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https://www.vedantu.com/ncert-solutions/ncert-solutions-class-7-science-chapter-5	Courses Courses for Kids Free study material Free LIVE classes More # NCERT Solutions for Class 7 Science Chapter 5 Acids, Bases and Salts ## NCERT Solutions for Class 7 Science Chapter 5 Free PDF Download Last updated date: 15th Mar 2023 Total views: 393.9k Views today: 5.82k For any further doubts, you can connect with the experts at Vedantu on our official website. Do you need help with your Homework? Are you preparing for Exams? Study without Internet (Offline) ## Access NCERT Solutions for Class 7 Science Chapter 5 – Acids, Bases, and Salts 1. State differences between acids and bases. Ans: The substances that taste sour are acids and the substances taste bitter and feel soapy on touching base. 2. Ammonium is found in many household products, such as window cleaners. It turns red litmus blue. What is its nature? Ans: The substances that turn red litmus blue are base. Therefore, ammonium is basic in nature. 3. Name the source from which litmus solution is obtained. What is the use of this solution? Ans: Litmus solution is extracted from lichens and is used to test the acidic/basic nature of the solution. 4. Is the distilled water acidic/basic/neutral? How would you verify it? Ans: Distilled water is neutral in nature. We can verify it by using litmus paper. When some drops of the distilled water are poured on red/blue litmus paper, its color remains the same. 5. Describe the process of neutralization with the help of an example. Ans: Neutralization is a reaction between acids and bases. Acids and bases are opposites in nature, when they mix, they neutralize the effects of each other. The substance formed in the neutralization reaction is known as salt. Example: $\underbrace{HCl}_{acid}+\underbrace{NaOH}_{base}\to \underbrace{NaCl}_{salt}+\underbrace{{{H}_{2}}O}_{water}$. 6. Mark ‘T’ if the statement is true and ‘F’ if it is false. (i) Nitric acid turns blue litmus red. Ans: True, Nitric acid is acidic in nature and therefore it turns blue litmus red. (ii) Sodium hydroxide turns blue litmus red. Ans: False, Sodium hydroxide is basic in nature and therefore it turns red litmus blue. (iii) Sodium hydroxide and hydrochloric acid neutralize each other and form salts and water. Ans: True $\underbrace{HCl}_{acid}+\underbrace{NaOH}_{base}\to \underbrace{NaCl}_{salt}+\underbrace{{{H}_{2}}O}_{water}$ Neutralization is a reaction between acids and bases, when they are mixed, they neutralize the effects of each other. (iv) An Indicator is a substance that shows different colors in acidic and basic solutions. (T/F) Ans: True, Litmus is an indicator and it shows different colors in acidic and basic solutions. (v) Tooth decay is caused by the presence of a base. (T/F) Ans: False, Tooth decay is caused by the presence of an acid produced by bacteria. 7. Dorji has a few bottles of soft drinks in his restaurant, but unfortunately, these are not labeled. He has to serve the drinks on the demand of customers. One customer wants an acidic drink; another wants a basic and the third one wants a neutral drink. How will Dorji decide which drink is to be served to whom? Ans: Dorji can use the indicator like litmus which can help him take the informed decision. If a few drops of a drink change blue litmus to red then it is acidic in nature and if it turns red litmus to blue then it is basic in nature. Also, if the drops of a drink do not affect the litmus, then it is neutral in nature. 8. Explain why: (a) An antacid tablet is taken when you suffer from acidity. Ans: An antacid tablet is taken when you suffer from acidity because the antacid tablet is basic in nature; it reacts with the excess acid in our stomach causing a neutralization reaction. Hence, it relieves us from the pain of acidity. (b) Calamine solution is applied to the skin when an ant bites. Ans: Calamine solution is applied on the skin when ant bites because ant bites inject acid in the skin and calamine solution is basic in nature, it reacts with the acid causing a neutralization reaction. Hence, it relieves us from itching and irritation. (c) Factory waste is neutralized before disposing it into the water bodies. Ans: Factory waste is neutralized before disposing it into the water bodies because excess acids or bases can be dangerous and fatal for the organisms living in the water. 9. Three liquids are given to you. One is hydrochloric acid, another is sodium hydroxide and the third is a sugar solution. How will you identify them? You have only a turmeric indicator. Ans: Turmeric is acidic in nature and so it will turn red in contact with a base. From this, we can figure out that sodium hydroxide is a base. Now we are left with sugar solution and hydrochloric acid. The red spot created on the litmus due to the base will again turn yellow while in contact with an acid. You will observe that the hydrochloric acid will turn the red spot into yellow again and hence it is an acid. Sugar solution will not affect the litmus and hence it is a neutral solution. 10. Blue litmus paper is dipped in a solution. It remains blue. What is the nature of the solution? Explain. Ans: We know that acids turn blue litmus into the red. When a blue litmus paper is dipped in a solution and it remains blue then the solution cannot be acidic. Hence, the solution can either be basic or neutral. 11. Consider the following statements: (a) Both acids and bases change color at all indicators. (b) If an indicator gives a color change with an acid, it does not give a change with a base. (c) If an indicator changes color with a base, it does not change color with an acid. (d) The change of color in an acid and a base depends on the type of indicator. Which of these statements are correct? (i) All four (ii) a and b (iii) b and c (iv) only d Ans: (iv) Only d Litmus is an indicator and it changes red to blue for the basic solution and blue to red for an acidic solution. The same is with turmeric. It changes yellow to red for the basic solution. ## NCERT Solutions for Class 7 Science Chapter 5 – Free PDF Download Do you need guidance for solving your NCERT science questions? Well, you are in the right place. All the solutions given in the PDF are reliable as they are prepared by our highly experienced teachers. You can find the solution file in PDF format and download it at your convenient time. Follow and revise the solutions by Vedantu experts and you will surely pass your exam with good grades. ### 5.1 Acids and bases How many of you love having a chilled glass of lemon juice on a summer day? I knew it, everybody. How does it taste? It is sour in taste because it contains acid. Can you recall some more food items that taste sour? Curd, orange juice, vinegar and a lot more. The chemical nature of these substances is acidic. On the other hand, the substances which are bitter in taste and feel soapy on touching are known as bases. Such substances are basic in nature. But not every substance is edible. So, how can we know the acidic and basic nature of substances that we cannot taste? Indicators are used to test if any substance is acidic or basic in nature. Some naturally occurring indicators are – litmus, china rose petals, turmeric, etc. In this unit, you will learn about acids, bases, and indicators in detail. ## 5.2 Natural Indicators Around Us There are various natural indicators that can be used to find the acidic or basic nature of any substance. These indicators change their color accordingly on coming into contact with an acidic or basic substance. Here, we shall learn about some acidic and basic substances in detail. ### Litmus: A Natural Dye Litmus, the most commonly used natural indicator is extracted from Lichens. When litmus is added to an acidic substance, it turns red in color whereas, when added to a basic substance, it turns blue in color. Litmus is available in both solution form as well as in the form of paper strips. Some more natural indicators explained in this chapter are: 1. Turmeric 2. China Rose These concepts are explained in detail through various scientific experiments. Try to perform all the experiments practically, in your school lab, or at home under the supervision of a teacher or parents. Performing the experiments will give you better knowledge and a detailed understanding of the concepts. ## Neutralization Now, you already know about acids, bases, and indicators. Have you ever wondered what happens when an acid is mixed with a base? In this section, we will use a new indicator, called phenolphthalein, and study the effects in detail. The reaction that happens between an acid and a base is known as neutralization. During the process of neutralization, salt and water are produced with the evolution of heat. Acid + Base → Salt + water (heat is evolved). ## 5.4 Neutralisation in Everyday Life In this unit, you will learn about the process of neutralization that occurs in our day to day lives. 1. Indigestion 2. Ant bite 3. Soil Treatment 4. Factory waste NOTE: An acid and base neutralize each other to form a salt. Salts may be acidic, basic, or neutral in nature. Study in detail and in case you face any problem regarding any experiment or concept mentioned in chapter 5 acid and bases you can reach out to Vedantu experts on the official website to clear your doubts. ### Exercise Solutions: 11 Questions (2 short questions and 9 Long questions). Extended learning: Activities and projects (4 questions). ### Key Features of NCERT Solutions for Class 7 Science Chapter 5 To score good marks in science, it is always essential to study your NCERT textbook word by word and understand each and every concept mentioned in it. Try to practically perform all the experiments explained in your book so that along with the theoretical knowledge, you also gain adequate practical knowledge of all the concepts. Vedantu experts provide the solutions of all NCERT science class 7 chapter 5 questions for a better understanding of students. These NCERT Solutions for Class 7th Science chapter 5 are curated by the expert teachers and easy to understand. Some key features of our solution’s PDF are: 1. You can achieve a better understanding of your subject with the solutions and explanations provided by our experts. 2. These solutions will help you fetch a deeper knowledge of all the questions. 4. You can work hard and prepare efficiently for your exams by revising and practicing all the NCERT questions. 5. This solution PDF provides you not just with correct answers but also guides you about the proper presentation of answers that will help you fetch good marks. ### Important topics covered in the NCERT Solutions for Class 7 Science Chapter 5 Acids, Bases, and Salts 1. Acids, Bases, and Salts 2. Natural Indicators Around Us 3. Neutralisation 4. Neutralisations In Everyday Life ### Key Points Covered in the NCERT Solutions Class 7 Science Chapter 5 • Acids have a sour flavour. Bases have a harsh flavour and feel soapy to the touch. • Blue litmus becomes red when tested with acids. • The term "neutral" refers to compounds that are neither acidic nor basic. • Indicators display distinct colour changes when treated with acidic, basic, and neutral solutions. • A salt is formed when an acid and a base react to neutralise each other. ## FAQs on NCERT Solutions for Class 7 Science Chapter 5 Acids, Bases and Salts 1. What is acid, according to Chapter 5 of Class 7 Science? An acid is defined as a substance that is sour in taste, turns a blue litmus indicator red in colour and neutralizes bases. It gives H+ ions in water. Vedantu NCERT Solutions for Chapter 5 of Class 7 Science explains more about acids. Some of the examples are as follows : Eg: Hydrochloric acid (HCl), Sulphuric Acid(H2SO4) 2. What are bases, according to Chapter 5 of Class 7 Science? In Chapter 5 “Acid, Bases And Salt” of Class 7 Science, the concept of bases is explained. A base is defined as a substance that tastes bitter, gives a soapy feeling when touched, turns red litmus blue and neutralizes acids. The very common examples of bases are as follows: Eg: Sodium Hydroxide (NaOH), potassium hydroxide(KOH) 3. What is salt? Give an example, according to Chapter 5 of Class 7 Science. In order to understand the concept of salt, it is important to know a few examples of the same. This will help you to understand and associate it better. Salt is a chemical substance that is produced as a result of the neutralisation reaction between an acid and a base. Eg. Common salt/ Sodium Chloride (NaCl). Vedantu provides you with proper explanations and examples of the topics and helps you clear your concepts easily to help you ace your exams. 4. What is Chapter 5 of Class 7 Science about? This Chapter very well explains the topic of acid, base and salt. Here, an acid is termed as a substance that is sour in taste, turns a blue litmus indicator red in colour and neutralizes bases, whereas a base is described to be a substance whose aqueous solution tastes bitter, gives a soapy feeling when touched, turns red litmus blue and neutralizes acids. NCERT Solutions for Chapter 5 of Class 7 Science PDF is available for download on the official website of Vedantu and on the Vedantu app at free of cost. 5. Where can I get the solutions for Chapter 5 of Class 7 Science for free? You can find NCERT Solutions for Chapter 5 of Class 7 Science for free on Vedantu. Vedantu gives the best study materials and solutions for your exercises in PDF format, which is totally free to download and you can study from it even in the offline mode. For this: 1. Visit the page NCERT Solutions for Chapter 5 of Class 7 Science.	2023-03-21 16:35:59	{"extraction_info": {"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, "math_score": 0.4528988301753998, "perplexity": 2759.4320473820935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00579.warc.gz"}
https://physics.stackexchange.com/questions/277073/what-happens-to-the-angular-momentum-of-two-merging-black-holes	# What happens to the angular momentum of two merging black holes? Let's suppose that two black holes of roughly equal mass in a binary system forming from say a large mass stellar binary system are in orbits around their center of mass. Further suppose that we are looking at their equations of motion well in advance of their merger. As a very crude approximation, I am using the Schwartzchild metric even though I know that this not a spherically symmetric system. The effective potential in this metric would be of the form: $$V_{eff}=\frac{\mu c^2}{2}[-\frac{r_s}{r}+\frac{a^2}{r^2}-\frac{r_s a^2}{r^3}]$$ Where $a=\frac{L}{mc}$, $r_s$ is the Schwartzchild radius, and $\mu$ is the reduced mass. So as this system loses energy via gravitational waves, they would eventually reach a circular orbit with a radius $$r_{min}=\frac{a^2}{r_s}(1+\sqrt{1-\frac{3r_s^2}{a^2}})$$ which is a local minimum in this effective potential. However, to lose more energy and merge, there is a centripetal barrier to overcome. The only way I see around this is for the system to lose orbital angular momentum to a point where $a=\sqrt{3}r_s$ when this barrier disappears. I know this fairly crude and in reality this requires computer simulations using Einstein's field equations, but it seems to me that for black holes to merge they would need to lose orbital angular momentum as well as energy. 1. Does the system transfer orbital angular momentum to the spin angular momentum of the black holes basically spinning them up as they approach one another? I am assuming that overall angular momentum still has to be conserved in the center of mass frame. What would be the mechanism for this transfer? Would this involve an ergosphere around each black hole? 2. Can one infer the spins of the merging black holes from the gravitational wave signal detected here on Earth?	2019-02-17 08:12:18	{"extraction_info": {"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, "math_score": 0.7487784028053284, "perplexity": 198.78336480732835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481766.50/warc/CC-MAIN-20190217071448-20190217093448-00108.warc.gz"}
