFESU6B6FG99UNABPFOU2LIIUGTX1KABJBPV, E8KUSUKKQEQWEWCMIEOY46Q8888QOSAAYOJ, ? 2.3. Length of largest left-truncatable prime in base n for 3<=n<=36: (since no such primes exist for base 2) 3, 6, 6, 17, 7, 15, 10, 24, 9, 32, 8, 26, 22, 25, 11, 43, 14, 37, 27, 37, 17, 53, 20, 39, 28, 46, 19, (about 82 in theory), 22, 44, 36, 49, 35, (about 76 in theory) 2.4. Number of left-truncatable primes in base n for 2<=n<=36: 0, 3, 16, 15, 454, 22, 446, 108, 4260, 75, 170053, 100, 34393, 9357, 27982, 362, 14979714, 685, 3062899, 59131, 1599447, 1372, 1052029701, 10484, 7028048, 98336, 69058060, 3926, (about 16844070429770 in theory), 11314, 35007483, 2527304, 240423316, 607905, (about 1631331033450 in theory) 3. Right-truncatable prime 3.1. Largest right-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for base 2) 71, 191, 2437, 108863, 6841, 4497359, 1355840309, 73939133, 6774006887, 18704078369, 122311273757, 6525460043032393259, 927920056668659, 16778492037124607, 4928397730238375565449, 5228233855704101657, 3013357583408354653, 1437849529085279949589, 101721177350595997080671, 185720479816277907890970001, 158208158913013692383, 192747244030905257036482742599289, 11360039924980123824119977, 522764314648992960422987767, 106521223483392113109841556843, 467437774672035454997088263971, 18980691336146397055451904000521, 206971354022501468249535515240921, 403878995374635723531460715056361, 9813093725765026702961210138094949, 10174889780995609522983172669668593, 18085876810004448001794542893991790487, 9520817609816167868579578513867491007, 8723727825272063982605771015871962141 3.2. Largest right-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist for base 2) 2122, 2333, 34222, 2155555, 25642, 21117717, 3444224222, 73939133, 29668286AA, 375BB5B515, B6C2CA8A8A, 2DD35B9D399395B3D, 72424E42EEE8E, 3B9BF319BD51FF, 5G4CEE8EC688CAC86G, DH17HB7BBD75BDB, 3EC8GI8GICIEG8C, 23HBH9D19HH9JDDJ9, 3824A4GGA4AG82KKA8, 5H975FFLLJF3HL3F33F3, DEK6ICCE8EE2K26, 3B5J511H5NJNN55B7JDBNN7H, JCMIIIEIIOIC4EIGO2, HJ1FHN97JF9P7PFFJ19, 2DMMKQEMAM4884QMAEAG2, 5953R9JHJ5PFF3R3H3D9N, 3K6QOO6682O4AG4GG6Q82C, JNHJ77DDNT7THDD177HD7B, JC642UIS2S8GOQUSKMII2A, 7HT59VF3PDRRJ7PD3371RB5, 3WEK8QAGQW8GW4E4KWGEAA2, 35X5FPF5R7XBXD9LRB1BRXXVT, T6CGG4G68I4MC26GCOYYCWCC, DZJZJPDDP7J55ZNPPZ71PD7H 3.3. Length of largest right-truncatable prime in base n for 3<=n<=36: (since no such primes exist for base 2) 4, 4, 5, 7, 5, 8, 10, 8, 10, 10, 10, 17, 13, 14, 18, 15, 15, 17, 18, 20, 15, 24, 18, 19, 21, 21, 22, 22, 22, 23, 23, 25, 24, 24 3.4. Number of right-truncatable primes in base n for 2<=n<=36: 0, 4, 7, 14, 36, 19, 68, 68, 83, 89, 179, 176, 439, 373, 414, 473, 839, 1010, 1577, 2271, 2848, 1762, 3376, 5913, 6795, 6352, 10319, 5866, 14639, 13303, 19439, 29982, 38956, 39323, 58857 4. Minimal prime 4.1. Largest minimal prime in base n written in base 10 for 2<=n<=36: 3, 13, 5, 3121, 5209, 2801, 76695841, 811, 66600049, 29156193474041220857161146715104735751776055777, 388177921, 13^32020*8+183, 105424857819287798806418819113233738918727566030978473259776662287591943095417282958456246916612161, 436635814641280043127962407363407208906111673434962498607709751248805460292422544779495998033626489944124062146459306989397233, 16^3544*9+145, ?, 249069897374447078426903207266791381270529, ?, (20^449*16-2809)/19, ?, 22^763*20+7041, (23^800873*106-7)/11, 973767003942195520947294504280890002680537875404412883659428819153939518991719953852457999342229586282557076411687300474817686178175693329, ?, ?, ?, ?, ?, 30^1023*12+1, ?, ?, ?, ?, ?, ? 4.2. Largest minimal prime in base n written in base n for 2<=n<=36: 11, 111, 11, 44441, 40041, 11111, 444444441, 1101, 66600049, 444444444444444444444444444444444444444444441, AA000001, 8032017111, 40000000000000000000000000000000000000000000000000000000000000000000000000000000000049, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, 90354291, ?, GG0000000000000000000000000000001, ?, G44799, ?, K0760EC1, 9E800873, M666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661, ?, ?, ?, ?, ?, C010221, ?, ?, ?, ?, ?, ? 4.3. Length of largest minimal prime in base n for 2<=n<=36: 2, 3, 2, 5, 5, 5, 9, 4, 8, 45, 8, 32021, 86, 107, 3545, (≥111334), 33, (≥110986), 449, (≥479150), 764, 800874, 100, (≥136967), (≥8773), (≥109006), (≥94538), (≥174240), 1024, (≥9896), (≥9750), (≥9961), (≥9377), (≥9599), (≥3935) 4.4. Number of minimal primes in base n for 2<=n<=36: (assuming the conjecture in https://mersenneforum.org/showpost.p...&postcount=675 is true) 2, 3, 3, 8, 7, 9, 15, 12, 26, 152, 17, 228, 240, 100, 483, 1280, 50, 3463, 651, 2601, 1242, 6021, 306, (17608 or 17609), 5664, 17215, 5784, (57296 or 57297), 220, (79199 ~ 79206), (45266 ~ 45283), (57708 or 57709), (56487 ~ 56490), (182392 or 182393), 6297 Last fiddled with by sweety439 on 2020-11-05 at 13:55
2020-11-03, 09:26 #2 sweety439 Nov 2016 249610 Posts 5. Repunit prime [it is conjectured that there are infinitely many repunit primes in base n, if n is not perfect power] 5.1. Smallest repunit prime in base n written in base 10 for 2<=n<=36 (0 if no such primes exist) 3, 13, 5, 31, 7, 2801, 73, 0, 11, 50544702849929377, 13, 30941, 211, 241, 17, 307, 19, 109912203092239643840221, 421, 463, 23, 292561, 601, 0, 321272407, 757, 29, 732541, 31, 917087137, 0, 1123, 2458736461986831391, (35^313-1)/34, 37 5.2. Smallest repunit prime in base n written in base n for 2<=n<=36 (0 if no such primes exist) 11, 111, 11, 111, 11, 11111, 111, 0, 11, 11111111111111111, 11, 11111, 111, 111, 11, 111, 11, 1111111111111111111, 111, 111, 11, 11111, 111, 0, 1111111, 111, 11, 11111, 11, 1111111, 0, 111, 1111111111111, 1313, 11 5.3. Length of smallest repunit prime in base n written in base n for 2<=n<=36 (0 if no such primes exist) 2, 3, 2, 3, 2, 5, 3, 0, 2, 17, 2, 5, 3, 3, 2, 3, 2, 19, 3, 3, 2, 5, 3, 0, 7, 3, 2, 5, 2, 7, 0, 3, 13, 313, 2 6. Weakly prime [it is conjectured that there are infinitely many weakly primes in base n for all n>=2] 6.1. Smallest weakly prime in base n written in base 10 for 2<=n<=36 127, 2, 373, 83, 28151, 223, 6211, 2789, 294001, 3347, 20837899, 4751, 6588721, 484439, 862789, 10513, 2078920243, 10909, 169402249, 2823167, 267895961, 68543, 1016960933671, 181141, 121660507, 6139219, 11646280537, 488651, ?, 356479, ?, ?, ?, 22549349, ? 6.2. Smallest weakly prime in base n written in base n for 2<=n<=36 1111111, 2, 11311, 313, 334155, 436, 14103, 3738, 294001, 2573, 6B8AB77, 2216, C371CD, 9880E, D2A45, 2267, 3723DE91, 1B43, 2CIF5C9, EAHFB, 27LD613, 5ED3, 95HCJA8C7, BEKG, A65P47, BEOBD, O4JHPIH, K111, ?, BTTA, ?, ?, ?, F0WM4, ? 6.3. Length of smallest weakly prime in base n written in base n for 2<=n<=36 7. Two-sided prime 7.1. Largest two-sided prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for base 2) 23, 11, 67, 839, 37, 1867, 173, 739397, 79, 105691, 379, 37573, 647, 3389, 631, 202715129, 211, 155863, 1283, 787817, 439, 109893629, 577, 4195880189, 1811, 14474071, 379, 21335388527, 2203, 1043557, 2939, 42741029, 2767, 50764713107 7.2. Largest two-sided prime in base n written in base n for 3<=n<=36: (since no such primes exist for base 2) 212, 23, 232, 3515, 52, 3513, 212, 739397, 72, 511B7, 232, D99B, 2D2, D3D, 232, 5H511HB, B2, J9D3, 2J2, 37LFJ, J2, DJ5BD5, N2, DF3LL97, 2D2, NF9N3, D2, T7TTH7H, 292, VR35, 2N2, VXF73, 292, NBJZZBN 7.3. Length of largest two-sided prime in base n for 3<=n<=36: (since no such primes exist for base 2) 3, 2, 3, 4, 2, 4, 3, 6, 2, 5, 3, 4, 3, 3, 3, 7, 2, 4, 3, 5, 2, 6, 2, 7, 3, 5, 2, 7, 3, 4, 3, 5, 3, 7 7.4. Number of two-sided primes in base n 0, 2, 3, 5, 9, 7, 22, 8, 15, 6, 35, 11, 37, 17, 22, 12, 69, 12, 68, 18, 44, 13, 145, 16, 47, 20, 77, 13, 291, 15, 89, 27, 74, 20, 241 8. Circular prime (data only available for bases <=12) 8.1. Largest circular prime in base n (repunit primes excluded) written in base 10 for 3<=n<=12: (since no such primes exist for base 2) (conjectured) 7, 1013, 3121, 211, 13143449029, 16244441, 4717103, 999331, 378470237117827, 2894561 8.2. Largest circular prime in base n (repunit primes excluded) written in base n for 3<=n<=12: (since no such primes exist for base 2) (conjectured) 21, 33311, 44441, 551, 643464321244, 75757331, 8778575, 999331, AA657365177398, B77115 8.3. Length of largest circular prime in base n (repunit primes excluded) for 3<=n<=12: (since no such primes exist for base 2) (conjectured) 2, 5, 5, 3, 12, 8, 7, 6, 14, 6 8.4. Number of circular primes in base n (repunit primes excluded) for 2<=n<=12: (conjectured) Last fiddled with by sweety439 on 2020-11-04 at 12:33
2020-11-03, 09:29 #3 sweety439 Nov 2016 9C016 Posts 9. Full-reptend prime [it is conjectured that there are infinitely many full-reptend primes in base n, if n is not square] Base//Full-reptend primes 2: 3, 5, 11, 13, 19, 29, 37, 53, 59, 61, 67, 83, 101, 107, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757, 773, 787, 797, 821, 827, 829, 853, 859, 877, 883, 907, 941, 947, 1019, 1061, 1091, 1109, 1117, 1123, 1171, 1187, 1213, 1229, 1237, 1259, 1277, 1283, 1291, 1301, 1307, 1373, 1381, 1427, 1451, 1453, 1483, 1493, 1499, 1523, 1531, 1549, 1571, 1619, 1621, 1637, 1667, 1669, 1693, 1733, 1741, 1747, 1787, 1861, 1867, 1877, 1901, 1907, 1931, 1949, 1973, 1979, 1987, 1997, 2027, 2029, 2053, 2069, 2083, 2099, 2131, 2141, 2213, 2221, 2237, 2243, 2267, 2269, 2293, 2309, 2333, 2339, 2357, 2371, 2389, 2437, 2459, 2467, 2477, 2531, 2539, 2549, 2557, 2579, 2621, 2659, 2677, 2683, 2693, 2699, 2707, 2741, 2789, 2797, 2803, 2819, 2837, 2843, 2851, 2861, 2909, 2939, 2957, 2963, 3011, 3019, 3037, 3067, 3083, 3187, 3203, 3253, 3299, 3307, 3323, 3347, 3371, 3413, 3461, 3467, 3469, 3491, 3499, 3517, 3533, 3539, 3547, 3557, 3571, 3581, 3613, 3637, 3643, 3659, 3677, 3691, 3701, 3709, 3733, 3779, 3797, 3803, 3851, 3853, 3877, 3907, 3917, 3923, 3931, 3947, 3989, 4003, 4013, 4019, 4021, 4091, 4093, ... 3: 2, 5, 7, 17, 19, 29, 31, 43, 53, 79, 89, 101, 113, 127, 137, 139, 149, 163, 173, 197, 199, 211, 223, 233, 257, 269, 281, 283, 293, 317, 331, 353, 379, 389, 401, 449, 461, 463, 487, 509, 521, 557, 569, 571, 593, 607, 617, 631, 641, 653, 677, 691, 701, 739, 751, 773, 797, 809, 811, 821, 823, 857, 859, 881, 907, 929, 941, 953, 977, 1013, 1039, 1049, 1061, 1063, 1087, 1097, 1109, 1123, 1193, 1217, 1229, 1231, 1277, 1279, 1291, 1301, 1327, 1361, 1373, 1409, 1423, 1433, 1447, 1459, 1481, 1483, 1493, 1553, 1567, 1579, 1601, 1613, 1627, 1637, 1663, 1697, 1699, 1709, 1721, 1723, 1733, 1747, 1831, 1889, 1901, 1913, 1949, 1951, 1973, 1987, 1997, 1999, 2011, 2069, 2081, 2083, 2129, 2141, 2143, 2153, 2213, 2237, 2239, 2273, 2309, 2311, 2333, 2347, 2357, 2371, 2381, 2393, 2417, 2467, 2477, 2503, 2539, 2549, 2609, 2633, 2647, 2657, 2659, 2683, 2693, 2707, 2719, 2729, 2731, 2741, 2753, 2767, 2777, 2789, 2801, 2837, 2861, 2897, 2909, 2957, 2969, 3041, 3089, 3137, 3163, 3209, 3257, 3259, 3271, 3307, 3329, 3331, 3389, 3391, 3413, 3449, 3461, 3463, 3533, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3617, 3643, 3677, 3701, 3727, 3761, 3797, 3821, 3823, 3833, 3917, 3919, 3929, 3931, 3943, 3989, 4001, 4003, 4013, 4027, 4049, 4073, ... 4: (none) 5: 2, 3, 7, 17, 23, 37, 43, 47, 53, 73, 83, 97, 103, 107, 113, 137, 157, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 317, 347, 353, 373, 383, 397, 433, 443, 463, 467, 503, 523, 547, 557, 563, 577, 587, 593, 607, 613, 617, 647, 653, 673, 677, 683, 727, 743, 757, 773, 787, 797, 857, 863, 877, 887, 907, 937, 947, 953, 967, 977, 983, 1013, 1033, 1093, 1097, 1103, 1153, 1163, 1187, 1193, 1213, 1217, 1223, 1237, 1277, 1283, 1307, 1327, 1367, 1373, 1427, 1433, 1483, 1487, 1493, 1523, 1543, 1553, 1567, 1583, 1607, 1613, 1637, 1663, 1667, 1693, 1697, 1733, 1747, 1777, 1787, 1823, 1847, 1877, 1907, 1913, 1933, 1987, 1993, 1997, 2003, 2017, 2027, 2053, 2063, 2083, 2087, 2113, 2143, 2153, 2203, 2207, 2213, 2237, 2243, 2267, 2273, 2293, 2297, 2333, 2347, 2357, 2377, 2383, 2393, 2417, 2423, 2437, 2447, 2467, 2473, 2477, 2503, 2543, 2557, 2617, 2633, 2647, 2657, 2663, 2677, 2683, 2687, 2693, 2713, 2753, 2767, 2777, 2797, 2833, 2837, 2843, 2887, 2897, 2903, 2917, 2927, 2957, 2963, 3023, 3037, 3067, 3083, 3163, 3167, 3187, 3203, 3217, 3253, 3307, 3323, 3343, 3347, 3373, 3407, 3413, 3433, 3463, 3467, 3517, 3527, 3533, 3547, 3557, 3583, 3593, 3607, 3613, 3617, 3623, 3643, 3673, 3677, 3697, 3767, 3793, 3797, 3803, 3833, 3847, 3863, 3907, 3917, 3923, 3943, 3947, 4003, 4007, 4013, 4027, 4057, 4073, 4093, ... 6: 11, 13, 17, 41, 59, 61, 79, 83, 89, 103, 107, 109, 113, 127, 131, 137, 151, 157, 179, 199, 223, 227, 229, 233, 251, 257, 271, 277, 347, 367, 373, 397, 401, 419, 443, 449, 467, 487, 491, 521, 563, 569, 587, 593, 613, 641, 659, 661, 683, 709, 733, 757, 761, 809, 823, 827, 829, 853, 857, 881, 929, 947, 953, 967, 971, 977, 991, 1019, 1039, 1049, 1063, 1069, 1091, 1097, 1117, 1163, 1187, 1193, 1213, 1217, 1237, 1259, 1279, 1283, 1289, 1303, 1307, 1327, 1361, 1381, 1409, 1423, 1427, 1429, 1433, 1451, 1471, 1481, 1499, 1523, 1543, 1549, 1553, 1567, 1601, 1619, 1621, 1663, 1667, 1669, 1759, 1789, 1811, 1831, 1861, 1879, 1889, 1907, 1913, 1979, 1999, 2027, 2029, 2053, 2081, 2099, 2129, 2143, 2153, 2221, 2243, 2267, 2269, 2273, 2293, 2297, 2389, 2393, 2411, 2417, 2437, 2441, 2459, 2503, 2531, 2551, 2557, 2579, 2609, 2633, 2657, 2699, 2729, 2749, 2767, 2777, 2791, 2797, 2801, 2819, 2843, 2887, 2897, 2917, 2939, 2963, 2969, 3011, 3041, 3061, 3079, 3083, 3089, 3109, 3137, 3203, 3209, 3229, 3251, 3253, 3257, 3271, 3299, 3301, 3319, 3323, 3329, 3347, 3371, 3391, 3449, 3463, 3467, 3469, 3491, 3517, 3539, 3583, 3593, 3617, 3659, 3709, 3733, 3761, 3779, 3803, 3823, 3833, 3847, 3853, 3929, 3943, 3947, 3967, 4001, 4019, 4049, 4073, 4091, 4093, ... 7: 2, 5, 11, 13, 17, 23, 41, 61, 67, 71, 79, 89, 97, 101, 107, 127, 151, 163, 173, 179, 211, 229, 239, 241, 257, 263, 269, 293, 347, 349, 359, 379, 397, 431, 433, 443, 461, 491, 499, 509, 521, 547, 577, 593, 599, 601, 631, 659, 677, 683, 733, 739, 743, 761, 773, 797, 823, 827, 857, 863, 907, 919, 929, 937, 941, 967, 991, 997, 1013, 1019, 1049, 1051, 1069, 1097, 1103, 1109, 1163, 1181, 1187, 1193, 1217, 1237, 1249, 1277, 1283, 1301, 1303, 1361, 1367, 1433, 1439, 1451, 1471, 1523, 1553, 1601, 1607, 1609, 1613, 1619, 1637, 1667, 1669, 1693, 1697, 1721, 1747, 1753, 1759, 1787, 1831, 1889, 1949, 1973, 1993, 2003, 2011, 2027, 2039, 2083, 2087, 2089, 2111, 2141, 2143, 2179, 2207, 2251, 2273, 2281, 2309, 2339, 2341, 2357, 2393, 2447, 2459, 2477, 2503, 2531, 2543, 2591, 2593, 2609, 2621, 2647, 2671, 2677, 2693, 2699, 2711, 2729, 2731, 2777, 2789, 2843, 2851, 2879, 2897, 2917, 2957, 2963, 3041, 3119, 3121, 3169, 3181, 3203, 3209, 3253, 3271, 3299, 3343, 3371, 3449, 3457, 3467, 3511, 3517, 3533, 3539, 3541, 3571, 3607, 3617, 3623, 3673, 3701, 3719, 3739, 3767, 3769, 3793, 3797, 3803, 3821, 3853, 3931, 3943, 3989, 4019, 4049, 4073, 4093, ... 8: 3, 5, 11, 29, 53, 59, 83, 101, 107, 131, 149, 173, 179, 197, 227, 269, 293, 317, 347, 389, 419, 443, 461, 467, 491, 509, 557, 563, 587, 653, 659, 677, 701, 773, 797, 821, 827, 941, 947, 1019, 1061, 1091, 1109, 1187, 1229, 1259, 1277, 1283, 1301, 1307, 1373, 1427, 1451, 1493, 1499, 1523, 1571, 1619, 1637, 1667, 1733, 1787, 1877, 1901, 1907, 1931, 1949, 1973, 1979, 1997, 2027, 2069, 2099, 2141, 2213, 2237, 2243, 2267, 2309, 2333, 2339, 2357, 2459, 2477, 2531, 2549, 2579, 2621, 2693, 2699, 2741, 2789, 2819, 2837, 2843, 2861, 2909, 2939, 2957, 2963, 3011, 3083, 3203, 3299, 3323, 3347, 3371, 3413, 3461, 3467, 3491, 3533, 3539, 3557, 3581, 3659, 3677, 3701, 3779, 3797, 3803, 3851, 3917, 3923, 3947, 3989, 4013, 4019, 4091, ... 9: 2 (no others) 10: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, 593, 619, 647, 659, 701, 709, 727, 743, 811, 821, 823, 857, 863, 887, 937, 941, 953, 971, 977, 983, 1019, 1021, 1033, 1051, 1063, 1069, 1087, 1091, 1097, 1103, 1109, 1153, 1171, 1181, 1193, 1217, 1223, 1229, 1259, 1291, 1297, 1301, 1303, 1327, 1367, 1381, 1429, 1433, 1447, 1487, 1531, 1543, 1549, 1553, 1567, 1571, 1579, 1583, 1607, 1619, 1621, 1663, 1697, 1709, 1741, 1777, 1783, 1789, 1811, 1823, 1847, 1861, 1873, 1913, 1949, 1979, 2017, 2029, 2063, 2069, 2099, 2113, 2137, 2141, 2143, 2153, 2179, 2207, 2221, 2251, 2269, 2273, 2297, 2309, 2339, 2341, 2371, 2383, 2389, 2411, 2417, 2423, 2447, 2459, 2473, 2539, 2543, 2549, 2579, 2593, 2617, 2621, 2633, 2657, 2663, 2687, 2699, 2713, 2731, 2741, 2753, 2767, 2777, 2789, 2819, 2833, 2851, 2861, 2887, 2897, 2903, 2909, 2927, 2939, 2971, 3011, 3019, 3023, 3137, 3167, 3221, 3251, 3257, 3259, 3299, 3301, 3313, 3331, 3343, 3371, 3389, 3407, 3433, 3461, 3463, 3469, 3527, 3539, 3571, 3581, 3593, 3607, 3617, 3623, 3659, 3673, 3701, 3709, 3727, 3767, 3779, 3821, 3833, 3847, 3863, 3943, 3967, 3989, 4007, 4019, 4051, 4057, 4073, 4091, ... 11: 2, 3, 13, 17, 23, 29, 31, 41, 47, 59, 67, 71, 73, 101, 103, 109, 149, 163, 173, 179, 197, 223, 233, 251, 277, 281, 293, 331, 367, 373, 383, 419, 443, 461, 463, 467, 487, 499, 557, 569, 587, 593, 599, 601, 613, 619, 643, 647, 673, 677, 683, 701, 719, 761, 769, 809, 821, 839, 853, 857, 863, 883, 937, 941, 947, 953, 971, 983, 991, 997, 1009, 1033, 1039, 1069, 1097, 1103, 1129, 1201, 1217, 1229, 1249, 1259, 1289, 1307, 1361, 1367, 1381, 1423, 1429, 1439, 1483, 1493, 1499, 1511, 1523, 1553, 1567, 1571, 1597, 1601, 1607, 1613, 1657, 1669, 1699, 1733, 1783, 1787, 1801, 1831, 1861, 1877, 1879, 1889, 1907, 1913, 1949, 1951, 1997, 2011, 2027, 2039, 2083, 2089, 2099, 2129, 2141, 2153, 2203, 2213, 2221, 2267, 2273, 2309, 2311, 2347, 2389, 2393, 2399, 2417, 2423, 2441, 2447, 2477, 2579, 2593, 2609, 2657, 2663, 2687, 2699, 2711, 2713, 2731, 2801, 2803, 2819, 2837, 2843, 2857, 2917, 2927, 2963, 2969, 2971, 3019, 3023, 3049, 3067, 3083, 3109, 3137, 3181, 3191, 3209, 3229, 3253, 3313, 3329, 3347, 3359, 3371, 3373, 3391, 3449, 3491, 3499, 3517, 3533, 3547, 3581, 3593, 3623, 3673, 3727, 3761, 3767, 3769, 3797, 3851, 3889, 3929, 3947, 3989, 4007, 4019, 4021, 4027, 4079, ... 12: 5, 7, 17, 31, 41, 43, 53, 67, 101, 103, 113, 127, 137, 139, 149, 151, 163, 173, 197, 223, 257, 269, 281, 283, 293, 317, 353, 367, 379, 389, 401, 449, 461, 509, 523, 547, 557, 569, 571, 593, 607, 617, 619, 631, 641, 653, 691, 701, 739, 751, 761, 773, 787, 797, 809, 821, 857, 881, 929, 953, 967, 977, 991, 1013, 1049, 1051, 1061, 1087, 1097, 1109, 1123, 1171, 1181, 1193, 1217, 1229, 1289, 1291, 1303, 1327, 1361, 1373, 1409, 1423, 1433, 1447, 1459, 1481, 1483, 1493, 1531, 1543, 1553, 1579, 1613, 1627, 1637, 1697, 1699, 1709, 1721, 1723, 1733, 1747, 1759, 1783, 1831, 1867, 1877, 1879, 1889, 1901, 1913, 1949, 1973, 1997, 1999, 2011, 2069, 2131, 2143, 2153, 2213, 2237, 2239, 2273, 2297, 2309, 2333, 2347, 2357, 2371, 2381, 2393, 2417, 2441, 2477, 2539, 2549, 2609, 2621, 2657, 2693, 2707, 2719, 2731, 2753, 2767, 2777, 2789, 2791, 2801, 2803, 2837, 2851, 2861, 2897, 2909, 2957, 2969, 3019, 3041, 3079, 3089, 3163, 3187, 3209, 3257, 3259, 3271, 3319, 3329, 3331, 3389, 3391, 3413, 3449, 3461, 3463, 3511, 3533, 3547, 3557, 3559, 3581, 3593, 3617, 3677, 3701, 3727, 3739, 3761, 3797, 3821, 3833, 3847, 3917, 3919, 3929, 3931, 3943, 3967, 3989, 4003, 4013, 4027, 4051, 4073, ... 13: 2, 5, 11, 19, 31, 37, 41, 47, 59, 67, 71, 73, 83, 89, 97, 109, 137, 149, 151, 167, 197, 227, 239, 241, 281, 293, 307, 317, 349, 353, 359, 379, 383, 397, 401, 431, 449, 457, 479, 487, 509, 541, 557, 577, 587, 593, 613, 617, 631, 643, 683, 691, 733, 743, 769, 773, 787, 811, 821, 827, 839, 863, 877, 929, 941, 947, 967, 977, 983, 1019, 1033, 1051, 1087, 1097, 1103, 1129, 1163, 1181, 1217, 1229, 1259, 1279, 1289, 1307, 1319, 1321, 1367, 1373, 1399, 1409, 1423, 1451, 1487, 1493, 1523, 1553, 1579, 1597, 1607, 1619, 1669, 1697, 1709, 1721, 1747, 1783, 1787, 1801, 1867, 1877, 1879, 1913, 1931, 1987, 1997, 2039, 2069, 2087, 2099, 2111, 2113, 2143, 2153, 2179, 2221, 2243, 2267, 2269, 2273, 2293, 2309, 2333, 2351, 2371, 2377, 2381, 2399, 2423, 2459, 2477, 2503, 2543, 2579, 2593, 2621, 2633, 2647, 2663, 2693, 2699, 2719, 2741, 2749, 2767, 2777, 2789, 2801, 2819, 2879, 2897, 2917, 2927, 2953, 2957, 2969, 2971, 3023, 3037, 3049, 3061, 3079, 3083, 3089, 3109, 3167, 3187, 3203, 3209, 3313, 3323, 3343, 3347, 3359, 3373, 3391, 3413, 3463, 3469, 3517, 3547, 3557, 3581, 3583, 3593, 3607, 3659, 3671, 3673, 3677, 3733, 3803, 3833, 3853, 3863, 3881, 3911, 3919, 3931, 3947, 3967, 3989, 4019, ... 14: 3, 17, 19, 23, 29, 53, 59, 73, 83, 89, 97, 109, 127, 131, 149, 151, 227, 239, 241, 251, 257, 263, 277, 283, 307, 313, 317, 353, 359, 373, 389, 419, 421, 431, 433, 467, 487, 521, 541, 557, 563, 587, 593, 599, 601, 613, 631, 643, 653, 701, 709, 743, 751, 757, 761, 769, 787, 821, 823, 857, 859, 863, 877, 881, 919, 929, 1031, 1049, 1087, 1091, 1093, 1097, 1103, 1117, 1123, 1153, 1193, 1213, 1217, 1229, 1249, 1259, 1291, 1303, 1307, 1361, 1367, 1373, 1427, 1433, 1439, 1453, 1471, 1489, 1493, 1531, 1549, 1553, 1571, 1583, 1601, 1607, 1627, 1663, 1697, 1699, 1709, 1721, 1733, 1753, 1789, 1831, 1867, 1871, 1877, 1889, 1901, 1907, 1931, 1933, 1979, 1993, 1997, 2039, 2053, 2069, 2087, 2089, 2099, 2111, 2113, 2131, 2143, 2203, 2207, 2237, 2243, 2267, 2269, 2273, 2281, 2371, 2393, 2411, 2423, 2437, 2441, 2447, 2543, 2549, 2579, 2593, 2609, 2617, 2659, 2671, 2741, 2777, 2797, 2819, 2837, 2879, 2897, 2909, 2927, 2939, 3001, 3041, 3061, 3083, 3109, 3119, 3169, 3209, 3221, 3229, 3271, 3301, 3307, 3323, 3331, 3343, 3413, 3433, 3449, 3457, 3491, 3499, 3511, 3547, 3557, 3581, 3607, 3613, 3617, 3623, 3637, 3643, 3659, 3677, 3719, 3733, 3767, 3779, 3847, 3917, 3923, 3943, 3947, 4003, 4013, 4049, 4073, 4091, ... 15: 2, 13, 19, 23, 29, 37, 41, 47, 73, 83, 89, 97, 101, 107, 139, 149, 151, 157, 167, 193, 199, 227, 263, 269, 271, 281, 313, 337, 347, 373, 379, 383, 389, 401, 433, 439, 449, 457, 461, 467, 499, 503, 509, 521, 563, 569, 577, 587, 613, 619, 631, 641, 647, 683, 691, 701, 733, 743, 751, 757, 809, 821, 827, 863, 881, 887, 919, 929, 947, 983, 1039, 1049, 1061, 1093, 1103, 1109, 1153, 1181, 1187, 1223, 1229, 1279, 1283, 1289, 1291, 1297, 1301, 1307, 1367, 1399, 1409, 1427, 1459, 1471, 1481, 1487, 1523, 1583, 1657, 1667, 1699, 1709, 1753, 1787, 1823, 1847, 1873, 1879, 1889, 1901, 1907, 1933, 1949, 1951, 1999, 2003, 2017, 2027, 2063, 2069, 2087, 2131, 2137, 2141, 2179, 2207, 2239, 2243, 2251, 2267, 2293, 2309, 2381, 2423, 2437, 2441, 2447, 2543, 2549, 2557, 2593, 2609, 2617, 2663, 2671, 2677, 2687, 2713, 2719, 2731, 2741, 2789, 2791, 2797, 2843, 2861, 2903, 2909, 2917, 2953, 2963, 2969, 3019, 3023, 3041, 3083, 3089, 3167, 3203, 3209, 3217, 3221, 3253, 3271, 3313, 3319, 3323, 3329, 3347, 3373, 3407, 3449, 3457, 3461, 3467, 3517, 3527, 3581, 3613, 3623, 3631, 3637, 3673, 3701, 3739, 3761, 3767, 3803, 3821, 3863, 3881, 3919, 3923, 3929, 3931, 3947, 3989, 4001, 4007, 4049, 4051, 4057, 4093, ... 16: (none) 17: 2, 3, 5, 7, 11, 23, 31, 37, 41, 61, 97, 107, 113, 131, 139, 167, 173, 193, 197, 211, 227, 233, 269, 277, 283, 311, 313, 317, 347, 367, 379, 401, 419, 431, 439, 449, 479, 487, 499, 503, 521, 547, 571, 607, 617, 641, 643, 653, 673, 677, 683, 691, 709, 719, 743, 751, 787, 809, 821, 823, 827, 839, 853, 857, 881, 887, 907, 911, 929, 941, 983, 997, 1009, 1013, 1049, 1051, 1091, 1117, 1129, 1151, 1153, 1163, 1187, 1193, 1201, 1217, 1229, 1297, 1319, 1367, 1433, 1439, 1451, 1493, 1499, 1523, 1553, 1567, 1601, 1609, 1621, 1627, 1637, 1669, 1693, 1697, 1723, 1847, 1877, 1901, 1907, 1931, 1949, 1979, 1999, 2011, 2029, 2063, 2069, 2081, 2111, 2113, 2153, 2207, 2213, 2251, 2267, 2273, 2309, 2339, 2357, 2383, 2411, 2417, 2441, 2459, 2477, 2521, 2539, 2543, 2557, 2579, 2621, 2647, 2657, 2659, 2663, 2693, 2713, 2749, 2777, 2819, 2879, 2887, 2897, 2917, 2953, 2963, 2969, 2999, 3019, 3023, 3037, 3083, 3089, 3121, 3167, 3169, 3191, 3203, 3253, 3257, 3259, 3301, 3359, 3371, 3373, 3389, 3407, 3457, 3461, 3491, 3529, 3533, 3539, 3581, 3593, 3677, 3701, 3733, 3767, 3769, 3779, 3797, 3803, 3847, 3881, 3907, 3917, 3947, 3967, 3989, 4001, 4007, 4019, 4049, 4051, 4057, 4073, ... 18: 5, 11, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 139, 149, 157, 163, 173, 179, 181, 197, 227, 251, 269, 277, 283, 293, 317, 347, 349, 379, 389, 397, 419, 421, 461, 467, 491, 509, 523, 541, 547, 557, 563, 571, 587, 613, 619, 653, 659, 661, 677, 683, 691, 701, 733, 739, 757, 773, 787, 797, 811, 821, 827, 853, 859, 877, 941, 947, 971, 1013, 1019, 1051, 1069, 1091, 1109, 1117, 1123, 1163, 1171, 1181, 1187, 1229, 1277, 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449, 463, 467, 479, 491, 499, 503, 509, 521, 569, 571, 587, 601, 619, 631, 641, 643, 647, 673, 677, 719, 727, 739, 773, 797, 829, 857, 877, 883, 919, 941, 947, 953, 967, 977, 1093, 1097, 1103, 1153, 1163, 1187, 1193, 1223, 1229, 1237, 1249, 1259, 1321, 1361, 1381, 1409, 1423, 1433, 1451, 1481, 1487, 1499, 1543, 1549, 1553, 1559, 1583, 1607, 1619, 1637, 1693, 1709, 1741, 1777, 1783, 1787, 1789, 1801, 1847, 1861, 1871, 1877, 1879, 1889, 1907, 1913, 1933, 1987, 1997, 1999, 2011, 2017, 2029, 2039, 2063, 2081, 2099, 2141, 2237, 2243, 2267, 2269, 2273, 2287, 2309, 2333, 2377, 2399, 2411, 2521, 2543, 2549, 2551, 2591, 2617, 2671, 2689, 2693, 2699, 2707, 2729, 2749, 2777, 2789, 2801, 2819, 2833, 2851, 2909, 2917, 2927, 2953, 2957, 2971, 2999, 3011, 3079, 3083, 3109, 3137, 3163, 3169, 3203, 3221, 3229, 3257, 3301, 3323, 3373, 3391, 3407, 3413, 3449, 3461, 3467, 3529, 3533, 3539, 3593, 3607, 3613, 3637, 3659, 3671, 3677, 3691, 3701, 3761, 3767, 3779, 3793, 3821, 3823, 3847, 3853, 3863, 3889, 3911, 3917, 3923, 3929, 3989, 4007, 4021, 4049, 4091, 4093, ... 20: 3, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 103, 107, 113, 137, 157, 163, 167, 173, 223, 227, 233, 257, 263, 277, 283, 293, 313, 317, 337, 347, 353, 367, 383, 397, 433, 443, 463, 467, 487, 503, 547, 557, 563, 587, 593, 607, 613, 647, 653, 673, 677, 683, 727, 743, 773, 797, 823, 853, 857, 863, 887, 907, 953, 977, 983, 1013, 1063, 1087, 1093, 1097, 1103, 1117, 1123, 1163, 1187, 1193, 1213, 1217, 1223, 1237, 1277, 1283, 1297, 1303, 1307, 1327, 1367, 1373, 1427, 1433, 1447, 1483, 1487, 1493, 1523, 1553, 1607, 1613, 1637, 1667, 1697, 1733, 1747, 1777, 1787, 1823, 1847, 1867, 1877, 1907, 1913, 1933, 1973, 1987, 1993, 1997, 2003, 2017, 2027, 2053, 2063, 2087, 2113, 2137, 2143, 2153, 2203, 2207, 2213, 2243, 2267, 2273, 2297, 2333, 2347, 2357, 2377, 2383, 2393, 2417, 2423, 2447, 2467, 2477, 2503, 2543, 2593, 2647, 2657, 2663, 2677, 2683, 2687, 2693, 2707, 2753, 2767, 2777, 2803, 2833, 2837, 2843, 2897, 2903, 2917, 2927, 2957, 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223, 227, 229, 233, 251, 257, 277, 281, 347, 353, 373, 397, 401, 419, 421, 443, 463, 467, 487, 491, 541, 563, 569, 587, 593, 607, 617, 641, 683, 709, 733, 751, 761, 809, 823, 829, 857, 877, 881, 929, 947, 953, 971, 977, 1019, 1039, 1049, 1063, 1069, 1087, 1091, 1097, 1163, 1187, 1193, 1213, 1217, 1231, 1237, 1259, 1279, 1283, 1289, 1307, 1327, 1361, 1409, 1423, 1427, 1429, 1433, 1447, 1453, 1471, 1499, 1523, 1553, 1567, 1571, 1601, 1619, 1663, 1667, 1693, 1697, 1721, 1741, 1787, 1789, 1811, 1889, 1907, 1913, 1931, 1951, 1979, 1999, 2003, 2027, 2053, 2099, 2129, 2143, 2153, 2239, 2243, 2267, 2273, 2293, 2297, 2311, 2339, 2393, 2411, 2417, 2437, 2441, 2459, 2503, 2551, 2557, 2579, 2609, 2633, 2647, 2657, 2677, 2699, 2719, 2729, 2749, 2753, 2767, 2777, 2791, 2797, 2819, 2843, 2887, 2897, 2917, 2939, 2963, 2969, 3037, 3041, 3061, 3083, 3089, 3137, 3203, 3209, 3229, 3251, 3257, 3271, 3299, 3301, 3323, 3329, 3347, 3371, 3449, 3463, 3467, 3469, 3491, 3539, 3541, 3559, 3583, 3593, 3617, 3637, 3659, 3709, 3727, 3761, 3779, 3803, 3823, 3833, 3851, 3877, 3919, 3923, 3929, 3943, 3947, 4001, 4019, 4021, 4049, 4073, ... 25: 2 (no others) 26: 3, 7, 29, 41, 43, 47, 53, 61, 73, 89, 97, 101, 107, 131, 137, 139, 157, 167, 173, 179, 193, 239, 251, 269, 271, 281, 283, 347, 353, 359, 373, 383, 389, 409, 419, 443, 449, 457, 463, 467, 479, 491, 563, 593, 617, 631, 653, 659, 701, 743, 761, 797, 829, 839, 863, 883, 929, 977, 983, 997, 1009, 1013, 1033, 1069, 1091, 1093, 1097, 1103, 1109, 1117, 1129, 1151, 1171, 1187, 1201, 1213, 1217, 1277, 1279, 1283, 1289, 1301, 1319, 1367, 1381, 1399, 1409, 1423, 1427, 1453, 1459, 1483, 1487, 1489, 1553, 1601, 1607, 1613, 1637, 1667, 1693, 1697, 1699, 1733, 1741, 1811, 1879, 1907, 1913, 1949, 1973, 1979, 2003, 2011, 2017, 2027, 2039, 2083, 2087, 2111, 2113, 2131, 2137, 2141, 2143, 2153, 2237, 2273, 2351, 2357, 2399, 2423, 2467, 2503, 2531, 2539, 2543, 2549, 2593, 2633, 2657, 2663, 2677, 2711, 2767, 2777, 2837, 2843, 2861, 2879, 2897, 2909, 2927, 2939, 2953, 2963, 3001, 3019, 3023, 3049, 3079, 3089, 3163, 3167, 3191, 3209, 3217, 3251, 3257, 3259, 3301, 3331, 3343, 3359, 3371, 3389, 3391, 3461, 3463, 3467, 3529, 3533, 3539, 3593, 3607, 3613, 3697, 3779, 3797, 3821, 3833, 3851, 3863, 3881, 3911, 3917, 3919, 3923, 4003, 4013, 4021, 4049, 4091, ... 27: 2, 5, 17, 29, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269, 281, 293, 317, 353, 389, 401, 449, 461, 509, 521, 557, 569, 593, 617, 641, 653, 677, 701, 773, 797, 809, 821, 857, 881, 929, 941, 953, 977, 1013, 1049, 1061, 1097, 1109, 1193, 1217, 1229, 1277, 1301, 1361, 1373, 1409, 1433, 1481, 1493, 1553, 1601, 1613, 1637, 1697, 1709, 1721, 1733, 1889, 1901, 1913, 1949, 1973, 1997, 2069, 2081, 2129, 2141, 2153, 2213, 2237, 2273, 2309, 2333, 2357, 2381, 2393, 2417, 2477, 2549, 2609, 2633, 2657, 2693, 2729, 2741, 2753, 2777, 2789, 2801, 2837, 2861, 2897, 2909, 2957, 2969, 3041, 3089, 3137, 3209, 3257, 3329, 3389, 3413, 3449, 3461, 3533, 3557, 3581, 3593, 3617, 3677, 3701, 3761, 3797, 3821, 3833, 3917, 3929, 3989, 4001, 4013, 4049, 4073, ... 28: 5, 11, 13, 17, 23, 41, 43, 67, 71, 73, 79, 89, 101, 107, 173, 179, 181, 191, 229, 257, 263, 269, 293, 313, 331, 347, 353, 359, 379, 397, 409, 431, 433, 443, 461, 463, 487, 491, 499, 509, 521, 571, 577, 593, 599, 659, 661, 677, 683, 733, 739, 743, 751, 769, 773, 797, 827, 829, 853, 857, 863, 881, 883, 907, 919, 929, 937, 941, 947, 967, 991, 997, 1013, 1019, 1031, 1049, 1069, 1087, 1097, 1103, 1109, 1153, 1163, 1181, 1187, 1193, 1217, 1277, 1283, 1301, 1321, 1367, 1433, 1439, 1489, 1499, 1523, 1553, 1583, 1601, 1607, 1609, 1613, 1619, 1637, 1663, 1667, 1669, 1693, 1697, 1741, 1753, 1759, 1787, 1871, 1889, 1949, 1973, 2003, 2011, 2027, 2029, 2039, 2089, 2111, 2113, 2141, 2143, 2161, 2179, 2207, 2251, 2273, 2309, 2311, 2357, 2393, 2423, 2441, 2447, 2459, 2477, 2503, 2531, 2543, 2591, 2609, 2617, 2621, 2671, 2683, 2693, 2699, 2711, 2729, 2731, 2777, 2789, 2843, 2861, 2879, 2897, 2917, 2927, 2957, 2963, 3011, 3019, 3037, 3041, 3067, 3119, 3181, 3187, 3203, 3209, 3271, 3299, 3319, 3343, 3347, 3371, 3433, 3449, 3457, 3461, 3467, 3533, 3539, 3541, 3607, 3617, 3623, 3673, 3701, 3709, 3769, 3793, 3797, 3803, 3821, 3847, 3851, 3877, 3907, 3943, 3989, 4019, 4049, 4073, ... 29: 2, 3, 11, 17, 19, 41, 43, 47, 73, 79, 89, 97, 101, 113, 127, 131, 137, 163, 191, 211, 229, 251, 263, 269, 293, 307, 311, 317, 331, 337, 359, 389, 409, 433, 443, 449, 461, 467, 479, 491, 503, 563, 569, 599, 601, 607, 653, 659, 677, 739, 743, 751, 769, 773, 797, 809, 827, 839, 853, 859, 887, 907, 911, 947, 971, 983, 997, 1013, 1033, 1063, 1087, 1091, 1117, 1123, 1129, 1163, 1181, 1187, 1201, 1229, 1237, 1249, 1279, 1291, 1297, 1303, 1307, 1319, 1361, 1373, 1409, 1429, 1433, 1439, 1447, 1453, 1471, 1481, 1487, 1489, 1493, 1511, 1523, 1549, 1583, 1597, 1607, 1609, 1613, 1667, 1693, 1697, 1709, 1721, 1723, 1759, 1777, 1787, 1867, 1877, 1931, 1933, 1951, 1999, 2003, 2011, 2027, 2069, 2099, 2129, 2143, 2207, 2243, 2251, 2273, 2293, 2309, 2339, 2347, 2351, 2357, 2381, 2393, 2399, 2417, 2447, 2467, 2473, 2477, 2531, 2579, 2591, 2593, 2657, 2671, 2689, 2699, 2707, 2711, 2741, 2753, 2767, 2801, 2803, 2857, 2861, 2879, 2897, 2903, 2917, 2939, 2999, 3001, 3089, 3169, 3209, 3217, 3221, 3251, 3323, 3343, 3347, 3433, 3449, 3463, 3469, 3491, 3499, 3511, 3517, 3527, 3557, 3581, 3593, 3617, 3623, 3637, 3671, 3673, 3691, 3701, 3727, 3733, 3739, 3767, 3797, 3889, 3917, 3923, 3929, 3947, 4013, 4019, 4049, 4079, 4091, ... 30: 11, 23, 41, 43, 47, 59, 61, 79, 89, 109, 131, 151, 167, 173, 179, 193, 197, 199, 251, 263, 281, 293, 307, 317, 349, 383, 419, 421, 433, 439, 449, 457, 491, 503, 521, 523, 541, 557, 569, 577, 641, 647, 653, 659, 673, 677, 743, 751, 761, 773, 787, 797, 809, 829, 863, 881, 887, 907, 919, 929, 937, 971, 983, 1013, 1019, 1021, 1033, 1039, 1049, 1069, 1091, 1103, 1223, 1231, 1361, 1367, 1373, 1399, 1409, 1429, 1451, 1471, 1481, 1483, 1487, 1493, 1499, 1549, 1571, 1583, 1601, 1607, 1613, 1619, 1627, 1637, 1657, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1811, 1823, 1831, 1847, 1861, 1867, 1873, 1877, 1889, 1931, 1973, 1979, 1987, 1993, 1997, 1999, 2017, 2029, 2063, 2081, 2087, 2099, 2129, 2137, 2203, 2207, 2213, 2237, 2269, 2311, 2333, 2339, 2341, 2347, 2357, 2377, 2389, 2411, 2423, 2441, 2447, 2459, 2467, 2473, 2477, 2531, 2543, 2551, 2579, 2593, 2609, 2617, 2663, 2683, 2687, 2693, 2699, 2713, 2729, 2749, 2801, 2803, 2819, 2837, 2857, 2903, 2927, 2939, 2953, 2957, 2969, 3023, 3041, 3061, 3079, 3089, 3163, 3167, 3181, 3209, 3229, 3251, 3271, 3299, 3313, 3329, 3407, 3413, 3433, 3449, 3457, 3491, 3511, 3527, 3533, 3539, 3547, 3557, 3559, 3623, 3659, 3677, 3697, 3709, 3761, 3767, 3779, 3793, 3797, 3863, 3881, 3907, 3917, 3919, 3929, 4001, 4003, 4007, 4013, 4019, 4021, 4049, 4057, ... 31: 2, 7, 17, 29, 47, 53, 59, 61, 67, 71, 73, 89, 107, 131, 137, 197, 227, 229, 241, 269, 277, 283, 307, 311, 313, 337, 353, 359, 379, 389, 401, 419, 431, 433, 439, 443, 449, 457, 461, 467, 479, 503, 509, 557, 563, 569, 599, 607, 673, 677, 683, 709, 727, 751, 757, 761, 773, 797, 809, 811, 821, 839, 881, 887, 907, 919, 929, 941, 971, 1009, 1013, 1021, 1039, 1049, 1051, 1063, 1087, 1097, 1103, 1109, 1151, 1153, 1163, 1181, 1187, 1193, 1201, 1223, 1259, 1277, 1279, 1297, 1303, 1307, 1327, 1399, 1423, 1427, 1451, 1453, 1459, 1481, 1523, 1549, 1553, 1559, 1583, 1619, 1669, 1697, 1787, 1801, 1823, 1831, 1847, 1867, 1877, 1879, 1907, 1913, 1931, 1949, 1997, 2003, 2069, 2087, 2089, 2137, 2161, 2203, 2213, 2239, 2267, 2269, 2293, 2297, 2309, 2339, 2377, 2393, 2417, 2423, 2441, 2459, 2467, 2473, 2539, 2543, 2551, 2557, 2591, 2617, 2621, 2633, 2657, 2663, 2671, 2693, 2699, 2707, 2711, 2741, 2749, 2767, 2789, 2801, 2887, 2903, 2909, 2939, 2957, 2963, 2969, 3023, 3037, 3041, 3079, 3083, 3119, 3121, 3137, 3167, 3203, 3253, 3271, 3313, 3319, 3329, 3331, 3361, 3407, 3413, 3433, 3491, 3511, 3529, 3533, 3539, 3557, 3559, 3583, 3613, 3617, 3631, 3659, 3673, 3691, 3701, 3733, 3739, 3767, 3779, 3793, 3797, 3823, 3863, 3881, 3907, 3911, 3917, 3929, 3931, 3947, 3989, 4003, 4007, 4019, 4021, 4027, 4057, 4073, 4079, ... 32: 3, 5, 13, 19, 29, 37, 53, 59, 67, 83, 107, 139, 149, 163, 173, 179, 197, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 443, 467, 509, 523, 547, 557, 563, 587, 613, 619, 653, 659, 677, 709, 757, 773, 787, 797, 827, 829, 853, 859, 877, 883, 907, 947, 1019, 1109, 1117, 1123, 1187, 1213, 1229, 1237, 1259, 1277, 1283, 1307, 1373, 1427, 1453, 1483, 1493, 1499, 1523, 1549, 1619, 1637, 1667, 1669, 1693, 1733, 1747, 1787, 1867, 1877, 1907, 1949, 1973, 1979, 1987, 1997, 2027, 2029, 2053, 2069, 2083, 2099, 2213, 2237, 2243, 2267, 2269, 2293, 2309, 2333, 2339, 2357, 2389, 2437, 2459, 2467, 2477, 2539, 2549, 2557, 2579, 2659, 2677, 2683, 2693, 2699, 2707, 2789, 2797, 2803, 2819, 2837, 2843, 2909, 2939, 2957, 2963, 3019, 3037, 3067, 3083, 3187, 3203, 3253, 3299, 3307, 3323, 3347, 3413, 3467, 3469, 3499, 3517, 3533, 3539, 3547, 3557, 3613, 3637, 3643, 3659, 3677, 3709, 3733, 3779, 3797, 3803, 3853, 3877, 3907, 3917, 3923, 3947, 3989, 4003, 4013, 4019, 4093, ... 33: 2, 5, 7, 13, 19, 23, 43, 47, 53, 59, 71, 73, 89, 113, 137, 179, 191, 251, 257, 269, 311, 317, 337, 349, 353, 383, 389, 409, 419, 439, 443, 449, 457, 467, 509, 547, 571, 587, 599, 601, 613, 617, 641, 647, 653, 683, 719, 733, 739, 773, 787, 797, 811, 839, 853, 863, 877, 911, 919, 929, 937, 971, 977, 983, 997, 1009, 1013, 1049, 1051, 1061, 1063, 1069, 1103, 1109, 1129, 1181, 1193, 1201, 1231, 1249, 1259, 1297, 1301, 1307, 1327, 1367, 1373, 1409, 1429, 1433, 1439, 1459, 1471, 1511, 1523, 1531, 1571, 1579, 1597, 1607, 1627, 1637, 1663, 1669, 1693, 1697, 1709, 1721, 1759, 1777, 1787, 1789, 1801, 1861, 1867, 1901, 1907, 1973, 1993, 1999, 2003, 2027, 2039, 2053, 2069, 2099, 2131, 2221, 2237, 2239, 2287, 2297, 2333, 2357, 2381, 2389, 2399, 2437, 2447, 2503, 2551, 2579, 2621, 2633, 2659, 2683, 2687, 2693, 2713, 2719, 2729, 2749, 2753, 2767, 2777, 2819, 2833, 2843, 2851, 2861, 2897, 2909, 2927, 2957, 2963, 3023, 3041, 3049, 3079, 3083, 3089, 3109, 3181, 3191, 3221, 3229, 3253, 3257, 3323, 3343, 3347, 3359, 3371, 3373, 3413, 3491, 3511, 3517, 3541, 3557, 3559, 3583, 3607, 3617, 3623, 3637, 3643, 3673, 3677, 3709, 3719, 3767, 3833, 3851, 3889, 3907, 3917, 3947, 3967, 4003, 4007, 4013, 4019, 4049, 4073, 4079, ... 34: 19, 23, 31, 41, 43, 53, 59, 67, 73, 79, 83, 101, 113, 149, 157, 167, 179, 193, 199, 233, 241, 251, 293, 311, 313, 337, 349, 367, 373, 389, 401, 431, 439, 449, 461, 467, 479, 491, 503, 509, 523, 557, 563, 587, 601, 613, 617, 641, 659, 661, 673, 701, 719, 733, 739, 743, 773, 797, 809, 839, 857, 881, 883, 887, 911, 929, 971, 983, 991, 1009, 1019, 1021, 1031, 1049, 1109, 1151, 1153, 1181, 1193, 1201, 1217, 1231, 1237, 1259, 1277, 1283, 1289, 1301, 1303, 1307, 1319, 1367, 1373, 1423, 1427, 1433, 1439, 1453, 1489, 1549, 1553, 1559, 1567, 1579, 1597, 1609, 1613, 1619, 1663, 1667, 1697, 1709, 1733, 1787, 1789, 1811, 1861, 1873, 1973, 1987, 1997, 1999, 2027, 2063, 2081, 2083, 2099, 2111, 2137, 2141, 2153, 2207, 2239, 2243, 2269, 2273, 2281, 2293, 2333, 2347, 2371, 2383, 2417, 2441, 2467, 2521, 2543, 2549, 2591, 2657, 2663, 2689, 2707, 2713, 2741, 2777, 2789, 2791, 2797, 2803, 2837, 2843, 2879, 2887, 2897, 2909, 2927, 2939, 2953, 2957, 2969, 2971, 2999, 3023, 3049, 3061, 3089, 3121, 3163, 3167, 3169, 3187, 3221, 3229, 3251, 3271, 3299, 3307, 3323, 3329, 3331, 3347, 3359, 3361, 3407, 3413, 3457, 3467, 3469, 3517, 3557, 3559, 3571, 3593, 3637, 3659, 3769, 3821, 3877, 3881, 3923, 4001, 4003, 4007, 4013, 4021, 4027, 4049, 4057, 4073, 4093, ... 35: 2, 3, 11, 37, 41, 47, 53, 61, 71, 79, 83, 89, 101, 103, 137, 151, 167, 179, 191, 197, 211, 223, 227, 229, 233, 239, 241, 269, 283, 317, 331, 359, 373, 379, 383, 409, 431, 457, 461, 467, 499, 503, 509, 521, 557, 563, 571, 587, 599, 601, 607, 617, 643, 647, 653, 659, 661, 673, 727, 739, 751, 757, 787, 829, 877, 881, 887, 911, 929, 941, 953, 977, 983, 1019, 1021, 1031, 1033, 1049, 1063, 1109, 1117, 1171, 1223, 1297, 1301, 1307, 1321, 1361, 1373, 1427, 1439, 1451, 1453, 1487, 1489, 1493, 1499, 1543, 1579, 1601, 1609, 1619, 1627, 1669, 1721, 1733, 1741, 1759, 1783, 1823, 1831, 1847, 1867, 1871, 1877, 1889, 1907, 1913, 1949, 1987, 1997, 1999, 2011, 2017, 2029, 2039, 2053, 2063, 2111, 2141, 2153, 2161, 2203, 2237, 2243, 2267, 2287, 2297, 2309, 2333, 2339, 2341, 2383, 2417, 2437, 2459, 2467, 2473, 2531, 2591, 2609, 2621, 2633, 2657, 2663, 2671, 2687, 2699, 2707, 2711, 2713, 2729, 2753, 2789, 2797, 2803, 2837, 2851, 2861, 2879, 2887, 2903, 3019, 3023, 3041, 3083, 3119, 3121, 3137, 3163, 3167, 3169, 3209, 3217, 3257, 3259, 3299, 3307, 3313, 3323, 3371, 3407, 3413, 3449, 3463, 3511, 3527, 3539, 3541, 3547, 3557, 3583, 3593, 3643, 3677, 3697, 3701, 3719, 3727, 3821, 3833, 3851, 3863, 3881, 3917, 3923, 3947, 3967, 3989, 4003, 4007, 4013, 4019, 4021, 4049, ... 36: (none) 10. Unique prime [it is conjectured that there are infinitely many unique primes in base n for all n>=2] Base//Period length of unique primes 2 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 54, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 147, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261, 280, 296, 312, 322, 334, 342, 345, 366, 374, 382, 398, 410, 414, 425, 447, 471, 507, 521, 550, 567, 579, 590, 600, 602, 607, 626, 690, 694, 712, 745, 795, 816, 889, 897, 909, 954, 990, 1106, 1192, 1224, 1230, 1279, 1384, 1386, 1402, 1464, 1512, 1554, 1562, 1600, 1670, 1683, 1727, 1781, 1834, 1904, 1990, 1992, 2008, 2037, 2203, 2281, 2298, 2353, 2406, 2456, 2499, 2536, 2838, 3006, 3074, 3217, 3415, 3418, 3481, 3766, 3817, 3927, ... 3 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 20, 21, 24, 26, 32, 33, 36, 40, 46, 60, 63, 64, 70, 71, 72, 86, 103, 108, 128, 130, 132, 143, 145, 154, 161, 236, 255, 261, 276, 279, 287, 304, 364, 430, 464, 513, 528, 541, 562, 665, 672, 680, 707, 718, 747, 760, 782, 828, 875, 892, 974, 984, 987, 1037, 1058, 1070, 1073, 1080, 1091, 1154, 1248, 1367, 1426, 1440, 1462, 1524, 1598, 1623, 1627, 1863, 1985, 2132, 2188, 2196, 2340, 2460, 2508, 2626, 2640, 2739, 2856, 3092, 3158, 3262, 3315, 3326, 3482, 3638, 3982, 4018, 4036, ... 4 1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 28, 40, 60, 92, 96, 104, 140, 148, 156, 300, 356, 408, 596, 612, 692, 732, 756, 800, 952, 996, 1004, 1228, 1268, 2240, 2532, 3060, 3796, 3824, 3944, ... 5 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 18, 24, 28, 47, 48, 49, 56, 57, 88, 90, 92, 108, 110, 116, 120, 127, 134, 141, 149, 161, 171, 181, 198, 202, 206, 236, 248, 288, 357, 384, 420, 458, 500, 530, 536, 619, 620, 694, 798, 897, 929, 981, 992, 1064, 1134, 1230, 1670, 1807, 2094, 2162, 2369, 2516, 2649, 2988, 3407, 3888, ... 6 1, 2, 3, 4, 5, 6, 7, 8, 18, 21, 22, 24, 29, 30, 42, 50, 62, 71, 86, 90, 94, 118, 124, 127, 129, 144, 154, 186, 192, 214, 271, 354, 360, 411, 480, 509, 558, 575, 663, 764, 814, 825, 874, 1028, 1049, 1050, 1102, 1113, 1131, 1158, 1376, 1464, 1468, 1535, 1622, 1782, 1834, 1924, 2096, 2176, 2409, 2464, 2816, 3013, 3438, 3453, 3663, ... 7 3, 5, 6, 8, 13, 18, 21, 28, 30, 34, 36, 46, 48, 50, 54, 55, 58, 63, 76, 84, 94, 105, 122, 131, 148, 149, 224, 280, 288, 296, 332, 352, 456, 528, 531, 581, 650, 654, 730, 740, 759, 1026, 1047, 1065, 1460, 1660, 1699, 1959, 2067, 2260, 2380, 2665, 2890, 3238, 4020, ... 8 1, 2, 3, 6, 9, 18, 30, 42, 78, 87, 114, 138, 189, 303, 318, 330, 408, 462, 504, 561, 1002, 1389, 1746, 1794, 2040, 2418, 2790, 3894, 4077, ... 9 1, 2, 4, 6, 10, 12, 16, 18, 20, 30, 32, 36, 54, 64, 66, 118, 138, 152, 182, 232, 264, 336, 340, 380, 414, 446, 492, 540, 624, 720, 762, 1066, 1094, 1098, 1170, 1230, 1254, 1320, 1428, 1546, 2018, 2574, 2724, 2804, 2920, 3074, 3316, 3646, ... 10 1, 2, 3, 4, 9, 10, 12, 14, 19, 23, 24, 36, 38, 39, 48, 62, 93, 106, 120, 134, 150, 196, 294, 317, 320, 385, 586, 597, 654, 738, 945, 1031, 1172, 1282, 1404, 1426, 1452, 1521, 1752, 1812, 1836, 1844, 1862, 2134, 2232, 2264, 2667, 3750, 3903, 3927, ... 11 2, 4, 5, 6, 8, 9, 10, 14, 15, 17, 18, 19, 20, 27, 36, 42, 45, 52, 60, 73, 91, 104, 139, 205, 234, 246, 318, 358, 388, 403, 458, 552, 810, 855, 878, 907, 1114, 1131, 1220, 1272, 1431, 1470, 1568, 1614, 1688, 1696, 1907, 2029, 2136, 2288, 2535, 2577, ... 12 1, 2, 3, 5, 10, 12, 19, 20, 21, 22, 56, 60, 63, 70, 80, 84, 92, 97, 109, 111, 123, 164, 189, 218, 276, 317, 353, 364, 386, 405, 456, 511, 636, 675, 701, 793, 945, 1090, 1268, 1272, 1971, 2088, 2368, 2482, 2893, 2966, 3290, ... 13 2, 3, 5, 6, 7, 8, 9, 12, 16, 22, 24, 28, 33, 34, 38, 78, 80, 102, 137, 140, 147, 224, 230, 283, 304, 341, 360, 372, 384, 418, 420, 436, 483, 568, 570, 594, 737, 744, 855, 883, 991, 1021, 1193, 1222, 1615, 1628, 1838, 2032, 2146, 2302, 2530, 2830, 2958, 3030, 3528, 3671, 3885, ... 14 1, 3, 4, 6, 7, 14, 19, 24, 31, 33, 35, 36, 41, 55, 60, 106, 114, 129, 152, 153, 172, 222, 265, 286, 400, 448, 560, 584, 864, 1006, 1335, 1363, 1520, 1536, 1659, 1862, 1925, 2332, 2458, 2687, 3381, 3512, 3870, 3976, ... 15 3, 4, 6, 7, 14, 24, 43, 54, 58, 73, 85, 93, 102, 184, 220, 221, 228, 232, 247, 291, 305, 486, 487, 505, 551, 552, 590, 1029, 1194, 1274, 1406, 1444, 1532, 1548, 1748, 1986, 2093, 2182, 2202, 2579, 2781, 3054, 3239, 3696, ... 16 2, 4, 6, 8, 10, 14, 20, 30, 46, 48, 52, 70, 74, 78, 150, 178, 204, 298, 306, 346, 366, 378, 400, 476, 498, 502, 614, 634, 1120, 1266, 1530, 1898, 1912, 1972, 2548, 2770, 3738, 3850, ... 17 1, 2, 3, 5, 7, 8, 11, 12, 14, 15, 34, 42, 46, 47, 48, 50, 71, 77, 94, 110, 114, 147, 154, 176, 228, 235, 258, 275, 338, 350, 419, 450, 480, 515, 589, 624, 666, 716, 724, 810, 815, 1232, 1490, 1934, 2106, 2391, 2732, 2904, 3462, 3912, 4053, ... 18 1, 2, 3, 6, 14, 17, 21, 24, 30, 33, 38, 45, 46, 72, 78, 114, 146, 168, 288, 414, 440, 448, 665, 792, 801, 816, 975, 1165, 1176, 1267, 1466, 1513, 1882, 1920, 1998, 2194, 2272, 2643, 2800, 2946, 3434, 3504, 3813, 3866, 3957, ... 19 2, 3, 4, 6, 19, 20, 31, 34, 47, 56, 59, 61, 70, 74, 91, 92, 96, 98, 107, 120, 145, 156, 168, 242, 276, 314, 326, 337, 387, 565, 602, 612, 892, 984, 1061, 1067, 1079, 1262, 1328, 2356, 3033, 3419, 3501, 3963, ... 20 1, 3, 4, 6, 8, 9, 10, 11, 17, 30, 98, 100, 110, 126, 154, 158, 160, 168, 178, 182, 228, 266, 270, 280, 340, 416, 480, 574, 774, 980, 1052, 1139, 1338, 1418, 1474, 1487, 1594, 1902, 2326, 3112, 3520, 3808, 3830, ... 21 2, 3, 5, 6, 8, 9, 10, 11, 14, 17, 26, 43, 64, 74, 81, 104, 192, 271, 321, 335, 348, 404, 437, 445, 516, 671, 694, 788, 1788, 1943, 2343, 2742, 3031, 3135, ... 22 2, 5, 6, 7, 10, 21, 25, 26, 69, 79, 86, 93, 100, 101, 154, 158, 161, 171, 202, 214, 294, 354, 359, 424, 454, 602, 687, 706, 744, 857, 1028, 1074, 1136, 1150, 1345, 1408, 1525, 1572, 1578, 1988, 2142, 2665, ... 23 2, 5, 8, 11, 15, 22, 26, 39, 42, 45, 54, 56, 132, 134, 145, 147, 196, 212, 218, 252, 343, 580, 662, 816, 820, 846, 1078, 1092, 1174, 1189, 1548, 1632, 2040, 2180, 2348, 2732, 3100, 3181, 4010, ... 24 1, 2, 3, 4, 5, 8, 14, 19, 22, 38, 45, 53, 54, 70, 71, 117, 140, 144, 169, 186, 192, 195, 196, 430, 653, 661, 744, 834, 855, 870, 927, 1128, 1158, 1390, 1516, 1555, 1617, 1844, 2022, 2060, 2208, 2812, 3153, 3952, ... 25 2, 4, 6, 12, 14, 24, 28, 44, 46, 54, 58, 60, 118, 124, 144, 192, 210, 250, 268, 310, 496, 532, 1258, 1494, 1944, 2050, 2498, 2728, 3324, 3418, 3646, 3862, 4014, ... 26 1, 2, 4, 7, 9, 18, 20, 22, 24, 30, 43, 69, 132, 140, 186, 200, 210, 218, 267, 347, 454, 495, 554, 585, 645, 694, 980, 1028, 1060, 1098, 1432, 1714, 1828, 3513, 3786, ... 27 2, 3, 12, 21, 24, 36, 87, 93, 171, 249, 276, 360, 480, 621, 732, 780, 1716, 3843, ... 28 1, 2, 3, 5, 6, 8, 17, 21, 38, 81, 91, 96, 102, 132, 148, 156, 240, 258, 260, 276, 457, 464, 465, 500, 506, 535, 684, 746, 838, 930, 982, 1015, 1189, 1296, 1335, 1345, 1390, 1423, 2062, 2723, 2893, 3078, ... 29 4, 5, 6, 7, 8, 14, 30, 32, 39, 45, 50, 76, 116, 151, 222, 357, 402, 462, 570, 588, 636, 671, 695, 844, 1498, 1650, 1770, 3175, 3195, 3312, 3538, 3719, ... 30 1, 2, 5, 9, 11, 12, 21, 36, 51, 64, 91, 163, 174, 195, 230, 278, 318, 342, 346, 424, 530, 569, 578, 795, 984, 1094, 1167, 1335, 1564, 1605, 1658, 1789, 2159, 2204, 2225, 3366, 3458, 3615, ... 31 3, 7, 12, 17, 24, 30, 31, 33, 40, 176, 218, 308, 404, 420, 630, 693, 890, 915, 922, 1475, 2122, 2185, 2487, 2541, 2907, 3387, 4055, ... 32 1, 6, 30, 85, 110, 120, 320, 1050, 1065, 1385, 2490, 3080, 3920, ... 33 1, 2, 3, 10, 16, 25, 28, 30, 35, 36, 45, 56, 76, 87, 110, 134, 135, 197, 200, 220, 228, 314, 324, 330, 396, 498, 583, 624, 725, 806, 940, 1145, 1240, 1644, 1750, 2171, 2268, 2675, 2781, 2790, 2808, 3581, ... 34 3, 6, 8, 10, 13, 20, 24, 56, 87, 154, 164, 196, 282, 363, 428, 652, 744, 780, 860, 902, 952, 1178, 1493, 1540, 1643, 1904, 2184, 2277, 2468, 2943, ... 35 2, 4, 6, 8, 18, 21, 22, 26, 42, 128, 154, 158, 170, 180, 184, 192, 254, 313, 450, 624, 737, 762, 798, 874, 912, 1002, 1006, 1098, 1234, 1297, 1418, 1714, 1926, 2325, 2343, 2368, 2998, 3567, 4064, ... 36 2, 4, 12, 62, 72, 96, 180, 240, 382, 514, 688, 732, 734, 962, 1048, 1088, 1232, 1408, 2088, 2176, 2248, 2724, 3180, ... Last fiddled with by sweety439 on 2020-11-04 at 12:33
2020-11-08, 11:31 #4 sweety439 Nov 2016 26×3×13 Posts OEIS sequences: #1 = Permutable prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many permutable primes) #2 = Circular prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many circular primes) #3 = Left-truncatable prime #4 = Right-truncatable prime #5 = Minimal prime #6 = Two-sided prime (there is conjectured to be infinitely repunit primes (weakly primes, full-reptend primes, unique primes) in any given base) A = Largest such prime in base n (written in base 10) B = Length of largest such prime in base n C = Number of such primes in base n Code: A B C #1 A317689 A?????? A?????? #2 A293142 A?????? A?????? #3 A103443 A103463 A076623 #4 A023107 A103483 A076586 #5 A326609 A330049 A330048 #6 A323137 A?????? A323390 Last fiddled with by sweety439 on 2020-11-08 at 11:31
2020-11-08, 11:52 #5 sweety439 Nov 2016 26·3·13 Posts Data for the minimal primes, the left-truncatable primes, and the right-truncatable primes in bases 2 to 128: https://github.com/xayahrainie4793/primes/tree/master Data is currently not complete "kernel n": data for minimal primes base n "left n" data for unsolved families for the "minimal prime problem" (like Sierpinski problem and Riesel problem) base n "ltp n" data for left-truncatable primes base n "rtp n" data for right-truncatable primes base n
2020-11-08, 11:55 #6 sweety439 Nov 2016 26·3·13 Posts
2020-11-08, 12:11 #7 sweety439 Nov 2016 26×3×13 Posts Last fiddled with by sweety439 on 2020-11-09 at 16:29
2020-11-08, 12:14 #8 sweety439 Nov 2016 26×3×13 Posts
2020-11-08, 12:21 #9 sweety439 Nov 2016 26·3·13 Posts #1 = Permutable prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many permutable primes) #2 = Circular prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many circular primes) #3 = Left-truncatable prime #4 = Right-truncatable prime #5 = Minimal prime #6 = Two-sided prime (there is conjectured to be infinitely repunit primes (weakly primes, full-reptend primes, unique primes) in any given base) A = Largest such prime in base n (written in base 10) B = Length of largest such prime in base n C = Number of such primes in base n 1A bases 3 to 20 2A bases 3 to 6 3A bases 3 to 53 (with missing terms) 3B bases 2 to 53 (with missing terms) 3C bases 2 to 53 (with missing terms) 4A bases 3 to 100 4B bases 2 to 53 4C bases 2 to 100 5A bases 2 to 42 (with missing terms) 5B bases 2 to 16 5C bases 2 to 16 6A bases 3 to 64 6C bases 2 to 64
2020-11-23, 01:10 #10 sweety439 Nov 2016 26·3·13 Posts The bases such that all minimal primes are known are 2-16, 18, 20, 22-24, 30, 42 and possible 60 The bases such that all left truncatable primes are known are 2-29, 31-35, 37-39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 89 The bases such that all right truncatable primes are known are 2-100 and possible higher bases
2020-11-23, 01:17 #11 sweety439 Nov 2016 26×3×13 Posts Puzzles: * Found all left truncatable primes in base b, for 2<=b<=256 * Found all right truncatable primes in base b, for 2<=b<=256 * Found all minimal primes in base b, for 2<=b<=256 (we allow strong probable primes >2^(2^16) to all prime bases 2<=p<=256 in place of proven primes, if the probable prime is <2^(2^16), then we need to prove its primality)
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Fri Nov 27 13:46:41 UTC 2020 up 78 days, 10:57, 5 users, load averages: 1.27, 1.40, 1.38 | 35,890 | 60,095 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2020-50 | latest | en | 0.581791 |
http://mathforum.org/mathimages/index.php?title=Buffon%27s_Needle&action=formedit | 1,511,449,962,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00284.warc.gz | 184,317,641 | 14,467 | # Edit Edit an Image Page: Buffon's Needle
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Image Title*: Upload a Math Image The Buffon's Needle problem is a mathematical method of approximating the value of pi $(\pi = 3.1415...)$involving repeatedly dropping needles on a sheet of lined paper and observing how often the needle intersects a line. The method was first used to approximate π by Georges-Louis Leclerc, the Comte de Buffon, in 1777. Buffon was a mathematician, and he wondered about the probability that a needle would lie across a line between two wooden strips on his floor. To test his question, he apparently threw bread sticks across his shoulder and counted when they crossed a line. Calculating the probability of an intersection for the Buffon's Needle problem was the first solution to a problem of geometric probability. The solution can be used to design a method for approximating the number π. Subsequent mathematicians have used this method with needles instead of bread sticks, or with computer simulations. We will show that when the distance between the lines is equal the length of the needle, an approximation of π can be calculated using the equation $\pi \approx {2\times \mbox{number of drops} \over \mbox{number of hits}}$ ====Will the Needle Intersect a Line?==== [[Image:situation2.jpg|right]] [[Image:willtheneedlecross ps10.jpg|right]] To prove that the Buffon's Needle experiment will give an approximation of π, we can consider which positions of the needle will cause an intersection. Since the needle drops are random, there is no reason why the needle should be more likely to intersect one line than another. As a result, we can simplify our proof by focusing on a particular strip of the paper bounded by two horizontal lines. The variable θ is the acute angle made by the needle and an imaginary line parallel to the ones on the paper. Since we are considering the case where the interline distance equals l, we might as well take that common distance to be 1 unit. Finally, ''d'' is the distance between the center of the needle and the nearest line. Also, there is no reason why the needle is more likely to fall at a certain angle or distance, so we can consider all values of θ and d equally probable. We can extend line segments from the center and tip of the needle to meet at a right angle. A needle will cut a line if the length of the green arrow, ''d'', is shorter than the length of the leg opposite θ. More precisely, it will intersect when $d \leq \left( \frac{1}{2} \right) \sin(\theta). \$ See case 1, where the needle falls at a relatively small angle with respect to the lines. Because of the small angle, the center of the needle would have to fall very close to one of the horizontal lines in order to intersect it. In case 2, the needle intersects even though the center of the needle is far from both lines because the angle is so large. ====The Probability of an Intersection==== In order to show that the Buffon's experiment gives an approximation for π, we need to show that there is a relationship between the probability of an intersection and the value of π. If we graph the possible values of θ along the X axis and ''d'' along the Y, we have the sample space for the trials. In the diagram below, the sample space is contained by the dashed lines. Each point on the graph represents some combination of an angle and a distance that a needle might occupy. [[image:Minigraph.jpg]] There will be an intersection if $d \leq \left ( \frac{1}{2} \right ) \sin(\theta) \$, which is represented by the blue region. The area under this curve represents all the combinations of distances and angles that will cause the needle to intersect a line. Since each of these combinations is equally likely, the probability is proportional to the area – that's what makes this a geometric probability problem. The area under the blue curve, which is equal to 1/2 in this case, can found by evaluating the integral $\int_0^{\frac {\pi}{2}} \frac{1}{2} \sin(\theta) d\theta = \frac {1}{2}$ Then, the area of the sample space can be found by multiplying the length of the rectangle by the height. $\frac {1}{2} * \frac {\pi}{2} = \frac {\pi}{4}$ The probability is equal to the ratio of the two areas in this case because each possible value of θ and ''d'' is equally probable. The probability of an intersection is $P_{hit} = \cfrac{ \frac{1}{2} }{\frac{\pi}{4}} = \frac {2}{\pi} = .6366197\ldots.\qquad \mbox{and thus} \qquad \pi = \frac 2{P_{hit}}.$ Thus, in order to approximate $\pi$, it remains only to approximate $P_{hit}$. ====Using Random Samples to Approximate π==== The original goal of the Buffon's needle method, approximating π, can be achieved by using probability to solve for π. If a large number of trials is conducted, the proportion of times a needle intersects a line will be close to the probability of an intersection. That is, the number of line hits divided by the number of drops will equal approximately the probability of hitting the line. $P_{hit} \approx \frac {\mbox{number of hits}}{\mbox{number of drops}}$ So, $\pi = \frac{2}{P_{hit}} \approx \frac {2}{\frac {\mbox{number of hits}}{\mbox{number of drops}}} = \frac {2 * {\mbox{number of drops}}}{\mbox{number of hits}}$ ====Watch a Simulation====
{{#iframe:http://mste.illinois.edu/reese/buffon/bufjava.html|405|500|thumb}}
Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Topology Other {{hide|1= ====Monte Carlo Methods==== The Buffon's needle problem was the first recorded use of a Monte Carlo method. These methods employ repeated random sampling to approximate a probability, instead of computing the probability directly. Monte Carlo calculations are especially useful when the nature of the problem makes a direct calculation impossible or unfeasible, and they have become more common as the introduction of computers makes randomization and conducting a large number of trials less laborious. π is an irrational number, which means that its value cannot be expressed exactly as a fraction a/b, where a and b are integers. This also means that a normal decimal repetition of pi is non-terminating and non-repeating, and mathematicians have been challenged with trying to determine increasingly accurate approximations. The timeline below shows the improvements in approximating π throughout history. In the past 50 years especially, improvements in computer capability allow more decimal places to be determined. Nonetheless, better methods of approximation are still desired. [[Image:history of pi2.jpg|800px]] A recent study conducted the Buffon's Needle experiment to approximate π using computer software. The researchers administered 30 trials for each number of drops, and averaged their estimates for π. They noted the improvement in accuracy as more trials were conducted. [[Image:box1.jpg]] These results show that the Buffon's Needle method approximation is relatively tedious. Compared to other computation techniques, Buffon's method is impractical because the estimates converge towards π rather slowly. Even when a large number of needles were dropped, this experiment gave a value of π that was inaccurate in the third decimal place. Regardless of the impracticality of the Buffon's Needle method, the historical significance of the problem as a Monte Carlo method means that it continues to be widely recognized. ====Generalization of the problem==== [[Image:picture 1.png|right]] The Buffon’s needle problem has been generalized so that the probability of an intersection can be calculated for a needle of any length and paper with any spacing. For a needle shorter than the distance between the lines, it can be shown by a similar argument to the case where ''d'' = 1 and ''l'' = 1 that the probability of a intersection is $\frac {2*l}{\pi*d}$. Note that this expression agrees with the normal case, where ''l'' =1 and ''d'' =1, so these variables disappear and the probability is $\frac {2}{\pi}$. The generalization of the problem is useful because it allows us to examine the relationship between length of the needle, distance between the lines, and probability of an intersection. The variable for length is in the numerator, so a longer needle will have a greater probability of an intersection. The variable for distance is in the denominator, so greater space between lines will decrease the probability of an intersection. To see how a longer needle will affect probability, follow this link: http://whistleralley.com/java/buffon_graph.htm ====Needles in Nature==== Applications of the Buffon's Needle method are even found in nature. The Centre for Mathematical Biology at the University of Bath found uses of the Buffon's Needle algorithm in a recent study of ant colonies. The researchers found that an ant can estimate the size of an anthill by visiting the hill twice and noting how often it recrosses its first path during the second trip. [[Image:one ant track.jpg|right]] Ants generally nest in groups of about 50 or 100, and the size of their nest preference is determined by the size of the colony. When a nest is destroyed, the colony must find a suitable replacement, so they send out scouts to find new potential homes. In the study, scout ants were provided with "nest cavities of different sizes, shapes, and configurations in order to examine preferences" [2]. From observations that ants prefer nests of a certain size related to the number of ants in the colony, researchers were able to draw the conclusion that scout ants must have a method of measuring areas. A scout initially begins exploration of a nest by walking around the site to leave tracks. Then, the ant will return later and walk a new path that repeatedly intersects the first tracks. The first track will be laced with a chemical that causes the ant to note each time it crosses the original path. The researchers believe that these scout ants can calculate an estimate for the nest's area using the number of intersections between its two visits. The ants can measure the size of their hill using a related and fairly intuitive method: If they are constantly intersecting their first path, the area must be small. If they rarely reintersects the first track, the area of the hill must be much larger so there is plenty of space for a non-intersecting second path. [[Image:willtheneedlecross ps4.jpg|left]] [[Image:Willtheneedlecross_ps5.jpg|left]] ''"In effect, an ant scout applies a variant of Buffon's needle theorem: The estimated area of a flat surface is inversely proportional to the number of intersections between the set of lines randomly scattered across the surface."'' [7] This idea can be related back to the generalization of the problem by imagining if the area between the lines was increased by making the parallel lines much further apart. A larger distance between the two lines would mean a much smaller probability of intersection. We can see in case 3 that when the distance between the lines is greater than the length of the needle, even very large angle won’t necessarily cause an intersection. This natural method of random motion allows the ants to gauge the size of their potential new hill regardless of its shape. Scout ants are even able to asses the area of a hill in complete darkness. The animals show that algorithms can be used to make decisions where an array of restrictions may prevent other methods from being effective. COOL LINK! : http://www.youtube.com/watch?feature=player_embedded&v=sJVivjuMfWA }} [1] http://www.maa.org/mathland/mathtrek_5_15_00.html [2] http://mste.illinois.edu/reese/buffon/bufjava.html [3] http://www.absoluteastronomy.com/topics/Monte_Carlo_method [4] The Number Pi. Eymard, Lafon, and Wilson. [5] Monte Carlo Methods Volume I: Basics. Kalos and Whitlock. [6] Heart of Mathematics. Burger and Starbird [7] http://math.tntech.edu/techreports/TR_2001_4.pdf Yes, it is. | 2,893 | 13,121 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2017-47 | longest | en | 0.940263 |
http://adg.stanford.edu/aa241/fuselayout/DEPRECATED/fusegm.html | 1,485,019,434,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281162.88/warc/CC-MAIN-20170116095121-00001-ip-10-171-10-70.ec2.internal.warc.gz | 6,429,813 | 2,879 | # Fuselage Geometry Calculations
This page does a number of computations associated with seating and fuselage geometry.
Number of Seats: Seat Pitch: Seat Width: Aisle Width: Nose Fineness: Tailcone Fineness: Main Deck Seat Layout: Upper Deck Seat Layout: Height / Width: Extra Forward Space: Extra Aft Space: Floor Height:
Fuselage Height: Fuselage Width: Fuselage Length: Wetted Area: # of Seat Rows: Wall Thickness: Nose Length: Cabin Length: Tailcone Length: Tailcone Height:
• Number of Seats is the total number of seats to be arranged as described in the airplane. The current program does not differentiate between first class and economy seating, so if you plan to describe an airplane with dual or tri-class seating, you should enter the actual number of seats and an effective seat pitch that is an average of the overall seat layout.
• Seat Pitch: Longitudinal distance from one seat to the corresponding point on the next seat. (i.e. the seat spacing from back of one row to the back of the next row, measured in inches).
• Seat Width: The width of the seat including armrests associated with that seat (inches).
• Aisle Width: The width of the aisle in inches.
• Nose Fineness: Ratio of nose length to fuselage maximum width. The nose length is taken to be the distance from the front of the airplane to the start of the constant section (or tail cone if there is no constant section)
• Tailcone Fineness: Ratio of tail cone length to fuselage maximum width. The tail cone length is taken to be the distance from the back of the airplane to the start of the constant section (or nose section if there is no constant section)
• Main Deck Seat Layout: Distribution of seats and aisles written as an integer. 32 means 3 seats together, then an aisle, then 2 seats. 353 means a twin aisle airplane with 3 seats then an aisle, then 5 seats in the center, then another aisle, then another 3 seats.
• Upper Deck Seat Layout: On airplanes with an upper deck the seat layout as described above. If the airplane has a single deck, enter 0. At the moment the cross-section is not drawn with an upper deck.
• Height / Width: The ratio of fuselage maximum height to width.
• Extra Forward Space: Extra space placed aft of the nose section and forward of the seats. This space may be used for lavatories, galleys, or closet space. Entering a negative value places seats in the tapering nose section, as one would do for a large airplane or SST.
• Extra Aft Space: Extra space placed aft of the seats and forward of the tail cone. This space may be used for lavatories, galleys, or closet space. Entering a negative value places seats in the tapering tail cone section, as one would do for a large airplane or SST.
• Floor Height: The vertical offset of the floor from the center of the cabin in units of cabin height. A value of 0 places the floor at the fuselage centerline, while a value of 0.5 would place the floor at the lowest point on the fuselage. Typical value: 0.15. | 674 | 2,991 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2017-04 | latest | en | 0.900563 |
https://www.reddit.com/r/news/comments/cmz4h/starting_in_2015_all_eggs_sold_in_california_must/ | 1,495,818,703,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608669.50/warc/CC-MAIN-20170526163521-20170526183521-00317.warc.gz | 1,177,187,834 | 60,692 | This is an archived post. You won't be able to vote or comment.
[–] 115 points116 points (15 children)
That's more motion than a lot of humans are allowed at cubicle farms.
[–] 22 points23 points (0 children)
And to be fair, I would NEVER eat an egg laid by a human in a cubicle farm.
[–] 3 points4 points (0 children)
The company I work for had my teeth removed to keep me from biting other employees to death.
[–] 1 point2 points (3 children)
My coworker and I recently moved to other cubicles in the office. He's been with the company for almost 15 years, but because he's not a manager, he can't have a window cube. There are several empty window cubes on the floor, and his new cube is next to the window, but there's a cube wall facing the window.
[–] 50 points51 points (21 children)
States that requires that starting in 2015 all shell (whole) eggs sold in California must come from hens who were able to stand up, lie down, turn around, and fully extend their limbs without touching one another or the sides of an enclosure. In other words: California will become a cage-free state.
I'm having a hard time following this reasoning. Making a slightly larger cage doesn't equal removing the cage.
[–] 31 points32 points (4 children)
At some point, free range becomes cheaper than providing a ton of individual gigantic cages. Whether this bill puts California beyond that point, I can't say.
[–] 10 points11 points (3 children)
If you think that someone in a multi-million dollar egg farm hasn't done the math to figure this out, you're sadly mistaken.
Want to know what the cost is? Compare the price of free range eggs to normal eggs.
[–] 20 points21 points (0 children)
As mentioned above, free-range eggs are sold at an inflated price simply because they can be -- same reason organic goods are so expensive. I believe the other poster quoted an actual cost increase of 25%.
[–] 2 points3 points (0 children)
i buy eggs from a lady at the end of the road for 2.00 a dozen. I have never bought farm fresh eggs for much more. I do not buy eggs from the store much these days.
[–] 9 points10 points (2 children)
It removes the issues associated with overpopulated cages (which are actually huge).
[–] 1 point2 points (1 child)
I've heard a third of stock die prematurely (source being Hugh Fearnly Whittingstal, so he has a bias, and it was on TV, so I can't link to it, but that's a giant cost to impose upon yourself).
[–] 9 points10 points (1 child)
Watch food inc.
You'll see how different it will be.
[–] 7 points8 points (0 children)
He didn't say anything about it not being different. He just said he doesn't see how presumably moving them to a larger cage will make California a "cage-free state". Perhaps the hope is that all hens will suddenly be free range, but I wouldn't count on it.
[–] 3 points4 points (3 children)
They'll just cut off their limbs. Voila! Smaller cages again.
[–] 0 points1 point (0 children)
Probably because it makes it uneconomical to uses cages.
[–] 34 points35 points (7 children)
As someone with an interest in hen BDSM, this is very sad news.
[–] 9 points10 points (6 children)
Well, it's supposed to be safe, sane and consHENsual.
[–] 20 points21 points (11 children)
Yay. Unfortunately it will only apply to whole eggs, and some soil for scratching would be nice too. This really just forces factory farms to increase the sizes of their cages.
[–] 23 points24 points (4 children)
baby steps...
first its bigger cages, then its free range, etc.
[–] 33 points34 points (3 children)
First they gave them bigger cages, and I did not speak up, for I was not a chicken.
[–] 14 points15 points (2 children)
wait..what...i don't....uh?
[–] 8 points9 points (1 child)
It's true, though.
[–] 8 points9 points (0 children)
fuck it, I'm gonna go look at lolcats...
[–] 2 points3 points (1 child)
Nice try hen!
[–] 2 points3 points (0 children)
:<
[–] 1 point2 points (0 children)
There are hens that can lay half an egg at a time? That's a hell of a trick.
[–] 0 points1 point (1 child)
I've never seen a way to buy non-whole eggs.
Someone want to enlighten me?
[–] 17 points18 points (6 children)
Is that a sobriety test?
[–] 2 points3 points (5 children)
They sure get off easy. At least they don't have to walk the line.
[–] 1 point2 points (2 children)
or caw out the alphabet.
[–] 1 point2 points (0 children)
or touch their beaks.
[–] 27 points28 points (107 children)
I wonder how this will effect egg prices.
[–] 27 points28 points (26 children)
My guess is price will double right off the bat. All the egg ranches effected will have to build more..... EARTHQUAKKKKEEE!!!! buildings or cut back on production birds.
[–] 11 points12 points (16 children)
according to an EU study, barn eggs cost only 25% more to produce
http://en.wikipedia.org/wiki/Free-range_eggs
[–] 3 points4 points (13 children)
and they charge triple for them.....
[–] 17 points18 points (8 children)
but they don't have to. They can only charge triple because they are marketed as a luxury item.
[–] 3 points4 points (7 children)
If this is true, shouldn't farmers be rushing to switch to free-range? If you can charge triple while only increasing cost 25%, it seems like a no brainer. Maybe I should become a free-range egg farmer. I could be rich!
[–] 15 points16 points * (2 children)
not everybody wants to pay triple when they don't have to. theres not enough demand
[–] 0 points1 point (2 children)
Not true, egg prices for "free" chickens and cage chickens are almost the same at least in finland, sometimes there are even cheaper free-range eggs than cage eggs available (it's all about competition and free market).
[–] 0 points1 point (1 child)
Interesting. Since they are similarly priced or even cheaper how popular are they compared to conventionally farmed eggs? If the chickens have a better standard of living and the eggs are the same price then the choice would seem pretty easy to buy them.
[–] 1 point2 points (1 child)
That's all well and good, but people should stop complaining about "stagnant wages in real terms" when this and a hundred other regulations increase the price (and hopefully also the quality) of the everyday stuff we buy.
[–] 8 points9 points (5 children)
Southern California? Yeah, I felt it too.
[–] 14 points15 points (4 children)
Yup, Escondido. I literally typed that during the earthquake.
[–] 1 point2 points (2 children)
Prices can only be raised for specialty products.
If they all follow the same regulation, it isn't a specialty anymore.
There won't be free-range eggs vs other types, there will just be one type. If anything, the price would decrease since the few who offer them will now just be another competitor.
[–] 8 points9 points (0 children)
After watching some of those clips a couple of years ago and see just how bad the conditions were, I have no issue in paying more for them.
This particular law doesn't affect me since im in Australia but I've been buying cage-free eggs literally since the day I saw the videos and have been paying extra for the privilege.
I hope for your sake that as part of this new law there are also pricing regulations put in place to stop the increases getting out of control. They will rise though since it'll make the process less efficient for farmers.
[–] 1 point2 points (0 children)
"affect"
/sorry
[–] 1 point2 points (0 children)
i wonder how ending human slavery will affect cotton prices.
[–] -1 points0 points (59 children)
This a million times over. As a college student who gets by on only 50 dollars a month in food, eggs are a staple part of my diet. I pray to the flying spaghetti monster that this won't jack up carton prices by a dollar or something ridiculous.
[–] 16 points17 points (36 children)
\$50 a month? I did \$30 a week in college and that was pushing it.
anyway have you tried eggwhites? The containers can be cheaper and you sometimes can get more for your dollar.
[–] 6 points7 points (1 child)
\$50 a month is totally doable. I ate ramen noodles made in a coffee maker cause I had no stove or microwave for YEEEEAAAARRRSSSS....
[–] 0 points1 point (0 children)
Thank god for cup noodles. 7 bucks for 24 packs at costco.
[–] 5 points6 points (15 children)
I did \$30 a week in college and that was pushing it.
Really? What were you eating?
I find it difficult to spend that much even when I feel like splurging. If I really need to stretch my budget I can go as low \$25 a month (but I'll be sick of beans and rice and frozen vegetables by the end of it).
[–] 6 points7 points * (7 children)
Id buy 1lb of chicken, rice, loaf bread, 2 boxes of pasta, fruit and veggies, a bottle of soda, some cold cuts , tea, bag of pretzels and a box of Life cereal + Gallon of Milk. That's around \$30 right there and thats with no lunch. I ate out for lunch a lot. Thats for 1 week. My roomates all spent about the same, some more some a bit less. So in all id spend around \$30 a week for home food, then another \$25 on lunch. So all together around \$55 a week. That was as low as I could go.
Im not sure id want to live on \$25 a month like you are, if thats the stuff you are eating. But that was when I was in college. Now I eat well, me and my mom spend around \$100 a week on food. But we live in nyc, so its more expensive here.
[–] 19 points20 points (6 children)
Id buy 1lb of chicken, rice, loaf bread, 2 boxes of pasta, fruit and veggies
Whoa there! You're eating like a normal human. You're not a real college student! You're an imposter!
[–] 2 points3 points (0 children)
You’re a phony. Hey, this guy’s a great big phony! Hey, you’re a great big phony you know that?
[–] 6 points7 points (2 children)
I'm sure you can find a way to spend four dollars a day on food.
[–] 2 points3 points (0 children)
Exactly. I, for instance, eat children.
[–] 1 point2 points (0 children)
Oh, I know it's possible. I just feel guilty knowing that I'm going through a budget in a week that could last me a month; and it's not really chump change either. The difference between the two over the course of a year is about \$1000. That's about 4 weeks working full time at my last crappy internship.
Strictly controlling costs like this are a large part of the reason that I am graduating debt free while many of my friends have run up thousands in debt.
[–] 1 point2 points (14 children)
Eggs where I am are about 1.50-1.99 for a dozen. With that, bargain bin bread at 1 dollar a loaf, and maybe peanut butter sometimes, my meals consist of a piece of toast and 5 eggs every day.
[–] 3 points4 points (2 children)
don't you get disgusted with eating the same crap everyday? Thats still like \$60 a month just on eggs.
[–] 6 points7 points (0 children)
He should switch to noodles and cheese only. I heard some people like that.
[–] 0 points1 point (0 children)
It turns out that you can do some very crazy things with eggs. I have half a dozen or so different ways of cooking them, and when I have seasoning salt or any other spice I can go ape-shit crazy and have dozens of different dishes.
[–] 0 points1 point (2 children)
Is that everything you eat? No veggies? (Very curious, here.)
[–] 0 points1 point (1 child)
No. Ever since I was a child my parents would rarely buy vegetables of any sort. When I first saw a honeydew, I thought it was an albino coconut if that's any indicator. I eat a banana that I find lying around maybe once a month or so, but otherwise I only eat eggs, toast, milk, and very occasionally cheese.
[–] 1 point2 points (0 children)
That is straight out tragic.
[–] 0 points1 point (0 children)
I was doing \$70 a month. Including cooking gas.
[–] 0 points1 point (1 child)
[–] 0 points1 point (0 children)
Saturday.
[–] 14 points15 points (8 children)
Or get higher quality protein from legumes?
[–] 1 point2 points (0 children)
Legumes were a big part of my college diet!
[–] 23 points24 points (8 children)
You'd torture chickens just so you could afford eggs?
[–] 2 points3 points (0 children)
It's hard to take your opinion on this matter seriously, Poopis_Food.
[–] 0 points1 point (1 child)
Rhetorical?
[–] 4 points5 points (0 children)
No. When you buy battery-caged eggs, you are paying for chickens to be tortured.
[–] 3 points4 points (1 child)
I hope you don't plan on still being a college student in 5 years.
[–] 0 points1 point (0 children)
Even grad students face similar budget constraints, and considering the average length of PhD programs, it's not unreasonable to think that many of them will still be students in 5 years.
[–] 0 points1 point (0 children)
[–] 0 points1 point (0 children)
By my senior year it was teriyaki and jack in the box every day. 100+ bucks a week eating out made me fat
[–] 4 points5 points (1 child)
What about egg farms that don't produce for the general public, but for industry? Presumably that accounts for the majority of farms in and shipping to CA. This only refers to whole eggs.
I can't sell an egg to a grocery shopper laid by a chicken who is crammed next to another chicken. But apparently I totally can sell egg products to them from a chicken crammed next to another chicken.
Surely this is where the biggest business is, right? Not the actual eggs in cartons, but bulk egg products sold to companies like Kraft, etc.
It's a benefit for sure. But the bill itself can be easily misread by those who aren't careful. This does not mean an end to animal cruelty to egg hens.
[–] 3 points4 points * (0 children)
Haha, 2015. I guess you can't really expect more from the US. Edit: And it doesn't really mean anything. Anyway. Plus, even if they are out of cages, it does not automatically equate to a significant improvement for the chickens. "Free range" indoors is fucking terrible. Breaks cut of (often also tongues), dead chickens everywhere from disease and stress.. My brother had a job over the summer in which is only task was to pick up dead or dying chickens who had stressed themselves to death. Unless there is some real protective legislation in place, chicken farming will remain "corporate".
[–] 6 points7 points (0 children)
As a proud owner of 3 ex-battery hens, I can't upvote this enough.
You should have seen the state they were in when I first got them, virtually bald due to pecking themselves/each other and floppy pale combs due to a lack of sunlight and decent food. Their eggs taste amazing too now that they get plenty of exercise and a good varied diet.
[–] 4 points5 points (5 children)
Breed hens with very short or no wings and they'll fit into the same tiny cage. Breeding hens this way to comply with the law (as the heading describes it anyway) will likely be cheaper than giving up millions of dollars in property investment.
[–] 2 points3 points (0 children)
But they're still allowed to throw the males in the blender, right?
[–] 2 points3 points (0 children)
Good law, good mental image
[–] 2 points3 points (0 children)
Fuck, here in New Zealand our animal rights laws go as far as "if it's got food and water it's legit" the SPCA recently had to actually buy a farm full of breeding bitches and puppies which were rotting in their own shit from the farm owner. They couldn't legally take them because they had food and water. Good Job John Key
[–] 2 points3 points (0 children)
Good stuff. A step in the right direction! I only eat free-range eggs, but I understand that it's not entirely practical considering the sheer amount of factory produced eggs in the US.
[–] 6 points7 points (1 child)
The Hokey-Pokey Act of 2015.
[–] 6 points7 points (10 children)
Thanks to direct democracy.
[–] 5 points6 points (5 children)
So the majority of people felt that our chickens should be given better conditions.
[–] 4 points5 points (0 children)
But sadly majority of people did not feel that gays should be allowed to marry.
[–] 0 points1 point (3 children)
Well, the majority of people who voted, at least.
[–] 0 points1 point (2 children)
If you didn't vote, and were able to, you don't get to complain. You had a chance to make your say.
[–] 2 points3 points (1 child)
That's not really true. It's hard to pigeonhole 360 degrees on opinion into only 2 choices, either yes or no. The individual has no say on changing anything, merely approving it.
[–] 4 points5 points (0 children)
No, this was thanks to representative democracy. It was a bill in the state legislature that was then signed by the governor. Proposition 2 was a result of direct democracy but only forces egg farmers within the state to change, while this new law requires all eggs imported into the state to essentially be cage-free. For better or worse.
[–] 3 points4 points (0 children)
It's sad that consumers didn't force this kind of action before CA created a law forcing it.
[–] 1 point2 points (0 children)
Such slow progress. It makes me feel like making a small farm in the backyard. Many people love Farmville and Harvest Moon, so it shouldn't be that bad, right?
[–] 1 point2 points (0 children)
So now the chickens will get "Yard time" just like the inmates?
[–] 1 point2 points (3 children)
It's possible for the price of eggs to go up in California, resulting in less eggs being eaten, and an overall decline in the egg industry resulting in some lost jobs.
GG California for making a law where there is such a thing as "unintended consequences" that cannot be forseen completely.
[–] 1 point2 points (0 children)
This just in: California egg farmers suddenly demanding tiny hens.
[–] 1 point2 points (0 children)
But seriously, though, I started buying pastured eggs from my local farmer's market for \$4 - \$5 a jumbo dozen, and they really make a difference. Eggs that come from happy, naturally-fed chickens > eggs that come from normal, cage-free, or even "free range" chickens.
[–] 1 point2 points (0 children)
Arnold Fucking Schwarzenegger. I've said it before: this is a man who gets things done. California is going to be a whole lot worse off when he's gone.
[–] 1 point2 points (0 children)
Yay. Only 5 years to go :)
[–] 1 point2 points (0 children)
\$10 for eggs? Are you kidding me? I feel sorry for Americans, it's unacceptable for example in Poland or Czech Republic to actually sell eggs from chickens aren't "able to stand up, lie down, turn around, and fully extend their limbs without touching one another or the sides of an enclosure".
[–] 1 point2 points (0 children)
I'm still very glad that I voted yes on this measure. I remember how sad it made me when I was first reading the ballot that animals were treated this way.
If I'm going to eat something, I'd rather it have been treated in at least some slightly humane way.
[–] 5 points6 points (0 children)
After literally just finishing Food Inc. (the credits are still paused on my PS3), I feel somewhat better knowing this. At least it's one small step in the right direction.
[–] 4 points5 points (19 children)
As an animal lover, this is good.
[–] 1 point2 points (18 children)
Animals, taste great, don't they? YUM
[–] 2 points3 points (16 children)
Yup. If we weren't supposed to eat them they wouldn't be made out of meat, would they?
[–] 2 points3 points (1 child)
That's what I've been saying about babies!
[–] 1 point2 points (0 children)
Mr. Swift? I thought you were dead!
[–] 0 points1 point (13 children)
That's such a retarded logical fallacy.
And no, it's irrelevant that "it's just a joke!".
[–] 1 point2 points (0 children)
it isn't a joke, it's delicious!
[–] 14 points15 points (54 children)
Starting in 2014, all eggs sold in California will cost \$20 a carton.
[–] 32 points33 points (51 children)
free range eggs start as low as \$2 a dozen, that is about 100% more then the cheapest eggs you can find at a normal grocery store.
[–] 15 points16 points (15 children)
Free range eggs is usually marketing bullshit for "they are still mistreated, just a bit less"
[–] 5 points6 points (11 children)
I get mine from a lady at the farmers market for \$3 a dozen, though I usually just give her \$2 for 6 because I won't eat that many in a week and I don't care about quarters.
[–] 1 point2 points (8 children)
Don't know why you were upvoted. If everyone bought food like you do we wouldn't have most of the problems we have with our food/health system (ie. less engineered food, better quality, less harm to the animals ---> healthier people, less medical issues)
[–] 5 points6 points (7 children)
(ie. less engineered food, better quality, less harm to the animals ---> healthier people, less medical issues)
What makes you think that less engineering leads to better quality?
[–] 0 points1 point (21 children)
What happens when the overall demand stays the same and the supply shrinks to almost nothing?
Unless you mean to tell me that 90% of the eggs sold in CA are free-range right now.
[–] 3 points4 points (3 children)
why would the supply shrink to almost nothing?
[–] 5 points6 points (2 children)
I'd imagine that the vast majority of the current suppliers would be in violation of this law, and depending on how many of them feel that it is more cost effective to come into compliance rather than just stopping selling in California, we could see the supply collapse.
I sincerely doubt that will be the case as this law is not that draconian, but we will see supply reduced marginally, which will cause prices to increase marginally. Though this will be offset by consumers switching to substitutes not affected by this regulation.
[–] 0 points1 point (5 children)
Why would supply shrink? Costs are recouped, the farmer doesn't suffer, the consumer may, but eggs are one of the cheapest proteins available even at 20 cents an egg.
[–] 0 points1 point (2 children)
Why would supply shrink?
Less room to house birds, less demand due to increased costs. (It will likely be a marginal decrease, but a decrease nonetheless.)
[–] 0 points1 point (1 child)
Recouping the recooping costs?
[–] 0 points1 point (0 children)
"The U.S. Department of Agriculture Food Safety and Inspection Service (FSIS) requires that chickens raised for their meat have access to the outside in order to receive the free-range certification. There is no requirement for access to pasture, and there may be access to only dirt or gravel . Free-range chicken eggs, however, have no legal definition in the United States. Likewise, free-range egg producers have no common standard on what the term means. Many egg farmers sell their eggs as free range merely because their cages are two or three inches above average size, or because there is a window in the shed."
From Wikipedia. Unfortunately the passage needs a citation. But I've come across this distinction before. I've noticed that I can find competing brands of free-range chicken eggs in regional grocery stores where I can't find a single free range chicken (part or whole) for sale.
[–] 3 points4 points (0 children)
They stopped selling eggs from cached hens in Germany a while ago and prices are not really that bad. I think that the price is still OK and I am a student without much money. I think that this is a good move.
[–] 1 point2 points (0 children)
[–] 5 points6 points (2 children)
Great, now we're going to have to chop their wings off first to make them profitable.
[–] 2 points3 points (0 children)
Well, they already chop the beak off....
[–] 1 point2 points (0 children)
In 2015, egg prices remain unaffected, but hotwings go through the roof!
[–] 2 points3 points (0 children)
this is why i live in california... occasionally the earthquakes shake some sense into people
[–] 2 points3 points (1 child)
Why does this not apply to cows and pigs as well?
[–] 3 points4 points (3 children)
You forgot one caveat; do the hokey pokey. (just kidding). A better title might have been: California passes law preventing chicken factory farming.
[–] 9 points10 points (2 children)
Doesn't mean you can't have a factory farm, you just have to be less (perceivably) cruel when doing it.
Thus, specifically, the chickens must be "able to stand up, lie down, turn around, and fully extend their limbs without touching one another or the sides of an enclosure."
Title is pretty good, since it seems true. Factory farms won't go out of business, either, so it's not prevented.
[–] 1 point2 points (0 children)
Yup, you're right on all counts. I was just trying to inject a little lightheartedness into an otherwise gloomy-news day. Perhaps the prevent part was wishful thinking, since I used to raise chickens myself and am rather fond of the silly birds.
[–] 3 points4 points (6 children)
In a state with 20% unemployment, minimum wage state workers, they're giving rights to chickens?
[–] 13 points14 points (5 children)
In a world where people starve to death, people are worrying about employment rates?
[–] 6 points7 points (4 children)
In a world where people starving to death are still having children, people are still worrying about food?
[–] 4 points5 points (0 children)
It's shitty all the way down.
[–] 1 point2 points (2 children)
Cannibalism would solve all our problems.
[–] 3 points4 points (1 child)
That's so fucking awesome. The way factory farms are run is the #1 reason why I stopped eating meat.
[–] 1 point2 points (2 children)
People there is no reason to freak about this or even care. It doesnt happen until 2015 and it wont matter then, cause the world ends on dec 22nd 2012. And we will all be dead.
So no reason to panic folks.
[–] 1 point2 points (1 child)
December 21, 2012, actually.
[–] 1 point2 points (7 children)
I AM GOING TO MOVE TO AZ AND FARM CHICKENS THE OLD WAY, AND THEN SELL THE EGGS ONLINE. CA WONT BE ABLE TO PROSECUTE ME ahahahahhaha!1111!!! I WIN
[–] 1 point2 points (1 child)
Given previous experiences with Fedex and UPS, I don't think many people would jump on the opportunity to buy eggs online.
[–] 1 point2 points (0 children)
IT WAS JUST A CRAZY THOUGHT I HAD. I THINK IT WOULD WORK
[–] 0 points1 point (4 children)
I wonder who's goin to collect the eggs?
[–] 1 point2 points (2 children)
PEOPLE.
[–] 0 points1 point (1 child)
I demand to see their papers…
[–] 0 points1 point (0 children)
i dont understand?
[–] 0 points1 point (0 children)
Illegal immigr...well shit.
[–] 1 point2 points (1 child)
I'm torn on issues like these. Initiatives like this are part of the reason private business has began to leave California. You wonder why this state has high unemployment?
That being said, I buy only free range eggs. I don't want to eat eggs from an animal literally stuffed in a cage.
There has to be a better solution that forcing business to change their actions through laws and more regulation. Why not tax breaks for companies who sell free range only eggs?
[–] 2 points3 points (0 children)
A tax break is a law. Sorry, the only way to keep humans from mistreating animals is with the law.
[–] 1 point2 points (0 children)
The hens must be able to get some eggsercise.
[–] 1 point2 points (11 children)
And this effects eggs how? This should be more for the chickens being sent off to be turned into food. It's not really such an improvement for the egg itself (I don't really buy into the whole "organic" BS). It will only drive up the prices and cause more lawsuits over useless stuff.
[–] 1 point2 points (0 children)
Now people will now buy cheap eggs from Mexico where the hens are treated even worse than the California ones before this law.
[–] 2 points3 points (3 children)
Which means that hens in California get better living conditions than prisoners in California! Clearly we have our priorities straight in this state. I guess prisoners can't lay eggs, though.
[–] 1 point2 points (0 children)
I guess prisoners can't lay eggs, though.
give us time, dammit
[–] 0 points1 point (0 children)
Cue "Chicken Fat". Robert Preston RIP.
[–] 0 points1 point (0 children)
[–] 0 points1 point (5 children)
So will they be carrying a free range label then?
[–] 0 points1 point (1 child)
In this thread: People complaining about slight price increases, which in their heads will make chicken eggs the same cost as Fabergé eggs, due to basic living standards for chickens. I wonder if they would be for the active torture and live vivisection of chickens if it mean a slight decrease in prices...
[–] 1 point2 points (0 children)
Yes. Serisouly Yes. Lots and lots of people would be for that. If it really did mean a decrease in price. Do you not realise that some people fundamentally don't think it matters what happens to animals?
[–] 0 points1 point (0 children)
yo... keep your chickens to yourself
[–] 0 points1 point (0 children)
Excellent, only 40,000,000,000 chickens to go before the law applies in 2015
[–] 0 points1 point (0 children)
They should call this the Hokey Pokey Initiative.
[–] 0 points1 point (0 children)
Wait. What? So if they can jump down, turn around and pick a bail of cotton it's OK?
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https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/Kerr_extremal_extended.ipynb | 1,686,347,550,000,000,000 | text/plain | crawl-data/CC-MAIN-2023-23/segments/1685224656833.99/warc/CC-MAIN-20230609201549-20230609231549-00359.warc.gz | 532,844,421 | 726,487 | { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Maximal extension of the extremal Kerr black hole\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/).\n", "\n", "The computations make use of tools developed through the [SageManifolds project](https://sagemanifolds.obspm.fr)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.5.beta2, Release Date: 2021-09-26'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX rendering:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To speed up computations, we ask for running them in parallel on 8 threads:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Parallelism().set(nproc=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime manifold\n", "\n", "We declare the Kerr spacetime as a 4-dimensional Lorentzian manifold $M$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then introduce (3+1 version of) the **Kerr coordinates** $(\\tilde{t},r,\\theta,\\tilde{\\varphi})$ as a chart KC on $M$, via the method chart(). The argument of the latter is a string (delimited by r\"...\" because of the backslash symbols) expressing the coordinates names, their ranges (the default is $(-\\infty,+\\infty)$) and their LaTeX symbols:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (M, (tt, r, th, tph))\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,({\\tilde{t}}, r, {\\theta}, {\\tilde{\\varphi}})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,({\\tilde{t}}, r, {\\theta}, {\\tilde{\\varphi}})\\right)$$" ], "text/plain": [ "Chart (M, (tt, r, th, tph))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC. = M.chart(r\"tt:\\tilde{t} r th:(0,pi):\\theta tph:(0,2*pi):periodic:\\tilde{\\varphi}\") \n", "print(KC); KC" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "tt: (-oo, +oo); r: (-oo, +oo); th: (0, pi); tph: [0, 2*pi] (periodic)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metric tensor \n", "\n", "The mass parameter $m$ of the extremal Kerr spacetime is declared as a symbolic variable:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "m = var('m', domain='real')\n", "assume(m>0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the (yet undefined) spacetime metric:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "g = M.metric()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and initialize it by providing its components in the coordinate frame associated with the Kerr coordinates, which is the current manifold's default frame:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} {\\tilde{t}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} {\\tilde{\\varphi}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{t}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\varphi}} + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} {\\tilde{t}} -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} r + {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} {\\tilde{\\varphi}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} {\\tilde{t}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{t}}\\otimes \\mathrm{d} {\\tilde{\\varphi}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{t}} + \\left( \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\varphi}} + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} {\\tilde{t}} -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} r + {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\tilde{\\varphi}}\\otimes \\mathrm{d} {\\tilde{\\varphi}}$$" ], "text/plain": [ "g = (2*m*r/(m^2*cos(th)^2 + r^2) - 1) dtt⊗dtt + 2*m*r/(m^2*cos(th)^2 + r^2) dtt⊗dr - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) dtt⊗dtph + 2*m*r/(m^2*cos(th)^2 + r^2) dr⊗dtt + (2*m*r/(m^2*cos(th)^2 + r^2) + 1) dr⊗dr - m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2 dr⊗dtph + (m^2*cos(th)^2 + r^2) dth⊗dth - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) dtph⊗dtt - m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2 dtph⊗dr + (2*m^3*r*sin(th)^2/(m^2*cos(th)^2 + r^2) + m^2 + r^2)*sin(th)^2 dtph⊗dtph" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho2 = r^2 + (m*cos(th))^2\n", "g[0,0] = - (1 - 2*m*r/rho2)\n", "g[0,1] = 2*m*r/rho2\n", "g[0,3] = -2*m^2*r*sin(th)^2/rho2\n", "g[1,1] = 1 + 2*m*r/rho2\n", "g[1,3] = -m*(1 + 2*m*r/rho2)*sin(th)^2\n", "g[2,2] = rho2\n", "g[3,3] = (r^2 + m^2 + 2*m^3*r*sin(th)^2/rho2)*sin(th)^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A matrix view of the components with respect to the manifold's default vector frame:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & 0 & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\\n", "\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 & 0 & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\\n", "0 & 0 & m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} & 0 \\\\\n", "-\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} & 0 & {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & 0 & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\\n", "\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 & 0 & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\\n", "0 & 0 & m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} & 0 \\\\\n", "-\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} & 0 & {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 2*m*r/(m^2*cos(th)^2 + r^2) - 1 2*m*r/(m^2*cos(th)^2 + r^2) 0 -2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2)]\n", "[ 2*m*r/(m^2*cos(th)^2 + r^2) 2*m*r/(m^2*cos(th)^2 + r^2) + 1 0 -m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2]\n", "[ 0 0 m^2*cos(th)^2 + r^2 0]\n", "[ -2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) -m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2 0 (2*m^3*r*sin(th)^2/(m^2*cos(th)^2 + r^2) + m^2 + r^2)*sin(th)^2]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The list of the non-vanishing components:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} g_{ \\, {\\tilde{t}} \\, {\\tilde{t}} }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, {\\tilde{t}}} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 \\\\ g_{ \\, {\\tilde{t}} \\, r }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, r} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, {\\tilde{t}} \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, {\\tilde{\\varphi}}} } & = & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, r \\, {\\tilde{t}} }^{ \\phantom{\\, r}\\phantom{\\, {\\tilde{t}}} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, r \\, r }^{ \\phantom{\\, r}\\phantom{\\, r} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 \\\\ g_{ \\, r \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, r}\\phantom{\\, {\\tilde{\\varphi}}} } & = & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ g_{ \\, {\\theta} \\, {\\theta} }^{ \\phantom{\\, {\\theta}}\\phantom{\\, {\\theta}} } & = & m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, {\\tilde{t}} }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, {\\tilde{t}}} } & = & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, r }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, r} } & = & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, {\\tilde{\\varphi}}} } & = & {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} g_{ \\, {\\tilde{t}} \\, {\\tilde{t}} }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, {\\tilde{t}}} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} - 1 \\\\ g_{ \\, {\\tilde{t}} \\, r }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, r} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, {\\tilde{t}} \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, {\\tilde{t}}}\\phantom{\\, {\\tilde{\\varphi}}} } & = & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, r \\, {\\tilde{t}} }^{ \\phantom{\\, r}\\phantom{\\, {\\tilde{t}}} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, r \\, r }^{ \\phantom{\\, r}\\phantom{\\, r} } & = & \\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1 \\\\ g_{ \\, r \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, r}\\phantom{\\, {\\tilde{\\varphi}}} } & = & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ g_{ \\, {\\theta} \\, {\\theta} }^{ \\phantom{\\, {\\theta}}\\phantom{\\, {\\theta}} } & = & m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, {\\tilde{t}} }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, {\\tilde{t}}} } & = & -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, r }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, r} } & = & -m {\\left(\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + 1\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ g_{ \\, {\\tilde{\\varphi}} \\, {\\tilde{\\varphi}} }^{ \\phantom{\\, {\\tilde{\\varphi}}}\\phantom{\\, {\\tilde{\\varphi}}} } & = & {\\left(\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} + m^{2} + r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\end{array}$$" ], "text/plain": [ "g_tt,tt = 2*m*r/(m^2*cos(th)^2 + r^2) - 1 \n", "g_tt,r = 2*m*r/(m^2*cos(th)^2 + r^2) \n", "g_tt,tph = -2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) \n", "g_r,tt = 2*m*r/(m^2*cos(th)^2 + r^2) \n", "g_r,r = 2*m*r/(m^2*cos(th)^2 + r^2) + 1 \n", "g_r,tph = -m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2 \n", "g_th,th = m^2*cos(th)^2 + r^2 \n", "g_tph,tt = -2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) \n", "g_tph,r = -m*(2*m*r/(m^2*cos(th)^2 + r^2) + 1)*sin(th)^2 \n", "g_tph,tph = (2*m^3*r*sin(th)^2/(m^2*cos(th)^2 + r^2) + m^2 + r^2)*sin(th)^2 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that we are dealing with a solution of the **vacuum Einstein equation**:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "#g.ricci().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regions $M_{\\rm I}$ and $M_{\\rm III}$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left( -\\infty, +\\infty \\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left( -\\infty, +\\infty \\right)$$" ], "text/plain": [ "tt: (-oo, +oo); r: (m, +oo); th: (-oo, +oo); tph: (-oo, +oo)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M_I = M.open_subset('M_I', latex_name=r'M_{\\rm I}', coord_def={KC: r>m})\n", "KC.restrict(M_I).coord_range()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, m \\right) ;\\quad {\\theta} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left( -\\infty, +\\infty \\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{t}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, m \\right) ;\\quad {\\theta} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\tilde{\\varphi}} :\\ \\left( -\\infty, +\\infty \\right)$$" ], "text/plain": [ "tt: (-oo, +oo); r: (-oo, m); th: (-oo, +oo); tph: (-oo, +oo)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M_III = M.open_subset('M_III', latex_name=r'M_{\\rm III}', coord_def={KC: r\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M_{\\rm I},(t, r, {\\theta}, {\\varphi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M_{\\rm I},(t, r, {\\theta}, {\\varphi})\\right)$$" ], "text/plain": [ "Chart (M_I, (t, r, th, ph))" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BL. = M_I.chart(r\"t r:(m,+oo) th:(0,pi):\\theta ph:(0,2*pi):periodic:\\varphi\") \n", "print(BL); BL" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\varphi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\varphi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "t: (-oo, +oo); r: (m, +oo); th: (0, pi); ph: [0, 2*pi] (periodic)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BL.coord_range()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -2 \\, m \\log\\left(\\frac{{\\left| -m + r \\right|}}{m}\\right) - \\frac{2 \\, m^{2}}{m - r} + {\\tilde{t}} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\varphi} & = & {\\tilde{\\varphi}} - \\frac{m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -2 \\, m \\log\\left(\\frac{{\\left| -m + r \\right|}}{m}\\right) - \\frac{2 \\, m^{2}}{m - r} + {\\tilde{t}} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\varphi} & = & {\\tilde{\\varphi}} - \\frac{m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "t = -2*m*log(abs(-m + r)/m) - 2*m^2/(m - r) + tt\n", "r = r\n", "th = th\n", "ph = tph - m/(m - r)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC_to_BL = KC.restrict(M_I).transition_map(BL, [tt + 2*m^2/(r-m) - 2*m*ln(abs(r-m)/m),\n", " r, th, tph + m/(r-m)])\n", "KC_to_BL.display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{t}} & = & -\\frac{2 \\, m^{2} \\log\\left(m\\right) - 2 \\, m r \\log\\left(m\\right) - 2 \\, m^{2} - {\\left(m - r\\right)} t - 2 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\varphi} - {\\varphi} r + m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{t}} & = & -\\frac{2 \\, m^{2} \\log\\left(m\\right) - 2 \\, m r \\log\\left(m\\right) - 2 \\, m^{2} - {\\left(m - r\\right)} t - 2 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\varphi} - {\\varphi} r + m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "tt = -(2*m^2*log(m) - 2*m*r*log(m) - 2*m^2 - (m - r)*t - 2*(m^2 - m*r)*log(-m + r))/(m - r)\n", "r = r\n", "th = th\n", "tph = (m*ph - ph*r + m)/(m - r)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC_to_BL.inverse().display()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( -\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} - 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} {\\varphi} + \\left( \\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( -\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} - 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} {\\varphi} + \\left( \\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$$" ], "text/plain": [ "g = -(m^2*cos(th)^2 - 2*m*r + r^2)/(m^2*cos(th)^2 + r^2) dt⊗dt - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) dt⊗dph + (m^2*cos(th)^2 + r^2)/(m^2 - 2*m*r + r^2) dr⊗dr + (m^2*cos(th)^2 + r^2) dth⊗dth - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) dph⊗dt + (2*m^3*r*sin(th)^4 + (m^2*r^2 + r^4 + (m^4 + m^2*r^2)*cos(th)^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2) dph⊗dph" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(BL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ingoing principal null geodesics" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\frac{\\partial}{\\partial {\\tilde{t}} }-\\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\frac{\\partial}{\\partial {\\tilde{t}} }-\\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "k = ∂/∂tt - ∂/∂r" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = M.vector_field(1, -1, 0, 0, name='k')\n", "k.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that $k$ is a null vector:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(k, k).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that $k$ is a geodesic vector field, i.e. obeys $\\nabla_k k = 0$:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "nabla = g.connection()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nabla(k).contract(k).