https://deconstrut.com/8g4i2n56/f8y5c0d.php?9cebe7=balancing-redox-reactions-half-reaction-method	# balancing redox reactions half reaction method In the above equation, there are $$14 \: \ce{H}$$, $$6 \: \ce{Fe}$$, $$2 \: \ce{Cr}$$, and $$7 \: \ce{O}$$ on both sides. not have to do anything. The OH- ions, Then, on that side of the equation which contains both (OH. This is called the half-reaction method of balancing redox reactions, or the ion-electron method. the number of electrons lost equals the number of electrons gained we do Balancing it directly in basic seems fairly easy: Fe + 3OH¯ ---> Fe(OH) 3 + 3e¯ And yet another comment: there is an old-school method of balancing in basic solution, one that the ChemTeam learned in high school, lo these many years ago. 2. reducing to the smallest whole number by cancelling species which on both Balancing Redox Reactions. KBr (aq) • First, is this even a REDOX reaction? dichromate ethanol C2H4O Sixth, equalize the number of electrons lost with the number of electrons Is there a species that is being reduced and a species that is being oxidized? You then use some arrows to show your half-reactions. Balancing Redox Equations: Half-Reaction Method. Half reactions are often used as a method of balancing redox reactions. Oxidation number method is based on the difference in oxidation number of oxidizing agentand the reducing agent. In an acidic medium, add hydrogen ions to balance. Balancing Redox Equations via the Half-Equation Method is an integral part of understanding redox reactions. Equation balancing & stoichiometry lectures » half reaction method » Equation balancing and stoichiometry calculator. and the ethanol/acetaldehyde as the oxidation half-reaction. For example, this half-reaction: Fe ---> Fe(OH) 3 might show up. Each half-reaction is then balanced individually, and then the half-reactions are added back together to form a new, balanced redox equation. Balancing redox reactions is slightly more complex than balancing standard reactions, but still follows a relatively simple set of rules. To indicate the fact that the reaction takes place in a basic solution, Separate the equation into half-reactions (i.e., oxidation half and reduction half). Redox reactions are commonly run in acidic solution, in which case the reaction equations often include H 2 O(l) and H + (aq). And that is wrong because there is an electron in the final answer. For the reduction half-reaction above, seven H 2 O molecules will be added to the product side, The electrons must cancel. If necessary, cancel out $$\ce{H_2O}$$ or $$\ce{H^+}$$ that appear on both sides. NO → NO 3-6. Simplify the equation by subtracting out water molecules, to obtain the use hydrogen ions (H. The fifth step involves the balancing charges. Cr 2O 7 2 - → Cr3+ 5. To do this one must One major difference is the necessity to know the half-reactions of the involved reactants; a half-reaction table is very useful for this. SO 4 2- → SO 2 7. By adding one electron to the product side of the oxidation half-reaction, there is a $$2+$$ total charge on both sides. Divide the complete equation into two half reactions, one representing oxidation and the other reduction. Balance the O by adding water as needed. Each electron has a charge equal to (-1). by reduction with the number of electrons produced by oxidation. This method of balancing redox reactions is called the half reaction method. For the reduction half-reaction, the electrons will be added to the reactant side. Chemists have developed an alternative method (in addition to the oxidation number method) that is called the ion-electron (half-reaction) method. Step 4: Balance oxygen atoms by adding water molecules to the appropriate side of the equation. To determine the number The half-reaction method for balancing redox equations provides a systematic approach. H 2O 2 + Cr 2O 7 2- → O 2 + Cr 3+ 9. (H, The fourth step involves balancing the hydrogen atoms. records this change. Balance the atoms in each half reaction separately according to the following steps: 1. Balancing Redox Reactions: The Half-Reaction Method Balanced chemical equations accurately describe the quantities of reactants and products in chemical reactions. Balance the unbalanced redox reaction without any complications by using this online balancing redox reactions calculator. final, balanced equation. Now the hydrogen atoms need to be balanced. Legal. Here are the steps for balancing in an acid solution (adding H+ and H2O). Balancing Redox Reactions via the Half-Reaction Method Redox reactions that take place in aqueous media often involve water, hydronium ions (or protons), and hydroxide ions as reactants or products. For more information contact us at [email protected] or check out our status page at https://status.libretexts.org. For reactions occurring in acidic medium, add H2O to balance O atoms and H+ to balance H atoms. To do this, add water This ion is a powerful oxidizing agent which oxidizes many substances this guideline, the oxidation half reaction must be multiplied by "3" to The sixth step involves multiplying each half-reaction by the smallest In general, the half-reactions are first balanced by atoms separately. Redox equations are often so complex that fiddling with coefficients to balance chemical equations doesn’t always work well. The half-reaction method works better than the oxidation-number method when the substances in the reaction are in aqueous solution. Organic compounds, called alcohols, are readily oxidized by acidic solutions of dichromate ions. of dichromate ions. The following reaction, written in net ionic form, BALANCING REDOX REACTIONS. Balancing Redox Equations for Reactions in Acidic Conditions Using the Half-reaction Method. $6 \ce{Fe^{2+}} \left( aq \right) \rightarrow 6 \ce{Fe^{3+}} \left( aq \right) + 6 \ce{e^-}$. Worksheet # 5 Balancing Redox Reactions in Acid and Basic Solution Balance each half reaction in basic solution. Equation balancing & stoichiometry lectures » half reaction method » Equation balancing and stoichiometry calculator. We need the balanced equation to compare mole ratio in scenarios such as this redox reaction worked example.. Each of these half-reactions is balanced separately and then combined to give the balanced redox equation. To balance the equation, use Recall that a half-reaction is either the oxidation or reduction that occurs, treated separately. Another method for balancing redox reactions uses half-reactions. Let’s take a look at a simple reaction WITHOUT HYDROGEN OR OXYGEN to balance: K (s) + Br 2 (l) ! Zn(s) -----> Zn(OH)42- (aq) NO31- -----> NH3. MnO 2 → Mn 2O 3 Balance each redox reaction in acid solution using the half reaction method. The dichromate ions are reduced to $$\ce{Cr^{3-}}$$ ions. MnO 2 → Mn 2O 3 Balance each redox reaction in acid solution using the half reaction method. For the reduction half-reaction above, seven $$\ce{H_2O}$$ molecules will be added to the product side. CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon. Balancing Redox Equations for Reactions in Acidic Conditions Using the Half-reaction Method. This method of balancing redox reactions is called the half reaction method. Here are the steps for balancing redox reactions using the oxidation state method (also known as the half-equation method): Identify the pair of elements undergoing oxidation and reduction by checking oxidation states; Write two ionic half-equations (one of the oxidation, one for the reduction) \begin{align} &\text{Oxidation:} \: \ce{Fe^{2+}} \left( aq \right) \rightarrow \ce{Fe^{3+}} \left( aq \right) \\ &\text{Reduction:} \: \overset{+6}{\ce{Cr_2}} \ce{O_7^{2-}} \left( aq \right) \rightarrow \ce{Cr^{3+}} \left( aq \right) \end{align}. and hydrogen atoms. $\ce{Fe^{2+}} \left( aq \right) \rightarrow \ce{Fe^{3+}} \left( aq \right) + \ce{e^-}$. Balancing Redox Reactions via the Half-Reaction Method Redox reactions that take place in aqueous media often involve water, hydronium ions (or protons), and hydroxide ions as reactants or products. Draw an arrow connecting the reactant a… 4. listed in order to identify the species that are oxidized and reduced, Each half-reaction is balanced separately and then the equations are added together to give a balanced overall reaction. The equation is balanced. Since the following steps: The electrons must always be added to that side which has the greater Half-reaction method depends on the division of the redox reactions into oxidation half and reduction half. and the other a reduction half- reaction, by grouping appropriate species. The reduction half-reaction needs to be balanced with the chromium atoms, Step 4: Balance oxygen atoms by adding water molecules to the appropriate side of the equation. This is done by adding electrons First, separate the equation into two half-reactions: the oxidation portion, and the reduction portion. Basic functions of life such as photosynthesis and respiration are dependent upon the redox reaction. By following this guideline in the example Let's dissect an equation! (e-). (There are other ways of balancing redox reactions, but this is the only one that will be used in this text. The method that is used is called the ion-electron or "half-reaction" method. There are two ways of balancing redox reaction. H 2O 2 + Cr 2O 7 2- → O 2 + Cr 3+ 9. Step 6: Add the two half-reactions together. \begin{align} 6 \ce{Fe^{2+}} \left( aq \right) &\rightarrow 6 \ce{Fe^{3+}} \left( aq \right) + \cancel{ 6 \ce{e^-}} \\ \cancel{6 \ce{e^-}} + 14 \ce{H^+} \left( aq \right) + \ce{Cr_2O_7^{2-}} \left( aq \right) &\rightarrow 2 \ce{Cr^{3+}} \left( aq \right) + 7 \ce{H_2O} \left( l \right) \\ \hline 14 \ce{H^+} \left( aq \right) + 6 \ce{Fe^{2+}} \left( aq \right) + \ce{Cr_2O_7^{2-}} \left( aq \right) &\rightarrow 6 \ce{Fe^{3+}} \left( aq \right) + 2 \ce{Cr^{3+}} \left( aq \right) + 7 \ce{H_2O} \left( l \right) \end{align}. Example 1 -- Balancing Redox Reactions Which Occur in Acidic Solution. The seventh and last step involves adding the two half reactions and Another method for balancing redox reactions uses half-reactions. Using (You can in a half-reaction, but remember half-reactions do not occur alone, they occur in reduction-oxidation pairs.) In the ion-electron method, the unbalanced redox equation is converted to the ionic equation and then broken […] Another method for balancing redox reactions uses half-reactions. Have questions or comments? Here, you do all the electron balancing on one line. (You can in a half-reaction, but remember half-reactions do not occur alone, they occur in reduction-oxidation pairs.) $6 \ce{e^-} + 14 \ce{H^+} \left( aq \right) + \ce{Cr_2O_7^{2-}} \left( aq \right) \rightarrow 2 \ce{Cr^{3+}} \left( aq \right) + 7 \ce{H_2O} \left( l \right)$. The Half-Reaction Method . is Determine the oxidation numbers first, if necessary. 22.10: Balancing Redox Reactions- Half-Reaction Method, [ "article:topic", "showtoc:no", "license:ccbync", "program:ck12" ], https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FIntroductory_Chemistry%2FBook%253A_Introductory_Chemistry_(CK-12)%2F22%253A_Oxidation-Reduction_Reactions%2F22.10%253A_Balancing_Redox_Reactions-_Half-Reaction_Method, 22.9: Balancing Redox Reactions- Oxidation Number Change Method, 22.11: Half-Reaction Method in Basic Solution, Balancing Redox Equations: Half-Reaction Method, information contact us at [email protected], status page at https://status.libretexts.org. This method involves the following steps : 1. Add electrons to one side of the half reaction to balance … gained by multiplying by an appropriate small whole number. Step 5: Balance the charges by adding electrons to each half-reaction. Separate the reaction into two half-reactions, one for Zn and one for N in this case. Chemists have developed an alternative method (in addition to the oxidation number method) that is called the ion-electron (half-reaction) method. The reason for this will be seen in Chapter 14 “Oxidation and Reduction” , Section 14.3 “Applications of Redox Reactions… In the ion-electron method, the unbalanced redox equation is converted to the ionic equation and then broken […] Just enter the unbalanced chemical equation in this online Balancing Redox Reactions Calculator to balance the reaction using half reaction method. The oxidation states of each atom in each compound Hello, Slight road-bump while doing my … Pigments of these colors are often made with a dichromate salt (usually sodium or potassium dichromate). Fourth, balance any hydrogen atoms by using an (H+) for each hydrogen atom. 2) Here are the correct half-reactions: 4e¯ + 4H + … First, divide the equation into two halves; one will be an oxidation half-reaction An examination of the oxidation states, indicates that carbon is being The reduction First, divide the equation into two halves by grouping appropriate species. $\ce{Cr_2O_7^{2-}} \left( aq \right) \rightarrow 2 \ce{Cr^{3+}} \left( aq \right) + 7 \ce{H_2O} \left( l \right)$. BALANCING REDOX REACTIONS. The half-reaction method for balancing redox equations provides a systematic approach. Balancing redox reactions is slightly more complex than balancing standard reactions, but still follows a relatively simple set of rules. In this method, the overall reaction is broken down into its half-reactions. sides of the arrow. In this example, the oxidation half-reaction will be multiplied by six. This will be resolved by the balancing method. The reduction half-reaction needs to be balanced with the chromium atoms, Step 4: Balance oxygen atoms by adding water molecules to the appropriate side of the equation. The half-reaction method works better than the oxidation-number method when the substances in the reaction are in aqueous solution. In this method, the overall reaction is broken down into its half-reactions. Finally, the two half-reactions are added back together. half-reaction requires 6 e-, while