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expression of $k$ with respect to the Boyer-Lindquist frame:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } -\\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\varphi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } -\\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\varphi} }$$" ], "text/plain": [ "k = (m^2 + r^2)/(m^2 - 2*m*r + r^2) ∂/∂t - ∂/∂r + m/(m^2 - 2*m*r + r^2) ∂/∂ph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k.display(BL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outgoing principal null geodesics" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{{\\left(m + r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial {\\tilde{t}} } + \\frac{{\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{{\\left(m + r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial {\\tilde{t}} } + \\frac{{\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }$$" ], "text/plain": [ "el = 1/2*(m + r)^2/(m^2 + r^2) ∂/∂tt + 1/2*(m - r)^2/(m^2 + r^2) ∂/∂r + m/(m^2 + r^2) ∂/∂tph" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "el = M.vector_field((r + m)^2/(2*(r^2 + m^2)),\n", " (r - m)^2/(2*(r^2 + m^2)),\n", " 0,\n", " m/(r^2 + m^2),\n", " name='el', latex_name=r'\\ell')\n", "el.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that $\\ell$ is a null vector:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(el, el).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expression of $\\ell$ with respect to the Boyer-Lindquist frame:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{1}{2} \\frac{\\partial}{\\partial t } + \\frac{{\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial r } + \\frac{m}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial {\\varphi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{1}{2} \\frac{\\partial}{\\partial t } + \\frac{{\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial r } + \\frac{m}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\frac{\\partial}{\\partial {\\varphi} }$$" ], "text/plain": [ "el = 1/2 ∂/∂t + 1/2*(m - r)^2/(m^2 + r^2) ∂/∂r + 1/2*m/(m^2 + r^2) ∂/∂ph" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "el.display(BL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Computation of $\\nabla_\\ell \\ell$:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( -\\frac{m^{5} + 2 \\, m^{4} r - 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{t}} } + \\left( -\\frac{m^{5} - 2 \\, m^{4} r + 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( -\\frac{m^{4} - m^{2} r^{2}}{m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( -\\frac{m^{5} + 2 \\, m^{4} r - 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{t}} } + \\left( -\\frac{m^{5} - 2 \\, m^{4} r + 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( -\\frac{m^{4} - m^{2} r^{2}}{m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }$$" ], "text/plain": [ "-1/2*(m^5 + 2*m^4*r - 2*m^2*r^3 - m*r^4)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂tt - 1/2*(m^5 - 2*m^4*r + 2*m^2*r^3 - m*r^4)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂r - (m^4 - m^2*r^2)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂tph" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc = nabla(el).contract(el)\n", "acc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check that $\\nabla_\\ell \\ell = \\kappa \\ell$:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{3} - m r^{2}}{m^{4} + 2 \\, m^{2} r^{2} + r^{4}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{3} - m r^{2}}{m^{4} + 2 \\, m^{2} r^{2} + r^{4}}$$" ], "text/plain": [ "-(m^3 - m*r^2)/(m^4 + 2*m^2*r^2 + r^4)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappa = acc[0] / el[0]\n", "kappa" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(m + r\\right)} {\\left(m - r\\right)} m}{{\\left(m^{2} + r^{2}\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(m + r\\right)} {\\left(m - r\\right)} m}{{\\left(m^{2} + r^{2}\\right)}^{2}}$$" ], "text/plain": [ "-(m + r)*(m - r)*m/(m^2 + r^2)^2" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappa.factor()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc == kappa*el" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outgoing Kerr coordinates on $M_{\\rm I}$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{\\tilde{t}}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\tilde{\\varphi}}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{\\tilde{t}}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( m , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\tilde{\\varphi}}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "to: (-oo, +oo); r: (m, +oo); th: (0, pi); oph: [0, 2*pi] (periodic)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "OKC. = M_I.chart(r\"to:\\tilde{\\tilde{t}} r:(m,+oo) th:(0,pi):\\theta oph:(0,2*pi):periodic:\\tilde{\\tilde{\\varphi}}\") \n", "OKC.coord_range()" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{\\tilde{t}}} & = & -2 \\, m \\log\\left(\\frac{{\\left| -m + r \\right|}}{m}\\right) - \\frac{2 \\, m^{2}}{m - r} + t \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & {\\varphi} - \\frac{m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{\\tilde{t}}} & = & -2 \\, m \\log\\left(\\frac{{\\left| -m + r \\right|}}{m}\\right) - \\frac{2 \\, m^{2}}{m - r} + t \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & {\\varphi} - \\frac{m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "to = -2*m*log(abs(-m + r)/m) - 2*m^2/(m - r) + t\n", "r = r\n", "th = th\n", "oph = ph - m/(m - r)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BL_to_OKC = BL.transition_map(OKC, [t + 2*m^2/(r-m) - 2*m*ln(abs(r-m)/m),\n", " r, th, ph + m/(r-m)])\n", "BL_to_OKC.display()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -\\frac{2 \\, m^{2} \\log\\left(m\\right) - 2 \\, m r \\log\\left(m\\right) - 2 \\, m^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 2 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\varphi} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -\\frac{2 \\, m^{2} \\log\\left(m\\right) - 2 \\, m r \\log\\left(m\\right) - 2 \\, m^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 2 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\varphi} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "t = -(2*m^2*log(m) - 2*m*r*log(m) - 2*m^2 - (m - r)*to - 2*(m^2 - m*r)*log(-m + r))/(m - r)\n", "r = r\n", "th = th\n", "ph = (m*oph - oph*r + m)/(m - r)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BL_to_OKC.inverse().display()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{\\tilde{t}}} & = & \\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m r \\log\\left(m\\right) - 4 \\, m^{2} + {\\left(m - r\\right)} {\\tilde{t}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & \\frac{{\\left(m - r\\right)} {\\tilde{\\varphi}} - 2 \\, m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{\\tilde{t}}} & = & \\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m r \\log\\left(m\\right) - 4 \\, m^{2} + {\\left(m - r\\right)} {\\tilde{t}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & \\frac{{\\left(m - r\\right)} {\\tilde{\\varphi}} - 2 \\, m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "to = (4*m^2*log(m) - 4*m*r*log(m) - 4*m^2 + (m - r)*tt - 4*(m^2 - m*r)*log(-m + r))/(m - r)\n", "r = r\n", "th = th\n", "oph = ((m - r)*tph - 2*m)/(m - r)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC_to_OKC = BL_to_OKC * KC_to_BL.restrict(M_I)\n", "KC_to_OKC.display()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{t}} & = & -\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m r \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + 2 \\, m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tilde{t}} & = & -\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m r \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{m - r} \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + 2 \\, m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "tt = -(4*m^2*log(m) - 4*m*r*log(m) - 4*m^2 - (m - r)*to - 4*(m^2 - m*r)*log(-m + r))/(m - r)\n", "r = r\n", "th = th\n", "tph = (m*oph - oph*r + 2*m)/(m - r)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "KC_to_OKC.inverse().display()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "M_I.set_default_chart(OKC)\n", "M_I.set_default_frame(OKC.frame())" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( -\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} - 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( -\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}} + \\left( -\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( \\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}} + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( -\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} r + \\left( \\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( -\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} - 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( -\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{t}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}} + \\left( -\\frac{2 \\, m r}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( \\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + 2 \\, m r + r^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}} + \\left( m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, m^{2} r \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{t}}} + \\left( -\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} r + \\left( \\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}\\otimes \\mathrm{d} {\\tilde{\\tilde{\\varphi}}}$$" ], "text/plain": [ "g = -(m^2*cos(th)^2 - 2*m*r + r^2)/(m^2*cos(th)^2 + r^2) dto⊗dto - 2*m*r/(m^2*cos(th)^2 + r^2) dto⊗dr - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) dto⊗doph - 2*m*r/(m^2*cos(th)^2 + r^2) dr⊗dto + (m^2*cos(th)^2 + 2*m*r + r^2)/(m^2*cos(th)^2 + r^2) dr⊗dr - (m^3*sin(th)^4 - (m^3 + 2*m^2*r + m*r^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2) dr⊗doph + (m^2*cos(th)^2 + r^2) dth⊗dth - 2*m^2*r*sin(th)^2/(m^2*cos(th)^2 + r^2) doph⊗dto - (m^3*sin(th)^4 - (m^3 + 2*m^2*r + m*r^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2) doph⊗dr + (2*m^3*r*sin(th)^4 + (m^2*r^2 + r^4 + (m^4 + m^2*r^2)*cos(th)^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2) doph⊗doph" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gI = g.restrict(M_I)\n", "gI.display()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{3} \\sin\\left({\\theta}\\right)^{4} - {\\left(m^{3} + 2 \\, m^{2} r + m r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}$$" ], "text/plain": [ "-(m^3*sin(th)^4 - (m^3 + 2*m^2*r + m*r^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gI[1,3]" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gI[1,3] == m*(1 + 2*m*r/rho2)*sin(th)^2" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, m^{3} r \\sin\\left({\\theta}\\right)^{4} + {\\left(m^{2} r^{2} + r^{4} + {\\left(m^{4} + m^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}$$" ], "text/plain": [ "(2*m^3*r*sin(th)^4 + (m^2*r^2 + r^4 + (m^4 + m^2*r^2)*cos(th)^2)*sin(th)^2)/(m^2*cos(th)^2 + r^2)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gI[3,3]" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[3,3] == (r^2 + m^2 + 2*m^3*r*sin(th)^2/rho2)*sin(th)^2" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} }+\\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} }+\\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "ol = ∂/∂to + ∂/∂r" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ol = M_I.vector_field({OKC.frame(): (1, 1, 0, 0)}, name='ol', \n", " latex_name=r\"\\ell'\")\n", "ol.display()" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{t}} } +\\frac{\\partial}{\\partial r } + \\left( \\frac{2 \\, m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{t}} } +\\frac{\\partial}{\\partial r } + \\left( \\frac{2 \\, m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\varphi}} }$$" ], "text/plain": [ "ol = (m^2 + 2*m*r + r^2)/(m^2 - 2*m*r + r^2) ∂/∂tt + ∂/∂r + 2*m/(m^2 - 2*m*r + r^2) ∂/∂tph" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ol.display(KC.restrict(M_I).frame())" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\left( \\frac{m^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } +\\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\varphi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell' = \\left( \\frac{m^{2} + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } +\\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\varphi} }$$" ], "text/plain": [ "ol = (m^2 + r^2)/(m^2 - 2*m*r + r^2) ∂/∂t + ∂/∂r + m/(m^2 - 2*m*r + r^2) ∂/∂ph" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ol.display(BL.frame())" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(ol, ol).expr()" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|3-indices|\\phantom{\\verb!x!}\\verb|components|\\phantom{\\verb!x!}\\verb|w.r.t.|\\phantom{\\verb!x!}\\verb|Coordinate|\\phantom{\\verb!x!}\\verb|frame|\\phantom{\\verb!x!}\\verb|(M_I,|\\phantom{\\verb!x!}\\verb|(∂/∂to,∂/∂r,∂/∂th,∂/∂oph)),|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|symmetry|\\phantom{\\verb!x!}\\verb|on|\\phantom{\\verb!x!}\\verb|the|\\phantom{\\verb!x!}\\verb|index|\\phantom{\\verb!x!}\\verb|positions|\\phantom{\\verb!x!}\\verb|(1,|\\phantom{\\verb!x!}\\verb|2)|\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|3-indices|\\phantom{\\verb!x!}\\verb|components|\\phantom{\\verb!x!}\\verb|w.r.t.|\\phantom{\\verb!x!}\\verb|Coordinate|\\phantom{\\verb!x!}\\verb|frame|\\phantom{\\verb!x!}\\verb|(M_I,|\\phantom{\\verb!x!}\\verb|(∂/∂to,∂/∂r,∂/∂th,∂/∂oph)),|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|symmetry|\\phantom{\\verb!x!}\\verb|on|\\phantom{\\verb!x!}\\verb|the|\\phantom{\\verb!x!}\\verb|index|\\phantom{\\verb!x!}\\verb|positions|\\phantom{\\verb!x!}\\verb|(1,|\\phantom{\\verb!x!}\\verb|2)|$$" ], "text/plain": [ "3-indices components w.r.t. Coordinate frame (M_I, (∂/∂to,∂/∂r,∂/∂th,∂/∂oph)), with symmetry on the index positions (1, 2)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nabla.coef(OKC.frame())" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nabla(ol).contract(ol).display()" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\left( \\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( \\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\left( \\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( \\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "el = 1/2*(m^2 - 2*m*r + r^2)/(m^2 + r^2) ∂/∂to + 1/2*(m^2 - 2*m*r + r^2)/(m^2 + r^2) ∂/∂r" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "elI = el.restrict(M_I)\n", "elI.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the relation $\\ell' = 2 \\frac{r^2 + m^2}{(r - m)^2} \\, \\ell$:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ol == 2*(r^2 + m^2)/(r - m)^2 * elI" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } -\\frac{\\partial}{\\partial r } + \\left( \\frac{2 \\, m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } -\\frac{\\partial}{\\partial r } + \\left( \\frac{2 \\, m}{m^{2} - 2 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }$$" ], "text/plain": [ "k = (m^2 + 2*m*r + r^2)/(m^2 - 2*m*r + r^2) ∂/∂to - ∂/∂r + 2*m/(m^2 - 2*m*r + r^2) ∂/∂oph" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kI = k.restrict(M_I)\n", "kI.display()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k' = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( -\\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k' = \\left( \\frac{m^{2} + 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( -\\frac{m^{2} - 2 \\, m r + r^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( \\frac{m}{m^{2} + r^{2}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }$$" ], "text/plain": [ "ok = 1/2*(m^2 + 2*m*r + r^2)/(m^2 + r^2) ∂/∂to - 1/2*(m^2 - 2*m*r + r^2)/(m^2 + r^2) ∂/∂r + m/(m^2 + r^2) ∂/∂oph" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ok = (r - m)^2/(2*(r^2 + m^2)) * kI\n", "ok.set_name('ok', latex_name=r\"k'\")\n", "ok.display()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} + r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} + r^{2}}$$" ], "text/plain": [ "-(m^2*cos(th)^2 + r^2)/(m^2 + r^2)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(k, el).expr()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} + r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{m^{2} + r^{2}}$$" ], "text/plain": [ "-(m^2*cos(th)^2 + r^2)/(m^2 + r^2)" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(ok, ol).expr()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}\\right)}}{{\\left(m - r\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}\\right)}}{{\\left(m - r\\right)}^{2}}$$" ], "text/plain": [ "-2*(m^2*cos(th)^2 + r^2)/(m - r)^2" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(k, ol).expr().factor()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}\\right)} {\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(m^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}\\right)} {\\left(m - r\\right)}^{2}}{2 \\, {\\left(m^{2} + r^{2}\\right)}^{2}}$$" ], "text/plain": [ "-1/2*(m^2*cos(th)^2 + r^2)*(m - r)^2/(m^2 + r^2)^2" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(ok, el).expr().factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Non-affinity coefficient of $k'$" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{m^{5} + 2 \\, m^{4} r - 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( -\\frac{m^{5} - 2 \\, m^{4} r + 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( \\frac{m^{4} - m^{2} r^{2}}{m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{m^{5} + 2 \\, m^{4} r - 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{t}}} } + \\left( -\\frac{m^{5} - 2 \\, m^{4} r + 2 \\, m^{2} r^{3} - m r^{4}}{2 \\, {\\left(m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}\\right)}} \\right) \\frac{\\partial}{\\partial r } + \\left( \\frac{m^{4} - m^{2} r^{2}}{m^{6} + 3 \\, m^{4} r^{2} + 3 \\, m^{2} r^{4} + r^{6}} \\right) \\frac{\\partial}{\\partial {\\tilde{\\tilde{\\varphi}}} }$$" ], "text/plain": [ "1/2*(m^5 + 2*m^4*r - 2*m^2*r^3 - m*r^4)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂to - 1/2*(m^5 - 2*m^4*r + 2*m^2*r^3 - m*r^4)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂r + (m^4 - m^2*r^2)/(m^6 + 3*m^4*r^2 + 3*m^2*r^4 + r^6) ∂/∂oph" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc_ok = nabla(ok).contract(ok)\n", "acc_ok.display()" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{\\left(m + r\\right)} {\\left(m - r\\right)} m}{{\\left(m^{2} + r^{2}\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{\\left(m + r\\right)} {\\left(m - r\\right)} m}{{\\left(m^{2} + r^{2}\\right)}^{2}}$$" ], "text/plain": [ "(m + r)*(m - r)*m/(m^2 + r^2)^2" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappa_ok = acc_ok[0] / ok[0]\n", "kappa_ok.factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check that $\\nabla_{k'} k' = \\kappa_{k'} k'$:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc_ok == kappa_ok * ok" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compactified coordinates on $M$" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(T, X, {\\theta}, {\\tilde{\\varphi}})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(T, X, {\\theta}, {\\tilde{\\varphi}})\\right)$$" ], "text/plain": [ "Chart (M, (T, X, th, tph))" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CC. = M.chart(r\"T X th:(0,pi):\\theta tph:(0,2*pi):periodic:\\tilde{\\varphi}\")\n", "CC" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(-\\frac{2 \\, m}{m - r} - \\frac{r - {\\tilde{t}}}{2 \\, m} - 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(\\frac{r + {\\tilde{t}}}{2 \\, m}\\right) \\\\ X & = & -\\pi \\mathrm{u}\\left(m - r\\right) - \\arctan\\left(-\\frac{2 \\, m}{m - r} - \\frac{r - {\\tilde{t}}}{2 \\, m} - 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(\\frac{r + {\\tilde{t}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & {\\tilde{\\varphi}} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(-\\frac{2 \\, m}{m - r} - \\frac{r - {\\tilde{t}}}{2 \\, m} - 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(\\frac{r + {\\tilde{t}}}{2 \\, m}\\right) \\\\ X & = & -\\pi \\mathrm{u}\\left(m - r\\right) - \\arctan\\left(-\\frac{2 \\, m}{m - r} - \\frac{r - {\\tilde{t}}}{2 \\, m} - 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(\\frac{r + {\\tilde{t}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & {\\tilde{\\varphi}} \\end{array}\\right.$$" ], "text/plain": [ "T = pi*unit_step(m - r) + arctan(-2*m/(m - r) - 1/2*(r - tt)/m - 2*log(abs((m - r)/m))) + arctan(1/2*(r + tt)/m)\n", "X = -pi*unit_step(m - r) - arctan(-2*m/(m - r) - 1/2*(r - tt)/m - 2*log(abs((m - r)/m))) + arctan(1/2*(r + tt)/m)\n", "th = th\n", "tph = tph" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc = (tt - r)/m + 4*m/(r - m) - 4*ln(abs((r - m)/m))\n", "vc = (tt + r)/m\n", "KC_to_CC = KC.transition_map(CC, [atan(uc/2) + atan(vc/2) + pi*unit_step(m - r),\n", " atan(vc/2) - atan(uc/2) - pi*unit_step(m - r),\n", " th,\n", " tph])\n", "KC_to_CC.display()" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\arctan\\left(-\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(4 \\, m \\log\\left(m\\right) + m\\right)} r + r^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{2 \\, {\\left(m^{2} - m r\\right)}}\\right) + \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ X & = & \\arctan\\left(-\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(4 \\, m \\log\\left(m\\right) + m\\right)} r + r^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{2 \\, {\\left(m^{2} - m r\\right)}}\\right) - \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + 2 \\, m}{m - r} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\arctan\\left(-\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(4 \\, m \\log\\left(m\\right) + m\\right)} r + r^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{2 \\, {\\left(m^{2} - m r\\right)}}\\right) + \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ X & = & \\arctan\\left(-\\frac{4 \\, m^{2} \\log\\left(m\\right) - 4 \\, m^{2} - {\\left(4 \\, m \\log\\left(m\\right) + m\\right)} r + r^{2} - {\\left(m - r\\right)} {\\tilde{\\tilde{t}}} - 4 \\, {\\left(m^{2} - m r\\right)} \\log\\left(-m + r\\right)}{2 \\, {\\left(m^{2} - m r\\right)}}\\right) - \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\varphi}} & = & \\frac{m {\\tilde{\\tilde{\\varphi}}} - {\\tilde{\\tilde{\\varphi}}} r + 2 \\, m}{m - r} \\end{array}\\right.$$" ], "text/plain": [ "T = arctan(-1/2*(4*m^2*log(m) - 4*m^2 - (4*m*log(m) + m)*r + r^2 - (m - r)*to - 4*(m^2 - m*r)*log(-m + r))/(m^2 - m*r)) + arctan(-1/2*(r - to)/m)\n", "X = arctan(-1/2*(4*m^2*log(m) - 4*m^2 - (4*m*log(m) + m)*r + r^2 - (m - r)*to - 4*(m^2 - m*r)*log(-m + r))/(m^2 - m*r)) - arctan(-1/2*(r - to)/m)\n", "th = th\n", "tph = (m*oph - oph*r + 2*m)/(m - r)" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "OKC_to_CC = KC_to_CC.restrict(M_I) * KC_to_OKC.inverse()\n", "OKC_to_CC.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime $(M', g)$" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "forget(r>m)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M',({\\tilde{\\tilde{t}}}, r, {\\theta}, {\\tilde{\\tilde{\\varphi}}})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M',({\\tilde{\\tilde{t}}}, r, {\\theta}, {\\tilde{\\tilde{\\varphi}}})\\right)$$" ], "text/plain": [ "Chart (M', (to, r, th, oph))" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Mp = Manifold(4, \"M'\", structure='Lorentzian')\n", "OKCp. = Mp.chart(r\"to:\\tilde{\\tilde{t}} r th:(0,pi):\\theta oph:(0,2*pi):periodic:\\tilde{\\tilde{\\varphi}}\") \n", "OKCp" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{\\tilde{t}}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\tilde{\\varphi}}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tilde{\\tilde{t}}} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\tilde{\\tilde{\\varphi}}} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "to: (-oo, +oo); r: (-oo, +oo); th: (0, pi); oph: [0, 2*pi] (periodic)" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "OKCp.coord_range()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M',(T, X, {\\theta}, {\\tilde{\\tilde{\\varphi}}})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M',(T, X, {\\theta}, {\\tilde{\\tilde{\\varphi}}})\\right)$$" ], "text/plain": [ "Chart (M', (T, X, th, oph))" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CCp. = Mp.chart(r\"T X th:(0,pi):\\theta oph:(0,2*pi):periodic:\\tilde{\\tilde{\\varphi}}\")\n", "CCp" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & -\\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(\\frac{2 \\, m}{m - r} + \\frac{r + {\\tilde{\\tilde{t}}}}{2 \\, m} + 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ X & = & -\\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(\\frac{2 \\, m}{m - r} + \\frac{r + {\\tilde{\\tilde{t}}}}{2 \\, m} + 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) - \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & {\\tilde{\\tilde{\\varphi}}} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & -\\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(\\frac{2 \\, m}{m - r} + \\frac{r + {\\tilde{\\tilde{t}}}}{2 \\, m} + 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) + \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ X & = & -\\pi \\mathrm{u}\\left(m - r\\right) + \\arctan\\left(\\frac{2 \\, m}{m - r} + \\frac{r + {\\tilde{\\tilde{t}}}}{2 \\, m} + 2 \\, \\log\\left({\\left| \\frac{m - r}{m} \\right|}\\right)\\right) - \\arctan\\left(-\\frac{r - {\\tilde{\\tilde{t}}}}{2 \\, m}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\tilde{\\tilde{\\varphi}}} & = & {\\tilde{\\tilde{\\varphi}}} \\end{array}\\right.$$" ], "text/plain": [ "T = -pi*unit_step(m - r) + arctan(2*m/(m - r) + 1/2*(r + to)/m + 2*log(abs((m - r)/m))) + arctan(-1/2*(r - to)/m)\n", "X = -pi*unit_step(m - r) + arctan(2*m/(m - r) + 1/2*(r + to)/m + 2*log(abs((m - r)/m))) - arctan(-1/2*(r - to)/m)\n", "th = th\n", "oph = oph" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc = (to - r)/m \n", "vc = (to + r)/m - 4*m/(r - m) + 4*ln(abs((r - m)/m))\n", "OKC_to_CCp = OKCp.transition_map(CCp, [atan(uc/2) + atan(vc/2) - pi*unit_step(m - r),\n", " atan(vc/2) - atan(uc/2) - pi*unit_step(m - r),\n", " th,\n", " oph])\n", "OKC_to_CCp.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot of principal null geodesics" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "lamb = var('lamb', latex_name=r'\\lambda')\n", "\n", "def inPNG(v0, th0, tph0):\n", " return M.curve({KC: [lamb + v0, -lamb, th0, tph0]}, param=lamb)\n", "\n", "def outPNG(u0, th0, oph0):\n", " return Mp.curve({OKCp: [u0 + r, r, th0, oph0]}, param=r)\n", "\n", "def outPNG_III(u0, th0, tph0):\n", " return M.curve({KC: [u0 + r - 4*m^2/(r - m) + 4*m*ln(abs(r - m)/m), \n", " r, th0, tph0]}, \n", " param=(r, -oo, 1))\n", "\n", "def inPNG_IIIp(v0, th0, oph0):\n", " return Mp.curve({OKCp: [v0 + lamb - 4*m^2/(lamb + m) - 4*m*ln(abs(lamb + m)/m), \n", " -lamb, th0, oph0]}, \n", " param=(lamb, -1, +oo))" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "graph0 = polygon([(0, pi), (-pi, 2*pi), (-2*pi, pi), (-pi, 0)], \n", " color='cornsilk', edgecolor='black') \\\n", " + polygon([(pi, 0), (0, pi), (-pi, 0), (0, -pi)], \n", " color='white', edgecolor='black') \\\n", " + polygon([(0, -pi), (-pi, 0), (-2*pi, -pi), (-pi, -2*pi)], \n", " color='cornsilk', edgecolor='black') " ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 15 graphics primitives" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph_PNG = Graphics()\n", "\n", "for L in [inPNG(0, pi/3, 0), inPNG(-4, pi/3, 0), inPNG(4, pi/3, 0)]:\n", " L.expr(chart2=CC)\n", " graph_PNG += L.plot(CC, ambient_coords=(X, T), color='green', style='--', \n", " max_range=100, plot_points=4, parameters={m: 1})\n", " \n", "for L in [outPNG(0, pi/3, 0), outPNG(-4, pi/3, 0), outPNG(4, pi/3, 0)]:\n", " L.expr(chart2=CCp)\n", " graph_PNG += L.plot(CCp, ambient_coords=(X, T), color='green', \n", " max_range=100, plot_points=4, parameters={m: 1})\n", "\n", "for L in [outPNG_III(0, pi/3, 0), outPNG_III(-4, pi/3, 0), outPNG_III(4, pi/3, 0)]:\n", " L.expr(chart2=CC)\n", " graph_PNG += L.plot(CC, ambient_coords=(X, T), color='green', \n", " prange=(-100, 0.999), plot_points=4, parameters={m: 1})\n", " \n", "for L in [inPNG_IIIp(0, pi/3, 0), inPNG_IIIp(-4, pi/3, 0), inPNG_IIIp(4, pi/3, 0)]:\n", " L.expr(chart2=CCp)\n", " graph_PNG += L.plot(CCp, ambient_coords=(X, T), color='green', style='--', \n", " prange=(-0.999, 100), plot_points=4, parameters={m: 1})\n", " \n", "graph = graph0 + graph_PNG \n", "graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of hypersurfaces of constant $r$" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "def plot_const_r(r0, color='red', linestyle=':', thickness=1, plot_points=300):\n", " return KC.plot(CC, ambient_coords=(X,T), fixed_coords={th: pi/3, tph: 0, r: r0},\n", " ranges={tt: (-100, 100)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1})\n", "\n", "def plot_const_tt(tt0, color='darkgrey', linestyle='-', thickness=1, plot_points=100):\n", " resu = KC.plot(CC, ambient_coords=(X,T), fixed_coords={th: pi/3, tph: 0, tt: tt0},\n", " ranges={r: (-100, -10)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1}) \\\n", " + KC.plot(CC, ambient_coords=(X,T), fixed_coords={th: pi/3, tph: 0, tt: tt0},\n", " ranges={r: (-10, 10)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1}) \\\n", " + KC.plot(CC, ambient_coords=(X,T), fixed_coords={th: pi/3, tph: 0, tt: tt0},\n", " ranges={r: (10, 100)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1})\n", " return resu" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "def plot_const_r_p(r0, color='red', linestyle=':', thickness=1, plot_points=300):\n", " return OKCp.plot(CCp, ambient_coords=(X,T), fixed_coords={th: pi/3, oph: 0, r: r0},\n", " ranges={to: (-100, 100)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1})\n", "\n", "def plot_const_to(to0, color='violet', linestyle='-', thickness=1, plot_points=100):\n", " resu = OKCp.plot(CCp, ambient_coords=(X,T), fixed_coords={th: pi/3, oph: 0, to: to0},\n", " ranges={r: (-100, -10)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1}) \\\n", " + OKCp.plot(CCp, ambient_coords=(X,T), fixed_coords={th: pi/3, oph: 0, to: to0},\n", " ranges={r: (-10, 10)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1}) \\\n", " + OKCp.plot(CCp, ambient_coords=(X,T), fixed_coords={th: pi/3, oph: 0, to: to0},\n", " ranges={r: (10, 100)}, color=color, style=linestyle,\n", " thickness=thickness, plot_points=plot_points, parameters={m: 1})\n", " return resu" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 36 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for r0 in [-10, -8, -6, -4, -2, 0.5, 1.5, 2, 2.5, 3, 5, 7, 9]:\n", " graph += plot_const_r(r0)\n", "graph += plot_const_r(0, color='maroon', linestyle='--', thickness=2)\n", "\n", "for r0 in [-10, -8, -6, -4, -2, 0.5]:\n", " graph += plot_const_r_p(r0)\n", "graph += plot_const_r_p(0, color='maroon', linestyle='--', thickness=2)\n", "\n", "show(graph, figsize=10, axes=False, frame=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of hypersurfaces of constant $\\tilde{t}$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 72 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tmin, tmax, dt = -10, 10, 2\n", "for i in range(int((tmax - tmin)/dt) + 1):\n", " ti = tmin + dt*i\n", " graph += plot_const_tt(ti) \n", "graph += plot_const_tt(0, thickness=2)\n", "show(graph, figsize=10, axes=False, frame=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of hypersurfaces of constant $\\tilde{\\tilde{t}}$" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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2sDiE7bsqkGVYumhi4kB0KwgEgrEQwkBw3DOlSEHOTrj8TvjhPUheDtoeKK9GFxFGZlAMHQ0dJCwPJziw13vAYoGlCyEiZMTTdXTqyNtTSVOLAc+9+3g+Zi/vxfwLO1vNyAORPvwKfs5SahpGwNDVTcbjL5Pwu2vRqNXsIgVzu4k5UX5IEmzbWYEMLBPiQCAQTBNCGAiOa6acPkiIg10bITpc+frxl2nfmEbG3/6GFYm1STF4ejgd2j8oAF7/17DTmC1WDhTUUVBcj7OjHasTIimN0fHTty9y5qc3cPvSK7j4q98Nn32gVitRC6v1kF9CL9W5u/jk0tvprK5D29TCmS/9ExsbFfsO1mJ+61MWXLgWaUkouTvLQZZZtjhEiAOBQDBlhDAQHLdMSRR897My4+Ca3xwSBUD9tVeQtTQFZ3sbkldG4tjnYmi1wvX3wo2XwYrFg07V1NLNtp3l9OiMzI0JIDbSH7Vahb9vMhud3mDdh1eypXIrp0WkDB+IdOHpyr8RcAsKQN+hpAF3vvkJiy47l3mrVqCRZXaTiKnDStxiTyQJcvPKkWVYtiQElRAHAoFgCoh2RcFxyZQjBak58H2q8rQOkJ5LSV4x6bsq8fF1Y21yzCFRANDcpkxFtFj7XzJbrOzcW8XmjALs7DSsXzOXeTGBqCXglCvgx3S6jFqssgVPBzdeP+3RkWsKjEbI3TXsZZdAP058+J7+r7+57QHMBgMxsbNYumg2JR0mcneUEezvxoq4UCqqWti+swKraGUUCARTQEQMBMcdUxIFfSH7R/8MZjNIErLFwr6vM8lPWk1EqA9LFgSjUg156vb1gs0f93cjtLZr2bqjnJ4eA4vmBREV4XvoSb1HB34+ZLcXcM5nT3BqeAofn/Msdho7qjpr8bR3H+yQ+MZHcM8/oGoreLgNuuyy6y9lz3tfULNtN80FJWQ+8Rop991GRKgPNiqJrdtLsewrJP63JyNJElt3lCHLMsvjQkXkQCAQTAoRMRAcV0xJFDS2QOI5kJ6r3OBtbLBYreTuqiQ/aTULw72JWziCKHj5HThQCJKEVZbJL6xnU9pBNGoVJ62ZQ0yk3+CbsLMTGx48mzXlT/TXFNhp7LBYLZz68bXDHRIvOhNyvgT34e2xKrWaM154BEmtBiD9sRdpKSoDYPZsbxI6aqjx8CZnRylBgR6sXBZGZU0ruXnlInIgEAgmhRAGguOGKacPHO1hXowy/wAw6Y2kf7CZqpo24peFEbtghOI9vQFeehc2ZaLTm0jLKmJvfg0xkf6csDoGVxeHYZf5ace3XPbBjcMKDdUqNS+f/PBwh0RPd5gfM6o3gv/COSTceQ0AFoORr266D9mqpDSCrj6XxBWR1NZ1kJ1dQFCAB/FLw6nqEwdWIQ4EAsHEEAZHQxAGR8cmUxIFJhO0tIO/T/9LOp2R9NT9aNu6SfKxwXdd/OjHGwzUt2jZuqcKCVi5NAw/n5F/NzaUpFJ67fWcVWmPX9H2EWsKBjokfn3Bq0pa4WAx3PkQvP00+HkPO8ao7eGlpafTXl4FwClPPMDKW6/s317z7/+SHT6XgEBP4ldEUFffQfb23ihCXNjwKMhhECZIAsEvDzFESfCLYcqRgr/8C9ZdohT5AZ1dejalF2CQ1JywZu7oomDjFqzVdewrayFtWxnurg6sXzt3TFFwzmc3sf+8Ffj/54VRzYuSg5ex8aI32N14kLyG/cqL3p5gZwtt7SMeY+vkyNmv/F//1z/95V+0V9T0fz3r9GQS5S7qmrrI3lZKgL8bCcvCqa5tY+uOMhE5EAgE40ZEDIYgIgbHFlMWBQDVdbD3IJy6lpZWLemZB7Hv6mL16ctwdHMe+RizGUPieeTcciuNHt7MjQ1kTrT/qAV9I5oXHYZOQxeudi5YZStGiwl7jd3o+3bp2V9QS82BEprTM5m/LIak63+DNMT7oLa+g6zcYvz93EhYHk59QydZ20qYFeBB/FIRORAIfs2IiIHguGfKouCDL6Fbq5gSnbqWuoYOtmQV4mI2svaDd3C0txn10NYuAz/+/WHaff1YnRDFvJiA8YmCE/6J7ROvQ039YZfnaucCwB9+fpTTPr4WrUELefuGHdvU0sVPafm0tfcQEB2C39ln0TArhuLy5mFTFgML8kn6v0epr+8ge1sp/r6uJC6PoLaunZztpSJyIBAIDouIGAxBRAyODaYsCmobYNF6eOJB+O35VFS1kLuznAA/N+KXhqNRMcxpsI+y1F3s6LDi7uZA4oqIwX4GQxgWKdhXDOsvg58/gnGuua/mIMl7Phv/mI/0u+vgz8qTeX1jJ5m5JXh5OJG0MgIbjRqz2cKeAzUUlzXh6+3CirjQQ2uUZfh2E3XLl5GZW4qfjyuJy8NpaOokK1dJMcQvC0M9ynsfDRE5EAiOf8R0xUkihMHRZ1rSBwBVtRAUQGFpI7v2VRNafJBlah2q31034u5Wq8yuvZUUlzcTVlVG3M3noVaPfgMdNX3Q9zc1AR+BPnFwkTWS5259E0cHF4rLmti1r6r35h6BRjN4LQ1NneTmlWMxmkhJjsHDY3BapH7zdjK6JPx6owYNTZ1kbSslwNeN+OVCHAgEvzZEKkFwXDJlUbBxC/z+72C1IgcFsCe/ll37qomN9GO5vhXV3KgRDzMYzKRmF1JS0UxcsCvLzls1OVEAiiCY4CjkvoLEj1XFPL/jYzK2FrNzbxWRYb4kr4wcJgoAPBw1qH7eQEdxKT9tOUB944C/c70B/+vuJDk/j8amLjJzS/DzcSVpRQR1jUqawTLAxXE8iLSCQPDrQDgfCo4ZpiVS0NAMtQ1YLRby9tdSWtHMohAPYuYFwbzbRzyko1NHxtZizAYTa5aH4RPgOeYlxhQF51ynTGm858YJLz0hMI5vTniPljIdbaYGklbPZ1aA+6j71+XtY/szryHZ2RF89+9JV6lZujiE8BBvsLeDje/iHxpEcpvy/jJzS0haEUHSiggyc0vI2lZK4vLwMQXQUIRDokDwy0dEDATHBFMWBV3dyn+vvADLu8+Ss6uSsspmljvLxJxwNmzfM+JhtfXtbEo7iI1Gzbqn/o3P/f8c8zKH7T5IXg5zIie0dKtVpqyimQ2b9tNUZSRc1hFbmMotmfcOdkgcQsiqFSy78TJkg4HKRx/DsGcn23dVsC+/VilKjAoDGxv8WhtJ1jfR1NJFxtYSfLxdSF7Zl1ooEZEDgUAwCFFjMARRY3DkmbIoqGtUrI4fvx/TuaeQlVtCU0s3CcvCmeXlCK99ADddrow47kWWZQqKG9hzoIagAHdWxIWiKSgBG82gaYsDmUxL4lhYZZnqmjb2H6ylS2sgKNCDBXMCcXG2H9kEaQSM3VpeXn4GbWWK8dHyZx+n2y+EkCBPli0JUeoI/vR/sCWbhi/eImN7Gd6eziStiKS5tZvMrcX4eLuQtCJiQpEDEDUHAsHxhig+nCRCGBxZpiV9YLXCU//BcMk5pBe30tmlIznKG1+VBSJDh+1usVjZsaeS8soW5kT7M99Ng+TvM2qXAoxTFFTWQmeX0o0wRo2BLMtU17Wz/2AtnV16AvxcmR87Cw/3ATf/hmaK//sqizUfsCJw0ZjioConj/+ecDGy1YqkVnPWho8o7rD2CoAIbLAq1s4uzjQ2d5GeU4yXhxPJKyNpae0mQ4gDgeBXgSg+FBzzTFkUtHUoKQKVCt0tV7H5YBNarYE1SdH4/uMpuPhWRTQMwGA0k5ZdRGV1KyvjQlkQE4B01jWKHfEojDtS8MZHcMZVo4oCWZaprW/nxy35ZG8rxcHelhNXxbIqPmqwKADYc4DIR99jc8Kj5Nbt4erv7h11fcHxcay69xblGhYLGbf+gcQls2lr7yE1qxCDLIGLM9Q34fvnR1i1IJCWNi0ZW4vx8nQmOT6yP81gFmkFgeBXj4gY9CJJ0q3ArShiKUZEDGaWaYkU/OER+OIHunO/JXV7ObIsszohGlcXe0U01DXA3EPn7erWk55TjMlkIWlFBN5eve19aVvBy2NE34EJpQ86uhSXxRHO09jcxd4DNbS0afHxdmZ+7Cx8vEZxXQSwWKBLC+6uZFRtx83OhQW+MaPvbjLxxtrfUNtbS7H0+ktJevhPpGYX4mhvy+rEKOxLy+GS2+CD52ny8Sc9pxhPDyeSV0bQ2t5Dek4x3p5OJK0YuQtiLETkQCA49hGphEkiUgkzz7T5FOj0tBeUk1ZvwEajZnViNE4ffAZnr1dmDwygqVlp2bOz07AqPgpnJztobQcPt1Gf8KejpqC9o4c9B2qob+zEw92RhXNm4evjMnyK42iYzYovgo0NPSYdD2c+z18Sbx0xrdBSVMYrK8/C1KMD4JLPX8MvKZ7UrEJsbTWkJEbjYKNSai1kmaZWLenZRXi4O7IqPrJfHPSlGYQ4EAh+WYhUguCYZMqiwGKB+x6D8mpadGa21Oqxt7dh7aoYnHq64W9PwZc/DDqkoqqF1Kwi3N0cOXFVrCIKTCY48WL465MjXmbCoqCjC274ExSUAKDTm9i2s5wftuTTrTWQsCycdatj8fN1Hb8o6NZCTAp89A0ABS2lPLfjncEjmwfgFRXG+sf+DCjpBZ+YCNxcHViTFIPJZGFzRgE9Rovy3i++FZ+vvmN1QhRtvYLAw92R1fGRtPamGcxmy/jW2YtIKwgEvwyEj4HgiDEtkYLmNvj6JxoSVpIpueHu5khyfAS2Nhqw84S8DUpaAOUJNr+wnn0HawkN9mLp4tmH3P5sbOCBO0fsQJhUpKC5BfYdxGIyU1hYR35hPSq1xJIFwUSE+kx4eBEAzk5w1/WwdD4AS/znsfGiNzjl42s489MbRixIXHrdJdi5ODPvgtNQaZQ/b1cXe9Ymx5CaVcjmjAJSEqJwDgsGH0+8vZxZnRhFWnYR6dnFrIqPZFVCFOnZRaRvLWbVykg0GvWwpY2G8DkQCI5/RCphCCKVMDNMiygwm0GjoaaqiexdVfh6uyhWwSVl8Mwb8MQD4GAPKN4AO3ZXUFbZwrzYQOZG+x96Uu/RgaPDiJeYSvqgtr6dXfuq0fYYiAr3ZW5MgCJYppmBrYwbf/PGuNfYozOyJbMQi8XKmqRoXJyV7xVd3TSbIC27CHdXB1bFR9HRqSOtN82QHB+JzQTEAYi0gkBwLCJSCYJjhmkRBS++DaddSXlpPVk7K5nl707Syt75AWVVsPsAGE0AmEwW0nOKqKhqZUVcKPNiAg6JAoMBks+Dp/8z7BKTFQXaHgMZ2YVkbC3BydGWk9fOZfH84OkTBV/+AG//r//LPvvkdaGJ41qjUdtDZ009jg62rE2OwUajZnNGAR2dOnjiVUg+H297NSkJvYIgpwg3VwdWJ0bR1qGkGUwirSAQ/GoQEYMhiIjB9DJthYZZOyjeXUpeYDhhId4sXTQblSwf8h6wWkGlokdnJD2nmJ4eI0krIvD1cRl8HqsVXnsfkpbD/ENV/pMRBVarTEFJAwcKarFt72BJVTGz/nTd+GsIxsudf1UKJd95ZsTN35VsISV4xYgFiTXbdvPZ1Xfj4OnGNT9/hEqjQW8wkZZVRI/eSMosJzy2boPrLwWgpU1LWlYRri72rE6IorNLiRy4uSoFijY2InIgEByviK6ESSKEwfQxLaLgQCHMiSK/qJ69+bVER/iyaF4QEsBVd0PEbHjwdwD94W9JglXxUbi5DkkXmExKbcEQJiMKWtq0bN9VQWenjqgIX+YV7sfG2wNWr5z4ezwcFssg18ZB69C1Ef7yWpb6zR9Wc2C1WHhp6Wk0H1QKItc8cCcp9yvzIgxGM+nZRXRpDayOj8LL0wnyi2BOFK1tWlJ7xcGqhCi6uvSkZRfi6urA6vgoIQ4EguMUkUoQHFWmRRTUNyEnnceeD35kb34t82ICFFHQ90QeNw96pyU2NnXxc3oBdrYaTlwVO1wU6A2QdB68+cmglycqCsxmCzv3VrEp7SAqSWJdyhwWzw/G5rxTZkYUwCFRUFk7bJOXgwffXvAfcuv2DOtWUKnVnP3qY0i9x6f+83mqc3cBYGerYXViNG4u9qRmFdK0/QAsPR2++xlPDydSEqPo7NaTllWIi4sdqxOj6ezUk5ZdhMkk0goCwS8ZETEYgogYTJ3pSh/Iskzet1spsdiwaH4QMRF+yobm1kE+BZXVreTmlePj7Uzi8oiRn2iNRnjsJTjv1H4DoomKgsbmLrbtLEevNzFvTiDR4X5Kt0F+ERSWwZnrxrRVnhIffAnX3wslGeDnPWzzWLMVtjzyLKmPPAuAZ0QIN279CltnJwBMZguZW0toadOSbG3H7/TV/UKktV1JKzg72bE6MYrubgOp2UW4OiuRBFsRORAIjitExEBwVJgWUVBcjvW9z8nNK6fEYsOyxSGHRMGefIhZA1uy+wch5ewoIzjIQ6meH+lmZbWCra3SnjgJUWA2W8jbU8mWzEIc7G1Zv3YusZH+h1oQv/oRbn9g5kQBwMkp8P5z4Ok24ua+gkSdWU+PWTdo2+o/3cKsFYsAaC2p4Pt7/69/m41GTXJ8JD5ezqRLbtQ1d8Ou/VBYiqe7EymJ0XRrDaT2CoT+SEJ2EUYRORAIfpGIiMEQRMRg8kxXpMDy8DPk2HhQO3ceK5eGMXvWABdDsxlefhf5+kvYVdhIUWkjc6L8mT8ncOSiP70B1l8Kv78BzjkZmJgoaG7tJjevHJ3eyII5QUSF+wy/jixDe6fioniUkWUZSZKo627E1da5P3LQUlzOKyvO7HdFvPh/rxBz+on9x1ksVrK3l1Lf0En8Zx8TZNH1Fzv2zVxwclSEQXePQYkkOCsFilOJHDzz3DPccdsd0/TuBQLBWIjiw0kihMHk6BMFVbUVbNnw3uREgSxjtljJzC2huaWbhOURBPr33mwHzD6wWKxszSunpraNJQtnExnmM/o5tT3w50fhxsthXvS4RYHFYmV/QR0FRfV4ejixIi70UN//0aKjC/7wD7j+Eli+aNTdrLKV5W+ei5udy6C0wo7XP+SbW/8CgKOPJzdv/w7nAWkJq1Vma14Z1TVtrJw/i9kR/v3b2jt62JJViJODklbo6TGSmlXYn2aYaGumLMvc+qe/8pL2fX4b+1veuvutCR0vEAgmjkglCI4Y/aKgroJPPn9ucqKgW4vxvBtJ27iTllYtqxKiDokCUKyOz70BY48Sxq6rbydxRcTYogDAyRGe/fuEREFHp45NaQcpLG5g/pxZrF0VM7oo6OqGdZfAtt0Tf88TxcUJyquUGosxUEkqnln3wLCCxLhrfkPMGUqUoKepla9v/jMDHwxUKomVS8MICfYiZ18NZTuL4V8vgyzj7ubImsRoenSKIHB0tO1PM6RlFWE0mSf0VtoNnWybsxf7QDve/vfbIq0gEBxDCGEgmBID0wdbvnuPtUvjscpWtlTkTOg8eqOZ1LPOp9MqkZIYja/3EP+BR/5Az/svsHlrKR2dOlISo5kV4D7GCQ1w8uXwcxYwvvSBLMsUlTbyU2o+VlnmxJRY5kT7oxrLl6BLCwG+yk17plGp4If34NS1h921r+ZgoDiQJIkzX/wnTr5eqG1tCFm1UkmDDLyEJLF8SQjhod5sq+ygeF8FtLQB4O7mSEpSNDqdaUrioE3fwfoPr6K0vYqsaz7mrotEzYFAcCwhhIFg0oxWU/DBga9Z+8Hl/Gf3R4c/icWCrqaBLTur6QnwZ03KHKWnvo93P4faBjplFT+3WDCZzKxNjjk0Mnk0enTg7QF+3uMSBTq9ifScYnburSIsxJt1KXPwcBtuGDSMQD8lFx8befh9p4umFsXf4TD0iYO8hv1k1+4EwMnXi/PffprrMj4j8a7rkEYomJQkiaULZxMV7kveeRdQ0GHq3+bu6sCaPnGQWYijgy0pSYcKFI3GscXBQFGw6ZK3WeI/TxQkCgTHGKLGYAiixmB8jFVoKMsyt/34EC/mvcdrp/6D6xb9ZtTzdD/yAqmBUciz/EkZ6N8PynTBxafQfNdNZITNw8HBllXxkTg6jH9+wXhEQX1jB1vzygFYsSSUAL8JFBFW1ymtk/Z24z9mqpx5tWL//P2749q9Td+Bh70bsixjtBix04xvrbIssze/loNF9czfm8fc89fAHMU3oqNTx5asQuztbEhJjEKnV4RCX4Gire3wmoOhomCx39xB1xKtjALBzCKKDyeJEAaHZzzdB+MRB51delLT81EbjaSsX4yT4/AbVk1BFTmFTXh6OJG0MuLwRW56A1x2O/z5NjZ4tI0pCixWK/vyaykobsDf15UVS0Kxtx/ujDgmay6CkCB4a+TxzTNCYakyQbJ3iuR4eTDtaTKqt484lbGzph7XWf7DjpFlmQN7K9hf1sIceyvz1y/r78ro6NSRmlWIna2GlKRo9HpTf4HiUHEwligYeC0hDgSCmUMUHwpmhPG2JEqSxPMnPcQtcZeRUbWDoQK0/Yuf2Jx+EBt7W9aeEjdYFFTWwo1/orSghqyDjfj7ufW2xY2j8r2tA7p7SG/eO6Yo6NYa2JxeQGFJAwvnzWJVfOTERQHAkw/C3ddP/LipEB0+YVEAsD4seVhBosVoZNMD/+aZ2LVUb9057BhJkpi3MJSFc2eRr1exe381sklJLbj1phUMRjNbMguxt7dhTWI0Wp2SVjD0phXGIwr6riXSCgLB0UdEDIYgIgajMxmfAlmWscpW1Co19d1N+Dv70FJcQ1puCc62alaftRK7IWFneUsO+V+ms2/NCUSE+rBkYfDYBYBDOFz6oKqmje27yrG11RC/LBwvjyNQODjdfJ8K/3gWfv4INONvFRzqkJj/1hd8e/uDAHiEz+am3K/7XRGHUlTayM69VURUFBN3+0X9kYPOLj1bMguwtdWwJjEavcFEalYRDg42LI7z5/TPrj2sKBiIiBwIBDODiBgIppXJmhdJkoRapeZgSwmRr5zIm5nfkHqwETcfN1KGigKrFassk+cRyL41JzAvNpC48YoCvQGu/D1pP344qiiwWKzk7akke3sp/n5unLRm7tREwY698ORriunSkSbAF+bFKF0RE2Bgt8JjOa8Sd/VFBK1cDEBbaSXf//Gfox4bFe7LMkMrJbMj2L6rAmvvQ4Wriz1rkmIwGi1sySzEzs6GlKRotD0GPvoxi/rOlnGLAhCRA4HgaCMiBkMQEYPhTIejoSzLvPr6M7h7J2O1NXDh+ng0msGOeZbf/52t8+Ko8Q4gbtFsIkIP41EwkNJKOs+7ktXr6giJTxkmCrq1BrK3ldLRpWPx/GAiQr2nPh75jY/g8Zch/2eY7lHLM8zuhnxivcKx09jRWlLByyvOxKRV0gsXf/oyMWesG/XYiqoWcvPKme3txPLEmH7h1tWtZ0tmIRqNmiXL/Ln6yz9zgfOleLu4ckrKwmGRocMhIgcCwfQiIgYTRJKkWyVJOgDkHu21HEtMl81xdW07Ht7J2DfWcOOuG3lz/6eDthtNFtIS1lLn5UfiioiJiQJgg1yGz6Uji4Kq2jZ+3HIAk9nCiatjiQwbwdZ4Mlzzm6MrCoxG+GwDNLZM+NBFfnOw09ixo34f1+1+jBMe+2P/tq9uvo/uhuZRjw0J9mKltZPKhk5y0/ZjtSoPFy7O9qxJisZoMvH5pu0c7Chm/hJvMKtJzSrsrzkYLyJyIBAcHYQw6EWW5RdkWZ4LrDjaazlWmC5RUFZcR872UmYHe3HG1adzxbLz+Wv6s3QZugHQ1TayJaOAdicXVq+KHdu4aCh6AxVXXset/72RU8IHiwKL1crOvVVkbyvF39eNk8brTTARjmakoLsHrr5bqTeYJDqTnh/KMrjPYQORZ5wAKK6IX93052EFowOZfdIK4jvrqOowsDWvrF8cmDUGnm98FklW8WT0v1noHz3I98BgEOJAIDjWEcJAMCLTJQqK9pSxbX8tYWYtK+NCUdtoeP6kh9h+1ee42DnTsb+Yn7/Lw9CpZW1yDD5eLoc/6QDSU/+H5YctnOazdJAo6NEZ2ZJRSElZE0sWBBO/LGzkyYuTpVsLEUnwY/r0nXOieLpD/ma44rxJn6K/5qB+L2+v68DR1wuAog2b2f3OZ6Mf6OxE8FVnk7AsnOqaNnJyi2npaWf9h1eR17qHuGUB2EgaNmcWYmOjVsSBQWlnFOJAIDi2EcJAMIzpEgX5hXXsLGslurmWpSsi+8P3kiQR4OxLXXMbnxfWYnC25YSkaNxdHSZ0/g0lqazb8zB3P72WJ2/7b78oqG/s4IctB9DpTaxNjiEq3Hd6UgcDMZnh8vMhLHh6zztRAnvHUU+hALJPHGRq89n329n9r2/8wyN01tSPeWyQk4bEF5+npq6dl779lor2WjZd8jYrQuazJikGq1VmS5846O1YEOJAIDi2EcWHQ/i1Fx9OV6Hh3t0VHKxoYV5sAHOjA4bdmBsqm8jcVUkrbfy+4A88uf5PYzokDmVjwc/k/u4mCn6TzH+veBlbta1ixlNQx/6COvx9XVm5NGzCBW/HJb+9Cxzt4eX/m9JpMqq2Y6expeYv77D7vc/xWziHC955Gu+YiDGP60xL5+ayLznN7QLcPe04JWkRarXyzNGtNbAlsxCVSmJNUjQmk2WQY6K93cS8I0RBokAweUTxoWDCTJco2Lm3ioMVLSz64jPmhXgNEwWVNa2k7yjHe/9+rlwTzxWLzuL6DfePb7YCSqTg/ldv4a5cFW/OuQVbtS0Go5n0nGL2F9QxLzaAVfGRMysKdu6DkoqZO/9EOG0tnHbClE+THLyM5QELWfvoH5CvS+TSze8eVhS06Ts4sfRJNrZtIdJTj67NQta2UiwWKwDOTnasSYrGapXZnFGARqNEDgy9Xgd6g2nM8w9FRA4EgplHRAyG8GuNGEyHKLDKMtt3VlBe1cLSOQFE9LTB4nmD9ukzyQkJcGO5pEW1fNEg++Td13zDQt/YUa8xyLxo/WPYurrT2q4lK7cUs9lC/LIw/H0nMOtgspxwMQQFwNtPzfy1jjB7Gg+S+M5F/SZIQ+2T+xjmaPjXd6jvMpB58eX4eLuQtCKiP3Kg7VEiBwBrkqKxWKyK50GvnbKIHAgEM4+YlTBJfo3CYDpEgcVqZeuOMmpq2lgR6k7I4sHTBmVZZt/BWvIL64n2cWRRQuygSIIsy/xYnsH6sFWjXqNPFDxaE8Wtj7yLrbMrpRXN5O2pxM3VgcTl4SPOW5gRmluhRw+zA4/M9Q5HfhF8txnuvmFaTjfUIdFeskGl0fT/zEa0Oe7WgtlCgxEycovx9nQmaWUkmsOIA1tbDWuEOBAIZhyRShCMi+kQBWaLlazcUmrr2kl8501C9u8dtN1qldm+u5L8wnoWbvyOxd99Myy9IElSvyh4ZecHvLbrw0Hb+0TBNfbL+N0bRag3bWXbznK276ogdLYXJyTHHDlRAMpExWNFFADsK4QX34aOrimdpr2jh4qqFrwNQXx1muKQePGTl/Jq4jnsef8LYIzZB85O4O6Kn2RiVcFumlu1ZOQUYzYraQUnRzvWJMUAsCWzELVa1euYqMxaEGkFgeDYQEQMhvBrihhMhygwmSxk5pbQ0qYlaUUE/s424Hiou8BssbJ1exm1De0sXxxKqJMK3FzG9Pe//Ye/8XzeO/1TGYfOPjCV1ZNVo6WjU8fSRbMJm+09qfc/afbkwyvvwSN/AI8jkLYYD2az4qmgnlxLpsFgZue+KiqrWwFQqyQsVhmVykzj59/Q+vU32KglLsv5mHO3/GHs2QebMuHae2j66h3SK7vw8HBk1crIfqfLHp2RLZmFWK1yf/3BwFkLEx1mJSIHAsH4EKmESfJrEQbTIQqMRjNpOcV0tXaR/NX/8HnuQXA6lI82msxkbi2htU1LYk4qAfdcM64b6cCagzuW/ZaXd37AKWGr+dT3Slqj55K9sxwbjZrE5RF4uE+zYdF4+DkL7n8MtnwMdkcwSjEetD2DfgbjO8RAWu80xIXzggie5YFaraK5pZvK6lZKi2ox63TU/+c/FOny+fhSFZsufWfs2Qc9OnB0oLmlm7TsItzdFXHQ5yUxsjgoxNZWLcSBQDBDiFSCYFSmQxToDSa2ZBbSrdWT4ibj42gDDvb923U6I5szCuno1JHiIRHw3ffjHvjTN7L59Ig1PLv9bRb6xPLxivspfulz0nKK8XR3Yl3KnKMjCgBOSITsL489UZC5HQKWQmnluA/p1hr4Ob0AqyyzLmUO4SHe2GjUqCQJX28Xli0O4aTkSAzlZQTdfTdxa67iVftrDj8QydEBenR43/8PVvvb097RQ3pOESaTpXezLWuSolGpJLZkFvS3M/YNYtLpRVpBIDhaCGHwK2M6REGPzsjmjAL0OgNrE6PxXLsCnn8YVMqvU1e3nk3pBRiNZtYmR+OdvAR2fDehnPzG0jR+LM9krnckn5/zMtvrTey9+GJio/xInulWxMNxNKYpjofFc+Eff1RSNeOgq1vf20Ko4oTkGJydRhE6Hrb8r/U9ap57DufFi9E7xXJgb9HhLyDLcLAY74ZaUhKi6ejUk5ZdhHGIOFCrVGzOKECSYG1yNCazEAcCwdFECINfEdMhCrq1BjZnFGAxW1j717/i9urbg6/RpuXn9AI0ahUn1hfhdvffwGLpFw3jYWBNQdqFH7M3p476xg4s/i0smDfOMcwzydLT4e9PH901jISTI9x+NXh5HHbX9o4efs4owEajZk1SDA4OtiPu11domB3aiYunitJ77sFQUsq+0k6ythf3+xWMup7NH8PpJ+Ll6URKYiSd3XrSsgoxmhRx1ScONBrVoI4FsxAHAsFRQwiDXwnTIQo6OnX8nF6ASpI4YfUcXP50E1x5Yf/2+sYOUjMLcXayY+2qGBxtNcrT6wQK4gaKgmfiHyE1vRiptBL7nPe4dPMt4zZBmlH+eBOcnHK0VzEybR3w2ItQ2zDqLvWNnWzOKMDR3pa1yTE4jJLPH9p9cOmL/8bORkXVY49R+9JLVFe3sSXrMN0EfSLur0/i+cSLrEmMpltrIDWzqH/aooODLWuSYtBo1COIgwIhDgSCI4wQBr8CpkMUtLX3sDmzADuNxNqeehwdbOH806B36E5FVQvpOcX4eLuQsjxUCfVfcjb8+y/jvkafKDg1LIWHYu8nd0cl/n5unBjizGm/f4Bb4i6bkEPijHHZubByydFdw1g8/TrsPTjsZVmWKSptJD2nCC9PZ9YkRWNnN3JKZqSWREdvT05/9u8AdGzZQu3jj9HR2cOPqfl0dOrGXpOXO3h74uHuSEpSNFqdYdAoZgd7G9YkRWOjUbM5oxBZ7hMHViEOBIIjjOhKGMIvrSthOkRBc0s36TlFuDjbs2rfNuwefhr2b+oPWRcUN7B7fzWhwV4smxuA6pTL4bxT4Y5rxn2NPlFwVthJ3BJwK83N3SyI8CZm3ux+z4OB3Qp9rYxHnJJyOFAEp64ds+XyqGI2D1ubyWxhx+5KKqtbiQr3ZdG8IFSqkVMyo/oU9PLpFXey/5NvkVQqim5ZSGLS9fjZ+pK4PAJ/33H8zRiNtOstpGYWYm8/eGaCXq8MWTIaLaxJikaSFM8DjVrFmqToUVMeoyG6FQSCQ4iuBMG0iIKGxk5Se9vNUhKjsbvlCsj6Arw8kGWZ3fur2b2/mtgof5YvCUFlZwtnrIPEZeO+Rp8ouCTsXK50vY6OTh2r42YTe/6VSM+/2b9fX7fCncuuwsfBc8LvZVr4bjNc+fsJ1UwccTQaRRwYDAC0tmn5KTWf2rp24peGsWRB8KRFAcCpTz5IaEo816Z9yo13/okHyh6gVF9Cek4RJeVNY6/t029h6em4mw2sSVKmLaYOMDeyt7dhTWI0trZqtmQWIMuwNjkGc69Lok5nnNC3QkQOBIKJIyIGQ/ilRAymQxRU17aRs6MMX28XEr/7Es361bBqBaC4GW7bWU5FdSuL5wcRHeGn2AR7T+yG3ScKbg6/lmTbE3BzcSBxRThO9jbw5ieQshIiQkc8VpZlsmrySApaOuH3NmlkWXmfPl5H7poTpUcHc9Zi+dvd5McnkV9Yh7ubIyvjwnB1sR/1sPGIgpHIqNrOaR9fx50ht7HAZgnREb4snBc0cpFoeTW8/iE8eCfY2NDZpTtkizzAv6BPMBiM5t62RlVvW6MSOXAUkQOBYMKIiAEgSdKfJUmSJUl6+miv5UgyHaKgvLKF7O2lzPJ3J2lREJptu6GoDFDC0hlbi6mqaSN+aZgiCrbvgZg1kJ037mtsKEnl/M9u5S8RfyJRs5bZszxZuyoGJzuN8kR+zW9GFQUA/yvYSPK7vzmyNQeSdGyLAgBHB1oe+iM/+UWSX1jHnOgATlwVOyOiAJSpjN9d9B+eqXwOG38dRSWNZOWWYDJbhu8cGgQP3wM2NtDUgquLQ68tsoXNA7oQ7O1sSEmKxs7Ohs2ZhVgsVtYkxWC1KpGDHhE5EAhmjF+sMJAkaTlwA7DnaK/lSDIdoqCotJHcneWEzfZm5aIg1I4O8O2bcM1v+p/kmlu6WRUfyeyg3gjBwlh46C5YtmBc19hQksqVX/6JxyMfJVazgLiFs1m+JASNBKy/HF5467DnOD/mlCNfkHjZ7fDtpiNzrUlgNFnI21PJJs8QVA72rEuZw/zYwFFTBzA1UQBgNZux31hEVtwznLsymeT4SBqbu9icUTD6DbykAuaeAF/9iKuLPWuTe7sQBhxjb6ekFeztbNgySBzIQhwIBDPIL1IYSJLkDLwHXA+0HeXlHDGmKgpkWWZ/QR0791YRE+nH0qYqVEtPh5p6UKv7XfJ6dEbWJsfg5+uqhK1LysHWVumhtzm8le2GklT+8N0TPB7+GLMdglmbHE1kmI9SZGi1wkmrYOGcw56nr+bgiIkDs1lZ3zFYXyDLMuWVLWzctI/yyhYWzZvFieX78Ng1ti6eqihor6jhpaWn8+3tD7D1r88jyzJvl33I+51vYjCY+Cn1IK3tIzhehs9WIgdrEwBwcbZnbXIMliERATs7TW/RoSIOzBbrIAtlIQ4EgunnF1ljIEnSW0CrLMt3SZK0Bdgly/LvRtnXDhho+eYCVB9vNQbTIQp276+msKSRBXMCiY3yR6qogeffhEf/RFu3kfScIjQaNasTog655P3lcXjvCzjw8yBL5NH4rjiVF37+lCt8f4uPlzOJyyNH7aOfyNpv+/EhGrTNfHLO88MmN/7SaWvvYefeSppbtQTP8mDRvCAlB59yAZyYDA/+buTjpigKQIkWvLziTJoOKE6IF37wPK3LvDn1k2tZHbCSOwPupKvbyMq4UIICRzFeampRJjM62NOtVUYzSxKsSYrByVGpJTAYzaRmFaLTmUhJjOr3POizUhY1BwLB4fnVDlGSJOli4H5guSzL+nEIg4eAvw59/XgSBlMVBVZZZseuCsoqW4hbGEykowpcnftv9A2NnWRuK1HaFeMj+1vLAGXM7+4DsHrlYa/zXVEqG7J3ssptFeGhXsQtCBkc4n73c2hsht9fP6H1g/JBb7aasVHb0NzTirfjDHQtdHWDrc0xMyNBpzexN7+G8soWXF3sWbIgGD+fAb+zJtOoEZzpEAV9FH73Mx+cdwMAnpGh3LJzA9n1uzn1k2uJ91/MgxH3U1ffRdzC2USG+Qw+2GCAhSfDhafBI38ElKFOA42O+sZp94mDHp2RNYnR2NgongdCHAgE4+NXWXwoSVIw8AxwuSzL+nEe9n+A24B/QTO0vBlhqqLAYrGSs72U8qoWVsaFEhnqA7+5Ga5XPqQrqlpIyynCu9cQp18U5ORBY4vibDgOUfBtfhr78ppJcE1g6eIgli0KHZ73Lq+CgpIJrb8PSZKwUdtQ0lZB5Csnzkxa4enXIXbt9J93gpjNVg4U1LHhp33U1rcTtzCY9WvmDhYFoIgCWQbd4D+F6RQFAFGnriWkt1ultbicvDc+Ijl4GRsufJ2c+l182/MFUeG+5O2p5EBBHYMeRuzs4Im/wG1X97/k5GjHmqQYJElic0Yh3Vql7dLOVkNKYjRODnaK14HJwtrkaGRZHrueYRREWkEgGJlfVMRAkqRzgM+BgeXQakAGrICdLMsjlEoPOsdx0644VVFgNlvIzC2lqaWLhGXhzApwVzZs34Nsb0eBvRt79tcoxkWLBzzdWyyw9DRYsQReffSw1/l6VwZNpRZklZWzUuLwGWv0siwfstGdBDNqgpRfpBTNnbFu+s45AWRZpqKqlb35NRgMZiLDfZgbHYDtWAOlLrwJXJzhjX8D0y8K+qjZtpv/rDofACdfL27fvwk7F2d21u8n2jMMRxsHDhTWs/9gLdERisHSsJSPtgf0hn7jrL7RzJbeugIXZyWCZTSaSc0uQqs1kNLvedAXYTiUfhgvInIg+LXwq0wlSJLkAoQMefm/wEHgMVmW943jHMeFMJiqKDCazKTnFNPRoSN5ZSS+3s7wxfdw9nqsksTufdUUlTYyJ9qf+bGBwz/Eq+uUITlj3ORlWebLnGz0DTbUyVVcf8qpODs4DN/RbIavfoSz109orsJY1z3qDonTTENTJ7v3V9PeoSMo0J2Fc4NGn4Y4kK9/BAcHWJc8Y6Kgj08vv4P9n34HwOr7bmPtgNqG/U2F/D3zeR6c90f2H2gYLjZlGU66VPHB+PDQk7tOZ2RLViFm8xBxYDKTllVEtxAHAsG4+VUKg5E4XI3BCPsf88JgqqJArzeRllNET4+RVQlReHk4wY69sOp8LF+/yVZXP2pq21kyUk74m59gTYJSLDYGRqOZrzN2YOpUsdeax4NnXYWdZpQb2U8ZcMZVsP1bmB8zofcyGn3i4JODGyi84Sfc7af4s5RlePFtOGUNRAzVnjNHe6eOPfurqW/sxMvDiUXzg/D2dJ7weWZaFAC0lpTzwqJTsJrN2Dg5cvu+n3AJ8AUgs3oHJ390NSsCFvJy4r/YvaeWAD834peFo1H3ZjTTc8HPG6LDB51Xp1daZI0mxSa5z4/BaLKQllVIl9ZASmIUdrY2bMksAAbXJowXIQ4Ev3SEMOjllyYMpioKtD1GUnufwFISo3BzPfQEbzhQRGarlbY2LfEDUwv9F2+DOWuVKvfbrhr1Gm3tPfyUtZ8ufQ/b5HSeOeeP2KoP8wRXUj6mmdFkkGWZqs46ZrsFYpWtqKQplNQ0t0LUanj7KTjzpOlb5Cj06IzsO1hLeWULzk52LJw7i1kB7pPquOj64See+N8jPDene8ZEQR8bfv93cl9URnEvve4Sznj+4f5tGVXbOeXja1gRsJDXU54kb2c1nu5OJK2MxNZmQKTIZIKGZggK6H9JbzCxJbMQo9FMSmJ0/++t0WQhLbuIrm49KQlR2NkJcSAQjIYQBpPkWBYGUxUFnV160rILkSSJlMRoJRSdtQP2F6K97DzSs4vRG00kr4wc/am0tBJmB446QKi0opntu8sp1ZWxR53Dm+f+39iioL0T3Gf2+2wwGzjns5s5P+bkqaUVrFbl3wwOTzKazBwsrKeotBGNRs3cmAAiQn3GNCgaizZ9B19feDIRxW04bfl8RkUBgLaphWfnnoCpR8/ymy7nlH//ZZCY6RMHa2ev5L8nPkV6TjFOjrasTjg0SIkb/gS79kPOl4M8I/QGE6lZRej1JtYkHRIHpl5x0NmlZ3ViFA72NmzOEOJAIBiKEAaT5FgVBlMVBW3tPaRlF2FnpyElIerQlLq/PklbUSXpv70atVrFqvioka1z//cdnHXSqO1vZouVnXsqKats4ef2n2lwKuOjc58eWxRYrbDsdDj9RMXsZoY4HmoOLBYrxWVN5BfWYbHKREf4Ehvpj43N5Gsu+tIHVc2VbLzinRkXBX3kf/E9vvOi8YoKG3F7RtV2rLKV1bNX0N6pIy2rCI1GRUpilHITzy+CLi2sWDzsWIPBTGr2IT8DdzdHQBEH6TlFygCu3t/vLZmFWK0ya5OFOBAIQAiDSXMsCoOpioKmli4yckpwcbZjVUIUdgOq2Osa2sneVoariz3JKyP7h9gMIr8Ilp0BH7+o3MSH0K01kLWthPbOHl6tew0nL/jk3OcOnz6wWuHrn5QIxJL5E3pPE2XK4uD1D+HnTHjvuWldl1WWqaxuZV9+LTq9kfAQb+bGBE7Z9OlI1BRMFbPVzOM5r3L93EvZtr0ai8XK6oQB6S1ZVoYuhQUPOs5gVAoPtT1K4aGH+0BxUEx7Zw+rE6JwFOJAIBiEEAaT5FgTBlMVBTV17WRvL8Xb05mkFRHKE6jZDFfcScnll5Jnscff142EZWFoNGM8nRaXQ2TosJera9vYtrMcs8rMfYV/Ye6s0PGJgqPAQHGw7crPWRYwvrkOAHy+EbbuhEf/PG1rqW/sZM+BGjo6dcwKcGfBnFljDjoaLyOKgqvvVsyZXjl8e+mRYn9TIfHvXMhy/wV8cuaLbN9ejU5nZFV8FF6eTvD4S/DcfxVXTZfBqS2j0UxattKVsDoxCk93pRjWZLaQkVNMW3sPqxKicHI8JA7WJEWPr5NjAEIcCH5JCGEwSY4lYTBVUVBa0cyOXRXMCnRnZVwY6t7qb7lby97nPuLg3EVEhPqwZEHwyDlsiwW+/AHOPWWYt4DVKrPnQA2FJQ1oXM1ck3czKSHLxy8KNm6BT7+D5x8G+yPnJCjLMt+WbOb0iLVHzTq5pU3LngPVNDV34+PlzMK5s/CaRKfBSIwaKfjgS0UYnH/atFxnvJj1BnJffgfvmAiiTx1uDpVRtZ1TP7mW5f4L+Ozsl8jLq6G9Q0fiigj8JZPSLXPKmhHPbTSZScsupqu3tsDLQxEHZrOFjK0ltLZpWRUfiZOTnRAHAgFCGEyaY0UYTEUUyLLMwaJ69ubXKjf+hcGoem+CFqOJ3D1VVNW0sWheENERvqPfIH9Mg7OvU4rABgw16tEZyd5WSmu7Fls/AxelXcspYasnFin4bINSt/Dus1MyNJoK7+77Ar3FML60QlMLODoo3g2TpKtbz978Gqpr23FzsWfhvCD8fV2nTaAca+mDrrpGXk+5kI7KGryiwrg57zvUI9SoDBQHX573Krt21dDQ2MXKZWEE981XKKkYsU3UZLKQllNEZ29tQZ/AMputZGwtpqVXHDj3iwNlQqMQB4JfI79KS+RfClMVBbv2VbM3v5Z5MQHEDRAFht0HSX35K2pr20hYHk5MpN/YN6WTVsOeHwaJgrqGDn7YfACd3ohDWM/kRAHAeacq+fqjOPBoW93e8U9l/M2tcPuDk7qOTm9i++4KNv68n9Y2LSuWhHLS2rkE+LkdOVGg08PPWdDWMS3XGw/O/j64BQcC0FJUxs43Pxlxvz775EW+sTjZ2ZO0IpKgWR5kbyulpLwJPvkWlpwClbXDjrWxUbM6Pgo3V0dSs4tobu0GQKNRkRwfibenE+k5SjvjmqRoVCoVWzIL+m2Wx4uwTxb8mhARgyEc7YjBVESBxWplW145lTVtwwbW1DV0kJVbglqvZ1VSDF6BXqOfqFsLaVvhtBP6X7JaZfbm11BQ3ECAnxtdHjWc+9VNExcFsgxvfKSkJzzdx/3eZoIJFSRm54GDHSyeN+7zG00WCorqKSxtQK1SMSc6gMgwn/6UznQxrkhBRQ3EpMAX/xk1ND8TVG/dyespFwLg5OfNHfs3YXsYc6zM6h0s8omlsKCF4rImFkT4EHtwL9J5p4468npwbUEkPl4ugNItk5VbQlNzF8krI3F1se8f37w2WUQOBL8uRMTgOGQqokD5YCyhuq6dhOXhg0RBfX0b2duU4URJJywYWxSAko++/E7FZAZl2t3mjAIKSxpYOHcWXd6TFAWgVJnf8whk7xj/MTOEJEk8f9JD3BJ3GddvuJ+P8r8dfeeEuHGLAovFSkFxA9/9uJfC0gaiwv047aT5xET6HR1RABAcAHt/hHXJ03r9wxG0cglzzzsFAG1DM3mjRA366DJ0c/b/buKs/91IdIwX82IC2FvSxO7YRciSpBTOjoCNRs2q+Eg8PZxIyy6msbkLAI1aRdKKCHx9XMjYWkxHlxI50KhVbM4ooKt7vLPWFETkQPBrQEQMhnC0IgZTEQV6g4mMnGI6u/Ukr4jE10d5WpJlmeKyJnbtqcSvtJiVN56NndMIswqGIstKF0JUmNJ1sKsCWxs18UvDyW3bzjmfTVIU9NHUonjiH8U0wkBkWeb/sl/i2kUX4efkPfJOL70NaxMhNnLU81hlmYrKFvYX1KLTmwib7c28mIBDnhHTzLFWUzAajfsLeWmpUvQ4O2k5V2/6YMz9Bzokfn3Bq9RWd7NzbxWhXS0se+tNVD+8N+rvjtlsJTO3mObWbpJXRvZPnLRYrGRtK6WhqZOkFRG4uzmyJbNg2AyG8SIiB4LjERExOI6YiijQ9hjYnF6AVmdkbVJMvyiwWmXy9lSyc28VUe62JLtLhxcFVivsPQiShDkshO27K8jaVoqfjwsnrZkzdVFQ3wRGI/h4HTOiAJSnwPsSb8HPyZu67kY+PPDN4B2MRrjvcaVCfgRkWaamrp0fNh9g264KPD2cOHntPJYtDjm2RMGn38J9j83IesbCd1403jERAFRmbae7NxI1GsnBy9h40Rvk1u3hzE9vIDDImZVLw6hw8STrmuuwmEaOGoBSW5C0UkklZOQUU9+ofPap1SoSl4fj7+tKZm4Jbe09rEmKQaNRhi9NNXJw/zP3T+h4geBYRgiDo0yfKKiqr+CnjW9NSBS0tfewKe0gVlnmhOSYfqMXQ2+Pd1lFM8sWBrN4zUJU14yj8v7bTbD8DNp3FfBTaj4VVS0sXTSbhGXhbKrMnHqk4O9Pw5nXTPy4I8gbez7lkq9+N7gg0dYW2vbBpecM27+puYufMwrIzC3B3s6GdatjSVweMS1+BKMx6UhBWydUDS/gOxLEnr1e+R9ZpuCbnw67f584aOhpplnXRkiQJ8nxUTS4uJO2rRSTafTp6UPTB3UNSsGlWq0iYXk4AX5uZOWW0NauVdIKUxQHyX9cxj/b/smfnvnThI4XCI5VRCphCEcylTAwUvDZVy+wKm75uI+ta+gge1vpMMfCzi4dGVtLMJrMJH3wHj4aGd7497jOKZvNFP2Qyx6LPS7O9sQvDcPN1YENJalTFwUAefuUNMLJKZM7/ggw3oLEtvYe9ubXUN/YiYebIwvmzsLfd+ZTT8dL+mAotTv28lrSuQBErl/NZV+9Ma7jLFYLapWadn0nNioNPV1WMlL342w1s+rMFYfmK4x0rMVK9vZS6huV9EGAnzIi3GqVydleSm19BwnLw/H0cCI1sxCT2TLhtMLjOa9y75bHWalbxNbHdou0guCYRqQSjnGGpg9WxS3HKlt5IO0pKjpqxjy2pLyJjK3F+Pq4sCYpul8U1Dd2sCntICqVxLrVc/C57gK4/tJxraenvZu03FJ2meyICPVh3erY6RUFAHHzj2lRAMMLEv+z+yPYfQDWXwbVdXR168neXsqPqflotQYSloezLiX2+BEFVisYJtaqNx0ExM3HtXdaYtmWbIzd2nEdp1apkWWZ8z+/lTM/vQFHFxVrd2WjQ8XmjEJ6dMbRj+2NEPj7upK5tYTa+nYAVCqJ+GXhBAa4k7WthJbWbtYkRWOjUbM5Y/yRgz5R8EDibWT99RNRkCj4xSAiBkM4EhGD0WoKmnpaWPnWBQBsvvRdQtxmDTpOlmX25deSX1RPZJgPixcoHgWyLFNU2sjufdX4+7kSH+mNjZf7uPP4VUW17NhWjNrRnuWJh25y0yoKtu2GnfvguktGbTk7lpBlmd/99AgrAxdxqRxDz7NvceDaqyhr6MLezoZ5sYGEBntNeurhRJk2UTBrOTxwJ9zy2+lf5GHY9sq7WM0WYs88CbfZgRM6dqAJ0tcXvIrVqCI1qwiAlMSoMZ/yB0YI4peFEdRrmmS1ymzNK6O6to34ZeH4eDqzJasQo1GJHIyVDhooCv626k6k3r9DUZAoOJYRzoeTZKaFweEKDSs7alnz/mXAYHFgsVjZtquCyurWQY6FZrOVHXsqqKhqJTrCj4UxfqiSz4N1q+AffxxzLQajmZ17KqmsaSOos4WlKfOx6/3AnlZRAPD0f+D1j5SWueMIvcFEfmE9xWWN2NiomRMVQESYD5ppbjsci2lNH7z9P1i2AOZOzF77WGCQODj3JaSPvifVPxITEqsTDk1aHAmrVWbrjjKq69pIWBY+SBzk7iynqqaV+KVh+Hi5HFYcjCQK+hDiQHAsI4TBBJEk6VbgVpT0SsxMCIPxdh8MFAdZV3yMh60HWbkltLRpWRkXSvAsT0Cx2M3aVkq3Vs+yRSGEBPf6E3y2QZlIN8bEwtr6drbvqsRqtRK3cDbBszz6P+CmXRT0YTaDRnP4/Y4BjEYzBcUNFJU2Yraa+aL2U05YuZTrllx0RNdxvNYUzBR94uCdtQ9zzoX/Qn/PTaTHxtHdY2BVfCTeY8ycsFplcvPKqKptI35pWP/fkVWWe43BWlkZF4avjwtbMgsxGs2sSYoZJA7GEgV9CHEgOFYRwmCSzFTEYKItiZUdtTy74y3uW3o7OdvKMZksJK6IwMdL+eCrqWsnN68cOzsNiSsicHd1UNrqbMe+iRuMZnbtraKiupUAPzeWfvsljiGz4LqLgRkSBbJ8TLUnjoXJZKGotJGCkgasVpmocF9iPv8c3Quv4HGHbnIjmyfJjIiC8mpIzYErL5j6uY4S9d1N+Dv7QGcXZmcHrBaJjK2K62Hyigj8xqj36BcB1a2sWBpGSNAhcbB9ZwUVVS2siAvFz9d1mDgYjyjoQ4gDwbHIeIXB8fH4dpwzGZ+C2W6B3DP/FlIzipA1FuYt8cHHyxmrVWbfwVoOFtUzy9+d5XGh2NqolZvv+svglLXwp1uGnU+WZapr28nbW4nVKrNiSSghQR5IH2tBtgIzGCn4PhXu+hukfap4GByDmMwWikubKCipx2y2EhHqQ2yUPw72NqA+Fdul87lFtZnrNyj96jMtDmYsUrB9N9xyP5y9HtyPvOW3bLVSlbOTg1/9gMbOjhP+9vsJn8PfWXH1fK7wcz4v+J6vUx5ldXwUWdtKSN9aTPzSQ3UEQ1FJEsvjQpEkidwdZciyrNSKSBLLloSABLl55SyPC2VNUjSpmYVsySygxHk392aMTxTAoVZGgNtuuw1AiAPBcYOIGAxhuiMGkxEF/Y6Fe6vw83Xlrvw/0mZo54cL3qK6UE9TcxcL5s4aPATJYlFmEMyJguTBbY/aHiM791ZSW99BUIA7SxbOVm54A5gxUQCwrwA+/BIe/sMxFzkwmy0UlzVRUNyAyWQhLMSbOdH+OI5gTNTXyljeUcM3F7w2Y2ObZzR90NeRYHfkRl0PxKw38K+gFRi7tTh4eXBPRTaqSaaXMqq2s+PqyzmvSINn4VbsbRzIzSunuqaN5UtCCZ09ugiVZZntuyooq2xh+ZIQwmZ7H3p9dyVlFc0sXxJCgJ8bn/60lR69gSbPEu5bc/2Efu4iciA4lhCphEkyncJgMqLAYrGyY3cl5VUtSjHhvFlUd9Zx4/8e5gL33+Bh70by8kO2x2NhtcoUljZw4GAdNjZqliwIPvQkZbHAN5tgXTIb6rfNnCg4RjGbLZSUN3OwuB6T0UJoiBdzogJwchzhvX/zEzg7wZoEZFnGZDVhq7alXd+Ju/30PnX/GmoKPr38DvZ/+h0Av934DmFrEiZ9rrwf/8eDnz1IT/Jivr7wNRxsHMjbXUlpRTOL5wcTHeE76rGyLLOjd99li0MIDzkkDnbsqaS0vJlm13L+tP0Rnp/zDG5qN9YkRePmOg5b8SHXEeJAcCwgfAyOMpMRBdoeIz+nF1BV08qKJaEsnh+EbJVpqbRwtdd11JiqeajqQXS2Q36e734OD/xbSSf00tjUxQ9bDrB3fw1hId6ccsK8weHVPfnwm1vI/u79mRUFOj188T10dU/veSeJyWThQGEd3/y4lz0Hqgn0d+fUdfNYtihkZFEA8NybyvcYJURsq7aloqOGyFdOHN/I5nFyxETBHx6BJ1+bmXOPg9izT+7///wvf5jSueJOOp8/3fcWufV7+Uvak6gkiaWLZhMT6ceufVXsL6hjtIcfqXffiFAftu+qoLis6dDrC2fT6dCId2cof1t8Lxeti8fe3oYtWYV0dOomtEYxeElwvCFqDGaAyYiC+sZOtu4oQ61WccKqWDzcHeno1JGzo4yubj1LFgSz0tOfjV9/SY9pyAdTWzs0t4Ik0a01sOdANdW17Xh5OrEuZU6/VfIglsxny8ZHOXXrXzglImXmIgV5++DiW2HbN7AgdvrPP04MRjNFpY0UlTZisVgJm+1NbJQfTo7jCKl//64SYRnAbNdAfjPntGmrOTiikQIXZxjPMK0ZIurk1ahtbbAYTRz86gdOfeIBpCl4WyTXqimqOhnHW+8ElBvxwrmzsLVRsze/FpPJzKJ5QSOmACRJIm5hMCqVRN4epUsnOsKPf219jXvzHufFxU8xqyeK6roO1iRGsyWrkC2ZhROOHIiaA8HxhBAG08xERYHVKrO/oJb8wnr8fFyIXxqOjY2aAwV1HCiow9nZjnWrY/t7tDMv/xhJktAae2jTdxDkGgC3X43RZCZ/fzVFpY3Y2WpYERdKSJDnqPnQDSWpnLPtgZkVBQBJy6AoDWb5z8z5D4NOb6KwpIGSsiZkZMJDfIiN9Jv4cCO1etCXfQ6JwJTFwRFPHzz4u5k9/2Gwc3Uh/IQkijZuoaumgdode5m1fNHkT1hVS0DWQTCrKG4r56/pz/LqKY8wJzoAGxs1eXuqMJksLF0cgmoUcbB4fhBqlcSufdVsLt/KvduUQsMbk09n9/4a8vZUIssyaxKjSRXiQPALRwiDaWSiokDbY2BrXjktLd3Mjw1kTrQ/7R06tmWX09GpIzbSn7kxAagHmOn03ehv/eEh0qq2ke57O13RSzlY1YbFKhMb5U9spB8ajXq0y5L2wwd43fIgV90Vz3NHoqYgeGIud9NBZ5eeguJ6KqpbUakkIsJ8iInw67ePHjeyDGdcBbdfDaesGbRpoDi45+dHOTd6PV4OI1fDj8ZRqSmQZahtAB/Pw7a3zhSxZ51E0cYtAJT+nDk1YXD+aXDB6QA0VhfwVfEm6j5t5OsLXiUyzBcbjZrcneWYzBZWxoUN+nvqQ5IkFsydRXbdTjy6Z/Hckn9xS/LZqFQqFs8PQpJg594qAFL6uxWEOBD8MhE1BtPERESBLMtUVLXww+Z8enoMpCRFExnuy869VfyUmo8sw4mrY1kwd9aIH2IADybcwUWO55IlBbG3pIngWZ6ctm4+82MDxxQFG0pSufOHv2EI8uG5K1+YWVFgMiktlOm5M3eNIbS0asnMLWHjz/upa+hgXmwgZ6xfwKJ5QRMXBaCkELw8R63i7xMHeVd/iZeDx6j57JE4aoWGO/dDRDLszj8y1xsB99Dg/v83aieWsx9GXxSgqYXEoDg2XPg62+r3cuanN6A19hAS7EXi8ghq6zvIzC3BbB55MuO/tr7GTdvvot6hDF/9bPbm1yLLMpIksWheEDGRfuzcW0VFVQspSdE4ONiwJbOQdlFzIPiFIYTBNDARUdCjM5KZW8LWvHIC/FxZt2YO3VoDGzfto7yyhQXzZnFSyhw83Z1GPF6nN7HnQA27c5qJc0+ixdzCq7VP4R2qHtaCOJS+lsTZ8Sms3LQFW+cZ7mNv7wQ/b3AZ+b1MF1arTFVNG5vSD7Ip/SAdnTqWLprN6SctYE6UP7Y2UwiMaTTw9lOwdvTKeUmSCHefjcli4oLPbxtXQeJR7T6YEwmfvgxRYUfumjPNNz9BSALUNZIcvKxfHFz4xe3IssysAHdWxUfS3NJNWnYRRpN50OEDzYtuP+l8Fs8PpqC4gZ17q/rFwcK5s4iN9GPXvmrKK1tISVTEQWpmIe0dPRNarhAHgmMZkUqYIuMVBVarTHFZI/sO1qJRq0hYFoYkSWzJKKSzS8/sWR4snBc0Yv88KGN+S8qbKK9qQSUpofGocF+ajc08/v7jfFP8M7cuvWLUdfaJgjNnJfFB4LXYaA3gOsNhZB8veOeZGTu90WimtKKZ4rJGenQmfLycSVyuTM0bKZc8KUwm6NGDq/NhPRg0Kg3+zt6HrTk46i2JDvZwxroje80hDKp9mY6W6VUr4d1noDda1icOtKae/mv5+biSkhhNek4RWzILWZ0Qhb2dzYiOhtERvqjVEjt2V2KxyixdNBtVb7pBkiR2769GlmVS+moOsgpZkxg95ryGkb4HIq0gOBYRwmAKjEcUyLJMbX0Hew/U0NmtJzzEG093R/IL62nv1OHr7cKKJaF4egx/qjaazFRWt1FW0UxbRw8O9jbMi1GG+NiqVbD+MmbfezO7rvkKVzvF10Bn0uNgM3jwy0DzovcX3oPNwlOVSvuU+Jn5xvTRo4PWdugdtztdtHUoIqmiqhVZlpk9y5OocN+Ruy+mSs5OOOlS2PMDRIePuet4ChKPuigA6NbC6x/COadAyKzD7z8DuM0OJPHuG5AkCFm9YhpO6ALnnTropeTgZQBYZStPb/svNy6+BC9PJ9Ymx5CaVcjm9AIOOGzj3vSRHQ0jQn1Qq1Rs21mO1WJl+ZJQVCqJ+XMCkSSJPQdq+sVBWlaREAeCXwzC4GgI4zU4OpwosFplauraOFjUQFtHD14eTri6OlDf0IFOb8Lf15U5Uf74eA82KjIYzNQ1dFBV20ZDYyeyLBPg70Z4iDf+vm6Hxvxqe+COvypjjBPiAHh//1c8kP4UP19yaCrjMEdDC1BcDrNnKaY9M8kjzyo3oLKsKZ/KbLZSVdtKSXkzrW1aHOxtCA/xJiLUZ3K1A+OlsUWZLXDaWnAa3wd+n0Pii3nvkXXFxyTMUn4+x4QoACithBVnwuevwappuCkfCxiN8P6XsHolhM8etKmgpZSlb57DioCFfH3BqzjZOtKtNfDlzzvoMHTR6lXO/WtuGLWDp7Kmla07ypgV4EH80rD+v8H9B2vZX1DH/NhAIsJ8SMsqQqszTFgcwHATpKuuuorNmzdzxhlnTO77IRCMgHA+nCTjEQajiQKrLNPW1kN1XRsVVa3oDSacHG1RSRJdWgMatYrZQZ5Ehvn0f3AYjWZa2rQ0tXTT2NRJa7uSq/T2dCIo0IPgQI9xt9YNHdl8oLn46DoaFpdDTf2kIxOyLNPW0UN5ZQsV1a2YTBb8fV2JCPUhwG+ASDoGkWWZzwq+57yYk5Ek6dgRBb9UtD3gtRDeegp+c+awzRlV2znl42v6xcELee/yaMZrPB3zJG4aV1YnRuExxs28pq6d7G2l+Pu5krAsvL8oeH9BHfsP1jIvJoCocF9Ss4rQ9hYUj3W+kRgoDiIjIykpKeE///kP11xzzcS+FwLBKAhhMEkOJwza2to48cQTueeee7Cx0WBvb4NGo8JqkdHpTVitMpJ0KG2qUavw9nLG28sZV2d7DEYz3VoDXd16Ojp1aHuMANjZafD1csHf1xV/X9fDi4H23p/pkEE4feKgx6SjTd/BKeFDREFpJbz2Pvz++mN2oJFOb6KiuoWKyhY6uvTY22kIDfYiPNQHZ6cj7PHf1KJYR5+9HjzdJ3WKd/Z+wQMZT9Fl0ApR0IvBaMZstiJJSjhdAjQaNRrNJOuhZRms1mF+EwPpEwd+Tl6UtlfxQOJt3LfiVtK3FtPdbWBVwthjm+saOsjKLcHby4WkFRH9az1QWMe+/FrmxgQQFeZDWk4xWq2BlMToCae3uru1xC5cT01tA6B8b4Q4EEwXQhhMksMJg7S0NC699FKefPLJyZ0fcHS0xdnJHjdXezzcHPH0cMLZyW5iQ3le/xBuewC68pXK+QG8teczrvruj/g7eVNxS9rgSMG23XDNPfDNmzOfX25oVoYnXXrOYUWIwWimpq6dqpo2Gps7kSSJWQHuhAZ74efjevSiA7v2Q/zZkPUFxM2f8OFt+g5iX11PY08LDyTdyt9X3TX9a5woP6TCYy/Dd28e0WFKFquV2voOyiqaqW8c/pmkUkkE+rsTGuw5OG02jdy88UFe3vU+9yfcwsOr70KSJEwmCxlbi2lt7yFpRQT+Y4xtbmjqJGNrCZ4ejiSvjMSmt9gxv6ievQdqmBPtT3SEL2nZExcHWm0Pp519LWkZ2wa97uPjQ1FRUd8HukAwacTY5RkiOTmZSy6+GJ1Oh729/Zg3c41GhYuzPa4uigDw9XbB1cVhej7wTloNX/5n2MsbSlK54fv7OSk0iTdPf3x4+mD5Itj749SvPx6aWuDvzygV4yMIA73BRF19bz1FUyeyDD7ezsQtnE1woAe2tsfAr+fCOaAtGPNJdDT60gdmq4WLYk/l4cwXmO0aOOMjmw+LoyOEBh0xcyOrLFNY3EBBcQMGoxkvDyfCnKyk3vd/IEnMOe9Ullx5AZ3deiqqWsnYWoKdnYaQIE9Cgr3GH5K/9Da4+Gw466QRNz+e8yov73q/v9Bwe/1e5npF4mTryKqEKLK3lZKRU0z8stHHNvv5uJKSEEVaThFpWUWsSojC1kbNnCh/JAn27K9BlmF1QiTp2cWkZhWOSxyMJgoArr32WiEKBEcUETEYwnhqDKxWKzfdeCPvvvcer778FLb2I3+ISIC9vQ1msxVTr6mKs5Mdnu5KlMDTwwl3N0c0o5gYTZSRRidXddZy7Xd/5rVT/9lfkHjEkOVBLX6yLNPZpae2oYO6+naaW7UAeHs6EzzLg6BAj8N6MRwvDK0pWOQ7p78g8b0zn+TSeWcd7SUeEXp0RrbuKKOppZuIUG8iw3xxc3WgImMbb667BICE313L+kf/3H9MW0cPFVVKXYnBYMbN1YE5Uf4Ez/IYO6r227vgwtPgzOHCYGhLos6sJ/zltcz1iuwvSLRaZbbmlVFd00Zc73Cl0Whp05KWXYSzkx2rE6Kw6xWxBcUN7N5fTUykH7FRfqRnF9N9mMjBaKLAS63mgrPO4pXPPxdTGQXTgogYzCAqlYqXX3kFgN9edTP/ffUxwqMXUFc/+Psso+TLAQL93fDxcqZHZ6K1TUt1XXt/PYKbqwOe7k54uDvi4e6Im4vDqI6H/RiN8MZHsCYBYiNHFAWg3JuL2ypZ+/7lbL70XUJyS+HOv8LmjxXzoZlEktDpTTQ2ddLQ1EVDUyc6vQm1WoW/jyvLFocQ6Oc2s10FU0VvgMtuh9uuHtPkaCCjFRo+f9JD+Dv5kBy0bCZXfHha20GlGlafMt1U17axbVcFGrWKNYnRg0aFS0ME40A83BzxcHNk4dwg6hs7KSlvImdHGaUVzcQtnI2ry+B23H7efmrEl0fyKXC0ceDTc57n1E+u5cxPb+gXByuXhmFnq2HH7kr0BhNzowNGFCNeHk6sSeptU8wsJCVR8USIifRDkmDXvureyEEUadlKK2NKYtQw47JRRYGTE5sMBhYaDDjedZdoZRQcUYQwmCQDxcHVN9zLf199jBNPXEvWttIR96+t76C2voOgAHeWLQ7Bxdme9s4eWtt6aGvX0tKmpayyGVkGlSTh6mqPu5sj7q6OuLs64ObqgJ3dgB+XRgN/exqcndlgUzNq98Fst0C2XPoea96/jLXvX07aic8QdP5pM/I9sVplOrt0tLRpaW7tpqVVS7fWACjiJ3iWJ34+Lvh4u0xblGTGse0VLePM/ozVfSBJEg8kKR/wLbo2NlfkcEHsqaOdaub486OQXwRp/5uxS/Q9Oc/q/X23G5oWGkc9jVJz4Eagvxt1DR3k7ankh80HiI70Y250wOBCxR6d0pkwJGU1kijoo88Eaag4WLIgGHt7G/bl16LXm1iycPaIhlkebo6sSVIMjjZnFLImMQoHB1uiI/yQJKnfNXF1QhRpOcWkZhWxOiEKr17PklFFgZcXm1xdWVRWBt99xxP33gsInwPBkUOkEoYwXh+DPvrSCv95/XX+++pjXHD+6Xy/+QBms3XE/VUqCatVJijQg/mxgYOefsxmKx2dPbS299De0UN7h46OLh1Wq/IzsrfT4OrigIuzHc7O9jhIMrs7i7j4x1tYF5Y4ZktiX7eCjVrD3mu/nVLroiwrHRhKZ4Wezi6dst5OZa0S4O7mqHRjfPc9PnNCsT/r6DrtHQkm0pLYd8N67dR/HPmag70HoaMLkpdP+6llWWb3/moKSxqJjfJnQa8Z0FCqsvN4Y+1FAMTfcTUnP37/Yc9ttlg5WFTPwaJ67O1sWLIgmEB/N+X8//sOLr8TyrP7I2FjiYKBZFRt5+rv7mXDRa8T6RHa/3ppRTM7dlcQ6O9O/NKRhy8BdHXr2ZJZiFqtIiUxGidH5W+ruKyRvD1VRIX7Mi8mgPScYjo6dSTHR+LkoB5dFGzaxCJfXzj9dAgLgw8/RNZouPvuu3nqqadEWkEwaURXwiSZqDCA4eLgskvO7vXs149yDaU1y2SyEDbbi3mxgaNaIVutMt1a5Qbc0amjs1tPV7eebq0ei0X52VllK04Odjg62uJgb4uDvQ329jbY2Wqws9Vga6PGxkZNo66ZgrYS1rvOQ5WzA+mckwHlw1y2ylisMhaLFbPZgslkwWA0YzCa0RvM6PRGdDoT2h4D2h5D/7VVKgkXZ3vcXR16UyFOuLs59Fdr/yIwm5VhSmNU8E/Up2CgCdJREQczgNUqk7uznMrqVpYsCCYq3HfUfaty8nhjjSIMVt5+Faf86y/jvk631kDenkrqGzsJ8HNjyYJgnHu6lWFdve6H4xUFfZitZjQqDd1GLRISTrZKPUBtfTvZ20vxcHcieWXEqHM3urUGUrMKkWVYkxTd31ZbUt7Ejt2VRIT6sHBuIJm5pdTUNvP880+TszVv0Dn6RcGi3kmTf/kL1NRAeDicfz7ynDlCHAimhKgxmCCSJN0K3MokBksNTSsAXHH5uWRtLaG2oWPY/rIMJpMFF2c7auraqaxpJTrCj9go/2E3VJVKwtXFAVcXB4JnHSpy/K44ld99/U/e3jMfr8RE9Mnx9OiUm3dnpw69wYTRNNIUOVe+pAo0vvDNzsO+NwmwtdPgYG+Do4Mtvt4uODl54+xoh6uLPU6OdmN3WXRroUsLAaPfJI55Fq5XbjiP/GHEzZMxLxqPffKM8d7nEBEC8XHTdkqL1UrO9jLq6jtIWBZG8CzPsfc3GCd9LWcnO1bFR1JT186ufVV8//N+YqP9iT37ZNRMXBSAMucC4OIvf0ePSdefVgj0dyclMZqMnGI2ZxSyKj5yRBHv7GTH2uQYtmQWsjmjgJTEaFxd7IkI9UGSJHbsqsBoMrNonj+/+/297N69d9Dxg0TB3/4GO3YoTxANDfDxx/Dww0g7dvDEE08AIq0gmFmEMOhFluUXgBf6IgYTPX4kcfDby8/tD6uORFe3AVsbNYF+7hQWN1BW0cLCubMICfYc88NsQ0kq536u1BQss1+IZmE4zBnecWC1yhhNZoxGCyazBbPZgsVipaOjlUc2P0OPvZq/JN6Cj6MnkkpCrZJQq1XYaNRoNGrsbDXY2KqnNpDonkdgXwFkfDb5cxxtHvszBAeOuGkqjoZ94kB1pIec/vsVOGv9tAkDi8VK9vZS6hs7SVwRTqC/+2GPKf35kE22T2zkhK8pSRJBgR74+7pyILeQAwdqqKxopsBhD/dmTkwUDORP8TdyysfXDKo58PZ05oRVMaRlF/FzegGrE6JGLIB0dLDtn8OwJVMRB26uDoSHeGNro2ZLZj433/J7du/ZN+i4YZGCefOgsxOefBJuvRX+/GfYtQuio5XZCkIcCGYYkUoYwmRSCQMZmla48orzKChpYPe+6gHXGD5QLiLUG4PRTHVtO14eTixZGDzi6OXRug8mylD75BlrZdxXoEQNpvHp9FhhJmyOdzUcODLOiENaSSeLxWIla1sJDU1dJK2IIMBvfP32L8adStOBIpAk7i7Lwtl/9NbAw7Ipk44HnuTrP9+BymJPs2MVt607D5VqcoJrqH1yX1qhR2ckPbsInd7EqvhIvEZxSdQbTKRlF9GjM7JqZRRenk5otT2sO+2qYekDFxcX3nnnHc4666zBIkavh6oqOPFEOOccWL8eXF2VbpL4eGS1WqQVBBNmvKmE46Q0/PihL3Jw3bXXcvUN9/LWO58RE+FH/NKw/n2UzoPBx5WUN6PXm0hcHo7ZYuWn1IPs2F2B0XhobvyooiBvH9xyv2IJO05mb9nH/s/9QJZZ+/7l1HY1TOl9j8r8mONfFGRuhy3Zg16aCVHwfWkaS/57Fv/Z/dGUz3VYpkkUZOaW0NjURfLKyHGLAl1rO/peS+/glUumJgoATkzilSfWc9X+G2izr8NfF0ZadjE9usmlK5KDl7HxojfIrdvDF0WHzMD6IgKurg5sySqktn7kwKK9nQ1rEqNxcbZnS1YBRSV1nHb2tcNEgaenJ6+//joGg4GdO3ditVrhgw+gsBDs7SEyEp57Du68E37/e7j4YkUo/Pvf/ZGDu3pbGV944YVJvVeBYCREKmEGGCmtcOUV52FjoyY9pxgAqzw8ctDcqqWzu5KEpWF0dOnZd7CG6rp2Fs8LYr9hX3/6YFikQNsDO/dBU+v4vQncXXEIDyP1vP/jsT1v4e04sknTlCmthK9+gJuvOKL2u9PK8/+F7h7FM4KZm5K4PmwVt8RdNrM1B20dcMFN8I8/TEmw9YmCppYukuMj8fMZf3TNwdOdu4rTqd2xF7PeMOk1AGC18kTGy9yb9SQPJN7GLavOprG5i9y8cn7YfIBli0NGdTEci+TgZRy8/nuCXJWR4VbZikpSYWurYXVCFFu3l5GZW8yyRSGEhQz/m7O11ZCSGE1qZj5nX3AD+fn5g7a7uLjw0EMPsW7dOlpbW8nLy6Ors5OEhx/G9rLL4Le/hYcfhtdegzffhMxMaGyE7dvh7LMBRFpBMGOIVMIQpppKGMhIaYXmlm42Zxb0C4I+cdDXxtjH4vlBBAW4s3t/DVW1bezT7qPEdh//PfcfI6cPpiE0vK1uD76OXtObVvghFa66G/b8AN5jF6Qds/TowEYDNjYzPiVxxrsVmlvhD/9QhmgtiJ3UKQaJgpUTEwXTzTtvPMT5d7zL6y9dym2X/60/HG8wmtm+q4KaunbCQ7xZPD8IzSQ7Zd7Y/QnvHfiKr85/pT+tYJVl8vZUUlrezPw5gb2WyIP//sbyKfjmm2/o6uqis7OTFStWYGtrS3Z2NrY2NiQtXYpba6sSIfj976GlBfbsgbfeUgSCjQ0UFUFQEKSkKFMZRVpBMA5Eu+IkmU5hACOLg7aOHjal5Q+K/KskJdJgthx6MXiWB21uVTz4w4vcMusmXNVuzI8NJDrCb+ROgKIyqK4ft0MfVit8+h0siEGOjWTpm2fTru+a3poDQ+8T4fEaLRjAkRqd3CcODjQX89PFb6NWHTutn2aLlcytJTS3Hn1R8HjOq/xzw+P8r34lJzz/JpLNYAdNWZYprWhm175qHB1siF8aPuFph6DUHJz6ybUs918wqOZAlmUOFNSxv6COyDAfFi8I7i/UHU0UuLm5sWnTJpYuXYrZbGb79u1UVlYSEx5OmJ8f2QcOoNVqWb58OcHBwcpBH34IeXnwf/8HcXHKjIt9+yAgAAoKwMZGiAPBuBDCYJJMtzCAkcVBV7eeH7ccwGw59P3XaFTIstzvEQBQbahiuyqd/5z5DwqLmigqacTNzYHli0OHf8hdfbciDtL/N77ogcmktOJdfRH88eaZLUjs0YGD/bTkto84n3yL4actJCcUz7go6EOWZfRmAw429nQZunGxG30c8ITQ6ZV/Hm4T/lmYzVYyc4tpbu2etCiwWiyoJjGQaigTaUns7NKzdUcZHZ065s8J7LUtnth7H00cgOJVkLe7ksAAd1YsCcVoNIwoCjw8PLj//vuZP38+CQkJuLq6IssyhYWF7Nm1C5/CQpbdfDN7i4qoqqoiNjaW+T4+qP76V7jnHoiOhtpa8PSEkhJwcYHZs/vPL8SB4HCI4sNjiJEKEl2c7Tn5hHnY2hz6kDSbrWjUaiUaICniIMgumAsdr0DbbWLx/GBOWB2LLMNPafnsPVCDZUCEgaf+Ct+/O/4PfBsbyP4S/ngzcMg+GWDt+5dT0VEzPd+AghIIiYeth/dNOBbR9nSy6eDmIyYKQMkfO9jYU9vVQMxr66evIPGbTRC4DLq6J3SY2ayMJm5u1bIqPmrSkYKPL76V/554CdnPvI7ZMLn6gj5RkL1zIX+rDj3sTd7VxZ4TVscQFeHLngM1pGYVTbgwsc8+eVv9Xv645bFB2yJCfUhaGUFjUydff7+T9WdcPWL6YPPmzVx33XXIssyPP/5IeXk5kiQRExNDypIldMbEsDk7m8jISBb6+lJw4AAZ27dj3LsXysrglVcUsy17e6U7YfduuO8+uPFGaGoSBYmCaUNEDIYwExGDPkaKHOh0Rn7cko9+QPeBpLFiMlkxY8JecuhdF8QtVCa+Wa0y+UX15BfU4eJsx/IloXh6DGhtbGhWvPDXjDOlAHCwGHr7ySs7ajn/81t57dR/TM9N0GqFJ1+DS8+BQL+pn+8IcqTSB6Mx7TUH1XWQuwvOPWXcAtLUKwra2npYlRCJj5fL4Q8aAWO3lsdnLcdiMOIS6MddxelIE2wp7BMFD668hYfer0dKXgFXXjDu4xuaOsnNK8disbJ8SSizAtwndP3c2t1EeMzGy2F4QWN9QyvrT7+avfv2D3p9qE+B2WwmLy+P8vJyQkJCiFu4EBsHB3Q6HdnZ2bS0tLAoLAzXzZvJiYjA1t6e5Lg4XBcuhEcfhWuuUf7t3Kk4I6rV8P77sHYtICIHgtERqYRJMpPCAEYWB3qDiU2pB9H2PsVYZSs9aHGWXHBytEXbc+jpJjLMh8Xzg1GpJNo7esjdWU5Hp47YSH/mxgQofu63P6i01+3aqHxoHI4fUuGsa2H7t0p7IcqHiyRJ6M0GWnRtzHLxn/bvxbHOIFFw0X9ZHDD/qKRCjqZ9sslkIX1rMe3tPaxOiMLba/IpjQOfb+STS5Tq+WU3XMrpz/59QsdPxtFwJAxGM9t3VlBTP/nCxMqOWv6a8QzPn/RXnGwdxx6INNC8aADl5eXkbduGfVMT8fHxeMbFYbVa2bNnD4WFhYSEhBATE0NOTg66nh4SIiPxX7hQOVirVQS3SqVE/mxtla+tVtBohDgQjIiwRD5GGa2Vcd2aOXy1KQ+rQYWEhLPkgqODIgpcXezp7FLmLhSXNdHZrSdxeQTubo6sWz2nP3pQW9/O8rhQPP9+txJyHG8u94Qk+PRlmBvV/1Lfh+6dPz3Mj2WZU685kGV4+R2IDIWTVk/+PEeIgaJgu+uNhIWfC407wXVyT8tTYaB98l2b/slZkevwdfIa+6DRSM9VOhPOPeWwuxpNZtKzi+ns0rE6MQrvUQx9xkvBV4c8AWLPPGlCxw4SBc7rkL7+Cc5cNymhZmerIXFFeH9hYlNzFyuXhY1oKDYaNd31fHJwAxUdNXx46tNceOHtw0SBi4sLDz/8MCEhISOeIzQ0FC+DgZyMDH4uKWGhszNRUVEsXrwYT0dHtu3eTWdbGwnLlrH72WfJMlhZ2umGf0MXqoUxqGepUXU0wL/+BX5+SpFicDB88QWSSiVaGQWTRkQMhjDTEYM+hkYOfBO9uOSLu3g8/FHcVV59a8HB3gad3oibqwMdnbr+NkdnJztWJ0T1D2sZGD2YGx3AnOgAVFot7DkIScsmsjDlKaSXaS1IPOUKWLUC7r998uc4AgxLH+hclQjMb85UCiiPErIsU9haRoxXeH9EZ8L87iHYsVcpUB0Dg9FMWlYR2h4DqxOiBqeqJoHFZOLfwSvRt3di5+rMH6pzUduOz7VzWKTggX/Dhs2w7ZtBv6uTYSqFiRlV2zn53aux+UBDR2HXoG1eXl58/vnnaLVaurq6iImJYe7cuWg0w5/FLBYLe/fupbCwkMDAQKV9cd8+2s4/n8wnnkAjO7K8MQRafVFZB7xfCWw8u7B/6w40F61S5iusXKkYIvUiIgeCgYhUwiQ5UsIADomD177+D5qb1ZwWuYYPznyajOwy2jt0AKgkCTs7DQajGRcXe7RaQ/9IZxsbNaviI/uf5KxWmQOFdeQX1uHu5sjK1J9wfeN9yN88vhvaP55TjJI+fWXQy9MmDiyW8UcxjhJHu6ZgPFisFq769o+kzF4xubTCEPE3FL3eRGpWIXqDmZTEKNzdJt7iN5TSn7N457TfAjD/ojM5/+2nxnXcqOmDtg6ls2IasFit7M+v5WBxA77eLqyICx112ulAtNoekk75Dbu3DTYvGpg+sFgsFBQUcODAARwcHFi6dCn+/v5QVwcXXaQYGMUqfhI1NTXk5uZiZ2dHQlwc7g2NaDuD0adbsGDBusBKj7+WnSW7CPUNZZ7LPEx5JiyNFmzm2OC43gGVq1o5d22t0tooSYfEwTtP8exfn+X2245tYS6YOURXwnFAf7fCmddi/sbCWT0n4mjnwAnJsXi6HzJSMRjN2GjUaLWG/imHoOR/N2cUUFHV0ns+ifmxgZy4Khaz2cKPS5Io/OgNZPtxegjMj1EKFoeIxYHdCh8f/G7yb1itVm5K1XWTP8cMMqoo6OyCzzcqIfhjAJWkwtXOmes33D+5boUxREGPzsjmzAIMRgtrk6OnRRQAHPx6QBrhrHXjOmaYKADYX6hsnCZRAKBWqVg4L4g1idF0dev5YfMBqmvbxjymr6ZgLFEAoFarmTt3LieffDKOjo6kpaWxdetWDB0dyuwDn0N20LNmzeKkk05Co9GwJT2bpj3+mLaA/QJ7KldXkq5LR7/lc1YmraS8tZyc1jTsrrLD8WxHzBUmOp+ow/ivzyA0VIkcvP8+oEQez7r9LDS3arjj3TtEt4LgsIiIwRCOZMSgj5EKEi0WK6nZhTS3aAHlpq9Wq1BJEmq1hL29La1t2v5zzIsJYG5MQP8TldlsZW9+DUWljfh6ObG8aB9OV543/tDrCE6KbfoO3O1ckSQJg9mAnWYSpkV/eAQ2bIG9Px5TngZjRgqKymDBSfDDe7B65dFb5AAmVZD41Y/w6AvK+3Aenhro6taTmlUEQEpiFC7O05M2kWWZpyNX0VlTj9rWhj9U52J3mFqNESMFmzLh9Csh+wtYMn9a1jYUg9HMjt0VVNe2Ezbbi8ULgoeNQh+r0PCGZ27g/gvvx8l2+PdXlmXKysrYs2cPkiQRFxd3yMRoAKZmEy1vNaHW2dA2t47Ic+YjSRL5777LPjs7QkNDCSkoINtsxsHXl9UnnICdxYaeh9MxOS/Gzr4Ih3ltSCevA7Wa1PJUTnv/NBKDEpmzaw7PPfWcSCv8ShERg+OIkXwO1GoVKQnR+HofShNYLFYsVisg0a3VM2vAeNv9BXXk7izv3a6YJS1ZEExKYhTdbd1sdApk26ZdjEsIvvwOXHLbsMiBh70bkiTxReGPzH/9tMn5HFx9Ebz8fxM/bgY5bPogfDbUbp9YrcYM01eQ2DdbIbVy6+EP8vGCxGUjioL2Th2bMwpQqyVOWBUzbaIAoPDbTXTW1AMQtiZhcqIAYE08fP4aLJ43bWsbip2thoRl4SxfHEJVTRs/bsmnZYAAH0sUvPnZmzxX+RxnfnAmWqN26KmRJIlwW1tOef99fJycyM7OJicnB6PxUNeRuc6M9i0tDpINnWWPs9t8kPT0dEwmE3OvuIKVK1dSWVnJwYAAVqlUGK1WNm3aRLe1B6dH1+B4qiMGYxRdNSuw7isl/8n7+d+dJ5EYnMhXl3zFM088I3wOBIdFRAyGcDQiBn2MFDmwWmUythZR36gUN6l7rZAdHW3R6YyEBHtRUt7cfw4fL2eSVkZga3OoyMlosrBp0z66DGaCAtxZuigEO7sxGlK+3QRbd8GDd8IIxVJHbGTzEeB4qCkYC1mW+TD/G34z53RU0uR0fktrN+k5xTg62rI6IQp7O5vDHzQBtr/2Pj/c+3+YenT85uOXiD1r9I6EUUVBU4sibI4gXd1KYWJbRw8RoT6EBLlx3kU3jdmSmFGZwanvncrywOV8fcnXwyMHu3fDbbchf/45lVoteXl5aDQaVqxYgWePJ90fd6P2UeN8sTMqRxWNjY1kZWVhZ2fHqlWrcLKxo/mdNOqM3jhbXHB3c6dR20CbQzsxJ8fgGeCJ+fG36G5LwKqCnk8uoMtaQeieKhwclc8zUZD460UUH06SoykMYHRxkJVbTG2D8nNUqySssoybiwNd3Xqiwv0oKGnojwa4OCsdC06Og0P9ldWt5OUWobKzZfmy8PGNyR1lONOUxEF+ETzyLLz6GDhNTw57MoxbFMgyXHMPXH4enJh0ZBc5Ab4vTaO6q55rF100fGNzK+wrUKIeA2YKNDR1krm1BHc3R5LjIwc5cU4nXXWN7H73M5LuuXHUqv9RRcHeg7D6AiVaMBHTrmnAapUpLGlg555yHvnHPzhwYOyaAmCQOPjm0m9wtBn9d7ynp4dt27YhF8ssrF+ITagNzhc6I9ke+h51dXWRmZaJd6034e2hSHo12OhoddAhW8141mqRXMOwSBaIAc+5Wkq/eJM6cwqRqmhczrTHebGn0sLcK/SFOPh1IlIJxykjpRVUKonElZH9qQOLVWlV6+jU4ebmSEFJPXOi/PpzoV3dBn5MPUhr++Bw5mw3W05+7P9w13aSnlNM3p7K/g6HEfnkW7jwJgZNe+o/16GCxJu/f3Bib9LODsqrobZhYsdNIxOKFEiS8sTa03PkFjgJvi9L57oN941ckLgxFU79LXQd+p2oqmkjPacYby9nVidEzZgoAHAJ8CX5DzdNXBQAxEbAP/8IiUtnbH2joVJJBAe68uKLT49LFAAkz05mw2UbmOU6C42qN+KWng7nngudgz+LHR0dWem0koW1C6l3rme733Z0Zh3s3w8xMbB/P/Zt9sRXxhNeH06tXT3dq2rw+FMgAdcHUBxVRFpcAcaLdTSFNGEpstD2hTPvyFaenP0Mjt5GTN+A/pqnYMEC+Oor4NDIZpFWEIyEMDg6BhnNBClhRTg5O8qormnDapVRqSRa27R4ezpzoLCeudH+lFe30tNjxGg083N6AYnLwwnsq0VwccZh03uscnKkuKyJPfuraWjqIn5p2MhT57w9wcsDDMYR2x37xIGNeoK/RuGzIfPziR0zjUwqffDNmzO+rqnyxAn3YbAYuX7D/QCDCxIvPRuWLwRPdwCKyxrJ21PF7CBPli8JQT1FP4CpMKYoaG1X1nzzb4/K2vpqCjIytw963cXFhYceeghHR0eMRiO2QzwZkmcnkzw7GYDd9buJ6WzDXqUCx0N/Z7Iso0/To0/TY7/CHp8lPpRsLeGHH34gITIS37PORl/ijX53N+pZahyvdaSnuocD5eV056uJ9fLihPXrycjIIGNPNgmJi8ktziWgOIDbWm/DphMcnz4L0/WPowu7CtnZH/voGPq+u33iAIQJkmAwIpUwhKOdShjISGkFWZbJzSunolppnVOpJKxWGV8fFxqbuoiJ9KOppYvWtkNPt0sXKTMWBvHR13S2dZMTu0gxd4kNJCbKv39s7ERp0DZz3Xd/5oX1f2O2W+D4DiopV5wEj2DueEo1BXoDjLf18ygxsFvh7TP+xRXzzx22ff/BOg4U1hEV7svi+UGTthYei56WNra+8BYJd16LvdvoxYZjioLUHDj/Rtjycb9V95FkrELDzz//HLVaTU1NDSqVitmzZxMeHo6np+eg96A364l8NpJor+hBNQeyLKP7QYch14D9Wnvsk+yVbh+DgZycHFrrWknoSsCu3m7QdlmW2b9/PwcOHCAiK4sl//wnVltbsr/9lnqtlv9n77zj6qrv//88d3PvZe9NAiFAyCSDkACJGkfcq+7Waq39VTtstf22tba29Vtbv93WWq21VaPWWfeMCSsBQkhICDOBsPe8e53z++PAJSSsIMTF6/HgQXLvued87uXee57nPV7vVxseJyVxKxnuDNYNrUM9qMJniw5JKWD/0I5mhRr9eitCc6Pc0shCWuGLpIVUwmlKEIQ7BEGoAko/6bWMaqK0giAIrF+TQEKsfDIdjRx095iICPOj9mgXgf6GccNh9lc0c7iqbXxHwuEa/MoOcHb2UpYmRXC4up3dhXVYrBNMvPtoD1x1u5yjnEQOt5MjvUfZ8uwNNA+1T//kbHbYcCn8c46mBs5AHwsKHnoU0s6av8XNkUa7FX6adScbo1fLN1bXw6W3Ija3sb+imaq6DpanRc8bFAAU/OYR8v/3Yf6cdhbHPiyccJtpZx+sSYd7vzXOqvtMabrZB9nZ2WRlZXHRRReRmppKV1cXO3fuZOfOnbS1jX3WdH/5G2Vla9jXUuLtVpAkCdu7MhToL9Djs9nH+9y1Wi1ZyVlsatuEoltB66pm1Jlq7/2CIJCens7auDgasrIo2r8fAGmJlqGGvVy65BtcufpKYlbEkBeahznZgm2XA8+hfnwCD+KssGP5aRHS9ktgYMC7z4W0woJO1ELE4CR9miIGo5oscrC/opmGJrkjYTRyEBXhT3vnEPExQWg0Kuobur37iY8NYt2qBHmssyjKuXNB/ndPv4WS8uM4XW7WrIgjPuaEK5/Sg/Dbv8E/HoKAyV+TEwsSd1+/Y/rIQXE5rEw7IzbDH7v74FA1VNXLtsifIv+F6TRkN1H+9vNkP1VK8Q/uoaPXxNqV8SyKD5m3Yw4eb+XhFdvwOF2odFq+VfkhfjGR47aZFgqGTZ/IXAqYHgomGogkiiKdnZ3U1tbS09ODr68vKSkpxOXloTx6lMKvn8/5z5zPhqgNvBL8CuJBEf1FerSrx0egnNVOLK9ZUPo4GHrjm5Tefh1+AQFs2rQJvX58uq+zs5M9e/YgaOH2w99gZfRK/jftf2k81siyZXJL55EjR1gVuIqwvUYE6wC6TC3WygBU/k4Mt0Wg0I1dGy5EDj7/WuhKmKU+jWAAk8NB+aEWjh3vAcbDQUfXENERAQQFGjhUNeY3EBbqy6Z1iahHC832H4av3QP/fQJnVAQHDjXT1NpPTFQgGSvj0GpOr35gFA6UCgWHb30b3UxMkCzWee1O+Ky3JH4c/aH0n/ws7y88mv4wOo+ezLWLiYqYO9fAifTqV7/PoedeA2DT3bdzzq/uGXf/tFDw6rvw7ftg72twElDMt2YDBSert7eXmqoq2js70ev1rFy5kpiYGIqai6h9rpbLXZdjuNiAdtX4z4aj3IH1bSvqVDWGsySEmkoG4uIoOnAAj8fD5s2bCQ4en3arvfMW9q/LwqT1cPUFVxPYO0D1z35G5SWXkJycjI+PDxUVFSyNSCbhSALisIQuW4ejyIFCGsZofhbFlvVwlhwNW4CDz7cWUgmfM02WVlizIpYli+X6AVGUUAgC7Z1DRIYH0N41RFePiQ1rErxfvt09Jj4qrMVmd8k7jouCjBXgZ0SjVrIhYxEb1y6iu2eY93dV0dl9wnvnQCVc802w2iZd52hB4q9z754ZFBTug6Rsud5gHjRnUODxwCvvQF3D3C5wnnXrkqt5JPH3mK12BsOa5h0KOiuqOPS8XPnuExTA5rtvH3f/jEYnb1oH3/s6RJ/ZUd9zAQUAIQYDm7/3Pc7r78ff35+9e/eStzuPZfuWcYX7CgyXGpDSpXEmSPYiO9a3rGgztBiuMCAE+sLGjQRGR3POOedgNBrZvXs3ra2t3sfkHc9jR/0z9Oz/N1HGKIryixgOCSFt2TJWJydTV1fH8PAwGRkZ1HbWUbuiDlWUB/uHVjTGZsReCyb7hXjK6737XEgrLAgWuhI+U5qsW2FVeiwKQaD2WDfiyNS99s5BosL96e414fF42LQhkeKyBtxukaFhGx/mVZOblYxfaDD847fyAfoGwM9IbHQQwUFGSsuPk7+3niWLw1ieFo1Ko5G3GTKB3mfSdcb5RxHnHyVb4e57kiuWnje5z8GadLjjKxAy9wWIcxopUCjg6/8jmz4lL567Rc6jevvNFBbWEdxpokuxh7vrX0LUOmY3eGmG+vDeh7yOmdk//H/oTkg9TQsFkiTXnoQFw11fm7c1TqS5ggJAbse9/HL8MzPJXrWKjrYOTP81IfVL9KzqIWFpAje9ehN91j5ev/Z1FAUKHHsd6LJ16HLlIkM6OuCJJ+DWW9FFRpKbm0tpaSl79uxh5cqVdGg6uPC5C8m6MZfXr30d3JCfn8+uXbvYfNttLAkJQa3RsO/IEVwuF+vXr2ffvn244x2s3N+OQzgXzXIH7kEdJvEafHs9KNVm8Pdf6FZY0EIq4WR9WlMJJ2qytMLh6nZq6mXrWUGQv2cjw/3o7bdg0GtYvTyWvWWN2EeiBWqVkuyNI9MZXS5YfzFsy4bfyu1ukiRR39DNoao2jAYtGzIWEejnM7bzaXLtg/Zh1jx5KXDmHRLnJX0wZAI/42eixqClfYDS/Y0E+vmwydGLZmsm39r1AIkBcdy1/pZ5OeaJExT946K58/D7qLRy1GhGkYLHn4M/PA7Fr53R+oI5hYK+Pjgh3C+JEpb/WnBVuRjKHKJ8uBylUok+Xs9Vb1/F47rH2WbZhs+5Pug2nFBrc+gQnHcevPcerFgh70uSOHz4MDU1Newc3EmjTyOvXfsaOrsb8beP48i9kvruQexmO4tSYgi+6yt03nQJe2OiCAsLIyEhgdLSUsLDw1mrX4v9HTuqSA9ivxPJ5ML4n+tRvfo4pKV5j7eQVvh8aaHGYJb6LIABTAwHAIer26iuGw8H4WF+DA5Z0ahVbFiTQOmB4wyb7IA81jlz7SJiogLhtfdheYrsM3CChoZtlOxvZNhkZ1lKFEsDVCiuvB0e+MG0Q4Vm7JD41k74+w7Z3e5jjmb+ItcUSJJEdV0nlTXtxEUHsm51Akqlwnvf6Am5qreetJC5q/aXRJHHN19BR3klAJf/8/9Ycf1lwAyhAOR00tu74FtfnbN1Tac5hYLiYjjnHNi5EzZsQPJIWF614Kp1YbjCgCZVg81mY//+/XS0drBqYBUBvQE8EvQId99294SDl05W3vE8HnzzQb4S+hUSjAmkK9Lx1LsQh8a2EQURhST/zQWdiHuxRLmtHHW0miVLllBSUkJISAgb/luOzfdLKAwuhIFBREM4xi8HoYofSwEuwMHnSws1Bp9zTVRzALA8NZq0ZLlga5T5unuGCfDzwePxsGdfAxsyFhEaPDKcSZLYs6+Bo43dcOm5MhTYHXCCoYu/nw9n56SQnBTO4eo2dtf0YF6zEqboTx/ViQ6JW5+9kTZT58QbBgfKRjZT1C/MRPMKBa+8Azd+e+72N8fyeERKy49TWdPOspRINiwNQ/mNH3nrIkZPyLubikn/x/bZjWyeREdefscLBeErUll+7SXADKHA7Zbfc4kJn10oAFi9Gn75S8jIkKHg5REouEqGAgAfHx+y1mWRa8olsC+QqoQqXna8zPOVz0+7+9EpiX4GP7aKW0kuT8ZSYUFIUGK8Sof/Pf4E3BtAwI8COJp7lP2x+7EtcqJqUbGucR3xB+JpLWll48aN9PX1sWfbUnwympA0AYjRCSgiDZieteDaWQNl8ud/oebgi6kFMPgMazI4SE+NYtnSsVZBSYLuXjMGvRaFQqBg71FWpccSFx3o3ab8UMuY18Efn4Arvy6HzkekVCpYkRbN1s1LsTncvL/tYo75hyK53XDCdLiJNAoHZ8VnEqQLmHijzDXwr9+Dr3HWr8e8RwrUKnnOwKcwymZ3uMjbU0dL+wCZGYtYtjQKoaMbKqpOWW9u3Ab+35rrue2dn8wZHLgsVrQjoHjOA/cgKBQzjxTc9zs4/ya5wPMMaU6hwGaD48fl2oK77kJCieUlC66jLgxXG9AsHXNFFG0i5h1m1P1q1FeocUW6uDf2XjK1mYiiOOY1Ul0Na9bIv5Gh4OodV/Mn4594tPNRtO1ahC0CpWmlFCgLsMe4USg9CP/8J0qPh7XZawlcHkiBWEBnz/9hOPhrAvQBLK1aiv0VOxuXbWTI4aDQYEV3vRbBNIyn342ytQJzfgCu346BygIcfPG0kEo4SZ+VVMKJmiytUFXXQWX1mNmQQiEQFKDH5Rax2ZxkZybR2jFI7dGxmQUJccGsTYlAUd8IK1InPJ7L5eFgZQuNzX1EtjWztr4Snz/8dMbrPdxdi7/Wd2Kfg/fy4HgL3H7jjPcHX+z0weCwjaKSo7g9IpvXJxIcND1cneiQ+PgFD8xJQaKtf5DKl95i7W3X81DJ4zODApC7XQ7Xwpev/NhrmInmPFLwwx/Cjh1w9CiSSitDQYML49VG1EvGBlaJJhHTDhOSRcJ4vRFVpApRFKmqqqK6uhpRJ/Kfwf/w9DVPY+jsg9/8Bn74Q/LERn6x4xc8JjxGEEHoMkecELUCFouF/Px8nE4n2dHRBGVlwVtvwbZtSJJEZWUl1dXVpAQGkn722QyXDWP/yI7arcaz3sMeyx70ahU53/oBzm++jceuRxkCnn61N/0xqoW0wmdfCzUGs9RnEQxgcjioOdrJoSNjPgYKhUCAnx4EGB62kZ2ZxMCQjYOVLd5tIsL8yFqXiEopwO8fl6cKhp9qiNPeOUhZcR2ioGDN2sXERQdNu05Jksh86ip6rP0TmyDd9zt5mt4rj824yO+MQoHFKl+BG6fPB58JtbYPUFp+HINBy+YNieMnao7OGZhEo3Cwv7OSwhv/Mzbw52NqxpGC9i6ICJU7Ps6Q5hwKQHYQPHAAKWcr5hfMuJvcGL9kRJ04BgWefg/mHWYkUcL3Bl+UIePraHp7e8krymPIOsQu9y4eveZRDBoDeY15vLzjZe6T7kMdp8Z4qRFlwPjHOhwOCgoKGB4eZlNKCuFp49//tbW1VFRUsHjRItZIEuakFFpeaCGyJxIxTGR/4H7Qu8jJORv3627cTW6U4eDpEDFU/wXNj6+C9HRgAQ4+61oAg1nqswoGMDkc1B3r4mDlWP+zUing5+uDSqmgf9DCpvWJuFweivc3eqPOgQF6chKD0OZcAf/7QxjJGZ8sh8PN/kPNtLYPEBOkJ2P9ErTaqU8wUzokut1y8eGnEQpEEYKWy0WXd3xl/o4zA0mSRGVNO9V1ncREBbJ+dTwq1QknjO4+iM+EFx6Bi7dNuR+ry4ZBo8fqsqFXT96GOhPNGApcLlh9AVx0Njz4o491zJlqzqFg9275hBkSguSSZChodmO81oh60RgUuLvcmHeYEXQCvjf4ovCfGIScTifv7HoH26CNUsceLo1aT+MeB5cKV6Bcr8R3my+CYuLX0+12s2fPHrq7u1m/bh1xTU2Qk+O9v6Ghgf379hG7dy/rf/ADbP7+lL9ZTuLxRHSSjtqoWgZDB8kZNCEdDMVlXIGydT+e6Az0GcNoL1zk3dcCHHx2tQAGs9RnGQzgdOBAga9Bi06nprvHRObaRajVSgpLjuHxyGOWDXotW1ZGYwgbqUWYokWx+e8vUe4bhhDgR8aqeLnLYQpNa59cdkjO6a+c/ET/iaQPXv8AliVDYvz8H2sSuVweSsobae8cYnlqFClLIk49AZst8MaHcM7mGQ2p6rb0sf7fV3Dvpm/OOK3QVnaI4j/9k/N/91MMYcEzh4JRvZ8HSxbDotgZHe/jaM6hwOmElBS45BKkh/6A+Xkz7rYRKEg4AQpa3ZifM6MIUGC83ojCMHV0RBRF3i16F0+Th3V1iQjqQAyX+mJcMX16SBRF9u3bR1NTE6uefJLkBx6Q6xRG1NLYSPG+fURGRbFx40acTieFHxUS1xBH2GAYncGdNAZWkpO/C2H7b3AedKOMUeJp9eCzTYMushfi5ff9Ahx8NrUABrPUZx0MYHI4qG/o5sDhsZSBSqVA76PBaNDS0TXE+tUJ+Pn5kLenHqdTHpik1ajIzVpCwH/fht174YmHJg79tndhyytl/+JU2juHiI0OZM3yuCmjB81D7Vzy8u08et4vyBwd+AMygGRdBsuWjpkvnaQvak3B0LCNPfsasNudbMiYO3vj0605cDscPJZ5KT3VR9GHBOJ56HJ+1PTPmdcUrE6fk3XPRPOSPgBoakLyD8H8uoi73Y3xeiPquBOgoMWN6VkTqggVxmuNCNqZRcH2F+0n/KMwBLVAQ/JRMs5ff8qchMkkSRKHKiqorasjNTWV9PT0cX+L9vZ29uzZQ6gosmn7dtwqFfl5+fi1+ZHcmYxFa6FmUQ2Z2zJRfWTDfkiN0t6ERxePT8nv0L38U7nIkgU4+CxqAQxmqc8DGMDkcHC0sZvyQ+PhwEerJiBAT0vbABkr44gI82N3UR0Wq9xtoFQqyHb1E5ZXAL/76ZQ+A5Ik0VxSxYF+F4JCYM2KOGKniB6IkohCUODyuOi1DRBpDJPvaOuU888THOsThYJD1VBaAV+79swdc0RNLX2UVTRj0GvIWpeIn+8kw6dEEX72e7j5KrkFcIY6HTjYed/vKPzt3wAQksO5/5oufpI9HgokScLhdGO1OrHaRn6aO1H+6wV8r9mOb+YqfI1aNKc5j+N0NOdQYLHIRYE/+hGSQof5OTPuLje+1/uiih17Hq5mF+ZnzaiiRqBAMz0USJJEzZs1hB0M44DPAZZds4ySAyWY7Ca25mwlJiJmxsscrStYFBxMxtatKE6A+e5Dhyg8eJAAjYbsK69EFEUKCgqQuiXWdK3BY/dQE1fN6l99A/Wtf8VmW41S2YfHE4xuiw6f7LF00wIcfLa0AAaz1OcFDGByODh2vIf9Fc3e7dQqJRqNktAQX44397FyWQwJscHk761nYMgKyBmEzIzFxEYHQk/f5OHpskOQfSW2N5+i3BhGW+cg0ZEBrFkRh49OPfFjgO9++Cter995qglSY4tc+DhiwfyJRwr+9hQ88BdoLjljRXMej8jByhaOHe8lPiaIjJVx4+sJTlZDM5x9LTz7MGxcM/l2E2gUDv556CWO3r6TaN9T5xW0l1fyj+wrkTweUCn429dEvn7Fndyz5hs0NvXSN2DBYnVis7uYyfeLWqXE16jFz9cHX6MOX6N25LdOngQ6S81LpKCwEK64AumDPEzl0Xh6PDIUxJwABU0uzM+ZUUWPQIF6BlDgkGh6tgn/Vn9e9H+RGy8/F/2Lr1CSncwHVQdJ1CWyavUqUpMn7hSaSE2vvkqpzUZkUBAbt21DeQJk9x46RMGxYxiNRnJyclAoFBQUFGDuNZNlykLRruBYWA3JF8ah6wrF+rYVZbgST5cHnfYQuqviEBbLdQcLcPDZ0QIYzFKfJzCAyeGg4XgPZSfAgUatRKVSEBkewLHjPSxbGklyYhh7yxrHDVJaHWlkyUXXyCOYL5mgqE2S4M0P4cKzkQSB1vZByg83I4oSq5bFkBAXPGGYeUKHxCETJG2GH38L7vraJw8FIPfaKxRnzBbZbHGwd18DQyYbq5fHsjg+ZPrcPXysdUqSxJHeetJDk0/drdPJYxsvo/tIHQC7zhK48Hs/Zb0+k64e0ynbfxwplQrCQ32JCPMnIswPo2EGQ7lGNG/pA0DsM2N+TUTsEzHeYEQVdQIUNLowP29GFavCeM3MoEAcFun6VxfOISd/C/sbP7vlZ/gcqZWLB/PzKQgw8dwHz7HFfwvxi+JZl7FuXARgUrlcdLz6KnuUSoKDg9m0aRNq9RicDwwMkP/BB+iUSnK2b0elUlFUVER/bz+b2ISmWkN7UDtR5/lg+KARS+9qFJ3ViBFpaLVH8Lln07jo0AIcfPq1AAaz1OcNDGByOGhs6mXfwSbvdqNwEBMVSN2xbpITw1meGsX+imaOt/R5t0sx9bD80s0I05kR7T8MCTE4fH05eLiFptZ+wkJ8yVgZh6/x1DD4hHDwQQFkZTCgdH3yUHCG1dzaz/6KJjQaFRvXLSYoYAYtknYHOJwzcqWcTqIkcsf7PycjYpk3rbDr/j+S/+uHUfr6orhkK/GXXolaOvVvqVQI+PhoMBi0GHw06MsPoX/tbfR/+hlunQ8mix2z2c6QyY7JZMcxUtMylXx81ESOQEJYqB8a9cRRk3mBgn/+E+rrEe/9FebnLIgDIsYbZS+CUbkaXJj/Y0YVr8J49cygwDPgoedfPfSae3ko6iEe/fKj+EzQGVLYXMiDbzzIjSE3Eh4WTlZWFlrtzECpp6eHgvx8/Pz9yc7OHnucJDF83XXkbd+OMiSE3NxctFqtt7shKyALbbGWQV0/Qa/chuHhV7G8LaIIUCAOgHa9Fp+z1AgjsLEAB59+LYDBLPV5BAOYHA6ON/dSeuAEONAoUQgKFsUHU13XSWJCCKuXx3KkpoPq+jE74/jYINaF+aDo7Ia1K049oMMBaWfB1Rd529E6u4fZX9GEze4iLTmSpUnhXh//UY3Cwc3Lr+C+zd8C5PTBxU99mWpr2ycPBZIEF94MX7kKrrl4Xg7hcnk4cLiF4y19xEYHkrEyDo16hnn4Ha/Ct+6D+nzZZvpj6OSagwvFZTye+yWCLrqI0CuvRFCNX5OPTk3S4jASYoPRaVXjIxuiCLXHIHXi+QwutwezxYHJbMdkdjA0bKWr24TLPbkbYlCAnshwf8JC/fA1atFqVFittvmJFPzpT4h1zZhX/QxxaAQKIk6AgmMuzC+YUSWMQIFqBlDQ7aHvqT5abC08FPMQT9745IRQMKrC5kKaO5rRd+jRarXk5ORgMMwAFl97jf5776Xg/vvRGQzk5OTg4zNyHLMZsyiSV1CAJEnk5uai1+spLi6mo6ODDTEb0H2kw6Fy4HO1D36iL+YXLSiUdkS7Dk39q+h/eyFCRDiwAAefdn0hwUAQhB8BVwApgA3YA/xQkqTa09jH5xIMYAo4aOmjtPy4dzvtSDFY0uIwqmraiYsJYt3qBBqaesYVLoZ3trPp6SdR5b80cb69qk5u6zvhysbtFqmqbaf2WBdGg5Y1K+IIDx3/Ovda+wn2CUQQBLotvXznDzfy198fo/fZ35J8/uVz+IrMUt/9OWzfCufmzvmu+wYslOyXJ2CuWRFHfGzQzFIHo2rvkrtHRgYYfVyNwsHfS3fw691rCL/kWnTx41s1w0P9WLI4lIhwfxQnr3X3XtnmOmP5rI49MCQDQkf3EH395indqJ1OB7958EEqj1SNuz0oKIhXX32VFStWoFQqUSgU3h+lUolKNQV0Wa2g1yNaRczPmBBNEr43+qIMH4tWuI7KUKBerMZwlWFGUODucDPw9AB1jjr+EPsHnr7h6fFQUFsLt94qj15eunTcY4eHh3n7w7fxUfmQk51DYOA0AGg2wxNPMHzTTeQVFaFUKsnNzR0HFdbiYvKqqnAFB5O7ZQu+vr6UlJTQ2trKuqR16D7UIbgElO2PEbA+E1PDMgTnMJIuDM1KNfqLjV6PhQU4+PTqiwoG7wLPA/sAFfAAsBxIkyTJMsN9fG7BACaHg6aWPkpOhAOtCkmUWJoUQWVNG1ERAWRmLKKja4i9ZY3eorIAHzU5uanotJMXFnLsOBSWyVfZIxoatrH/UDO9fWZiowNZuSwGvY9m3MNerHmbL79xDwZBQ2XvhUT84O4pnfw+y/KIItV1nVTXdRDorydz7eLTyqnPpzweD3969FGiI9chnFDAlrQolOTE8KnXeemtoFHDi49+7HW43R56+sx0dg/T0TWE2eLw3me323nwwQepHpktMCpfX1/uvfdeEhISJt2vj48PAQEBBAYGEhAQgL+/P0ajEaGjAzZsQPzDo5j7shEtogwFYWOvgbPOieUlC+rEEShQTg8FriYXQ88NcdB1kIdjH+a5G547NVJw/Dj8/Ofyz0lrbxpsYuPfN/Lj+B8TpYli06ZNhIeHT3tcAEtPD3n79uHxeMjNzR37jtu5E/uDD5J3113YXS5ycnLw9/dn3759NDc3k5GWgeYDDTqzFhJqCchdi/k/NlALSCYJTawN/blKhMiFyMGnWV9IMDhZgiCEAt1AriRJ+TN8zOcaDGByOGhu7aN4/3HvdjqtCo9HIi05ksM1bYSF+JK1LpGBQQsFxbI3P4BBpyZ317sYf/D1iU/cD/wFXngTSl4H3fiRrk0t/VRUteJxi6QmR5CcKKcXBuxDbNlxA5W9dUQYQtlz0wtyzYHbDVNd4Z0JOZ1yt8TSxDnZ3cCgdWQUto3U5EjSkiNnV43/9CswNAx33jwn6xpdW0l5o3dMN4CPSmBT1lKCAs9szcPJstqcdHUP09rey7e+8z9UHKocd/9MoGAyKRQK/P38iKptIVq6FDwqGQpCT4CC2hEoWKLGcOUMoeCoi+EXhtnj2cPf4/7Oi9e/OGX6YDIVNhdy6Y5L+VHCj4hXxbN+/XriT4rknKJdu+Dqq7EVFJDf3Izdbicn54SIgyThcDrJz8/HbDaTm5tLQEAA+/fvp7GxkdXLV6Pepcavzw9PtocgfyumnUbo60XSBaM2lWP4zTbv67AAB58+LYxdljXq/tI/2QaCIGgFQfAb/QHm/hvsU6bJpjLGxQSTuXbM+tTucKNUKjhS187ytGh6+8wUFNcT4K/nrJwUr3mRxe7iwxUbGKg8NvEBf3QH5L80DgpAntqWEBfMBWenszghhMqadt7bVUXN8TbOff5mWk2dvHnV42iVGnlkc9keSN8mewl8knrqFVizXT7pfQx5PCKHq9v4ML8aATgnN5X0lKjZt+jVN0LljLNm06qppY8P82u8UCAhkbwoGL9lbv7b/PbkD5QkGQYbmuW/+TxAAYDeR0NYiJ57f3r/KVAQFBTESy+9xGWXXcbSpUtJSkpi0aJFxMfHExsbS3R0NBEREQQGBo5r4xuVKIpYe234W8/DZnFRk1pDt7sbUZRh2FkzAgVLZw4Fzionw/8Z5kPPh/wt7m9TQ4HLBT098u8JtDluM6/d8Bq/bPwlVa4qSkpKqK6unro9dP16uPNOfOLi2LJlCwaDgd27d9PT0yPfLwhoh4bIve8+/ESR3bt309fXx9q1a0lMTOTA4QM4z3LSF9WHqkBF/+/fwHjWEGg1CFoRV8BaLK9YkDzSyO4WpjJ+VvW5jRgIcmL2NSBQkqTsKbb7OfCzk2//PEcMRjVZ5KClrZ+9ZY3e7Xx0apwuDyvSoqmsbsfXqCV74xLcbpG8PXXekK5SqWDz+sWEBxsnNkHqG4C7fgEP/g9EnRr6HBq2UXb4OH29Vo7a69m6Np2NienegsQlxijeK0uC798OcRNMZjxT6uiWIwbrV846etHVPUz5oWYsViepSyNIXTLLKMHJmsK2eqYSJYnDVW3jpm7aFRYuys4gKMDA3R/9mt+VPjG5CVJvP+RcBT//Hnzpoo+1lqk0V90HkiRhsVgYHByUf/buxeLSsmz4LJSSkrLYMmwaGyCnHZbplhFYGog6RY3hcsOk8wtOlOOgA8ubFv7Lf3kh7gVeve7VqSMF5eWQkQH794+zNT5Zhc2F/KH4D9y79F7qa+tJSkpi1apV07czuly4gKKiIvr6+sjKyiIyMlKOyN15J6477qCwt5f+/n42b95MWFgYBw8epL6+nhXLVyCVeYg4HoU72U3QuUGYd5gRbSI4RNTmIxi+n44QGuR9fRciB58OfeFTCYIg/BW4ENgsSVLrFNtpgRMvZX2B1i8CGMDkcNDWMcie0mOMvjtkOHCzMi2Gytp2fHQacrOWIAgCBcVH6R+QSzgESWT9gRLif37HqSeo9i644jb46wMTFqON+hRoHUbuXnwXTqtETFQA6SlRDIoDSEhj5kdzcAL8JGS1OTlY2Upr+wChwUbWrIjD3+/jDS4C5Ir/xPiPnWZxuTzsLWsY513Rr+ngtnMv8F5Zz8gh0WYHn0mcGedA8+pT0D6MaYcVUa2lO6ub2s5a7HY5ahI+HE56Rzpdfl0MrxsmKTmJ4OCJvTlGZS+xY3vfxlPCU7wV9xavXffa9OmDwUHIz5e9DAICZrTuoooi2mrbiI6OZsOGDZMXVZaVweWXw86deBIT2bt3L52dnWzYsIHY2LG5FW6bjaI9e+gdHCQrK4uIiAgOHz5MTU0Ny5YtQ6wWiaqOQvTtJ2idA/MHGkSXBtQ+qKJEjLdEeAsxF+Dg06EvNBgIgvAX4DIgR5Kkxmk2P/mxn/sag5M1GRy0dw5SVDIeDhxON6vSY6mq7UCtVpCblYxGo2LvvgY6uoa8+1y5LIalSRMURI2e0CVJ/hm5sjnZvGhFWCpNLX0cqenAZnMSHxtM2tJInAob9/7rLv7wr260T/15zvL8p61nXpWHPM2wZdHtFqlv6KK6rhOVSsHKZTHExZxmx8FkcrlgURZ87Xr4+V2z3o3Z4qCguB6TWY4ASaJI17//TXSAhov+fD9av7GUwIlw8O8LH+LLyy+HmqOyFfOjv4bAuZnhMJHmDQqefRZPxlbM78tzCYw3ySOORVGko6ODnqIe4mrj6PDr4EjEERj50/n5+ZGRkUFoaOi43UmShL3Ajj3PziPCI+yO283r170+q5qC6eT0OFn68FK2BG3hQv2FBAYEsnnz5om9DiwW+MlP5J/QUERRpLS0lJaWFjIyMli8eLG83XXX4RkYYO9PfkJnVxcbN24kKiqKI0eOUFVVRVpaGu4GNzGHosHTTcAtsVhfseGxa8ADqjglxgtBCPTzvh4LcPDJaqZg8AlXcc2tRtIHfwEuB7acLhR8UTVacwDw1a//EICv3HQFUREBbNqQSFHpMSQJbHYXPj5qDhxuYfXyWGrqO9lVWEtuVjKb1idSfqiZhqZeACqOtGJr72Zl9vghLl4ouOVuiImEX949qaPhorgQ4qKDaGjqpbqug6bWPoLDfDgsmXlf0cya4U6i+YTA4KMiMOqnBQNRlGhs7uVITQdOp5vERaEsS4ma1JxnVlKp4PUnP5ZvwcCgld176nC5ZN8Ap9NGx29/h/XwYVSpSSi14ztGBEHg4W0/J1DnT0bEMvnG/iHoHwTl/JUuzRsUWCx4HvgL5ms3QaAe35vGxiMrFApC+kLQ1+kR0gTciW7UjWpcI/n/4eFhdu3aRWJiIitWrECtViNJErYPbTiKHTwoPEh5XPnpQUFPD7zyClxxBZwEHBNJo9Tw9OVPc8GOC7BF27hWeS0fffTRxF4HBgP88Y/yv0URhULBhg0bUKvVlJWV4XK5WLp0KdxxB0q3m41ZWZSUlLBnzx42bNhAeno6CoWCyspKUlJSaFE0EnUonsH/Ogm4NhjrG1Y87Tbcx8B8fzXGB7MRdEpvzQHAnXfeCbAAB59Sfa4iBoIgPAJcD1wKnFiFNSRJkm2G+/jCRQxGNVnkoKNriMKSo94ech+dGrvDxer0OOoauvB4RHKzkvE1ajlS20FVbYd3n7EqD+svWIvy5Jznw/+CyDAGLtw0I0dDt1uksbmXmvpObHYXlbbDFFkKeOLK+0kImPlwmTMlUZRoaevnSG0HZouD+JgglqVEfWpaEE9Ud6+JguKj3nHb3dYOhu/9La62dgSFglvzXiR63RQnXLcbi8fBR83FXJx01ryleOYzfeDp92D69xCCWonvl31R+I29Xx0VDqyvW9Gs0qC/SI8gCLjdblpbW6mtrWVoaCxSptPpWLtmLf4H/XEecHKvcC918XW8fu1pRgrKy+ViwdLSKWsMTlZhcyEX7LiAc6LP4dagWxFFkezs7Im9DqqrZfB49VVISUGSpHGpgrS0NBnqJQmxtJR9QHNzM+vWrSMhIcE7qCk5ORmxTySiNAKtzYb/BRLWFzrxBCWDoEAVq8V43dggqYXIwSenL2QqQRCEyZ7MVyVJ+tcM9/GFBQOYORzofTRYbU5Wr4ilobEHu8Mtj2f2158ypCksxJdN6xNRn3SVPBopGGxr4sWvPTMjR0OPR+R4Sx9V9e3YrG5U7cdJz0hh8ZqUqQcLzZdOqnVwuT00NvVSd6wLq81FZLg/y1OjCPCf2djc01b/IHz1+/CbH0FK0mk/vK1jkD37GrzV7PXWOjx/+AfSIdkNc9PdX+ecX/1g6p188ydU9tWzfHX5jEY2z0bzBgW1tXh+83dMy3+KoFHIUOB7AhQcdGB9w4pmjQb9dv0pqR9RFDl69CiHDh1CFEUESSC9I51wUzg/Uv6IhtiG04eCj6nC5kKueekaXrvqNQZqBzCZTGRlZRHmF4bYLyIOiHgGPYi9TsR9dYghi0GvQhmqRBmipMPRQXVXNTHpMaxYtQLhlVfgS19COnKE/WYzDQ0NZGRkkJiYSH19PQcOHCApKQm6rYRWxKPHB78v+WIvdOJucYMASlU/vreGIwTJNuoLcPDJ6AsJBnOhLzoYwORw0Nk9TEFx/alwsDyG4839mK0OcjKXEBxkoK1jkL37GhBHNvYXRHLOXeWdsDgKBZkfHuUPO1WoDn4gT1GcoSRJorK6hs73DzKwKBmVSkFcdBCL4kIICjz1C3zO1dsPmZfCw7+E87cwMGilsbmXptZ+3G4PcTFBLE2KIGAuCgunUs1R+PbP4Jk/Q9gkEy8nUUNTL2UnzMo4YD6AtqgQ4Z+FAIQsTeT2ktdR6aaJcjz/OpLHw52hB2c0svl0Na+RgjeLMO0NR4gMxvdmfxTGE6Cg3IH1LSvaDC0+F/hM+Z6yWCyUFZcRWRFJsCWYw1GHaTG2kLkuk6RFSfP/fjxJdrcdnUqHzWHj0HuHCDoaRIhl7PMl6AUUAQoUgQqU/kokh4inV8TT40Gyyp9Zl8KFLdZG1NmRqOuKYOtWJEniwIEDHD16lFWrVpGcnMzRo0cpLy9n8eLFCA6BoD1B+Lv9MJ4r4djdj3vYH0QXSqMD3+8sRtAtRA4+KS2AwSy1AAayThcOVqXH0No+yOCQlc2ZSYSF+NLbbyZ/bz1utxyiVigENm9IROuHN32w+4K/sjy/Ab527axD0GaLg5dL8/B3hOJ0iOh9NMREBRATGUhQoGFu2gBPliRh+vWjtOdm0+RUMDhsQ6dVkRAbTNLisFNcHD9tqjvWxcHKsWad/MF8glw9qL/7CqLbjaBQ8NWPnic2c4owdlfvOJibUbfCaWreoMDpxDOkwPSMGcFHwPdG3/FQsN+B9W0r2nVafM6bGgpAHpts/o8ZR4uD0ohSzL5m733h4eGsXbt2ZnMNRlVfD3feCQ8/DEsmni8x5XokCfdxN+WvlpNsScZhcHDU9yjh6eEkrk5EoTshtdfRARddJB9r40ZEi4in10NPWQ+KWgVajxZFhALtai3aY+9A5hoODQ5SW1vL8uXLSU1NpaGhgbKyMhISElCKSvyK/Ai2BGA4V8C1sxWXFAcqAWWoEuP1RhQ+Cu86F+DgzOkLWXy4oLnTZAWJEWF+5GxcQv5eGQ6sNid6Hw0HK1tZsSwapVKgYG89WesTiQz355ycFHYV1uJwehBFify9R3nL/Jq3pmB5eBos3SAftOwQrEwF9RT2yhNpsAvfn97NQxcG8Oh1/8I5pKK5tZ+6Y92oVUrCQnwJC/UlKNCAv58PqlkUx0mShM3uon/AQm+/mY7OIUzL1qPodxIZ7k96ahQRYf7zAyGTqb0LBoZg2anjkadSdV0nh6vbvP9/q+8t4qN9CLunjD63POVw8z3fmBoKmtth7Xa59fTqC4GxgkSADnPP6T2XCTRvUCCKeK77JqYVP0MI95MLDQ1j7wn7Pju2d23y9MBzp4cC0Spifs6Ms8fJlVyJv8afe6LuoaNdrrXp6uri3XffZcWKFSQlzTB6oFSCn9/EfiBTSJIkXPUu7IV2PG0eYoNiuc12GwNBA/zf6v/jQO0BzDozq1atGltHaCisXCkXJQIKgwKFQUFUfBRNjU1U76om0ZGI77u+2O2r0VUfZPlPLkapVHL48GFEUSQtLQ2FQsG+ffuIi4tjeNlx3DUxhH8Yjv7CFDjmxlXtxNNhx3z/MYw/TEER6LNQkPgp1ULE4CQtRAzGa7LIQVfPsBcOYCxysDw1mr4BM51dw2SuXURMVCD9gxY+yq/1phXcoou4VAObU07wMujug5Qt8Kt74JtfPr1FDgzh3HYtN20ZZF+ijl3XP0OsXxT9Axa6e0x09QzT129BlCQEAfyMOowGHXq9Br1eg0Ylj5tWKpVIkoTHI+L2iNjtLixWBxark2GTHbtDrkL30amJCPcnSgvhzcdRnTf3w5RmpF/9Gf7yJDQXjxtUNZkkSeJITTtVdWNTMl/seZHUJRFsfsfG3j8+AUBUxnJu2f0CyqkATZLgH8/DdZeA0XDSXZL3pFPff5wlQQmn/dTmNX3Q48H0WDcKnYjxG5HjoaDUju09G9pMLT7nzAAKTCKmHSacw04udF2If5y/t6agra2NsrIyHI4xh8zg4GDWrVs3598tkijhqnZhL7Lj6fKgjFXis9kHVaKKopYizn/mfNZHr+cvG/7CkUNHSEhIYO3atacaIU3gD9La2kpxcTExgTGkDyTiqlGh8FOg26KjQdXA4crDpKSksHz5cpqbmyktLSUmJgadVoeqUEXMUAy6bAHxmfdwxp0DogNlpB7jjX7e134hcnBmtJBKmKUWwOBUTQYH3b0m8vbUewvXDHoNFquTZSmRDJvstLYPsH51AvGxwbT197Bzdw065VgR3tpV8SyOP6GuYM/+2bsJShLNwx1sefYGAPJu2EGs35g7oscjMjRsY2DIyuCQzXvCt9oceDwTfwY0GiUGvRaDXoPRoCM40EBQgB6f0TTBE8/LI477Ds2rmc+kcjqh5hisSJ12U2nEzbDmBDfDHd07WLk0jvuzv4O5s4fXvv5Dmgr3cXvJ64QkL554Rw4HHKmHNenTHnNPaznZO67l7+f/8rTSCvMKBaVHMRWGoDAoMN5oHA8FxXZsH9jQbtTic/b0UOAZ9GB+xozdYedc+7mExYWdUmjodDqpqKigsXGsc1oQBJYtW0ZKSsrkDoUeD9jtoNNNGTWQJAnnYSf2Qjtin4hqsQrdZh2quPFjrwubCzn/mfP5zTm/4aLwiygtLSUqKorMzMwxS2iTCS69FL73PTm1cII6OjrYs2cPISEhbEzZiPPVdlw9/ijDFfSm9VHWXkZycjIrV670gkRUVBQGqw2xLohF/YvQrnQhebQ4K0XQgsLHI6dwArXe57IAB/OrBTCYpRbAYGJNBgc9I3AgngQHqckR2Owujjf3kZoWyi1F36F5sIMnM/6GuV/07jctOYJlKVHjv4Sr6qC14/THGpvMDN/3a/4nY5DfXP0bfLXGGT43CbdHxOP2ICgEVEoFSqVi+pDvkEmel3AaRZOfhCRJ4mBlK/UN3d7b/t35bzJSF3N/9ne8z1OSJHqq6gmbKjXx+8fh1w9Dbd60ky5nU3Mwv4WGezEVBqMI98N4exgK/QlQsNeO7UMbuk06dFt100NBrwfTDhN2yU6uJZe4uLgpuw+6u7spLS3FarV6b/Pz8yMrK2vi75kZWCJLTgnLGxZcVS7US9TosnWooieH6vq+epKC5FRGe3s7e/fuJTg4mE2bNqFWq+VowTe+AdddB1u2TPgcCgsLCQgIILuxEeG1UqyX/gZPu4QtycZeYS8JSxJYs2aNd/8RERH4arU4yiSW9C5Bk6EGkwVnnQYcJhQqO753J3nrOxbgYH61AAaz1AIYTK5J4aDPRF5RvTdU7+OjwWp1sjQpHKvTTkvzEC/2vcBPLvwKK8NSqahspe6Ek1R8bBDrViWM5ee/9gM42gi7Xji9gsSePth8JTz8C9iWQ21fAzqVdsxG+fOk2/8HEmLlAVVTSIaCFuobxnL+/+j4B5lpS8dBwYzldEJ5JUxVf3DS8WcKB/MKBd0eTE+bUHiGMd4RjcIwdhVuL7Jj+8iGbrMO3ZbpocDd4cb8rBmb2kaWKYukuKQZtSS63W6OHDlCbe2YxYpSqfQ6Co5Tfz+89x6cdx4EBZ36fPo9mF8wIw6KGC4xoEmbebHr67Wv88i+R3jsrMfYX7IfX19fsrOzx7skjp4XTnotent7KSgokB+zaRManQ5HqR3bLjsetYeKoAr80v1Yu3atN8oQFhZGYGAgw3uHSe1MRZPgQFHwAY64i0EjofBVynUevgtwMN9aAINZagEMptZkcNDbZ2Z3Ud0pcLDPXkyffYDzAy5gWUoUackRCIJA7UflVJhERn1lx3kdWG3yMBe/WUzlc7lgxHkuZ8d1tJm62HX9M/MHBw8+An7G06+L+Lj6v79DRBjcePmkm0iSxIHDLRxtlKFAQuKxjsfYlJbG/dnf4fjuYiJWpuIzzZU/AB8UQHw0TJZimEKjcFDUWk7pV15Gozz1JDavUJB/BNOeMBRBWjl9cEKkwFZgw77bji5Hh0/u9K2l7hY35ufMWIwW1g+sJy0u7bR9Cvr7+ykpKcFkMnlvS09PJzU1dUag5qxzYv2vFcEgYLzaiDLs9AoUR02Q1kWt45kLnmHf3n1otVpycnLQ6/XyZ+/GG2HbNrj11lMePzAwQH5+PjqdjtykJHRXXonnz//C2pyIu9FNu1871gwrGVkZdHd3U1RURGhoKIFdXQwMhZPemY56iRplsBLHXgeCWkRwDuF7ZwyKIPm9sQAH86OFscsLmhdNNrI5JNjIls3JKBSCbJ9sczLoGWCdLpNrll5EemoUR2raOVTVhiRJLD1rDRvXJXq/CLt7TewsqMFmc4LeR4aCzh45ejBsmmpJ46VWg9OJ8NCjPJd1HwBbn72RpqG2aR44Sw0NyymFM627bz9tKHi0/VEvFAw0NPPcVbfzt3UX0rCzaOpjSRL84o/w0N9ntdTRboX8G55Fo9Rgd48fVz2fUODucmPa6YuirwnjjYbxUJA3AgW5M4MCV4ML0w4TpgATawbWzAoKQB4JvW3bNqKjx2C1srKSvXv34h7pCqG/H555Rv49IkmSsOXZsPzHgipehd+tfqcNBSCPbH7nhnfY176PG9+5kczsTNxuNx999JEMKyoVREeD/8TzLgIDA9myZQsOh4NdNTVY169HGeOH8QYj+ov1RNoiiS6MpuL9CsLCwti8eTM9PT30hYYSvDGYg1EHcR114u5wo+1+B8mlQHQqMf17GHFITjMujGz+ZLUQMThJCxGDmWmyyEFfv5ldRXV4PCIePOi0KtxOWBQfQoCfjgOHW1mcEMKaFXEoBIGePRUUNA3j1stFiTqtmtysJfLEwep6uP5b8NzDp+fq19kDGy6GP/yM5rNXegsS5zVycKYkSfDP/8Dl50+a458ICv7W/jdyli3n/uzvIHk8PHn2tbSWHARg9Ve/xCV/+9+pjztkApUSDB/PwbHfNkjmU1fxg8zb+NrKa+YXCjrdmJ8xo/AD4wUuFLHyzAFJkrDn2bEX2NFt1eGzefoTu7PGieUVC8MRw6zpWMOauDUf29FQkiSqq6uprKz03ubn50d2djaG2tpxNQaiTcT6mhVXvQvdFh26zdOnPKbTaOTgytQreeTcR8jLy8PpdJKTkzOxhfJJMplM5OXlIQgCubm5GFUqcLnwePQMPD+A0CPQs7iHpC8lMTA4QEFBAYGBgYRptbTXWVjTugp1oAeV7zCOplAErYCgA+MNBpTBau9rtBA5mDstpBJmqQUwmLkmgoMB+xBffvHHfMlwA1qlFkEQ8NGpsNpcxMcEERriy/6DTcTGBLF+tVxXMFx1jLxWCzab3A6oUirYtCGR8FA/EEV5AqMoyvnOmX4Zmi3eNrrmoXa2v3grfz335+TGbZj7F8JmB4Uwo5bBj63aY7D2InjzScjNPOXuiaDgkfZHyF22wltTkPe/D7P7F38EIHBxHN8ofQPNSS2HgFxY+aMH4Ud3nrar4mQ6sebg4S0/44V7354fKGi2Yf5nH4pQLcZbgscZ6th327EX2vE52wdd1vTdJI5D8qyEwbhBVresZl3cujm1OW5ra6O4uBiPRx5gpVar2ZyVRWhAAKjVeHokzC+akWwShssNqJNO0+djCu1t2UuUbxTxAfHY7XYKCgowm81s3ryZ0JAQ+P73ZZ+DH/1owsdbLBby8vLweDzkPvccfnY7vPIKkkei560eVBUqLAEWIm6KYMg9RH5+PgEBAUQOD9M0pGNtx1o0QRrUS1XY8x3gsSJIDny/G48ycGzM9wIczI0WwGCWWgCD09OJcPDwoz/jSellGgZbeOvif9FW5cIjiigEAZ1Ohc3uIiYqkOiIAErLjxMR7sfGtYtRKhXY7S7y3y5jcCT/LAiwblUCCXHBcuvWtXfAprXw3a+dzuLgyRfg4m14QgJQKpR4RA+9tgHCDXPUSdDeBUnZ8NKjsP2sudnndOrtlycpngRJM4GCtn0VPLHlS0geD4JSyS0fPU/MhtUTH6euAS65FZ75E6xdMWfLlySJ29+4l8fv+Q80jb9vTqCgw4356WEUHTUYLxVQbNnoPa7tIxuOPQ58zvFBt3F6KLCX2bG9Y6MvqY/VDavJjMucl9kHQ0NDFBQUeLsWBEFg9erVxNnjsLxpQRmkxHC1wXuynGv12/q5b9d9/Cr3VxwoPUB/fz9ZWVlEPv44BAfDFCdjm81GXl4eDpOJ3PBwAnJyvPd17e9Cel9CKSjxvdIXS5CF/Px8/Pz8iIqKoqGsgfXNa9AY1Wje/TP2rLsQFC4waPD9si/KoAU4mEst1Bgs6IzoxJqDO575OdVdx9h53VNkJqazdXMySqUCUZKw293otGpa2wdpaRtg47pFdHUPU1hyFLfbg06n5qz9BUT2yOY7kgSlB45zuLoNSaGA1emw9DRHLA8Mwc9/D2/tRKmQv2B+kv87Nj519dzVHESGwSMPzMhL4GPL6ZRhJyRoVlDgtFh55avfRxq5Ms3+4f+bHApALjQ8/P6cQgGA1Wqj9s8N8wcFz5hQBKsw/mr9eCjYOQIF584MCmyFNmzv2OhJ7WFlw8p5gwIAf39/tm3bRlhYmHyDCOZ3zVhetaBOVuP7Vd95gwKAo/1H+dfBf3HFS1eQkZlBeHg4hYWFNN9885RQAODj48OWLVvw8fdnd38//b29UCTXrYRnhKO4XsGQZgjr81Z0lTpyc3IZHh6mtbWVJFMTxfFlOJwijvO+iy5XhySqkZwSpsd78fTKNRejNQd33HUHdz59Jw8//PC8vRYLWgCDBc2BvHCw9FYsf7RS8X4NAEGBBs7avBTVCBw4nG50WhUd3UM0NPWyaUMSfQMW8vbW43S5Uf3qHjbdcgFJi8bmz1fXdVKyvxHPD78JF2yVb+zum9nCggPh4Hvw1S95b/rm6huBOSxIFAS4+WqIifz4+5pOjz8HK86VAeEESZJE+aHmKaEA4P3/eZD+o8cBiF63kpzJWh1fex9u/LZsZnS69tTTaF5rCjrcmJ/oRdFdh/EqDQqD3NMvSRK2D2w49jrwOd8H3YapoUCSJKw7rdh32elc2cnq2tVkxWXN+5TE0c6AlPgU1rSsIXYglpqwGkr8SnB4HNPv4GNoffR63r3xXUrbSrnshctYuXYlcXFxFBcXc/ToUfj97+Huuyd9vE6nY8uWLfj6+rJ75056vv51OHYMgLD4MPxv8KcptAlnvhPV+yq2bNyCxWKhKSmJ5JUJ7I3ai0N04djvQOdXDXYRacg2AgcyyFpcFirSK9Ccr+FbP/vWQkHiPGoBDBY0J1IoFPz9749x25VfG9etEBigZ+soHIgyHGg1Krp6TNQe7WTzhiRMJju7i+qwO90oFApWS2ZWvfKSd9/NbQPsLqrD4XTD356SPfr7B2e2sOCRIqrXP4CuXuL8o9h9/Q5gDuGgul4+ac+3Nq2Fb90MmrF2v1EoOHa8V/7/JFBQ9/ZH7H/8WQDUeh8uf/J3k1seKwTw8TmjUHDhLy9kn2ffJI+cXnKkwIzC6MFX/yEKf/nkL0kStvdtOEoc6C/Qo1s3PRTY3pUjC+1r21lbufaMQMGoxA6RuL1xBEgBlMeV0xLYQl9/H++//z4DAwPzeuzNcZvHwUHG2gyWLFlCeXk5VQEBSFrtmL/BBNJoNHLhYlgY+T//OV3GMYOx0PBQ4q6O43DcYRyNDoSXBHLTc7HZbBxvbyd1+SL2hu/B7hrGYV2Czp4HPn6g1GJ6yoSp3cQFOy6goquCXbfs4q6vLHQrzKcWwGBBc6bJWhkDA/Sclb0UlWoMDjQaFb39Fo7UtJO9MQm73cWuwjqsNifC0kSSY4PYtDzKa3rUN2Dhg93VmC48F371g2ld98bJZIY7fgI7XgUYBwePHnj24z/x4gPw04dOuZKfc61aBrff6P2vJEnsrxgPBQ+3PXwKFNgGhnj9G2PFY+f+5scEJyWcun/7yFXpxdvg8d/IRZ9zpKmg4MMPP8QYZ+S2N27jH+X/OO19u9vdmJ8aRhGswPf/RSHc/xPghJN8qQP9hXq0a6cuDpVECesbVhxlDloyW1h/YD1ZsWcOChzlDkz/NqHwVxD4jUDWXLTGazpkt9vZuXMnzc3N87qGUTi4Lv06VEoVq1atYtmyZVQajVRcfTXTVaSp1Wqys7MJDQ+noKCAjh07YGTNwcHBLL9kOfsT92NxWOAlyI3OxeFw0NDezrLWOvbElmE1uLAHbEWX64PkkJCsThyPWwlvC+e9G98jKy5roZVxnrVQfDgiQRDuAO5AhqWlC8WHs9dkrYyDQ1Z2FdbicosoFAIatRK3W8Tf34fVy+PYU3oMQYDcrGSMBvkLsb++hfzaHpwj8wxUKgWb1ycRFuoLRWXybIWZXNm2dkB0xLjcfLelj2CfsaLE0TqE05bLJfvZz+GJ9BT99d9yzn9bNiCf9MoqmmhsktMqo1CwNX3VKY6GkiRx4MkXePeeB1iUu4FrX37s1FY3pxPOvg4uOht++M05XfpM0geSJHHn23fySNkjPH7x43xtzcyKTN1tIzUFTeX4LqpEuOc7wEg64G0rznIn+ov0aFfPAApes+I84qQ5q5ms4qwzBgWSW8L6rhXnASfatSMTHSsOQEYGtpISCoeGxkULUlJSSE9Pn3zOwhzq2cPPcunSS2lvaufAgQMsEkUydu5E8dhjU3YIeTwe9hYW0tnWRmZvLzHf/rb3vsHBQQp2FZDankpwfzDCeoF8ez5qjZqkpCQO7z/Ehs616G1+aIr+gmPt7SAoELUCATcHoIoYSxEtFCSenhaKD09TkiT9VZKkNGD9J72Wz7omixwE+Os5KzsF9UjkwOnyoFQpGBq2UV7RxOYNiSgEgY8KahkatgEQdPfP2faPR/E1yiFgt1skb28dxyoa4MKvyF0HM1FMpPxFVrgPOmQ75jBDMEqFkt1Nxaz454WzTyuo1fMLBZIEb3wI+yoAECWJ0gPHx0HBX9r+MiEUgFy4teaWa/hG6etc/LdfT9z/rlbDdZfCtpxT7/sYmmlNgSAIPLz9Yb659pvc9sZtvHv03Wn37W5zY9phQhGmxPcsC8KtNwEjUPDWCBRcMgMo8EhYXrXgrHLSlN10RqFAHBIx/duE85C8Vv0FegSlAHFx8Pjj+CxezFlnnUVCQoL3MTU1NRQWFuKc5whV23Abt795Oxc/dzFR8VFs2LCB44LA3uXL8TimrnlQKpVkZWcTHRXF3sjIcZGOgIAAcs7KoSqmiuaYZqRSiRxzDpJDor6+nhWDPRSHFmPyHcK6/nYeFR5FUihQKpSYnzLh7hhfkLgQOZh7LUQMTtJCu+LcabLIwdCwjY8Ka3C55MiBWq1EFCUMeg0b1iyieH8jNruTnI1LCBoeAsAVGc7esgY6u8cgd4lBYGXuChTqGU5jtDsgdSvceAX8cqyQqnmo/eObIN1xL4SFwM++e/qPnak8HkSFgtL9x2lukx3xJCT+1PonzlmeMbvZBwCNLbAodo4XO7tCQ0mS+Ef5P/jyyi+jVU1+Qne3ylCgVA/he0c8gnZkEJQoYX3T6j3RalfMAApetuCqd3E8+zibCzefMShwHXdhedmCoBYwXG1AFTn5+1iS5JPmwYMHvbcZDAZycnLw9Z2FdfgMdaJ98hvXvcFQ79Cpw5emkCiKlJWVcfz4cdY2NrL4Bz/wRhpMJhO7d+8m2BRMaksq+ML+8P04tHYWCSKHTFbiWuJIcaSgW+bCcVgApx1BJ3tTqKIWIgenq4WIwYI+cU0WOfD38+GszSloRoDA5fKgEASsVid7yxrYmLEIo0FHXlEdPQZfiItC7XKy+a1XWRI75shWb5HI39eAs+ywXFw4nXRa+OBZ+Pld426ek4LEJQmQEHP6j5uJGlsAEAUFxWWN46Dg962/nxAKRLeb4/kl0+87rxiWb4OyQ3O65Nl2HwiCwG0Zt6FVadnXto8nDzx5yjajUKASu/F9YCPC8EiNxUiNgPOQE8OlhumhwC1hedGC66iLxtzGMwYFkiRh32vH/IwZZbgS36/5ngoFAwPwyivyb+TXJTk5mdzcXO/J2GKx8MEHH9DR0TFvaz3RPvni5y7GP8Sf7Oxs+ru7yXviCRw225SPVygUrFu3jkSnk7JFi6g/YYCUr68vW7dupd+vnwOJB8ADGQ0ZGE2+7DF1s6N3B+2xLQwF9uCoVKM98jxofZBUakzPmHC3LUQO5ksLYLCgedWUcJB9Ahy45ZYkh8NN0b5jrF8dT2CAgfy99XR2D8GxJhTPvMpqj4mMlXHe9GZ3j4kP6voZfurVKSumvUpKkOsBquqgrdN784lwcOMb3+e0I2nf/Rp85arTe8xMVFEFqVvx5JdSVHqM1nb5RCEh8X8t/8d5y9dPGCnIf/AR/n3uDbz17ftwWaf48t68Dh57EDKWz9mS56ol8aWql7jl9VvGFSS6W0agIEKF8XtLEIrzITR0rEbgsBPDZQY0y6eeNii5JMz/MeNqdNGwpYHs/OwzAwVOCcsrFnnE80YdxuvHD3XyqrERrrxS/n2CwsPD2bZtmzdK4Ha7KSgooKam5vTfszPUKBz4qH2QkAgLC2NrQAAWvZ5du3aNGyU9kQRBYM0NN5C8ZAkHDh2itrrae5/RaGTr1q3YfGwUxxYjhoikHU0jaiCKm6O/wqqdH7I/+CD90QM40m9Cs1YPkgAimJ7sx926AAfzoYVUwklaSCXMjyZLKwyb7HxUUIPT5UGhEFApFfJvlZLNG5KoONJKV/cwGzIWERvkAz46kCS6e4Yp2tfoBQqVUmDjukQiwyce/DJObjekb4Nzs+HPvxh3V/NQO3aPg+SgRaf3BD0e2SkwOmJ2UyEnk92B+62dFIYn0t1nBkBC5MHm33Dxys0TQkFr6UH+ufUar7vh1/JfIurkE39bJ/QNzLkx01z6FJxckHhz6M2YnjWhcndi3NiLcNZIIaYoYfmvBVeVC8MV048glpwyFLjb3Bzbcozcj3LPCBR4+jyYXzQjDo2MSk6dYp1uNwwPg5+fPNToJLlcLkpKSmhvb/feFhsby7p161BNsP1c6lj/MSKMEXjsHvLz8xEEYUYpDUmSqCwooLqzk2WBgaSdc473vWu1Wtm1exfdQ92IjSJXeK6gPbydhvBjpKUv40D5AVaaVxDSGoqmcyfOkI3yZ85oxPcGP1SxC2mFmWghlbCgT5Umixz4+eo4OycFrUaOHHg8Ip6R3/l761m5LIaY6ED2ljVwrGtkiuH//JqwB37Pti2pY0WJHomC4qNU/+pxpMFJ3++yVCp45e/w25+cclecfxTJQYswOczc8Pr3Zp5W6OiG1RfIofk5lFOpZHfoYi8UiIj8sulXk0KB02zh1RPcDXN+dMepUABw/x/hy9+Vv1znSHNtXnRiQeI/3vgH/U/3o4pQYsy/B6FoNzBWOOiqdmG4cgZQ4JAwP2fG3e7m6NajZwwK3K1uTE+aQAS/W/ymhgKQ36NBQRNCAchtgZs2bSItLc17W0tLCzt37pz2Cv7jyC26uWDHBVz03EUodUq2hoai6Ohg10cfMTg4OOVjBUFg+dq1pNfXc2RggMOHD3ujHKJK5M/df2bQM4h/ij9CtkBUVxRpzcuoPlTNah8dFep9dEW34Yw4G02kDQxGEARMO0y4mlzeYyxEDj6+FiIGJ2khYjC/mixyYDLLkQOHU44cyO2MKiRJImfjEo4d7+FoYw/LU6NIKcxHcLvh6zfgcnso2d9Ie+eQ9xhRvmo2ZC9DrZ5B+2Frh1yRHz5+dkLrcAc5O64HZliQKElQUAqrl4GvceptZyj7mx+xe0hg2Ci/D0U8/Pz4/Xxp9bZJCw3f+OZPKP/nfwCIXr+SWz76D4qJTi4WqzznYclpRkYm0Xw6GrqaXPQ/048nzE3kV6IQBDeoVEgiWF6x4KobgYKUqU+2ol3E/KwZsVekfms9Wz7YckagwHXMhflFM6oIFYZrDSh0M7gea2yEn/4UfvlLWDT136i1tZXi4mJEUR5ZrNFo2Lx5MyEhczQP5CQVNhdy/jPnsy56HW+n/S/Cj+8j/7vfxTIymTE4ePqBW7W1tVRUVLAkPp6kVWlsf3Y7FZ0VvH3N21jqLdjtdnLicuA9sKgtHI6tIPloBQeTk0l1pBHZEIk6TYWrxgZuDyhUGG8KQJ2wMJVxKi1EDBb0qdRkkQNfo46zc1LRaVWIooQkSjidbhQKgd1FdSyKC2bZ0kgOV7dTsX4T0m3ySVvd1Mqm9Ymkp0R5j9FucvHB7iqGhqe5cvJ44Pyb5HkKJynGL/L0ChIFAXI2zBkUmC0OdroMXijwCG5+3PiTKaGg9s0PvVCgNui54snfnQoFTzwvw5BB/5mBAvNzZvRBIpF/vxJnUy3vHP9QhoKRbgLD1TOAApuI+RkzYp9I3dl1ZwwKnJVOzM+bUSeoMd5gnBkUgOyN0doq/55GMTExnHPOOfj4yM/D6XSya9cuGhoaPs7SJ9WoCdK+tn1sr/oxnjdfZcu2bfj7+5OXl0dXV9e0+1ianMya/Hzqm5p46KWHONR5iPdufI/NizezZcsW9Ho9eU15cCUYlUbWNKylYdE6Vq1eTbXmCK2LmnBVuVFVvgeiCwQ5EuRqXIgczIUWwGBBZ1yTwYHRoOWs7BR0WhUeUZKrtx0uNBoleXvqiQz3Z/XyWOqOdbHvQBNicTmsOBehcB9pSyPJzkxCpZTf0markw8+OkJza//kC1Eq4cnfwa//Z8K7T+5WMDnMUz+xglL42amQcboaGLLyYX4NFoV8UncrnHz/6N3cuObCSaHA3NXL6//vx97/n//QTwhKTBi/kckMDz4Cr07vETBTnQkoUMWoMJ7rREhezI7297js2cuo+kcVrqMujFcb0SRPAwVWEfPTcm6/9uxatr639YxAgb3MjuVVC5p0DYarDQjq02glTU6G3bvl3zNQQEAA5557LqGh8pwRSZIoKyvjwIED3kjCXGoUDqp6qjjSW4WmtZWcxx4jJCCAgoIC2tqmB+noS7ZT0f4maao0dmzYwYZoeSS6VqslNzcXo9HI7srdeK7woAvSsbphNW1Frax66y3qFVU0LWnCnXYhqqWB4KMGAczPmnAdW4CDj6uFVMJJWkglnDlNllawWB3szK/B7nCjVAhIyNBgtTnJzlyC1eqg9MBxIsP92Xi8GuXVF3oNhkxmO0Wlxxg22b3HWRwfwqrlsV5omFCDw3I6IPDU4sXmoXbebczn66uunfoJPf0KPPo05L8kQ8cs1NU9TGHpMTwe+cvcpbTznZrv8c31100KBZIk8dwVX6f+nV0ALL3obK558dGJPQ0GhiDAb0rXuplqXqHguAvz82ZUEWC8QovgpwdAdImUPFJCwlACZevLuPj8i6fcj2gWMT1jQrJK1Gyt4ex3zp53KJAkCXu+HXu+HW2mFp9zfGbnLzELiaJIRUUF9fX13tuioqLIzMycl6JEi9OCQWPAc+wofOlL8PQzlAwO0tbWxrp168YZM50os9Mszz7orODVc1+m/9gA0TExbNiwAeXIZ8flclFQUMDg4CDZmdlo87S4j7qpD68lZIOeimPHSHAnsKh+ESpND26zBjxK0OkxXuuHOmkhrXCyFlIJC/rUa7LIgUGv5eycFHx0cuRAEMBssWPQa8nfW49Op2bT+iS6uofJj0nG5ZFkV8DCffgadZyTk0p8bJD3OA1NvXyYV82waZK2PVGEs66Bn/x2wrvj/KO8UPDU4VcnTyvcdAUUvTprKGho6iW/uN4LBbqeNr5RfceUUABQ/s//eKHAEB7CxX/73/HbdvXC//sxDJtk8PmsQEGsCuMrtyJcL0/HHPUdSLGm8NyS57ik5JIpZyuIJhHTUyYkm0TN2WcOCmzv2rDn2/E5y2f2UHDwIBgM8u/TkEKhYPXq1axdu9Z7W3t7O7t27cJut0/xyNnJoDEAcGf179j2LX/sSfFkZmaSkJBAaWnpOEAZ1YlQ8N6N73H24Tayfv972tva2Lt3L56RgtjRuQuBgYEUFBdg32pHs1ZDclcKliKBlUlLOO6u4diSetz2QJSuXtCrQKWQW1HrFyIHs9VCxOAkLUQMzrwmjxw4+aigBpvdhVIpIIoSAX56hkw2Nq1PRKVSUlh8FKNBS/bjj6Izm+G1JwD5C7qxuY/y8kbEkWiCQiGwenksi+NDTv2y3lkEyYsgNorJZHXZWP7EdiRpmoJESTqtk68oSRw+0krtsW7vbQ56+UXxXVx3wdendTQcbGrjv7feTVPhPq579XGSR8dTj2rPfhkM3vrXnIyHnlcoaByBgjgVxi8ZEQ6WgcOBtGET5hfMuJvdGK81okpQcefbd2LUGPnNtt+csh9xaCRS4Jao3lrNOW+eM/9Q4JGwvCa3Teq369GumdpgaUp1d8Pzz8O110JY2Kx20dnZSVFRkfdEq9fryc3NnRenxFGHxPP0K3iufDGq3/+RipYW6urqSE9PJzU1FUEQToGCjbEbZTAvL6cjOpo9e/YQEhLCpk2bvBEOt9tNUVERvb29bNq0Cd/jvjg+cNBj7EFZ8ksOX3UZUYpYkuuSUYYq8Qy5wSaCKGD4ki+apXKqaSFyMPOIwQIYnKQFMPhkNBkcWG0yHFhtLpQKGQ4CAw0MDlrJXLsIo0GOIqiVAjlr4jEEj08FDB1toehwO2bFWBg1Mtyfdavj0WknsHO1O+SiRIN+wnVOa5987g2wbiU88IMZPW+ny83efY109Yx9Rod8uri9/Dvcm3XHjG2ORY+Hxo/2kHjCkCWbzcmw2YFCENCoBDQ6DVqNCuVUKZVpdEagIF6FMaQU4ZytoFB4zYjcrTIUnFh5DvIV4fHB4yQEJADgGfRgflquBzmy5Qjb3tg2/1DglDC/ZMZ93I3h8mk8Cs6gBgYGyM/PxzEy22D0Knw+OhYKmwv56t/O44OnIPyFt9Fl5VBdXU1lZSVLly5lccpib/eBFwpOlCTR/a9/UejnR2BQEJs3b/a6PHo8Hvbs2UNXVxdZWVkEDQVhecWCSWvCc76Hw/WHCJfCSalbiqK1CskvDEnjD2rtuI6VLzocLIDBLLUABp+cpoaDWqw2J0qFgEeUCAky0jdgZv3qBIICZYdEUZTIXeSP3933w9/+VzYbQh68dLCyhYamXu+x1Gola1fGERMVOHbiFUXIuUp2AfzT/ZOu80Q42H39DuL8T4gy/OtFOepw9qZpn+/gkJXCkmNYbWPDcAa1Daz7xo8o++GVfO0bD844DC1JEp3dw3T1DDM4ZGNwyIrTNbFHgUqpQKNR4aNTExxkICTISEiQEZ1uat/7eYWCBhfm/4xAwap2hOVp8PzzSJde5TUjMl5nRB1/6hrL2svY+MRG/nbh3/hqwlcxPW1CUAoc2XqEba/NPxSIVhHz82Y8PR6MXzKiXjSDaZ/TaXgY9u6FjRtlk6OPIavVSl5eHiaT7AMiCAKZmZnExs79fIzC5kK2P30+P9t6P9/P+j4A9fX1HDhwgCOuI/yx+Y+8e+O7p0IBQF8fpKXR+8ADFAQH4+vrS05ODhqNfFL3eDwUFxfT0dFBZmYmoWIoQ88O4cKFw/YCh5aEEmpIIO1IEooALZIHJCvgYZzx1RcZDhbAYJZaAINPVpPBgc3u4qOCGizWMTgIDTHS02tm7ap4IsP8yN9bj83qIOfZpwn65XchMX5sx8eO03bzjyj9/vdwCWNXzFHh/qxZGYfeZ+QK79V3YeliSJu6Grx5qJ3vf/S/PHbBAwTqZuC2eIIkSaKhqZcDh1oQRz5/apWCFt8afvPuT3nz0FJW/fUxhPjJvRNMHd1o/YwotDqaWvuoO9aFyezAoNcQ4K8nwN+HgLID+Dc2In33azidbhxOj/zb5cbpdGOxOOjtt3jBxGjQEhJk9MKCn6/OCyZnBAoSVBivNiKoBNi/Hyl9NebnLbg73fhe54sqbuLiuVGHxPfL3ifPJw+D0UDllkrO/e+58w8FwyKmHXJxo/E6o3ewz8dWeTlkZMD+/bBmzcfendPpZM+ePXR3j6WrVq5cSXJy8pwXRtb01pCsDEPx24eQfvITLBq46z93cbbmbAwhBrZv2e4tMDxFPT0QGkp/fz/5+fno9XpycnLQ6WQjM1EUKSkpobW1lQ0bNhBpiKT3X70oHAqs0Qc5FGAnSAoivSEdQSGCxYrkVIFKi+FyI5r0LzYcLIDBLLUABp+8poKDXQU1mE+Ag/BQX7p6TKxKjyU+NojC4qMMDdvYuG4xkQE62fxkNC1QXI59VTplFc3jDJGUCoH01GiSFoeiHB2fLIqyLa1m+pDw8cFWBEGQ0wrDJsgvgdzMCT0N7HYX+w420dE1dnx/Px+OaEr5fsGv+GnWndOmDyRR5N/n3oAzPJqQa67FIwlERwaQnBROSJBRTofoZp7fttqc9Pab6e0z09dvYXDIigRo1Er8/XwAD/f84KfsL68Y97g5gYJjMhSoF6sxrOpAKMqHW28dcyjscuN7va/X8nYyubvdtD/RTpurjffWvMdDhx6adyjw9HowPyunLIw3GFEGz67odEI5nXKdQVjYjN6DM5HH46GsrIympibvbUlJSaxatQrFXI8Nr6/HsXE9P/zmEkrjVVR2V/LqBa8ycHSAsLAwsrKypu6S+O9/GezpIS8szNu+OOrTIIoi+/bto7m5mXXr1hETEkPnPzvRDeswZ5mp6NuHvyaUVRWLwTwMPlokTTBIAvpL9WiXy5+NLyIcLIDBLLUABp8OTQYHdoeLXQW1mCwOFCM1BxFhfnR2D7M8NZoli8Mo3t9AR9cQGXsLWHy0Bl58dNy+paL9tLoVlFkEXCeE2w16LavSY4gK80W44MuwMQPu/960az37uZtoHGyVaw7aLLBmuzzFMXv92DEliaaWfg4cbsblHusrT0wI4SPr+/wg7zc8mHoLP1BtQDg3R3ZjnERFjz5LTbsZ34wMbAfLuey71+HvPwIhJrOcDrnzZrh1mvbKSeRyeegfsNDbb6a7d5Dvfu/HHDpUOW4bX19f7rvvPpYuXYpSqUSpVKJQKE75t0ajISAggKCgIPz9/cddKbqOujC/MAIFVxkQHnoQnnoKqbgc0ysuPD0eGQpipoGCTjfmHWYEX4E79Xey49gOti7aypvXvTlvUOBud2N+zoygF/C9wReF32ejwUuSJI4cOUJVVZX3tsjISDZu3Djn7YwfVr3JeS9dioDA+ze+z1mLz6Krq4uioiICAgLYvHmzN01wiu6+G1pbGX7sMfLy8lAqleTm5mIwyF0Qoiiyf/9+GhsbWbt2LXHRcbT9qw3fbl8sjU9z4IIojJpg1jSuRJIUCFoBaVACj4T+EgPalV9MOFgAg1lqAQw+PZoSDgrrMJntXjiIDPejo2uY1OQI0pIjOVjZwrHjvaTpRJadu3bsClyS4IIvQ0ggzn/+nkNVbeNqDwCCAvQsO15HxKJIhJz1Jy/rFI0rSPzSv4i3ayEq3NuZ0Ndv5kBlK/0DFu9j1Gol61cnsKPpBX64+7dypKAxGuFb90FT8YR+CgD1FfWUVbYjOp10/uMfXPHAd1m05YR8rSjCbx+FKy/42M6Gk6UPgoKCeO6551i0aBEOhwOPx4Moing8nnH/FkURu93O0NAQkiShUCgICAggMDCQMFsYxnwjqsUqjFeNpA8AqXsQ05sKxD4R4w3Th+bdHW7Mz5hRBCo4lH2I814+j3VR63jnhndQKpRolHNfBOhqlIFGGarEeO0k0xE/rpqb4YEH4Cc/gbi4Od99Y2MjZWVl3gLOgICAcSH7j6vR7oPKlv3cUuKi4oosXrvpbQwaA729vRQUFGAwGCY/pscjf34UCsxmM3l5eUiSNK6rQpIkysvLOXbsGKtXr2bx4sU07mgkuCkY6xIr+332o0fP2pYMpO5hBI8ZSRUCKg36i/VoV33x4GABDGapBTD4dGkyOHA43OwqqmXYNAYHURH+tHcOkbQolFXpMdQe7eZwdRsJscGsbTuK4qKz5S+b/kEw6r0h2v4BC+WHW8aduAH8jDqSk8KJjQpArZ76BHVyt0KcXxQ9fWaq6zvp6h7/+YuJCmTNilj+fODJMSgYTR80tcEEtQWSJFF3tIuDlS1YDh+m7U9/Ys2Nl3HhiUWSnT0QEXq6L/GEmsuaArfbzeDgIAMDA/T39yM2iCQfS6bX0MuR2CME9PcSFBpKXGYuqrdViP0ixhuNqCKngYI2OVKgCFFQsbmC818635s+cHqcZD+Zzbc3fJuvrfnarF6DieSsdmJ51SLXQ1xlRNDMk3FRTQ3cdBM8/TSkpMzLIbq6uigsLPS2M/r4+JCbm/uxv/dObEksWPMw6Zd9nQtuEgg9/wp2XCE7iQ4ODpKfn49arSY3Nxe9fuIuIMrK4O67sT73HHkHD+JyucjNzR09uSFJEhUVFdTV1bFy5UqWLFlC/cv1hNaE4vDvZX/wATSGANbvj0bShSHoJSSrBkTQXzjWUvpFgYMFMJilFsDg06dJ4cDpZndhHUMmmxcOoiMDaOsYJD42iHWrEmhu62dfeSPhByvYeM4q1JsyxnZc3yh3EfzqHiSgrWOQQ1VtmC2OccdXSBJRUYFERQYQGuyL3kc9YQ1A00Abt/73Pn7iOQerbywW3fgwtkGvJWNlHBFhfvy2+LHxUACTeh9IksSBwy0cbeyh7/XX6X72WQLiY/h/ZW+iMcqhVT4ogC/9Pyh4GdKXzvalBua50LBeHiikXKzEnmunv6+bgXfeYTAmkbSWDPQePVwGoalTA4672Y3pOROqcBUHsw6OgwIftc8pI5vnAg4c5Q6sb1tRp6kxXGpAUJ4ZN8P51OgJetT8SKVSkZ2d7bVWPl1N6FPQ20uRtZYwQxhLgpd4tzWZTOTl5QFM7q9QXw933QX//Cd2Pz/y8vKw2Wzk5uYSGBgIyJ+Pw4cPU1NTQ3p6OikpKdS8XUPYwTA87nYOrGoHATJ7MpF6JRR6N+KgAIISnwt80K3VeffzeYeDBTCYpRbA4NOpyeDA6XSzq6iOoeExOIiJkuEgKiKAzIxF9PaZKSqux+jnQ3bmEnxG2/L++548QOnD5yBEdkqUJInWjkFq6joZGJp4CJNapcRo0KLTqVAoFLjdIlabE7PFwUSfJ51OzbKlkSyKC0GhEE6FAkGAB/4CB4+cUg/hEUVKy4/T0jZA97+epO8dec7Bl999enwKwe6QLZm/du3HcjacTyhw1jmxvGhBvUSN4UoDgscFGg2ixYNphxn3oJsjS47Q6eokJCSE1NRUIiIiToEwrzNilIqDGw9y/ovnT1hoOFdwIEkS9iI79l12tGu1+Jx/5iyOz4SsViv5+fkMD8vnCUEQ2LBhA3GnmcKYEApGJYrw0ksMX3wuP8//Bb/c+ksMGoO3ldLlcpGTk0NAQMDkB3A4cAAFBQWYTKZxfgySJFFVVcWRI0dIS0sjLS2NIzuPELYvDEEvcCiuApfKzcaaRCSTAYW9E9EvAVDgc54PuvVfDDhYAIPTlCAIdwB3INtEL10Ag0+fJoUDl5vdRfUMDlnH4CAygPauIUKDjWxan4jZ4qCg+CiC1UaO2orfRSPugC7XpIV+/QMWGpp6aWkbwOWe2BNgKh13NHL2qlWsTkpEoZBPJBNCAcAbH0BDM3znVu/jPR6RPfsa6OoZxvnBO9Q/9iQAa79+PRf++RfyRsMm6B+ChJjTXt/JOiNQkKzGcIUBoagAbr4Z8a2PMBcEIZpEfG/0RRGmoKOjg6qqKvr7+wkMDCQ1NZXo6GgEQRhrbYxTcWDDAS544YIpuw9G4eDv+/9OzZ01JAUlnda6JUnC9oENR4kDXY4OXY7uzEDBoUNw9tmwcyesWDHvh3O5XBQVFY1rZ1y+fDkpKSkzer5TQgFASQls3EjtS39nbe33WBe1jjeuewODxoDdbic/Px+LxTK5+dLQEGRlwT334LrhBu8Mhc2bNxN2gjNkdXU1hw8fJiUlhfT0dCoLKwneE4zW5qIyqRqrr4eshqVIthCEEAGpRwIJfLb5oMv8/MPBAhjMUgsRg0+3JocDD3lFdQwOWRFOSCt0dQ/j7+dD9sYkXE4PBS8XYDH4smL1IpYsHvlC6RuAr35fditcfmo+VzRZ6P3t43TlZtOn92VoyIbD6R63jSCA3kdDUKCB0GBfJLWJi1+9BadK8DokTgoFE8jtFikqPUpvv5kYRx/v3vD/APCNCueOg++i9RsJu3735/BeHhx6f8pOhuk0r1BQ68Ty0glQoBSgvR3xoYcxL/0holXC90ZflGFjHQuSJNHd3U11dTXd3d34+fmx3Hc5+jw9qkUqDqw/wAX/mRoKTtxXSVsJmTGZp7VuySNhfcOK87ATn/N90K2bm8K8GamzE558Er76VYiIOCOHPLHSf1SLFy9mzZo1U7YzTgsFo6qvhyVLvPbJJ8KB0+mksLCQgYEBNm/eTHh4+PjHShL86ldw9dWQkjLOJjkrK4vIyDGr77q6Og4ePMiSJUtYuXIllSWH8CsMwNdlpHZxHf0+/Wy2bkY66kFBP6IYAAoVPmf5oNv0+YaDBTCYpRbA4NOvyeDA5fKQt6eO/kErgiAgSRJRkf709prR+2jI2bgEwe3i7fw63C4P61bFkxAfAhYrXP8t+Mm3YP2qUw/o8cCFN8Nt18GV20duEnG5PYiihFKpQKNWjp3o+wchdgM9f/8ZG0yPA3BN6nYeLP77xFDwQT6EBsOqZYAMBYUlR+kbsJCdmcTxF1/l/f95EI/DyZee/yupl5039tj+Qag5Blkn1E6cpuYVCmqcWF62oF6qxnC5AWGgD7RaRMEgzzKwjUBB6OQeAL29vbQWtBJbGcug/yD16+u55qNrWB+7/rR9Cn6+++fE+MVMm1aQXBKWly24jrkwXGrwGuN83iVJktfGeFQRERFs3LjRa098omYMBWMHgMJCCuPggme3sy5qHe/f9D4qhQq32+01YcrMzCQmZpIomMsF/f14QkLYu3cvnZ2dp2x/9OhRysvLvWBz5OARdLt1BFuDaYiqoT24l5yPBKTgLBSKAUQpGADdFh0+2T7e1+LzBgcLYDBLLYDBZ0OTwoHbQ/7eevr6LQiC/D0UFe5P/6AVtUpBTlYyGrWC8o8qaLJDSoSR5euTx7cziuKpExJPZzCSJMG/X4ItG2kOVLDqyYsZsA9NHinYeg0kJcDjv/FCQf8IFISGyJGBvqPHqfzPG+T8+E758aUHZWfH4MDZv4icIShIUWO4bCRScMEFiCo/TNsfQ7JL+N7kizJkamMgZ5XcCcAiKAguwDpoxYqVDSs3sDRp6Yz77yVJ4lvvfIu/7vvrlDUHol3EMuK4aLzaiDpxDiyOT1dmszxZcdUqMJ5qlDXfampqorS01Fsz4+/vT05OjtdkCGYBBQB79sCmTZCfT2G8QHlHOd/e8G3v3R6Ph5KSkqnHNt98Mxw5AiUliOB1Qly/fj3x8WNupw0NDZSVlZGQkEBGRgY1VTVIuySih6JpiW6mMaCRHHLhCCjDFXi6PIAwLmX0eYODBTCYpRbA4LOjyeDA7fZQUHyUnj6zFw4iw/0YNtnlXuisZIyDA9Q+9RaHlq0mKsKfDWsWoVYp4ObvQ3Q4/O8PTz2g1QZ/eRJuvxECZvbeGE0f/Hjj/+NXOd9DQkIhnBSWdbth2Izbz5fCkmOnQMEp8nhg5Xmyu+Jff3U6L9k4zSsUVDuxvDICBZcbEEZqLMR9VZgKgpEUWhkKpnELdB52YnnNgmaZhrKVZWx/fjvb47ZzV+JdtLW2odFoSE5OJikpacIr2pM1XUGiaBIxP2tGNInyFMdpzJXmTXNsiTwbdXd3U1hYiNstp810Op23VXBWUDCqPXvkeoET9Er1K5yXeB4GjWFcSmP16tUsWbJk/OMrK2FgALLlgWGiKFJWVsbx48dZu3Ytixcv9m7a3NxMSUkJMTExbNiwgdqKQ1j2uknsS6QrrIvasFpyTOnQFIRysB6PfyIICnSbdei2fP7gYAEMZqkFMPhsaVI48IgUFh+lu9c00goIYSG+WG0unE432ZlJBAUaaO8cpLisAb2Phk0bkvB95kWICIMTw/Wjau+CtRfCP34L28+aemGHa3jjtUe5RPWmN1JQ3H6Ab7x7H69f9fexqYwjkQi320NByVEGBqxkb0wiNHia0bhNbeBnnNQIaTrNOxS8bJHb+i4bgYIPP0TMyMH0rA3JPRIpCJoaChwVDqxvWNEs11C2XIaCE2sKzGYzNTU1HD9+HKVSyZIlS1i6dOm0gHAiHLx+7etcvPRiADz9Hsw7zEgeCd8bpk5vzLvsdmhqgvh4mCPTodloaGiIvLy8ce2MGRsyuPH9G2cHBSeqthaWLqXL3EXSX5JYG7WWN697E4PGMM6fYNmyZaSlpZ0aaZMk2LcP1q8fZ3a0atUqkpPHZp20trZSXFzsTYkcPXqUnrwe0rpSGfQboDKqkuz9Ihi2ogwV8PTI50Rtlhafs3w+V3CwAAaz1AIYfPY0GRx4PHIBX2e3PFVOIQgEBxnweESGTXay1icSEaRnePstFN18K3Z/fzZkJBAVESDv2GQ+dd6B2QKj3gFTaPd3bmXpjjz+9vId3J/zXQRBmHhk89ZrcH3pYgrS1zE4ZCV74xJCg42UPvo0lq4+Nt9zO2r9CTn0F96Ei88Bn9mfLOYVCqrkSIFmmQb9pXoZCpqbEdfkYPp+IRh8Md5kRBk4DRQccGB904pmtYayZWVsf277pIWGVquV2tpaGhoa0Ov1ZGZmenvcJ5MkSTyy7xG+uvqr6NV62Vb5WTOCVpDnHgR8glDwKZPNZiM/P5+hIXm+hyiJ/LP7n9x/2f2zh4LCQvmKv6gIsrIobC7k/GfOZ130unFwMFrvkJSUxOrVq8fDwfPPww03QF0dJCYiSRKHDh2itraW5cuXk5qa6t20o6ODoqIi75yGxiNHaNnfx8r2FVgNNipiKtgYuBHFXgUKgx3RIn++tJlafM75/MDBAhjMUgtg8NnUVHCwZ98xOrrkz4BCIRDo74NKpaS718T6NYuIrzqMM2kxpT0O2juHSFkSQfpHH6D429NQ8vqpIODxyJ0Ak0QNflv8GD/98Lf8z+Y7+Hnud8d9mY2Dg2ufIuIf71CQuhqToCZnYxLBQUbMnT38Zfk5OE0W/OOi+Wb527KRUVMbrDxXHil93aWzep3mFQqOyLUA46AA8Ax6MD/RB2oNxi/7TnvSte+zY3vXhnatln0p+6aEghM1PDxMcXExw8PDrFixgiVLlsyo1a72YC2B7wSiC9VhvM6IwvApmHvQ2gq//z1873swWRHeGZTL5aKgqIDe7jH78PT0dFJTU2fXvilJ8MorcPnlMNLxMBEcwFghYVxcHOvWrRubt+HxyICRm3vCbsf8DFJTU0lPT/eub9TpMTg4mE2bNtHc2Ej93gYyOjNwK9wciD3Ahj1tKEKvQmFpQTTIY6m167X4nPv5gIMFMJilFsDgs6tJ4UAU2buvwTtRUalUYDRo8PP1oaVtgJXpMSxNDEey2qjZdYBKj5ZgHxWZx6vRf+2aU4sO39kFl98G+948pb1xJi2Jo3CwyBDPPTH34HC4ydm4hMAA2Rb2ta//DwefegmANbdcw8WPPDD24OOtsmXyLL6MzwgUpGvQXzICBSYTnuffxmw7DxQCvjf5ovCf+qRrL7Zj+8CGdoOWfUtmDgWj8ng8HDp0iPr6eqKioli3bh1a7eSTJp21TgZfGmSPZw+D5w9y8/qbT/epz4+qquTWvBdfhLS0T3o1mJ1mtu/YTro7nS3+W7y3L1q0iIyMjFlPZ5QkCU+TDXe7Askh0TrQSmlTKdsXb0cjaZDcErjBZrHRb+pHCpKIXxOPJkKDIkjhhU927ZIBYWQdNTU1HDp06JRIQ09PDwUFBfj7+5OdnU1bWxuVhYdZ37gcQWPgYPQB1vgvQlkRiiJYntkBjDO2+izDwQIYzFILYPDZ1mRwIIoSxWUNtHYMAqBSKfDRqgkL8+NYYw9Lk8JZsXsnws9/T0/JO5Qc7cXtFlmzMo44hRsix0xUkCSoroe05HHHHgcFm76FcPlt8LXr4JJtp6yzuq2JmtIO1FodOdkp+PnKocu2fRX8I/tKALT+vnyr8kMMvkb494vyviabYz+N5hUKKp1Y/nsSFACef72K6UgyQkwEvl8NnHYCob3Iju0jG7osHaWLS08bCk5Ue3s7paWlKJVKNmzYMM4EZ1SjNQzqpWp+rPsxfyn/y5zZJ3+edGKh4bs3vEuQNYhDhw557w8LC2PTpk0zKv4EkNwS7iY3rloXzoNDSB4dqJGHUSkBFQgqAQcO1Bo1Ko0KlOAYduDudKPxjLSOKkEZqkSpNaP6/V2of3Qdimsu8x7n2LFj7N+/n4SEBNauXeuFl76+PvLz8zEajeTk5NC5dy8H2vpZ35uJxqzhcMxhliWmoP5IjcLZi6iVPRU0qzXoL9R/puFgpmDwCZXcLmhB8yOFQsGjf/87AF/9utxZ8JWbrkChEMhcu5iS8kZa2gZwu0XsgpvOriFSkyOoruvEkZlDRsEmQhdHsS0mjPKKZorLGmkrKWb1Zdno1o840AmCDAWSBD39EBY8caQgPBR0p/a/t7YPUH2gH9+WNjYIQ9zF89y36VvE+Ubyzvd/4d1u633fxRAaDG9/BD/+LWzNguTFp+xvOs0rFIx2DSyXJ9Z5oaDXg2lwK0KsR4YC36mhwJZvw55nR5ejozTu40EBQFRUFOeeey4lJSXk5eWRmppKWlqa9+Rg32vH9qFN/rLfrudPwp/wKDzc9sZtKAQFt6y+5fRfjM+hJus+0Ov1lJSUeI2odu7cSU5OzqTDkESbiOuoC1etC9cxFzhBEaBAs0RAXf8GqjuuRPAdS9l5RA9Zj2YRpgrjjctlEyQjRvr7+9m7ay8BngDSo9JRDirxdBhxXvkoHAXVDhOapRrUS9UkJiaiVqspKSnB5XKRmZmJUqkkODiYLVu2kJ+fz+7du8nNzWVtby97i/ayrnMVK5tXUuOsIvHI62iW/wCF1oFo1+I84JSHL10kv89/97vfAXDnnXcCfGbgYCZaiBicpIWIwedDk0YOJIl95cdpau0HQKNRoVQIJC0O40h1OyHBRrIyEtA89DekGy6nReVD+f5G0GpYnhbNovgQFKNh/Pt+By+/zf/9/SruKfzdtI6GHo/Ioao26hu6iYkKZP2SELqtPWx+Tb5CfUL7FfK/KbcfhqYmcXvpGyhHr8J6+mQTpNPUfEKB47AD62tWNCs03i9LAM9/8zFVJSME+sjpA+PkUCBJEvbdduyFdnRbdJTGlrL92Y8HBSdKFEWqq6upqqoiODiYDRs2IBQLOPY40G3Sods6ZnEsSRI//PCHXLL0EjbHbf5Yx/3YqqyEiy6CN9+E9PRPZAnTtSSOhuVPbGc8cd6BZ9Ajg0CdC3eTGyRQRipRL1WjSdagCFNMWZ8wkUMiyFe9+fn5wNjwJXFYxFnrxFXcg3vIAJKAKl6FNkNLr18ve0r2EBoayqZNm7y+F6MdF6MTHgebm9lbVs7KnjSCzfEcCzlGzPoYtB9qEXQgX19LqNM18hAtxWcvcrCQSpilFsDg86PJ4ECSJMoqmmhs6gNAq1EhIZGeEk1ldRtatYLsXz6A8fZr4YbLsTtcHDrSxvGWPvx9dSxPiyYy3B+hup6X3nuCq+0v89NNE0CByyVHFKLC6e41sb+iGYvVwYq0GJYsDvVu2zzUzllPXc/lv+kmKmU9xjVriNi8EYNBh6Z/gMi1KcREB6HVnF6Ab16h4JAD6+sjUHCx3vtcPN0eTI+0o7D3Y7w3HYVx8tSHJEnYdtpw7HXgc44PJZElcwoFJ6qnp4eS4hIWNy0mciBynDf+RHJ5XOw+vpttiaemgc6I2tvhkUfgm9+EqKgzfviZ+hQMDw97Jx4CqBQqsgOy0R7T4un2gBJUCSr5Kn6JevJ00v/9n2zk9I1vjLt5MjgYHfzkcDjIycmRu1Dsdli8GPHmb+C65oc4K5y4m9wIRgF3spsScwk+oT5s3rwZzcjI9dEJj4IgkJubi7moiCKTmVRrKpFNkbT6txLsPox+YBM4LEi+svWytxVX+dmCgwUwmKUWwODzpang4GBlK/UN8tAYnU6Ny+VhzfJYqus7cTndbMpMIiRopF2xb4C+C27h0Pe/S4/OiL+fD8ekGu4p+znfz7xlwkiBdN/v6Ck+TO0v7qWja4jgQANrV8Xj7+cDl94KV10II+t5809PMKAJQxsVhaergyUbluOpOoq1rYfeJUtAgIgwfxbFBRMdGTBtJfi8QkHFCBSsGokUjKzF3enG/IwZhZ8C45UqFMETh5VhBAret+EodeBzng8lYfMHBSDntU0vmXAfdXMk/Aj6NXpWrlw5qWvikwee5JbXb/lC1hycrnnR6BAkqV0itSsVo9OIK8FFYEYg6kQ1gnYGhbLf/jb4+8Mvf3nKXYXNhVz2/GW8es2rZMdne293OBwUFBQwPDw8Nkyprg4WL4aRv6un24NjvwPHIQeSS6Lbr5vuuG7Wn78e3Yg/hMViIS8vD4/HQ25uLna7ncL8fBb1hhDfu4JefS96zUGMjm1IEiAzkGzzfeVnCw4WwGCWWgCDz5+mgoPDVW3UHO0CQO+jxmZ3k7EyluMt/fQPWFg30E58zRHZCfHtj5ByNtBjE3m7rBSdw082TurtIdioRb9uOUqlAqfLzfCwne6OfqxuCT9fHWnJkcRGB8onUY8HfvhrODcbzs2lrqaVA1Xt2Bsa6PjH49z8n78QsXKkEr1vALvBSEv7AM2t/fQNWAgK0LNiWQxhkzgjnhEoOKEQC8Dd7sL8eDcKPwHjNyJQ+EydPrC+Y8W534l+u57i4OL5hQKHhPk/ZtxtbgxXGmhWNHPw4EF8fX3ZuHHjhJ/zuRrZPGtZrVBTAykpMEnefj40G0dD0Spi+cCC+5CbId0Q1eHVmHQm0tLSWLZs2czaGaexHDc5TPhqfRElEYfb4X2PuFwu9uzZQ09Pz/h5CUeOgMkEmfLgLMkh4TjkwFZkAxP0BfQRcVEExkUy+NtsNvLy8nA4HOTm5uJ++mkK/P2J1iaz+FgSZrUZxRYF/ru0iE5AVIJCiSpRhfFqI4LqswEHC2AwSy2AwedTU8FBVW0HR2o7ANDrNVitTlalxzIwaKGptZ/k1kZWfOMKFEr5ZPfXt37P/5Q9wj253+O6uKvo3rWPweAQbAo1oiShUinwNegICTYSHRlAaLBx0i/HumPdHKxsQdfXwZEf30fK9rO4/Ptfp7DwVWKvvXHMIXFE3b0mKo60MjBoJTLcnxVp0XIEYkRnBArWyAV7Y1DgxvyMCUV3Hca17SiuvXzSfUiihPUtK86DTvQX6ykOmF8oEC0jFscDIxbHcfKV5ODgIMXFxVgsFlavXs2iRYtOjfh8knDwCVginy4USJKE84AT20c2kEC7VUu1UM3RY0e925ziPTCVPB74z3/gkksmnQ/xvfe+x4HOA+N8DjweD6WlpbS2tpKRkSFbIl9wgQwb7747fs0eieF9w1jyLPg4fRASBXzPkSd7OhyOceOfBZuN/LIygsVgUupTcEpOXAd/R2DKNxEFPSh8QJBTJcZrjAjqTz8cLIDBLLUABp9fTQYHANV1nRyubgPAoNdgsTpJTY5Aq1FRcaSVkCAjG1fG8HDFU1x51e/o2LqSjc++NO5kMvpZ8t5mscK/XoTzcyExYWwh5ZUQH03tgJOKI61yq2RaNLb+QUS3B93vHuXYizu46PvhfHjTjlPgQJIkWtoHOFzVhtXqJCEumGUpUUiie/6g4OCIPfHJUNDqxvSsCWWoEt9rDAj6KWoKRAnr61aclU70l+gp9ptfKPAMjlgcOyWM1xtRhY9PG7jdbg4ePEhDQwOxsbFkZGR4c8/eNY/AAcBfL/zrnK5vSp3hiMHpQoG7w431HSueNg+alRp8zvZBYVAgSRJ1dXVUVFR4tw0KCmLz5s3e0P2kammBpCR4+mn40pcm3GQyEyRRFDlw4ADHjh1j+fLlpAQFIfj6TvramU1mql+rJrotGh+XD5oVGnQ5Ojx6DwUFBQwNDZGdnY3abidv506M2hCWdaxFsAvYNloIqg/B0+8BlxzpUMWpMF5rRNB8uuFgAQxmqQUw+HxrKjioO9bFwcpWYAwOEuKCiY8JpnhPHU6XixePP8F2lR9fuf5HCGEhYzvu6YMdr8K3b/GarGCxQtRaeOqPcOm5Y9su3ULNN77GocWppCyJYHlq1PirVUmitbGanPfkLxSvffJJ8ogiDcd7qartwGS28Mc//I795RXjtpkTKBixJ9ZmaPG5wGcMClrcmHYMo+quwvj1SISUxEn3IXkkLP+14Kp2YbjcwF7D3vmFgm4PpmdNCKoRi+MpLJhbWlooKytDo9GQmZlJcPD47g9JkrzDr1qHW4nx++SdCOdSpwMFkkPCttuGY58DRYgC/XY96rhT/QtG5xOIomwQdHLHwqRqbZ3W6XEyOJAkiSNHjlBVVUVycjIrV65EaGuDggK47rpT9mO32ynYXYB/mz9JA0kITgHdBh2qTBVF+4ro6+tj0/r16O+/n7wLLkCtMrCiZQWaQQ3mpFaCapR4xGBQqUGhQhmjxPc6XwTtpxcOFsBglloAg8+/poKDhqZeyg42IQgCPj5qbDYXYSG+HBkuIOj/s3fe4VHc59q+Z3tVL0g00YvoVUhCCBwXcLdxrwlOnLicJE61k5w056R8iRM7TuzEvfdugyuoAwKJ3gVCAtT79p2d+X1/jCqogEC47ZOLC2d2vxQcpAABAABJREFU2i67M/e85XlbxyNZbKROTGLqpGR0bjf4g5AQC4WbtYLC/NdhSrdpcMflToUQ7Crez+4aN1MmDmPa5G5QsHs/uL2wYBbQ0z455/oXGBXZe3V6S4uLb1x4KyUlQwgF3ZzfAOQKGfdLbgzRQRzv3o70zOMQF9frPoQi8LzpQd4vY7/Cznrr0EJB6EgI98tudJE6HNc7+m2X7JDb7Wbjxo00NTUxbdo0Jk+efEJqYXvtdhY8toCHVzw89GmFs9SVcLJQIIRA3iXj/cSLCAisS6yYF5i1Udp9qLm5ubNzAECv17No0SKST+b9VFX1+7474ODezHv5RdYverx24MABtmzZohkbffghuiee0GoOeklPBINB8vPzcTe5ybBloN+uRzJLmJeYKfGWUFNbQ1paGlFRUeTm5CBklZmNs7FX22lzf0LsiDRCbVqtEarWjum8wYlk+WLCQRgMBqkwGHw91B8cVB5tYkNJOTqdhNlkwBPwU+k7QiChlsuTLmPPvmoiIyzMe/S/xEgheLk9xNzqgsi+pyIqikrJtkoOH2lk+tThuNd+iqeukfnfvVEzMvrefbBpGxS/1xl1qGyt4q5PfsPjy/9Igv1EH4O+agqcTifPP/88F1544cnld3tRoDSA94NeoKBcxv2yG8PIrtxqXxIhged1D/IhGftKO+tNQwsFcpmM+zU3hmQD9mvs6Cwnb9Wrqio7d+5k7969JCYmsmDBAqzWrvM7qzUHZ8HH4GShQGlU8K7xEioPYZxsxHaebUBr6w75fD7y8/NpaWnpXDZz5kwmTpzYd1Hi3/8O998Phw+Ds+/f0866nUyOm4xBd2JnSce45aTERNJmzMDQT6QiFApRVFREXV0dadPSiN4bTXBHEP0wPYdGHuKA6wDz5s0j8bHHyB05Ejl5ODM8M4g8GIlrjItoQyShAwqIEOiM6BP1OG50oLPqvnBwEAaDQSoMBl8f9QcHx6pbKNp0EEWotMgtOE12HCY7GdOHo7v+bjbfeQctZhtjoi2kzp+Azdqemw4EtKf+2Pbpfr/4CygKLfd+n+LSw7haPcyrrWD4LRfz4ORs3DX1mBx2frA/F2ukE6rrYERSr+db5aolpCqdkYO+oCAmJoaHHnoIk8mEzWYjNTWVUaNGnZKffaAkgHe1F/N8M9bzu0HBQRn3q24MCTKOt29H+s+/+nyyE7LA/ZqbUEUIx9UOivRFQwoFwR1BPO96MI5rbyPrB1j6U21tbaer34IFC0hK6vr3+Ny7Fc6QTgYKhCzwF/jxr/eji9BhO9+GccLJ2R53VygU6iwO7FBKSgpz587tHVqPHoXNm+HSS09qJkhBZQH/r+j/8eIVL3amFUCbqFhUVER0dDQZqamYd++GpUt73YeqqhQXF1NZWcncuXMZbR6t1VDUKLQNb6PUUkrqqHhG1daS63Dg9/tJFanE7IjBK+8jKuRHts4CvQBVQhen08y97F8sOAiDwSAVBoOvl/qDg4dyXyKqaRQmnRGTwYjdZsbl9jPP18CozJkc9Evs3leNLCuMiHeQMi6R+JWr0E+dAI/+ESEETU+8zkFbNBX2aCKcFhaWrCequorN0yazcW0p9pkzsTntTJ0+jvHzJmIx933hXf7qt9jXWM66658nzhA9YKFhW1sbO3bs4NixY0RGRjJ9+nSSkpIGbB/rhIJuU+UA5APa07hxrBH7mH1IP/sRvPsu9NbuF2xvETwawnGtgyJpaKHAX+zH95Gvy3BJNzgo6Nyf309xcTE1NTVMmjSJadOmdd7EOuBgddlqdt2xC5vx7LUTngmdDBTIB2S8H3pRXSqWdAuWDMugQQt65v87FBcXR0ZGRr9Drk5GfZkggTYXIT8/H3NLC1n/+Af2TZugj5kOQgi2bNlCWVkZ06dPZ9LESchbZXxrfYSUEPti9hGVHsX4CePJf/99XJLEVHsqsZtika0+nBMikbcp2qABBXTROpw3O9E5vzhwEAaDQSoMBl8/9QYH/2/jY/x03Z/5vwX3Msk3ByG09eJjndQ1uBibEsfslBjUljYOPfIaB6fNwO2MREJgN+rRmU14fUFCiorVYmTS+GGMGxOHXqfD6wvw9rOfoIuJxVVczNjRI2iNHwZ2GxPHJzJ5fCIGw4lPUh01B2pAJfGdOIrXn1xNQWNjI9u3b6e+vp64uDhmzJhBXB/1AP7NfnxrfCdAQXB/EM/r3Z7GDf2kDwIC98tuQjXtUCCGDgqEEPhz/fjz/ZjTzFi/YT25vvmT3Pf+/fvZsWMHkZGRpKWl4WwPbQshaPA2EG+PJ6SGeg1nn5aGaLriQFCgtqp4P/Ii75MxjDFgW25DHzu4VFRv6gjxd9x3bDYbWVlZJ15rhdBcEMeOhZ/9bMD99gcHLpeL/JwcQqEQmUuWEBMT0+d+uo9t7ihgFF6B71Mfwe1BWiwteKbUMPG68yh8/HGaDAamxE0hpjBGK3RN9BCsjAYRBJ0JXYQO5y3aVNEvAhyEweAUJUnSncCdgA6YFAaDr5e6w8FVf1vOq22rO2cftLb5yC3aT0gRKIrKyOQojtW0ElFfR9rq94j4zjWI+Bhax42jodGNxxtAVQVWi5FYh4lYvwfdmJHg9eENqXySuwd3XSNH/vQnho0exq3vPUVgz0H2miMpO1SHzWoibd7YzjHM3bW36iCzz70E/8FAj+UDFRoKIaipqWHHjh20tLQwfPhw5syZ0yOH7t/kx/ehNvLYem43KNgbxPOGB+NEI/bUo0h/+D08/DBER594HL/A9ZILpV7BeZ2TQqVw6KBAFXg/1IySrOdYsaQP0A43SDU1NbFhwwb8fr8WZh49uvM1d9DNsmeW8Z253zmzaYWjR+GBB+Ceewas0j9Z9QcFQhEENgbw5fmQzBK282wYpxrPGGR1V8dTfDAYBMBgMJCens6wYcN6rvjb38KoUfDNb57UfjvgYPn45bx61as9XvP7/RQUFNDa2kr6mDEkDeANUVZWRmlpKaNHj2b+/PnodDrkCpnWt1qRXBItSdWMvG4CG0o2UldXx+Thk4nMi8QaMGDR7UMWM8AoQQgkh4TzFif6aP3nDgdhMBikwhGDr69UVeX227/D441PcEnmObx9x6OdF0a3J0Bu0X78gRCKojIiKYrWhlbcsiBpWCSL5o1Fr2t3Ncwrhlffg0f/CC+/C7feA007cL2ymryQDY/DTtnPfo5cV8eV/7qfaauu7TyHNpefjSXltLb5mD51OBPHJXSew5kwLxJCUFlZybZt2xBCMG/ePIYPH94FBcc9dQd3B/G86cE4pd0bfu2n2gX7449P6BFXfe1mQk0qjhscFAaHEApCAs87Wvuj7UIb5tmnF44eSLIsU1JSQmVlJSkpKcyePRuj0filqTnoDwrkChnvGi9qg6pFipZYT87G+DTk8Xg67Yw7NHv2bCZMmNDPVgOrsLKQSEsk0xJOLNgMhUJs+Ne/qE5MZM78+Ywb13d7LXRFN4YNG8aiRYswGAyIkKB2dS3G7UZki0xkSjlbDLUck2UmjhiHoyiCKF805llm5K0ySAoIPZKtHQ5iNTj4xr3fYO32tfxzxT87pzOeDYXBYJAKg8HXW51w8MQTPP3fv/SoOfD7ZfI3lNHm8qEK0TlHob7RTYRJx4z33iUpKQpp3gx4+Gl45d/g8iB27ufoxIls3n4UU9DPjh//lEB1DVa7jXsMegy7PoO4rvCmoqjs3FvFvrJaEuMjWDAnBVWR+4SCNz94k6yFWaf0Pv1+P5s3b6aqqorZ+tnE7Y7DvMiM9ZxuULAziOdtD6ZUE7ZLu+Xte7GvVb0q7ufdqG3tUBAYQigICtyvuglVhrBfYcc0+cTR1kMhIQQVFRWUlpZitVpJS0sjOjp6aODA74eKChg9GgYyBhpAfUGB6lE7Q+T6EXpsy20Yhp3hlEg/kmWZDRs2UF1d3bls3LhxzJ49u6tQtrIS3ntPa9s8heiFV/byu9zf8ausX/VIK6i7d7O1upqyxkamTJnCtGnT+o2K1NTUUFRURERERA+TpprdNfhW+4jyRaFvKeTAlUkcPHqQ8WPHY15vJrklGb25AsUVB1YrKDokiwYH/634L3esvoPZgdls+eOWsxo5CIPBIBUGg7D6K0iUZYX1mw9RW9eG3qDDZDQwac8OjoT0NIwfj1NSGTEhmehIG3q9DpfbT+XRJppavIxIiiK0qYg9e6swjxxJtEnigjgb5hsv7fU8auraKC4tx+/384+//431G0t7vB4bG8uNf72Rd1vfZd0t6xgdNbrX/fQlIQTHVh/DXmqnKrGK5JXJRMdo6YHO6YnT24v5tm2FJ5+Ev/xFu9B1/7w87VDgVnHe6KTAVzBkUKB6VdwvuVEaFBzXODCmnHqV/Omqra2NDRs20NbWxowZMzqfcu9afRePbH6EXXfsYkr8lNM7yBmyRO4LCgLbAvg+9oEE1nOsmGaZhiRtMJCEEGzfvp19+/Z1LktISCA9PV1zoVy9Gq68Eg4ePCU/hy3VW1j81OITTJA6jrl/71627djB6NGjmTdvXr8tvU1NTeTn52M0GsnKysLR7ofQUN/AwXfKGFc7Hr1NT92UOra1bWNM8nCkLTCuZSq6yDZUfwQoQAhkvcx58nlkL8zmgfMe4Mc//vFZTSuEwWCQCoNBWNA/HKiqoGRbBeWVjVgtRvx+mSl2iJ85gcOVjdTUtREIajPqdZJEgreNiZOTiSzZwtsiAmG24N25k+jMdAwGA7NnjGTU8N4LohobW1m2/Ba2b9/ZY3lH+iA6JZrsp7MBThkO/Bv8+D7xIc2V2GTYRGtbK9OmTSPFl4LvfV/P6YnPPquBwccfQzfbYNWl4nrehfALDQo8QwgFrSquF1wIX7vFcdLZe7o9XoqisH37dg4cOEBycjLz58/HZDKRV5HHkpQlp38Atxu2boVZs/qcGzDgLnqBAhFqr8vYEsQ0w4T1XCs628m3sQ6VysvL2bx5c2dRot1uJysrC6fFAqoKg+hc6MshEYBLLqFy3DiKMzKIi4vrApE+5Ha7ycvLIxQKsXjxYm3MM+0zNz7dwMSj44l2xeIb4WWjuZikkXEo5TomHZmEPkYPTX5U1QBCh6JXiL4xGuNo41mvOQiDwSAVBoOwOtQfHAgh2FdWy/bdx3DYzXi8Aew2E+N0MhOffZ7A0nTUe/+C+e3/oj//Rlof+TN5bRJtRgMVv/0dCa42bnjjMbbY4zla1cyEsQnMTB2Brlub3cnWFFS2Vp4yHHRAgSXdgmWZBVVV2bVrF64NLqbWTkU3U0fExREnWDV3D+eqbSqu51wIWeC8yUmBa+igQGlQcL3gQpLaLY7PYKX86aiqqori4mL0ej0LFy7URv8Cfyv6G5GWyM+t5qA3KFBbVdyvuVHqFGwrbJhnDW1dxqmqvr6egoICZFkGwGg0kpGR0fmZDkbd4eCjGz/CpG+/+a9ZA1FR1I8fT2FhYadls62fuRQdBYxtbW09iiU9Hg95az4kqjaCye45qBLsjNmJfpIeudzN1CMz0Ps8YIxA0hnQoQM9OK51YBx7duEgDAaDVBgMwuqu/uAAoKqmlY0l5RgMOhSPj6DeQEz1MUaNiCXSqENJnUh1o4fyygYcNjMJkSZa9pQR/8rrTH/o14gxIykrr2frziPExzpZNH+s5rbYj6Ph/fffz/XXX9+j5bADDs4bdx6PXvRov+/Jv96P71MflgwLlqWWzpt/R6tiVVwVB4YdYO68uYwcMQKefhquuaZHsaHSouB+3g0qOG5yUNA6dFAQqgrhftGtVXdf70QX8fk/4XaX1+tl48aN1NfXM3XqVKZMmcL3P/o+/9r0r8HXHNTUwFNPaRX5x1frD6DeoEAul/G86UEySthX2jEkf37Rlv7U8WTudrsBbSDZXFlm7AMPwKZNp1Rn0KGCygLyK/K5d/G9vb7e1tZGXl4eQggyMjL6bWcMhUKsX7+empqarkmOdEGDr8nHouAi9OV66hx11CXtx9XSzOTWTOxBO+ZYM6Kx/Z4rgf0qO6ZJprMGB2EwGKTCYBDW8RoIDtyeAOs3H9JGIetCqLEx1De6UFXtt2W1GEkZFUtDo5vGZg86SULSScydOaozhVDX4GL9pkMYDDpmT0vmupvu6jVS8MEHH+DxeGhqamL27Nk9KqurXFXEWmMxG8wIIXrNGfuL/Pg+82HJtGDJ7gYF7QZB5oVmdFk6SktLOXr0KCkREcy+6iqM770H2dkAKE3tUKADx40OClqGDgrkQ5rToj5Rj+NazWb2iyhVVdmzZw+7d+8mLi6OtLQ0frz2x4MvSNy+Hc45Bz77DGbMOOnNjoeCtBFpBIoC+Nb5MIwxYL/c/oVIHfSnYDDI+vXrqa2t7Vw2sbaWGd/+NrrTLMRcfWA1S0Yv0dIKtbWwahXcfz++SZMoLCyktbWVefPm9WhJPV7dJzlOnjyZ6dOnI0mSZq28bh21jY0ssk7DdiCZUCBEQVQB7jg3adULiXPFo2urQESMRhuwALZLbZhnmM8KHITBYJAKg0FYvWkgOFBUlb37a9hzoAYJiSSrxJgj5Zi37sRjNLNrxly8NjuL4wxEeFyUJo7myLHmHoOUPN4An+bu4r5f/Jrdu/f02H/39IGqqmzdupWysjLGjh3L7NmzexRPbanewrff+zZvXP1Gj7RCJxQstmBZ0g0K2iMI3bsShBAcPnyYLVu2YDEYWJiRQWxsLEqjgus5F5JRwnmTk/ym/CGDgsA2bYCTYYwBx0ptpO0XXfX19axfvx5JkkhLS+M3xb/h35v/zVvXvMVlky8b0mOfAAUJaVpL5z5Ziw5lW07bEfJsSVVVtm3bxoEDBzqXdbQNGvtwLhxIjd5Gxj40lrlJczUTJJ1Zs12+917IzERRFDZv3kxFRUWPG35v6j5eeuTIkSxYsAC9Xo/a2krJQw9RPmkSsl2GrbBCXUGzo5GjvjU4IhcxpmkcukhQW7v2Z73AimW+ZcjhIAwGg1QYDMLqSwPBAYDL7Sf/w1I8kh5h6ArXxrU0MbdyH5EN9bB9L2Lty501CiOHR7Ngdgp+v5/ll6wiv/DkfAoOHTpEaWkpMTExpKend7ZS9VZz4C/041vbCxR0LD8urQDA0aO4IyLYUFxMS0sLiyYvwv6JXWu7utFJfuPQQIEQ7R79OX6tAHKFrd8pfl80+Xw+1q9fT1NTEzNnzuSDhg/41pxvEWEeuuvJ8VCwwLIA92tap4j9krPX0nmmdfDgQUpLSzuLEp1OJ1lZWdjt9gG27F39OSRCe+3Qvn1s376d5ORkFi5c2C+IHD16lI0bNxIVFUV6ejpWqxUhBM988gy2Fhu1xlpuGnMTgQ/96EJ6qlOO0uxvY3rtdHRWEJ6u77Uly4IlS/sNDxUchMFgkAqDQVj96WTggLLDhHI20LwsC9lmw+mwUPyXf+Gpb2TcOZlMylqIIUGblHi0qpmNJeVYzDr+/Oc/kV+4uceuoqKiWLduHbNmzer1fBoaGigqKkKSpB750e5wUDi1EMsG7aJjXdJ18/bl+/Dn+DsvSD2gQFVh+nRYsgTln/9k+9rtJG9KRufQEbsqlvz6IYICVeBdrVXNW5ZYsCy2fC5tdKer7l0Lo0ePZu7cuRxqPcTGoxu5aeZNA+9g71646SZ47jmYPLnfVY+HgrmuuXje86CL0OG4+otTqDlY1dbWUrh2LaH2qJjRaGTx4sV92noPpBPgoKIKWlth3rzOdaqrq9mwYQNWq5XMzMzOFsXe1NTUREFBAZIkkZmZyctlL/OzN+9gdc0VVC+/hviEBGanzqbuzTri6uJwR7g44ChjemUKBp0VdF3pEdNcE7blWi3PUMBBGAwGqTAYhDWQTgoOOqQoUFPHP7OvoelIFXqziZ/XbsFg6aoIrzxaz/JLVvUYMAMaFNx7771kZmaycOHCPnutfT4fhYWFtLS0MG/ePFJSUrT9tlby7H+e5c7AnT2gQAiBP8+PP8+PJduCdXEfN/X168HhIBQ3BfcLbgKmAEXxRRiTjVxbeC2LRi46s1AQFLjfcBM6FMJ2kQ3zzC9W1fxgVFFRwebNm3E6nWzUbeR/C//35GoOKivhD3+AX/xCswXuQz2g4PqPmHlgJoH1AYxTjdgvtn8p0i8nI9ehQ+Tt3InH7we0osSZM2cyYcKEQYFjQWUBP/3kp7xz7TvEX3a9Nlhp9eoe67S1tVFQUEAwGGTRokUkJib2uT+v10thYSFNLU3848g/SJu8gAeeqaHhllsoDAYxmUwsWrSIw3nlJO5OxBwyUR5bQVIwAZvLqZUbtN+KjZON2K+wg+7Mw0EYDAapMBiEdTI6KTj49k/htQ/wBYL8pf13NmL4MFYdLOhcZaCWxNjYWDZu3EhMTAyZmZl9hjUVRaGkpITDhw8zadIkZsyYgT/fjz/XT9OcJsZdqBUpCiHwr/PjL/RjXWbFktF/MVfomNYRoIvR4bjewUfbP6L1cCsVagV3Xn4nDsvgeuyPl+puNy5qUnCsdGAcd/aNi4ZKLS0tFBUVEQgEKNWVcv/W+8+IQ2J3KPj0yk+ZsnEKoYoQ1m9YMS80fykjLf0pGAxSWFhIfX1957Jhw4axcOHCQU1o7CjQrdu1CfuIMdgjT4xABAIBNmzYQF1dHampqUyZMkWrwVEEaouK2qoivAIREOQdyqOmqoYUWwoJoxMYmzoWfYweT8hDQUEBfr+ftLQ0ajeUwLERjGoeRZupDbPehMVn1aYyavYn6EfqcV7vBOOZhYMwGAxSYTAI62Q1IBzc92co3sLBuBief/tjABZcfgHLX3oY6BsKnE4n77//PllZms1xR393h+mLpY/KbCEEBw4cYOvWrcwOzSbuYFxnRCCoBPnhmh/yK+lXmEu1IUmWtD6gwOOBm28mdPf/4dqYgD5Bj/M6J3k1eax4cQXXjr6W5ZblREdFk5mZedpjc5V6BfdLboQqcFzrOKu2vGdLwWCQjRs3Ul1dzWHjYX6+/ef89+L/9g0HwSDU1UFCQg9DqQ51h4Lc83MZkz8GFLBfacc4+qsDVT304IOotbVsv/pq9u/f37nYbDazaNGiQfkdqEJl/mPziTBH8P4172K3OE9cR1XZt3kfDdsaSJKSiPPHIVpE5xP+QJJUL1KinlprG8eUYyTNTUJv03No/SGm107D7LfQYjhCDKNASJpLIqCL1SYzSjbpjMHByYLBF7tvJaywvsDS6XQ8+p//cNuqVXzzOz/jmefe7LnC//0MPn2Z2rQuS9ukFcuA/iMFf/3rX2loaOhs14qPj2fp0qX4/X7Wrl3b2eN9vCRJYuLEiWRZsog7GEftmFqMi7SbRIOngSm7pmAuNePP8vcNBQC1tchiFK6ieAxJBpzXd0FB+sh0Hr76YZZmL8XtdvPZZ5/1eT4nI7lCxvW0C0wQ8c2IryQUAJhMJjIzM0lNTSVFTuGR6Y8w0j6y7w127oSRI7W/j1MnFFRvY+O8jaSsSUEXoSPitoivLhQAKAq6UIhZs2axePHizuhZIBAgJyeHXbt2oarqKe1SJ+l48IIHSfp4Pc0piXhcTZ2vqS4Vf7Ef91Nuhn00jGk104itjkU0nzwUAAidDbXeTHxlPLOOzSLh3QTsH9iZtcfL7qjNHEmoJEoZgV8KICxdO1YbVdoebUNtVvnb3/7GD3/4Q+666y7+9a9/ndJ7HIzCEYPjFI4YhHWq6jdyUHGU9zOuoKRBu+Csynud6NSJ/aYPUlNTKSoqoq6ujvT0dJLbPeK727JmZWURFRXVY3shBP5cP/58P/J8mXxPPtHR0WRkZKCsUwhsCvAny594zfRavw6JwZ1BPO94MI7Xcp15x/J6LTTsOB9ZlsnMzCQ2NvaUPrfgLu04hpEG7FfZ0Vm+Hs8pHYVtHXnn7W3byU7J7rlSW5tW47FoEXS7DnVAwd7qvRSPKSaqLArzPDPW86xfqs6NMyGfz8eGDRt6pBY6PCT6czDsTSXrXuTT391K4ZULeOG8NVAMofJQr+sKBB6TB328nnJTOS8cfIEFYxdw3YzrtNeDAuEVyM0yrRWtmN1mjGrfwBYwBmiwNRARjMDpc6LoFPRqt3oiPZoF+GjDaUcOhiyVIEnSU0AZsKf9zwEhRO+f4JdQYTAIazDqEw7uf4hn73+I8vb17jiQx8pv/mhAm2NFUTonz6WlpTFixAhAuxjm5+fj8Xh6VGZ3h4KO2oGGhgYK8guYUjeFhLoEbBfaqB1X29mtsOnbm4i19byZa+6H7cOTLrGTV9k7FHQoEAhQUFBAS0sLaWlpDB8+fMDPSghBYEMA36c+TNNM2C75crUjngm53W6Kiopobm3m4aMPc8uSWwasOeiAgsbqRj6L+gxLq0WzNv4KFGmetDweaGmB9u+Zqqrs3buXnd0iK0ajkYULF3YC9clIqIIdBTtw5bmYKqae8LouTodpignDaAO6JB27D+xm957d7Pfux53g5k/L/9RrTUfH+ZVtLSMpEMX4uOnojuhQG3uPbISkIAgdOnTahMluq1kvsGKeZz4tOBhKMFCBEuBjwApEAavEVyT0EAaDsAarXuGgzcVDc5bTfLQGyengs5lTBoSC7vvbuHEjR48eZcGCBZ1ubB1FWE1NTSxatIikpCT8OX78BX6s51ixpGtpAiEELW+2IHYLDo4+yNQrp2K326lsreSF7S/w88yfd17MhBCdxYrmokew3j2bvKm2k2pJDIVCbNy4URvhPHs248eP7/MzEqrA97GPwKZA794JXyOFQiFKSkqoqKhgTdMaMuZncNvcdjioq4OXX4Zrr4WEhE4oiKyK5Gnj0xitRuxX2b+yqZc+lZmpQcErr/RY3GEs5W/vWgCYMGECM2bM6HdyolAFwW1B/Pl+1NaeN2vJKWGeZcY01YQ+oec+Htn0CA+ue5D7xtyHXWdnxowZjBs3rmtc9HFq+utf2Wgw4BkxgilTpjAxeSKhshAtm1swN5iROPE3INrzFd1fM6YasV1q48c/GdxUxqEEgzYgUQjhO6UNvyQKg0FYp6Pe4OBPCbNwtbl5xWLmoD/QY/2+oKD7/jZv3szhw4eZN29epze7oiisX7+e6qpqFhsWY95lxvoNK5ZF7VCgCrzveQnuCKI/T09BQwGKopCVldVxYQDgvX3vMSNhBvHF8QSKA1gyDVjcuRSO0XP+uytP2qegu1NdX65xQhZ43vIg75e1J905X6Mn3T4khKCsrIySLSUc8B4geWoyqxas0iYrZmRAYSHuqeNZ8fwKMqsz+bH6Yy3Fc5n9C2sPPaTavx+amiAt7YSXAoEAmzZtoqqqqnNZZGQk6enpOJ0nFhWGjobwfOBBresJBLoEHe9Fv8fT3qd55/p3TjBBemTTI9yx+g6+v/D7/GXZX9i+fTuHDh0iJiaGefPmnZDiA6C1FcXrZVd9Pfv27cNutzNr1iySkpJoeuw5KqQJRLcOI8rXy7bHSXJKOG518NPf/fSU4WAowWCbEKL3q9gXRJIk3QH8BEgCdgE/EELkn+S2YTAI67TUHQ6e/Pf/set79/IsUHfcegNBQYeEEJSWlnLw4EFmz57NhAkTAA0OKp+vJKoyCtdsF6Mu0vrdhSrwvuMluCuI/TI7pmmmzhSE1+tl8eLFxMbGElSCzPr3LH7h+QXL5eXYV9gxzzWTezh30OZF+/btY9u2bYwaNYr58+d3Pq2pHhX3K9pkP8eVDowTvsJFcoNQQ0MDa9atQQjBBdkXdFbYu4NuVj63km9Wf5PzxHknOFeG1VMdoLV169ZOt0S9Xt9j/oHqUfF95iO4LdhjW0N8EMtCPYZZsRQeKezVIbE7FPz9/L93/jvU19dTUlKCy+Vi3LhxpKam9tmt09raypYtW2ioaWC4YzjjE8bjMDioO1ZH49FGElrjsMl2pAF6A8zLzPzyjV+eEhwMJRgUCyEWnNJGZ1GSJF0DPAfcARQCtwO3AVOFEJUnsX0YDMI6bXXAwZOPP44Z8B73+slCQYeEEGzbto39+/czY8YMJk2chPcDL8GtQRpnNlLqL2X69OlMnjgZz9se5L0y9svtmKZ2tboFg0EKCgpobm4mIyODxNhEGl5uQBwW/Mr6K+677T5a1rzFEy//lD0rlwzavOjIkSNs3LiR2NhYMjIy0Lv1WjtioL0d8Qs62e/zVoeVcmNjI2Mnj2XixIl895nv8qPaHzHKNIqIyyMwTfxyWhufMT35JKSkwLJl/a7W3NxMUVERHo+nc9mI4SOYLk0nlB+Cbkygi9dhX2HHMKrn9/J4h8Rntz3bKxR0SFEUysrKOo3KJk6cyMSJEzu7J8TDjxCqFMhLb0WulFHqFSTRtQ8hqUg6HUIRPdIHAtFrqkE7eSjwFHDfU/dx5y/u5Lt3fbffz2UowaBUCDFn4DU/H0mStBEoFUJ8r9uyPcDbQogT5m5KkmQGuqOdEzgaBoOwTlc1NTWMGjWqc758h04VCjokhGDXrl3s2bWHdG86tmM2bJfYME03dS7PcGdgrbFiv7J3f/yOsbGNVY1ktmSib9bjXeFl8brF+EI+vremgavLbYzeW3NajoYNDQ0UFBQQF4oj9XAqOpsOx3UO9NFfbnveoZaqquRszKHhSAOjdrQy2rgCYnQkXJ+APib82ZGRAVlZ8Mc/DriqLMuUlpZSUVFBpC+SKTVTcAa7pRSMYF2mFfRJOknrAnnlFfjHPzpX6YCDrFFZrC5b3ScUdJff72fPnj0cPHgQvV7P5JjJJDclo+7ygzChi9ZhGG3AMNyALk5HQ7CB/W+9SO2oEegNBobFDSPWF4tltzZUSS/rsYQs6IUeqf1/fWl11GpuuPuGPl8fSjAIAv8EPgHyhRCeATbp2O5iIcR7p3SwU5QkSSa0h7OrhBBvdVv+IDBLCLGkl21+A/z6+OVhMAjrdHXVVVfx+uuvn7D8z3/+Mz/96U8HtU+hCGqersFUZaJxXiMTLtAsYUWofXmNieaFzYz7xrg+L16hthD1T9Sj9+rxfsNLysIUXt31Kte9cR0ZIzP46MaPzojNceuWVuQPZNxWN5HXRRKdHH3a+/w6qM3bxmf/eI9sZQXHnJWMunkMETHha9FgJEKCujfrMO3rCcl1MXVEXxhNQko3U6S33oLf/14DhG5pgF+u/SV/yP/DSUFB53GFwL3TjTvPjaXJgs/goy25DcsMCwmTEk5opxR+GfcuL+5tXozVRvSqHoEgqA8S0ocwqAaMISO6AdILl314GbmFuX2+PtRdCR0bKcBmIAdYBxT0VZQoSdImIcT8UzrYKUqSpGTgGJAhhCjqtvw+4BYhxKRetglHDMIaErW0tDB8eDJeb8+fhE6n48UXX+Saa645pf0JWeB+3U2oPERreivFdcWMHz+eWdNn4X3Di3xIpimtiZKGEqZMmcK0adNODHc2K7hfcCNkwZE5R9hTuwfHCAdX5VzVWVPgkT14ZS+jIvv26B9I/k1+fB/60E/SUxxZTJunjfT0dIYNGzbofX4d5Gpyse2xbUwMTuS9+Pdw2Vwk2ZJYnL74lNrvwmp31HzdjdrQVVzoNrnZk7iHFlsLACNHjmTmzJl9+h50rym4YfoN/LHgjzx3+XMnFCR2l1wh4/vUh1KloB+px7jASLWpmoqKchoaGxFAREQEMTExRJmjiKyIxLjPiOSXIAFUfQX+gg2YJlyBQTWiSiqKpGBUjZ1pBb/OT7O1mYAxgF7VY5bNKLJCbVotS5cu7fPchhIMjgD3A0uBJUDHZAkByGigsK79T5EQwt++3U4hxLRTOtgpqhsYpAsh1ndb/gvgJiFE/2PKCNcYhHVm1NbWxvnnn8f+nTuxuj0cO+71U4UDERS4X3ETOhrCcY0D41gjBw8eZOumraQ1pWFrteG4Wpsx0FEA2DEzoQMOlDoF1wsuJJOE43oHuigdq4tW4znmYXtoO/etvA/b3/9JzvsP862Vxn5NkPo8TyHwfeYjsD6AOU3rlOjooKipqWHu3LmdnRVh9VTboTbqXqojpIbwn+dh5vgUfljwa5wt0Uy3TmfKlCmkpqb22RL3lVdLC5xzDvz971o6oQ8JobUgeld7O+2F0WtpA+94LyVbSmhubu5cX6/Xk5qayvhx4zB0m0VyfKFh0ZEizn/+fOYPn8/7171/AhwoLQq+T3zIe2X0yXqsy6wYUgxdcH7ppfiFoPaf/6ShqgHLHgsJ1QkgoCqyiiNRR7CELEyon0BEIAJFUpB1MhbFgtpuaFAdUU1lTCVus+Y2arPZePrpp/noo49YvXo1ixcv7vcjHEow6PHkL0nSFDRI6ACFjkkUAq3EYyNQBHxfCDG4Idonf26nnEroZR9hMAjrtNQBBXv27OHjd5/ggyVX8S6w9bj1ThYOREDgesmFUqvguM6BcZR28VI9Ko3PNEIzVM2uYvoF0ztvGvv372fr1q1MmDCBWbNmoRzT5hHoIrVhSDqHrrP74LbRt5FhzCAlJYV527fTWlvBXMcLAKcEByIk8LzjQd4tYz3fimVBl+2yqqps2bKFgwcPMnXqVFJTU8OV9e0SQtC2oY3gp0FKKSX66mgWeAwwdy5i82aqJyTReqyVHTt2nNbQoC+9mprg3nvhrru0keC9SAQEng88yLu66np0MTocVzk6vQiEEJSXl7Nt27Ye9T/GYJCJR48y/oc/5MntT/ZaaFhQWcAFz1/QAw6EKghsDODL9SFZJGzn2DBOM574/S4qQgSCBGMW4fvMhwgIzAvM6Ma2EvjzA4Rm3o2uwYnL4sIUNGFWzcg6GaNqpNZRy4H4A/hMWvRRr9eTkZHB9ddfT3FxMWvWrBkQCuBzLD6UJGkaGiQsA7KAjsSiEEIMefVMe/FhiRDijm7LdgPv9FZ82Mv2YTAIa9DqDgWfrn6GeXOn82fHZHyhEGudDvJdPecKDAQHqk/F/YIbtVnVbFGHa5XTSouC+0U3wi/wLPNQdKCIESNGsHDhwk44KCsro7S0lOmR0xm2ZRiGYQbs12rWw8e3JNZV1VFcXExSUhKLFi3imPtYp0PiycCB6lPxvOohVBXSuiF6KXwUQrB371527NihQci8eV/fp992CVnQ+l4rYpfgCekJMm7KYNHoRdDcDOvWwdKlEB2NT/Zx24u3cbH9YpxWJ+np6URHh2s2uitUFcLzuqeHUZFptgnb+TYk44kQGggE2LFjB4cOHeqxXEiCNY1rSByV2KujYQccnDvuXF5f+jqedzwoNQrmBWas2VYkc+/AqzQpeN/3EqoIaUZF59gQDkHjukb0xXqCUpAaZw3JLckYhAGBIKQLsTtpNw2Ohs79DB8+nJkzZ3LJJZecEhTA0ILBMSHEwL6n2roSMBO4AvjFWQKDjnbF7wLrge8A3wZShRAVJ7F9GAzCGpR6gwKaW3l05EJqQyEknY7622/g4Uee67FdX3CgelTcz7tR3SqOG7qmDip1Cq4XXUh6CccNDvQxeo4dO0ZRURHDhw8nLS2t84Z7ZO0RbIU2fPE+kr+VjM50IhR0FBpWV1dTVFREjM1G5ujRVA93sOyZZdy/7H6unXZtn++7E1K87e2II/pvR6yoqGDTpk3Ex8eTnp7e5yjpr7qUJoW2V9vwN/j5ifQT7rz5ThaNXNTrukII7lp9F69ufZWHpj2EKWRi7ty5pKSknN2T/jzlckFrKyQnQzegFEIQKA7g+8TXVf1mBPvFdkypA7d3trS0sHfvXiorT+xmj4+PZ/To0QwfPrxHlKagooDEfYnEbY5DF63Dfom9E9qPlxCCwN8+xheYiy7CiOk8Ew22BuoO1RG1OYoYbwxHI48iCYnhbcPx6/1YFAu1jlp2D9tNSN81cWDevHkMGzaMiy666JShAIa++HC+EKLkFLc7JIQ4K8nFdoOjn6IZHO0EfiiEyDvJbcNgENYpq1coALjvz7z498c50P47u6e8iF/8v0f557+f7bH98XCgulRcz7kQAYHzBmdnGDR0NKSlBCLaUwLOrgvksWPHWL9+PcnJyaSlpSFvkfGu9hIcEyTPmEfK2BQ8cR4ufOnCPs2L6uvrKVizBofPx+JbbgEDWAxaSqDV30qkJbLH+qFq7Xwkk6S1I8aeHPvX1dVRWFiIzWZj8eLFpzz05ssu+YCM+y031aFqbuEWHrrpoZ5Q0NAAb78Nl10G3eZh3LX6Lh4reYwn5z+JyWVi3LhxzJo1q1/b36+MXngBbrwRvF6wat9b1aviecdDqKzr5qkfpse+0n5qrbHHjvHeWw/wtq6Jc+POP6H6X5Ik4uPjSUhIIM4ah6XAgnJYwTDfwD+M/+Cexff0WpCouBVcb7sQ5QKX+QD7p7fR5Goizh1Hak0qqqRSFlfG6KbR2GRbZ5HhwYSDlEeV09GZqNfrWbp0KRaLZdBQAENviVwJXCyEKB9o/W7blQgh5p7SwT4HhcEgrFNVn1AAsHs/qy+8lU3Vmu/hLR+/wOjFC/j+j37fJxysPHel9gSuCJw3OjtvtnKZjPt1N/phehzXOHq1xK2qqqKosIjpwekkHErQwpvnWamoqKC4uJjCtkL2mPfwzrXv9NmS2FJaSl5lJQaTiSVLlmC323m4+GEeWP9Aj7SCfEDG/YYbfbwex7UOdPZTSwu0traSn5+PEOIEq+avqoQQ+PP8+PP8bLRs5Db5Nl676bUTIwWlpTB3LpSUwJw5Pba/a/Vd/Hvzv8m9NJe6sjqioqJIT0//6sNVdbVmFb18OaBV/3ve8CA8Xfcw8yIz1qWnPmly3a9uIusPz/Pzt+7k9+f/lYMHD1JeXo7X29OaLMYTw/Tq6aiSyv6R+2mLayO/Kh+7xc7548/HoDMQCoXw+/3oa/WMPzQendCxa9guLR0gYFzDOMY2jaXeXk9tZC1TaqcgpCCqKqFKcCjxEMecXeXKVquVb3zjGwghTgsKYGjBwA5cDqwEXMAzQohPT2K7z4QQ55zSwT4HhcEgrFNRv1AA8PK7lPzkft6vb0LS67j0b//LzO/eiBCiTzh47PrHuDLtSi1NEKVBQeco5HFG7Ffae82ZgnbjaHirAcMuA3Vj6hh37TgMBgO5h3P57bu/5TuJ32HkyJEsSlvUb37f7XaTm5uLqqpkZ2fTrDb3qDkYdmgY3tVejBO00cx9nc9A8nq9FBQU4PF4SE9PJzExceCNvqRSfSqet7Wn2+cjnueXnl/y4U0f9pk+6EtCCD499CnnjjuXxsZG1q9fj6IoLFq0qNNK+assoQp8eT4C+V1zRySLhP1yO8bxp56WemTTI9z5/h38avy3+M2Nj/cYLNbc3ExlZSWVFZUkH0tmbONYmmxN7EjagWyQe9+hgNHNoxlfP54Waws7k3cSMAQwKkamV00nxhtDc0oNEQIMFUl4nV7MLjM+YytbU3YTMARQVa1OIjY2liVLlhAMBk8bCmAIwaDHxpIUA1wGPBWerhjW100DQsGPfgdPvIJn0VzaoiOJf/cTDP/vPvjezQB9w4Gk4/mnnue6W7T57v5iP76PfJhmmLBd1PeIYiELPO9pFdnBRUHyW/JJSkpCTpK58GUtffDo4kcp3VR6QqFizx0JuOcefPPmkRMTgyzLZGdn0yJayH4qm+8FvsdtwdswzzNjPd+qucadhmRZpqioiPr6eubPn9/paf9VUqimvTDOp/Ibx294quUpPrrxo1OGguP16OZHMQoj4zzjqK+vZ/r06UyaNOmr2fHx4YeojT7cwXNQjiqdiw2jDdgvt/dIq52sHtn0CHd8cAffT+vbvEj1tAPdoRD+mX6ODjtKS2sLbrf7BFdTvapnas1UhrmGUR5bTnXEXiJ37yTu/OuIL01Gp+iwX2Yn+FQRsmUmTbYmYrwxtCS0UBJZAgY6oWDkyJEsXLgQv99/RqAAzhIYfBUVBoOwTkYDQoEsw7V3wjmZEApBXjEsS4dbVoK9K+TbX+TghRde4JL4SwgUdXkC9HXBV1oUPK95UBoV7JdoMxKqq6vJL8in1FXKFuMW3r72baxGK0ePHmXDhg0kJyezcOHC3vPTt98OM2bgX7WK3Nxc/H4/SxYvIfhZEONeI+8Oe5ebb7v5jN2Auk+RnDZtGlOmTPnK3NwC2wN4P/BCLHxb+jYfN3w8MBSUlcH3vw8PPgj9jLG+e/XdPLzpYR676DHmG+azb98+RowYwfz5879yRZ2hu3+LO/ImhLm9G0MCS7YFS7plUHDa4VPwrOd8blzvQfrkE7BYeqwTqg7hftUNIbSIxNien6ksywSDQWRZZteBXSTmJhIbisV0oQnbNBuSqhL87CCeLfHoo/TYLrHhWu1CrVZpsjQR54ujPLqMsvhyJJ3UOfipw4PE5/OdMSiAkweDr3evUFhhDUIDQgGA0QivPQqf5MH+cqiqgZr6HlAAWlHTX266n++kfbvHclVVueH6G3jpPy9hPdfaLxTIFTKuJ1wIv8B5q7NzcNL+wH4eOPYAM+wzuG/0fZh02vIRI0aQnp5OVVVVZxj6BP3nP3DnnVgsFrKzs3EYHTQ93YRxvxH/BX5W3rJSs2I+Qw8WOp2O+fPnM3XqVHbu3ElJSUnnk9OXVUIReNd48b7jRZossdKw8uSgALSqe7O5R/V9b3po+UPcMe8Ovv3+t9mkbCI9PZ2amho+++wz2tr6vO5/6RTcF8SV/D+dUCDZJZy3OLFmDi5i1d286MblP0NKTz8BCoK7g7iedqGz64j4dsQJUABgNBqx2+3YW+2k5qYSb4knYlUExdI6vNtK8W+S8WyMxzjGiOUSC83P1hKsDeKyuYj1x3IgcSeHErQiw47f0qxZs5g5c+YZh4JTUThicJzCEYOw+tPJQIFavB1ltw/l/b2ItDR00QqmleOQIs3wk/thzCi442aEAF+ulUCxFdNsHz9ffS8PP9J/t0J3CSEIbA7g+9iHYZQB+5V2dDbtRtK9JfHxpY+zacMmEhMTSU9P74wQVFdXU1hYeMLyTnm98OKLqFfeQtsrHuQmmZ2jdzJz+UxiYmLYXb+bVe+u4uUrXz5lh8T+dOjQIUpKShg2bBhpaWlfyidf1aXift2NUqWg+4aOi3ZdxLbabWckfXC8uhckvnbVa5w34jwKCwvx+XwsWLCAESNGnNHjnU0JIQisD+D7rMtWXJ/UXuzqGNxzbV+jk7sf05/rx5/vx5hqxH5x/zU0gS0BvKu9WkrjSjttUhv/vGwEd1t+i5j7LcyLzASSA8jvyMhSEL3sxaSPZVvydtqi2wgEumolFi5cyOjRo/F6vUMCBeFUwiAVBoOw+tJAUCAEBPcZ8b5tAZ0RVB+6SCNqmw5UH1XWdex47FfEpYzgnLefwfO+A/mAEesyL+a5AUDwP3fez8NPPtNjv73BgQhpT6PBrUGt8+Dcrien3nwKampqKCgoOAECampqKCws7PQUMBi69WKXlBC85bd4b3wCyWbCvNJM4Z5C2traWLx4MV6j95RMkE5FNTU1FBUV4XQ6yczMxGo9/aFOZ0sd1fLoQHepjgtzLmRbzSlCgapq6SijccCoAWg3s78W/ZVVc1YRY9XqQjZt2sTRo0eZPHky06ZN+9KZSYmQ0EaLb++akWycasR+qR3JMLg00wlQ8NhjsGhRp5OiCLa7d+6VsSy1YMmw9Bmp62H/PU/r/pH0EiIoOPJcBbZjdh6LfZxLx19KwqYE/DY/Np0F1aeyObmUkM2Ft/3+K0kSmZmZJCUlDRkUQBgMBq0wGITVmwaCAtUl4fnQTqjchC42hHFYKzrfEXQGgSS58O2ORtFPJ3f1vfjUalbc/DiqS4/9Yjem8VoBk1xuwP2OnZ9/eC//zXm8x/67w0Hn02i1gu1CG+aZXcYrfZkXQRcEJCQk9ICD2tpabURyXBwZGRkYDAZEUOD92EtwSxDjJCO2i2zobDpkWSY/P5+WlhYWL16Mz+QbMjhobm4mPz8fvV7PkiVLcDgcZ2zfQyEh2q1xP9UiOFwMK95ecepQAH22K56MKloqKDxSyHXTrmPfvn3s2LGDhIQE0tLSvjRWyqpHxf2qu0eRoSVyD5a7Fw269uQEKJBlmDoV7r4bvv99rU7nFQ9Ki4L9MjumSX2bIwm5HSD2yFjPs2JZqKUh1D0VuNfZUVx6yuaXUbuvlkUNiwjqqrFYkggqITYP34wwuPG2v4+O73dcXNyQQgGEwWDQCoNBWMdrICgIlhnxrraDUNDZvajNJoTo+YSrj6yjfGM+oyZfCYCqVhF1mw19nIoQENhkwZdrxZAiY7/YzQ/u+12vBYnPPvgsFwYvBB04rnL0cFvrDwo61AEB8fHxZGRkdMJBXV0dBQUFREdHs2jcIgLvBVBdKrbzbZhmGJDq66F9MmIoFKKgoIDGxkYyMzMJWAJkP52Nw+Rgy+1b0OvOnNmOx+MhLy8PWZbJysoiKirqjO37TEr1qHje1VoRzYvMKJkKK14aJBSANhdg9WpYsQJiYk5p09/m/Jbf5P6Gxy5+jNvm3EZdXR3r169Hr9eTnp5OzCnu72xLqVNwveRCtLXfm/RoN+qpA7sY9qU+0wehECgKoTo97lfbjbqu6Zqr0JtUj4r7FTdKnaLZf7cDhNKk4H6gDCEMHDvXj2evhwn1E9gqrWeWfwpep4GtI7egODQ7ZiEEBoOBpUuXEh0dPeRQAGEwGLTCYBBWd/UHBUKAv8CKf70VfXwIpU4Aesw1azBFHEb/i2sRDS7kNw/gJ4uQD/I/+A2NtbsZXbmeb+z4GDFyFN4P7QT3mLEs9GFZ7EPS9d/K+MT3nuDmP9/cI8d6MlDQob7goL62noq3KxhbPxZ9oh7HFe1OhrffDsXF2lNs+wU1FApRWFhIQ0MDGRkZBK1BjrQeIWNUxhn89DX5/X7y8/Nxu91kZmYSHx9/xo9xOpLLZTxve0AF+6V2AqMCLH9h+eCh4DTVveagAw68Xi9FRUW0tLQwZ86cL+yEyw4TL9q7ACWbhEP3AYa0sVrIfxDqFQoCAc1iOS6O4J4gnrc9GJIN2K/qqtPpTUpTu/13sN3+O1kD81B1CPeLblRDiC3DNhHbkMToptEYpxsI7pFxGdvYFV1IQC+jOByoqorJZGLZsmVEREScFSiAcFdCWGGdtvqFgiB43nbgX29BF6Wg1BswTpZxLNmO+VcZqNdej3zIhOq1YPr5TUQkvIk+1kPGeb/GYLSye3gCQd0Y2p6OJFhmwn6JG+sSDQpAyzk++LdfcfcdN/c4J1WorHp0Fa998FrnslOBAoDExEQyMzM1++OCAkKhEGqriuUjC2PrxlIZW0lJSglqRHtXwO23wz//2QkFAAaDgczMTBISEigoKMDgMZAxKoOQGuJHH/2IipYBx5KctDo6I6Kjo8nLy6OqquqM7ft0JBSBb60P9/Oa+2PEdyLOHBQ0NcFLL2l/n6IkSeLhFQ9r3QrvfZvHSx/HZrOxdOlSUlJS2Lx5M5s2beq9G+VzkhAC/0Y/7pe6oECXoCNilR3Ds3+FoqJB7bfPSMGLL8KoUfg/a8DzugfjRCOOGxz9QkGoKoTrKRfowPktZycUyIdkXE824zN4yYsvYHTLBEY3jcZkOUhwu58mUxMHUstwOQwErBZUVcVisXDuueeeVSg4FYUjBscpHDEIC/qHAtUt4X7TidKgB51AkkLY5lWjtpkIlEWi+o5rSbSqmGf5MH/vXPZm/Z5ho5bibqvCGTUCQ4IH28Uy+tjeW/PkI3ru+ub/8d+Cx3os76g5GLZw2ClBQXfV1dWRn5/POHUco8tHI5kl7JfZcTld5Obm4nQ6ycrKwmRqD+EKoXUq2Ls84RVFYcOGDVRXV5OWloYhykD6E+nAma856DhWVVUV8+fP/1wHCCktCp63PCjHlM5eek/Ic+YiBadRY9AhIQT3fHQP2SnZXDr50s7l5eXllJSU4HQ6mTt3LnHtsxg+L3W0dQa3dCsynGTEfpkdySRp37tQSCvEPAX1130gWlvxPVVGwDVWs1E+p+92YOhmR57Q3hHRDhDBXUHcb7tpNlSzc/geFgYzMVebMc02ESjxU+eop46PqR0+DIEG9i7h4orlVxAbGXvWoSCcShikwmAQVn9QoDTqcL/uRPVJEJQwjA6hW/8xctxihNGG6cAHmH6ShT73HYi0oC5eTnCPmcBWMzqTj2rxFttfLCI2cQpGz14W+3ch5b/e42kcQKjgX2/BX2RFnyzzi/U/5eHHT6w5MFxlIOvCrFOGAtBm1ze93YRuv46W+BZG3DACo1O7+DY3N5Obm4vdbicrK0srWvvOd+DYMXj//R7nq6oqGzdu5OjRo6SlpSEixJAVJKqqSklJCeXl5cycOZNJkyadsX2frIK7g3jf92o2vFfYMYww4A66z2z6QFHA79d668/AgCQhBEVHijpTPS0tLWzevJmmpibGjBnDjBkzPpfCRNWn4nnNQ6iiawiSOaN93oEkQX09DCJ11C8UtLjxfALyPhnr+VYs8y397AkC2wJ43zvR/tu9wU3wkyDVEdU0ja9met1cRA0YxgWQ95mojqimLbWGIw316PR6VCHQW/TctecuJg+bzKuXvso1V1xzViMFYTAYpMJg8PVWf1AQqtLjft0JAkRAh2mGn2C5EVw6jCObsV2gomushPEpXTvM2wh//Q/Kv/6N57MElGYdH7x8Mwe3rUZvMvKjd5/Emt3zJqK26fC8byd0zIBlkR9Lug+k3msOkODZ557lphtuOqX3GToawvOWB9WrEsoIkVeTR2xcLJmZmZ0tiy0tLeTm5mK1WlmyZAnm3FztZnXJJSfsT1VVNm3aRGVlJQsWLECKkjrhYONtG4m3n7m6ACEEO3bsYO/evUyePJnp06efFZdEIbd3apQGMU5p79Sw6M48FAyBXtv1Gle/fnVnzQFo/2aHDh1ix44dSJLEjBkzGDNmzFlznFQatXy92tIeLdOB7WIb5hntgLJnD0ybBuvWQVbWSe+3PyhQ16zD/Z6KMmI29isd/XceCIG/0I9/nR/THBO25TYknYSqqtR+UItlq4WjkeU4s53EbEpEaVTQjw6g7DdzJKoC72wPlVXH0Ol0qKpKVFQU2dnZFNcUc+ELFzK6ZDSHPjx0VtMH4RqDsMI6RfUHBfIhI66XIxAChCxpULDTiISKbVkrjrQj6KJ1GhQ8+QqUH9E21OvBYkafZMCZtQ+D5wDLL3+SUeOWogRltu/ar4VKFUXzQdhjou2pCJRWHY5rXVgztbqDvmoOEHDrzbfyyiuvnNR7VN0q3jVeXE+7kBwSEd+JID4znqwlWTQ1NXXWHACdFzKfz0dOTg7+rKwuKDjOI77DuXD06NFs3LgRpUkh59YcbpxxI7G22EH9e/SljpvYzJkz2bt3L5s3bx5yl0SlTqHtiTaC24PYLrRpZlJDCQWHDsFVV2l/nwGtnLqyR80BaP9m48ePZ/ny5SQnJ7N582bWrl1Lc3PzGTlmf5LLZdoeb+uEAsmqORl2QgHAiBHw3//CwoUnvd/+oEBpVnAdmIGaNBnnzc4BocD3iQ//Oj+WLAu2FRoUuFwuDj59EMtWC/WJ5Yx98i6ic6K19zEBlP1mKmMO4fV/2gMKYmNjWbp0KSaTiTlxc5i+bvpZh4JTUThicJzCEYOvp3qDAq/sQy/pkA448XxgBz2gExiGhwgdMmHa9ya2qA1I45NR//gM8ksfE6q1oObsQYwdg250JIbkEMZJQfRRKhysQFx0G013vovaGstn7/6AuG9Ecc7WXYQWX4Vv5HUox4wYJwWxne9BZznxt5lTsYFzb72F0PqehWP9OSSCljbwF/nxb/Qj6SUsGRbMaeYedrL19fXk5+cTExPTI3LQ1tZGTk4OpvYxzNbf/x62bTshpQDaBbWkpIRDhw4xd+5cxo0bB8Cnhz5lQsyEM5pWADh8+DCbNm0iOTmZtLS03uc+nIaEEARLg3g/9qKL1mmdGu2tbEMaKThwAO66Cx5+GCZMOCO77K1bobvq6+spKSnB5XIxfvx4pk2bNiSuk4GSAN41Xmj/euvidDiu65okOlj1BwWhqhDul91IZkk7VkzfxxKKwPuel+COILblNszzzCiKwv69+xGfCYa1DkNOl4mbG4f7ORdCgVCsB/1hG0dGHME9yc3Ro0eR0N5ifHw8ixcvxmAwfO6FhuFUwilKkqQ7gTvRoiiTwmDw9VFvUCCE4OLXv8PStnP5VuPtYAAsKjqzQG3VYzvPg9lZTkiJw78lCvmgGSQJ/TAFvTMARgnVbSR0TA8hCePkINYlPvSRKkKBin/UEKlMRRepIFp9CBzoE0NYs3wYUuTj77cA5FZuZMVrt7EoeTYTN6bwyKMv9ni9L4fEQEkAf4EfERSY55uxZFjQWXsPFnbAQXR0dOfFrOMzys3NxWAwkK2qWKuq4LbbTgAD0G5AW7ZsoaysjNmzZzNm3BhmPDIDf8h/xmsOgM6ZD7GxsWRkZJyxm5nqU/G+70XeK2Oaa8J2rq0rv/wlSB/0pg44qPPW8erKV09IG6iqyv79+9m1axdGo5FZs2YxcuTIM5JeEGp7KmZTV5GhYbwBxxUOJPNx+8/N1Xwcfvc7bWbEAOoPCoL7g3hed6Gv2YXj9uHoUsf1fY6ywPOGB/mgrHknpJqoq6tjy+YtpOxLId4Tj0X5ELNaiyvmm0g6CV+UD/NhM8dEHk3jPdS2f/+EEJ0dQHq9/nOHAgiDwaAVjhh8vdRf+mD7mmpG7khFRsYYJUFAh84osPM6uiuX4F0fhbzXgi5awTzXj2msC51ZBWtXMZO48UcEzXPxzb0DEZCwnevBPNmL0BsIHTYgl5uQDALDyFCfQABdUJA+fA7vXvkfLAZzn1MZX3zxRa6+6mqCO4L4c/2obSqmWSasWVZ0EQNnDxsaGsjLyyM6OprMzMzOG63L5SInJwe9Xk92djY2m02z7u3FalcIwfbt29m3bx8zZ87EOsw6ZAWJQGfrpcPhYPHixVgs/ReUDaTQEa0GQwQEtotsmKZ0hZ2/rFDQISEEilAw6Aw0eBuIs53YleD1etmyZQvHjh0jMTGROXPm4HQ6B39Mv8D9hpvQoW5Fhmnt3QC9DUF65hl44gkNEAaAkv6gIFCqzTEwDg9gX/9bpIcfBFPvKQTVr+J52UOoJoTjKgeh5BDbt2/naPlR5tXNI8IdgeMqB9Ibz+CWlyPFOXCb3FirrNRNraVK2UFTKITaDtPDhw/vjGJ9EaAAwmAwaIXB4OujvqCgu3GRQGUv+xjHOCzJ4Ji2k9A9r+BdcT+SGsT66e8xvfxdpJgIeOxF+N0/YG9O1xTFjVsgEEQsXIj3MzvBnWbMu17A+uQFSPpuFzxZhm/9GC7Ihhsu73Gex0OB1WhpP8++RzY//s3HuWz0ZRgnG7EutaKPO7UwbQccREVFsXjx4k44cLvd5OTkIEkS2WVl2D/7DN55p8/Iwc6dO9mzZw/Tpk3DMdwxpHDQ0tJCXl4eBoOBJUuWYO/WVnmyEmp7wVmuH/0IPfbL7D1C3GcNCkpLYcECzVhqkO2KA6msqYy5/53L38772wlphQ5VV1dTWlqKz+dj8uTJTJ48uec8jZOQ0txeZNjUXgcioVl5zx4gEiDEoKFACIG/wI8/x495fvscg36mMKpuFfcLbtQ2Fdu1Nsq95ezatQuTMLGwdiEGlwHHRSBFOXG/6EaKlGhVW7HX22kZX8HB2AZcLlenN8TIkSNZuHAhOp3uCwMFEC4+DCusftUfFPjW2vCvtwICfZzKFKbwLu+ybvz7eA9Mw3vBnzFNU4i4sQ7ztyZrUABwfjb89kc9RysvnA1ZC5HMYF/hwTblAIHU6/C8Y0e0PzwpwSAHczZAfCzYerYc9gUF0I8Jkqpy25O3sSZuDY6rHKcMBQBxcXFkZWXR0tJCfn4+cnuxocPhYOnSpQDkJCfjSU/Xoga9SJIkpk2bRmpqKjt37qTtSFsnECjizJvrREVFsWzZMoQQrF27ltbW1lPaXnVpNwd/jh9LhgXnzc7PBwoARo6Ef/1L+3uINC56HDdOv7FHQeLxSkpK4vzzz2fy5Mns3buXjz76iOrq6pM+hlwh43rM1QUFZnDc5OgfCsrKNL+M04AC38c+7d9xVgDrny9EOlze536UZgXX0y5Un4pvhY/Pdn7G9u3bGZs0lsz6TIxeI86MBrjmGlzPtCDFSDQHm7HX23E3vcQB7xbczc2dUJCSkvKFhIJTUThicJzCEYOvvvqEAhW8H9sIbtduvrrYEGqjAcsiHy1NO7HsnYtkAduKVkyJbRAxQGhVCPjvC/CNxTCu6+k4WGbE844Dw2iZg65nWfv7v+GqqmVV7muMWDi7c73+oKC75Godd3/nD/znkyd6LB+oIPFk1NjYSF5eHpGRkT0iB16vl5ycHFRVJTs7G4fZ3K8BzZ49e9ixY0eP9sIWfwuugIuRkWf25ufz+cjLy8Pn85GZmXlSBj7yARnPu55OX35jSs/38mVPH/SlgQoSu8vlclFaWkptbS3Dhw9n1qxZ/UZlAlsDeN/vVmQYrcNxff+FfwBkZEBiIrz5Zp+r9AkFxxcOWg7Aj38Mr7wC2pNyDym1Cq4XXQiDYM/EPRxtPUpCQgIzx81E964OERQ4b3CitgRxv+JCSjbQ7G4lwuXEvyzA1qYtBFtbkdu/+2PHjmXu3LlIkvSFhIJwKmGQCoPBV1t9QoECntV25D0mQEIXraA267Ce5wVZwrfOgs5dTc6SHFxPPcANm2Wk0jXaE74QcOP/wKrrYFl618GaW2FUGjz7d7j8gq7l2/cg71NxH8nEKx3hqV8tRAkFSMlayM2rn0H66f+xZ4ydecGn+4UCpUWHL8+KvNeMFBPiF0U/5d8vPt1jnTMJBxEREWRlZfWAg9zcXEIuF9l//zvO996Dfm7C+/btY9u2bUycOJGZM2dy7RvXsunYpiFJKwSDQQoKCmhubiY9PZ2kpKRe1xMhzdY4sDGAcYIR28U2dPaegdTPBQpaWiAvT+vfH+LBUR1w8Nru19h/936iLH0fTwjBkSNH2Lp1K7Isk5qaysSJE3uMdO4