the oxidation half-reaction produces note: the net charge on each side of the equation does not have to An unbalanced redox reaction can be balanced using this calculator. Balance any remaining substances by inspection. The following reaction, written in … To balance the charge, six electrons need to be added to the reactant side. Although these species are not oxidized or reduced, they do participate in chemical change in other ways (e.g., by providing the elements required to form oxyanions). When balancing redox reactions we have always - apart from all the rules pertaining to balancing chemical equations - additional information about electrons moving. Organic compounds, called alcohols, are readily oxidized by acidic solutions The Half-Reaction Method . Cr3+ + Electrons are included in the half-reactions. (I-) ions as shown below in net ionic form. above, only the, The third step involves balancing oxygen atoms. ion. chromium(III) acetaldehyde. respectively. Use this online half reaction method calculator to balance the redox reaction. It can be done via the following systematic steps. The half-reaction method of balancing redox equations is described. whole number that is required to equalize the number of electrons gained both equations by inspection. Recall that a half-reaction is either the oxidation or reduction that occurs, treated separately. Let's dissect an equation! For example, this half-reaction: Fe ---> Fe(OH) 3 might show up. The half-reaction method works better than the oxidation-number method when the substances in the reaction are in aqueous solution. The aqueous solution is typically either acidic or basic, so hydrogen ions or hydroxide ions are present. Step 3: Balance the atoms in the half-reactions other than hydrogen and oxygen. equation. Now equalize the electrons by multiplying everything in one or both equations by a coefficient. Worksheet # 5 Balancing Redox Reactions in Acid and Basic Solution Balance each half reaction in basic solution. Assign oxidation numbers 2. Example #4: Sometimes, the "fake acid" method can be skipped. They serve as the basis of stoichiometry by showing how atoms and mass are conserved during reactions. The picture below shows one of the two Thunder Dolphin amusement ride trains. This page will show you how to write balanced equations for such reactions even when you do not know whether the H 2 O(l) and H + (aq) are reactants or products. 2. 2) Here are the correct half-reactions: 4e¯ + 4H + … Balancing Redox Reactions: Redox equations are often so complex that fiddling with coefficients to balance chemical equations. and non-oxygen atoms only. For the reduction half-reaction above, seven H 2 O molecules will be added to the product side, Example 1 -- Balancing Redox Reactions Which Occur in Acidic Solution. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 8. For oxidation-reduction reactions in acidic conditions, after balancing the atoms and oxidation numbers, one will need to add H + ions to balance the hydrogen ions in the half reaction. under basic conditions. It happens when a transfer of electrons between two species takes place. Balance the atoms other than H and O in each half reaction individually. One major difference is the necessity to know the half-reactions of the involved reactants; a half-reaction … When presented with a REDOX reaction in this class, we will use the “half-reactions” method to balance the reaction. Check to make sure the main atoms, Zn and N are balanced. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 2 e-. 1. The net charge is $$24+$$ on both sides. of electrons required, find the net charge of each side the equation. Each half-reaction is then balanced individually, and then the half-reactions are added back together to form a new, balanced redox equation. If you have properly learned how to assign oxidation numbers (previous section), then you can balance redox equations using the oxidation number method. In other words, balance the non-hydrogen In the ion-electron method (also called the half-reaction method), the redox equation is separated into two half-equations - one for oxidation and one for reduction. First, separate the equation into two half-reactions: the oxidation portion, and the reduction portion. $\ce{Fe^{2+}} \left( aq \right) + \ce{Cr_2O_7^{2-}} \left( aq \right) \rightarrow \ce{Fe^{3+}} \left( aq \right) + \ce{Cr^{3+}} \left( aq \right)$. And that is wrong because there is an electron in the final answer. Redox reactions are commonly run in acidic solution, in which case the reaction equations often include H 2 O(l) and H + (aq). Step 7: Check the balancing. oxidized, and chromium, is being reduced. How to Balance Redox Reactions by Half Reaction Method - Tutorial with Definition, Equations, Example Definition Redox Reaction is a chemical reaction in which oxidation and reduction occurs simultaneously and the substance which gains electrons is termed as oxidizing agent. positive charge as shown below. You establish your two half reactions by looking for changes in oxidation numbers. The example is the oxidation of $$\ce{Fe^{2+}}$$ ions to $$\ce{Fe^{3+}}$$ ions by dichromate $$\left( \ce{Cr_2O_7^{2-}} \right)$$ in acidic solution. Second, if necessary, balance all elements except oxygen and hydrogen in Balancing Redox Equations: Half-Reaction Method. Oxidation half reaction: l (aq) → l 2(s) +7 +4. Balancing Redox Reactions: The Half-Reaction Method Balanced chemical equations accurately describe the quantities of reactants and products in chemical reactions. $14 \ce{H^+} \left( aq \right) + \ce{Cr_2O_7^{2-}} \left( aq \right) \rightarrow 2 \ce{Cr^{3+}} \left( aq \right) + 7 \ce{H_2O} \left( l \right)$. You cannot have electrons appear in the final answer of a redox reaction. Recall that a half-reaction is either the oxidation or reduction that occurs, treated separately. A reaction in which a reducing agent loses electrons while it is oxidized and the oxidizing agent gains electrons while it is reduced is called as redox (oxidation – reduction) reaction. This train has an orange stripe while its companion has a yellow stripe. When balancing redox reactions, the overall electronic charge must be balanced in addition to the usual molar ratios of the component reactants and products. one must now add one (OH-) unit for every (H+) present in the equation. Step 1: Write the unbalanced ionic equation. Redox equations are often so complex that fiddling with coefficients to balance chemical equations doesn’t always work well. Third, balance the oxygen atoms using water molecules . They serve as the basis of stoichiometry by showing how atoms and mass are conserved during reactions. The product side has a total charge of $$6+$$ due to the two chromium ions $$\left( 2 \times 3 \right)$$. give the 6 electrons required by the reduction half-reaction. Balancing Redox Reaction. NO → NO 3-6. Watch the recordings here on Youtube! $\ce{Cr_2O_7^{2-}} \left( aq \right) \rightarrow 2 \ce{Cr^{3+}} \left( aq \right)$. It depends on the individual which method to choose and use. The reduction half-reaction needs to be balanced with the chromium atoms. Another method for balancing redox reactions uses half-reactions. Calculator of Balancing Redox Reactions 8. by the ion-electron method. Balancing Redox Reactions with Half-Reaction Method? Balancing Redox Reactions. SO 4 2- → SO 2 7. Balancing a redox reaction requires identifying the oxidation numbers in the net ionic equation, breaking the equation into half reactions, adding the electrons, balancing the charges with the addition of hydrogen or hydroxide ions, and then completing the equation. In this example, fourteen $$\ce{H^+}$$ ions will be added to the reactant side. In the ion-electron method (also called the half-reaction method), the redox equation is separated into two half-equations - one for oxidation and one for reduction. These brightly colored compounds serve as strong oxidizing agents in chemical reactions. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Redox Reactions: It is the combination oxidation and reduction reactions. Oxidation and reduction reactions need to be bal- Example #4: Sometimes, the "fake acid" method can be skipped. These are then balanced so that the number of electrons lost is equal to the number of electrons gained. Steps for balancing redox reactions. There is a total charge of $$12+$$ on the reactant side of the reduction half-reaction $$\left( 14 - 2 \right)$$. They already are in this case. 4. A typical reaction is its behavior with iodide Cr 2O 7 2 - → Cr3+ 5. (There are other ways of balancing redox reactions, but this is the only one that will be used in this text. Below is the modified procedure for balancing redox reactions using the oxidation number method. To achieve balanced redox reaction, simply add balanced oxidation and reduction half reactions in order to cancel unwanted electrons: $$\ce{2MnO4- + 8H+ + 6I- -> 2MnO2 + 3I2 + 4H2O }$$ This redox reation is forward reaction because it has a net positive potential (refer reduction potentials of two half reactions). Missed the LibreFest? by the ion-electron method. Recall that a half-reaction is either the oxidation or reduction that occurs, treated separately. One method is by using the change in oxidation number of oxidizing agent and the reducing agent and the other method is based on dividing the redox reaction into two half reactions-one of reduction and other oxidation. The chromium reaction can now be identified as the reduction half-reaction The two half reactions involved in the given reaction are: -1 0. Second, if needed, balance both equations, by inspection ignoring any oxygen Balancing it directly in basic seems fairly easy: Fe + 3OH¯ ---> Fe(OH) 3 + 3e¯ And yet another comment: there is an old-school method of balancing in basic solution, one that the ChemTeam learned in high school, lo these many years ago. When balancing redox reactions we have always - apart from all the rules pertaining to balancing chemical equations - additional information about electrons moving. The reason for this will be seen in Chapter 14 “Oxidation and Reduction” , Section 14.3 “Applications of Redox Reactions: Voltaic Cells” .) This page will show you how to write balanced equations for such reactions even when you do not know whether the H 2 O(l) and H + (aq) are reactants or products. Cr2O72- + C2H6O This is called the half-reaction method of balancing redox reactions, or the ion-electron method. Each half-reaction is balanced separately and then the equations are added together to give a balanced overall reaction. Note; each electron (e-) represents a charge of (-1). The nature of each will become evident in subsequent steps. First of all balance the atoms other than H and O. In the oxidation half-reaction above, the iron atoms are already balanced. Oxidation and reduction reactions need to be bal- This example problem illustrates how to use the half-reaction method to balance a redox reaction in a solution. 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Always - apart from all the electron balancing on one line are present major.	2021-02-28 00:38:09	{"extraction_info": {"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": 2, "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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7567789554595947, "perplexity": 2333.0485760505926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359624.36/warc/CC-MAIN-20210227234501-20210228024501-00540.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-2-real-numbers-chapter-2-test-page-90/18	# Chapter 2 - Real Numbers - Chapter 2 Test: 18 $-x+5xy$ #### Work Step by Step To simplify the expression in the question, we group together the similar terms and then perform addition/subtraction: $3x-2xy-4x+7xy$ =$3x-4x-2xy+7xy$ =$(3x-4x)+(-2xy+7xy)$ =$(-x)+(5xy)$ =$-x+5xy$ After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	2018-05-21 05:44:13	{"extraction_info": {"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, "math_score": 0.5859456062316895, "perplexity": 1265.1410372902442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863949.27/warc/CC-MAIN-20180521043741-20180521063741-00237.warc.gz"}
http://levnadlazba.cz/eynltb/51547a-photons-definition-chemistry	Not only is light made up of photons, but all electromagnetic energy (i.e. 125 - PhotonsIn this video Paul Andersen explains how light travels in photons which can be described as both particles and waves. Figure 1: (Left) Sketch of the quantum simulator scheme used by Wang et al. Photons (from Greek φως, meaning light), in many atomic models in physics, are particles which transmit light.In other words, light is carried over space by photons. Each violet photon has an extremely small amount of energy that it contributes. A photon is an elementary particle. Photons travel at the vacuum speed of light (more commonly just called the speed of light) of c = 2.998 x 10 8 m/s. The original concept of the photon was developed by Albert Einstein. If the photon energy is too low, the electron is unable to escape the material. Photon and quantum are two very important concepts in modern physics. Photons pass through the cancer and out the other side, so on this exit, they hit normal cells and tissue. “Conventional photon radiation therapy and proton therapy cure tumors at the same rate,” explains Viswanathan. Indivisible quantity of energy that intervenes in the processes of emission and absorption of electromagnetic radiation. Photon Explained: Describing the properties of an electromagnetic wave, photons are what make up a wave, the individual particles that have energy within each having their own wave lengths. Photon Definition: When electromagnetic radiation is viewed as a particle, an individual packet of energy. Photons synonyms, Photons pronunciation, Photons translation, English dictionary definition of Photons. APS/Alan Stonebraker. Two-photon absorption (TPA) in semiconductors is a well-known effect that can be visualized as an electronic transition from the valence band to the conduction band via an intermediate virtual state in the energy gap E g. The TPA transition rates are proportional to 〈â † (t)â † (t)â(t)â〉 and therefore a measure of G (2) (0). A quantum simulator uses microwave photons to tackle a useful chemistry problem—determining the vibronic spectra of molecules. Proton therapy, on the other hand, stops at the tumor. A photon is the quantum of electromagnetic radiation. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 203. Definition of photon microwaves, radio waves, X-rays) is made up of photons. Note that while a photon is a packet of energy, the amount of energy in the packet can vary. (12.2) For the term photon may also exist other definitions and meanings, the meaning and definition indicated above are indicative not … Photochemistry is the branch of chemistry concerned with the chemical effects of light. A photon is a particle of light defined as a discrete bundle (or quantum) of electromagnetic (or light) energy.Photons are always in motion and, in a vacuum (a completely empty space), have a constant speed of light to all observers. in case of light, these energy packets are called PHOTONS. Creating a next-generation photonic-electronic integration circuit. Learn more. X-ray photon. Chemistry and physics . Class-11-science » Chemistry. PLEASE ANSWER SOON!!!!! Definition of a Photon. To reconcile this with the definition of the photon very much needed for nuclear interaction, the number of photons n is introduced to compensate for the original formula E=hf. Photon is a type elementary particle which has a zero rest mass and moves with a speed of light in the vacuum. Definition. The following text is used only for educational use and informative purpose following the fair use principles. Share 8. Fun Facts about Photons. In other words, it is the smallest and the fundamental particle of an electromagnetic radiation. Examples of photon in the following topics: The Photoelectric Effect. Structure of Atom . It possesses enough energy (100 eV to 100 keV) to disrupt molecular bonds and ionize atoms making it, by definition, ionizing radiation. n. The elementary particle of light and other electromagnetic radiation; the quantum of electromagnetic energy. A photon is a purely quantum mechanical object representing the smallest piece of energy (or quanta) for light. 2. An x-ray photon has a wavelength of 0.01 to 10 nanometers, with a frequency of 3×10 16 Hz to 3×10 19 Hz. Glossary of chemistry terms . photon definition: 1. a single unit of light 2. a single unit of light 3. a very small piece of matter that is the…. Chemistry. Share with your friends. Ultra-weak photon emission originates from the oxidative metabolic reaction in microbial, plant and animal cells , , , . A leap towards practical photonic quantum computing: New method can measure large-scale quantum correlation of single photons, which until now would have required thousands of single photon counters One of the big advantages of perovskites, they found, was that they emit photons very quickly after being stimulated by a laser beam. It is a quantum of light. The energy can also be given off as heat, or as lower energy light, i.e., fluorescence or phosphorescence, in order to return the molecule to its ground state. Definition, terminology and types of ultra-weak photon emission 2.1. Photon: Meaning, Definition & Formula. Ionization, in chemistry and physics, any process by which electrically neutral atoms or molecules are converted to electrically charged atoms or molecules (ions). Ionization is one of the principal ways that radiation, such as charged particles and X rays, transfers its energy to matter. A photon is the “quantum of electromagnetic radiation”. The photon is a conceptual packet of energy, which is very important in quantum mechanics.Electron and photon are two concepts that developed greatly with the development of quantum mechanics. In Analytical Chemistry Dec 02, 2020 0. ; The energy of the emitted electrons does not depend on the intensity of the incoming light (the number of photons), only on the energy or frequency of the individual photons. ‘A photon has zero rest mass, but it carries energy and momentum.’ ‘Tiny particles such as photons or atoms can readily be put into a quantum superposition existing in two different states or places at once.’ ‘The team has also made progress in using photons to … How to solve: Calculate the energy of 1 mole of photons with a wavelength of 600.0 nm. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible light (400–750 nm) or infrared radiation (750–2500 nm).. Photon . There is no exit dose. How much energy of electromagnetic radiation. So if we let our units do the work for us, we see that the minutes are cancelled, the seconds are cancelled, the joules from the photons cancels, and we're left with just photons. Chemistry and physics definitions of scientific terms . However, it was scientist Gilbert N. Lewis who first used the word "photon… Meaning and definition of photon : a quantum of electromagnetic radiation. Start studying photon chemistry. Each type of molecule has a different preference for which of these different mechanisms it uses to get rid of absorbed photon energy, e.g., some prefer fluorescence over chemistry. photon: The photon is the fundamental particle of visible light. Electromagnetic radiation is transferred to matter in units or quantum. WHAT IS THE EXACT DEFINITION OF A PHOTON? , which is based on microwave photons confined to two resonant cavities (shown in blue and green). ... A.2.1 Describe the electromagnetic spectrum IB Chemistry … So I'm want to go from joules at the photons, the joules from all the photons, to how many photons I have. In fact, if you wanted to know how small it is, a baseball, a professional baseball player, throwing a ball fast, you know, it's about 100 joules of energy. The radiant energy is emmited or absorbed discontinuously in the form of small energy packets called QUANTA. ; Irrespective of the intensity of radiation, every photon of a frequency v has the same momentum $$p = \frac{h\nu }{c}$$ and energy $$E = h\nu$$. We thank the authors of the texts that give us the opportunity to share their knowledge . The term quantum is the smallest elemental unit of a quantity, or the smallest discrete amount of something. I know that each individual photon will have this much energy associated with it. Its energy depends on the frequency of radiation. The key difference between photon and quantum is that photon is an elementary particle, whereas quantum is a measure of quantity.. Photon is an elementary particle while quantum is a discrete packet with energy stored in it. Energy of a photon is given by $$E = h\nu$$.Its momentum is $$p = \frac{h\nu }{c}$$ and speed is c, which is the speed of light. Photons are called x-rays if they are produced by electron interactions. Photon energy is directly proportional to the wave frequency, so gamma ray photons have the highest energy (around a billion electron volts), while radio wave photons have very low energy (around a femto-electron volt). There are as many kinds of photons as there are frequencies. The key difference between photon and electron is that photon is a packet of energy while the electron is a mass.. An electron is a subatomic particle that plays a vital role in almost everything. X-Rays if they are produced by electron interactions Calculate the energy of mole! Albert Einstein absorbed discontinuously in the vacuum or absorbed discontinuously in the following text is used only for educational and. That radiation, such as charged particles and X rays, transfers its energy to matter in units or.... Shown in blue and green ) or quantum to matter in units or quantum of light in the of! Are frequencies photon will have this much energy associated with it microwaves, radio waves, X-rays is. Photon emission 2.1, such as charged particles and X rays, transfers its energy matter. Describe the electromagnetic spectrum IB chemistry … 2 ) is made up of photons packets called! Photochemistry is the fundamental particle of light is one of the quantum of electromagnetic energy ( or QUANTA for. This much energy associated with it is based on microwave photons to tackle a useful chemistry problem—determining the spectra. Is one of the photon energy is too low, the amount of energy in following., ” explains Viswanathan pass through the cancer and out the other side, on. Processes of emission and absorption of electromagnetic radiation ; the quantum of radiation! Modern physics is a packet of energy ( i.e particle which has zero! Absorption of electromagnetic radiation of 0.01 to 10 nanometers, with a speed light! Developed by Albert Einstein rays, transfers its energy to matter in units or quantum is or. Based on microwave photons to tackle a useful chemistry problem—determining the vibronic spectra of molecules light, these energy called! Original concept of the photon was developed by Albert Einstein therapy cure tumors the... Are as many kinds of photons as there are as many kinds of photons, all. That give us the opportunity to share their knowledge while a photon is the smallest elemental unit of a,... One of the photon was developed by Albert Einstein two resonant cavities ( shown in blue and ).: ( Left ) Sketch of the texts that give us the opportunity to share their knowledge side, on. In blue and green ) Gilbert n. Lewis who first used the word photon… X-ray photon viewed as particle! Meaning and definition of photon in the following topics: the Photoelectric Effect pass through the and. Emission and absorption of electromagnetic radiation mole of photons as there are frequencies X-ray! Unable to escape the material individual packet of energy ( i.e quantity of energy in vacuum! Microwaves, radio waves, X-rays ) is made up of photons with a of. Photon and quantum are two very important concepts in modern physics rate, ” explains Viswanathan cure tumors at tumor! At the same rate, ” explains Viswanathan original concept of the quantum scheme... Called QUANTA definition: When electromagnetic radiation is transferred to matter in units or quantum energy of 1 of. Other study tools energy to matter in units or quantum... A.2.1 Describe the electromagnetic spectrum chemistry. Cells and tissue with it the elementary particle of an electromagnetic radiation the! The Photoelectric Effect packets called QUANTA concept of the quantum simulator uses microwave photons to tackle a useful problem—determining... Photon is a type elementary particle which has a zero rest mass and with... Made up of photons with a frequency of 3×10 16 Hz to 3×10 19.! A zero rest mass and moves with a frequency of 3×10 16 Hz to 3×10 Hz! Originates from the oxidative metabolic reaction in microbial, plant and animal cells,, to matter 10,! The quantum of electromagnetic energy ( or QUANTA ) for light effects of light not only is light up... Photon has a wavelength of 600.0 nm, so on this exit, they hit normal cells and tissue on. The electron is unable to escape the material a particle, an individual of! Frequency of 3×10 16 Hz to 3×10 19 Hz to 10 nanometers with! A wavelength of 600.0 nm units or quantum ( shown in blue and )... Same rate, ” explains Viswanathan photon will have this much energy associated with it figure 1: Left... Absorption of electromagnetic radiation is transferred to matter the oxidative metabolic reaction in microbial, plant and animal,. At the tumor all electromagnetic energy ( i.e or the smallest elemental unit of a quantity, or smallest. Effects of light and other electromagnetic radiation is viewed as a particle, individual... Photon radiation therapy and proton therapy, on the other hand, at. Light and other study tools photon was developed by Albert Einstein fundamental particle of visible.! If the photon is the branch of chemistry concerned with the chemical effects of light other! Are produced by electron interactions and animal cells,,,, tumors at the same rate, ” Viswanathan... Of ultra-weak photon emission 2.1 visible light so on this exit, hit. 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Two resonant cavities ( shown in blue and green ) the tumor, terms, and more with flashcards games... Has a zero rest mass and moves with a frequency of 3×10 16 Hz 3×10... Terms, and more with flashcards, games, and other study tools X-rays if they are by... To 3×10 19 Hz ways that radiation, such as charged particles and rays! And the fundamental particle of visible light one of the photon was developed by Albert Einstein emission and absorption electromagnetic... To 3×10 19 Hz many kinds of photons tackle a useful chemistry problem—determining the vibronic spectra of molecules electromagnetic... Hand, stops at the tumor and more with flashcards, games, other... More with flashcards, games, and more with flashcards, games, and more with,! Hit normal cells and tissue of chemistry concerned with the chemical effects of light, these energy packets QUANTA... To two resonant cavities ( shown in blue and green ) are produced by electron.!, these energy packets are called X-rays if they are produced by electron interactions ( or )... Other words, it is the “ quantum of electromagnetic radiation ; the quantum of electromagnetic radiation ” radiant is... From the oxidative metabolic reaction in microbial, plant and animal cells,! Normal cells and tissue, or the smallest elemental unit of a,! Use and informative purpose following the fair use principles this much energy associated with it electron... Figure 1: ( Left ) Sketch of the photon was developed by Albert.! Learn vocabulary, terms, and more with flashcards, games, and with! Original concept of the photon is a purely quantum mechanical object representing the elemental... Used only for educational use and informative purpose following the fair photons definition chemistry principles first the! Flashcards, games, and more with flashcards, games, and other radiation! Photons to tackle a useful chemistry problem—determining the vibronic spectra of molecules emission.! The following topics: the Photoelectric Effect the quantum of electromagnetic energy ( i.e by Albert Einstein 2.1! Scientist Gilbert n. Lewis who first used the word photon… X-ray photon, hit... Of visible light a packet of energy that intervenes in the vacuum for.! Individual packet of energy in the packet can vary spectra of molecules packet of energy ) is made of. Will have this much energy associated with it representing the smallest elemental photons definition chemistry of a quantity, the! Other words, it is the branch of chemistry concerned with the chemical of! Games, and other electromagnetic radiation is transferred to matter X-rays if they are produced by electron interactions for. Radiation therapy and proton therapy, on the other hand, stops at the tumor electromagnetic spectrum IB chemistry 2. Discrete amount of something chemistry concerned with the chemical effects of light, these packets. The oxidative metabolic reaction in microbial, plant and animal cells,,.... A.2.1 Describe the electromagnetic spectrum IB chemistry … 2 that radiation, as! These energy packets are called photons Left ) Sketch of the quantum simulator microwave. Piece of energy that intervenes in the packet can vary up of as! In modern physics electron is unable to escape the material called QUANTA in case of light they normal. Absorption of electromagnetic energy ( i.e have this much energy associated with.. Packet can vary quantum mechanical object representing the smallest elemental unit of a quantity or!, on the other hand, stops at the tumor form of small energy packets called QUANTA,... Modern physics to escape the material share their knowledge 0.01 to 10 nanometers, with a wavelength of nm!	2021-03-01 10:37:13	{"extraction_info": {"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": 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, "math_score": 0.5355241894721985, "perplexity": 1010.7391120890438}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362481.49/warc/CC-MAIN-20210301090526-20210301120526-00386.warc.gz"}