+jrhDhjEG7Cu1Fs8BVV4ObW0wc2avL/cJBbLA/bpWx9BRONifQsdCuF5w4Tf52ZCwAUu0hZkzZ5JgTsDzggcAx3I/ymEXnk2xMBxaGltwep3IBx9i0yWzUSWJYFArphw/fjyzZ8/+wkIBhMFg0AqDwVdX/ULBuw7kMiMICV2EgurVYb/QTXCfCXmvGfMCH9aFLXxSU8zdj9/Otz1jufuvb2A2mBHNbYjv/g71llUwczqSSaCLUpCMaGF2VYXuedl7fgd5G5Hf+Aj3G06qKzfy1hMrCclebnzvKazPPcv/BQrYd/mCXqFA9Ur411sJbDEj2QTWTC+macE+TZCGEg58Ph+5n35KsLWV7AsuIGKAp/MDBw6wZcsWxo8fT+zYWJY+o6UlhgIOQqEQ69evp6amhoULFzJq1KgeryuNCp43PSj1CtZzrJgXmE+ovv/cIgVnwBL5VCSE4GjbUUZGjkQVKjqp/xu4LMvs3LmTsrKyTmvl+Ph4REjgecuDvLfL58I0z4TtfFu/OX5AM88yGHr+Vo5TX1Cg+lTcL7tRahUcVzswBsrgpz+FJ5/s1TnRtddF8M0gbaY29ozbw6QZkxgzZgyiUeB63oVkknDe6CR030N4Em5ATZFoq3fhDDgJzTnGhuZd6Dwe/O1RiA7Y/SJDAYTBYNAKg8FXU31CQQjcbzsIlWtQIDkUkCVsyz34C60otQr2qFxM350HTS1gs/JxdTErX7+bH8TfwY9jvo96xIzwHHchlQT6RAXTxCCmaQF0jm6/s1YX2K1gMCBXGmh7xUrdke188NLNSKPM/O+1NaSPnHsCFIgg+Ess+Ddqyyxpfixz/RqAdKzTT0Hi6cJBU1MTubm5REREsHjx4s4ZCn6/n9zcXPx+P9lz5xI5YkS/+zl48CAlJSWMHTuW+PHxQwoHHY6MFRUVzJ49mwntngCBbVovvc6p02yNk068GX2u6QNZ1qIGUVGnPCPgdBQIBbj05UtZOXVlv2mFDjU3N1NaWkpjYyNjksYwYd8ERHXXd916wcCWw5361a/go49g/fpebaD7hAKXiusFF8ItcFzXPop8wwb45S+1wthu6Q6Xy0VlXiWJWxJptbcif0Nm/JTxGAyGzgmJOocOxw0O5IOylpaIb8PXKnDINuQLZNZXbMRgMOD3+wGYMmUK06ZN+8JDAYTBYNAKg8FXT31CgQzuN52EKg0gQLIK0IF1mQffWjuSTuA48Cf0c4bBjZfDytsRIT3+nz9JW7EOk99Co66S5GEhDAvi0UWoSAaB8OtQGvTIebXI3uFgNGGeGcCS7kNnO/H3JldL1P1HRhI61n/2B95esIX//vlFrA8+gzCYkC/6DsE9JuQyEyhgnh3Asqj3fcHZgYPjBywFAgFyP/4YX10dS+LjierFNrm7ysvL2bRpEykpKSROTGTZs8v45eJf8s3Z3xz0ufUlIQTbtm1j//79pE5IZfTh0cg7ZUwzTNgusJ3YQ89Xt6ZgIJ1KzUH3bSq2V2BaY8IqtxfPGsCx0oFxwilATUkJbN8O3zzxO9AXFHTYKgtV4LzeiT6uczxpj/NramriwIEDBHcFSa1KJTg8SOx1sZis2vc3dCSE+yU3ulgdjqssyH96Ha91Od6RXkK1IeyqjeC6H1D0rYvRG43I7YWGqampTJ069UsBBRAGg0ErDAZfLfUJBUFwve5EOaZBAWaBziowL/DhW2dHHyPjuNLT+aQvFAh80IK/bARCGDFNC7AzaRMz/v001q37YH0vLXtvfYiat43A1b/Gv9GCpAPrOV5MU4NIf3gIKo7BY38G4L1nniXu42Qmz7waRQliTNRBXSuq5ADJjC42hGlqEHNqEF1E710A3TXUcJCXl4fD4TgBDvJeew2P3c6S9jHJ/amiooLi4mJGjhxJ6qxUnBatmNMddOMwOQZ9fr1JCEHZ+jJseTYsqgX7hXYsM3t/kv1CQMHhw/Cb32h/zvIUyVOFg9BR7aYq/NpvJagPsmfCHqImRJGcnExcXFyPGoRTVV9QEKrWjitZJJw3ONFF6uA//9FmKzz/PCGgsrKSsrIyWlpaGOMbw7jKcRinGXFc6uhMbcjlMu5X3BiSDDiudRBYW41vs5W26GoktwObzob/PD/r9xdhaW3F154+mD59OlOmTAH4UkABhMFg0AqDwVdHfUJBQML1qgOlpj18rBfoY1SMEwL4C20YhzVh/8M3kF74O8ybQWhzM55to1Gb9JimB7Bm+NA52383qkr1wd3cX/4aDyy7D7Oh9zYs1SPhW2sjuMeMcXIAe+srSA018MPbtO6DV1dx+3MmRtXHMXrCOcy+4iYSZo5DZxUYxsjo45WBurdO0FDCQcf0xePhIBgMkpeXh7utjaz584kZoN3uyJEjbNiwodMM5qmtT/GH/D+c0bSCEILAxgC+z3yEokJsjNpI7NhYFixYcIKF8hcCCgD27YNVqzSTn89hgmR3ONj07U3MS57X63rBvUE8b3qgvftUF6MjdGGI8oZyqqqq8Pv9mEwmkpKSGD58OImJiSc6U+bmag6Hr70GMTE9XuoLCuTD2s1cH6fHcV3XGGTltdeo37ePoxdcwJEjR5BlmaSkJCZ5J2EsNmKeZ8Z6QdeIZfmAjPs1N4YUA46VdgIb/fhyAjQlNWJqMGNTDbgtH7FxhA273Y7HoxUldp/s+WWBAgiDwaAVBoOvhvqCAtUv4X7FiVLffkOQQD8shD5eIbjVohUZzqlHuv9BxL0/xLcpmsBWO/pQBbZVURgS26+AqqoNSho3mpyKDSx/bRXLRi/izcv/1QUHx2ogIbZHjji4x4TnIzs6p4rjChcFrvWdLYmPDP8uL5yrTUm0xUVz987PsERFwHNvwr6DcP9PTvlzOBtwYLfbWbJkSRccBALk/+tftCUmknXBBcTG9j9E6dixY6xfv167eUwdzrJnlwFnpuZA9ah43vUQKgtpTnvLrByrPsaGDRuIj48nPT29y7zpiwIFXxAJIfjgwAdcOOHCXi2R/Rv9+D72df5/wygD9mu6Og+EEDQ3N3Ps2DGqqqpobW1Fp9ORkJDA8OHDSU5Oxmq1at0Xjz2muR12iyz0BQUdMGIYZdAcCnUhaqqqOFZdTXV1NbIsY7fbGTlyJGPHjkW/WY8/X/OmsCy1dO1nj7Yf4wQjtsttBP78KX4xn9phtTgbnViNVpqN71MyzIK9rQ1P+/2ge63KlwkKIAwGg1YYDL786hMKfBLul50ojXo6JpwYRobArBI6YMKW3oB5TAMkJxKq0eN5z4Hq0mFN2o05XSCNTu46yGsfwDd/BDs+gTEj+bg8n0vf+G5POEicDT/5Lvz49h7npzTqcL/pRHaF+GX1VRycKzoLDV+/8X/Y9fpqjHYb1776CGPPyYBHnoVte+Dff+jVfnggfR5wIH/6KfmyTIvPR1ZW1oBeAtXV1RQWFpKYmMjI1JEse+704UAul/G87QEV7JfYe+S7a2trKSws7CyklCU5DAX96Pntz+MP+bltzm3azINPvASLu2YeGKcZsV9i7+nmeZzcbjdVVVUcO3aMhoYGhBDExMSQnJxMUlISZrMZvV6PXq/nsdLHuGNNTygQQuDa6CL0aQh/sp/KSZW0uFpwuVwIIYj0+xk+Zw4jRozouPnh+9hHoDiAdZkVS0ZX6ii4I4jnHQ/GqUZsl9jw5/oJFAU4FnmQGF8yFoOJ+sWNbDu8DbtejycUAknqMRjsywYFEAaDQSsMBl9u9QkFHgnXy07UZr3m96mAcayMKksoxwzYL3Zj+v0diLLDBB76EF+uDb3Dg32ljD6ul9+IPwAf5cKl53Uu6oCD88cs5q3L/430WSGMHdXD3KhDBWUlDPuvjZiouZiu8OCYrF1QW49UkfP7h1j2mx/iTE7UVj4Ja9iBNJRw0NLSQk5ODna7naysLMztQ29kWaYgN5fm5mYWZ2cT30vbWHfV1NRQWFhIXFwco6aP4pznzmHB8AW8vPLlUzofoQj8uX78hX4MKQbsl9nROU8EqqamJvLz8zGajDxU+xBF1UVfHCjYulXzMMjLg1mzPu+z4X/W/A//LP4nT654kqsOXYW8v6sd0Zxpxppt7TWq0JcCgQA1Bw9y7LPPqElOJqSc6ISpomIymNDr9eh0OoZVDWN83XiORB7h0MhDREZFEhERQWRkJMM+/BDH6NFw8cVA+8Cm970Et3VNSOw89tYA3ve8mGaasF5oxf9qFYEyOxXxFSS2JmLR6aja9yd2nbcIh8OB2+0GYN68eYwdOxb4ckIBhMFg0AqDwZdXfUKBW8L1cgRqi06DghAYJwVRmvWoLTocV7gxjgqhltfhzYlDro/DPL4G6y2zkZ7+f3Dlip4HCgb7HMTySXkBLYE2rpq8otfXocvR8ArLLB6Ofxm1woFthQdzarDPbQDIWQ8PPAavPgKWgSfOHa+hhoPc3FysVitLlizphIPQD39IQVwcjZMns3jxYhISEvrdT11dHfn5+cTGxpIyPYVoezSRlkiEECd141FaFDxveVCOKViyLVjSLf32z9c01fD+x+8jKzKp81PJmph1am98qFRbCy+8ADfcoLkAfs4SQvCzd37GBdsvYLbU7s4pge0iG+ZZp/5dBGDjRrjhBpScHJrMZkKhEKv3rebJLU9y4bgLuXrq1SiKgqqo2LfZcZY5Cc0OYV9mx2ptBxGfD6w9bcSF0uWlYLvEhnlG1/n5N/nxfejDPNeM5QIL/ldrCRywcCimjBHuUZjtZg7PPMT+6jIcNTV4EhMRksSCBQtIaS8C/bJCAYRnJYT1NVOfUOCScL3YDgV6oY1AnhokVGNAeHQ4r2vD+PHzKBVBXJ9MINQWg/1yF7YrTEhv/BsuO7/ngWobYPJS+LSg1/M4d0wmV01egSjZwfr//RGBoK/H691tjv/7nceIWCljmhbE+4GdwNYBLrCRTg0I/IH+1+tD/c1WuP7663nllVcGtV/Q5hQsWbJEMzzKzSUQ0M7R8MtfknnhhcTFxZGfn09tbW2/+0lISCArK4umpiYObTuETW/jYNNBsp/JpqKlos/thBAEdwVx/deFcAmctzixZvY/OMcddHPVO1fxu8rfkRiRSPOeZpqamgb1/s+4EhPhnnu+EFAAoDap3FdxXycUKHoFx3WOwUMBwMKFsG8f+hEjiI+P5+2jb3Nb7m3MnzKfey++l/HjxzNxwkRGHRiFs8yJ9Xwr8RfFY7PZNCior4fJk7WixXaJkMDzmgd5v4x9pb0nFKxvh4KFZiznW/B94MN/wExZ7AFGukdjNggOpmzRoMDhwDNsGEKSWLhw4VcCCk5FYTAI60uvPqGgTadBQWs7FMg6TNP8yIeNSDpw3tCGwVdJ8KnttL0ah2QSOK+px1SZo+34vCUnGq2YTXDdpTBnWr/nVLf2E0Y++g5XvHM3gZB2k+xt9oH0+AvY3vofzLMDeD+249/S80Lrb2njk/v+TKDNBbOnadGCqAgtvTAIDTUcZGdn94SD2FgMs2aRuWgR8cEgBfn51NTU9Luf+Ph4lixZQmtrK3l5eUiqxJHWIyx9ZukJcCCEILg/iOtJl1aQNtaA8ztODCP7nwDYvdDwlete4cLzLsThcJCTkzMgvJwVtbXBp59qf3/OCh0J0fZEG6JN+855jV7U61SM407DeOnxxzUDp/bfV2+Fhh03+eDOILbLbFgWHNdeGhUF3/oWZGYCIIIC98tu5HIZxzUOTJO1qJ4QAl+eD9+nPiyZFiznWPA+fYTA1gAH4g6Q4hqDOcLMvsDLHHLX4lBVPB4PAkhLS2P0aC0V+HWBAgiDQVhfcvUFBUqrjrYXnKhtOjC0Q8EMP8H9JvQRKs4b2tBFqviOTMBz6aMYJyk4b2hD/84rcNV3tchAb4qKgD/8FGKi+j2vxJ/cw+71T7C2Yj1XvHUnn5QX9D4QyWFHinJgPceDea4f3yd2/KUaHFTkF/OvWedT9MBjfPbrB7p2fqAcFl6idSoMQkMJB5GRkZ1wkJOT0xk50JeUkLFqFQkmEwUFBQNO6IuNjWXJkiW4XC4ObjnIp9d/CtAJB0LtihB4XvEgGSQc1zuwXzmwH39v3Qdms5klS5Z0RjaOHDky6M/gjKisDM49V/v7c1RwdxDXsy5oD1Lp4nQk3ZFEwpgEql3VvLzz1Oo/AKiogB/8ANauBfqAgoDA/ZIb+ZCM42oH5unHRSaamrRun1//GpKSEH6B60UXoWMhHNc7OqFFCIF/nTZG25JtwZJlwfu2l2CVgwNxBxjfNg5TlIldE3dxZMJwbIEAHiEQQpCent5po/11ggII1xicoHCNwZdHfUJBixYpEB6pJxTsNmNIDuG43AU56/FsHIlsmY41y4d5oV+r7xMCdu2Hacf1jgsBN/8Arr4ILj73pM/x4/J8Ln79O4RUhSUjF/LBVY/1OSVRCPCtsxLYbMX6DQ/+mIP8e85yZK8PJEmbvrhgFrjccOev4Hc/gpT+7Yf701DWHLS2tpKTk4PFYmHJkiVYLBaorEQZPrxzfkF6ejrJycn97qd77cK42eNY/sJyLlEv4ZfmXyKaBIaxBiyZFoyjT+7pdaCWREVRKC4u5siRIz0q0M+6AgGoroakJDCfRrh+kBJCENgQwPdpt3bEFK09ULJo6Zk/5P2BX6775Uk7JPZQXR3Ex/PI5kdPgALVp+J+0Y3SqOC41oFx1HH/tmvXwmWXQVERTJuG6tXWV5tVHNe3WyLTNX45UBzAeq4V83wzrtddyAdkyuLKGN86HoMtxHblTepGxGO2WPD7/QhVJT0jg+HDhwNfLSgI1xiE9ZVWn1DQrMP1QjsUGNuhYLqf4E4zxtEyjpUulCYdbTvTkI0TsF/SiiXNj7ShFDZu0ar/j4cCAG/7BfJkiv5UFRZeDO9+gllvQkIizhrNm5f/q3cocLkhvxhJAutSH+Z5Pnyf2rE0jiP7f7+vrSME79/5SxRZBqdDm9iYMkK7gXwB0wodkYNAINA5R4FRo9Dr9SzaupUkvZ6ioiKqqqr63U9HeiLgDdC6ppUiUcQvPL/AEG/AucqJ8wbnGYMCAL1eT1paGuPHj6ekpITdu3fzuTw8mc2a4+HnAQWqwPuhtwcUmGaYcFzfBQUA9y2+jzvm3cG33/s2j5c+fnI7Ly3VincTEnqHApeK6xkXaouK8ybniVAAsGCB5gg5dSqqW8X1rAu1VcVxU08o8K72EigOdHYltD1dh7w/yMG4A0xonYAh1sCWESXUxzkx19Xh93oRQpCRmfmVhIJTURgMwvrSqU8oaGqHAm87FAQlTNM0KDBNDmK/zI1So+B6IRJVisH5rQCmye32wg8+Ab/7R983WbsNnnsQ8Y0slFYd8hEDwQNGgnuNBMuMhKr1qL72i2YgCIsXUirVs+K121g8cj6Hv5dLlDWC3Q0HOmsOOvXUq3DRreDxdsHBfB++z+zMTv8ew2Zqtqu1O/ay4Z9Pd20XDMI518Hf/jvoz/Ksw4Gqov/gAxZt2UJycjJFRUUcO3asz32IoMC820zmwUxSKlJoNjVjusWE7Sobv9n7m34LErvrVMyLJEli9uzZpKamsnPnTrZu3Xr24aCyEu68U/v7LEoEBe5X3AQ3d3XIWLIs2C6xneBRIEkSD694uBMOHit5rP+d+3xw/vnw29/2mj5QmhVcz7gQfq149ITBVs3NcPQoOBxwzz2obrT1fQLnzU4Mw9qhQBV43/USLA1iu9iGaaaJ1hdakav1lEftZkLLBPSRCpuTNtFMAFNEBP6YGIQkkZmZ2RnF+rpCAYRTCSconEr4YqtPKGhsTx/4u6DAODWAvNuCaZYf27leQntk3G/a0VlD2G8Aw7BuMwcCAfD6ITryhGMqf3sTeVgGsn48oSoDhPqudJccKobRMgeidvGN9VcxZ8TUzpoCn+xn3H+WMTtxak+HxKYWcHlg9PDO/QgBvjwrgY1WgmMP8ehN80EIDFYLd5SuIXpMu9Xww09D5nyYlXpan+tQphXa2trIycnBZDKRnZ2NRacDkwlVVdm4YQNHjx1j0aJFjOg2lVH1qQQ2BQgUBxABgWmGCWWmQt72PHQ6HdMXTGfJC0uAgU2QTsfRsKysjNLSUkaPHs38+fNPy/P/lLRnj9aq+MIL0O7HP9RS3e0h/Np2TwEJbBfbMM/sP2ohhOAHH/6AtBFpXDf9uv4PsmsXTx37gG+t/1lPKKhXcL3gQjJKOG5woI86cboi3/wmbNoE27ejtArcz7tBgONGB/oYbX2hCDzveJB3y9gvtWOcZKT5mXrUWh2VIyoZUzMGKR6Kva/gjXagdzgIhEIAZGZmMmzYMOCrCwVhH4NTlCRJdwJ3okVRJoXB4IunPqGgoR0KAu01BSEJ48Qg8j4zloU+LFk+5D0mPKvtGEIHcVzmRpo8Sgv5/+IvcNu1MC6lx7FEQCKww0Rgmxm1sf8K977kk3zYZyg4FobQR2kQ0qtDYh8SAvxFFvyFNo65P+WNv1wNwNhzMrjx/ad79vUrCjS3QlxMH3sbWGcVDiwWWLMG9R//oPh//5cjVVWkpaUxPGY4gQ0B/Jv9oIJ5thnLIos2IAfNPS83NxeACXMncMErFwB9w8GZsDmurKykuLiYxMREFi1ahMEwuO/DF1kdN2bhar8fGMFxjQPjmFPrPBBCsLlqM/OHz+/5QnU1JCbySMl/TogUhKraxx07tXHHOkcf8FVbC+XlKOPn43pegwjnjc7O74ZQBJ4321sVr7BjHGuk8ZlGRJ2g2lTCSHUhUqLEhrgNBP0uaG0laLeD0cjixYtJbG8N/apCAYTBYNAKRwy+mOoTCur1uF5ydkGBImEYKxMqM2HN8mJe6CewwYQv34FpWgDb+R6kjoeRukY493r4w0/gom8AmhmSv9hCYKul18iAZFO12QoxKpJNRdKBCIHq1qHU6ZFrdOjU4592BMbUINZMH/pItXc42LoL7voVvPMExPacSujfbMa31s6BfW/x0Uu3o6ohLvrX/cxddW3XSnf/L5Rsh4I3B2Wb3HmmZwkOlixZgnXHDnjwQdT//Ictm/dh2GlgZNtIJL2kGdCkWXq9SXg8HnJzc1FVlYlzJnLBaxocFK0qYphjWOd6Z3L2QYcrY3R0NJmZmZ3Wz18FyRUy7pfd0J49kBySNsI4sZen9gH07r53ufTlS3sWJCoKzJzJjqlxzEjN7QEFHcfWx7cPQ7L28t394AOtJTEyklBtCPfzbiR7OxS0fz9ESOB53YN8SPMvMI4yUv9UPVKTRP2IoyQdHYUUH6LInoMSYUNVVeRgEEmSWJyV1Wm89VWGAgiDwaAVBoMvnvqCglCdHvdLTkSwHQpUCcNImdBhI7ZzvZhmBvB9ZiOwxYKl6B9YHr8YKe64UcCyDEYjqk/Cv8FCoMQCak8g0CeGMKUGMI6T0UWpfboT51Zu5NJXv8cPzdfxw8i7UeqTQOm2sk5gSfNjWejjk6P53PL+T/nsumeZGjdBg5Qf/gbu/yl0pAm6KbDLhOcDG8fKC1nzyrdQ9H7u2v4JzqR2J8Ede6GmDs49fee+oYQDl8tFwacFRAYimZ44HaleIlQdQrQJFIPC4ajDxJ8Tz+iJ/c9H6GiHDIVCTJwzkcd3Pc6fvvEn9DrtZjYUA5EaGxvJz8/HarWSlZWlDQAaKm3fruXjP/oIZswYssMEd2ozA2jPquniddoI414spE9GfY1sfufRH3Lvjn9w3sXdoOCAjPt1N4aRBhxXO5BMvfyw2tpg7Fi45x5Ct/4U9wtudFHtkYX2iYpCFrhfdROqDOG4yoEuWUf9E/Xo2nS0Tmoh7kA8DIdC/cdIrY2E7HZCdjtIEllZWZ1W3V91KIAwGAxaYTD4YqlPKKjVIgXI7VAgJPRJIZSjBmwrPJgmBvG870AuM2LLbsXcktN109yyE37zd3jqb4ioKAJbzfjyrBDsdjHUCUwVq7GwCf0//2fA8+zNvEj1SwRKzfiLLT32rYtUsF/oQU50YzVaOosR+0srAMhHDDQ9DwF3K22ji0n9dvaJNsFCwPY9MHPqwB9uPzpTcCCCglB1CKVK6fxbbdbuQiF9CNNwE8aoIIb/9xP031tB6cQxHD58mPnz53e6zfUlv99PTk4OwWCQJUuWEBkZSX5FPrHWWG7/4PYhGYjUYbqk0+nIysrC6XSesX33UHW1NnJ51SqtZfEMSwhBoCiAb223dsSxBhwrHUjm05/L0QEHz2Y+gNtp5o41d/aIFHQAiXG8EfuVdiRDP8c8dAhZSsb9qg99QntkoWOCY3uxZOhYCMc1DoiDhica0Hl0BCpfxznyOhgFeY58TFYTAZcLRZaRzGaysrM7h3t9HaAAwmAwaIXB4IujPqGgRo/r5QiQAQMgCfRxCkqtAfslbgzDQ7jfdKBUgyPjKMb04woKN5TCnx8h9MCjeNZFozZ0yxnrBOY5fiwL/OjMQc1+2Ono9zx7QMEFf8f6f4/At6+HCWMAbdSzf72FwGYLiI4LoMC80I8108c1792NR/bx5iUPYS7aBpPGQscApePkPeol8GEMNFuxLPBjyfAhdU95v/cJXH0HlK6GKRNO/sPuRf3BwVP3PsUVc65AeAWEtFCuCAlQtP/uWNYRnsYA+mF6DMkG9El6ApEBcrflYjAayF6yBOu//gU334xISKCkpIRDhw4xf/58xowZ0+85+v1+8vLy8Pl8ZC7OZPFLiznUfAij3sjHN348JAORPB4PeXl5yLLM4sWLiY6OHnijL5CEqrXyBbd0dR6YZpmwrTix82DQxxCCH7zzPe75zlM8NTVIy8+7oCBQEsC72otpuknrdujNtrq5GR58EH7xC+Qj4H7FjWGEAcc1XZEFERC4XnKh1Co4r3OiRCg0PtGIPqBHmatg3WxBJMvk6T7BajHibS94lSSJJUuWdI4D/7pAAYTBYNAKg8EXQ31CQXV3KBCgA32MgtJgwHGFC12Uivs1J8IPjtduxrBiCvz8Dm2nsgwGA0KW8OXbCJSY0eYvazJOCWBb4kO3b4tWxNdLSP94nRApqKyBS1bBcw+eYJusNOjxrLaj1HTdyfWJIUrnrmX5h7ewInE+r3+/BOl3P4K7bu3zmEIBf7EFf5EVXaSKNcOHcWJQq51QVfg0X7NzHoREEELVBkLHtD9Ko46fvfwL/ruhZyuaTtLxxPeeYOWyldrTngHtbz09/r9kkdAn6dHH60+4AbjdbtatW4fBYCA7O1sLzbe1IerrKW1p4eDBgz0m2vWlQCBAXl4ebrebJ5ue5IOjHzDMMYz1q9YPemTzQPL7/eTn5+N2u8nMzBxwcuQpy+2GHTtg+nStPe8MSQQF7tfdhA6GOpdZllqwZFhOaTriyejfm/5Nzl/uZOb5N3PHDf8g2hqNv8iP7zMf5vlmrOf3M5FxzRr45jcJvrYZT74dw5j2aIZRW7/DBEltVHHc4CBgCtDydAsGWY9eKkGvpqOOVsmz5GJvbsRtMCCsVnTtDpcxMVqR7tcJCiAMBoNWGAw+f/UJBVV6XK90gwID6CIU1GYDjpUuJLPA/ZoTySRwXOVCL5o1C+OOi8+qnxByTMQ95ceItq7CKl1sCPsFXgzD2y+W514PTju82X9fdm/pg4EkVAhssmipi47ogUll38KNLC28gusts/j37U9gPol9KQ16vGtthA4bkZwKlrkBTKkBdPb23/RHuRqcxMf2uQ/VJbVDgJHQUQNKnR6EhGRW0Q8PYYhXwKnw44f/l3+/+HSPbc9EzYHb7SYnJwedTkd2dja2W2+FQ4cQxcVs2bqVsrKyk3IgbHY389x7zxFBBM6JTn5S8BNg4FbG05EsyxQWFtLY2Kh1VAwfPvBGJ6vSUpg7F0pKYM6cM7JL1aXietGFWtdRUAD2S+yYpp/5QsrHc/7Ot3Pv4fsLv88PFv6Aef+dx3sj32PywcnavILsgUEkWNqGZ42CcaIR+xX2zmiG6lVxv+DWTI1ucOAKufC+5EWv6rFQipAXEhopk2crICo2mtbWVoQsozMYyF62rDPC83WDAgiDwaAVBoPPV31CwTEDrlecEKILCuwqwq3DcZULVAn3Gw50BheOtf+D7unf90gBCAV8T1QRaEmlM0qgE1gX+zDP83d1KoDmROjy9BnOh36gQAj6rE7splC1Hvc7jm6AIjgyfTcLd36Df533G741Y+WA+wm0ufjoZ3/kyOpdXHzPYzjlSaBKSHYVfWwQ/dvPoZ8RC5ech/DpED4J1Sch/O3/3apDbdWOr4tSMAwPaX9GhNDFKj0OP5QFiT3gYNw4bKoKU6YghGDr1q0cOHCAOXPmMH78+N63by803Fe7j//O/C+qT+tWuH3t7Tx+8eNMiR86HwBFUdi4cSPHjh1j3rx5A6Y+Tlo+Hxw6pBXenYEiR6WuvR3R3X69N7W3I6acxiCkPvRY7t8557J7KL0umyv/tRYhBB//52MWNixk+5TtLFnZTzTrP/+BpiYCK+7B+54X07Se6QbV3Q4FbhXHjQ4aXA0obyjohQ57poNQTgh5jEy+bh3RlYdpHjMG9Hr0ej3Z2dlERUUBX08ogDAYDFphMPj81CcUHDXgerUDCgCjQGdREX4djqtdCLcO9zsODEkhHMPzkR55DJ5+oNNOVtlRh6dkPEpdtxB+Ugj7hW70Md1Mjnbvh4S4Ab0A+o0UrLgFZk6BP/58wPer+iU8H9gJHex6YvOPayTx41+hi7Yj/vjzfp+qDn5awPMX3QqAyWnnewWfYGM4Sp325B+qAuFr37dRoLOqSBaBZBNIFhWdU8WQrMGAzjHwdeCswUF2NjajEZ59FnHrrWzbsYP9+/cze/ZsJkzoWTdxfPfBvGHzKCwspKmpiYyMDBITE/EEPTT7mxkRMfi5Ev1JVVVKS0s5dOgQM2bMYPLkyUNynMFKLpdxv9qtHdEp4bzBiT7+1NsRB9Ijmx7hzvfv4NX6bK780eOQMlZzIdwZ5K1Rb7Hq8Kr+Zyv87ncE3Cl4nRdjmm3CdqGt8zegulRcz7kQAYHzRidHqo9gXG3EICQcH/6Z4Lm/JjhGJs+YR0J0FPX19UiKgt7hYOmyZR03xK8tFEAYDAatMBh8PuoLCuQjBtyvOkFBgwKTQDJqJkbOa9pQ6gx4VtsxDvdgXxnozEF2KLC2Fe/6YWBsf+qS2qMEC/xIx3dkLb1GSz281XcKYcD0wbNvQEIsXJB9Uu9bCPAXWvAX2TqX6fVV7BP/5A9jDvLKpQ/2263w7nfvZcvT2jz6MdmLuGn1M0jdfAxEANi2A2nHLujuezBIDSUceDwe1q1bhyRJLDWbsV10ERQWIubMYfv27ezbt49Zs2YxceJEoO+WxFAoRGFhIQ0NDWRkZPCzDT8jvyJ/SNMKQgh27tzJnj17mDRpEjNmzDi9nP3Ro1rx3fe/DyMGDzSB7QG873qh/TKvT9TjuL4fE6HT0CObHuGH79zBdzO1QkMU8LzhQS6TsV9mxzjVyF2r7+LFnS9SdncZsbZuKS5FAb0e/0Y/vo99mBeYsZ7XVYOgtqq4nnchQgLHjQ72H9hP1LooDCYDjoU2AuuC+Ef7yDcXkhQXS21zM5IkYZAkss85JwwF7QqDwSAVBoOzrz6hoNKA+7V2KNADFoGk076vzmtcyIeN+D61YZriw/bTTKTrL4ZfaUOHhAzeT20Ed3TduHWRCvZL3RiGKb2fSG0DuD0wrvebx2BqCk5WwX1GPO87On0PAnYPS7zLGJ8yvF+HRH+ri0fmrqDtqDbG+Lw/38ui76/qudL//g3yi+GTF+AMuPYNNRzk5OQAkD15Mvb22gIhBDt27GDv3r3MnDmT4WOGDzglsaioiNraWibMmsDlH1wODG3NAcD+/fvZunUrY8aMYe7cuYO3UN61C664At58E1JP3e5aCIG/wI8/x9+5zDDegOPKPvwCTlOPbHqEn795BwefjiT2gUfgims1b4GjmreAcXzXGOTylnLGRo9FCKHd+FtaYOlSfHc8gb9mDOZ0M9ZlXVCgNCud9se2G2xs37qd5OJkDIRwTJTx747GN9ZHgaGA4Tt3UDVlCjqjEYPJxNKlSzuv4193KIAwGAxaYTA4u+oTCioMuF/vgAIBVgECdEZwXO0iuMuEv9CGeZ4P61If0hsfwMLZMDIZpVmH+3UbanNXiN6UGsB2rgeptzqrw0e1p3xb37nck4KCQ5VQeQyyFg7KfTBUrcf9uhPh07ZVcLNcupyEFGe/cFC+bj3PLr8JAL3JyLeL3iax+4RIRQE5dHKTIU9SZw0OlizB/s9/wuTJiMsu63wqLwwW8tSRp/r1KVAUpXPE8/iZ47li9RXA0MPB4cOH2bRpE8nJyaSlpaHXn/mQfX8SisD7gZfgtm7tiHNN2C7oozXwNNUxEOmeOXfx180xiBtX4c6L6ntsMiArMte8fg0rJqxg1ZQb8P9mDX7HUixLLFgWdxUmKk0KrudcSHoJ0zUmSjeWMm7HOAw2A47Cx/FNvx1Pipsi03pGjhrJ0SNH0IVCGC0Wlp57bqfPRBgKNIXHLof1hVefUHC4Z6RAsmlWxzozOK5tI7BZmx9gWdiC1fWuViS38kIYmUzwgJG2pyO7oEAvsK1wY7+wDygQAm79Idx6T5/nedKRgtc/gGvvPKniw95kSFJw3tyGLlqLaOhxsEa3hsBhHfes/b8+txuzdBGLfqBFCZSgzJu33kPI322Co16vQcHho3Dld6ChaVDn111DOZXRbreTnZ0NQE5ODp79+2H3biRJImViChuDG8kwZfBa9mv9+hTo9XrS09NJTk7mwNYDvHHBGwC8v//9QZ/bySglJYWMjAxqamo6/Q7OllS3Nra4OxRYz7FiWz60UPDDeXfz14seQvz417g+i+x/bDJg0BlIciTxs1e+TfEb2/E7lmI9x4o1q1ukoEGbtigZJaQrJTbkbWD8jvGYnCbs8+z4pt+Oa0wbRab1jDp6hKNHj6LT6zE6HGEoOE2FIwbHKRwxODvqEwrKDbjfcGoWrTptWqEISuidKvaVLvw5NoJ7TNjO82Je/xj8+gHY9RkiLhZfgZXA+q6nfp3dj+OaAPq4PlIHHSo7rI1KTp14wkunlD4IheBYbY8piYOR6pNwv2pHqdVIRpVU5POPMmxG3/3soUCAxzKuoG7nPgAW/WAV5/3p3p4rHT4Kt/wAnvgrjE85rXPs0FBGDrxeL+vWrUMIwdKlSxFGwUXPnE9pww5eXfIqbUfbSE1NJXWAULuqqhQXF3PkyBGmz5nO5HFacaBP9mE1Dp2tcX19PQUFBdjtdrKysrTBUSerXbvg0kvhnXdOOpUQqgrhftmN8HQUFID9Ujum1KGZ69ABBfdO+Q5/+FUO6l8exX1kDiKkFQfq4/qPlKhPPY3r/WbUWbeyNXUrS69Y2vmaUqdog5JsEsHlQbYWbWXm4ZkYDQEsW17DP+WbtI5ppdhYTIoEFYqCTlEwRUaydOlSHO3eD2Eo6KlwKmGQCoPB0KtvKDDifsPRBQVOFeGT0Meo2C934f3ITuiwEftFbkyTZe1p/1AlYkQK7nfthMq7LoDGiQHsyz1I/UXP6xohJrLPvPtQ1hQMJCGD+x0HoUPt70kSKOfUcn/TX/hz9k96TSvU7tzHY+mXoQS1J9Sb1zzHmKXHPVF3tFOGQlok4QyY2gw1HOTk5BBSQhQX/JmbntpA20fvMn/2hezevZudO3cydepUUlNT+y32U1WVzZs3c/jwYRYsWECRq4hfrfsVa29eO6RphZaWFvLy8jAYDCxZsgS73X5yGx47Bg8/DHfdBSfhjxDcEcTznkeLsgGSXcJxrQND8tBMguyAgu8v/D5/X/Rb1F8/iGvkXUgWfd9jk7tJqALvG80E98Kbo97itsO3UfStIv4/e+cdJ0V9N+BnZraXa9Sj995776IURYqAimCP3STGFE1iYkksUd8Ye1dQQUFQUUDa0Zv03vsdHFzbvjvt/WOuwu017gB1n0/8QHZnZmf3jp1nvr9v6V2/N8oZY1CSGCeSPTCbPZv20PVkVyzVLFgSswjtiyezYQabrVto3MRooS0KAlZRZPC11+Z/xjEpuJjYUkKMq5KoUnCkGCnwi5hqqjjHeAl850I5acY1zovlo3/Cyg0gCKgJjfF8ElcgBbqGXV+Cc0wpUqDrcPNDcMdjxT5dbikIhmDCb2DzzvJ/KMUgmMHVcTfmvXNzz1dAWlKb4FYz4+Y+mD9foTC12rVk6DN/AKDRwF4kNSvmgicIEInA6Dvg9Y8r51yrcFnB4XDQvW93zvjP0KDdrZhvmkr3ttcA0KZNG9q3b58vCCXd5IiiSPfu3WnSpAkbN26kudDciER8Mpjj2ccrfH6lkZCQwJAhQwBYunQp2dnZZduxbl34979LlQJd0wksCeCfVyAFUh2JuHvjLo8UDH8F1e/EW+8RRJcJ9zR36VKwaw/+WVlE9gs4x7q4c+qdzJk4h171ehlRj+nGoKST3U6yZ/0eup3shsWlYmkuEdoXz/lG59li2UyTpUs4euQIoihitdliUlCJxMQgxmUjqhQcvkAK4nKloI6CY4QP/9du1PMS7kkezHX8sGs/HDuFfMSM59N4tOzcLyKLhmtMBrY/di79RlgQ4Pk/w8N3XPRUhSIFWTkQkUGqvH9SQrMGOFvvxdI8I/+x5/UXaH6sQ1Q56PXwHYz/9P+YuuBT4uvXKf7AFouRIHmJg5aKnGsVyYEv4mPc1+N49sSzVI+vzZ4R4/FFInDsGMgyrVu3pkOHDuzdu5edO3eWKAeCINC1a1eaNWvG0T1HmTlkJkCVy4HL5WLw4MHYbDaWLVvGyZMnS98pGDQmLAaDUTfRQhq+L3yE1xX8Hlg6WnBPc1dJOSJcIAWd/4Iy7Ha8H2cjJom4ppZeBqnLGv43DiMfUHGOd2JpZ0EQBMa1Hod6WiXrkyzO286zt+VeTu08RffU7liqS5gXvENotUx6w3S227bTpHkzjgwdihSJYBNFhgwZEpOCSiS2lHABsaWEqiGaFEQOmfHPdRntgQUdIUFDzxExNZSxDwngn+NGlwXck7xIDh847OiqRnizg2CKnbwuhmLgJK5bZaTmCaWfTLYH4t3FhtGv5PJBNHQdgivthDcUrIe/KLzIrkYb+HbCu5dWL6/rRjJiCW2Ty3e4yltWuLBPQcdqHUlJSUFVFAY/+SSuG2+EZ54BYP/+/Wzfvr1MPQR0XWf79u0cOHCAhi0bcnPKzXSs3ZG5k+ZW6D2XFUVR2LRpEydPnqRly5a0b98+ejljKS2R1fMqvi98aNm5DboEsF9rx9rNWukzD/IoIgXXvoq86Tz+BTqm+hKuKUmllkHqso7vKx/KURnXsAjmnrXzn5OPy/hm+jhhOcGihEV0FDvSPa075tpmpAYS4TVhztRPZY91B40tFg6pKpIkYbdaGTx0aP4I7JgUlEwsx6CCxMSg8okqBQfN+OcVlgIVPUfC3ETG1j+Ab7YbQQTXJC/Swnnwj1fRU+YQ2FKfyK6CdQJzzQycs+5GmPEfqFbKpDtdh8EToUNreO3pIk9dkhRk5RiyUdG69ZJ4fyYk1yCYOIrQ6oJGSPubbKHn+EalRkdCOV7kQBB3cs2Ln3zmv/DFN7BlQaWVM1aGHERrXhQMBo2cA5+PQb174y7U/Cevh0CLFi3o2LFjqXKQ1xehQfMGNG/ZvGjDnSpC13UOHDjAjh07qFGjBr169So+KdHvhz17oE0buCAvQT4o45vjM2aGAIJVwDnRWSXtjfO4UAoiOyIEvgtgbmnGObaUscmAHlTwvXoARUw2WjE3LjhX+aiMb5YPasHaxLWQA51OdCJsz6C2kk1Ybk9qg1T2u/fTaOdODrVujaRp2OPiGDx4cEwKykEsxyDGVUFUKThwgRQkqujZEubmMtY+QXxfxiFYwH2LBylBg77d0KZOwbukYREpsPb045wmICz4oHQpACNK8OcH4daxRR6+5EjB5AdhWvSSx0tiwTJYtxl7nxD2QYH8h1se6UJwhZ3Pd31b7LICwPHVm3i7+2i+nvY7dE27eIMp4+Cfj1Vqj4NLXVaIJgUAdrudQYMGYXK5SNm6Fe+JE0bmPtCiRQs6d+6cLwilLSu0b9+eNm3acOLgCc4cPcPJnJNcM/2aKl1WEASBli1bMnDgQHJycliyZAmZmcWUjzqd0L17ESnQdZ3QmhC+mQVSIFYXcd/jvqxSEF6YSuDbAJZGQZzjyyAFIR3vB+dQAi7cbY8UlYLDRqRAqaGQ4kqhmlKNPql9SHWnsu/A14Tl9pyqd5KD7v00btzYkAJdx2GxMGTIkJgUVBGxiMEFxCIGlUdUKdhvxv/tBVKQKWFpHcHSOYT/azdinIZrohdx305o2QQ15ML7lbtg6JCo4zzzAZa05TDjtbJl1weCxTYxqpTlg5UbwGyG3pUzCa8Iue1i8whtthJcWnDBeJu3Wd3oR74eV7QJkhqJ8Hr74WQfPwXANf/+M31+F6VHPcCm7dCtQ6VUKkDFIgclSUFh8iMHmZkMevFF3GvX5l9EDx8+zObNm2nWrBmdO3cuNbSel7xYt0ldbltjNIqq6iZIYFzM1q5dS3Z2Nl26dCk6XjotzRgo9JvfQHIyuqzj/8aPvLegJ4K5pRnnjc4q6WSYR2EpeGX4K4RXhgmtCmFNX4T9mesQcocSRUML5I5HztJwjVIxtSmIykQORPDP9hOsHmRt3FpauFpQf2d9TPUlxBoSkY0RjtQ9win7AeqvXs2hgQORJCm/z0VepCUmBWUntpRQQWJiUDlElYJ9uVKAAOgISblS0D6CuXUY/1w3Uk0F13gfIiFoMwR5yu/wJd4DsvEFKNg1XBO8mLYtMfIFbh5T+gkpijEL4Zr+8Pff5j98NeYUFIuuG30IGtcHILzVSmBxgRy8y7usbLTwIjk4tmI9n1x3G+g6otnMPWu+pnaHYqYNbtsNvcbAtx/A8BKm35X7tMsuB2WVgjyCwSArUlKIhEIMGjq0yL/XI0eO8NNPP9G0aVO6dOlSqhzk5SgkN0pm2rppwOWRA1VV2bp1K0eOHKFJkyZ07tzZ6JS4cyeMGAELFqA1aIt3ZqFxyXBRh8Cq4EIpCP0YIrwpjH2IHVvf0v+daH4N35upaEEB1z01MSUXRAoieyP4v/bjqeZhY+JGutboSuL6REx1VMQfvyLSejJH6x/ldLXTJLltnE7PQgqHcVWrxqChQ7HmDkiLSUH5iC0lxLhiRJWCvZZipMCEpVMYc/MI/q/dmOoquG/yItp0sFkJ/+9bfO4CKRCrK8QN2oMpWYURg8smBWDccd9zC1xbcNGrNCnYfcDIA6jKDnevvAe9xxhlkYC1cxjHtX7ypuPcy70MPDaCcV8XrVZoNLBXfpRAk4vpiphHp7awYDpcM6BST7usywrllQLIXVYYPBiL3U7K8uV4HnsMDh8GoEmTJnTv3j0/elDaDVDLli3p3LkzacfS+LjnxwAMnzEcWa3aroWSJNGtWze6devGsWPHWL58OYFAANq3h1OnkONb4XnXUyAFJnBOdBbpEFgVFJGCYa8Q/CZIeFMIx67/YWuSVer+msfowKiFBdz7/oWpZsGlJrIrgn+On/MJ59lSYwv9G/QncV0i5mZmxOoWIq0nc7jOQdKs+6lTvTqn07PQdA3VKsSk4DIRixjkIgjCg8CDGLLUMhYxqBhRpWCPBf98JxdKgbVrCKmOQuB7J+amMs7rfQhpqegfzybY/4+ENxYk25maRHB1PoTQdSi8+RzccmPZTkqWjTB/ISo1UvD+TPjbS5D6U6WF4S/iZCocPg4DexV5jfAOC4GFeZ8rLHJ/z/V3dcJpKVgyUcJh3u8/gbM79gLQ8+Hbue6lv0Z/rdWboEYStGxaaadfUuTgw08/5P3I++WSgsKEQiFSli4lcvYsg2rWJG706Pznjh07xsaNG2ncuDHdunUr9WKaJxI169XEV83H6JajS9y+MsnMzGTt2rWoqkrv3r2JPxlPYEHBZEQhXsA92Y1Us2pnLxSRgiGvEPg6gHxYxtkpHcunf4fp042S1yio2Sq+6V7QBVxTXEgJQn5SbnhHGP+3fs7Gn+Vok6P0rd0XbaGGuZGGIISJHLZzsN5BMqufpfrChRwZOBARCAgh/nDgD/xrxL+4u8vdMSmoILGlhAoSW0qoONGkILzbQuD7YqSgRxAxUSX4oxNL6wiOEX4ECfSZP+BfURO58fD8Y1u6hnAMDhijkr9eACOHlC1hTpZhyGSYfAM8aISIq2T5oBj5uFyEd1oILCiQA0vnEGld91A/Ljl/WSF9zwHe7X0jatjooX/b95/QZGjfiw+madDnRqPHwTvPV+p5RpMDBLBNsrHsxWXlloI8QqEQKSkpRCIRBg0aRJzTmZ+Xcfz4cTZu3EjDhg3p1q1bqRMP84Yg1atXjx49evD8mueZ0mFKlS8r5L2PDWs3kLQrkXo59fMfNzUy4ZzgRLRXbZC3iBQMfAX/l36UVAXXTU7MzUpvraxmqHinexDOpOJqvR9p2rj850KbQwR+CJAan0p252y6xHUh/F0Yc2szrFlGJKEvB+oewFPfS2JiIkePHkWUZRLsdvqPGsXvl/yeN396k9eHv86cJ+fEpKACxJYSYlxWyioFYjVDCmx9gghOjeAiF5aOYRyj/AiChhYQ8MqTC0mBjn2YH2e3swjLVhsPjRtR9ix6QYAbrjEmL1KFOQWXQwrS0o3qh32HijxsbR/BMbJgWSGy1cbij/cVWVao2aYFw577Y/4+8+75I8HM7ItfQxRh3gfw+jOVfvrRlhXQIfJlhBNrT1T42DabjUGDBmG1WkmZP5+cO+4wJAdo2LAhPXv25Pjx42zatAmtuOqMQjRq1IjevXtz+vRpUlal8MnWT6q8CVIeFtVC5+Odi0iBubsZ162uyyoFL/d7Gd8MH2q6irvZbsyP3Aheb4n7q+m5Q48sIm55FlLnZvnP+db5CP4Q5FTCKaRhEt3juxtS0NYMZogk9mNfnX34zQdJ2LGDo0ePIkkSibVrM/D667Farbw+8nXu63wf//vf/2JSUMXExCDGJRNVCnZeIAVJKlqGCVv/AIg6oeVOrD2COK4JIMgR1JuewPumhJqW28rVpOMc58PWJQxvT4dpvwNPyV9ORdA0Yw7C4/dBtw5VIwXhMHQdCUtWX/qxSiMpHjKz4fzFa7zWdhEcowrkYLJyC0OOjS4iBz0fmEqTIUaUwJt6lu8f+Xvxa++1axiis/8w/Ot1I/GxksiTg/t+c3ORxyujfbLNZmPgwIFYLRZSRowgx1NwQ9SgQQN69erFiRMn2LhxY6lyUK9ePfr160d2RjavtXkNi2CpcjlQ0hQ873pQTxm9jXVRZ2/dvawR1uDz+6rsdeECKej1Mr5PfGheDddUF6bEENSsCa4ShnilKXg/9SJaVaPz4stPQ4cOAGQsy0BeInOq+ilq3VSLJnITAt8EsLQWYNMGIjsi7Kmzh0gzGZfFwrH69RFlmcSEBAYMGIA5V7qDwSD7/28/p749FZOCKiYmBjEuieKkICAH2bLseKHwdq4UZJqwDQqghwVCqx3Y+gewDwwaM33SbXi7/x+aZizfCA4N9y0eLM1yk78evw9SvoQ4d9lOTJZhyCT4fB5QhZGCQMhoL1xc86DKxmqFHz+Dft2Lf7ptUTm4kzuLyIEgiox57wVsifGYbFYaRDlOPuu3wlfzwVO5FyW/HGBntwOYexft5V9ZcjDo+uuxJSWRsmIFOXv25D9Xv359evfuzcmTJ9mwYUOpclC7dm0GDBhA0Bfk5ZYvYxfsDP5kMGnetAqfXzQiuyN4P/Ki+4yfnWCHuKEe2o5uhqqqLFmyhNTU1Ep/XSgqBf/p+h+8n3hBA/ftbky1TDBsGHz8cdT8GeWkgne6F1HLxPXPTohZxnnqus6JuScQ14icqXuGJlObkJCWYPRA6GxB9waI2Dqxq/YuqOPFZrNxXBQRRZFqNhv9C0lBLKfg8hLLMbiAWI5B2YkWKfh27gb6HbguN9FLR0zS0DIl7EP9qBkSkW027EP82LqFQdeJrMrGv7EJaLmVB0kq7olexDgN3vscunaALu3Kd3KhMPz9P3DzGFZU8/88ShLLyrFT4PVB+1bFPl10+QY+E2fQb0ojOtU2ZiMcXrKa+PrJVC9LcmE4bAhJJeGL+Bnx5V1sT9/LwokfMvOV76tkKmM4HGbFggUEz51jUP36xF93Xf5zp06dYt26ddStW5devXqVmnOQlZXFypUrEc0iy7XlPD/ieSxS5Ywy1nWd4LIg4bUFlSJSsoSrzVHEvp1g82Yi7dqxceNGUlNTyzRJsjwUloKXOryE/ws/glPAfYsbcc4nsHIlvP9+kT4ahcnrWmhKNuEarSPM+wruuotAIMDxr45T+0RtclrlUH9cfZStCoEFASydTGhhHXmfws7kHVhr+dCWLOFU794IokiNGjXo168fptyppzEpqDxiyYcVJCYGZSOaFIS2WQn+aNTXa7pGwOXF5Y/DPjyAespEZK8Fx7V+rB2MJLjQ/3YSDPTHyCoEU30Z51ifUa4oyzDsZhjar0jvgVLJGy3MZehTcOCIEcWoXaNyj1sSQ2+GeBd8/V7UTS6UA0unEJahHjRdLXZkc4mcy4C7/wgvPQktmpS+fRQKS8GiSR/Ru26XKh3ZHA6FWDFvHkGbjYGDBpFQqBnP6dOnWbduHcnJyfTq1cvoHVACHo+HFStWIEkSAwcOZE/2Hmo6a15SQqIe0vHN9aEcUvIfM3cw4xzlRAj6jDkJXbuC242u6+zdu5ddu3aRnJxMz549sZRQGVAWCkvBiy1fxP+lH6m6hOtmF6JDhM8+g40b4b//LXZ/+aCM7ysfpmohXKMEhHrG7IO01DTSv02nwbkGKN0ValxXg9DGEMFFQSzdLWhL1iHHdWJH3V24OroIhUKknT6NoCjUcLnoO2pUTAqqiJgYVJCYGJROVCnYaiWY33RHJ91ylmrhGuzpsJ4uoe7Ih804R/uxtIoYg4FS7IQ3FZTVmduEceZWJuQTCoPFXPYZBHkjhX93NyvaOqo+UjByGrgc8OVblX/saBw+BrVrgtNR4mYXysGahBTeTvgfc8a9fpEceE6lEVcvufgD5XiNpMdnH4fcn3V5KU4K8qhSOQiHWbFiBQGvl0H16pHQs2f+c6mpqaxdu5batWvTu3fvUuXA5/OxYsUKNE3jv2f+y5HAkQo3QVIzcocgZRUsZ9iH27H2KHkIUlpaGuvXr8dqtdKnT58islMeikhB4xfxz/FjamDCNdFVpk6KeQ2KzM1MOP87EqFWdSKzZrF923bMG800zGqIebAZVz8XofUhgouDWHtaUbNU5AMRttfZQaLzLB6LhbOqiiAI1ExIoM+gQTEpqEJiVQkxqoSoUrClsBSAmKBRM1KLmXU/Ju5kLeQjZlxjfYYUKOB/01NECqy9gjhH5UrB8dMwappRu2+zlm8wUSgMdWuzWUi/PMsHbz4Hz/yhao4djaaNDCkoReovzDnomz2Ia4/dyPivH8pPSJSDIRb+4VleazOEtG27iz9QvBsWfGpIgaYZXSTLQUlSAFU3shnAarUycOBAnGfOkLJ/P9nZ2fnP1alTh759+3LmzJn8/gEl4XK5GDJkCGazmQdqPECyKbncCYm6rhP+KYznPU+BFFjAdasLW89CnQzPnoWXXjL+LERycjLXXHMNkiSxdOlSTpwofyVHYSl4IfkF/F/5MTc345qcKwX//jc8+WTU/cM7wvjn+DG3NuOc4EL48gtOP/00ixYuwrbRRsOshtivsxtSsCZXCnpbUPafQT4ks63udmr2rEFOWhrpoRCoKrVq1aLv4MExKbhKiIlBjDITVQo2WwkuKSwFKlqOiGOkj6niVBr6m+Ka4CW1+jG0kIB3pgvZ3yh3ax3HcD+OAcGC3KZQCDS9YmvbcW5W/HMiA3Y/e3lyChrVq9RGQGVm3iLoNqrUbovWthGcowvkYAq3MfrYRMZ//TBhJcymd2aw4fWPUSNGV0Q5t7Niseg63P4YPFb2UsbSpCCPKpeDG2/EWbMmKSkpZGUVVHUkJyfTr18/0tPTyyQHdrudwYMH43a6+X3y72lgblBmOVDPq3g/9hpNi/KGIFUTibsnDnOTC8pdz5wxLtBnzlx0HJfLxdChQ6lbty7r169n27ZtpZ53HoWl4PnE541EwI6WosOQLJao//bCW8JGRUEHM879bxDOyWLdyZOs2bOXNultqJdVD8doB7buNoIrgwSXBbH2s6LsTEPOcrE1eSt1e9Um/dw5ztWvjy5JJAN9+vTJj9jEpODKE1tKuIDYUkLxlCgFhQb6iPEqmlfEMdJP+CcbWpaIa4KPddo67vniHyx2LsTljzc2lnScY3wFlQeKYlx8KtITQFFg6m/ZNq4bfY+/XKoU6DroYQHNI6KHBZAFdBkQQTDrCGZjJoMYpyGYij0EbNkFc36AJx8udjhTlbJrP8z4Gp54qEyVGpG9uZ0ndePLfx7zCA85xT0dJvD+gAmc2WZk7/d4cBojXv5b9AN9Mtsom7z+mlJfs6xSUJiqXFaIRCKsWLIEf1YWA4cNI7FWrfznzp49y+rVq6lRowZ9+vTJv3ONhizLrF69mozMDGZ6ZvLXEX+lU+1Oxb8nVSe0LkRoRQgKFUJYOllwDHcgWCuWSKjrOgcPHmT79u3YbDZatmxJkyZNop57vhT0eJR/O/5NaGUIay8r9mFla6+cvyTQ3Yol+RCHn3mavZMmgclM70BvLEctOK53YOlgIZQSIrQ6hG2ADfmUjHxMZludrTSuFuDYvn1kNWqEJgjUqVOnSI5HTAqqlliOQQWJicHFRJWCn6wElzkx7kYFhHgV3SfiGOEjvMGO5hNxTfRiqqUS2ifh/9aNmBukEqzG9ERTcqE7ncefhQNHYd775W8tnJlN5sQ7GN92P6be3YtIga6AesaEclZCPWtCTZdQs0WIlCVgpiO4dKREFSlZwZSsYKqjILp14679H6/AlgXlW+64QhSZagmYmodx3eDn/IGDvNv7xvwZClO++4im15ThCzktPWqZZkWkII8qlYO1a1m5bh2+Ro0YOGQIiYkFo7rz5KB69er07du3VDlQFIV169Zx9uxZevfuTbVa1cgIZFA3rm7BNmkK/m/8aOcKjECIE3De4CwyfvhS8Hg87Nu3j+PHj2OxWGjRogXNmjXLL/WDolLwnPAckU0RbINt2PoWWr7485+hfn148MEix9d1ndDqEKGUENY+Vs41PcfOXTsJBoM0btiYFsdboO5XcY51Ym5jJrg0SHhdGNtgG3LKIWSS2VZ/O80GNePg7t3kZGWhCgL1atWi1+DB+VUhMSmoemJiUEFiYlCUaFIQ3GQltLyQFMSp6H4R50gfwdUO9IiAe5IHqbpGeK+ZwHd5w5MgXT/LviFrGNN9UNEXS1lnlOLdflO5z/PC6gOLz4F8yIJ83IRy0mwMYZJ0pBoqUi0FKUFDjNcQ41QEq45g0cFkvB1dFkAGzS+i5YhoORJqhoSSJqF7jTsbsZqCuZmMpamMVEfJK6q4vPgD8NX3RmfHpIQy7RI5ZMY/z5VfGppZK40nnX/i4bQOLHn8XwC4kmty/0/f46iWGP1AH30Jf3ketv8ItaoXeepSpCCPKpUDv5+V69bh9XoZOHAgSUlJ+c+lp6ezevVqkpKSipTMRUNVVTZs2MDp06fZZdrF9BPTWT5tOQ2cDQiuCBJeH86fdQAYd+iD7AjmUsR3/364/Xajf0DLlmV6Xz6fj/379+d3DWzevDnNmzfnwx0f8sAPD/C77r/j6cjTyDtlHCMdWLsWWi7QdfjDH6BhQ3jkkUIP64SWhQitDRHpEmF7YBXZukbdOnVo17Y90mIJ+aCMc7wTc0szwcVBwhvC2IfaCR8II58Ms6PuVlo2NLFblvEFAiiKQgOrlR7XXx+TgstMTAwqSEwMCogqBRtshFY4yJMCMU5FC4o4rvURWuUAHVyTvEiJ2kV3qZh0nm/wd370LGPT7XMxiSY4etJYq69IbbamkXrHfUyovoZGnUfxTqNX0A85UNNNYNIx1VMwN5QxNZSRaqhFKx4qgOYTUE6ZkI9YkA+b0YMigkvD2i6MpV0YKankpjmVSnoGNOsHM14z5KCMyEdN+Oa48+VgAxt4v/5r3DAjh6NL1wLQeuy13PT569FDzDle+HYxTBlb5OdWGVKQR5XKQTDIyg8/xFutGgOHDy8iB+fOnWPVqlUkJibSv3//UuVA0zQ2b97M0aNHmZczj4gnwjumdxA9BbYoVhdxjnFiqlPysfI5fhyeeQb+9jfjYl0OgsEg+/fv5/Dhwyiawnfnv6NBvQb8xfsXlKMKzjFOLO1KL3XUdZ2c+Tno23QO1znMEfcRqisKHVasoNprb+CfG0I+IuOc4MTc3ExwYZDwT2Hs19gJ7QqgnNXY2WgHrfs1ZfvcufirVUOxWmnYsCHdu3ePScEVICYGFSQmBgZRpWC9jdDKAikQ3Cp6WMAx3E8wxYlg1nFPMpoThbZYCS5xkBcpEBMU3Ld40B0qnoiPRFs8kbNnsXS4Dv7xO7h/atTzica6n5ZQ7S+L8Q35DY2lbmDWMTeNYGkZwdxERqiqEQaRCHr9XqgvvUWk9mAiey3oYRFTPRlrtxDmZvLliSJkZpc5WlAY+XiuHCjGz2Yve3k77lnaPr2WUGYOAGM//A8dyjLBcsNW6NoenxauNCnIo0rl4JlnWNW6NZ7c3gSF5eD8+fOsXLmShIQE+vfvXyQsH+08d/y0A3GdSL2ceoVOFGwDbNj62BCkqhuTXBxvr3+blC0pTEiYQPfT3XHJLnz9fVibW3E6nTgcDmNt/7e/hb590caPx+/34/F48OR4MK82k3Q2iQN1DmDpaKJx06YkJiaihzV8X/lRTiq4JrowNTER+D5AZGsE+7V2QivSkMMOdjfeTZtr2rF582ZCfj+yotBIUeh2yy0xKbhCxMSggsTEoAQpWGczIgJ5UuBSQRawDwsQXOZAcGq4J3kRHDrBVXbC6wv1KGiQgfMmocgd+/lAJv0/u5l3wwPoP+1RcEfvxX4hmk/gwIrzSLsTqU51hLph7B1lLC0iCJXTlK5kAkH4cBYMHwAtmqDLIB+0EN5mRTllRkxUsfUIYWkbjp68WFnouc2gytnwRkmT8H3pRg8bX9InOMEc/z+RXpgLgC0xnge3LsRVUvOmtHRoNYjQ849zjXtRpUpBHlUpB7Iss3LlSjzZ2QwYNIhq1arlP5eRkcHKlSuJj48vVQ4iByIE5gfQ/QXfp+lx6TS7pRlSjQqEqWQZzp+H6tUrlIybl1Pwz47/5JGTj6CEFHY13sU5/VyR+RgOux3niRPI1arhNZtRVRVBF2h/tj01c2oS6huiZjcXpqFD4b770KfciW+mDyVNwTXZhamBicD8AJHtEewj7AS3BJHPyeyrvYE2jZ1sPHmSSFwcEVmmScOGdO3RIz8KFZOCy09MDCrIr10MokrBWhuh1RdIgSpgH+wnuNSJmKjhusmLYNEJLHIS2VWwfmntGcReuBwRIBRGXbGOu+QfmL57HjOuf5mb21xf6vmpmSKhDXZCu02okRDrrIsZNqUPzlpVffUtO0qqRGijHfmAGcGpY+8bxNI+fMnLGMWi60YnxH7d4enHyr27miHinRmH7jfkQLPJbNr5FBumv03dHh0Z99ErJDUtOZQdWLWGEUdfY+v5fZUuBXlUqRy89RarsrLIbtmSAQMHUr16Qc5EnhzExcXRv3//i7oNan6NwIIA8t6CslFd1NlffT+Wrha6dO1CRI2Uv9vkli1G18PNm6FL+T7PPCl4se2L3HP8HgS7gOsWF1KChKZpBINBfD4ffr8//0+zyURcfDxxzjjsK+1oRzScY51Y2liM3hV//zva2En4tjdEPa/ivtmNVFci8E2AyO4I9pF2/CnnUUMWDrY+SKsBrVi3ZAlKIEDE6aRpo0Z06d49JgVXmJgYVJBfsxhElYI1NkJrCkmBUwVdwDYgQHCpE1MtBdd4Lwjg+8aFcjT3y1PXsPc4h21wMXc8730Bf3wOdfcS7trySqlyoJ6TCK6zIe+3IFvDvOl5id989BlJr/0T66iyr69XGuu2gNkE3TpE3UTNFAmttRPZY0FM1LAPCGBuIVcolaJEPv4KmjQwhjlVAM0j4p3pRss2zEWXNOadfZabn7kTu7Xk7oqFcwpWdXiKjpa6FT6P0qgyOcjKQv7hB1bXqUNWVhb9+/enRo2CKElmZiYrVqzA7XYzYMAALBYLyhmF8OYwkR0RKNTvydTEhGOUg+OZx/npp58QEgT+uv+v/Hjbj+XrkJiTA6tXQ79+EB9f5t3ypOCNlm9w89GbkWpLuCbltjgujK7DQw/BhAkweLDxUETH95UP5biC6yYX5uZmOHkS6tdHC2j4PvOh5Wi4bnUh1ZTwz/Mj75VxjHLgW+NBydE4Wm0VLUZ0Z/X27UYzp3CY5oEAnaZNi0nBVUBMDCrIr1UMokrBKhuhdYWkwKGBAPY+QQLLHZjqKbhu9KIrAr6v3Khnc+/cRR1nl0NYhlQr/gV1HfYehDYtUDWVu374C1/s/Y4j9y2nrrt2/mZqpkhwjR15rwUxTuNEi70M3HIDXeu15dvR/8PuukI/ozF3GWIw+51SN1XOSgRX2VGOWJCSFRzX+DHVLltDmsuFFij689PQ+Crxc26/fSg2c/F3uxclGv7+ffD64fuPK5ZIWgaqMnKgKAqrv/2WDF2nf//+1KxZUIqZlZXFyuUrqReuRzN/M7S0C5JMreC4zoGlvSX/AnjixAk2bNjAruAuvsj6gsXTFl/SbIXSyJOCTxt/yugTozG3MOMc6yy+AsLngzFjDDkYOxYtpOH7woearuKa5MLcyAwzZ8Jdd6H9tAfvigR0v45rigupuoR/jh/5oCEFnlUeNK/Gqdb7adw4jlWbNyNYrYRySyc7duwYk4KrhF+dGAiC0Aj4GzAEqA2kAjOA53Rdj5TjOL86MShOCnQdgqvthNfZyZcCuwYmHVuPIMHlTsxNZJw3+NB8Ir5ZbrSc3Fi5qOCaGMDcoJjWufMWQY1q0LdbkYdVTWVT2g561e0MGDkEwdV2IjutRji+T5D1CasYOftO/rO7Nrc/9yn2OnWq9oMpCVmGbI/xXsq6ywkTwaUO1HMS1s5hbP2DxrCoymDtZthzEO6eXOFD6DL4f3Ai7y8QgXXOVQy5sxlmk4hUaK272OqDHK8hS1Xc7KnK5CAzE6VFC9a88grnnU769etHrVq1ULNUwlvChDeHIXzBPiawdLRgH2hHdF6cbZqamsqatWs4EDzA9KzpLJq6qGxycO4cfPklTJwINUrI8cglTwrm1pvLwNSBWLtZsV9rRxBLELTcYWOaT8P3uQ/No+G62YWpbq7cBwJoM+fjDV6LLuu4p7gRE0T8s/3IR2Tso+14fsxEi4ik9z5D3Q71WbVqFaLPR8hioRXQ/qabYlJwFfFrnJXQCuP9/AZoC/wOuA/415U8qaudqFKwsrAUGF0ABYuOtVuI4DIn5pYRnGN8qBkS3ulx+VIgRLJwO2YVLwW6biTsfTL7oqckUaJX3c5oYZ1vZ2wm4x0X8kEL9kEB4u/NZn3SSkbOuYsx9nbctygb+8adVfmxlI7ZXC4pADA3UHBP82AfEiC824rnvXjCuyyljTwoGynr4OMvS52fUBKCGZw3+LH1D+Q/1tvfn/2v+fh04F3snvMDUEJJYrzbkIKTqUazqjK26S33eVZV++SkJEwpKfS9+WaS45PZ98M+zn90Hs/rHmMsciEpCNqCmK8xk/D7BJwjncVKARjzGAYOGEhLR0vuSrqLR79/tGzncuoU/P73xp+l8Namt3jkh0dYWnMpA1MHYh9ix35dFCnQNLj/fti2zZCCHA3vJ140v4Z7qtuQgoMH4fhx1IgVr/9aUME91Y0YL+Kb5UM+akhBzpIcVFkgJ+N9ki1+Vi5bhiRJhCwW2tSqFZOCnzG/mIhBcQiC8Dhwv67rUWfFCoJgBQrHSt3AqV9DxCCqFKywE95YIAXYdESbjqVdmNBqB5YOIRzDAygni5a8iQkqrpuykRJLuEuJRIw5CLai4Wldh8geC8EVdmS/xlva27S+rho3dbzu4tHJAdm4CF0p1m+BV9+Ht/8NiWVf/y2M5hMILncQ2WvF1DiC89oAYtwl9ECIRAxZqaQQfuSAGf98V/7PVo4EWL/6OXp9MJHxyx8vufpg+Tp44AlY9Bk0qLqoTmVEDnRVRz2vop5VUdNV1DQV9YyKHirme1EEcyszSmuFFQdWYLPbGDhwIDZb6bM4MjMzSVmRgtVmZejgoWXapyy8tektHv/hcZYlLqO5tzmO6x1YO5SQ6Hj2LIwYAS+9hNppEN4ZXgRRMPIGknIjftddhyom4b32TQRJwDXFyFHwzfShpCrYRtnwLMxBU3TCI8PYa9lYvWwZVo+HQFISbdu2pW3btvkvGZOCq4df3VJCcQiC8Cxwna7r3UrY5h/AUxc+/ksXg6hSkD8KOff3wqojOnUsLSOE1tmxdg1hHxJA3le09750fheu+y2Ijatf/GJeH9zzJ2MKYfPGFz2tpEkEljpQU82YW4ax9vdxz9o/MX33PJ7sfT8vb/qQPnW78H1oJJYJo8HlvPg1LicrN8B/3oG570Epo3pLQz5sxr/IiR4Bx5AAlvaRS7u2V7CvQXEo6RK+2S50X8F7PHx+HVNr/Z4PJj9TcvVBJFLu8smKUJIcfPSXjxjXeRxajoYe0Y0kQdWQAbTcP2WKdCYsjrApjNhRpPqA6oguIzKQk5PDihUr8qc3luVCn7ePIAlMz5nOSyNfuqScg7c2vcVTPzzFctdy6ih1jITBC4cxFYemoaQbyweCXcB9qxsxriDioe4/h/dbEcFpwn2bG8Ei4P3Ci3pWxTLCgnehB03VoOZahJH9WLNmDXarFX8wSPvUVFo/+mi+oMak4Ori17iUUARBEJoCDwNvl7Lpv4H4Qv/VK3nznz9RpWDZBVJg0RHdGuYmhhTYegeNMPhmK/7vCvXcT/bg1qcjNojSQjfLA6lnLpoEqAUF/IsceKfHgSzgmuzBNcaPOUngg5H/5ppGfXlm7Ru0SmrCd92fwvK7Z2BhStV9MGVlQE/49sNLlgIAc1OZuDtzsLSUCSx04fvKjeatoBksTIEGveBU2iWfF4CppkrcnR6Epjn5jzWt3puV6ko6p/cuedXCYjFyDqY8YiSZVjJaUCCyz0xgkZOnW/+He3vfU/R5TeOOf93BrFmzUE+raOc0tCwNzaOh+3X0oA4RipUCwSZgaihh7WbCfpOdw/0PszKwkrScgs81Pj6eQYMGEQ6HSUlJIRQqYSploX0GDx6MqqoMZSgTZkyIPpXx4EEYNsz4sxje2vQWL//wMuvt66kr1sU9zV2yFOi6MUr5yBGU0xq+T32IcSLuaYWk4K23UA5m4Z1vRowz457mBhN4Z3jRzmlIwyW8C7xouo7VsQitaQ1Wp6RgFwT8wSAdO3aMScEvhKs+YhDtjv4Cuuu6/lOhfeoAK4AVuq7fXc7X+0UnH0aVgqUOwltsFJYCKUFDSpaJbLdjHxDA2jNUKKKQu1kbP46R4ehd/hQFTKb8RCfIXTbYZSGY4kBXwd4/iLVz0WOsOLGBEV/eRf24ZDbcNocEexycPgN1alVZxnuZycgylhAqeXCSfMSMf6ETFHCM8GNpXvJI5YvI8cLs72HS9ZUaVfFF/Lz05AvcY/srzkIVI1ItBWu3EJaWkeKbOPn8MOZu+NsjMKj3JZ2DroKSakI5ZkY+bEZNl8jrqAlG5OAvP/yFdze8W2Q/URB5d8K7jOs4zpicKQkgARLGGrwFpJoSplompFoSUi0JwSUUtII+eRLt9ttZ/6c/cTonh969e1OvXsG9g9frJSUlBZPJxKBBg7DbS0+8DAQCLFm+hHOec3yQ+QFf3PrFxZGDo0fhiSfgX/+CxkWjbG9teosPf/iQeZZ5uOJd+T0KSiQ1Ffr2Rf73Z/iOtcaUbMI12VUw2fHUKZRrbsU35SvEWjZctxjNxvJKFLVBGpHFYTRRw3Wbm8xIJhs3bsSVkYGvWjU616pF84EDi7zHmBRcffxilhIEQagOFBOfLsIxXddDudvXAZYDG4DbdV0v18LtL1kMoklBYLGDyLZcKRAwhg1V1xCrKci7bdiH+bF2DONf4ETeU6hx0c53sTs3I7z97+Jf8L3P4fNv4IdPwG6EWtUMkcAiJ8opM5bWYeyDA4iuor+DF+UUbNzF5voSh/ypTGo9qoo+nXLQpK8x6Onvv630Q2tBgcBCJ/JBC5aOIRxDAlXX1rkM5Ccant3Df1Z2o5X1Rtp3u73INoJNw9opjKVjGCn+gn9uhYSwyN9LQddByxSRj5mRj5pRTpjz8x0uQtARXBpivMqf5jzJ299/UOTpS6pWyMyEKVPQXnmFDVlZnDp1il69elG/fv38TQrLwcCBA3E4Su79ABAKhViyfAnnc87zSdYnLLxnYZmaIL216S2+/eFbPjF9gq2ODddkF6K9bIIa2enH/10EU2MTrgmuImWM8nEZ3xdepFom3De70RXdkAKfRqBXAHGliE6YhDlTOf32y2w5cgS3243X66VrOEzTKVNikYKfAb8YMSgPgiDUxZCCzcAUXdfLnRb9SxWDsksBSDUVRLeGfMCC4zo/lpYRfHPdKMfzrlA6juEBrMomY+xu3drFv+j6LbB4FfztUXQFQhtshNbbEd0ajmv9mBteXLlwkRR4Q9C0H1/f2o6b6m8pc4fEKmXBcmPoU+vmVXJ4XYfIdiuBZQ7EOA3nDT5MNcv4q+z1wfNvwsTR0LHNJZ3HhdUH7cR6vNllBNUTOzJo1Isk1Whx4ZljaipjbR9GSsybXJn7hh7+O9RLhj8/cNF71b0iaqaImiWhZUqoGSJqugk9EP2CJyYpmJvKmBvJmOop+fJUlX0OtHCYTZs3c+L0aXr06EHDQsONfD4fKSkpiKLIoEGDyiQHkUiEpSlL8Xq8DBowqEjfBFQV/H5wOvOXrN7a+BY7F+zkGfEZrK2sOG+M0qOgMLoOr75KuMdUAikS5tZmY7+8uQ379iG//yO+ardhqmfCNcmFHtbxTveih3UyO2Ti2OAAGyTd5ubIgW3sOH0ad0YG3mrV6N69O40LRTRiUnB186sTg0LLByeAqUD+N6mu62fKcZxfnBhElYJFDiI7cqVABAQwJStg1VGOmnGO9mOqLxuNb9ILNS6yzMfyUO/oofQcL8S58u8glFQJ/wInWpaErUcIW+9gsXfBF0mBOTeha+c+1Mb1uCvl6XK1T/65o2aI+L9zoWZIOK7xly0xUVGg5w3wxEMwfmSFXztaSeL2z+Yy767HAWjaeQRDH/4/bKerF0zPvBCzkaciZhxFdIQRuzUGWUDNNEZZa9kiqKVHEQSbhqmxjLmxjLmhjOiO/r1VJXKg6zB6NFqdOvx0zz0cP36c7t2706hRo/xNKiIHiqKwZs0azp07x7nEc4zsOtJYVrigJfK7699F/VFlsjAZa28r9iGl9CjI4+RJQre/QnDQ37F0tuAY6SiyX+TjlfiPt8Lc1IxzcoLR02CGD13ROd3sNNV3VAfVQ7UbdPaKYfbu3UucJOGRZXoeO0bDP/85/1gxKbj6+TWKwe3AR8U9p+vRvrWKPc4vSgyiSsFCB5GduaHL3Ou7qZ6CLuiop8y4bvQhJqlG4yJP7vqlRcddbwWm+2+DtfOKrTBA02DIJOjcDv2FpwiuchDebEWqreK4zh/1zrdYKTiXAdWT8gUjr0Pi9N3z+PyGV6/MssKeA7B+K0wdb+ROVDG6AoGlDiLbbVjahXFc4y99aaEcIfviKGl0sq7rzBx/Lwd+WI5oNrNsWgLJffvybv3/omxzlniXXy5MOqZkBXMTGVPj3JHZ5XhLVSIHX34JtWqhDxjATz/9xNGjRy+6Y/b7/aSkpAAwaNAgnM7Scz1UVWX1utWcTT3LMt8y/jz2zzQiHpYsgWHD+HjXN9RbXo8OYgfix8RjbV+2uQu6rhNaFSK0ImTIxFB7kTHa4R1hAt8GMLcy4RzrQsvJlQJ0DiUfosGBBghxGkmf38yOPz3KwUiE+Lg4PF4vvTp0oH7z5vk3BzEp+HnwqxODyuKXJAZRpWCBk8iu3FKyPCloIKPLAmq6Cdc4L4JVNybvhYwN8iYnStVV44JdUnOfb35EtrckcKwDmk/E3i+ItVsoaoJisVKgadB3LHTvCK89nb+tqqn8bulzTG03lm7J7SvjYyof730BT74AZ7de1iTI8C4LgR+dSIkqzjE+pKRSUmcCQaN0sV5yuV6nJCnIw5t6lrl3/oFrX3qS7a5zjJlzH0Ma9mbOmDcQj7tQz5jQPCJajoiaIxoDmrRiPitBR4zXEKupSEkqUpKGmKQiJaoITv2SP94qW1bQdfS9e9kcCHDkyBG6du1K06ZN85/2+/2sWLECTdMYNGgQLlfpU0N1XWf9tvUcP3Ccg+GD3DLiFprWaMqXP35J+/XtsVvs1J1aF3OdsiWc6JpO8LVthL2NsA22YetrKyoFT35OwHYdlo5WHKMdaBmaUX1g0tibuJcWx1sgVROIn5rI5l2bOXbsGPEnT+JNTqZ39+7UbV6wjBaTgp8PMTGoIL8UMYgmBf7vnch7cqVAAjQwNZbR/CJ6tohrgg9dBt/XhRoXJaq4015FTLbDPTdHf9GjJ9Hr1ie4wkF4qw1TPRnHdf4SL2JRlw8Alq4xsv+7tCt237ASZu3pLQxueGkZ7+VGlis0CvdSUc9J+Oa50PwizlG+kqsWBt0ETRvBBy+V+fhlkYLi+PHoqnw5+HrsGxcl0ek66H4BzSui7T6L8NNmxHuuRUwkejVLJVElcvDuu/Db36IfOsTWM2c4dOgQXbp0oVmzZvmbBAIBUlJSyiUHADsO72Dzps3IaoiOh0UaMYY09xna390eyV228lhd0fF/cR75iICj1h6s9w0o8nxoXZDgkhBWy17sf+yNmq7im+FDMSvscu+iXWo7TKGTuNY9wYZ/PElqWhpxcXH4cnLos3Mnyf/4R37eQ0wKfl7ExKCC/BLEoFgp0HKlYG8hKVDB3ExGzTbu6lwTvajnJQI/FGpcVEfGNd6L+OTTxt3n7+8p/kUPH0ce808Cd05HE1xGeWOXcIl3fVGlQNPKVAr4v58+5bdLn/3V5BwA6GHwL3Qh77dg6xPE1jdY/Ge8ehPUSIKWTYt58mIqKgV5/Hh0FZPmPcqiSR/Ro07Hsu2UkQXVovS+qEQqXQ5CIVi6FEaNQtd1tm3bxsGDB+ncuTPNC91JB4NBUlJSUBSFgQMHlvn75EDqAXJmZdDM14qD9i10++1gRFPZDEoP6/i+9KGcUnAOCGHpU7tQmbBOKCVAaHUEW18btsE21DQV72deQpYQ+5z76JDeAXM9M7am+1h36ijnVBW3ouArNDsij5gU/Pz41Tc4+rUSVQrmFyMFLWSU8xJ6UMR9swfluJnA9wWNi8zNIrhHnUG0Ay//DX5XfEsIXYbA0Vb4ps5DrGkh7vYcbF0rKAUAT/8Xbv99qX3/H+hyK7e1vZEp3z3GF3u+K8endAmMvQc+m3t5XqsYBCs4b/Bh6x8gtNaGf64L/cLBPgD9ul82KVAjEeJ/OMLarq/Ro05HNF0jrBR3UoXYtB1aDIQNW8v1WhWh0mcr2GwwyshvEebPp1PTprRo0YKtW7dy4MCB/M3sdjuDBg3CYrGwfPlyMjMzSz20FtDQ5mo09DZlY/JGjjXIYPVPq9G00quuNZ8x90A9FcY1yY6lb3IRKQjOzzSkoPZR7EPsqKdUvNO9eCUvB+MO0jG9IxZbJpaxZlaFvGSYTLhCIfy6zoCzZ2NS8CsiJga/IKJKwbdO5H25UmDCkIKWEZQ0CUED180ewjusBFMKsqgtHUM4k1citB0I2/cYXzDFXOmVE+B520Z4hw37ED+uW/1IiSV/iZUoBQBtW0DntqWu4UuixAcj/3355EDXoWHdy3KXWxKCAPbeIVzjfcgnTHhmxKNmFvNP+bUP4fulJR7rUqUg68gJ3uh4LQsfe4a1f/8vuq7z0I//YNzcB0uWg85t4anfQqdLK6ksK1UyeCkjA267DeGjj+jYsSMtW7Zk27Zt7N+/P3+TPDlwuVykpKSQnp4e9XDKGYXUN1IRM0RmtJ7BsDuGsTS4lNPHT7No6aISuyuqmSrej71oPhX3u9dhnvO//Od0TSfwfYDwNhF7YCH2a6sTORIhZ3oOWaYsztQ+Q/vU9liqBxBfGEjKou/xZmdjdzgIJiYysF49atx1V/7xYlLwyye2lHABP9elhKhS8I0L+WDuergJUATMrcPIx82IVh3XBC/BVXbkfQXrwrZ+AWy9QwiBAPzfB/D4by7qe6+rEFpjJ7TeinR6G84HEpBaJpR6nqVKQQXIq1ao5azOC4P/eMnH+zmhZoj45rrR/QLOMT7MjQr1hhhzF/TsbJQuFsOlSgGApii83X005/YeAmDirDc52cFeYs7BRRw/DbWqXzRYqyqo9GWFw4ehSRMQBHRdZ9euXezdu5f27dvTunXr/M0KlyX27t2bunXrFjmn8MYwviU+dqm7WNZxGf9sOxXh978n9enHuXXt37k18VaqOarRo1sP6tSpUySRUElT8H3hQ7AJRhfEozugeXNwudBVHf9cP/K+CI7rnVg7Wsnelo06XyXTnonWQqPmjpqYW5rRhmmsXL4UPRBAyshArlGDAdddR2JigQjHpODnTSzHoIL8HMWgWClQwT/PhXzYnN+4CEXA3CaMfNiMFK/hHOMlsMhldJUDQMdxbQBrrVNGg5UojYvUcxL+752o5yVsvQPYWIfQt/SLSqlSsHEbfD4P/vUnY3xvOdB0DQGjle1p7xnquqM0XboUsnIgHDEuYle6LXMh9LCA7zsnylEzjmEBrJ1z79RLKFusDCnIY//8JcyccB8A1Vo04YEtP7Dk5LqyyUEwBG2GwG3j4enHKnwO5aFKEhJXroRz59DHjWP37t3s2bOHdu3a0aZNQUREVVU2bNjA6dOn83sgaF4N/7d+lCMKb+tvc77bef4z4j8IR47A734Hr77Kiepmrv/0em5KuIkW1hbUqFGDjh07kpSUhHxUxvelD6m6hGuwD7FxoeWDiI5vtg/lSATnNw+iz3yOo/tkamypQXZCNgmdEhBXiFgcpwg717Oqdk3MZjO6qqJmZzPwm2+Inzkzvyw3JgU/f2I5Br8SokmBb26uFABIeoEUHLAgVVNxjPbh+9pdIAWijnOsD2vHMDz6FEx+8KI1fl2H0EYbnk/j0AMR3L13YO8brhwpADh2CnbtB2v5p/KJgoggCGxI3UbTt4dUzbLCF99Ay4Gl5j5cbgSrjmucD2uXMIHFTgJLHegaxgVC0yBUNKRfmVIA0GLUUBr0MQaYZhw4wtaPZzO8cX++Gf82y46v480tn0Xf2W6D916Mmr9SFVTJssLHH8OHHyIA7dq1o23btuzatYtdu3aRd/MlSRK9evWicePGbNy4kWNLj+F5x4P3tJfx2njO9jhrSIEgQNOm8O230LQpDeIb8N3U75jtn03N1jUJh8MsWbKEPfP24PvCh6m+CfdkG+KwfvCXvxjvJaTh/dyLckLBdJ3MnvuHsznlDDW31CTcIExyz2TEFBFLJwse/zekuJ3Ys7PRwmF0QWDI2LHEf/FFTAp+pcQiBhfwc4oYRJWCOS6UY7kXfLMOsoilbZjIfgumugr2gX58X8eh+3K90KLhvsmHqW5uGDot3cgYb9cy/7XUHJHAD06Ukyas3UPY37kXIf0sLP2i1Lvnci0fXGJznsJNkCq9WuH0Gdh3GIb2rbxjVjKhrVaCSxyYGsu4RvsQugyBaRPgT0Yr4sqWgjxOrtvCh4MnAuCqXYOHdy/F4nSw7ewe2tdoiSSWodQuM9uIyCTXLHXTyqBSIwehkFHCV6iMde/evezcuZPWrVvTrl27/PC/FtI4Pes0rhMuUhNTGZAxgNt63sar175asESg60bUTpLy/z1ouoYoiIQiIU5/d5qkPUmkxqVyusVpkuslU/3kSczJyUg1G6HN08Crc6D5Pk6qqTT0NKRFWgukDhLmWmZCi0NYO0ukt81k00+bqB4Xh/fECUyhEAPbt8c5aFD++4hJwS+HWMTgF06xUqCAb7a7kBRQIAV7LZgby9h6BfHOLJACwa0Sd5vHkIKPvzJ67SfXzJcCXYfwbguej+JQs0Vck704BgcRPnweZvy3cqQgGIL/fmD8eYkh+ipNSKxb+6qWAgBb5zCuCV6UUyY8n8eh/fHPMNyoY68qKQCo37sLrcYMN17nzDnW/+9jADrVaoMkSiw/vo6b5j4UPSFR12HcPUa06jJRqZEDm82Qgn37YOpUCIdp3bo1HTp0yBcEXdeRj8p43/fiSnOxpckWdtfYzVMdnuKV4a8UyRtg61bjeFsLqjZEQURXdda+v5akPUkEuweJGxtHfGIchw8fZpXPx9o9JwlMDyDnyGyutQZ1z3L6O/rRIq0F1p5WTEkmQwqaezn21cNs3LSR5Nq1yQkGsdaty+CMDJxdu+a/ZkwKfp3ExOBnSFQp+MqNcjy3Ta9ZB9lYPojstmBpHcHcOozvKzdEjB+7WEMh7jYPUjUNTqXBH5+D+QVZ7FpQwP+tk8D3LizNZOLu8GBePANOpho5AHVqFXd6+ZQ5UrB2s1GimFrmkRYlUlgOnl7zOhE1UinH5b8fGHkQVznmxsbPFVnAE5iIUqdjlUpBHkOffgwht/HNmpffwX8uI/85RVOZf3h59GoFQYD//A1e+Xuln1dJVPqyQk4O7NkD584B0KpVKzp27MixncdI/SAV3wwfgktgfq/5DDs0jEP2Q9SWa7NhwwZUtVC78IYN4aOPjD/zzimk4fvcR6esTvzV9lf67e+HFqfR84MPuGHBAkb0HEH/s/2x2+2473AzbHAnutYZh22rHWs/K5ggnBLGOsDK7gan2TVqFI0zMkg/ehSXJDFo6FDs//gHuN1ATAp+zcSWEi7gal9KKFYKZPB+5UY9dYEUtIog77Ni7RxCTFQJLnOQN8Pe1FDGdaPXmH6XR1p6fhhXPmbC/4MLZHAMD2BpHTGiCV1GwiN3wMN3lHie5a4+yMoxuhxWIqqmkhXKobojCUVTMImXMNtA16HdMOO9/2ZK5Z1kFaL5BHyzXajndN5W/sy/rV9VmRTk8d2Df2XLBzMB6PnQ7Vz3n7/mP1dah8R8giE4nwn161TZeV5IpS4rFFoO0yM6obUhgmuChMUw3nZeltZcygMLH+DRno/y6rWvcvr0adavX0/NmjXp06cPpmJmcKjZKr4vfOg+HedEJ2kJaQz6eBAAG+2PEi80w5/dFzFexNU3A6FxLYIrIPxTGNswG7pXJ7whjKVLgE3STs77fDRv3pxD+/eTdOQI/davxzxvXv7rxaTgl0msKqGCXM1iEFUKZrlRUwtJgSJgbi4jH7Bg7RlE1yCyqSDL39w2jPM6P4KE0aPgs7lGJYDJhK5gtDTebMPUUMY50ld0kl1WDiTElRjyL5cUrN4Evbvkt1itCrJDHgZ/fit/7HXvpeccXGIOxOXG6/UTeXwfNB7M2d77aTOgfLMTyv16qWd5re1QdFWl1yN3MuzZx4s8nycHk1uP5qNRLxR/kMkPwpl0WP7lZf2sK1MO9LPniTz2LsGO96DLJmy9bJxOPs2WnVtYmLmQuIZxvHpdQU7B2bNnWbNmDfHx8fTv3x+L358/REkJuPHN8iFYBFyTXUjVjX8rJ3JOMOjjQfyz3j8ZfWA0promXBMc0LsbgeEvEonrhn2kHTVNJbI1gjhYZO3eLwlbrTSrVo19gQC1atemd9OmmKxWqGbMP4lJwS+XsopB1Y+Hi1EpFCsFkVwpSCskBaqAqYkhBbb+AdRzUpEeBdbeQez9CrXR3XvICI+HIyiZVvzzjfHI9iF+rHndC3Ud3vwUbh4DSQklnme5pOD4aRh+K7z/Itxy4yV8OiXjtjjpWLM1U74zyuEuSQ5+RlLgi/gZ+c1dHGy8n7XN15C8vi1BsYQ2ypWAu04txn74H+p0bkdCo3oXPT+8cX/mT3iPuu4SlqGefBgk8bJ/1nnLCkAROchbVgBKlQM9rBPeEia0XkJveT/meC/2m+oiJUos3rSY2Wmz+U3yb2hSo0mR/WrVqsXAgQNZtWoVy5Yto29CAu6JEwnP209gN0jJEq6JLkRnwepvgx3H2X7iCRTvaMwtzVhusIAk4n/oe+R0G44bHMgHZeQ9MpGBEdaeW4utdm2aqyq7vV4aHDhAj6FDEZOS8o8Zk4IYEIsYXMTVGDGIKgVfxKGezb3TNuugCZjqySjHzdgHBZAPWVBOFepRMDyAtVPu+m6heQS6ohLe4iS4yo6UpOIc7UeqUWi980Qq9BgNb/8bbrw26nlWqHnRTzuM7ndVPML4kqsVPpsLb02HlbPLNMfhSnNhTkGvOl0IrbcSWuXE0jGE45pAlQ8wKss5Pr/+Hf7W58HilxVUFU6fhQaXb0kBKhY5ULNVIlsihDeH0SM6lvYWbL1tSDUk0HXe2vgmDyx8iEd7PsojLR7hp59+onHjxnTr1q1I0mFOTg5r1qwhEorQV+6J6YANS2cLjuscCKaC7XRdJ/TmRkKZLbB0sbCy2Uo++ehx/td8GaZ0M85xTiJbI8iHZTI6n2OLdyvJNWuSUL06e/fupVkkQufXX0eYOxeSjShSTAp++cQiBr8QipWCcK4UpBeSAl1AqqWgnDRjHxIgvM2Glpn7vKTjvKHQND5FgYn3w7D+aFNux/+9u6AMsX8Q4cLfigZ1YM+yEqMF5ZaCvJB8tw4V+lzKS15CIsC0+X+kT90uNIyvW8pehaiXDIN6/SyloHdcC+h8Lfanfoc44gYCC53oARHn9b6Lf9aXkZ3n9vPyxg/YenZP8TkHf3gWlqyGrQuqXBwLU9bIga7pyAdlwlvCKIcUsIC1sxVbTxtivJi3E4ev6cZRcSuPPvZofkmiKIps3LgRXdfp1q0bYu7vVXx8PEP7DCV9ejpitoXsTtk0HNkQQSwkBapOYEGASGYLbANs2AbYaH+gIW953yB8IkB4vAnTRhPKKYUjrY9w2HeYtgsWEOrXj73nztG2TRvatG2LcOut+VGZmBTEKEwsYpCLIAgPAg9iVGq0vBoiBsVLgYDnMzfa+dyLvgkQdaREDTVDwj4gQGidHT2YW45o1XDd5MVUp1AEQFXh2f8RaXUDgTNdwKLjHOnH3FApegK6Du9/AVPGGY1oolChSMHL78KyNTD/48saMlY1lTWnNjOgQY/L9pqXk6jVB3/7D4wZDt06EDlkxv+tC1NtBec4H6Kt6r4DIv4A6//3MfV7dqbx4IvHY5eYkHj4GJw5D327Vdn5lURJkYNPnvuE0fbR6B4dqY6EtYsVS1sLgqXo7/Jbm97i1J8foEmfUdz59HdFogPHjx9n48aNJCcn06tXL0wmE8ppBf8cP3pI4Vzwa7a2jqdOnTp069YNm81mTE+c40M5HMFxrRlrjzgjMfEzH6o3yEP6fdyvPUZrsTU76u/AH+ejW/fuHD18mNOnT9Pl889p2rQpvPJK/nnEpODXQyz5sIJcLUsJxUmBFhLwfuZGy8iTAh1MIDo0dL+IrVeI4Go7qMaXjxiv4proLTrUKBBEEx0EFzuI7LVibhXGMTxQ/MVh137oNw6+fg+G9Cn2PCs8+2DRCti5D/7wm/J8LJXKs2veoGlig7ItK2zfAw3qVnrlRGVSnpJE5bQJ3xwXotsQR9FV+d8DWUdO8OHQyfjS0qndqQ33rp2HUEzEpbAcfDv+nYubIek6pJ6N2qK7KokqB4LIh7/7kFv/cCum5OKjGW9teosHfiioPhAEoaBpUS6pqamsW7eOpMQkelh6EFkRMfIJupxD/MNvSH3+eTaeOgVAh2YdqL6uOup5GdfHkzC/9jhKx6H4pmcj2M04b3SSOTcTxaOwvf52EuVU2m7dyqaxY8nKzqZXz57UXbsWOnSAVq2AmBT82oiJQQW5GsSgWCkICnhnxKFl5X6xSoBFR7AYVQiW9mHC623klSNKyTKuCT5Ee6Gf78GjyFNfxT/pPRCs2IcFsLYtpcb/7HljNkAxVMVApMuFruvc8f2fyp5zUL2jkRR3GVv3lodSpSAchmVroWsHqGlkn6vnJbxfuhFMuiGQCaWP9i0PuqbxXt+xpG3dDcC4j1+h/eQbit32x6Or2J6+j8d73nPxky+9DW98AruWgMtZqedYFnRd5+HfPMcbn35c5PGScg6KlYInnjCGLs2cWSRKdv7UebJnZ1PNWw2pm4R7uBtBKng+FAqxb/U+am2qhSiIBIYGqF1NxyTUwzfLh3hqF7722Zg8PdEUjV0tdlGzQ02art/BKlUlrOv0y8mh+m9/W+QcY1Lw6yMmBhXkSotBsVIQyJWC7EJSYNdAB0EyehLIOwsuyuYWYZyj/UXWj7UQBJdZiexyYqoTwnlDCDEuyoVAVeGzeXDLmKhru5ckBV99D80bQae2Zd+nCihXQuLWXZBcC2rXuHwnWEbKFCnIyoE63eCDl4pUgKg5Ir5ZbnRFwD3Rg1S9cuXgyNI1TB81DYCEhvV4cMciozSuBH44nMLQhr0LlhXS0o3KmdzOipcTzSsQWOwkctDMEyl/4p3l7xd5vjg5KFYKAObMgbNn4f7788VAPiLj/86PHtHZnbybnMQcBgwYgDu3yRBAZH8E/1w/erzOwSZ7OJGTSk1PLdqdaUeOM4eDiQfpmNoRzawhj5Spn2gmw2xm9erVZIUzuH7GHGqsWgsHD0JNo09JTAp+ncTEoIJcSTEoVgr8At7pcWieXCkQQXBq6LKA4NCQ4jWUowVDh6w9gtgHFi1HU86IeD+PA0XAPjiItVuo5GX9VRthxFRI+bLY5MBLkgJdh26jYOQQeOYPZd+viigsBwsnfsg1jftd6VMqF+XqaHgiFeonX5TTofkEfF+50XwirgleTMlqlANUjOmjpnFk6RoARrz6d3rcPzXqtmm+dJq+PYTBDXsVn5DoD4DTUannF43IATOBhU4wgWNQAFOrML/9Q8nVClGl4AL0oEIwJUL4pzCmxiac1zsJmoKsXLmSSCRC/5o1SRw0iPCMPQT3JWFuZcY5xgl3TMHn7o9SdxLBZA+BpjJJG5IQk0Tibo1DOHOUw7/7HVtvvZU4t53fH/oLQS3AyiEzqNfBaOcdk4JfLzExqCBXSgyKlQKvgGd6oWFHIgguDT0gIiapoIN2LveOXtBxXFOoHBHQNQhtsBFaZUXMOoF9vB1LtzJOLjyRWmyZWKUsH6iq0d3uCoSFi0PVVP5v00fc3+VWHOZixj1n5cB/P4Sp46FJg8t/glGozDbHWii3S+J5E65xXswNlNJ3KiNp23bzbq8xANTt0ZG7V84pcfuoCYn/9z58MAu2/FBkWFFlo0cgsMxBZIcNc/MIjuv8+UtyJSUk3v7M7Xwof1iqFMj/nUMgrRVafB3sw+xYu1nztw2Hw6xatQpvpoe+x5thDtXH1teGbbANdAh+cpTwqURs7UKITz9CYPzbmBpZcN3kQhEVtmzZwvHjx2m2YwedPvyQ82++RK/jRoXF8mnLqWGpEZOCXzGxIUo/I4qVAo+I59P4XCkQjP/FaeheEamWgu4XC6TApOMa7ysiBWqmESUIrbZj6+ghrvXy0qUgEoG5C427+qqSgmDuFLqrRArAKGV8rOfdOMx2dp07wFf7fii6QVaO0cfgfOaVOcFiqJAUHD8N19wCew5c9JRo03FP9GJKVvDNdiMfqbwLb3KnttRqbyS7nd64HW/q2RK3LzyyuchshWH94bF7q7SKRUmT8HwST2SvFcd1Ppw3Fs3TKWm2wod//ZARoRFRpUALavi/8+PzDEF06MTd6cDW3VZkW6vVyoBOA+iV2hsxXIdzXc9hHWSFCPi/9BM+nYhjpAOhTgKBce9gbmnCdbOLzDMnWPLdd5w+fZqePXvS5bbbENu1o6Y1iZTbUwAY/PFgRtwwIiYFMUolJgZXmOKkQM0W8XwSh+4XMJIJdYQEDT1bxFRPQT1rQvfnliM6NdxTPJibGD0KdB1CW6x4Po5H92q4r0/Dfq2OMPXG0k/m28Vw22/h0LGLnqoUKTh9Bur1MJLgrlI+2P4lk7/5bdGpjE0awMGV0KPTFTuvwlQ4UlCrOlRLBLn4aIBgAdd4L+ZGMr6vXUQOVJ4ctLx+WP7f93+/tIQtDfLkICuUQ0AJGQ+2awm331QlPQ10DULrbXg/i0Ow6sRNy8HaIVKsg0STA3RY9OIivvzyy6IP6zqRXRE8b3mI7I3gGOnA9be2SLWsxj/YQsgHZQIfBXAINnKabWW7fzsrv19J1gdZyPu8OHuko54LE/wxhLWXDWm0hS3btrB0/XrMhw9zzY4dNARo2RJ+/BFGjKBBfAMWTFqAbb2Nzes3x6QgRqnElhIu4HIuJRQrBVki3ulx6KFCUpCooWdJSPUiqKfM5Fce1FJwjS8oNdO8Av4FLpRjZqydQ9jfvB0h4IFFM8p+UsdOwQWtbCut+iArBz6cBXffDPHu0re/Alxyh8Qq5nJMSdRV8M93Ih+w4BztNwZoXSKFlxOaXtOfKd99VLZz0XUEQSDVe5Zq9gSskgWeeMGQtXtuueTzAtA8Iv7vnSgnTdh6hYyW0WUY3aHrOkNum0LK7A1FHi+cc6BmqwQWBFAOKZhbmXFc50B0596PzZoF770HP/6IjkAoJURoTQhzCzOORocQe3Um84ctKNvrougKp7XvaZAwBHNGAuHq+znZzcTJkycRRZE2LVvSfPt2xLvvNqYjHjoELhcQyymIUUCs8+FVTnFS4Dsj450Rh03LC+ToiIkaWpaEVFtBPVWwFGBuEcY5yo9gNm46IrssxvREM7hu8mJuLEOLJyEzq2wnlJ5hlLFVlRSA0QPgsXsrvv9loHCHxCnfPYaAwOQzSfCHZ2DJF6XOiqhKKkUKcryGoBUzxyAPQQLn9X4CCwxB0BWwtr80OajdsQ3x9euQczKVYys3EPEHsJQhiVAQBFRN5ZpZ02gUX8/IOYjIEJEv6XzyiOwzE1jkBIuOa3L5cive3vo5KW030DHcmu3f7c1/PK9DonxcZpQ2CsEu4JzoxNLygqW8unWhRQu0cyF8CxTUUyr2IXasfawISlvCKWcR1pix1ZHI7pRN7ZTrkLLs7Ki7k3R3Ou4MN61lmaYdOmBt0wbatIHu3WHDhpgUxLgkYhGDC7gcEYPipEBJl/DMcCEoEjo6AgJCnIruERETNLTsgluYwoOQNK+Af5ET5YgFS9sw9qEBxKyzkBQPpZSF5eP1QctB8LdHoFDGeKVKwfY98ONKeOj2ErsoXi2omsrDi//JLW1uoF+2Cz6ZDc8+DrYyfqaVTKVFCv72H/hyPuxPKXVTXYfAIiMJzzHcXySHpSJsfn8mCNBy1FBc5Sz7LPPI5jKihyGw1ElklxVzyzCOa6M0+YrCW1s+44Efn+LRbrfzypAn+O0fni2+CdIfPmTqM1MRrMXnRUT2RQjMDyBYBJxjnZjqm9BVneDiIOFNYSydLFibh/H/oKFjwjbehlJNwWKxYBEE6NLFmIoYHw/Tp0Oh76yYFMS4kFhVQgWpajEoTgrkNAnf53GgCvlSkC6cpYZYHdEsoIfyqhKM1sWWNpGiUQITOK71Y2mWexc17GZjLXnWm2U7KU2DrxdAry7GTACqoHnRJ7ONNshbF1TpiOWqQNEU1p3eSv/63a/I61fq8sHhY3Au0/hZlwFdh+BSB+EtNuzX+LF1vjQ5uBSKyMF1L2P9ZC7cNr7cy1JKqoR/vgvNL+K4xo+lbfG5BNEoLAWvDn0SQRDKPXhJl3Mv/pvDmN3pOLLmIP7zCTSvhn+OH+WUjP38XIQJ1xFIMSOdOYjT8iNSi2S4776CA3k88Prr8Oyz8Nxz8LvfATEpiFE8saqEq5BipeCkCd9ncbltjHUEQLPJWHUbsqrmS4Hg0HDf6sHSJoLmEfHNcRFY4MLcTCburpwCKQB49Sn44/1lPzFRhAmjqk4KAKZN+FlKAcBnyz/iztdvKZqQeJmo9JyCpo3KLAVgFADYhwawdg0RXOwktOXKREygICFx1clNbN+/Af75KqxcX+b9dQ2C63ITDO06cbfnYG136VIAxpLHS/c9zb19inZuzFtWmDVrVv5j6nkV74dewtvDOEY4cGo/IO7bjnwsgud9D2q2imtQFvp5D4HldsxNLLjHqkh4IRQy/nv4YThwwIgQPPEE7N4Njz4KxKQgxqUTixhcQFVFDIqTgshRE/7ZbtANKUAAJGP+AaECZ8tLMhScOuGtVoIrHAhWHcdwf1EhOJ9prIGXZwLgS28bneVe+TtQRVJw5hxUT7ysE/IqE+3Z/+J5/V2q/U6+rAmJVZJoePQkzP4e7r+tXCWjug7B5XbCP9mxD/Fj63blIgeZwWyS7Ano2R5ktw2LVHpvDs0j4p/vRDllwtY7hK1P2RIMCxNNCnQdQqvthNbZMTUP80TKn3j9neIjB2PbjsU/348YJ+Ic78RUy4SuaYQ3RAguDWJqYMIx2kFwaRB5n4ytvw3bwKIljezaBSNGQFYWDBkCX3+d/28rJgUxSiIWMbiKKFYKDphzpQBAN9ocYyR+FZYCc9swS7p9RXpmFt7P3QSXOLG0DRN/YZRA12H8vfDAk+U7uYQ4Y9mBKpx9cPfjcPNDlXOsK4B4+0Tc86ZzW9sbmfLdY5clclBl1QcnTsOr70NmTrl2EwSMrpk9ggSXOQltqljkQFMUji5fx4LfP03KM/+t0DGS7AkA/HHLm4ybfT+RbTtK3D6yz4LnozjUHBHXzV5jtHhlSYEKgQVOQuvs2AcGcN3o57X/K77PwS233ML0p6djaWkh7u44QwrCOv6vAwSXBLEmn8He9BS+WT7kIzLOm5zY/csQ7rjDyB+I5CaAtmtnVB3ccAOcO5f/eEwKYlQWsYjBBVR2xKA4KQjvshD4odDdmglQBGNaopJ7ZyDo2IcGUFpl8793vuFO+W5MCTpxI8KY60fJnF6+DtzOYtsYl0aVDkTaugtCEehd+aV1l5O8Ukanxc4bw/9ZZa9zOUoSK4quQ2ilndAGO/bBfmzdyxc5iPgDvFS3O0oojCu5Jr8/vLrYiYtl4cejq/jxsbt5domOcHID1vjEoud6iQmGeUSVggj4vjXKgx0j/EUGkpWUc/DZZ58xefJk1EwV35c+tBwN5/V2hIcewDfoOcTqDlwdTiHd0B/+8AeYPRv274d16+B//4O774aePY