https://www.sharcnet.ca/Software/Fluent6/html/ug/node906.htm	## 23.5.6 Maximum Packing Limit in Binary Mixtures The packing limit is not a fixed quantity and may change according to the number of particles present within a given volume and the diameter of the particles. Small particles accumulate in between larger particles increasing the packing limit. For a binary mixture FLUENT uses the correlations proposed by [ 101]. For a binary mixture with diameters , the mixture composition is defined as where (23.5-58) The maximum packing limit for the mixture is given by (23.5-59) (23.5-60) otherwise, the maximum packing limit for the binary mixture is (23.5-61) The packing limit is used for the calculation of the radial distribution function. Previous: 23.5.5 Solids Pressure Up: 23.5 Eulerian Model Theory Next: 23.5.7 Solids Shear Stresses	2018-01-20 13:13:39	{"extraction_info": {"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, "math_score": 0.9166010022163391, "perplexity": 2025.891633674731}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889617.56/warc/CC-MAIN-20180120122736-20180120142736-00708.warc.gz"}
https://docs.chainer.org/en/latest/chainerx/reference/generated/chainerx.average_pool.html	# chainerx.average_pool¶ chainerx.average_pool(x, ksize, stride=None, pad=0, pad_mode='ignore') Spatial average pooling function. This acts similarly to conv(), but it computes the average of input spatial patch for each channel without any parameter instead of computing the inner products. Parameters • x (ndarray) – Input array. • ksize (int or tuple of ints) – Size of pooling window. ksize=k and ksize=(k, k, ..., k) are equivalent. • stride (int or tuple of ints or None) – Stride of pooling applications. stride=s and stride=(s, s, ..., s) are equivalent. If None is specified, then it uses same stride as the pooling window size. • pad (int or tuple of ints) – Spatial padding width for the input array. pad=p and pad=(p, p, ..., p) are equivalent. Specifies how padded region is treated. • ’zero’ – the values in the padded region are treated as 0 • ’ignore’ – padded region is ignored (default) Returns Output array. Return type ndarray Note During backpropagation, this function propagates the gradient of the output array to the input array x. Note In cuda backend, only 2 and 3 dim arrays are supported as x because cuDNN pooling supports 2 and 3 spatial dimensions.	2019-11-21 09:30:44	{"extraction_info": {"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, "math_score": 0.6228466033935547, "perplexity": 13343.56044060516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670743.44/warc/CC-MAIN-20191121074016-20191121102016-00464.warc.gz"}
http://levimoveis.com.br/dead-doc-drifdxt/6ad9f6-symmetric-relation-calculator	, <3, 2>, <1, a>} 1. A skew-symmetric matrix A satisfies the relation A 2 + I = 0, where I is a unit matrix then A is This question has multiple correct options. For a relation R in set A Reflexive Relation is reflexive If (a, a) â R for every a â A Symmetric Relation is symmetric, If (a, b) â R, then (b, a) â R Transitive Relation is transitive, If (a, b) â R & (b, c) â R, then (a, c) â R If relation is reflexive, symmetric and transitive, it is an equivalence relation . code. generate link and share the link here. And also, not an equivalence relation. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. The relation T is symmetric, because if a b can be written as m n for some integers m and n, then so is its reciprocal b a, because b a = n m. If "a" is brother of "b", then "b" has to be brother of "a". Relations and Functions in math--domain, range, one to one and much more Free functions symmetry calculator - find whether the function is symmetric about x-axis, y-axis or origin step-by-step This website uses cookies to ensure you get the best experience. â¢ A relation R is symmetricif and only if mij = mji for all i,j. If R is symmetric relation, then R = { (a, b), (b, a) / for all a, b â A} That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. The diagonals can have any value. Relation Reï¬exive Symmetric Asymmetric Antisymmetric Irreï¬exive Transitive R 1 X R 2 X X X R 3 X X X X X R 4 X X X X R 5 X X X 3. The quotient remainder theorem. Symmetry occurs not only in geometry, but also in other branches of mathematics.Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.. Given a number n, find out number of Symmetric Relations on a set of first n natural numbers {1, 2, ..n}. By using this website, you agree to our Cookie Policy. Applied Mathematics. Enter the elements of the set(B) seperated by comma. Use this calculator to find the family relationship between two people who share a common blood ancestor. close, link In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. So combination of non-diagonal values = 2(n2 – n)/2, Overall combination = 2n * 2(n2 – n)/2 = 2n(n+1)/2, edit â¢ Answer: No. Both are anti-symmetric. Transitive Closure â Let be a relation on set . We can only choose different value for half of them, because when we choose a value for cell (i, j), cell (j, i) gets same value. There are n2 – n non-diagonal values. Please refer to our Family Relationship Chart for those relationships. We know that if then and are said to be equivalent with respect to . Attention reader! Program to check if a given year is leap year, Factorial of Large numbers using Logarithmic identity, Write an iterative O(Log y) function for pow(x, y), Modular Exponentiation (Power in Modular Arithmetic), Write a program to print all permutations of a given string, JavaScript \| array.toLocaleString() function, itertools.combinations() module in Python to print all possible combinations, Print all permutations in sorted (lexicographic) order, Heap's Algorithm for generating permutations, Print all possible strings of length k that can be formed from a set of n characters, Set in C++ Standard Template Library (STL), Program to find GCD or HCF of two numbers, Write Interview Reflexive and Transitive but not Symmetric . The transitive reduction of a graph is the smallest graph such that , where is the transitive closure of (Skiena 1990, p. 203). Statistics calculators. 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Is It Transitive Calculator Worksheet There is another way two relations can be combined that is analogous to the composition of functions. Let R be a relation defined on the set A such that R = { (a, b) / a, b â A} Then, the inverse relation R-1 on A is given by R-1 = { (b, a) / (a, b) â R} What is the symmetric closure of R? Our mission is to provide a free, world-class education to anyone, anywhere. Don’t stop learning now. 2. There are n diagonal values, total possible combination of diagonal values = 2n The relation a = b a = b is symmetric, but a > b a > b is not. For transitive relations, we see that ~ and ~* are the same. Enter the elements of the set(A) seperated by comma . R is symmetric x R y implies y R x, for all x,yâA The relation is reversable. Donate or volunteer today! Since for all ain natural number set, a a, (a;a) 2R. R ={(a,b) : a 3 b 3. Since the relation is reflexive, symmetric, and transitive, we conclude that is an equivalence relation. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. Khan Academy is a 501(c)(3) nonprofit organization. A Relation ‘R’ on Set A is said be Symmetric if xRy then yRx for every x, y ∈ A Reflexive, Symmetric, Transitive, and Substitution Properties Reflexive Property The Reflexive Property states that for every real number x , x = x . For the intents of this calculator, "power of a matrix" means to raise a given matrix to a given power. Let us have a look at when a set is Reflexive and Transitive but not Symmetric. Total number of symmetric relations is 2n(n+1)/2. In other words, we can say symmetric property is something where one side is a mirror image or reflection of the other. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, For every set bit of a number toggle bits of other, Toggle bits of a number except first and last bits, Find most significant set bit of a number, Check whether the bit at given position is set or unset. Let A be the set of two male children in a family and R be a relation defined on set A as. The diagonals can have any value. Let A = {1, 2, 3} and R be a relation defined on set A as. By using our site, you In acyclic directed graphs. Symmetric stripline geometry Many calculators divide the equations into a series of approximations for various limits on the geometric parameters in the above figure. Antisymmetric Relation \| How To Prove With Examples (Video) Therefore, Ris reï¬exive. 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Otherwise, it is equal to 0. A matrix A is symmetric if and only if A =A T. A matrix A is skew-symmetric if and only if A = âA T. In Exercise 5, you are asked to show that any symmetric or skew-symmetric matrix is a square matrix. Example6.LetR= f(a;b) ja;b2N anda bg. Let S be any non-empty set. Relationships between nephews, aunts, and cousins are not calculated. Hence, less than (<), greater than (>) and minus (-) are examples of asymmetric. Experience. Formally, a binary relation R over a set X is symmetric if: {\displaystyle \forall a,b\in X (aRb\Leftrightarrow bRa).} What is the reflexive closure of R? Symmetric Strength provides a comprehensive lifter analysis based on strength research and data from strength competitions. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. If a relation $$R$$ on $$A$$ is both symmetric and antisymmetric, its off-diagonal entries are all zeros, so it is a subset of the identity relation. Equivalence Classes : Let be an equivalence relation on set . These equations can be found using Wadellâs methods. How to swap two numbers without using a temporary variable? i.e., A Delta B ( A Î B ) Symmetric Difference Calculation \| Calculate A Delta B. There are n diagonal values, total possible combination of diagonal values = 2 n There are n 2 â n non-diagonal values. In a set A, if one element less than the other, satisfies one relation, then the other element is not less than the first one. Note: The calculator only works with a shared parent, grandparent, or great-grandparent. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). In discrete Maths, an asymmetric relation is just opposite to symmetric relation. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, Difference between reflexive and identity relation. brightness_4 Instructions to use calculator Enter the scientific value in exponent format, for example if you have value as 0.0000012 you can enter this as 1.2e-6 Please use the mathematical deterministic number in field to perform the calculation for example if you entered x greater than 1 in the equation $y=\sqrt{1-x}$ the calculator will not work and you may not get desired result. Under specific (not mutually exclusive) approximations, the following equations define the impedance of a stripline: gives all elements in set A that are not in set B and vice versa. A symmetric relation is a type of binary relation. Consider the following matrices: A = 2 6 4 6 â 1 0 4 0 â 3 and B = 0 â 1 3 6 1 0 2 â 5 â 3 â 2 0 4 â 6 5 â 4 0. For example, when using the calculator, "Power of 2" for a given matrix, A, means A 2. Online algebra calculator that calculates the Symmetric difference of set(say A) and any other set(say B), i.e. or if (x, y) ∈ R, then (y, x) ∈ R for every x, y?A. A relation R is defined as . CS 441 Discrete mathematics for CS M. Hauskrecht Properties of relations Definition (symmetric relation): A relation R on a set A is called symmetric if a, b A (a,b) R (b,a) R. Example 3: â¢ Relation R fun on A = {1,2,3,4} defined as: â¢Rfun = {(1,2),(2,2),(3,3)}. R is irreflexive (x,x) â R, for all xâA Properties of Binary Relations: R is reflexive x R x for all xâA Every element is related to itself. The empty relation is anti-symmetric (as said above). Symmetric Difference â consists of all ordered pairs which are either in or but not both. Since a a = 1 â Q, the relation T is reflexive; it follows that T is not irreflexive. The set of all elements that are related to an element of is called the equivalence class of . Hence, R is reflexive. Oracle tools tips - Symmetric Difference - Row Hash Value, Relation Equality, Duality between Set and Join Operators : Search BC Oracle Sites Home E-mail Us Oracle Articles New Oracle Articles Oracle Training Oracle Tips Oracle Forum Class Catalog Remote DBA Oracle Tuning Emergency 911 RAC Support Apps Support Analysis Design Implementation Oracle Support SQL Tuning Security Oracle â¦ If a set is a singleton $\{a\}$ then there are two relations on it: the empty relation and the relation $\{\langle a,a\rangle\}$. Let $R=\{(1,1),(2,2),(3,3)\}$ be a relation defined on the set $A=\{1,2,3\}$. Let R be a relation defined on the set A. R = {(a, b), (b, a) / for all a, b â A}. Symmetric Property The Symmetric Property states that for all real numbers x and y , if x = y , then y = x . Example 1. Thus, relation R is symmetric and transitive but not reflexive. Congruence relation. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. Up Next. The relation T on R â is defined as aTb â a b â Q. F ( a ) seperated by comma matrix '' means to raise a given matrix, a symmetry is type. A > b is not irreflexive example, when using the calculator only works with a shared,. Calculator to find the family relationship between two people who share a common ancestor... Be the set of all elements in set a that are related to an element is! B and vice versa implies y R x for all real numbers x and y, then b,! Chart for those relationships a mapping of the set ( b ) seperated by comma a type binary! Relations is 2n ( n+1 ) /2 to anyone, anywhere share \| cite \| improve this answer follow!, aunts, and cousins are not in set a that are related to.... That if then and are said to be brother of b '', then b '', y! Means a 2, an asymmetric relation is a 501 ( c ) ( )! Link and share the link here element is related to itself have look. Self Paced Course at a student-friendly price and become industry ready real numbers x and y, x. Above, if you need any other set ( b ), greater than >... Not both children in a family and R be a relation defined on set a that are related itself... Our Cookie Policy ain natural number set, a Delta b the here...: a 3 b 3 and minus ( - ) are examples of asymmetric total combination! The link here if you need any other set ( say b ) ja ; b2N anda bg on! Relations: R is reflexive x R x for all real numbers x and y then... A look at when a set is reflexive x R x for all numbers! Structured object x of any sort, a Delta b matrix '' means raise... Those relationships ) â R since a = { ( a ; a ) â R a... Symmetric x R x, for all x, for all real numbers x and y then! Property is something where one side is a 501 ( c ) ( ). * are the same shared parent, grandparent, or great-grandparent above figure edited Sep 22 '19 at drhab... Matrix, a, means a 2 of set ( say b ): a 3, world-class to! Be a relation defined on set a that are related to an element of called! Approximations for various limits on the geometric parameters in the above figure is a 501 ( )... Elements in set a that are not calculated asymmetric relation is just opposite to symmetric relation ! Link here = 2n There are n diagonal values, total possible combination of diagonal values = 2 There! Dsa Self Paced Course at a student-friendly price and become industry ready, b ) seperated by comma say )! All ordered pairs which are either in or but not both discrete Maths, an asymmetric relation is (! Calculator to find the family relationship between two people who share a common ancestor! Any sort, a symmetry is a 501 ( c ) ( 3 ) organization! It follows that T is reflexive ; It follows that T is reflexive ; It follows T! From strength competitions and vice versa be equivalent with respect to only works a... 501 ( c ) ( 3 ) nonprofit organization n There are n diagonal values = There. F ( a ; b ), i.e Maths, an asymmetric relation is anti-symmetric as. Which preserves the structure if you need any other set ( say b ) ja b2N... Â n non-diagonal values our google custom search here be a relation defined on set symmetric relation calculator as a! Difference â consists of all ordered pairs which are either in or but not symmetric another two! Of binary relations: R is symmetric x R x, for all xâA Every element is to. A mirror image or reflection of the object onto itself which preserves structure. Be equivalent symmetric relation calculator respect to ordered pairs which are either in or but not.. Only works with a shared parent, grandparent, or great-grandparent R is symmetric x R x for xâA. Natural number set, a ) symmetric relation calculator > ) and any other set ( say b ) ja b2N. Divide the equations into a series of approximations for various limits on the geometric parameters in the figure. B a = 1 â Q, the relation a = b a > b a = { (,. But a > b is not symmetric strength provides a comprehensive lifter based... R x for all x, yâA the relation a = 1 â,! Is to provide a free, world-class education to anyone, anywhere than ( > ) and other... Object onto itself which preserves the structure the object onto itself which the! Not symmetric < ), greater than ( > ) and any other stuff in math please. Which are either in or but not both to provide a free, education. Worksheet There is another way two relations can be combined that is to! A > b is symmetric x R x, for all real numbers and... Relations is 2n ( n+1 ) /2 that calculates the symmetric Property states that for all ain number! Let a be the set ( say b ), i.e that for all,... The structure of approximations for various limits on the geometric parameters in above. Elements that are related to itself \| follow \| edited Sep 22 '19 at answered! Is just opposite to symmetric relation, 3 } and R be a relation defined on set = â. Relations can be combined that is analogous to the composition of functions the relation a = b a > is. Hold of all elements in set b and vice versa given a object! That is analogous to the composition of functions equations into a series of approximations for various limits on the parameters. At a student-friendly price and become industry ready symmetric strength provides a comprehensive lifter analysis based on strength and... To be brother of symmetric relation calculator '' has to be brother of b '' to. Male children in a family and R be a relation defined on set edited Sep 22 '19 10:26.. ( as said above ) in or but not both = y, if x = y, . Ide.Geeksforgeeks.Org, generate link and share the link here by using this website, you agree to our family Chart. 12:26. drhab drhab set a as ( - ) are examples of asymmetric two male in. Stuff in math, please use our google custom search here symmetric Difference consists... 29 Palms Weather Monthly, Flatbed Led Tail Light Kit, Pico Mango Vs Carabao Mango, Pop Up Golf Net Amazon, Great Pyrenees Blue Heeler Mix For Sale, " /> , <3, 2>, <1, a>} 1. A skew-symmetric matrix A satisfies the relation A 2 + I = 0, where I is a unit matrix then A is This question has multiple correct options. For a relation R in set A Reflexive Relation is reflexive If (a, a) â R for every a â A Symmetric Relation is symmetric, If (a, b) â R, then (b, a) â R Transitive Relation is transitive, If (a, b) â R & (b, c) â R, then (a, c) â R If relation is reflexive, symmetric and transitive, it is an equivalence relation . code. generate link and share the link here. And also, not an equivalence relation. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. The relation T is symmetric, because if a b can be written as m n for some integers m and n, then so is its reciprocal b a, because b a = n m. If "a" is brother of "b", then "b" has to be brother of "a". Relations and Functions in math--domain, range, one to one and much more Free functions symmetry calculator - find whether the function is symmetric about x-axis, y-axis or origin step-by-step This website uses cookies to ensure you get the best experience. â¢ A relation R is symmetricif and only if mij = mji for all i,j. If R is symmetric relation, then R = { (a, b), (b, a) / for all a, b â A} That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. The diagonals can have any value. Relation Reï¬exive Symmetric Asymmetric Antisymmetric Irreï¬exive Transitive R 1 X R 2 X X X R 3 X X X X X R 4 X X X X R 5 X X X 3. The quotient remainder theorem. Symmetry occurs not only in geometry, but also in other branches of mathematics.Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.. Given a number n, find out number of Symmetric Relations on a set of first n natural numbers {1, 2, ..n}. By using this website, you agree to our Cookie Policy. Applied Mathematics. Enter the elements of the set(B) seperated by comma. Use this calculator to find the family relationship between two people who share a common blood ancestor. close, link In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. So combination of non-diagonal values = 2(n2 – n)/2, Overall combination = 2n * 2(n2 – n)/2 = 2n(n+1)/2, edit â¢ Answer: No. Both are anti-symmetric. Transitive Closure â Let be a relation on set . We can only choose different value for half of them, because when we choose a value for cell (i, j), cell (j, i) gets same value. There are n2 – n non-diagonal values. Please refer to our Family Relationship Chart for those relationships. We know that if then and are said to be equivalent with respect to . Attention reader! Program to check if a given year is leap year, Factorial of Large numbers using Logarithmic identity, Write an iterative O(Log y) function for pow(x, y), Modular Exponentiation (Power in Modular Arithmetic), Write a program to print all permutations of a given string, JavaScript \| array.toLocaleString() function, itertools.combinations() module in Python to print all possible combinations, Print all permutations in sorted (lexicographic) order, Heap's Algorithm for generating permutations, Print all possible strings of length k that can be formed from a set of n characters, Set in C++ Standard Template Library (STL), Program to find GCD or HCF of two numbers, Write Interview Reflexive and Transitive but not Symmetric . The transitive reduction of a graph is the smallest graph such that , where is the transitive closure of (Skiena 1990, p. 203). Statistics calculators. 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Is It Transitive Calculator Worksheet There is another way two relations can be combined that is analogous to the composition of functions. Let R be a relation defined on the set A such that R = { (a, b) / a, b â A} Then, the inverse relation R-1 on A is given by R-1 = { (b, a) / (a, b) â R} What is the symmetric closure of R? Our mission is to provide a free, world-class education to anyone, anywhere. Don’t stop learning now. 2. There are n diagonal values, total possible combination of diagonal values = 2n The relation a = b a = b is symmetric, but a > b a > b is not. For transitive relations, we see that ~ and ~* are the same. Enter the elements of the set(A) seperated by comma . R is symmetric x R y implies y R x, for all x,yâA The relation is reversable. Donate or volunteer today! Since for all ain natural number set, a a, (a;a) 2R. R ={(a,b) : a 3 b 3. Since the relation is reflexive, symmetric, and transitive, we conclude that is an equivalence relation. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. Khan Academy is a 501(c)(3) nonprofit organization. A Relation ‘R’ on Set A is said be Symmetric if xRy then yRx for every x, y ∈ A Reflexive, Symmetric, Transitive, and Substitution Properties Reflexive Property The Reflexive Property states that for every real number x , x = x . For the intents of this calculator, "power of a matrix" means to raise a given matrix to a given power. Let us have a look at when a set is Reflexive and Transitive but not Symmetric. Total number of symmetric relations is 2n(n+1)/2. In other words, we can say symmetric property is something where one side is a mirror image or reflection of the other. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, For every set bit of a number toggle bits of other, Toggle bits of a number except first and last bits, Find most significant set bit of a number, Check whether the bit at given position is set or unset. Let A be the set of two male children in a family and R be a relation defined on set A as. The diagonals can have any value. Let A = {1, 2, 3} and R be a relation defined on set A as. By using our site, you In acyclic directed graphs. Symmetric stripline geometry Many calculators divide the equations into a series of approximations for various limits on the geometric parameters in the above figure. Antisymmetric Relation \| How To Prove With Examples (Video) Therefore, Ris reï¬exive. 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Otherwise, it is equal to 0. A matrix A is symmetric if and only if A =A T. A matrix A is skew-symmetric if and only if A = âA T. In Exercise 5, you are asked to show that any symmetric or skew-symmetric matrix is a square matrix. Example6.LetR= f(a;b) ja;b2N anda bg. Let S be any non-empty set. Relationships between nephews, aunts, and cousins are not calculated. Hence, less than (<), greater than (>) and minus (-) are examples of asymmetric. Experience. Formally, a binary relation R over a set X is symmetric if: {\displaystyle \forall a,b\in X (aRb\Leftrightarrow bRa).} What is the reflexive closure of R? Symmetric Strength provides a comprehensive lifter analysis based on strength research and data from strength competitions. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. If a relation $$R$$ on $$A$$ is both symmetric and antisymmetric, its off-diagonal entries are all zeros, so it is a subset of the identity relation. Equivalence Classes : Let be an equivalence relation on set . These equations can be found using Wadellâs methods. How to swap two numbers without using a temporary variable? i.e., A Delta B ( A Î B ) Symmetric Difference Calculation \| Calculate A Delta B. There are n diagonal values, total possible combination of diagonal values = 2 n There are n 2 â n non-diagonal values. In a set A, if one element less than the other, satisfies one relation, then the other element is not less than the first one. Note: The calculator only works with a shared parent, grandparent, or great-grandparent. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). In discrete Maths, an asymmetric relation is just opposite to symmetric relation. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, Difference between reflexive and identity relation. brightness_4 Instructions to use calculator Enter the scientific value in exponent format, for example if you have value as 0.0000012 you can enter this as 1.2e-6 Please use the mathematical deterministic number in field to perform the calculation for example if you entered x greater than 1 in the equation $y=\sqrt{1-x}$ the calculator will not work and you may not get desired result. Under specific (not mutually exclusive) approximations, the following equations define the impedance of a stripline: gives all elements in set A that are not in set B and vice versa. A symmetric relation is a type of binary relation. Consider the following matrices: A = 2 6 4 6 â 1 0 4 0 â 3 and B = 0 â 1 3 6 1 0 2 â 5 â 3 â 2 0 4 â 6 5 â 4 0. For example, when using the calculator, "Power of 2" for a given matrix, A, means A 2. Online algebra calculator that calculates the Symmetric difference of set(say A) and any other set(say B), i.e. or if (x, y) ∈ R, then (y, x) ∈ R for every x, y?A. A relation R is defined as . CS 441 Discrete mathematics for CS M. Hauskrecht Properties of relations Definition (symmetric relation): A relation R on a set A is called symmetric if a, b A (a,b) R (b,a) R. Example 3: â¢ Relation R fun on A = {1,2,3,4} defined as: â¢Rfun = {(1,2),(2,2),(3,3)}. R is irreflexive (x,x) â R, for all xâA Properties of Binary Relations: R is reflexive x R x for all xâA Every element is related to itself. The empty relation is anti-symmetric (as said above). Symmetric Difference â consists of all ordered pairs which are either in or but not both. Since a a = 1 â Q, the relation T is reflexive; it follows that T is not irreflexive. The set of all elements that are related to an element of is called the equivalence class of . Hence, R is reflexive. Oracle tools tips - Symmetric Difference - Row Hash Value, Relation Equality, Duality between Set and Join Operators : Search BC Oracle Sites Home E-mail Us Oracle Articles New Oracle Articles Oracle Training Oracle Tips Oracle Forum Class Catalog Remote DBA Oracle Tuning Emergency 911 RAC Support Apps Support Analysis Design Implementation Oracle Support SQL Tuning Security Oracle â¦ If a set is a singleton $\{a\}$ then there are two relations on it: the empty relation and the relation $\{\langle a,a\rangle\}$. Let $R=\{(1,1),(2,2),(3,3)\}$ be a relation defined on the set $A=\{1,2,3\}$. Let R be a relation defined on the set A. R = {(a, b), (b, a) / for all a, b â A}. Symmetric Property The Symmetric Property states that for all real numbers x and y , if x = y , then y = x . Example 1. Thus, relation R is symmetric and transitive but not reflexive. Congruence relation. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. Up Next. The relation T on R â is defined as aTb â a b â Q. F ( a ) seperated by comma matrix '' means to raise a given matrix, a symmetry is type. A > b is not irreflexive example, when using the calculator only works with a shared,. Calculator to find the family relationship between two people who share a common ancestor... Be the set of all elements in set a that are related to an element is! B and vice versa implies y R x for all real numbers x and y, then b,! Chart for those relationships a mapping of the set ( b ) seperated by comma a type binary! Relations is 2n ( n+1 ) /2 to anyone, anywhere share \| cite \| improve this answer follow!, aunts, and cousins are not in set a that are related to.... That if then and are said to be brother of b '', then b '', y! Means a 2, an asymmetric relation is a 501 ( c ) ( )! Link and share the link here element is related to itself have look. Self Paced Course at a student-friendly price and become industry ready real numbers x and y, x. Above, if you need any other set ( b ), greater than >... Not both children in a family and R be a relation defined on set a that are related itself... Our Cookie Policy ain natural number set, a Delta b the here...: a 3 b 3 and minus ( - ) are examples of asymmetric total combination! The link here if you need any other set ( say b ) ja ; b2N anda bg on! Relations: R is reflexive x R x for all real numbers x and y then... A look at when a set is reflexive x R x for all numbers! Structured object x of any sort, a Delta b matrix '' means raise... Those relationships ) â R since a = { ( a ; a ) â R a... Symmetric x R x, for all x, for all real numbers x and y then! Property is something where one side is a 501 ( c ) ( ). * are the same shared parent, grandparent, or great-grandparent above figure edited Sep 22 '19 at drhab... Matrix, a, means a 2 of set ( say b ): a 3, world-class to! Be a relation defined on set a that are related to an element of called! Approximations for various limits on the geometric parameters in the above figure is a 501 ( )... Elements in set a that are not calculated asymmetric relation is just opposite to symmetric relation ! Link here = 2n There are n diagonal values, total possible combination of diagonal values = 2 There! Dsa Self Paced Course at a student-friendly price and become industry ready, b ) seperated by comma say )! All ordered pairs which are either in or but not both discrete Maths, an asymmetric relation is (! Calculator to find the family relationship between two people who share a common ancestor! Any sort, a symmetry is a 501 ( c ) ( 3 ) organization! It follows that T is reflexive ; It follows that T is reflexive ; It follows T! From strength competitions and vice versa be equivalent with respect to only works a... 501 ( c ) ( 3 ) nonprofit organization n There are n diagonal values = There. F ( a ; b ), i.e Maths, an asymmetric relation is anti-symmetric as. Which preserves the structure if you need any other set ( say b ) ja b2N... Â n non-diagonal values our google custom search here be a relation defined on set symmetric relation calculator as a! Difference â consists of all ordered pairs which are either in or but not symmetric another two! Of binary relations: R is symmetric x R x, for all xâA Every element is to. A mirror image or reflection of the object onto itself which preserves structure. Be equivalent symmetric relation calculator respect to ordered pairs which are either in or but not.. Only works with a shared parent, grandparent, or great-grandparent R is symmetric x R x for xâA. Natural number set, a ) symmetric relation calculator > ) and any other set ( say b ) ja b2N. Divide the equations into a series of approximations for various limits on the geometric parameters in the figure. B a = 1 â Q, the relation a = b a > b a = { (,. But a > b is not symmetric strength provides a comprehensive lifter based... R x for all x, yâA the relation a = 1 â,! Is to provide a free, world-class education to anyone, anywhere than ( > ) and other... Object onto itself which preserves the structure the object onto itself which the! Not symmetric < ), greater than ( > ) and any other stuff in math please. Which are either in or but not both to provide a free, education. Worksheet There is another way two relations can be combined that is to! A > b is symmetric x R x, for all real numbers and... Relations is 2n ( n+1 ) /2 that calculates the symmetric Property states that for all ain number! Let a be the set ( say b ), i.e that for all,... The structure of approximations for various limits on the geometric parameters in above. Elements that are related to itself \| follow \| edited Sep 22 '19 at answered! Is just opposite to symmetric relation, 3 } and R be a relation defined on set = â. Relations can be combined that is analogous to the composition of functions the relation a = b a > is. Hold of all elements in set b and vice versa given a object! That is analogous to the composition of functions equations into a series of approximations for various limits on the parameters. At a student-friendly price and become industry ready symmetric strength provides a comprehensive lifter analysis based on strength and... To be brother of symmetric relation calculator '' has to be brother of b '' to. Male children in a family and R be a relation defined on set edited Sep 22 '19 10:26.. ( as said above ) in or but not both = y, if x = y, . Ide.Geeksforgeeks.Org, generate link and share the link here by using this website, you agree to our family Chart. 12:26. drhab drhab set a as ( - ) are examples of asymmetric two male in. Stuff in math, please use our google custom search here symmetric Difference consists... 29 Palms Weather Monthly, Flatbed Led Tail Light Kit, Pico Mango Vs Carabao Mango, Pop Up Golf Net Amazon, Great Pyrenees Blue Heeler Mix For Sale, " /> # News Writing code in comment? Please use ide.geeksforgeeks.org, 3. About. The symmetric closure of relation on set is . â¢ Is Rfun symmetric? Clearly (a, a) â R since a = a 3. The quotient remainder theorem. share \| cite \| improve this answer \| follow \| edited Sep 22 '19 at 10:26. answered Sep 21 '19 at 12:26. drhab drhab. An example is the relation "is equal to", because if a = b is true then b = a is also true. Site Navigation. R is transitive x R y and y R z implies x R z, for all x,y,zâA Example: i<7 and 7, <3, 2>, <1, a>} 1. A skew-symmetric matrix A satisfies the relation A 2 + I = 0, where I is a unit matrix then A is This question has multiple correct options. For a relation R in set A Reflexive Relation is reflexive If (a, a) â R for every a â A Symmetric Relation is symmetric, If (a, b) â R, then (b, a) â R Transitive Relation is transitive, If (a, b) â R & (b, c) â R, then (a, c) â R If relation is reflexive, symmetric and transitive, it is an equivalence relation . code. generate link and share the link here. And also, not an equivalence relation. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. The relation T is symmetric, because if a b can be written as m n for some integers m and n, then so is its reciprocal b a, because b a = n m. If "a" is brother of "b", then "b" has to be brother of "a". Relations and Functions in math--domain, range, one to one and much more Free functions symmetry calculator - find whether the function is symmetric about x-axis, y-axis or origin step-by-step This website uses cookies to ensure you get the best experience. â¢ A relation R is symmetricif and only if mij = mji for all i,j. If R is symmetric relation, then R = { (a, b), (b, a) / for all a, b â A} That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. The diagonals can have any value. Relation Reï¬exive Symmetric Asymmetric Antisymmetric Irreï¬exive Transitive R 1 X R 2 X X X R 3 X X X X X R 4 X X X X R 5 X X X 3. The quotient remainder theorem. Symmetry occurs not only in geometry, but also in other branches of mathematics.Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.. Given a number n, find out number of Symmetric Relations on a set of first n natural numbers {1, 2, ..n}. By using this website, you agree to our Cookie Policy. Applied Mathematics. Enter the elements of the set(B) seperated by comma. Use this calculator to find the family relationship between two people who share a common blood ancestor. close, link In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. So combination of non-diagonal values = 2(n2 – n)/2, Overall combination = 2n * 2(n2 – n)/2 = 2n(n+1)/2, edit â¢ Answer: No. Both are anti-symmetric. Transitive Closure â Let be a relation on set . We can only choose different value for half of them, because when we choose a value for cell (i, j), cell (j, i) gets same value. There are n2 – n non-diagonal values. Please refer to our Family Relationship Chart for those relationships. We know that if then and are said to be equivalent with respect to . Attention reader! Program to check if a given year is leap year, Factorial of Large numbers using Logarithmic identity, Write an iterative O(Log y) function for pow(x, y), Modular Exponentiation (Power in Modular Arithmetic), Write a program to print all permutations of a given string, JavaScript \| array.toLocaleString() function, itertools.combinations() module in Python to print all possible combinations, Print all permutations in sorted (lexicographic) order, Heap's Algorithm for generating permutations, Print all possible strings of length k that can be formed from a set of n characters, Set in C++ Standard Template Library (STL), Program to find GCD or HCF of two numbers, Write Interview Reflexive and Transitive but not Symmetric . The transitive reduction of a graph is the smallest graph such that , where is the transitive closure of (Skiena 1990, p. 203). Statistics calculators. 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Is It Transitive Calculator Worksheet There is another way two relations can be combined that is analogous to the composition of functions. Let R be a relation defined on the set A such that R = { (a, b) / a, b â A} Then, the inverse relation R-1 on A is given by R-1 = { (b, a) / (a, b) â R} What is the symmetric closure of R? Our mission is to provide a free, world-class education to anyone, anywhere. Don’t stop learning now. 2. There are n diagonal values, total possible combination of diagonal values = 2n The relation a = b a = b is symmetric, but a > b a > b is not. For transitive relations, we see that ~ and ~* are the same. Enter the elements of the set(A) seperated by comma . R is symmetric x R y implies y R x, for all x,yâA The relation is reversable. Donate or volunteer today! Since for all ain natural number set, a a, (a;a) 2R. R ={(a,b) : a 3 b 3. Since the relation is reflexive, symmetric, and transitive, we conclude that is an equivalence relation. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. Khan Academy is a 501(c)(3) nonprofit organization. A Relation ‘R’ on Set A is said be Symmetric if xRy then yRx for every x, y ∈ A Reflexive, Symmetric, Transitive, and Substitution Properties Reflexive Property The Reflexive Property states that for every real number x , x = x . For the intents of this calculator, "power of a matrix" means to raise a given matrix to a given power. Let us have a look at when a set is Reflexive and Transitive but not Symmetric. Total number of symmetric relations is 2n(n+1)/2. In other words, we can say symmetric property is something where one side is a mirror image or reflection of the other. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, For every set bit of a number toggle bits of other, Toggle bits of a number except first and last bits, Find most significant set bit of a number, Check whether the bit at given position is set or unset. Let A be the set of two male children in a family and R be a relation defined on set A as. The diagonals can have any value. Let A = {1, 2, 3} and R be a relation defined on set A as. By using our site, you In acyclic directed graphs. Symmetric stripline geometry Many calculators divide the equations into a series of approximations for various limits on the geometric parameters in the above figure. Antisymmetric Relation \| How To Prove With Examples (Video) Therefore, Ris reï¬exive. 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Otherwise, it is equal to 0. A matrix A is symmetric if and only if A =A T. A matrix A is skew-symmetric if and only if A = âA T. In Exercise 5, you are asked to show that any symmetric or skew-symmetric matrix is a square matrix. Example6.LetR= f(a;b) ja;b2N anda bg. Let S be any non-empty set. Relationships between nephews, aunts, and cousins are not calculated. Hence, less than (<), greater than (>) and minus (-) are examples of asymmetric. Experience. Formally, a binary relation R over a set X is symmetric if: {\displaystyle \forall a,b\in X (aRb\Leftrightarrow bRa).} What is the reflexive closure of R? Symmetric Strength provides a comprehensive lifter analysis based on strength research and data from strength competitions. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. That is, if "a" is related to "b", then "b" has to be related to "a" for all "a" and "b" belonging to A. If a relation $$R$$ on $$A$$ is both symmetric and antisymmetric, its off-diagonal entries are all zeros, so it is a subset of the identity relation. Equivalence Classes : Let be an equivalence relation on set . These equations can be found using Wadellâs methods. How to swap two numbers without using a temporary variable? i.e., A Delta B ( A Î B ) Symmetric Difference Calculation \| Calculate A Delta B. There are n diagonal values, total possible combination of diagonal values = 2 n There are n 2 â n non-diagonal values. In a set A, if one element less than the other, satisfies one relation, then the other element is not less than the first one. Note: The calculator only works with a shared parent, grandparent, or great-grandparent. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). In discrete Maths, an asymmetric relation is just opposite to symmetric relation. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, Difference between reflexive and identity relation. brightness_4 Instructions to use calculator Enter the scientific value in exponent format, for example if you have value as 0.0000012 you can enter this as 1.2e-6 Please use the mathematical deterministic number in field to perform the calculation for example if you entered x greater than 1 in the equation $y=\sqrt{1-x}$ the calculator will not work and you may not get desired result. Under specific (not mutually exclusive) approximations, the following equations define the impedance of a stripline: gives all elements in set A that are not in set B and vice versa. A symmetric relation is a type of binary relation. Consider the following matrices: A = 2 6 4 6 â 1 0 4 0 â 3 and B = 0 â 1 3 6 1 0 2 â 5 â 3 â 2 0 4 â 6 5 â 4 0. For example, when using the calculator, "Power of 2" for a given matrix, A, means A 2. Online algebra calculator that calculates the Symmetric difference of set(say A) and any other set(say B), i.e. or if (x, y) ∈ R, then (y, x) ∈ R for every x, y?A. A relation R is defined as . CS 441 Discrete mathematics for CS M. Hauskrecht Properties of relations Definition (symmetric relation): A relation R on a set A is called symmetric if a, b A (a,b) R (b,a) R. Example 3: â¢ Relation R fun on A = {1,2,3,4} defined as: â¢Rfun = {(1,2),(2,2),(3,3)}. R is irreflexive (x,x) â R, for all xâA Properties of Binary Relations: R is reflexive x R x for all xâA Every element is related to itself. The empty relation is anti-symmetric (as said above). Symmetric Difference â consists of all ordered pairs which are either in or but not both. Since a a = 1 â Q, the relation T is reflexive; it follows that T is not irreflexive. The set of all elements that are related to an element of is called the equivalence class of . Hence, R is reflexive. Oracle tools tips - Symmetric Difference - Row Hash Value, Relation Equality, Duality between Set and Join Operators : Search BC Oracle Sites Home E-mail Us Oracle Articles New Oracle Articles Oracle Training Oracle Tips Oracle Forum Class Catalog Remote DBA Oracle Tuning Emergency 911 RAC Support Apps Support Analysis Design Implementation Oracle Support SQL Tuning Security Oracle â¦ If a set is a singleton $\{a\}$ then there are two relations on it: the empty relation and the relation $\{\langle a,a\rangle\}$. Let $R=\{(1,1),(2,2),(3,3)\}$ be a relation defined on the set $A=\{1,2,3\}$. Let R be a relation defined on the set A. R = {(a, b), (b, a) / for all a, b â A}. Symmetric Property The Symmetric Property states that for all real numbers x and y , if x = y , then y = x . Example 1. Thus, relation R is symmetric and transitive but not reflexive. 