0DahqIYkwKYpSJWPJhBalMMShOCkI/WY2EwTxMOigiRuggd73SruG80QcqBH50onoE3pXe4QvnDBbe8gHJrpqXdF4AZHvgnRnwwFRWZO3+2U5JvCzMWwThCEy6HlVTEQQBURA56z9PLWfxkycrytUsBXlcqhx8Mf5eDny/DIC7Vs6m3iU0jkrZNJ+/z3ic+D59mD3+zfxqBSVNwv9dboLhMD+WcuYS5BFNCrSAgG+OG/W8hOtGL+bGF8u6rus88ugzvP7uxXLw6X8/ZVRwFILDKGVUDigElwUwtzDjvNGFkJ0On34KU6dCrVqQng6bN8Ptt0NGBrzwAjz2GBCLFMQoO7GlhCtMcVIQXG0juKxQpECiIEKQ17SojozrJg/hrVZ8X8YhujXi7/AwflpPMuRMhnxxG2m+9KIvNvNbuOm+glBjWdiyC154i3V7V1WtFGzabuQx/JwFdNEK+G4xYPQ5EAWRrWd20/itQZW6rHBZpCAQhAHj4ccVFT6EIIBtQBBbzyDB5U5Cm8r3O9Pq+mvy/77v28UVPg+AQd1H89ffvsuSk+v5v58+LppgaMtNMGxfuVKg5hjtxrUcEfdkT7FSAKB5JJ7p8B/u7XtxQuLUR6Yy79g8XNNchNeFCS4LYutnxznRhRD2GjLw4IMF7Z9r1jTyCg4cgFtvhT59gJgUxKgaYmJQBVwoBV27tMe/yEForYPcpALDA7S8vxhYugYxN5XxfhGPctKMY6QP12QvUjWN5kmNWH7zZzSKr4tJvGCB1OWAurXBUsYBSQBD+rBy49sMW/XHqo0U7NhrdDuswv72Vc5b/4IZrxV5qEPNVkxsNbLScg4uW6TAZoXWzSH+0qJh+XLQK0hwuYPQhrL/7rQYNSR/+WD/d0su6TwAhh83cezQNTza8i58s9yEVtmx9QjhvtWDlFixMdLRpEBJl/DOiAMN3Ld6ok6iVM8Z2wmqwBuz/nxxzoGucdfbdzH9z9OJ7IrguNGBfbAdYfp0aNgQ0tLgpZcMQRg50pCEjRuNfgWffAK9e8ekIEaVEVtKuIBLXUq4SAo6t8c3z4VyqPBFO+8zz71YWjSsXULI+6xoOSLWLmGjgZE1+s/mtPcMoiBWeFlhxfH1jJx9T2z54BKorPbJP4flg2gUzsi39Q9g7x0q034fDb2ZE2s2AfDg9kVUb9m04ucw+wci36QS7PYHIlKE16u9zJM33VnhJkjRpEA+YcI/14UYr+GaUNCK/EKUMxK+L92IcRqum7yITh1d13nw1n/x1tdFW0GLgsinr33KrQ/dajxw6hQsXgwtWkC/fjBlCtSrB6+8AooCmzZBly4xKYhRIWItka8AF0lBh/Z4P3OjpuV9zHl5BAV3z2INBcGkE17vwNRIxjXOh1S9+LuQwtz23R9I859jnXITCcOHGfXpGF/UelhA9wtoARE9JBj/hQV0WQBZIPXEEdp+d5LZXV6nb+Jw9BUSAREEkw4mHcGiI1h1BJuO6NARHBqiW0P4tf62THoA+nSFR+8q8nDh9sl/XfkKY1sMx1bOi9EVkYK8KZHVky75UIIA9v5BEHVCqxygga1PqNQAUasbhuWLwYEflldYDNRzEoHIJJT2ZsxNwmxtmcJL377O5rmbK9QhMZoURPab8c93Yaqn4LrRixDlsMppE77ZLsSkXCmw6Uap5woHz3b8D2gCb837MH97TdeY+uhUTDVMRhOkevXgjjuMXgUHDxr/32YzEg7few86doxJQYwq59f6VV/pXCgFXVp3IOeDOHRPwdyDIgg6YjUV7ZwJsbrRp8DURC5TxF2PwPvdXmb6N/PRD3chK2zGVNuN5hHRfGKhvIVC5F7ww0IIj9eKufVgeldrAGkmFB10VQAVdMWQiOKOIdg1xDgNMUFDTFCRklSk6ipSNRUh2irGA08aJZH/+lPpb+xqpX0raFC32Kfy5OBcIBObyYqqqUgXLvVE4YpFCm64Ezq3gzeerbRD2vuGQILQSgd6WMA+OFji73K9Hp3z/+45fabcr6dHILjGTnizzbiDv8mD2Z3O4Oo9+Gb824yZcx/j5j5YLjmIJgXhrVYCix2YW0VwjvRHFWT5pAnfbDemvL4jucMTAz86iGy34Rjq53/3PYmaJfLuivfz98srZQQMOTh5Et580yhFNJvh8cehaVN4/vmYFMS4LMTEIBdBEB4EHqQCeRcXSkGnRh3JeScO5LxqAygcJcCiQcS4ADuu8xkZ08W8qi6Del5CPSehnjMZf8+Q0H0iiSTxCK3RmmjsV/bSwhzE0dyM6NYQnTqCU0N0agj23Lt/qVBJYqO85YNA1Pekq6AHBfSgiBYQ0Lyi8V+OiJYtIadZCHsKLoBigopUS8FUW0WqrWBKVgxZ6NAKHKUPy7mq+esjJT4tiRK1XTXwhn0Mn3U7j3SbVuqywhVdPnjl74asVTL2XiEEi05wiQM9IOIY4Y/eL0CI8vdS0HWQ95sJLHOihwRsfYPYuocQXnwd3vscjqzJ75A4Zs593L3gCaZf/3Kpxy2+zXHBMom1awj7kEBU2ZGPmfB97cZUV8E11otgyZWChU4iOy04Rvow1VXwfRHHCzf+C0szmdc/+CR//yJy0KIFvPuu0cBI142/HztGoFq1mBTEuCzExCAXXdffAN7IyzEo634XSkEHdxe8H7oKBQgKf5PkPmgCe78A1o5hhNyR93oYlLMm1LMm1DMSSroJLVPM74ooJmpI1VWs7cOISSpSoooQJ3MkcoJbZk7j9Y5PMbrZkKjnmS8FdTrzvTYGS04AqkfPKxAkEFw6uFSifbfrEVAzDFlRz5pQz0oE11pAFkDQkWqpmJr/BlMDGXNYKTFn4qrmyAmoVR1KmQboMNtpmdSEKd8ZZWTR5OCK5xSUoyVyebF1CSM6dPzfO9ECIq4xUcLuhX4VhDImpqqZIoElTpRjZszNItiHBpDic5MLx14LHVsbdf2SxPDG/fl2/DvUcJS+XFKsFGi5d/o7bNgHBrD2iL48Ejlkxv+NC1NDGdcYnzHxVMuVgt0WHKP8mGoreD+PQ7DoxE3y8Zr7rwhWvUifg3w5+OwzJq1cCZMnwy23wKlTMSmIcVmJJR9eQHmSD4tIwfef0DqjB5HtNgwZKOhLkI9Dxd4rhKVtGC1bQkkzoaaZUNJyJQCjyZFUU8FUS0WqqSLVVJCqq/kCkY8sQ5O+8MFLhIb0wmayous6nrCPeFvRoTKFmxd91/lJbB1HwncfwTWV/+Wi66Cdl1BOm4z/juhoQZshCskK5oYK5qYRpGT151GooCjgagXvvgBTx5e6eWkJiVdcCgBWbzJkpwzvp6LIx0345roRnRrO632YahfNm8k5kcqWj75E13Xq9+5C82sHRj2WLkNovZ3QRhuiS8M+NFC062cphJQwL65/lz/1uveiZYVipUAG/3cu5MO5jYvaRS8Djhww4//WhbmpjPN6H4IpVwoWOInsseAc5UeqpeCdGYdg13BPMpIRoeQmSIUHL8WWD2JUFrEGRxWkrGJQWAqWzfmCxlt7QLD4e2vBoWJqKiOIoKabUNMlY2iSpCPVUDElK0b4vbaKWE0tdlnhIgJBeOU9GHsdtG0BwL/Wvsn03d+w7Obp+dUKxXY0PJcBca6yj2WuKKEwJLRFffttlE6jkI+bUY6b0EMiglPD3CSCuZmMuZF8sfhcLagqrNoILZpAnVpl2yVXDmbs/oZ99y6iWWIj4CqRAoC/vwyLV8K6b6r0ZdRMEf93LtRzEvb+wRLvuovdP0MksttKeJcVPShg6xHC1isY/Xfl3c+gawfo2r7IwxtStzHo81svGtlcnBRoIQHfHBdqugnXGB/mJtEFJLLHgv97J+aWEZyjjGUTXYPAD04iey04R/uRaih4Z+VKwWQvoqPo921UOQA+B8ZNmMC1GRkxKYhRKcTEoIKURQw8Hg/jR4/Dmm3l/WlvYw04uXihNHcYkk7u5EQQE3MlINlYg5dqqpWa6X8w8xiDv7gVt8XFspuncyDz6JXtaKgosGkHNGlghOIxvjiV0ybkw2bkQxa0TAnMOuZmESytIpgby7+I6gdVU1l2fB3XNO4HXEVScJnRVQiuthPeYEOqpWLtFMbSKhw1q18LCkT2WYjssqKmmRCsGuZWEWzdQ0hJpfQkaNYfHr0THr7joqeKjGwe+wYf7ph9sRT4BHxfudF8opEMXCd6dVB4h4XAQieWdhEc1/kRRON32z/fibzfgvN6o7rIOzMO0anhmnSxFOR/RiXIwePx8byuKDEpiFEpxMSggpQmBl6vlydu/QtPd3+m5AOZNESXjuDSEOONzH0pQTeSA+NVBKd+aaH0tHTjv05tikxTzJMDSZA4F8ikb72uRaVg5z741//gtaehRrVLOIHKQc0Qiey3IO+3oJ4zgUXD0lzG0i6MqYFy5ZcbzmXAjLlw8xioXaNCh3h+3dt8vHMOqb70X5UUFEY+aSK0wYZyxAxmsLSKILq1glwDHdRMCfmQGXQwNzF+B8xNK08U8+SgaUIDdp8/WEQK1BwR3yw3uiLgnuhBqh5dQkJbrQQXO7F0CuG4xkhI1NVcKThowXmDDylJwzvTXaoU5BFNDgCeeuop/vGPf1zq248RIyYGFaU0MVixYgW33Xgb23+/PcoRjPHJgtXoCYAIqEYvgbzIAQAWHam6iqmmglRHwVRXQUzQyn4hfO9zeOQp8O+/aMzyZ7u+4bb5j1HPncz+excXjRRs3wNPvgjvvQjJlTBzoSQOHIG5C+Gh20tN3ANQzxuSENltRcuWEONULG0jWNqFK9zB7pLZsReuuQWWfGGULZYTb9hHs3eGkh7I4B/9HuGpfiVXOFwWVm+CJ56H+R9DnLvUzSsTzSMS3mkhsteCHsYItIkgiAKCXcfSOoyldSR/Hb6yeWTx0/xv86c80nUa/zfsr4YUZIh4v3QjSOCa6EVKKEEKNtkILncUqVLQ1dychENmnGN8SInlk4I8oslBUlISR44cyftCjxGjwsTEoIKUJgaKojBt2jRusd1C0zZ1adC2JoJNQ/NIKGcktHMm0AQw66ACmoDg0jA3j2BpEUawY5T8ZRpliMpZE1qGkXgouFXMjWXMTWQjpF7SuvvZ8+D1QdOGRdoN5+UUdK7Vhvnj3yPBHoeu62XO/K5Uvl8Kv/kz7F9RJjHIQ9dBTTUR3mVcQIiImOrJWDuFMbeI/GyWGvKWD7ad3cOA+t1ZeHTVJXVIrDR27IU3PoHn/wKJV+Zic2zlBj4ZbnT76/PYvVzz3B8v7YCyDMOnwBMPRU2qvTCnYNnxdfQx9yT8dTUEp4Z7YvRuhmDMYAitcmDrFcTWP1ggBd8aiYrOG31I8RreWW5El4ZrYtmlIA+/P0DLDsM5ndvbIS4ujsWLF9OjR49yHSdGjOKIdT6sIkwmE5988gnTpk1j1p9mMXP6/zFh3Ij853UZ5KNmIrusRljUrCG6VeQDFiJbbUg1FKydw1i7hPIv/FpIQDllQjluNvbdYTPW3ZtGsLSOYG4iX1wPXqt6/rp9HsUlGm4+s4uHF/+TOWPfKGifnCeDVS0Lo4bCqU3l3k0QwFTXiKI4hgSQD1oI77Din+9CsGtY2oexdryCUYQyUDin4MfJH9MjuSN3/fAXpnz3GAnWOEY0jZ6FX+V0aA3vPH/lXh8qf6iWphm5LC5nsU9fKAXng5k8N/tDpuuDcdVScN/kR7RHywEo1Pa5XwBb71CBFHzjQj5qxjXWhxhXSAomeaMeLxqBQJDrx91LVpaH8ePHs3jx4pgUxLgixMSgAuTJAcDk237LTMiXA8EMlhYylhYyao5IeJON8HYrWHSsnUNoXpHAYgfB1XZs3UJYu4QQbTqWZnJ+CZaaWbDu7p/rRnBqWNuFsXQodDGUZfjbf+DGa6FXl+KrD4A4i4sTnlSGfHGbUa1wygNdRhqh8T5dL/tnV14EM1jaRLC0iaBmiIS324jssBLeaMfUSMbWLYSpcdk6RlaITdvh90/D7HcuErFoREs0/GDkv2lZrTF9613hHANNg3OZ4HaCw35FTqFwpLJSfnZWK3zwUrFPFVd9kHCmNl/xFWv0tXxifYvPzS9j5eKMSF2HYIqd8CY79kEBbD2MWRC6kisFx3KlwJ27fOCuuBSMHnsPG3/aycKFC+nXrx/Hjh2jcePG5f8sYsS4RGLTFStInhxMmjSJybf9ltlfL7hoGylewzEsQPw9OViayIS32tA8Is4xPswtIgRX28l5N4HQFit6oQRoKUnD3jtE3O0e3LfnYGkZIbzNiue9BHxzXCinTGAywfK1cCotqhQA+VMZvREfQ764jTNuAf77T2hcv+o/pH+9DlMqb01dqqbhGBIg/v5sHCN96EEB32w3ng/iCW+1opdj6nSZiXPll4OWhZKqDyRR4i+97yfO6uZg5jHm7FtYBSdcBrI90LCXMU76qqASzEBVjURRuWh5YXFSENlnwfe1C2sTFfu4bH44uZxxcx8krISL7KvrEFziMKRgmL+IFPjmuZCPm3GN8yG4Kk8K8qoPBEGISUGMK0ZMDC6BssgBgBin4Rzlxz3FaKjo/8aFYNaJuyMHc1OZ4BIHng/jkY9cnFRgqqkacvFANo4RPtRsYxa85/M4IjMWsqJb9VJLEgvLwbhlf0a/e3LVJx6CUTHRunmlH1Ywg7VdBPdUD+5bPEg1VAJLHOS8lUAgxY7mrcTwQcum8Pa/yxQtKE9J4rvbZjLxm0cqZWRzuYl3w5x3qrQDYqlUoPNhiew/DPV7wtrN+Q8VJwXh7Vb83zqxtIrgHOPjmmZ9+Wb826T50skJ+wpOT4PAQgfhrVYc1/qxdTGkQVfAN9eFcsKMa5wXwanhm1W5UhAjxpUmlnx4ARUZu5yXkDhr1sU5BxeiaxDeZCO42o4Yr+Ec7UOQILDUgXLCjLlFBMeQAGJc8evnug7yYTOhDTbU02bCepiZ7ve49+5xOCwl9yk4mHkMT8RH12wbrPkJ7ppcpvf3c0DNEQlvsRLZYUWXBSxtI9h6BJGqXWIegq7DmXNG2D3K+jWUv09BZY1s/rlyZNlapo+cCkC/P97P0Kcfu7QDBkOwMAWG9QO3q1gpCG20EUxxYO0cwj6s6NwDTdcQBZFzgQzcJhfqoiQi+yw4RvqxtjVCUboMvrlulFMmY0iSXTekIC430TAmBTGucsqafBiLGFQCZY0cAAgi2HqGiJuWg2DS8c6IQz5qxjnRi/N6H8ppEzkfxhPeZi02P0sQwNJMZmv/JfyWh7F6zzPN9xDK5zWRj5acMtI8qRFda7dDXrEOz5PPknb+5KW+9dI5ehK27a7yl5HiNRyDg8Tfl419QBD5qBnPBwn4vnahnL6EVJpIBBr3gbmLom5SkeZFeVMZb2t7I1O+e+zyRg4OHYP/fQT+6EO0qpwiOQaVEDGw24wuoMVIAQgEV9kJphgVBRdKAYAoiGi6xuiZ97Li3WNEcpsUFZGCr90op024JsSkIMYvm5gYVBLlkQMAqbqGe4oHa9cQwRQHga9dmBrJxN+dg6VVmMCPTnyz3KjZF/+I8nIKUhscw9FpCa4hh8Gs4/sqDu+XbtRzJY/9TbuxH+2fiGPI3LtJ86Vf0vsulT//Gx5/rmpfoxCCFWw9QsTfm43jOh9qpoT3szi8n7uRj5nKnwxvtcLc92BIn2KfvpSOhnlycE/HSVSzJ5TzxC6BHXvhn/8HprKNh64K0rbvyf+7o3ripR3szDl46G9w+kzxUrDEQWidHfvAAPYB0cdBC6rITPMXdAx04eUa/0ZvZiwt6BHwzXGjpOZGCqw6vpm5UhBbPojxCyS2lHABFVlKKEx5lhXykA+b8X/vBLOO60YfpmQV+ZiJwCJjQp3jGj+WthEEIcrsA3KXGA6ZCaY40LJFLB3D2PsHo35pHcw8xtDPbsFpcxeZrVDpHDtljPitgjG/ZSHvcwmts6OeMSElK9h6B42Oepd4o1rZbY41XWND6rbL0xlR0y5qjHU5+WDgBE5t2AbAw7uXkNS0UcUPtn4L3P1HPnx9Enetf6FACnTBmFuwx4LjWmOaaTQKLxMc6L2eQWvGMaRhb+aMehP5m2ooZ3IjBZbcSEFCbqTAFpOCGD8fYksJV4jyRg4AzE1l4m73ILp0vJ/HEd5hwdxIIS63IiHwgwv/d05WHdpcfKLh/CUIUx7G0ixC3J052AcFiOyx4Hkv+pJE81UHOPKijOz3MuSL28gJeSv5k8ilUb0rJgWQu/TSXMZ9mwfXTV4Qdfxfu/F+Ekdkv7lsEYQ5P8CS1UUeqorZB5/s/Jp+MyZfnmWFKygFciCIPz0DgJptW1yaFAD06sJbn95RVApUAf88F5F9FpzX+0uWggj4ZhcsE/Ts3ZJvx7/DT8d3kz7TjHLWhPummBTE+PUQ62NQBZTU5yAaYpyG+2YPgSUOAgtdKGkhHMMCOEf6MTeW8Sy0Er+vFXfUnMJL4x8tWn1gtRpf9IEggtOBrXsYS5sIwRUOAj86Ce+04hjux1SrUE1ku5aYHryDRTcOYGbqSuKsrir4JHJ54gVjOuHtN1Xda5SCIIC5sYypkYxy0kRorR3/N26kGgq2PkHMLUqIILz7OTRrZCS2UXUDkaa2G8uKExuZ8p2RiFdlCYmDJxk/i2kTqub4pWB22Hl4zzLO7thLMDPn0g4WCPLBxs94YP3zBVIgC0Y+QKoJ11gf5qbRJyTq4dxlgnQT7oleTHUVAIbV6cfeWtsQMmy4JnhQJZXgrISYFMT4VRBbSriAS11KKExFlhUAwtutBJY4MCUrOG/0ser8eu758ik+MX9Mq0hr7APKPsJWOWXC/6MDLUPC2i2EvV/0sbXfH1pOl9ptK39Z4eG/Q+tm8MDUyj3uJaKcNhFcY0c5ZkaqqWDrG8TcrBhB0PX8LjxVPSWxyqsVNM1ojDWsPwzuXbnHvgIsfe5x+v1rLv+ccTPP3fg0ekjEN9uNmiHhGu/FXF+Juq8eBu9XbtTzkiEFudMUL3z8ne1fcMPuW4mracU90R+Tghg/W2KzEipIZYoBVFwOlFMmfPNchIQQ1wVHUqOem2/GvoOwIZHQejvm5hGcI/3GsKY8flwBsmK0Ii6ErhrDX0Jr7YguDce1fswNFSMr/Y1P4O6bCcXZafXucOxmW9XmHFyFKKdMBFfbUU6ULAiXa3RynhwIgsBHo16oktf4JfDWls/4x9dP8bxpELc/9R663xiGpPtFXDd5MdWOPjZZC+WOWM4UcU30YkrOkwIB71dutAzjcQTI+sLODnkXbzV8hc/Gv4TVFGVmdDHEpCDG1URMDCpIZYsBVFwO1u7ZgTC/Fg2EBsSPCeFqYVypIgfNBH5wIjiMZEWpRu4X4C0Pgd0etTWsmikSWOhEOWXG0jGEo+1JhJ7XwbvPw6ih+SOb3RZX5ctBTm4OQ/zlneZXHuQTJkKr7SinzEi1Fez9A5gaKQgfzERetpIhIzOrXAryUDXjZyqJEhnBLKrZLzFzP49TaRAOw6Wu61cQVZaRzCVNBysbF1YfaB6pYGzyJE+J/Su0kIDvSzdadq4U5ApEvixk5UqBDr4v3YhJGpt6LmL0t3czpGFvvh77RpnkICYFMa42YsmHVxEVSUhccWID1yy4lX/VewpXIwn5myRCm40vI0tzGfdUD4JJxzM9jvBui7HT2/+G91+MekwpScN1sxfHNX4ie6x45jdBXro+P8JwYfvkSitllGWjF8CnsyvneFWEuYGC62YvrkkeEMH3VRy+L9z4LQ2Z7dt+2aQADCGQRIld5w7Q+K1BlZeQ+PZ0GDGtco5VAWZPeZT3+49n9UtvIwdDFTpGnhTMPdmdV3fUQsstSQVw31qKFAQFfLPcaDkirkkXSMGXuVIwqZAUVDOmLg5t0Ztvxr/NsuPreGH9u6WeY0wKYvyciUUMLqAqIgZ5lDVycGFJok2yEVxhDHKxdgtiH5w78lWGwI9OIrutRje3IQFjCuOWXXA+A4ZHn+CnZudGD06YsXYKYJdWIAztCRiljL9Z+FemX/8f6rprV86b/2EZtG8F9etUzvGqGF0H5YgZ30ornLOQIqTQ6Fo7nTtUfovnkqj0nIP0DEg9A53aVs4JloOIP8BLdbujhMI4a1Xn90fWIErl66VQJFKw0o5KbXw1HizT2GQtkHvx9+ZKQc1cKQjmPu7JlQK1kBTc5EEoFBzYkLqNjjVbYyshYhCTghhXK7Gxy+VEEIQHgQepwihKWaoVovUpcAwOIsZrBJc60DwSzlE+BDM4Rvox1VUILHGgnpdwjvEhvvIuZOWUKAZSgtGcJbzFSnCpFTmjBc7ETExdkmie1Ihlt8wA4FwgA0VTL31ZYeSQS9v/MiMIEK6fzRjT3dSjEa86XsKyMA7fkQj2/oFLb7VcRvKaIAGVU61Qs5rx3xXg8OJVKCGjbLDl6GGXJgVDn0RpacY3x42UoOKaUHKjIS2QGynwi7gne/OX3/IjCN4LpUA1ShQvuP73rNMJgO1n9/Lyxg94b8RzRZYVYlIQ45dAbCkhF13X39B1vQ1QpcPPS1pWKGlKIoCtSxjnjT7kI2a8X7rRAgKCANZOYdyTvajnJbwz4lCffdHo1lcKggC2rmHibs9BaFwT79KmBNfa0Atd86bOf7xylhUys+GZ/xotkn8G5CUabju3h7/VbUbNx5vi6HUK9YyE58N4/AucaJ7L88+ncPvkx5c/T0AOVuxAoTD87p+w71DlnmAZ2ffNj/l/b33j8HLtW0QKkieivLcJ31duTLUV3JM8JUuBX8A7040WEHHf7CmQgoCAb6YbzWfIAip4Z7kRqxcvBYU5F8zkq/0LikxljElBjF8KsaWEC6jKpYTCXLisUL1rIqNm31PilMT8fdMkfHPcCFYd1wQvUqJxJVdzRHxzXGgeCdf1PswcggNHYMTgUs9HVyG01kZovR2pjoJzlB8pQau8hESfH9oOhfdeKDGScTVwUfWBpSFs2g6DeqNb7IS3Wwmts6OHBaydwth6BxEdVf/vSNVUUn1nqR9XJ3/oT7k4kQpj7jRyUXp2rpqTjIIaifBS/Z6Ec7xY4908fnIDksVSpn0vjBTI/1mNXx2JuZmK88YAQglxT80n4J0Zhx4WcE8uyD/Q/ALeWW70gCEFegS8X7qRaqi4J5QsBXksPrqaG+b8hiENezPj2pcZf9ODMSmIcVUTq0qoIJdLDKBADmYum4n5fhP9G3YvVQryULNFfF+50cMCrnFFa7D9813IR8zYM+dgXfoqwvpvytbp7k//QtnhxT/mTbSQgHN4AEubSOXJQaF+AFcrZS1J1MMQ2mwjtNEOOth6BLF1C5XpgnKpBOQgo7+6h3s6TfrZTGU8vHgVM66/A4D2k25g3CevlGm/C6UgvNVGcIkDSws/jusjRk5NFDRvrhTIuVKQVEgKZrrRQyLuyR6jRLGcUpDH4qOruWH2b4hLdeH/NBSTghhXNbGqhJ8BecsKE4dMJPKjzO2mcWWSAjByBNxTPEhJKt6ZcchHjBIwwQrOsT6s3UMEEycQ+OsidL2MP+ZJN2B6+Bribs/B3FTGP9+F/wcnzVxGtYJfDrDm1ObSjxMNQQCP1xiRexUSVQoiEXjvczh4NH9bwQr2PsawJmunEKH1dnLeSyC02YoevXy+UrBKFhrE1Sn/VMYreBOw99vF+X9vVcZlhMJS8MqQJwmtsRFc4sTaNYxjTBmlQMFYPsiTgrwIQhEpiMNUs/xSANC3Vldabm6CZ7E/JgUxfjHEIgYXcDkjBnlUtM8BGJUJ/u+MCIFjRMHseIDwLguBRU5M1UM4z7+H+Ptby3zHrqsakb02AoudiC4N5w0+wolenBYHYFxEXRZn+d6oPwCtBsGfHoCHbi/fvlVMiZECWYaEdkYp6M1jit1f84gE19iJ7LIgxmnY+gWxtIlUWYCkQtUKt/0WLOaofS6qCl3TeKVJX3xnzmGyWXn89CYsTkeJ+1wkBcuchLfYsC15Btt/r0Vo3SzqvppHxDvTDRq4JnuREnKlwCvgnRWHHjEiCHpQxPuVG1NNJXdqYvneVyynIMbPjVhVws+IisxWyEMwg/NGH4FFDgLfu9D9AWw9jDtya7sIUqKGb6YFb9ZYnNtyMHVOKP2gDzyJEOfC+vxfMNVR8H/rwjsjDvtgE3rnMP+36UPe3T6r/MsKTge89FcY0LPs+1wG/r+9+w6Pqkz7OP59pvfQEZAuTQQBBUSKIKCgIiAgxcKiq7vqWlFf1153Xde6rm1FRZGqAiooVRALoggKCApK7z3T+3n/OJNJIQkJqYT7c125IDPnnHkyKfObp9zPcYcPzGbw/1poqDJ4kjgHBrB1DhNaZic410Xkhzj2XiFMTUu+k2NeeVcrnF2nNWfWOs5SyqEXl24jimjLkuX49x4AoHn/nsULBb0fIPSZS98hsb8fa58eenntAiQyDfin6UW0XKN9GDNyhIIcPQhaMEcoGO5DFW26Q5qEAlGVSTCoJEoUDgzgGBDE4NT0bZeDCvsFeq0DU4M47j8n8U89Dd9CEw4VwNohWvgF27cGl76pkrGGPmQRWuogtEivezCoa3+e++EtLpx6TfHDwajLi35sOShymeMivrIbayVwXeHX92H40o7/QzemhjHsFwTT80BKS1Y4GN56wPFDAUAxeqJKk2/vfixuJ1FfgLNGXFbosblCQa8HCM52E9tqxtlnH5aOFuDsAs9NHE2FAgO4R/kweHKEgqketIR+u4QCIQonQwl5VMRQQk4lGVYACP9oJbTYieWsCI6LA+lx2KQffFP12vCOznuxXmgv2gWTyfTExehGM8HPnSibxuHem+i5aOiJTUj88jt4+lX45C393XgFKdbeB7c/Ak0awp1/LvL1s4okBb+0kzxowtyybGsgvPnTNFwWZ/7DCgcPw6q10LMr2Is2j6U0BQ4c4se3ptPjnr8UWL8gZyh4rvuDBGe5ie8z4bpgF+aLusHr/4Dhl+Z7buKIPnygTOAe5cXg1v+u5R1WyNpPwVRXQoE49cjkw5PUiZRPzsl2TgTnZX6i6y0EZrnQUjvOGlzgGbwN68YPCK5sQHCJ/fhz0f71Klx1a3rSmqVlDPdYL8quUe3TVixvvwBfxM8jX71UvC+ydg3wuOBIgT+XZa7YGyLVqA7u4m1NrRSYm8fw/MmL4xJ/dg2E+Q6SvtIdW9A0jW93rS54QuLXP8Dl14PXX6qPW1TO2jXpdd/NRQsFXR8kMN2j72440ou5gw0eHw/9e+V7buKwAd9UzzGhIJFpwDfVDZo+rKD5U6HgNAkFQhRGegzyqOgegywl7TmIbTHjn+3CWDuOa5g/uwBMPE74JyehLxyYW8VwXuIvcBtmPl4Av2/V3yXnWO6oxSH0pYPIjzaizY7iGhDE6bKhaRqqki9HhPLbJTEvLatTDE8AAEf7SURBVA6R1TbCy21ocYWtcxhbl3DuHTJLoNAJickkbNsFTU6vdEtGc4aCZ895iMAHHn0zpCt9GE1HoFrBv4eJQwZ80zwom6YXOnJlhwL/NDcoffgg6U0NH5yWmmgooUCcgqTH4CRX0p4Dc9MY7lFekkeM+Ka4s9+hmkzYzgnjDL5P7De9yEsyWMALxeCLYPyNeihIZnd/KxM4+gZxDvZh2ZlBfGpdfvttB72njClehcQly2HR18X6ukrqhENBNKpXbywBZQJb5zCeGzOxnRsm/IONzP9lEF5pRYuX6NJA7gqJV386njm/f5F9p8EATRuWWyiIeH0sfvg5goeOFHpcrlDQ/mH8UzKA1GZIB36Flr30n5N8JA6mQoE9qfcUZIWCowb8U/MJBfUkFAhRFBIMKrGShgNTvQTuMV6IKbzve0gcSn27lcIS/Am3ZTrJo6kyykcK+VF4fxb0v0pftpeDpVUMz7WZKJNG7TntaHugY/HKJ7/8Nrxbfjsulqin4JHn4YIRpdIOg03D3itExg1HMbeIElriwDshg8gvlhKXGsgKB4/2uI1uDXJUN7zjUfjos5JdvBi+ee5Nvn7mNf5z5oX8NndxvsfkDAX/bv0I/qkeDM6kHgoyktCsEdx3C3Q79vuUOGDEN82DwZHUJxo6U6HgSGr4wKivPkhkSigQorhkKCGPyjKUkFNJhxWSPr2ymxYy4Brhw1Q3e3Z84qgB/wwXWsSAa5gv/5nzK9fAB3P0cV7rsYu9tRgEFzmJrrXyoWkG/3W9xLwxbx1/QmKmT59rUA7vYks8fLDuN9izH/qX/gtD4pCB0DIHsU0WjHXi2C8IYWpSOksct2fu5se96xj6zELodg78eVTJL3ocvt37+E/bvsRDYQxmM3/7eT7VmzXKdUzOUPBMs0cJfJyaEDjMrw+tHMmE6hn5Xj++34h/uhuDO4nrSl+6HHXicKoHwazhHuUlcdSorwrJCgXFnOcqoUBUNTKUUIWUtOfA4NZwj9GXb/mmuonvzF6lavxiLu7X+mJwR/BN8xDdlM9fz3Pbw7/u10NB8tgZ9coMzoEBHAP8DNOG84r3DW6Y/gjHDZ0Zbj0U/LE13+uWllKZU3BWqzIJBQDGmklcQ/24r/KCWcP/gRv/DDfxvcXbfTA/r62ezPDZf2Pq+F7lEgoAljzxEvFUdcvOf7mq0FDwrwaPEZjpxtwohmuETw8FC5dBqwv0fT7yiO9LhQKPvjtoOhRkzTWwaHpPQVYoqC+hQIjikmBwkihxOLDrk7NMdRP4ZrjTJZTpfDaGQT1wj/RhbhYjMNtFZHUBJeAWfwNdL4ej+QdNa/sonqt8tHa2YKLvfeJbitBvu3EznNUfPvvi+MeegFKbaOj1wf8m6xsRlRFTgzjuMT6cQ30k/QZ872UQ+NRJ4uiJ/5o+2esu7q7el7Gz7ype+eQTdGDDJn5KDQ9ZPS563XdzrvtzhoKnazxO8FMXljZRnENyTILt2hEevA1aNM11bnxvKhRkpEKBPU8osOpzDRKHc4SCKyQUCFFcUuDoJFKSIkig1/d3DfcR+MSFf6YL52V+LK3rw+PjUYDzrHWEnK0JLnSS9Bmw9Qzl7s4+owmc067Qrn/TaQlqjAsSnOPE/6GLr+sv5tzBp1PPXcCwQstmMPW/0K/0//iW6uqDRBLuegIanAaN6pdeI/NQCiwtYpibZxJdayX0tZ3oWxasHcPYuoUL3V44P8akxtOP/UC3C1sxzDgeTdMY07bsikwtevDfaKnen+53/wVHrRrp+9Kh4Jw/8U/Hk4QWObCeE8Z+YVD/kUom9eGl6hlw23W5rhvfY8Q/w42hRhLXCB8GW55QYE/iHukjcUjfeVRCgRAnTuYY5FEZ5xjkVdI5B1oCgp85if5qwXFxAGv7qN4L0KYP2t1/JdLzVkJLHVjaRnAMCOS/WU2Owkf5PoYG+5fGMP1Qm+9My+l0bW3q1ap1nIaV3u6LZbIkMR4HU/lmaS0K4ZU2wivsKIOGrVsYa6dwoVsN576ABivXkKhVjb/++gaXNu/DkJb9y6St277+gYn9RgPgblCXW9cuwuzQC2llh4Jx/MPwJJEf7dh6BLF1C2d/y197D/79Bqyepw8zpcR3G/XdD2slcI/I3tMgcdCAb3o+oaBBHNdQCQVC5HVK75WglLICK9Drp3bUNO2nim1R6Spxz4ERHJcFUFaN4DwXWjiIrQvw9rOonl2wucIY3EkCc50kAwZcg/NsMLNmA1x7B0x/FVo1z/8xFNTtY2ZrzT84c15bDk0MoIZnclqT/CeU8dY0mPk5zJlY4nBQZnUKyjkUACiLvouj9ewI4W/thL60E1ltxd4rhLl1ETZpUgo6n40ReLPpPwC9GNKPe9dxbr12pdZOTdNYeP/T6c/7PHTHMaHgznOu4/HIU0TWW3D0D2DtGMl9kcEX6/NYcoaCXaZ8NzpKHDTim+bG4NSHFRIHUqHgdAkFQpRUVZ1j8AxQdoPBlUBJ5xwoBfb+QWznhfR9EL6yow3oAy4n7N6HZdcXuEb49Hdr0zwk/TlegZo21MeBqxXwIp9Dk/Y1SY7cSSaZMKMeR1YXsF9Ak4bQqd0xSyKLq0yLF736nl4JsgIYnBqO/kE812VirJUg8KkL32QP8d2F7T2chHHjYcXqXDdPXf8pXd8bVqpzDjbMmseu738GoPaZLTj7miuA7FAwvtMNPOb9B7FfLTgH5QkFobC+82b9unDdyPTN8Z0mvVJh1p4GWaHgQAGhoGFMQoEQpaDKBQOl1EDgIuDuim5LWSuVcNArhP2CIOHldkKLHfo6+n+/Dnc+hrlBGPeY1ES4yR4Sh1M/Lm4XvPE01K0F/gAkCt8cqHnj+tS5NsKm2r/AwtoEFzrQ8p7Stzs8cTdYirnQPIcyr2hYtxY0a1y61ywmY80krmF+XCO9EAff+xkE5jhJevP5VT50BHbshlju6kkj21yaLoJUWuEgEY3hqFUdgH5P3YvBaEyHgns7/pWHDz5JfLsZ1zA/ljZ5NvF66FnoOyrXz1Fsuym7/kCO8sWJA0Z8090YXElco/KGgkKqeBZAQoEQx6pScwyUUnWBH4EhwEFgC8cZSkgNO+TsKHcDOyvzHIO8SjrnACDyk5XgAgeWtlEcvQ+hMjP1d3Ckyst+4EYLKVzDfZjqpf6ARyJw/lAYOkCfRX4cmgbRn6z4F9uhdoTqV4TTde1TX4g+pNChrd4jUQwVVea4ImlJ9AmKX9nRogrbeSG9xHIRRjwKLZ98giJeH+tmzKXT9SN5ffUUbl7wCI+0u4s7996HFjDgGubH1CCfEo+//QG/bEzv/hjbZsqeK5BjAmGu+gUjfST25wkFxRzpkVAgTjWnXB0DpRfpnwi8rmnaymKc+ncgM8fHztJvXdkqac8BgLVDBOegANENFgLza6HVqav3Btz5GMbEYdxXeTFUT+Cb5sle6mi1wq3j4MrCt9LNohSo9j6us13Lof0+jr7rJrYjx19zgwHeng7f/1SstpdbKNA0fb+BI5llc/1iUgawnh0h44ajWDuGCX9rx/t2hv790bR86wBkyVk+eeZv849fc6IIrB435/x5VDoU/Lv1o9yx5X5IKNxXeY8NBQcP66WmWzXPDgVbTdlzBQoLBftSoaCRhAIhSlul7zFQSj0KPHKcwzoD5wMjgV6apiWUUk04RXoMspRGz0HsDzP+j136cq8O61FDroV3noNundBiEPjERWyLGceAANazcnQJx2Kwez80bnDcx9h0eCvDp9zGC9H/0CHZEUefINZOEX0iXSAITkeR21uuPQWRCFRvBy8/DteXT7Gg4kgcNBBc5CS+3Yy57kEc43ti+PBZ6N2t4HOSCZJaErPRzNGwl2q2kv3MZw0fvNnsJYbtuBpTvTjOIf50IaI0TYO+o+H0evDeC0Bq46+ZLkyNY7iGZL/Yp4saZeiVDhP7jPhnpkLBEAkFQhRVUXsMToZgUAs4zjo3tgLTgEFAzi/ICCSAyZqmjS3i41X65YqFKZVwsEN/12asmcA15DAGt0n/Q65paBgIzncQXWvDfkEQa5fUcrNbH4Yvv4NVnxVp9v6mw1vpP2Us/5e4j1GRq/SlkRcF9HeImgaz50PPLpBjHXxeFTJ8sGQ5tG0JdWqW/WOdAE2D2AYLwcV2iCSw9wlh6ZQ47uqFjYe3cN57w3nlokeLPKyw/5eNLHn8RS554RHc9eumQ8HMBlPovWeA/j29OFDwC/e3P4LNCp3O0gPpbBfmJjGcg/MJBdVSoWCPEf8sCQVCnIgqEwyKSinVCMj5Sl4fmA8MB1ZomlakIYKTPRhA6YSD+F4j/g/cKGcS95U+DI89AeEovPw4mgbhr+2El9uzC9Rs2wm79kL3c4v8GJsOb+VPc+9lepu3cC5rhLFGAucQP0btCLTpAw/fATdfm++5p+KcguJIhhShpQ6ia62YmsRwDvTnns+RR3HnHCTjcSb0Gs6eVeuwVfNgf340926fyPyac2h/5BxsPYPYzgvnH0hWr9PnkaTujP5uJvCxC3PTVChILbSI700VNcoZCma6MTeO6ZUSJRQIUSynXB0DTdO25/xcKeVP/fePooaCqqKkdQ5Ar2DoHuPFN92Db4oHV5tzMSaPAqnVDD1DKFeS0EIHyaDCecnpqCan629Zl34HfQruvs7SokYTvr56Okopjpy2m/ic2vje8+AcZMT8wxxomH+FwQoNBd+tgq++h3v+Wn6PWVy/b8XwzOs4n7gbS+t6BD5z4n0nA8fFASyt8l8OmjXnAODqT8cDFBoOvnnuf+xZtQ6AWHUrz2/+kBXVv6WRrwnOy/1YWkfzP3H7bug1Al59Cq65guimVCg4I4ZzUJ5QMD270mFijwn/zGN7FIpKQoEQRVdlJh+K3EpjQqKxZlLfthnwRUaSuGKMfsdmPYPZOkZwDvYT22jB/6EbLQLM/xIGXqMXQSoClXrXeN2KuxigBhCvE8T/gYvQzmb60snlq/Sx/ZQK7ylYt1HfhroMN30qsd37YM168Ojvwj3XZWJqHCfwsZvg4nyWiqbknJB4x6In8UX8+R63/5eNLH3yZf0Tg2LBxTVY7vqOxlpj3KO8BYcC0MtJf/I2jBpE9LdUKGgRzR0K9mSHAveVPhK7JRQIUZ6qzFBCaakKQwk5lcawQq5tm1ssx3TFEFg8Fc7TX5Rj20z4Z7kwVk/iGubFsOFn6Hx2sR5j0+Gt9Jl6FRlmD0ubz8X0Yy3MDb04/9YR9e+74bqRFR8KTmKaBpHVVkJfODDWi+Mams+EwJREMsF2726aVmuIpmnp8Ab6EMJbF4xg949rAcgcdAH3nDcFR3W9RoExo4DAFArDkm/hkgsBiP5qIfCpE3OrKM7LAqjUW5T0ngg19fLH8V1m/LMkFAhRGk655Yoif6XRc2Bwa7hH+zC4kvh/60b81XegS4f0/ebGcdyjU4WQpmSQaJGqQTDzc9h/qEiP0aJGE5aMnkxmzEuvzQOJDtxJbJ8L72NrSQwaJaGgqI56833OlQJbpwjuMV6SR434JnlIHMr/199oMNK0WkPC8QiXfXhDriJI374wIR0KGvceywOdP8TVyIjnKm/BoQBg6sdw1W2wex/R9XoosLTJEwp2p4oX1coTCprKnAIhypMEg1NAqYQDh4ZrlA9DzQS+w5cS22nRS+2u1seZTXUTuK9KDTtM9hDfHIY7H4NJHxX5MbLCgT8aYIGaj+caL9gteN/P4OX/vM7P+9ZXjlDQaxi8Pqli21CQ92dCqwsgGMr3blP9BO6rvWDW8E3xEN9bcElls8FEbXuNdIXEAxs2sfSJlzBbXPQZ/CKDL3wBW8cormH+3Htp5GfclbDiEyJHGhKY69QLaV2SJxTMcGOsncA93Ed8Z45QkGNCYlFJKBDixMlQQh5VbSghp9IYVtCi4J/lJr7LhOuHhzFrv8O0V9L3JwMK/4duEkcMuHptx9zRXexNkXwRP26rC4ADRw7z85s7OIc+BGzf0OBvbdIvJhXmX69Cl45FmmBZ7g4c0sPaRRcUelgylPo+HTLgvtKHqX7+Ew+yViu8v2YWT81sSK1AY/oNeRmbpxYZlySxnV3IfAKAZSv0+Ri9uxFZZyH4mRNLu6i+jDErFOTZKCm+M7V0sVkM5+USCoQoLafccsXSUpWDAZRSOIinCh1tNuO8+AiWPJv0aRHwf+wmvsOE8zI/lr1f6UsZxwwp1uP8Z+VE7lv6LAYUG6zv4QpfiKlxHOdlBY+Pi6LTIuD/yE18vwn3CF/+5YrRw8H4R//CkF8GcnbXG9ixezmt7muG9bQibExw7Z1wNJPIE+8TnO/E0j6C4+JgOivGd6ZCQV19T4TY9tSERAkFQpQ6mWMg8lUawwrKBM7BfsytogTmVSeyNABX3wZen36/FVzDfJhbRgl87CIyzwsz5ugz4IrIHw3w3trZhOMRajlqYB53ur6Wfa8B33uFd4GXuSOZ8E1xqm6Xk1nz4NEXivw8Kyv63hd14/imu4n9kf8LfXKnlbtqv03LzmNYsuQBqo8MFC0UALz9byL3v0VwvgtrhwJCwWk5QoH0FAhR4SQYnIJKJRwYwXlpAEu7CMHvGxLWOsHhzNz3XxbAek6EYPVRhO56D42iDSlkTTTceGQL0wa/SFyL02fq1WTu/QrPi+ejkn58kz1E1pz4Towl8vkSfTdAf6BiHr8gu/bCps3FGrpRFj0cmJvE8H/kJjDPQWyrifheI6HlNjLf9uCf5uGX4K+8edZLDJp5C8s8OwrflVHT4MFn4JeNRNY6CS6ribVTGHv/7FAQ25EjFAzLEQrOkFAgREWrMgWORPGURhEkZUB/B2iBEHfBviC2epl6SWSjUS+EdGEQ5UwSXuZC27sf+6S/oCY+CzWr53vN/FYfdKzblj5Tr+LuvR8x8ZahuEceJfiDleA8F/E9YRx9g8WesV4iA/vAmgVgt5XjgxbB3/6kfxSTMoNziJ/Iz1bCy+xE16S+LrPGthobuS/5KG3Oqc/z/e5HKcUX25Yzce1MoIAiSJk+WPAV4SZXEDrszK6OmSMU+D9Mbak8zEdsa/5FjopKQoEQpUvmGORR1ecY5FUqcw40CH9jJ/ytHdu26dhs36GeeyjXMZE1FoLznJj3fYPz1uqoJvWOuU5hSxI3H91OLXt1PFa3fkMiQeQXO8GFToy1EzgHF7KG/lSwaYteKdJ2vOUBhdMSkPQZ0PwG/vfdS7w6+wX6jR3LC/0eTNczKEr55PAKM6Ev3Vg7h7D3DmWHgu2p3RPr67snpkNBixjOyyQUCFGWZI6BKJJSGVZQYO8Rwt47SLjxSEId7jhmmNvaPopzqJ9Yg+74l7dE80ZzjYUfr05Bs2qN8FjdbDq8lZueHkb8zD5Y3X/gvsqLFlL43vUQ21KO3QbPvwlTZpff4x3PmFvhpvtLfBllBGO1JP/b8w6r7nuBER9Ctwl7COfYajpnhcSrPx3PxxsX6nds2QGDrye8KK6Hgq55QsG2gkJBVEKBEJWIDCWIUhlWALB1CaMsGsEFjdDmRXBkfI06P/sF3tIihhrhIzDThe9fPlwZczHce22xixcttuzmw4YR+iR81D0tgftaL4G5TvwfuLH1CGHrVsDmPaVp3W96Nb/KYsrLkCig1nExvbZqMu8/8RgXp3YY2b/uN0x5eiKywkFDTz261u+g3+j1Ea4ziNCqOti6hbD1yCcUnB7HNTRvKAhIKBCiEpGhhDxOtaGEnEpjWAEg8ouF4FwH5nWf4Ly/Iap101z3Jw4Y8U00omxGDCOPcsmCscWqaJhVPtltcfHF6EnUc9XRhzO+tRH+xo65WQzHpQEMdvnZLq7XVk3moSmP8Lf/GVHRBCjFuEVTaVTYrpnJJHt9+9m9LE7TDe2xnR/C1j1HKNhqwj/TjamhvlVybIuZwCdZeyQEil2XQkKBECdGhhJEsZXGsAKAtW0U5+AAsXaXE/ilHVqe5fHG2gncN8ZJ2kwcfM9GnY2qWBUNsyokNtp8hF3d+pE8clQfzugexjXcT3y3Cd+7HuJ7ynhJYyJRau/ST5g/ABddBSvXlPhSr62azC3zHuGmxXX0UAB0/dvYwkMBwMPPEb3nK5puaM+mlqux9yggFAzNEQpaSigQorKSYCByKa1wYGkVwzU8QGybGf9/Q2hfrsp1f8ju4yrLaCJHtzDB8hHn+toX6/otajTh9ateoUm9MzD4g+nbzc1ieP7kRTn1kr+R1dbilE8ous3boXaHiq9ncOgouBwFrvIoqtdWTebmBY9wz85zMW3YD0CN5o3p+9j4Qs/TNAidcS3uM/7C3Noz6fZb//RSxtiWVCholAoFf+QIBZdJKBCispJgII5RWuHA3DSGa3gm8WB1fF+fQTKsv43MmlPw9aEV+IfvxFQzgH9ObaIbileXoOlZnam1YCbJ00/jka9eZK//AAAGj75dtPXsCMGFToJznGjHqdxbbA3rwUO3Q+PTS/nCxdS4Acx8E5o2POFLZIWCO2sNxv3+z/qNSnH5G09jdtgLPE/bc4DwV3bC+9tgvyDI6LE90xMSFy79Ef9MN+ZGqeGDrFDQSkKBEJWdBAORr1ILB42SuMcESLob4Z/mxnc490TDczv0wHWjGUvrKIFPnYS/L/582AM/r6L77f9j8Fuj0+FAGcHRL4hzkJ/o7xa872WQOFCKQwtmM9z5Z/2FuaJs2wXf/lisipJ5ZYWC28++hhav/0oiGgPgvNvG0bhH5wLP0w4dJXTHl4S/s2PvE8TWNZyekPh0k4fpuLKPvlVyzlDQOorzUgkFQlR2EgxSlFK3KKXWA99XdFsqi9IKB6YmRtyjfSQOx4m+kkGNP4y55hQoIzjabMC6/DVCSz2EltmL9VpXt1YDetrPwHrYR5+pV6fDAYClTRTPtZkoo4Z3kl4tsdSGFn7fCh99VkoXOwHvz4Thf4HoiXWHpEPBuX9i8A8Z7F/3GwB1zmpV6BCCpkHo53pEzrkRe9cD2Dpnr85IbrHx5523YmuWxHG5j00/7ifwiQuLhAIhThqyKiGPU3lVQkFKY7WCPxrgqVee5e7Iv0nak9QYG8ZYLU9Boo2bCR89k9BSB5Z2kVw78B2XprHpyLb0aoWvr55GTXv2uLsWg+BiB9E1NixtIzj6B1Alraj834n63gT7VoGxAvZuSCZhy3Zo3qTYp+YMBS/0fYDgwcPMueVBNs1byg3fzqbuWa3yPU+LJwhNCxPZ3RB7vwC2TpH0fdHfU0sQU1slf710Pa1Xnsf+Bts5c0w1CQVCVDBZlSBKTUl7DrLmFLyizWTz0BVYHGZ8k5wktuepA9CyGbYuYRwNfyC61kxglgstVsQHUYoWYTvrv2vPFbW7Us2aO9QpMzgHBHFc6ie6sZSGFsZdCTu/r7hQYDCUSihQSuGsXZMrp7/Kjd99XHAoSELwtYNEdjXAce6uY0NB1gZIg/3ENlo4a1V3fqq2kg67zmPar4XsrZAPCQVCVBwJBqJITjQc5C1e1LlVW9yjjqL2bsf3vpv4vmNfVK0LX8O15Vli2834prtJhopYrSiZxLNuC081vhKjwcjXO1ayx78/97Xb5hhaeK+EqxacjhKXID5hI2+Gx14s9mn5hYIsSinqnNky3/O0JAQ/cxINt8bRcj3WC7MnJUY35d4AKbbRQmCOE0ubKH2ub85VbS/n6k/HF77xUg4SCoSoWDKUkIcMJRSuOMMKhVU0TC5bg39jF5IBG67hfkwNchQ7iETAZCK+34L/QzfKoeEe4cPgKcJeCKl30vFknDPfHIDRYEwXQcpJi0FoqYPIahvmllEcAwIYbCfwu3DX49DkdLjtuuKfWxKvvQcN6sHl/Yt+Sp5QsG3ZCmq3aYGzTs1Cz9MSEJgYJXa4Ds5BQSyts+c0RDfl3gApHQrOjOIYqA8FZe2tcCB0mDnD38wVRvKSUCBE2ZGhBFEmitpzcLwyx4Ze7XFfE8ZYM4Zvso3Y1hw9B1YrGI2YDqzDvexmiGp43/cUrevfYIAjmZjufZrP+7+AL+rnwqnXHNNzoMzg6B/EOcRHfJsJ7zse4jtPoEK4ywn2gpf0lZmbri1RKPDu2MO0K2/itXMvYePnSwo8T4tDYLaL2IGaOH99Jnco2JijrHEBoQCyyyd/NPQVlFL4Iv58H0tCgRCVgwQDUWzHCwdF3ftAWcFVYx6mzd/g/9BN9Hdz7gNsVozBXbgHbMPgSOKb4ia2owgv3oEgfLKQ5rtCLBk9ucBwAGBpGcMzzovBk8Q31U3oKztacYoZPj4ebhhdjBNKKJnUN3Dac+zXUpC8oQBNY/YN9xLJ9BHYf4h10/Lv4tdi4J/pJrbNjGuIF8tzo9L3RX/LXcEw9lsqFLTNHQqyGA1GbCYrW47u4Iw3+h4zrCChQIjKQ4KBOCEFhYPiboikLumJ69GGmM+IE5jtyl3kqGUzmPsuhqbVcQ89gLFuAv8MN9HfzAVfEOD0evDLIujZJV0+2WV24C3gnarBk8Q92oete4jwdzZ8UzwkjhTxV0PTYNfe8ttQaeNm+Md/YdvOIh2e35yC5f95m61ffgeA5/R6XPLSo8ecp0XA/4GL+OYkrh5bMLdWUE0fWssVCi4LEPvVQmBuKhQMKHwlSSNPfQY2uyDXnAMJBUJULrK7ojhheXdlfCcZ4X/hacXaEAlAnVYD5yAfwac2E/j0XLSownp29ox3QmFUv+G4rrmSQIubCHzsItkvmGtW/DHMZghH4Ln/0eLma/l+7EyUUvijAQKxEHWdtXK3wQD288OYm8QIzHHhnZiBo28AS7to4Ts1/rENzuoHcyZCvx5F+npLpPUZsG05FFKRMEt+oWDf2l/54uHn9AOUYsiEZ7BVyz2XJhlW+D90kdhvwL3gBkxdhwHdAIj+aibwqV6XwHFpgOgGC8HPnFjOihZpeWnWsALA1Z+OJxKJ8t59syQUCFGJSDAQJZIzHIx98x5sfa18cdUkzmvQsVjXUQZweKehMqwE57dHi4Ht3NQLv90GVw9F9TsPZ5sAIVeS0CInmt+ArWeo4BfuQ0fgjfeh01mogX0AuOHzB/hp/waWjH6f01y1j/166ifwjM0k+IWT4DwXsU36C57BVcDExKYNYcZr0OmsYn29JyQUBqNBXw1xHPmFgng4wsw/3ZWubtjtjutp2rtbrvOSIYV/hptkpgH3aB+mW/+phywguiF7tYHjkjyhYECgyFtdZ4WDeCLODXPux7LWyrzP50koEKKSkKEEUWLpYYUGI4m8EmXnir3Fv4hSqGcfwH7b6di6hgh94ST0jS17KeHt18OZLVGJOI7Gv2LvHST8nZ3gZ86C5wQ0OA02LIFUKAB4vOcd+KL+Yyok5mqKFZwDAziH+ojvMeF9J6Pg4QujUZ8EWKNa8b/m4powFdr00VdtFKKgJYmLH36W/b9sBKBuu9Zc+Oiduc5LBhT+aW6ShxK4lo/H5MrMDgXrc0wsLEEoyBIJR9n16j7M71qYN1tCgRCViQQDUSpMJhOT3p3EqL6jSlQ+WSmwhz7Htuxpwt84CC3NUx754efg4quxtc/U90HYYMH/kRutoNdKp0PfGvm19+BIZnrOwfHCAYClRQzPdZmYGsYJfOzG/4mTZDCfV8AVq+GFCSf09RbLxRfAo+P1VRsFKCgUbP7iW777zzsAGK0Wrpj4PKYc10n6FL6pHpJBA+42KzCZD+s9NaRCwdzs1QbRDRaCc51YzoqcUCjImlPww8p1zJ8yX0KBEJWMBANRakprbwV6dcU+0Iq9r5/ID3aC8x1oWSUMbr8eJjwDNiuWNlFcI3zEdxv1FzV/Aa9Q+w/B4y/BgmUAucLBJ78vLrQpBoeGc7Afx6V+4lvNeN/OIPprnt6Dn9fD29P1FQNlqWUzuOaKAu8uKBRE/QFm33BP+rh+T95DnbbZhYwSmQZ8Uz1oUQ336EyMA8+C914Ak4nILzkmFg4MEF2fCgXtIzgGBE84FMicAiEqLylwlIcUOCq50thbIUvk030EN7TO3pkvq5SBpsHMz2HwRSSOWPF94EYZNFwjfBhr5vMCffjoMd39R8Neqtn073EkHsFqKryKYdKvCC50Ettk0Ysi9Q1gcGt6W4r7CllcL0zQ5zMMuTjfuwuraAiwdtonzL39Eep3asc1cyeiDPp7gsQRA/7pblDg+vzPGFvWgGceACDyS+7hgmjW5+0jOC6WUCDEyUYKHIkKU2o9B8kk1qduwLnjFb14Ts69E379HcbeBfOWYqydwHO1Fywavsme/Gsd1Kimv4DPmANHMgHSoeC9tbPo+M7l+dY5yMng0nAO8eMc5Ce+04T37QwiP1nRKONQoGnw/WpYvynfu48XCgDajbqcm36Yy5AJz2SHgkMGfFM8YAT3GC/GET3gsn4ARNblHi6IrkuFgrMlFAhR1UmPQR7SY1B6SqXnYOceqJ5BbH8G/lkuTPXiuK7woazo2x6f0SR9aDKsCMx2Ed9lwnlJAEubPNsRHzikLy188t5cRYk2Hd6a3pUxv/LJ+UmGFKGlDqJrrRgbxHAsuB9TIzM8cXfxv8aiyqdnoiihID/x/Ub8M9woRxJ31w0Y2jZI3xdZayH4eXbPQHStheA8J5YOERz9JRQIcbKSHgNR4Uql5+D0euB0YDZtw735X8T3GfFN9+gbK2WFgpmfw9zFGGz6UIKlVZTApy7C39tyT1ysXRN+/OyYSoU55xwUVCExL4NdwzkwgGuUFy1kwNf2XwQbjS14EmRJrN9Y7FCQTCTY/MW3+V4uvseIf5obgyuJ+6wfMHS5EBZ9DUBkTSoUpHoGomusBOe5sHaUUCDEqUKCgShTpTassO8gpuWzcV/wB8lMA76pbn2yoabBh3Nhjj6JUBnBcWkA23khQksdhBblmLgIetAAWPxNekgBcoeDOxc/VeRmmRvF8YzLxN4rTMTXkswJ1Yj8YjnxHRvz2rAJOl2SnjiZ5Xg9BctfeptJl1zLxzf8HxGvL317fJcJ33Q3hupJXKN8GDq3hLefhT7diPyshwBLhwiOi4JEf7YSnO/E2imMvZ+EAiFOFTKUkIcMJZSNUhlWSO2cmNgTxzerJsoErit9GO0hsFiOeUcd+dlKcIEDc1N9O2CVVW050wetLoB7/grjb8x1zh9HtlHdlkENe7XitS0cIfHVr4QyuxDb7MRYP47jwgCm+sXZeCEfiQQs/hp6d9O/Ro4fCvb+vJ43ewwjGYuBUoxbNJVG3c8ltt2E/yM3prpxXH22o7ZtgfP06pSRrBDQUQ8B0Z+sBBc6sZ4Txn6hhAIhqgIZShCVSqn0HBgMoGkYb7wB99Z/AOj7Gvjseij4/ie47E/gDwBgPTuCa7if2E4zvikekr7Uq1uGG5Z9CHfdcMxDNK/emBr2amzP3M2lH/y50DoHuezZj3HQMFyu+bhGeSEGvvcz8H/iJJFZgl8zoxEuuqDIoSAejjBz3Hg9FADn33WDHgq2mPF/6MZUP45rhA/10utw1W0QiRD5KXcoiKyWUCDEqUyCgSg3pRIOlIIRl2G87FzcY7wY7El8Uz3E9xj1/QPMZohkTzo0N43hHuMlGTTgfd9DfH9qvWPLZvq1Vq/TlzLmEU1G+Xn/huMWQUprcjqs+gz6dsfcKI57rBfHAD/xHWa8EzIILnbkXxypMJ8shGvvhKj+9RRlouGih/7NgdTqhdPObkOfh28nusmMf6YLc6MYrmE+lBl9V8jP3iWy3kNwQfZwQWSVldAiJ9ZzQxIKhDhFSTAQ5apUwsG1w6BXVwzOJK7mX2GonsQ3zUPM3RZmvQk1q+fa7dBUJ4HnmkwM9tRyxj9SBYqCIRg0DlIVAXM6o3rRKyQCesg4s2W6hLAygLV9lIwbjmLrFiKy1krm/6rpZZ6LOkExkQCTESyWIoWCPxZ9zYqXJwJ6dcOh7zxHcouLwMcuzM1jOIf6UZM/hE1bwGIhHDwzu2egb5DIj1ZCi51YO4ew9ylkD4oCSCgQomqQOQZ5yByD8lEqcw4+WQgjb0b7fh7+DR2I7zDhvNyPpc5h6DlMHyr404j04VoUAnNcxP4wY++b2p3x5/VwZov0C3peWUsZa9qq8+O42ZgMhew7Nm8pfL4EXnrsmLuSQUX4OxuR1TaURcPWJYy1U1h/934cRQkFocNHee3cS/Ht3gfAgOceokPvG/TaA6mdEFUsAt2GwNABhC+9V+8ZSA0XRFZaCS1xYu0Swn6BhAIhqqKizjGQ3RVTlFK3ALcgvSjlIu+WzdOg+OFgUD9YNBXVrjmuNj4Cc10EZrvQBoD1qiHQo3Ouw5UFnEP8qdUKTpKHjNj7nqlvFbx5O1TzHFMdMWu1wm+HNxceCgC8ftiyIz1JMieDQ8NxYQhb5zChb+2EvrITXmnD1jWE9ezIsQFhxWo4vR6v7Vt83FCgaRpzbn0oHQqa9e1O+y436AWK2uXYDtlqhaUzCG+smT1c0CdEZKWN0BIHtq4hbL0kFAhxqpMegzykx6B8lVr55Cmz0U6vTzDYm+gaG/YLA/q2zZGIvldCw/q5Do/8ZCW4yIGpURzngMMYOvaGYZekywHnR9M0/vXdG4xtd0WRiiAVJnHUQHi5neg6C8qpYesWwto+kl3yuesgfjvNTOtua45bvGjN1I+ZNW48APYa1bnxte/RfquZ/e7/0GG4+0l45gHC2+sT+iI1XNA7ROQHG6GlDmznhQrfwroAEgqEOHnIqgRxUiiVOQfJJLw/C/XJAhwXB7Fmbdv8lR3tjsdg8PX6eH0O1g4RXCN8JPYa8c2oReLNCfDQ7YU+zP7gIf67alLhRZA0Ldf8hoIYqyVxDgzg+XMm5sYxQgsdeCdkEF2v10B4699D6Hvm8UMBQNMLzqN5vx6YzHaueWAJ2sYaOPoHcPROvdDv2gvrfiP8k1MPBV1SoeD7VCjoJqFACJFNegzykB6DilHinoNQGGxWfRKgphH+wU5oqQNLs4M46v+EOr9TvqclDhvwz3SjBRTOwX7Mrv36dsNOR77HH7d8cqeBMLAPPHVvsZqfOGgktMxO7HcLBz17GXF0NL3P7VjkMscJv8bhiQpTrDrOQX4sZ6Q2lUhVTAx/byG01IW1awh7rxCRFTZCyxzYzg9h6y6hQIhTgfQYiJNKiXsO7DY9FKxYDd2HYmu0A8dAP9EtNQkc6IkW0+DjBeQtSWiskcRzjRdjgzj+D9yEb/gI7Z+vFPgwecsnHwgeyn3AA7fC0AHFaztgrJXAdYWfJe1mkLH5EIvVYv5hfgqSRQgFhw34p1TDrKrhHuXNDgVvT4drbif8nZnQUhe28/RQEP4uFQq6B7H3kFAghMhNJh+KSqNUJiTWrQ1nNAW7DWu7KMqmEfjEhf9tDde9/4eaXytd7S+Lsmq4rvATWmYnpP0fiWZeHLF4gSsGssLBCz+8TTVrnl6lYZcUr705vLZqMg8uf4RZm9vSuedUwj80IL7DhGuoH4Mzd6Dx7z2AyW7D5K+Of6YLZddwX+3FmJGj/nONaoTPGE1omVsfLugRIrzcRvjrVCjofvwhj7wkFAhR9clQQh4ylFDxSm1C4r6D4HERO+DCP9OF0R7EdU0Mg6Pgn/noeguBeU6M1WO4Bnsx1Dh+p9oPe9bQ0F2P01y19R0c5yyG4ZeA21Xkpua3JDG+24h/lhtl1nCN9KVf9DVNY/Jl11HPcSEdu9yKuUEC5xV+DLbU1xUKg91GeIWN0JeO7FDwrY3wNw5sPYLYz5dQIMSpRoYSxEmrVCYkJhJw6VgY/4ReiXC0j2TcgW+yh8TEhbBqXb6nWc6M4h5+AG3LQbwTHMS2Ft6plkgmGDvnnuwiSHv2w80PwMYtRW5qVih44IyRvLD/LFSqcqOpfgL31frvrn+qm8Qh/df1lze/4JzmD9PhnL+xdtUEbJcfzA4FkQhcOJLQv9fooeD8ENbuIcLf2PVQ0FNCgRCicBIMRKVU4nBgNMK/7od7b9KvVzeB+yovJDV82/sRn7264MduZMJ9+ucY6+jzDkLf2QrcLdFoMPLxsDeyKyQ2rg6H1sA57YrUzJw9BU/EuqBuul+vyJh1/Ywk7tFeMIN3YgZH/uuiwdERWG0ePpgwgPp/qo3ZZc2+oMVC6MqnCWu9sXUPYuseIvKNnfC3duy9gti7SSgQQhROhhLykKGEyqVUhhVCYfjoc7h6KMmAwj/DSSJTH7s3N44XeJqWhPBXVsIrnJib6dUDDfb8f19yrlZYMvp9fVjhOPKtaHjoiF7SOW9bYvoOiL+8t5BfvpzOtt+/oP3Vgxn8xtPZB+3YTWhHs/QcAtv5YcJf2wkvt2O/IIitq4QCIU5lMpQgqoRSGVaYsxhuexi27MDg1HCP8WOqn8A/w0n0wTnHrFTIooIB7PcNwFVrAfE9Jnzveojvyn9oIWtCosVgJvnim3DHo4U26ZhQkExNGswnFAAoM6xf8x5z/ncdW36bj/O0Glz8r/uzD/hmJaG/fqaHgh6pUPBVKhT0llAghCg6CQai0itxOBhxKfw8H5o2BEBZwTXMh8W+hYDnWsLfFbD8wOWEi3tjbm/BM9aLcifxTUkNLSSPPbxFjSasvu4T6tdrRjzDxf7AoWMPooCegmffgAtHFRhSvDv3MP///pH+fNCr/8BWLbtHK5ToTviCe7H1CGDrFia0zE74Ozv2PkFsXSQUCCGKToKBOCmUOBw0rK9XSHzgGVj0NcoIjltqYO0SIvSVh+Bie/6vyY/eCee2x+BJ4h7tw9Y1THiZHf90N0nvsb8+BmWA60dxQ5cDXDBlzDEVEgvcEKlzBxg2kIKKCnw+/gmivgAAHa4ZRouLLwBA8wcJzQ4R/s6JvVcQW7cIoS/tRFbY9bLQnSUUCCGKR4KBOGmUOBwkk7BhE2zZDuivwY7eIexnbyey0kJgskKL5XPegUMw5M+odRuw9wrhGuUjcdSA9x1PuoRxLprGQ2eMIu7z5SqfXOguiReeD7eMzbfZv366kF8/XgCAs05NLnrm/qyHIfzCJsIbG2A/34u1a5jQUjuR7+3Y+6b2iigmCQVCCAkG4qRSonBgMsGHb8ANY/TPI/oLp+08Dee2l4jty8A33U0ymOdde4Zb/zfTB4C5URzPOC+mZjECc1wEPnGRDOQ458Bhmp09gmW1/5qukPj08tcLDgWffQHfrCyw2cGDRzA77ABc/O8HsVfP0LdkWOIgbO2DvclGrN3jhJY4iPxgx94vgO0cCQVCiBMjqxLykFUJJ4cSr1aY/ik89TIsnZHeajm+x4j/Q1d6DoKxZj4TCfKIbrAQXKTvq+DoG8TcJopCg08XQdeObDL76fLuFRyNeAveEOnSsVCvLkx4psDHObp1Jz+9P5MLHrgVNEVwSoTo7nrY+wewdogQ+sJB5EebHgo6SSgQQhxLViWIKq3EwwpdOuh7GmT1BgCm2hHcc66Gw4fwTfYQ255nBcL+Q3DX4+D1pW+ytIniuS4TUyO998D/oYtEphEu7w91a7Fo6zccjXi57ZyxvND3AeLJfJZHzpkILz5SaHOrNTmd3g/eBklFYI6T6K46OLa/poeCxXoocPSXUCCEKDkJBuKkVaJw0LQhPHaXXgjp198hFgOTCePwHrgv3ISxbgL/DDeRNZbsc8IR+GQhrN+U61IGp4ZrcADnFT6Sh4x4384gNPUIyx66Jz188GK/B/not3l0fOdyvUJilmRSn+zgch63yVocArNdxDZacPbZj+WhfoQWOYissuG4KIC1o4QCIUTJyVBCHjKUcPIp0bCC1wet+8Ct4+Dvt6Rv1mJJgnPNRDdmYD03hL13CGUA4nF9rkIBtCiEv7MTWm4m4dvD7PZLuH74pRgMKv8iSBeOgv49cz02wMo3p3Jky3Z63XczVo8bLQr+WW7i2xWuAYcwnWUmtNBB5CcbjosDWM+WUCCEKJwMJYhTRol6DjxumPIy3DYu183q3idwPDUQex8/kR9t+D9ykQwrPRT4/PochXwoC0x0TaBz8jx+b5jJ8K3X4p+cQWyHKdeWzX2mXs1e334YeRl07ZjrGsGDh1n88LN8+/yb/Pfsiwnt8+Ob4Sa+24Br6mhMKz4iuMBB5CcrjgF+CQVCiFIlwUBUCSUKB727gdMBO/dAalkgN45B/eNebJ2juIb7SOw24ZvkIXHQoE8s/OvfYdfeYy6VtSRxUOdenHdjPVwjvZAE/1QPvg9dNI03T4eDmxc+Cn+5Wl+qmMMXj71I+EgmAK36XUzs8/okDxtxj/Jj+uQxgqdfR/RnK46BAazto8V+riQUCCEKI8FAVBklnpD4+vtw/7/0ZYxtWkD/XgCYQ+txX+sFo4Z3UgbRTsNh3SJocFqu03PVKeh9H6rHFZhXzMZ9rRfnID/Jw0Z8Ez3UX96WZZfP4G1fd9i4Odc19v68nlVvTQOg+mnN6X7OMyT9CnfyPYw1QgTXNiO6xorjkgDWdhIKhBClT4JBilLqFqXUeuD7im6LOHElCgeP3glLZoA1x26FH30GXS7HeHgznqu9mJtFCXziIbixKVo4Bn9sA/IpXmQyQc8uUL8uSqVWL1yfiaN/kNgWM9U/OAvb7AiZs+Yy9KOb2OPfj6ZpfH7XE2jJJNVrtWTkzQsxYMLdejmGJx4i+AFE11pxXBrAepaEAiFE2ZDJh3nI5MOqoUQTEn1+uOsJPSjUqQkLlsGlfQG92mBkpZXQlw6Mwc24Pr+dN17uz82LHiu4TkEeWgRC39iJ/GgjVstHf/+lRG1hJriuY9G4B2ja6mIuHvEmtnpW3CMCKFeS4Mcmor+79Z6CthIKhBDFV9TJhxIM8pBgUHWccDjYsx8uvw5eeAR6dM6+feUaOKcdKEV8lwn/TCvRSILr4n/hjHNrHxsKjmTCvgPQ+oz827fLhH+2i7ghxiXRgfR+fhN92txC1973Es3YQ93LQzDzU4JNbyK6wYrz0gCWMyUUCCFOTFGDQcHrroQ4yWUNKwCMuuYOpkHRwkG9OrDiEzAYsnc7/GMb9BoOk16EYZdgahDnoy7TMC+txyTDJCzREERDkGMUguff1FcvbPzy2MfoMxLT1UNxXz0G/zQ3cyJziFxzFIezDr9ufp/zXr8UJs8n+FMzomErzssCWNpIKBBClD0JBqJKO+FwkBUKbn8EqlfTiyF99i706gqk5hQseYS72l/DldN/J8QtxLdn4BgQwNwkVd3w+lFw5WXHXjuZ1FdCNGuMMSOJdcge1ty5kHg4ytrv32HYrH+iUASrXUW0tUVCgRCiXEkwEFXeCYcDpaB5Y73WAegv5sCM6c9x92+vcfv5f+LZvg+gVv8Xc7uvCWb2xD/Dg+WsCPbeQQxNTs//ugYDPHJH9qcu0Nrv4vsXJ9Csb3fqOZ38/q/fqGk6D9cgP5bW+W35WDgJBUKIEyVzDPKQOQZVV4k3XvL6mPDzDIZf9k++ubIjl/xvRq45BZoG0TVWQkvtoMDe+SiWhf9BXXlJ7nkGy1fpSx0b1c91+fBRL7FghOS7ERK04WHnAzx43fV6hcRikFAghMiPVD4UIo8SLWWc+jGBM3vxwPx/MvHJS7jk5Um5Jxr+sRV1/9NY24Xw/DkTc4sYwa9q4A2MIbY2Tq78/de/w7OvH/MQVqcHvm1K0twOf4+NzDZ+qldIzLm3wnFIKBBClJQEA3FKOdFwMLH2Xh7p6GNMr7Hc/reXUDYbbNkBBw/rBxw4DB/Mha07MTg1nAMDuK/JxHB2U/xbzsc/3U18j1E/dukMuC/33gjJsML3rpn4VgOu4T4a9ayXq3zy/sCh47ZRQoEQojRIMBCnnOKGg9dWTWbcyn8Tv/1PPN//QdTvWyEahQHXwBMv6Qed1wl+XQLNGmU/Tr0ErtE+fdfFoMI3KYPAXCdJSzWoX5eVb05l0YPP4P3jEP6pbpIHDbjnXo/59DBAem+F8+p3wGN1FdpGCQVCiNIicwzykDkGp46izDk4pqLhnv3Qti88/zC0bQmtm2dPTgS9ByEW15c8AtzyIBgMaC89TnStldB8BVoS+8gIr/btiSVek0vHvE9Gg/p4RgYwJvbBafnPKViz/1dqO2pQz1Un1+0SCoQQRSF1DIQ4juOtVjgmFCgF9evqtQz69QRbqmjB4aP6zMMa1aDHMLioJ/zncf2+Lh3AYEAZwHp2BPP8SQQSg/B/0JBOHcdzZserCEZ24+m0CmPtFkD+oSCpJbnm07uJJmN8MXpSOhxIKBBClDbpMchDegxOPfn1HOQbCvLasgNMRhg0Ds4/F159Cr5ZCa2aQa0aBT5eMqqx5s6V1K7ZkV9/nkGLmj/TaNFS2LgsO2zkY9PhrfSZehVui4svRk8iw+CWUCCEKDIpiXyCJBicmnKGg3EvD2PC/hmFhwJNg66X68sQr7sSWjXPHj7I6ahXr5p4TjvwByCZZPva33in7ygATj+vI9cvnAK//gHtWh+3nVnhwGVyUHNOdX7+9jcJBUKIIpGhBCGKIWtYQUNjwpdTuaRb78I3RFIK3nlOH1qonqHfFono/85eAHO/gPdegM+XwLjxcHgtzJwHf/07q3JUQ+w84jIwm4sUCkCfkPjZ0Lfo9toItm3ew4LPF0goEEKUKlmVIESKyWTivXffY5RxFPPGL+OjWfMKP6FtSz0UHDoCK1ZDl8vhxbfAbgO7FWIx6N8TvvsYLGbo043w/57ml48XAGBz2GnzwDOwa2+R2xgMhrhj3JPwmmLBOxIKhBClT3oMhMjBZDIx6d1JGDAUvXzy3U/Cmg1wx/XQrZM+vHB5f/2+WjWy5xs0rM8af4B4SF+O2H7MEMzdz9WrIBZBzomG8z6fJ6FACFEmJBgIkUex91b4x//pGyPlfIEPheHrH6BrB3juTRg1COZ9yc+TPkof0ukvVxV5CEFWHwghyosEAyHyUaxwkDXpMBiCeUvhv+/CtVfAX++Hb2fB5FnQ4UyC/3qV/cEQAKfZbdTdtbdIwUBCgRCiPFW5YKCUuhR4GGgPBIBlmqZdUbGtEiejYvccPP0qvDMdOneAtq3g5/n6aoXfvwLAMeRi7vH62DhzHqYP5+aqklgQCQVCiPJWpZYrKqWGAW8C9wNfAApop2nah8W4hixXFLkUeVfGI5l65cMWTUvlcSUUCCFK0ym3XFEpZQJeAu7RNO2tHHf9VkFNElVEkXsOqmfoH4kELP4WVv4My1aA0aAXLlIK7roRduyGKy/TPy+AhAIhREWpMsEA6AQ0AJJKqdXAacBPwN2apv1S0ElKKSuQs9ycu6BjxamrWMMKdz4GH30OGW5ocwa0aQEGBUYTfPYFLF2uB4MCSCgQQlSkqhQMmqX+fRS4C9gKjAe+VEq11DTtcAHn/R14pMxbJ056RQ4HN18LIy7Tly6a9F+xxQ8/h3fbTpr360GbO67HXEBvgYQCIURFq/TBQCn1KMd/4e5MdrGmpzRN+yh17jhgJzACeKOAc/8JPJ/jc3fqHCGOUaRw0PoMyFpscPAwbNzMhimzObRzD+s+mEubfavyvbaEAiFEZVDpgwHwX2DacY7ZSvYQwPqsGzVNiyilNgMFTv/WNC0CRLI+L7AErhApRQoHiQRcOAq+/4mwgkNJfZLvaTUyMDvsx1xTQoEQorKo9MFA07SDwMHjHaeU+hH9Bb4V8HXqNjPQBNhWhk0Up6DjhgOjES7qBc0bs7taBryqH1u/2znHXEtCgRCiMqn0waCoNE3zKqVeBx5TSu1ADwP3pO7+oOJaJqqq44aDB24FYN9L2Ytk6g/sk+saEgqEEJVNlQkGKfcAcWASYAdWABdqmnakQlslqqzjhoNvfuDw4y+lP63Vqln6/xIKhBCVUZUKBpqmxYC7Ux9ClItCw8GirzkcCKaPrdG8MSChQAhReVWpYCBERSkwHPzfTRyZ/ils3o7F7cRRq4aEAiFEpSbBQIhSUlA4CB7SR7JcdWoRCoUlFAghKjUJBkKUorzhYGoiQSTTB4DV6ZBQIISo9CQYCFHKcoaDa8bexYd2G/FQmE+Pevn+j+0SCoQQlZoEAyHKQM5wMGT6dM5q34bfJRQIIU4CEgyEKCNZ4cBoNLJw4UIJBUKIk4LSNK2i21CpKKU8QGZmZiYej6eimyOEEEKUCq/XS0ZGBkCGpmnego4zFHSHEEIIIU49EgyEEEIIkSbBQAghhBBpEgyEEEIIkSbBQAghhBBpEgyEEEIIkSbBQAghhBBpEgyEEEIIkSbBIEUpdYtSaj3wfUW3RQghhKgoUvkwj6zKhzt27JDKh0IIIaoMr9dLw4YN4TiVDyUY5KGUagDsrOh2CCGEEGXkdE3TdhV0pwSDPJRSCqgP+Erxsm70sHF6KV8X9KGPLqV8zbK+dlldV57n8rnuyfg8n2zfv7J8jkGe5yyn4vPsBnZrhbz4y+6KeaSerAKT1InQswYAvsK6b07w2snSvmZZX7sMr5v1X3mey/a6Wf89aZ7nk+37V5bPcer68jxzyj7Pxz1PJh+e/F45Ca9dlm0uK/I8l4+T8bmQ57nsr1vW1y4rJ+PzLEMJ5SFrQiPHmfAhSkae5/Ihz3PZk+e4fMjznD/pMSgfEeCx1L+i7MjzXD7keS578hyXD3me8yE9BkIIIYRIkx4DIYQQQqRJMBBCCCFEmgQDIYQQQqRJMBBCCCFEmgSDCqCUulQptUIpFVJKHVRKzazoNlVVSimrUuonpZSmlOpQ0e2pSpRSTZRSbymltqR+lv9QSj2mlLJUdNtOdkqpm1PPa1gp9aNSqmdFt6kqUUr9XSn1g1LKp5Tar5SarZRqVdHtqiwkGJQzpdQwYBLwDnA20B2YUqGNqtqeAXZXdCOqqNbof0P+ArQF7gT+CvyjIht1slNKjQReBJ4COgJfAZ8rpRpVZLuqmAvQiwSdB/RHrwK8QCnlrNBWVRKyXLEcKaVMwFbgEU3T3qrg5lR5SqmBwPPAMOAXoKOmaT9VaKOqOKXUPcBNmqY1q+i2nKyUUiuAVZqm3ZTjtg3AbE3T/l5xLau6lFK1gf3ABZqmLavo9lQ06TEoX52ABkBSKbVaKbVHKfW5UqptRTesqlFK1QXeBK4BghXcnFNJBnC4ohtxskoNw5wDLMhz1wLg/PJv0SkjI/Wv/OwiwaC8Zb2LehR4ErgMOAJ8qZSqUVGNqmpSO2ROBF7XNG1lBTfnlKGUag7cCrxe0W05idUCjMC+PLfvA04r/+ZUfam/F88DX2uatq6i21MZSDAoBUqpR1OT2wr7OJfs5/spTdM+0jTtR2AcoAEjKuwLOEkU43m+FfAA/6zgJp+UivE85zynPjAP+EDTtAkV0/IqJe8Yr8rnNlE6/gu0B0ZXdEMqC9l2uXT8F5h2nGO2ou+DDbA+60ZN0yJKqc2ATCw6vqI+zw+iTyqK5NhWFWClUmqypmljy6Z5VUZRn2cgHQqWAMuBG8uuWaeEg0CCY3sH6nBsL4IoIaXUy8DlQC9N03ZWdHsqCwkGpUDTtIPov9CFUkr9iL5ZRyvg69RtZqAJsK0Mm1glFON5vg09HGSpD8wHRgIryqZ1VUdRn2cApVQD9FDwIzBO07RkWbatqtM0LZr6O9EfmJXjrv7AxxXTqqonNXzwMjAU6K1p2pYKblKlIsGgHGma5lVKvQ48ppTagR4G7knd/UHFtaxq0TRte87PlVL+1H//kHcFpSfVU7AU2A7cDdTO6qHRNG1vxbXspPc8MEkptZLsXphGyNyN0vQKMAYYDPiUUlk9NJmapoUqrlmVgwSD8ncPEEevZWBHfwd7oaZpRyq0VUIU30XAGamPvIFLHXu4KApN06YrpWoCDwP1gHXAJZqmSa9i6claCro0z+3j0Ccun9KkjoEQQggh0mRVghBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIcqFUupKpdRGpVRcKaWlPjKVUvfkOGa4UiqQ4/4jSqk5FdluIU41somSEKJcKaX6AwuACFBf07TDee7/K/AAcBvwiaZpifJvpRCnLukxEEKUK03TFgJrASvQP+d9SqnGwBVAF03TZkkoEKL8STAQQlSEV1L/3pp1g1LqNGACcJ2maXsqpFVCCBlKEEKUP6WUE9gJVAM6AjuAqcBNmqb9UYFNE+KUJz0GQohyp2laAJiY+vTvwGTgTgkFQlQ86TEQQlQIpdQZwEZAAf00TVtcwU0SQiA9BkKIirMFyOohOLsiGyKEyCbBQAhR7pRSCngD+Cx1081KKfl7JEQlIL+IQoiK8BLwBXAHeq9Bc2BgRTZICKGTYCCEKFdKqX8AGzRNm6Lpk5yOWboohKg4MvlQCFFulFL3AWia9nSO26qhL110AK01TdtYMa0TQoD0GAghyolS6jagWs5QAKBp2lHgffTVCbdUQNOEEDlIj4EQokwppeoBjwKXo++NcMwfHaVUP2Ah4AWaaZp2qFwbKYRIkx4DIUSZUEpdrJTaiD5McCNwGrAyn+M+AuamPvUAO5RSa5RSLcutsUKINOkxEEIIIUSa9BgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIk2CgRBCCCHSJBgIIYQQIu3/AbhbGYA6SrjMAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 110 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tmin, tmax, dt = -10, 10, 2\n", "for i in range(int((tmax - tmin)/dt) + 1):\n", " ti = tmin + dt*i\n", " graph += plot_const_to(ti) \n", "graph += plot_const_to(0, thickness=2)\n", "\n", "graph += line([(-pi,0), (0, pi)], color='black', thickness=3) \\\n", " + line([(-pi,0), (0, -pi)], color='black', thickness=3)\n", "\n", "show(graph, figsize=10, axes=False, frame=True)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [], "source": [ "graph.save('exk_CPdiag_M0-raw.svg', figsize=10, axes=False, frame=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Maximal extension" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( {\\tilde{t}}, r \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{1}{2} \\, r + \\frac{1}{2} \\, {\\tilde{t}}\\right) - \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} {\\tilde{t}} + r {\\left(4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 4}{2 \\, {\\left(r - 1\\right)}}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( {\\tilde{t}}, r \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{1}{2} \\, r + \\frac{1}{2} \\, {\\tilde{t}}\\right) - \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} {\\tilde{t}} + r {\\left(4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 4}{2 \\, {\\left(r - 1\\right)}}\\right)$$" ], "text/plain": [ "(tt, r) |--> pi*unit_step(-r + 1) + arctan(1/2*r + 1/2*tt) - arctan(1/2*(r^2 - (r - 1)*tt + r*(4*log(abs(r - 1)) - 1) - 4*log(abs(r - 1)) - 4)/(r - 1))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( {\\tilde{t}}, r \\right) \\ {\\mapsto} \\ -\\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{1}{2} \\, r + \\frac{1}{2} \\, {\\tilde{t}}\\right) + \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} {\\tilde{t}} + r {\\left(4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 4}{2 \\, {\\left(r - 1\\right)}}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( {\\tilde{t}}, r \\right) \\ {\\mapsto} \\ -\\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{1}{2} \\, r + \\frac{1}{2} \\, {\\tilde{t}}\\right) + \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} {\\tilde{t}} + r {\\left(4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 4 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 4}{2 \\, {\\left(r - 1\\right)}}\\right)$$" ], "text/plain": [ "(tt, r) |--> -pi*unit_step(-r + 1) + arctan(1/2*r + 1/2*tt) + arctan(1/2*(r^2 - (r - 1)*tt + r*(4*log(abs(r - 1)) - 1) - 4*log(abs(r - 1)) - 4)/(r - 1))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Tc(tt, r) = KC_to_CC(tt, r, th, tph)[0].subs(m=1).simplify_full()\n", "Xc(tt, r) = KC_to_CC(tt, r, th, tph)[1].subs(m=1).simplify_full()\n", "show(Tc)\n", "show(Xc)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( t, r \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{r^{2} + {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right) - \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( t, r \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{r^{2} + {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right) - \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right)$$" ], "text/plain": [ "(t, r) |--> pi*unit_step(-r + 1) + arctan(1/2*(r^2 + (r - 1)*t + r*(2*log(abs(r - 1)) - 1) - 2*log(abs(r - 1)) - 2)/(r - 1)) - arctan(1/2*(r^2 - (r - 1)*t + r*(2*log(abs(r - 1)) - 1) - 2*log(abs(r - 1)) - 2)/(r - 1))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( t, r \\right) \\ {\\mapsto} \\ -\\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{r^{2} + {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right) + \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( t, r \\right) \\ {\\mapsto} \\ -\\pi \\mathrm{u}\\left(-r + 1\\right) + \\arctan\\left(\\frac{r^{2} + {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right) + \\arctan\\left(\\frac{r^{2} - {\\left(r - 1\\right)} t + r {\\left(2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 1\\right)} - 2 \\, \\log\\left({\\left| r - 1 \\right|}\\right) - 2}{2 \\, {\\left(r - 1\\right)}}\\right)$$" ], "text/plain": [ "(t, r) |--> -pi*unit_step(-r + 1) + arctan(1/2*(r^2 + (r - 1)*t + r*(2*log(abs(r - 1)) - 1) - 2*log(abs(r - 1)) - 2)/(r - 1)) + arctan(1/2*(r^2 - (r - 1)*t + r*(2*log(abs(r - 1)) - 1) - 2*log(abs(r - 1)) - 2)/(r - 1))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TBL(t, r) = Tc(t - 2/(r-1) + 2*ln(abs(r-1)), r).simplify_full()\n", "XBL(t, r) = Xc(t - 2/(r-1) + 2*ln(abs(r-1)), r).simplify_full()\n", "show(TBL)\n", "show(XBL)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "def plot_I(n, t_values=None, r_min=1.0001, r_max=100, \n", " color_t='dimgray', linestyle_t='-', \n", " r_values=None, t_min=-100, t_max=100, \n", " color_r='red', linestyle_r=':', \n", " plot_null_geod=True, hor_thickness=3):\n", " n2 = 2*n\n", " res = polygon([(pi, n2*pi), (0, (n2 + 1)*pi), (-pi, n2*pi), (0, (n2 - 1)*pi)], \n", " color='white', edgecolor='black')\n", " if r_values is not None:\n", " for r0 in r_values:\n", " res += parametric_plot((Xc(tt, r0), Tc(tt, r0) + n2*pi), (tt, t_min, t_max), \n", " color=color_r, linestyle=linestyle_r)\n", " if t_values is not None:\n", " for t0 in t_values:\n", " res += parametric_plot((XBL(t0, r), TBL(t0, r) + n2*pi), (r, r_min, r_max), \n", " color=color_t, linestyle=linestyle_t)\n", " if plot_null_geod:\n", " res += line([(pi/2, -pi/2 + n2*pi), (-pi/2, pi/2 + n2*pi)], color='green', \n", " linestyle='--')\n", " res += line([(-pi/2, -pi/2 + n2*pi), (pi/2, pi/2 + n2*pi)], color='green')\n", " res += line([(-pi, n2*pi), (0, (n2 + 1)*pi)], color='black', thickness=hor_thickness)\n", " res += line([(-pi, n2*pi), (0, (n2 - 1)*pi)], color='black', thickness=hor_thickness)\n", " return res\n", "\n", "def plot_III(n, t_values=None, r_min=-100, r_max=0.9999, \n", " color_t='dimgray', linestyle_t='-', \n", " r_values=None, t_min=-100, t_max=100, \n", " color_r='red', linestyle_r=':', \n", " plot_null_geod=True):\n", " n2 = 2*n\n", " res = polygon([(0, (n2 + 1)*pi), (-pi, (n2 + 2)*pi), (-2*pi, (n2 + 1)*pi), (-pi, n2*pi)], \n", " color='cornsilk', edgecolor='black')\n", " res += parametric_plot((Xc(tt, 0), Tc(tt, 0) + n2*pi), (tt, t_min, t_max), color='maroon', \n", " linestyle='--', thickness=2)\n", " if r_values is not None:\n", " for r0 in r_values:\n", " res += parametric_plot((Xc(tt, r0), Tc(tt, r0) + n2*pi), (tt, t_min, t_max), \n", " color=color_r, linestyle=linestyle_r)\n", " if t_values is not None:\n", " for t0 in t_values:\n", " res += parametric_plot((XBL(t0, r), TBL(t0, r) + n2*pi), (r, r_min, r_max), \n", " color=color_t, linestyle=linestyle_t)\n", " if plot_null_geod:\n", " res += line([(-pi/2, pi/2 + n2*pi), (-3*pi/2, 3*pi/2 + n2*pi)], color='green', \n", " linestyle='--')\n", " res += line([(-3*pi/2, pi/2 + n2*pi), (-pi/2, 3*pi/2 + n2*pi)], color='green')\n", " return res" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_val_I = [1.2, 1.4, 1.6, 1.8, 2, 4, 6, 8, 10]\n", "r_val_III = [-10, -8, -6, -4, -2, 0.2, 0.4, 0.6, 0.8]\n", "show(graphics_array([plot_I(0, r_values=r_val_I), \n", " plot_III(0, r_values=r_val_III)]), axes=True)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 135 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = Graphics()\n", "for n in [-2..2]:\n", " graph += plot_I(n, r_values=r_val_I) + plot_III(n, r_values=r_val_III)\n", "show(graph, figsize=10, axes=False, ymin=-3*pi, ymax=3*pi)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "graph.save('exk_CPdiag_maximal-raw.svg', figsize=10, axes=False,\n", " ymin=-3*pi, ymax=3*pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Near-horizon region" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 99 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_val_I = [1.1, 1.2, 1.3, 1.4, 1.5]\n", "r_val_III = [0.9, 0.8, 0.7, 0.6, 0.5]\n", "t_val = [-8, -6, -4, -2, 0, 2, 4, 6, 8]\n", "graph = Graphics()\n", "for n in [-1..1]:\n", " graph += plot_I(n, t_values=t_val, r_max=1.5, \n", " r_values=r_val_I, linestyle_r='-', \n", " plot_null_geod=False, hor_thickness=4) \n", " graph += plot_III(n, t_values=t_val, r_min=0.5, \n", " r_values=r_val_III, linestyle_r='-', \n", " plot_null_geod=False)\n", "show(graph, figsize=8, axes=False, frame=True, ymin=-pi, ymax=2*pi)" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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 | 711,143 | 1,034,238 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2023-23 | latest | en | 0.554771 |
https://customscholars.com/cj-317-criminal-justice-statistics/ | 1,627,652,941,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153966.60/warc/CC-MAIN-20210730122926-20210730152926-00144.warc.gz | 202,106,689 | 10,132 | # CJ 317 Criminal Justice Statistics
CJ 317 Criminal Justice Statistics
Chapter 2 Practice
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For 1-21: Below are the numbers of time respondents reported shoplifting in the past. Fill in the table below with the frequencies and percents for each category
Times Shoplifted
f
%
cf
c%
7
23
6
24
5
54
4
127
3
215
2
375
1
255
22. What does N equal? _______
23. What is the level of measurement? _______
Of 75 convicted criminals, 22 were sentenced for burglary, 34 were sentenced for armed robbery, and 19 were sentenced for theft (3 points). Show work for #58-60
24. What proportion of the criminals was sentenced for burglary?
25. What percentage of the criminals was not sentenced for armed robbery?
26. What percentage of the criminals was sentenced for theft?
Given the following frequency distribution
Score
f
20
1
19
2
18
4
17
1
15
1
12
3
8
2
4
1
27. What is the cumulative frequency of score 18? Show work.
28. What is the cumulative percentage of score 18? Show work.
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Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result. | 651 | 2,720 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2021-31 | latest | en | 0.8999 |
https://www.broadbentmaths.com/pages/shape_problemsolving_and_handling_data_223587.cfm | 1,643,443,529,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300573.3/warc/CC-MAIN-20220129062503-20220129092503-00196.warc.gz | 732,746,895 | 7,782 | Friday, 18 October 2013
I seem to have been doing a lot of 2D shape exploration recently, so here are two shape activities I’ll share with you for KS1 and KS2. They both use sorting diagrams – ideal for integrating data handling into a shape topic.
KS1 Half shapes
Organisation: Pairs or small groups.
Resources: Each group has a large piece of paper (A1 - flip chart size) with 3 sections labeled 3 sides4 sides5 or more sides. They also have a selection of squares, rectangles, (sides between 5-10cm), and triangles (equilateral and isosceles –incl. right angled isosceles).
Each child chooses a shape, fold it in half and cut along the fold.
Can you make the shape again with the two pieces?
Can you make the shape again with the two pieces?
Draw round each new shape on coloured paper, cut it out and place it on the sorting chart. It is useful to have different coloured paper for each child so you know which shapes are made by each starting shape.
How many sides did the start shape have?
How many corners or vertices? What is the shape called?
Which new shapes did the two parts make? Look at one at a time.
How many sides? How many vertices? What is the shape called?
Which shapes have more sides than the starting shape?
Did any have fewer sides?
KS2 Three parts of a shape
Organisation: Pairs or small groups.
Resources: Each group has a large piece of paper (A1 – flip chart size) with a Carroll diagram drawn on. You can label these to meet the expected outcomes for your year (eg symmetrical, not symmetrical, quadrilaterals, not quadrilaterals, regular polygon, not a regular polygon, right angle, no right angles)
Give each child two identical squares (sides between 5-10cm) one of which they cut along the diagonal fold.
Ask them arrange these 3 parts to make different shapes
Can you make a right angled- triangle? A rectangle?
Can you make a trapezium? A parallelogram?
Draw round each new shape paper, cut it out and place it on the Carroll diagram
How many other shapes can you make?3 part shapes 300x221 Shape, problem solving and handling data
How many sides? How many vertices?
What is each shape called? Which are irregular?
Which have no right angles? Which have obtuse angles?
As a challenge ask pupils only use the full square and cut this along a line from the halfway point on one side of the square to an opposite corner.
Ask them to arrange these two pieces to make different shapes and record each shape by drawing around it and writing a description: number of sides, lengths and position of sides (2 parallel sides, pairs of sides the same length….), number of vertices, types of angles…
Give a rule that only sides that are the same length can be joined together.
How many shapes can you make now?
Website design by SiteBuilder Bespoke | 641 | 2,826 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2022-05 | longest | en | 0.941669 |
https://c2.com/cybords/wiki.cgi?PowerAnalysis | 1,723,098,665,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640723918.41/warc/CC-MAIN-20240808062406-20240808092406-00167.warc.gz | 114,451,920 | 2,522 | # Power Analysis
I use a half-wave rectifier to sample the ac line voltage in my downstairs shop. This fluctuates with daily variations in the grid load and with the load I present to the household circuit leading to my shop.
Like many dirty measurements, I find them interesting to interpret by watching them over time with my Arduino based SensorServer. I've found the voltage dips twice a day, around 5am and 5pm, independent of what I do. Have a look here:
Here is the circuit I use:
```
```
I feed this with 12 vac output from a wall transformer. I step this down with a 2k/500 ohm voltage divider, rectify this with a signal diode and smooth with a .1 capacitor in front of an Arduino analog input.
``` +----|>|-----------+-----o to ADC
| |
o---/\/\/\---+---/\/\/\---+ ---
12vac 2k 500 | --- .1
| |
o-------------------------+-----+-----o
```
I calibrated this by comparing the ADC to reference measurements made with a Fluke digital volt-meter. I took samples with and without my space heater on so as to bracket a range of values. I fit this data to a linear curve to arrive at this formula:
``` volts = adc * 0.1397 + 5.5.
```
The 5.5 offset is presumably due to the diode drop, magnified by the fact that it operates in a voltage-scaled portion of the circuit.
Whole House Power Consumption
I would like to measure my whole house power consumption with high resolution in time and watts. I notice that my power company, PortlandGeneralElectric, is already doing so with a "smart" power meter from Sensus:
JoelWestvold, AMI director at PGE, writes that they see a future where they control my large-load devices so as to equalize the load on their mains:
They already control my electric meter which I now know has the ability to remotely disconnect my whole house through 900MHz radio instructions from them through Sensus.
I've written to Joel hoping to get access to some of the data he has collected. Until then, I'm measuring my power consumption by periodically clipping a RadioShack ac ammeter around the big wires in my breaker box.
I've found, for the whole house:
• 4,400 watts -- dinner time, with house guests and space heater
• 400 watts -- dead of night, 100 watts of lighting to read meter
Looking at the lower number, I see that at 9 cents a killowatt-hour, I'm spending 20 bucks a month just to keep night lights and wall transformers warm.
Last edited February 28, 2010 | 582 | 2,481 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-33 | latest | en | 0.946625 |
https://www.forextime.com/education/forex-tutorials/the-stochastic-oscillator | 1,603,704,450,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107891203.69/warc/CC-MAIN-20201026090458-20201026120458-00076.warc.gz | 735,992,031 | 31,482 | Risk warning: Trading is risky. Your capital is at risk. Exinity Limited is regulated by FSC (Mauritius).
Risk warning: Trading is risky. Your capital is at risk. Exinity Limited is regulated by FSC (Mauritius).
# The Stochastic Oscillator
The Stochastic Oscillator is a very popular technical analysis tool, available on almost all trading platforms and used by many traders all over the world. It was developed by George Lane, a famous technical analyst, based on the premise that prices tend to close near the high of the candlestick during upward price movements, and near the lower end of the candlestick during downward movements. Similarly, the Stochastic determines where the price closed in relation to a specific price range over a chosen time period. During an uptrend prices tend to close near the top of a specific range, whereas during a downtrend they cluster near the bottom. The Scholastic Oscillator consists of two lines; %K and %D. Major signals are generated using %D.
### Fast Stochastics Formula
The most popular periods for Stochastics are 5 and 14. During volatility the period of 5 or 9 is used, whereas the period of 14 is widely used for the rest of the markets.
Assuming a period of 5, a highest high of 30, a lowest low of 10 and a current close of 20, the formula above can be used the calculate the %K line:
The %K determines where the price closed in relation to a range (i.e. period) of candlesticks. For example, a reading above 80 implies that the current closing price is near the highest high of the range, which is in fact the highest price of the last 5 candlesticks. On the other hand, a reading below 20 puts the closing price near the lowest low of the range, which is in fact the lowest price of the last 5 candlesticks.
The second line, %D, is estimated by smoothing %K. Simply put, it is the 3-period simple moving average of %K:
%D = SMA (%K,3)
This is known as a Fast Stochastic.
### Slow Stochastics
Fast Stochastics produce early signals, meaning that a further smoothing of the %K and %D lines is preferred by many traders.
By taking an additional 3-period Simple Moving Average of %D and %K, the corresponding Slow Stochastics are calculated as follows:
%K = SMA(%K,3)
%D = SMA(%D,3)
The Stochastic Oscillator ranges between 0 and 100. A reading of 0 means that the latest closing price is equal to the lowest price of the price range over the chosen time period.
A reading of 100 means that the latest closing price is equal to the highest price recorded for the price range over the chosen time period.
A reading above 80 is considered to be an indication that the market has reached extreme overbought levels, whereas a reading below 20 indicates that the market has declined to extreme oversold levels.
A buy signal is generated when both %K and %D lines fall and cross over below the 20 oversold level. For further affirmative signals, traders may also wait for the %D line to rise above 20.
Conversely, a sell signal is generated when both %K and %D lines rise and cross above the overbought level of 80. Once again, if additional confirmation is required then traders wait for %D to fall below 80. It is worth noting that some traders wait for %K instead of %D to fall below the overbought level or rise above the oversold level to initiate an entry in the market. Similarly, for faster signals, traders watch the %K line instead of the slower %D line.
Apart from the 20 and 80 extreme levels, traders may also use the 30 and 70 levels at times. When trend-following indicators fail during sideways markets, the Stochastic Oscillator may produce timely signals.
### Stochastics and Divergence
Apart from the oscillation of Stochastics between 0 and 100 and the crossing of the fast line, %K, and the slow line, %D, divergence may also by incorporated for signals.
A bearish divergence occurs when the slow line (%D) rises above 80 and forms two successively lower tops while the price rallies. Similarly, a bullish divergence occurs when both %K and %D fall below the oversold level of 20, and %D forms two successively higher bottoms while the price continues to decline.
### Combination of Stochastics with RSI
Stochastics may also be combined with the popular Relative Strength Index (RSI) for potentially more precise signals and alerts.
For example, if the RSI is in the overbought area above 70, and %K and %D cross above 80, then this might produce an alert for an impending turning point on the price chart.
On the other hand, if the Stochastics cross below the 20 oversold level and the RSI is also below 30 then this might produce a bullish alert.
### Conclusion
The Stochastic Oscillator is used by beginners and advanced traders alike. It is useful in both trending and ranging markets as it produces a varied range of signals. A crossover of the Stochastics above the overbought level or below the oversold level may be more common in a sideways market. On the other hand, a divergence (either positive or negative) between the oscillator and price may be more common during trending markets. It is wise to note that indicators and oscillators are better tools when they are combined with others, including, and especially, the price itself.
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Disclaimer: This written/visual material is comprised of personal opinions and ideas. The content should not be construed as containing any type of investment advice and/or a solicitation for any transactions. It does not imply an obligation to purchase investment services, nor does it guarantee or predict future performance. FXTM, its affiliates, agents, directors, officers or employees do not guarantee the accuracy, validity, timeliness or completeness of any information or data made available and assume no liability for any loss arising from any investment based on the same.
Risk Warning: There is a high level of risk involved with trading leveraged products such as forex and CFDs. You should not risk more than you can afford to lose, it is possible that you may lose more than your initial investment. You should not trade unless you fully understand the true extent of your exposure to the risk of loss. When trading, you must always take into consideration your level of experience. If the risks involved seem unclear to you, please seek independent financial advice. | 1,465 | 6,722 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-45 | longest | en | 0.943438 |
https://anthrogenica.com/showthread.php?15959-G25-Iron-Age-Calculator&s=289c9c23ae75b5a714367a70dc6f0cd3&p=521902 | 1,550,524,041,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247488374.18/warc/CC-MAIN-20190218200135-20190218222135-00017.warc.gz | 496,702,951 | 19,459 | # Thread: G25 Iron Age Calculator
1. pen=0.001
[1] "distance%=1.8199"
PV_scaled
Nordic_IA,68.2
England_IA,12
Balkans_IA,11.4
Finland_IA,5
Hungary_IA,2.2
Anatolia_IA,1
Pakistan_Butkara_IA,0.2
pen=0
[1] "distance%=1.6"
PV_scaled
Nordic_IA,62.8
Balkans_IA,17.2
Finland_IA,15.8
Anatolia_IA,2.8
Baltic_IA,1.4
2. ## The Following 2 Users Say Thank You to PoxVoldius For This Useful Post:
JMcB (11-30-2018), michal3141 (11-30-2018)
3. +Finland IA
"distance%=3.1506"
Nordic_IA,32.2
Balkans_IA,24.6
Baltic_IA,20.8
Hungary_IA,16.2
Anatolia_IA,4.6
Turkmenistan_IA,1.6
On pen=0 I get exactly the same as without it...
"distance%=2.5424"
Balkans_IA,37.8
Baltic_IA,36.2
Nordic_IA,11
Hungary_IA,9.2
Turkmenistan_IA,5.4
Pakistan_Butkara_IA,0.4
"1. CLOSEST SINGLE ITEM DISTANCE%"
England_IA Nordic_IA Hungary_IA Finland_IAA236
7.035386 7.332753 7.785020 8.984307
Baltic_IA Balkans_IA Anatolia_IA Turkmenistan_IA
11.307732 11.672505 13.424895 13.985657
4. ## The Following 2 Users Say Thank You to Username For This Useful Post:
Просигој (11-30-2018), JMcB (11-30-2018)
5. More Finland_IA samples:
Code:
```Levanluhta_IA:DA234,0.103579,-0.004062,0.099183,0.076874,-0.001846,0.009761,0.007755,0.019384,0.0045,-0.028793,0.023871,-0.007343,0.016353,-0.014038,-0.00285,-0.009281,-0.007302,-0.005701,-0.003268,-0.000125,0.014474,-0.003462,0,0.001928,0.001317
Levanluhta_IA:DA238,0.099026,-0.081242,0.117662,0.084626,-0.028313,-0.001394,-0.00094,0.009,0.001432,-0.036994,0.038648,-0.005095,0.032705,-0.016377,-0.004343,0.002784,0.012908,0.005574,-0.010684,0.004127,0.018592,0.005564,-0.003944,-0.002289,-0.001317
Levanluhta_IA:JK1968,0.10927,-0.016248,0.095789,0.079781,-0.003385,0.01506,0.00611,0.017768,0.006954,-0.033531,0.029555,-0.016186,0.011001,-0.015964,-0.003529,-0.008088,-0.011474,-0.005954,-0.012947,0.002001,0.019965,0.002102,-0.006655,0.007109,0.00467
Levanluhta_IA:JK1970,0.105855,-0.042652,0.110496,0.075905,-0.015387,0.010877,0.011751,0.010615,0.002045,-0.022051,0.04011,-0.004646,0.019029,-0.026699,-0.015472,0.000663,0.005737,-0.006588,-0.00264,-0.002626,0.013601,-0.011623,0.003821,0.00964,-0.001317
Levanluhta_IA_o:DA236,0.12862,0.123895,0.075047,0.074936,0.042777,0.023148,-0.000705,0.007615,0.005113,-0.00893,0.000812,0.001349,-0.011893,-0.015414,0.02443,0.015115,-0.005998,0.001394,0.005279,0.012881,0.013726,0.005317,-0.000616,0.004579,0.00491
Levanluhta_IA_o:JK2065,0.135449,0.121864,0.083344,0.072352,0.047393,0.019522,-0.0094,0.005077,0.011453,0.001276,0.001137,0.002548,-0.011001,-0.013625,0.034609,0.0118,-0.004563,0.001647,0.012067,0.019384,0.000374,-0.001237,-0.004683,-0.002048,0.005389```
And don't the Scythian samples belong to Iron Age also?
6. ## The Following User Says Thank You to ph2ter For This Useful Post:
JMcB (11-30-2018)
7. How are Brits scoring such high Finland_IA in these models? The Finland_IA sample must be an early Germanic.
8. Could someone run mine if its no trouble? Thanks in advance
,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,PC11,PC1 2,PC13,PC14,PC15,PC16,PC17,PC18,PC19,PC20,PC21,PC2 2,PC23,PC24,PC25
Dibran_scaled,0.127482,0.150298,0.020365,-0.02584,0.028621,-0.007251,0.00611,0.002769,-0.002863,0.022233,0.001624,0.007343,-0.011596,0.003165,-0.02158,0.006895,0.030379,-0.00266,0.006159,-0.007379,-0.010606,0.000124,0.000986,0.000964,-0.002036
,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,PC11,PC1 2,PC13,PC14,PC15,PC16,PC17,PC18,PC19,PC20,PC21,PC2 2,PC23,PC24,PC25
Dibran,0.0112,0.0148,0.0054,-0.008,0.0093,-0.0026,0.0026,0.0012,-0.0014,0.0122,0.001,0.0049,-0.0078,0.0023,-0.0159,0.0052,0.0233,-0.0021,0.0049,-0.0059,-0.0085,0.0001,0.0008,0.0008,-0.0017
9. ## The Following User Says Thank You to Dibran For This Useful Post:
JMcB (11-30-2018)
10. Originally Posted by J Man
How are Brits scoring such high Finland_IA in these models? The Finland_IA sample must be an early Germanic.
It is more "northern Europe" than it is like modern "Finnish", so not much of a Siberian component to it. In the clustering I was doing, it grouped with the Balts.
11. ## The Following 3 Users Say Thank You to randwulf For This Useful Post:
J Man (11-30-2018), JMcB (12-20-2018), PoxVoldius (11-30-2018)
12. Originally Posted by randwulf
It is more "northern Europe" than it is like modern "Finnish", so not much of a Siberian component to it. In the clustering I was doing, it grouped with the Balts.
Hmm if it groups with Balts it is a bit strange then that some people get Baltic_IA and no Finland_IA while others get Finland_IA and no Baltic_IA in this calculator. Or maybe it is not so strange and I just do not have a good understanding of all of this lol.
13. Originally Posted by J Man
Hmm if it groups with Balts it is a bit strange then that some people get Baltic_IA and no Finland_IA while others get Finland_IA and no Baltic_IA in this calculator. Or maybe it is not so strange and I just do not have a good understanding of all of this lol.
I was clustering at a fairly "low" K level. It was more like the less-Siberian tinged north European samples than modern Finns is all I mean by that. There may still be some distinctions.
14. ## The Following 2 Users Say Thank You to randwulf For This Useful Post:
J Man (11-30-2018), JMcB (12-20-2018)
15. Originally Posted by Dibran
Could someone run mine if its no trouble? Thanks in advance
,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,PC11,PC1 2,PC13,PC14,PC15,PC16,PC17,PC18,PC19,PC20,PC21,PC2 2,PC23,PC24,PC25
Dibran_scaled,0.127482,0.150298,0.020365,-0.02584,0.028621,-0.007251,0.00611,0.002769,-0.002863,0.022233,0.001624,0.007343,-0.011596,0.003165,-0.02158,0.006895,0.030379,-0.00266,0.006159,-0.007379,-0.010606,0.000124,0.000986,0.000964,-0.002036
,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,PC11,PC1 2,PC13,PC14,PC15,PC16,PC17,PC18,PC19,PC20,PC21,PC2 2,PC23,PC24,PC25
Dibran,0.0112,0.0148,0.0054,-0.008,0.0093,-0.0026,0.0026,0.0012,-0.0014,0.0122,0.001,0.0049,-0.0078,0.0023,-0.0159,0.0052,0.0233,-0.0021,0.0049,-0.0059,-0.0085,0.0001,0.0008,0.0008,-0.0017
Here you go
"distance%=3.3122"
Dibran_scaled
Balkans_IA,80
England_IA,7
Nordic_IA,4.2
Hungary_IA,2.4
Anatolia_IA,2.2
Finland_IA,2
Baltic_IA,1.2
Turkmenistan_IA,1
pen=0
"distance%=3.035"
Dibran_scaled
Balkans_IA,79.6
Baltic_IA,9.6
England_IA,8.8
Pakistan_Butkara_IA,1.4
Turkmenistan_IA,0.6
"1. CLOSEST SINGLE ITEM DISTANCE%"
Balkans_IA England_IA Hungary_IA Anatolia_IA
4.576255 10.807633 12.112909 12.478423
Nordic_IA Finland_IAA236 Turkmenistan_IA Baltic_IA
14.243275 14.516786 16.406939 18.960005
16. ## The Following 3 Users Say Thank You to Username For This Useful Post:
Dibran (11-30-2018), JMcB (12-02-2018), michal3141 (11-30-2018)
Here you go
"distance%=3.3122"
Dibran_scaled
Balkans_IA,80
England_IA,7
Nordic_IA,4.2
Hungary_IA,2.4
Anatolia_IA,2.2
Finland_IA,2
Baltic_IA,1.2
Turkmenistan_IA,1
pen=0
"distance%=3.035"
Dibran_scaled
Balkans_IA,79.6
Baltic_IA,9.6
England_IA,8.8
Pakistan_Butkara_IA,1.4
Turkmenistan_IA,0.6
"1. CLOSEST SINGLE ITEM DISTANCE%"
Balkans_IA England_IA Hungary_IA Anatolia_IA
4.576255 10.807633 12.112909 12.478423
Nordic_IA Finland_IAA236 Turkmenistan_IA Baltic_IA
14.243275 14.516786 16.406939 18.960005
Thanks!
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• | 3,176 | 7,299 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2019-09 | latest | en | 0.951892 |
https://www.stat.math.ethz.ch/pipermail/r-help/2014-December/424177.html | 1,653,510,112,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00657.warc.gz | 1,188,173,629 | 2,409 | [R] keep only the first value of a numeric sequence
Richard M. Heiberger rmh at temple.edu
Mon Dec 15 14:18:53 CET 2014
```we can speed this up a lot
> system.time(for (i in 1:2000) ifelse(c(0, diff(data\$mydata)) != 1, 0, 1))
user system elapsed
0.122 0.012 0.132
> system.time(for (i in 1:2000) as.numeric( c(0, diff(data\$mydata))==1))
user system elapsed
0.073 0.007 0.078
> ifelse(c(0, diff(data\$mydata)) != 1, 0, 1)
[1] 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
> as.numeric( c(0, diff(data\$mydata))==1)
[1] 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
>
On Mon, Dec 15, 2014 at 7:18 AM, Jorge I Velez <jorgeivanvelez at gmail.com> wrote:
> Dear jeff6868,
>
> Here is one way:
>
> ifelse(with(data, c(0, diff(mydata))) != 1, 0, 1)
>
> You could also take a look at ?rle
>
> HTH,
> Jorge.-
>
>
>
> On Mon, Dec 15, 2014 at 9:33 PM, jeff6868 <geoffrey_klein at etu.u-bourgogne.fr
>> wrote:
>>
>> Hello dear R-helpers,
>>
>> I have a small problem in my algorithm. I have sequences of "0" and "1"
>> values in a column of a huge data frame, and I just would like to keep the
>> first value of each sequences of "1" values, such like in this example:
>>
>> data <-
>>
>> data.frame(mydata=c(0,0,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,1,1,1,1),final_wished_data=c(0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0))
>>
>> Any easy way to do this?
>>
>> Thanks everybody!
>>
>>
>>
>>
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/keep-only-the-first-value-of-a-numeric-sequence-tp4700774.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
``` | 857 | 2,313 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2022-21 | latest | en | 0.706031 |
https://www.intechopen.com/books/application-of-geographic-information-systems/demand-allocation-in-water-distribution-network-modelling-a-gis-based-approach-using-voronoi-diagram | 1,623,907,975,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487629209.28/warc/CC-MAIN-20210617041347-20210617071347-00301.warc.gz | 732,667,307 | 104,526 | Open access peer-reviewed chapter
# Demand Allocation in Water Distribution Network Modelling – A GIS-Based Approach Using Voronoi Diagrams with Constraints
By Nicolai Guth and Philipp Klingel
Submitted: May 9th 2011Reviewed: May 21st 2012Published: October 31st 2012
DOI: 10.5772/50014
## 1. Introduction
In water distribution network modelling the topology of the network is commonly mapped as a (directed) graph consisting of nodes and links (Walski et al., 2001). Pipe sections with constant parameters are modelled as links. Intersections, water inlets, points of water withdrawal and locations of pipe parameter changes are modelled as nodes. Coordinates related to the nodes define the spatial location. To calculate the hydraulic system state (pressures and flows) the water demand of the consumers is assigned to the relevant nodes as the driving parameter (demand driven simulation). Figure 1 schematically shows the abstraction of a water distribution network.
To reduce the model size typically not every known demand (e.g. demand at a house connection) is modelled as a node. Besides, location and demand of consumers are often not known, especially in developing countries.
To allocate demands to the nodes Voronoi diagrams might be used. The Voronoi diagram is also known as Thiessen polygon and dual to the Delaunay triangulation (c.f. fig. 2, left sketch). The Voronoi diagram is based on a set of nodes and defines one area for each node with every point within the area being closer to the originating node of the area than to any other node. In the following these areas are referred to as Voronoi regions. They represent the catchment areas of the nodes. The borders of the Voronoi regions constitute of lines called bi-sectors. Thus, known demands (value and location) can be allocated to the closest nodes according to the Euclidean distance. This approach is also commonly applied to determine, for example, the rainfall catchment areas of inlets of sewer networks.
If demands and their location are not known, they can be determined based on the size of the Voronoi regions, the population distribution and density and a consumption per capita value. Alternatively, building areas can be allocated to the nearest nodes based on the Voronoi diagrams if the correspondent data is available. In this case the actual demand is calculated by using a coefficient relating the population to a building area unit and a consumption per capita value. The sketch on the right in figure 2 schematically shows the allocation of demands (in this case building areas) to nodes using a Voronoi diagram.
Pipe network data, population distribution and building data are commonly stored and managed in geographic information systems (GIS). Thus, a GIS-application to allocate water demand values to the network model nodes is self-evident and commonly applied.
The calculation of common Voronoi diagrams is based on a set of nodes and the Euclidean distance between the nodes and the points of the areas. Various well known and often used algorithms to generate such Voronoi diagrams exist, for example the sweep-algorithm (Fortune, 1986; Preparata and Shamos, 1985) and the divide-and-conquer-approach (Shamos, 1975).
The approach to allocate demands using such common Voronoi diagrams follows the assumption that a consumer is connected to the closest existing pipe and to the closest existing node respectively. Boundaries and obstacles are not considered as constraints. In this context, areas with different population densities, for example, constitute boundaries and railway trails and lakes within the supply area, for example, constitute obstacles which cannot be passed by distribution pipes. Thus, with common Voronoi diagrams consumers, areas or building areas are possibly allocated to nodes which are closest according to the Euclidean distance but are not closest if boundaries or obstacles are considered. This constitutes a significant limitation of the application of Voronoi diagrams based on the Euclidean distance for the allocation of water demand.
If boundaries are convex, no obstacles are located in between two originating nodes of a bi-sector. The Voronoi diagram can still be calculated based on the Euclidean distance. The convex boundaries can be considered easily by intersecting the Voronoi diagram with the convex boundary. Conversely, sections of non-convex boundaries or obstacles might be located in between two originating nodes of a bi-sector. In these cases the determination of the bi-sectors based on the Euclidean distance is not sufficient any more. The shortest way to bypass the non-convex section or obstacle respectively has to be considered instead.
Okabe et al. (2000) describe this problem as “Voronoi diagrams with obstacles” and introduce the “shortest path Voronoi diagram”. Thereby, obstacles are supposed to be considered by calculating Voronoi diagrams based on the shortest path instead of the Euclidean distance. A satisfactory solution of this approach would result in an increased model accuracy and therefore higher reliability of the simulation calculations.
Figure 3 illustrates the difference between a Voronoi diagram, which is determined based on the Euclidean distance (left sketch) and based on the shortest path (right sketch). Not considering (convex sections of) the boundaries, for example, results in an allocation of areas to node n1 which can only be part of the Voronoi regions of the nodes n4 and n5 if the boundaries given in the example are respected. Not considering the shortest path to bypass non-convex sections of the boundaries leads, for example, to an allocation of an area to node n2 instead of node n1. Accordingly, an area is allocated to node n3 instead of node n2 if the shortest path to bypass the obstacle given in the example is ignored and the Voronoi diagram is determined based on the Euclidean distance.
Several authors have tackled this problem. The approach of Aronov (1987) considers non-convex boundaries but not obstacles within the Voronoi regions. The approach of Papadopoulou and Lee (1998) does consider obstacles as constraints but only if specific conditions are given. None of the known approaches solves the problem satisfactorily for an application in the given context. The consideration of both, non-convex boundaries and obstacles would be desirable.
In this context, the additively weighted Voronoi diagram is of particular interest. Johnson and Mehl (1939) invented the additive weights of originating nodes of Voronoi diagrams to model the development of crystals, which grow with different speed into different directions. Every node is weighted with a positive or negative constant (additive constant) which is subtracted from the distance function when calculating the Voronoi diagram. Thus, contrary to a common Voronoi diagram based on two nodes, the bi-sector is not a straight line in the geometric centre between the nodes if the two nodes are weighted with different constants. The bi-sector constitutes a hyperbola being closer to the node with the smaller weight (Aurenhammer, 1991).
This chapter presents a novel approach to calculate Voronoi diagrams based on the shortest path instead of the Euclidean distance considering non-convex boundaries and obstacles, which Guth (2009) has developed in his Bachelor thesis. At critical points of boundaries and obstacles, the so called subordinated nodes are temporarily defined and weighted with an additive constant to consider the shortest path as distance function for the calculation of the Voronoi diagram. The approach is presented in section 2 of this chapter. The resultant algorithm is expounded in section 3. The testing of the algorithm and the implementation of the algorithm as a GIS-tool based on the software package ESRI ArcGIS (Ormsby et al., 2004) are demonstrated in sections 4 and 5.
## 2. Approach
The basis of the novel approach described herein is a geometric and iterative method to calculate Voronoi diagrams. Thereby, the pairs of originating nodes of a bi-sector (the immediate neighbours) have to be determined first. Each node of a pair is defined to be the origin (centre) of concentric circles. Circles with the same radius are intersected. The intersection points constitute points of the bi-sector. Thus, the Voronoi diagram based on the Euclidean distance can be calculated.
As discussed in section 1, to consider non-convex boundaries and obstacles, the determination of the Voronoi diagram has to be based on the shortest path. Thus, the shortest paths from every point of a bi-sector to each of the originating nodes of the bi-sector have the same length. This leads to a linear form of the bi-sector if the points of the bi-sector are ‘visible’ from both originating nodes (the length of the shortest path is equal to the length of the Euclidean distance) and to a hyperbolic form if a non-convex boundary section or an obstacle leads to a shortest path which is longer than the Euclidean distance (c.f. fig. 3).
When considering boundaries and obstacles they are assumed to be represented by polygons with vertices, which is the case in the context of the development of a GIS-solution. The critical points of bounding polygons are the extreme vertices of non-convex sections. Accordingly, the critical points of obstacles are the extreme vertices of convex sections. These critical points are identified and added to the set of given nodes (primary nodes) as subordinated nodes. A subordinated node is always related to the closest primary node. An additive constant which represents the shortest path length to that primary node is assigned to each subordinated node. In figure 4 an example of three primary nodes (n1, n2 and n3), a bounding polygon and three obstacles is given. Subordinated nodes are defined at all critical points of the boundary and the obstacles. For example, the three subordinated nodes n11, n12 and n13 are related to node n1. The additive constant of the subordinated node n12 is also shown exemplarily in figure 4.
Even though the principle idea of using additively weighted nodes was invented by Johnson and Mehl (1939), their approach to calculate the Voronoi diagram cannot be applied successfully to solve the given problem. Transferred to the given context, the approach does only solve configurations where the additive constant of a subordinated node is shorter than the distance between the primary node and the related subordinated node (Okabe et al., 2000). In the given case the additive constant is always equal to the distance between primary and subordinated node. Thus, the development of a novel solution is needed.
Like the computation of Voronoi diagrams based on a set of primary nodes by intersecting circles, the determination based on primary and subordinated nodes can be regarded as the projection of the intersection of cones. Each node (located in the x-y-plane) represents the tip of a cone which is opened upwards. All cones have the same cone angle. The cones at the subordinated nodes are moved vertically up (z-direction) by the value of their additive constant. At a certain height (z-value), the intersection of the cones can be represented by the intersection of circles with the radius of the cones at that specific height (z-value). Cones related to primary nodes have the same radii at the same height. Thus, the projection (to the x-y-plane) of the intersection of cones related to primary nodes results in a linear shaped section of the according bi-sector. Accordingly, the intersection of the cones related to a primary and a subordinated node results in a hyperbolic shape due to the different radii at a certain height of the cones.
To simplify the calculation, the projected cones are treated (discretised) as concentric circles. The height above the plane is reflected by the circle’s radius. Circles with the same radii are intersected to calculate bi-sector points. For the subordinated nodes’ circles, the radii are decreased by the respective additive constant. Resultant radii below zero are not admissible.
For the calculation of the Voronoi diagram the radii of the circles are increased successively. For each radius (iteration), the circles which are related to the primary nodes or their subordinated nodes are intersected in several calculation steps. In one calculation step the circles of two nodes are intersected. If there is an intersection point which is visible from both circles’ centres (originating nodes) and is not located within another circle, the point is stored as bi-sector point. Visibility may be limited by the bounding polygon or an obstacle. The difference between the radii of two sequent iterations constitutes the discretisation of the iterative approach.
The result of the approach is a Voronoi diagram consisting of polygons with discretely determined vertices. As GIS do not store mathematical functions, this is not a drawback. The resulting polygons can be directly stored without any further processing.
Figure 5 shows a schematic illustration of the approach. The given configuration comprehends two primary nodes (n1 and n2). A boundary polygon constitutes a critical point. The pertinent subordinated node n21 is related to the closest primary node, node n2. In the area visible from both primary nodes (right of the ‘visibility boundary’ of node n2) the bi-sector between the nodes is linear. The bi-sector vertices (black squares in the figure) are determined by intersecting concentric circles with the same radii. In the area not visible from node n2 (left of the ‘visibility boundary’ of node n2), the bi-sector has a hyperbolic shape. The vertices (black rhombi in the figure) are determined by intersecting the concentric circles of the primary node n1 and the subordinated node n21. The radii of the circles with the subordinated node n21 as origin are always decreased by the additive constant, which is the length of the shortest path between the nodes n2 and n21. In the figure, circles which are intersected, are plotted in the same colour.
## 3. Algorithm
### 3.1. Overview
For the realisation of the approach described in the previous section, an algorithm was developed, tested (c.f. section 4) and finally implemented in a GIS-tool (c.f. section 5). An overview of the individual steps of the algorithm is given in figure 6.
First, the subordinated nodes of the given configuration are identified and weighted with an additive constant. Next, points of the bi-sectors are calculated by intersecting circles with corresponding radii and the nodes as origin. Finally, based on the calculated set of bi-sector points, the Voronoi diagram is determined. Thus, the algorithm can be divided into three principle parts: initialization, computation and creation of the resulting Voronoi diagram. Each of the following subsections describes one of the three parts.
### 3.2. Initialization
Identifying the subordinated nodes constitutes the first step of the initialization. Therefore, the bounding polygon and the polygons which describe the obstacles are analysed regarding the exterior angle at each vertex. For the bounding polygon this is facilitated by calculating the azimuths of the current vertex to the predecessor (t1 in equation 1) and the successor (t2 in equation 1) vertices. The difference between the azimuths is subtracted from the full circle. Thus, the outer angle β is calculated by equation 1:
β = 2π – (t1 – t2)
The result is normalised to β є [0;2π) by successive subtraction of 2π where required. Assuming that the polygon is defined clockwise, the vertex is marked as a subordinated node if it holds that β < π. The angles β of all vertices are added (∑β) and compared with the theoretical angular sum W. W is computed by equation 2, where n is the number of vertices:
W = (n + 2) π
If ∑β = W, the polygon is defined clockwise and the marks are correct. Otherwise, the order of the vertices is switched and the algorithm is executed again. For the obstacle polygons, the same algorithm is used but the marks are switched in the end. Thus, only the vertices which stick out of the obstacle (convex sections) are considered as subordinated nodes. The identified subordinated nodes are added to the list of originating nodes.
In the succesive step, with the algorithm of Dijkstra (1959), the relation of subordinated nodes and primary nodes is determined and the additive constant for each subordinate node is calculated. The Dijkstra algorithm analyses the graph based on all subordinated and primary nodes with links between pairs of nodes which are visible to each other considering the given boundaries and obstacles. From each subordinated node the possible paths to all primary nodes are calculated. Thus, the shortest path determines the primary node related to the subordinated node. Furthermore, the length of the shortest path constitutes the additive constant.
### 3.3. Computation of bi-sector points
As mentioned before, the bi-sectors between the Voronoi regions are made up of intersection points of circle intersections. Node pair by node pair, circles of all nodes are intersected with each other to determine the intersection points. The process starts with a randomly chosen pair of nodes.
For the circles to be intersected, the minimum and maximum radius and obligatory radii are determined first. The minimum radius is where both circles touch. To identify the maximum radius, the maximal possible distances from each originating node (centres of the circles) to a visible point within the boundary are calculated. The shorter distance is used as maximum radius. The obligatory radii for each pair of nodes are those where the intersection points lie on a segment of the boundary or obstacle polygon. When the circles of a primary and a subordinated node are intersected, the obligatory radii have to be determined iteratively.
The iteration method is described here below and illustrated in figure 7. B1 is the starting vertex of a segment, IP the unknown intersection point of circles with the centres (originating nodes) n1 and n2. The vector v points into the direction of the segment and is normalised to (length) 1. The unknown vectors u and w point from the intersection point to the respective centres.
To compute the unknown vectors, the following constraints (equations 3 to 7) are used with ux, uy, wx, wy, vx, vy as x- and y-components of the respective vectors, n1x, n1y, n2x, n2y, B1x, B1y as x- and y-coordinates of the respective points and m as length multiplication factor of vector v, which expresses the distance from B1 to IP:
ux + n1x – n2x – wx = 0
uy + n1y – n2y – wy = 0
m vx + wx + B1x – n1x = 0
m vy + wy + B1y – n1y = 0
wx² + wy²=ux² + uy²E1
Equation 3 and 4 express a closed vector-path from IP via n1 and n2 back to IP. Equation 5 and 6 represent the closed path from B1 via IP and n1 back to B1. Equation 7 guarantees, that the vectors u and w have an equal length. Taking the constraints into account, m can be computed using equation 8:
m = n2x² - 2· n2x· B1x + n2y² - 2· n2y· B1y + 2 · n1x· B1x - n1x² + 2· n1y· B1y - n1y² 2· (n2x · v+ n2y · v- n1x · vx - n1y · vy)E2
Finally, IP can be calculated with equation 9:
IP = B1 + m v
In the first iteration, the centres are moved in normal direction away from the segment by the value of the additive constant. The normal direction is used as temporary vector for u and w and IP is computed. In the next iterations, the centres are moved in direction of the last u and w respectively. After the changes of u and w fall below a given bound, the final radii are calculated by adding the distance from IP to the centre and the additive constant.
After the minimum, maximum and obligatory radii are identified the intersection points (bi-sector points) related to the pair of nodes are calculated. Beginning with the minimum radii, the circles of the pair of nodes are intersected. For each intersection point it is checked if the point is visible from both centres and if no other centre is closer to the point. If one of the constraints is not fulfilled, the point is dismissed. Otherwise, the point is stored in a list, individually created for each pair of nodes. After the first intersections with the minimum radius, the radius is increased. The new radius is determined with a function, which takes the preceding intersection results into account. For small bends of the resulting bi-sectors the increment is larger than for intersections which form a strong bend. Increments may also be negative if necessary. When the maximum radius is reached, the obligatory radii for the points on the boundary and the obstacles are processed and the next pair of nodes is chosen.
### 3.4. Determination of Voronoi diagram
As the intersection points are stored in lists without order, the resulting polygons of the bi-sectors cannot be created directly. For each list a polyline is created first. This is done by picking the first point in the list and searching for the point with the greatest distance to it. This point is defined as the starting point of the polyline. Next, the closest point to the starting node is searched for, defined as the next point and marked. The process is repeated until no unmarked points are left on the list. To form the resulting Voronoi diagram, the individual polylines are merged by comparing the coordinates of the polylines’ starting points and endpoints and assembling the nearest ones.
## 4. Testing
The developed approach and algorithm respectively are tested in order to evaluate the functionality and performance. Several configurations of given sets of nodes and boundaries are analysed by comparing the Voronoi diagram based on the Euclidean distance and the Voronoi diagram calculated with the novel approach. The comparison is mainly based on the size of the Voronoi regions. Two of the tested cases are discussed in the following.
The first case is a synthetic example configuration solely created to test the functionality of the developed algorithm. It consists of only three originating nodes (n1, n2, n3), a non-convex boundary and three obstacles located within the boundary. Figure 8 shows the case and the calculated Voronoi diagrams based on the Euclidean distance and the shortest path. The individual sizes of the areas and the differences are shown in table 1. The differences do not sum up to zero as the approach is approximate and small holes between the individual Voronoi regions may occur. Furthermore, the values in the table are rounded to two decimal places.
Node Voronoi region based on the Euclidean distance [length²] Voronoi region based on the shortest path [length²] Difference [length²] Difference [%] n1 2,067.60 1,889.24 -178.36 -8.6 n2 2,210.80 2,213.44 2.63 0.1 n3 2,120.66 2,296.30 175.65 8.3
### Table 1.
Comparison of the Voronoi region sizes of case 1
The Voronoi region of node n1 decreases significantly in size (-8.6%) with the new approach compared to the Euclidean Voronoi diagram due to the large area on the left. Considering the bounding polygon, this area is not visible from the primary node n1. Thus, within the shortest path Voronoi diagram, the specific area is allocated to the Voronoi regions of the nodes n2 and n3 instead of n1. The Voronoi region of node n2 remains almost the same (0.1%): it gains area from the region of node n1, but nearly the same amount is allocated to the region of node n3 in the upper part of the image, where the bisector is bent to the right around the obstacle. Coming closer to the boundary the same bi-sector is bending a little to the left again. This is due to the change of the shortest path to bypass the left obstacle from the way around the obstacle on the left hand side to the way around on the right hand side (between the two obstacles). Within the Euclidean Voronoi region of node n3 no obstacles or non-convex sections of the bounding polygon are located which might have an influence on the bi-sectors if the Voronoi diagram is calculated based on the shortest path. Thus, it gains area of the Voronoi regions of both nodes n1 and n2 (8.3%).
The second case is a detail of an existing city in Algeria. It consists of 20 originating nodes (n1, n2, …, n20), a non-convex boundary and several obstacles located within the boundary. Figure 9 shows the case and the calculated Voronoi diagrams based on the Euclidean distance and the shortest path. The individual sizes of the Voronoi regions and the differences are shown in table 2. In addition to the explanation given already for table 1, the area differences do not sum up to zero as only a small detail of the data set is shown.
Case 2 clearly shows, that the Voronoi diagram based on the Euclidean distance relates areas to nodes, which are closer to other nodes, if boundaries or obstacles are respected. This is the case, for example, for the nodes n7, n11 and n12. To node n11 the area to the right is assigned, which can only be reached by passing through the Voronoi region of node n7. To the two nodes close to the obstacle in the centre, n7 and n12, areas on the opposite side of the obstacle are allocated. Contrarily, all Voronoi regions of the shortest path Voronoi diagram have a direct connection to the related originating node. As ascertained in table 2, the differences in the area sizes are up to 13.3% gain and -12,7% loss respectively.
Node Voronoi region based on the Euclidean distance [length²] Voronoi region based on the shortest path [length²] Difference [length²] Difference [%] n1 33,820.06 38,722.92 -4,902.86 -12.70 n2 28,519.46 25,179.86 3,339.60 13.30 n3 20,510.38 20,517.97 -7.59 0.00 n4 14,185.69 13,991.04 194.65 1.40 n5 19,486.64 20,731.79 -1,245.15 -6.00 n6 36,329.44 35,075.23 1,254.21 3.60 n7 29,521.51 33,492.01 -3,970.49 -11.90 n8 15,188.57 14,350.52 838.05 5.80 n9 3,656.39 3,656.57 -0.18 0.00 n10 2,809.11 2,809.19 -0.08 0.00 n11 23,676.38 25,289.44 -1,613.06 -6.40 n12 16,706.28 16,185.26 521.03 3.20 n13 16,916.03 17,686.10 -770.07 -4.40 n14 21,487.65 20,796.47 691.18 3.30 n15 7,085.54 7,085.79 -0.25 0.00 n16 6,603.06 6,603.53 -0.46 0.00 n17 3,779.35 3,831.44 -52.09 -1.40 n18 3,156.40 2,834.48 321.92 11.40 n19 11,720.82 11,494.35 226.47 2.00 n20 23,474.75 22,949.54 525.21 2.30
### Table 2.
Comparison of the Voronoi region sizes of case 2
## 5. GIS-tool
Due to the spatial reference of the water distribution network data and the basic data for demand determination such like population density, population distribution, building areas etc. a GIS-application to determine and allocate water demand values to the network model nodes is advantageous. Following is a description of a GIS-tool implemented as an independent library of functions and integrated into ESRI ArcGIS (version 9).
ArcGIS, a product of the company ESRI, constitutes of several interlinked GIS products. The desktop application ArcMapsupports visualising, analysing and editing of spatial data and linked attributes. The desktop application ArcCatalogenables data management. The data is commonly stored in relational data bases (geodatabases) but using single files (e.g. shape files) is possible too. Geometric objects (features) are modelled as vector data through defining shape and location of the object. Three principle feature typesexist: Point features(punctual objects), line features(linear objects with start point, end point and vertices) and polygon features(areas defined by a polygon where the start and end points have the same location). Attributes (without spatial reference) can be linked to features. Featuresof the same type and with identical characteristics are stored in object classes (feature classes). All ArcGIS products are based on the library ArcObjects, developed as Microsoft Component Object Model (COM). ArcObjectsoffers numerous functionalities for the extension of ArcGIS products or the integration of applications into ArcGIS products. For further details on ArcGIS it is referred to the technical literature, c.f. e.g. Ormsby et al. (2004). The application for demand allocation described in this section is based on the ArcGIS data concept and the ArcObjectsfunctionalities. The application was implemented as a dynamically linked library (DLL) which is integrated into ArcMapas a toolbar with an own user interface.
The demand allocation consists of two principle steps: (1) The calculation of the catchment areas of the nodes (Voronoi regions related to the originating nodes) and (2) the determination of the water demand within the catchment area and its allocation to the corresponding node.
For the calculation of the catchment areas (first step), input parameters are the demand nodes of the network model graph, the boundaries of the populated areas and the obstacles within the populated areas. The nodes have to be provided as point featuresin a point feature class, the boundaries and obstacles as polygon featuresin polygon feature classes. With the approach described in the previous sections the Voronoi diagram is calculated based on the nodes and stored in another polygon feature class. The references between Voronoi regions (catchment areas) and originating nodes are saved as an attribute of the nodes.
For the calculation of the demand per catchment area (second step) three options are developed and implemented considering the commonly available data basis: (A) Values and locations of the demands are given as point features, (B) areas with numbers of the population living there are given as polygon featuresor (C) building areas are given as polygon featuresand areas with the population are also given as polygon features. Moreover, option B and C need a constant demand per capita value as input parameter
Option A) The demand values [volume/time] are accumulated per catchment area by intersecting the catchment areas (polygon features) and the demands (point features) according to the spatial references. Finally, the accumulated demands per catchment area are allocated to the originating nodes.
Option B) The population per catchment area [inhabitants] is determined by intersecting the areas with constant values of the population (polygon features) and the catchment areas (polygon features) according to the spatial reference. To calculate the demand per node [volume/time], the population values [inhabitants] of the catchment area are multiplied with the demand per capita [volume/inhabitant/time].
Option C) The population per building area [inhabitants] is determined by intersecting the areas with constant values of the population (polygon features) and the building areas (polygon features) according to the spatial reference. The building areas, and thus the population, are accumulated per catchment area by intersecting the building areas (polygon features) and the catchment areas (polygon features) according to the spatial references. Finally, the demand per node [volume/time] is calculated by multiplying the population values of the catchment areas [inhabitants] and the demand per capita [volume/in-habitant/time].
Figure 10 shows an exemplary detail of the visualised result of a demand allocation with the GIS-tool. In the example, the nodes of the network model (black dots), a building area data set (dark green and orange areas) and a population density data set (transparent blue and transparent green areas) are given (as point feature classand polygon feature classes). Moreover, a satellite picture of the setting is used as basic layer. Based on the set of nodes and the bounding population density polygons, the Voronoi diagram was calculated applying the novel approach (polygon feature class). The Voronoi regions (polygon features) constitute the catchment areas of the nodes (red lines). Considering the given data, the demand is determined based on the population density and the building distribution (option C).
For each population density area (polygon feature) the number of inhabitants is calculated by multiplying the respective density and area. Next, the determined population is related to the building areas. Therefore, the total building area per population density area is determined by intersecting the two polygon feature classesaccording to their spatial reference. With the number of inhabitants and the total area of buildings per population density area the inhabitants per building area unit are calculated for each population density area. After accumulating the building areas per node according to the node catchment areas the number of population per node can be calculated. Finally, with the specific per capita demand, the demand per node is determined. Non domestic consumers with given demands (orange areas in the figure), such like industries or administrations, are excluded from the process described and allocated to the nodes directly.
## 6. Conclusion
The need for a more precise demand allocation in order to increase the accuracy of water distribution network models led to the development of a novel approach to calculate Voronoi diagrams with constraints. The constraints considered are convex and non-convex boundary and obstacle polygons. Thus, the approach basically solves the problem of generating Voronoi diagrams in arbitrary environments.
By means of a geometric approach, namely successive circle intersection with discrete radii, the bi-sectors which form the Voronoi diagram are determined. Thus, the result is not a mathematically exact solution but an iterative approximation. Hereby, the accuracy can be controlled by the distances between the individual radii. For GIS software, the discretisation does not present a drawback as only polygons with discrete vertices can be stored.
At the moment, the algorithm is not comparable with other algorithms determining Voronoi diagrams based on the Euclidean distance (sweep-algorithm, divide-and-conquer-approach) regarding the computation speed. But the advantages of increased accuracy of the results of an application for demand allocation in water distribution network modelling (and possibly in other applications) outbalance the speed issue. Furthermore, with an enhanced radius controlling mechanism and a reduction of the circle combinations for which intersections are computed, there is still potential for improvements. Moreover, the overall speed could be increased by using highly parallel computations, since each circle combination can be worked at separately. This could be facilitated by means of GPU or multi CPU usage.
Another method to compute the shortest path Voronoi diagram following the described approach is the analytic representation of the bi-sectors. A bi-sector between just two nodes can be defined as a mathematical function. The major challenge is to identify those sections of the functions, which make up the bi-sectors of the total Voronoi diagram based on more than two nodes by intersecting the functions. Due to the mathematical properties the function intersections cannot be computed directly but only iteratively. Thus, in a mathematical sense, the approach is not exact as well. A benefit of the analytically described bi-sectors is the fact that only two points per function have to be calculated. To compute a Voronoi diagram polygon, the relevant vertices can be simply calculated with a free choice of density using the determined functions. Thus, the computation has no impact on the time needed for the actual determination of the mathematical description of the Voronoi diagram. An analytic solution is currently being developed by the authors.
Furthermore, a GIS-tool to allocate the water demand was developed and presented in section 5. The GIS-tool consists of two principle calculation steps. First, the catchment areas of the nodes are computed using the developed approach to calculate Voronoi diagrams. The second step consists of three options to determine the demand. The most precise result is achieved by applying option A due to the superior input data. In this case, values and location of demands are known and directly allocated to the nodes according to the Voronoi diagram. If such input data is not available, the distribution of water demand has to be determined first. Option B offers an approach to determine the water demand based on the population distribution, which is considered to be constant for defined areas. Option C follows the same approach but provides a higher accuracy by relating the population (and thus, the demand) to the building density instead of considering a constant population distribution for specific areas. The developed GIS-tool has been already successfully applied in several network modelling projects of the Institute for Water and River Basin Management of the Karlsruhe Institute of Technology and proofed to be a useful solution for demand allocation.
Finally, it is worth mentioning that an application of the presented approach is not limited to demand allocation in water distribution network modelling. A broad field of applications is conceivable, such as determination of rainfall catchment areas, modelling of growth processes or stochastic analysis.
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© 2012 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
## How to cite and reference
### Cite this chapter Copy to clipboard
Nicolai Guth and Philipp Klingel (October 31st 2012). Demand Allocation in Water Distribution Network Modelling – A GIS-Based Approach Using Voronoi Diagrams with Constraints, Application of Geographic Information Systems, Bhuiyan Monwar Alam, IntechOpen, DOI: 10.5772/50014. Available from:
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http://geoinsyssoft.com/outerjoins/ | 1,563,616,192,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526506.44/warc/CC-MAIN-20190720091347-20190720113347-00295.warc.gz | 62,926,754 | 8,283 | OUTERJOINS
RightOuterJoin [Pair]
Performs an right outer join using two key-value RDDs. Please note that the keys must be generally comparable to make this work correctly.
Listing Variants
def rightOuterJoin[W](other: RDD[(K, W)]): RDD[(K, (Option[V], W))]
def rightOuterJoin[W](other: RDD[(K, W)], numPartitions: Int): RDD[(K, (Option[V], W))]
def rightOuterJoin[W](other: RDD[(K, W)], partitioner: Partitioner): RDD[(K, (Option[V], W))]
LeftOuterJoin [Pair]
Performs an left outer join using two key-value RDDs. Please note that the keys must be generally comparable to make this work correctly.
Listing Variants
def leftOuterJoin[W](other: RDD[(K, W)]): RDD[(K, (V, Option[W]))]
def leftOuterJoin[W](other: RDD[(K, W)], numPartitions: Int): RDD[(K, (V, Option[W]))]
def leftOuterJoin[W](other: RDD[(K, W)], partitioner: Partitioner): RDD[(K, (V, Option[W]))
FullOuterJoin [Pair]
Performs the full outer join between two paired RDDs.
Listing Variants
def fullOuterJoin[W](other: RDD[(K, W)], numPartitions: Int): RDD[(K, (Option[V], Option[W]))]
def fullOuterJoin[W](other: RDD[(K, W)]): RDD[(K, (Option[V], Option[W]))]
def fullOuterJoin[W](other: RDD[(K, W)], partitioner: Partitioner): RDD[(K, (Option[V], Option[W]))] | 370 | 1,241 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2019-30 | latest | en | 0.58845 |
http://www.cfd-online.com/Forums/main/13519-reimann-problem.html | 1,475,221,488,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738662058.98/warc/CC-MAIN-20160924173742-00289-ip-10-143-35-109.ec2.internal.warc.gz | 388,427,191 | 14,922 | # Reimann problem
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May 24, 2007, 20:34 Reimann problem #1 Shuo Guest Posts: n/a What's the difference between the Riemann problem and the shock tube?
May 25, 2007, 05:13 Re: Reimann problem #2 Tom Guest Posts: n/a The Riemann problem is a method and the shock tube is an example of the method.
May 25, 2007, 13:34 Re: Reimann problem #3 jinwon Guest Posts: n/a I guess you have confusions about the concept of the Riemann problem. Riemann problem is a problem containing one single wave. That is, u(x,t=0)=uL for x x0 Like above, the problem is spatially divided by two region but constant. If it is not constant(i.e. uL(x),uR(x)), it is called the Generalized Riemann problem. The shock tube problem is a very famous example used to simulate such a riemann problem. The reason you confused may be the difference between the exact solution and the numerical solution of the Riemann problem. There are a number of books available on this issue. For example, computational gasdynamics written by Culbert B. Laney. Good luck
May 25, 2007, 14:51 Re: Reimann problem #4 Remi Guest Posts: n/a is there any other example of the Riemann problem ?
May 26, 2007, 10:09 Re: Reimann problem #5 Tom Guest Posts: n/a A dam breaking in shallow water is one. Any problem governed by a hyperbolic equation has a Riemann problem (look up the theory of Riemann invariants in a book on pdes).
May 28, 2007, 15:44 Re: Reimann problem #6 Remi Guest Posts: n/a Do you think someone can see it in two-phase flows ? any advice will be very much appreciated.
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All times are GMT -4. The time now is 03:44. | 634 | 2,246 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2016-40 | latest | en | 0.918187 |
http://de.metamath.org/mpeuni/nfiotad.html | 1,726,095,350,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651405.61/warc/CC-MAIN-20240911215612-20240912005612-00137.warc.gz | 10,935,763 | 4,184 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > nfiotad Structured version Visualization version GIF version
Description: Deduction version of nfiota 5772. (Contributed by NM, 18-Feb-2013.)
Hypotheses
Ref Expression
Assertion
Ref Expression
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 dfiota2 5769 . 2 (℩𝑦𝜓) = {𝑧 ∣ ∀𝑦(𝜓𝑦 = 𝑧)}
2 nfv 1830 . . . 4 𝑧𝜑
3 nfiotad.1 . . . . 5 𝑦𝜑
4 nfiotad.2 . . . . . . 7 (𝜑 → Ⅎ𝑥𝜓)
54adantr 480 . . . . . 6 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
6 nfcvf 2774 . . . . . . . 8 (¬ ∀𝑥 𝑥 = 𝑦𝑥𝑦)
76adantl 481 . . . . . . 7 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → 𝑥𝑦)
8 nfcvd 2752 . . . . . . 7 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → 𝑥𝑧)
97, 8nfeqd 2758 . . . . . 6 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥 𝑦 = 𝑧)
105, 9nfbid 1820 . . . . 5 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥(𝜓𝑦 = 𝑧))
113, 10nfald2 2319 . . . 4 (𝜑 → Ⅎ𝑥𝑦(𝜓𝑦 = 𝑧))
122, 11nfabd 2771 . . 3 (𝜑𝑥{𝑧 ∣ ∀𝑦(𝜓𝑦 = 𝑧)})
1312nfunid 4379 . 2 (𝜑𝑥 {𝑧 ∣ ∀𝑦(𝜓𝑦 = 𝑧)})
141, 13nfcxfrd 2750 1 (𝜑𝑥(℩𝑦𝜓))
Colors of variables: wff setvar class Syntax hints: ¬ wn 3 → wi 4 ↔ wb 195 ∧ wa 383 ∀wal 1473 Ⅎwnf 1699 {cab 2596 Ⅎwnfc 2738 ∪ cuni 4372 ℩cio 5766 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-sn 4126 df-uni 4373 df-iota 5768 This theorem is referenced by: nfiota 5772 nfriotad 6519
Copyright terms: Public domain W3C validator | 990 | 1,682 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2024-38 | latest | en | 0.138314 |
https://www.daniweb.com/programming/software-development/threads/247515/pascal-code-for-matrix-inversion | 1,716,082,956,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057631.79/warc/CC-MAIN-20240519005014-20240519035014-00750.warc.gz | 660,232,997 | 18,196 | I have a symmetrical matrix A 8 x 8.
First I need to find matrix B = A[sup]T[/sup]*A;
Next I need to inverse B and find C = B[sup]-1[/sup];
any code?
any code?
I am absolute beginner here, so I don't know have I some points to give them to you ....
If I have points, I will give you the points if you help me.
Thanks.
Please do not answer to this question, until I post an example here ....
I developed the multiplying of Matrices At*A, now I need to develope the Inverse of the result Matrice of multiplying ....
``````unit Unit1;
{\$mode objfpc}{\$H+}
interface
uses
Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
StdCtrls, Grids;
type
T_Matrix_AT = array[1..4, 1..8] of Double;
T_Matrix_A = array[1..8, 1..4] of Double;
T_Matrix_MLTPL = array[1..4, 1..4] of Double;
T_Matrix_INV = array[1..4, 1..4] of Double;
{ TForm1 }
TForm1 = class(TForm)
Btn_Multiply_: TButton;
Btn_Inverse_: TButton;
StrGrid_A: TStringGrid;
StrGrid_AT_A: TStringGrid;
StrGrid_AT: TStringGrid;
StrGrid_AT_A_INV: TStringGrid;
procedure Btn_Multiply_Click(Sender: TObject);
procedure Btn_Inverse_Click(Sender: TObject);
procedure FormCreate(Sender: TObject);
private
_Matrix_AT: T_Matrix_AT;
_Matrix_A: T_Matrix_A;
_Matrix_MLTPL: T_Matrix_MLTPL;
_Matrix_INV: T_Matrix_INV;
{ private declarations }
public
{ public declarations }
end;
var
Form1: TForm1;
implementation
{ TForm1 }
procedure TForm1.FormCreate(Sender: TObject);
var
I: Integer;
J: Integer;
begin
_Matrix_A[1,1] := -0.993;
_Matrix_AT[1,1] := -0.993;
_Matrix_A[2,1] := -0.404;
_Matrix_AT[1,2] := -0.404;
_Matrix_A[3,1] := +0.877;
_Matrix_AT[1,3] := +0.877;
_Matrix_A[4,1] := +0.493;
_Matrix_AT[1,4] := +0.493;
_Matrix_A[5,1] := +0;
_Matrix_AT[1,5] := +0;
_Matrix_A[6,1] := +0;
_Matrix_AT[1,6] := +0;
_Matrix_A[7,1] := +0;
_Matrix_AT[1,7] := +0;
_Matrix_A[8,1] := +0;
_Matrix_AT[1,8] := +0;
//................................
_Matrix_A[1,2] := +0.119;
_Matrix_AT[2,1] := +0.119;
_Matrix_A[2,2] := -0.915;
_Matrix_AT[2,2] := -0.915;
_Matrix_A[3,2] := +0.480;
_Matrix_AT[2,3] := +0.480;
_Matrix_A[4,2] := -0.870;
_Matrix_AT[2,4] := -0.870;
_Matrix_A[5,2] := +0;
_Matrix_AT[2,5] := +0;
_Matrix_A[6,2] := +0;
_Matrix_AT[2,6] := +0;
_Matrix_A[7,2] := +0;
_Matrix_AT[2,7] := +0;
_Matrix_A[8,2] := +0;
_Matrix_AT[2,8] := +0;
//................................
_Matrix_A[1,3] := +0;
_Matrix_AT[3,1] := +0;
_Matrix_A[2,3] := -0;
_Matrix_AT[3,2] := -0;
_Matrix_A[3,3] := +0;
_Matrix_AT[3,3] := +0;
_Matrix_A[4,3] := -0.493;
_Matrix_AT[3,4] := -0.493;
_Matrix_A[5,3] := -0.790;
_Matrix_AT[3,5] := -0.790;
_Matrix_A[6,3] := -0.936;
_Matrix_AT[3,6] := -0.936;
_Matrix_A[7,3] := +0.163;
_Matrix_AT[3,7] := +0.163;
_Matrix_A[8,3] := +0.997;
_Matrix_AT[3,8] := +0.997;
//................................
_Matrix_A[1,4] := +0;
_Matrix_AT[4,1] := +0;
_Matrix_A[2,4] := -0;
_Matrix_AT[4,2] := -0;
_Matrix_A[3,4] := +0;
_Matrix_AT[4,3] := +0;
_Matrix_A[4,4] := +0.870;
_Matrix_AT[4,4] := +0.870;
_Matrix_A[5,4] := +0.613;
_Matrix_AT[4,5] := +0.613;
_Matrix_A[6,4] := -0.353;
_Matrix_AT[4,6] := -0.353;
_Matrix_A[7,4] := +0.987;
_Matrix_AT[4,7] := +0.987;
_Matrix_A[8,4] := -0.077;
_Matrix_AT[4,8] := -0.077;
//................................
for I := 1 to 8 do
begin
for J := 1 to 4 do
begin
StrGrid_AT.Cells[I, J] := FloatToSTr(_Matrix_AT[J, I]);
StrGrid_A.Cells[J, I] := FloatToSTr(_Matrix_A[I, J]);
end;
end;
StrGrid_AT.Cells[0,0] := 'At';
StrGrid_A.Cells[0,0] := 'A';
StrGrid_AT_A.Cells[0,0] := 'At * A';
StrGrid_AT_A_INV.Cells[0,0] := 'INVERSED';
end;
procedure TForm1.Btn_Multiply_Click(Sender: TObject);
var
I: Integer;
J: Integer;
K: Integer;
D: Double;
begin
for K := 1 to 4 do
begin
for J := 1 to 4 do
begin
D := 0;
for I := 1 to 8 do
begin
D := D + _Matrix_AT[K,I]*_Matrix_A[I,J];
end;
StrGrid_AT_A.Cells[J,K] := FloatToStr(D);
_Matrix_MLTPL[K,J] := D;
end;
end;
end;
procedure TForm1.Btn_Inverse_Click(Sender: TObject);
begin
(*
// Inversing ....
_Matrix_INV[..., ...] := ...;
*)
end;
initialization
{\$I Unit1.lrs}
end.``````
I found many links with samples, how to invert 2x2, 3x3 or #x# Matrix ....
These explanations are not solution for me, sorry !!!!
I need Mathematical formulas, that can be programmed on Pascal, or Pascal code ....
And when I search the web about it in pascal ,I found a right place,pascal sourcefiles....(sorry this problem is out of my range)...there is a man named Alan R. Miller who wrote a lot of pascal source about these problems http://infohost.nmt.edu/~armiller/pascal.htm
Hope this helps....
In the old days SWAG (Software Archive Group) was active and their collection is still out there.
That unit has a routine for inversion but I note that it does not check for division by zero or do pivotting to optimize the result but it may be useful as a start.
The mathematics of inversion is that reducing to the unit matrix of the subject matrix accomplishes the reverse process, turning the unit matrix into the inverse of the subject matrix, so you can just augment the subject matrix with the unit matrix of the same size and crunch away with the Gaussian elimination method.
pogson,
Sorry but:
procedure matinv(a:matrix;var ainv:matrix;n:integer);
does not invert correctly, the result matrix ainv is equal to a matrix;
pogson,
Sorry but:
procedure matinv(a:matrix;var ainv:matrix;n:integer);
does not invert correctly, the result matrix ainv is equal to a matrix;
Works for me. Maybe you inverted the identity matrix. ;-)
``````[B][I]sh-3.2\$ ./test
1.000 2.000 4.000
2.000 3.000 5.000
3.000 4.000 4.000
-4.000 4.000 -1.000
3.500 -4.000 1.500
-0.500 1.000 -0.500
1.000 0.000 0.000
0.000 1.000 0.000
-0.000 0.000 1.000
sh-3.2\$ cat test.pas
program test;
uses algebra;
var a,a1,c:matrix;i,j:integer;
begin
a[1,1]:=1.0;
a[2,1]:=2.0;
a[3,1]:=3.0;
a[1,2]:=2.0;
a[2,2]:=3.0;
a[3,2]:=4.0;
a[1,3]:=4.0;
a[2,3]:=5.0;
a[3,3]:=4.0;
matinv(a,a1,3);
for i:= 1 to 3 do begin for j:= 1 to 3 do begin write(a[i,j]:5:3,' ') end; writeln end;
writeln;
for i:= 1 to 3 do begin for j:= 1 to 3 do begin write(a1[i,j]:5:3,' ') end; writeln end;
writeln;
matmult(a,a1,c,3);
for i:= 1 to 3 do begin for j:= 1 to 3 do begin write(c[i,j]:5:3,' ') end; writeln end;
end.
[/I][/B]``````
pogson,
Sorry it was a hidden problem of another procedure before conversion ....
The procedure before conversion did requare the matrix as var parameter and did change it inside itself, so I did send to conversion changed matrix and the result was confused ....
I did correct the problem, and send the matrix as normal parameter, it does not change inside previous procedure and after that goes to conversion in right content ....
Thanks !
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Question
Medium
Solving time: 3 mins
# Discuss the continuity of the function f, where f is defined by:is a continuous function?
## Text solutionVerified
: Give n function is
In interval,
Therefore, f is continuous in this interval.
At x=1
L.H.L. and R.H.L.
As, L.H.L. R.H.L.
Therefore, f(x) is discontinuous at x=1
At x=3, L.H.L . and R.H.L.
As, L.H.L. R.H.L.
Hence F is discontinuous
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Question Text Discuss the continuity of the function f, where f is defined by: is a continuous function? Updated On Oct 7, 2023 Topic Continuity and Differentiability Subject Mathematics Class Class 12 Answer Type Text solution:1 Video solution: 2 Upvotes 284 Avg. Video Duration 7 min | 403 | 1,606 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-30 | latest | en | 0.812776 |
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