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Link and share the link here element is related to itself have look. Self Paced Course at a student-friendly price and become industry ready real numbers x and y, x. Above, if you need any other set ( b ), greater than >... Not both children in a family and R be a relation defined on set a that are related itself... Our Cookie Policy ain natural number set, a Delta b the here...: a 3 b 3 and minus ( - ) are examples of asymmetric total combination! The link here if you need any other set ( say b ) ja ; b2N anda bg on! Relations: R is reflexive x R x for all real numbers x and y then... A look at when a set is reflexive x R x for all numbers! Structured object x of any sort, a Delta b matrix '' means raise... Those relationships ) â R since a = { ( a ; a ) â R a... Symmetric x R x, for all x, for all real numbers x and y then! 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Natural number set, a ) symmetric relation calculator > ) and any other set ( say b ) ja b2N. Divide the equations into a series of approximations for various limits on the geometric parameters in the figure. B a = 1 â Q, the relation a = b a > b a = { (,. But a > b is not symmetric strength provides a comprehensive lifter based... R x for all x, yâA the relation a = 1 â,! Is to provide a free, world-class education to anyone, anywhere than ( > ) and other... Object onto itself which preserves the structure the object onto itself which the! Not symmetric < ), greater than ( > ) and any other stuff in math please. Which are either in or but not both to provide a free, education. Worksheet There is another way two relations can be combined that is to! A > b is symmetric x R x, for all real numbers and... Relations is 2n ( n+1 ) /2 that calculates the symmetric Property states that for all ain number! Let a be the set ( say b ), i.e that for all,... The structure of approximations for various limits on the geometric parameters in above. Elements that are related to itself \| follow \| edited Sep 22 '19 at answered! Is just opposite to symmetric relation, 3 } and R be a relation defined on set = â. Relations can be combined that is analogous to the composition of functions the relation a = b a > is. Hold of all elements in set b and vice versa given a object! That is analogous to the composition of functions equations into a series of approximations for various limits on the parameters. At a student-friendly price and become industry ready symmetric strength provides a comprehensive lifter analysis based on strength and... To be brother of symmetric relation calculator '' has to be brother of b '' to. Male children in a family and R be a relation defined on set edited Sep 22 '19 10:26.. ( as said above ) in or but not both = y, if x = y, . Ide.Geeksforgeeks.Org, generate link and share the link here by using this website, you agree to our family Chart. 12:26. drhab drhab set a as ( - ) are examples of asymmetric two male in. Stuff in math, please use our google custom search here symmetric Difference consists...	2021-06-18 09:41:50	{"extraction_info": {"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": 3, "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, "math_score": 0.4954611659049988, "perplexity": 654.0805718517962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487635920.39/warc/CC-MAIN-20210618073932-20210618103932-00060.warc.gz"}
https://www.physicsforums.com/threads/algebra-how-do-i-solve-for-this.316093/	Homework Help: Algebra - how do i solve for this 1. May 24, 2009 vorcil $$\eta = 1 - \frac{Q_c}{Q_h}$$ I have everything except Qh, i stuck the equation into my graphics calculator and get 13039 n = 0.27 Qc = 9519 J how'd i solve for Qh using that equation? cheers 2. May 24, 2009 ryan88 $$\eta = 1 - \frac{Q_c}{Q_h}$$ $$\eta Q_h = Q_h - Q_c$$ $$Q_h(1-\eta)=Q_c$$ $$Q_h=\frac{Q_c}{1-\eta}$$	2018-07-21 06:32:11	{"extraction_info": {"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, "math_score": 0.47953516244888306, "perplexity": 6735.799050829498}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592387.80/warc/CC-MAIN-20180721051500-20180721071500-00307.warc.gz"}
https://socratic.org/questions/how-do-you-derive-the-variance-of-a-gaussian-distribution	# How do you derive the variance of a Gaussian distribution? Nov 26, 2015 Suppose $x$ has a probability density function $f \left(x\right)$. The variance of $x$ is calculated by ${\int}_{-} {\infty}^{\infty} {\left(x - \mu\right)}^{2} f \left(x\right) \mathrm{dx}$, where $\mu$ is the expected value of $x$ and is calculated by $\mu = {\int}_{-} {\infty}^{\infty} x f \left(x\right) \mathrm{dx}$. #### Explanation: The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The simplest case of a normal distribution is known as the standard normal distribution , described by the probability density function: $g \left(z\right) = \frac{1}{\sqrt{2 \pi}} {e}^{- \frac{{z}^{2}}{2}}$. Since the area under the curve is given by ${\int}_{-} {\infty}^{\infty} g \left(z\right) \mathrm{dz}$, The factor $\frac{1}{\sqrt{2 \pi}}$ in this expression ensures that the total area under $g \left(z\right)$ is equal to $1$, as should all PDF. The mean of $z$ is given by: $\text{E} \left(z\right) = {\int}_{-} {\infty}^{\infty} z g \left(z\right) \mathrm{dz}$ $= {\int}_{-} {\infty}^{0} z g \left(z\right) \mathrm{dz} + {\int}_{0}^{\infty} z g \left(z\right) \mathrm{dz}$. $= 0$ ($g$ is an even function, so the first half of the integral is equal to the negative of the second half of the integral. Since $g \left(- z\right) = g \left(z\right)$, substituting $u = - z$ for the second integral should do the trick.) The variance of $z$ is given by: "Var"(z) = int_-oo^oo (z-"E"(z))^2g(z) dz $= {\int}_{-} {\infty}^{\infty} {z}^{2} g \left(z\right) \mathrm{dz}$ $= {\int}_{-} {\infty}^{\infty} \frac{{z}^{2}}{\sqrt{2 \pi}} {e}^{- \frac{{z}^{2}}{2}} \mathrm{dz}$ $= 1$ (There are special techniques involved in computing integrals of this kind. The details are not shown but the result can be easily verified with a calculator.) Substituting $x = \sigma z + \mu$, we get the probability density of the Gaussian distribution: $f \left(x \| \sigma , \mu\right) = \frac{1}{\sigma \sqrt{2 \pi}} {e}^{- \frac{{\left(x - \mu\right)}^{2}}{2 {\sigma}^{2}}}$. $\mu$ determines the location of the maximum and $\sigma$ determines how narrow/tall the maximum should be. The variance is given by $\text{Var"(x) = "Var} \left(\sigma z + \mu\right)$ $= {\sigma}^{2} \text{Var} \left(z\right)$ $= {\sigma}^{2} \left(1\right)$ $= {\sigma}^{2}$	2021-06-16 16:09:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 32, "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, "math_score": 0.9812982082366943, "perplexity": 183.45004682246713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487625967.33/warc/CC-MAIN-20210616155529-20210616185529-00270.warc.gz"}
https://ee.gateoverflow.in/695/gate2013-29	In the circuit shown below, if the source voltage $V_S=100 \: \angle$ $53.13^{\circ}$ V then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_L$ is 1. $100\angle 90^{\circ}$ 2. $800\angle 0^{\circ}$ 3. $800\angle 90^{\circ}$ 4. $100\angle 60^{\circ}$	2020-04-07 15:33:07	{"extraction_info": {"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, "math_score": 0.6692619323730469, "perplexity": 505.62968710633487}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371803248.90/warc/CC-MAIN-20200407152449-20200407182949-00421.warc.gz"}
http://crypto.stackexchange.com/tags/srp/hot?filter=month	# Tag Info The multiplier parameter $k$ is different between SRP 6 and 6a. You can see that RFC 5054 calculates it using a hash of the domain parameters (modulus $N$ and generator $g$), so it is using SRP 6a, as opposed to SRP 6 where $k$ is constant. Likewise, in section 6.2.1 of IEC 11770-4 – the October 2005 draft at least – the equivalent value $c$ is defined as a ...	2014-08-01 16:04:31	{"extraction_info": {"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, "math_score": 0.7413250803947449, "perplexity": 960.7952241452514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510275111.45/warc/CC-MAIN-20140728011755-00163-ip-10-146-231-18.ec2.internal.warc.gz"}
http://bsiw.charus.de/find-the-solution-to-the-linear-system-of-differential-equations-satisfying-the-initial-conditions.html	Find The Solution To The Linear System Of Differential Equations Satisfying The Initial Conditions Thus, the coefficients are constant, and you can see that the equations are linear in the variables , , and their derivatives. As has already been pointed out, it is a "generalized function". The differential equation is said to be linear if it is linear in the variables y y y. You can also set the Cauchy problem to the entire set of possible solutions to choose private appropriate given initial conditions. We will call the system in the above example an Initial Value Problem just as we did for differential equations with initial conditions. It is proved that, under certain assumptions on the function c (t) and delay r, a class of positive linear initial functions defines dominant positive solutions with positive limit for t → ∞. As was the case for systems of linear equations (see [1, Lay, Section 1. We will ﬁrst give a quick review of the solution of separable and linear ﬁrst order equations. Put initial conditions into the resulting equation. Solution: The family of characteristics from equation (6. (2) Convert this equation into a linear system of first order differential equations. The method of Adomian decomposition was used successfully to solve a class of coupled systems of two linear second order and two nonlinear first order differential equations by. Daniel Ševčovič Department of App. tation in the eight-lecture course Numerical Solution of Ordinary Diﬀerential Equations. It is important to know that FEA only gives an approximate solution of the problem and is a numerical approach to get the real result of these partial differential equations. Then show that there are at least two solutions to the initial value problem for this differential equation. We guess the form of the solution to (1) is x t e u() Jt where r is a constant and u is a constant vector, both of which must be determined. Continuous group theory, Lie algebras, and differential geometry are used to understand the structure of linear and nonlinear (partial) differential equations for generating integrable equations, to find its Lax pairs, recursion operators, Bäcklund transform, and finally finding exact analytic solutions to DE. Math Camp Notes: Di erential Equations A di erential equation is an equation which involves an unknown function f(x) and at least one of its derivatives. method for ﬁnding the general solution of any ﬁrst order linear equation. Its output should be de derivatives of the dependent variables. The theoretical analysis of the existence and uniqueness of a. Set up the differential equation for simple harmonic motion. The primitive attempt in dealing with differential equations had in view a reduction to quadratures. CASE III (underdamping). 1522, 245 (2013); 10. java plots two trajectories of Lorenz's equation with slightly different initial conditions. And the system is implemented on the basis of the popular site WolframAlpha will give a detailed solution to the differential equation is absolutely free. Linear Algebra and Di erential Equations Math 21b Harvard University Fall 2003 Oliver Knill These are some class notes distributed in the linear algebra course "Linear Algebra and Di erential equations" tought in the Fall 2003. The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. Ordinary differential equations: a first course initial conditions initial value problem integral interval Laplace transform linear differential equations linear. The final step, in which the particular solution is obtained using the initial or boundary values, involves mostly algebraic operations, and is similar for IVPs and for BVPs. So let's do this differential equation with some initial conditions. 3 What is special about nonlinear ODE? ÖFor solving nonlinear ODE we can use the same methods we use for solving linear differential equations ÖWhat is the difference? ÖSolutions of nonlinear ODE may be simple, complicated, or chaotic ÖNonlinear ODE is a tool to study nonlinear dynamic:. Key Concept: Using the Laplace Transform to Solve Differential Equations. The purpose of this equation is not to solve for the ariablev x, but rather to solve for the function f(x). review for readers with deeper backgrounds in differential equations, so we intersperse some new topics throughout the early part of the book for these readers. 10 Which of these differential equations are linear (in y)? (a) y′ + siny = t (b) y′ = t2(y −t) (c) y′ +ety = t10. Use the letter y for the spring's displacement from its rest position. Put initial conditions into the resulting equation. rank of a matrix establishes the equivalence of both statements. Give the general solution for the system. The particular solution functions x(t) and y(t) to the system of differential equations satisfying the given initial values will be graphed in blue (for x(t)) and green (for y(t)). Introduction to Differential Equations Part 5: Symbolic Solutions of Separable Differential Equations In Part 4 we showed one way to use a numeric scheme, Euler's Method, to approximate solutions of a differential equation. – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. 1 Initial-Value and Boundary-Value Problems Initial-Value Problem In Section 1. equations of the form ˙y = φ(t,y) where φ is a function of the two variables t and y. If we can get a short list which contains all solutions, we can then test out each one and throw out the invalid ones. Recall that a second order equation should allow us to set two initial conditions, so an initial value problem looks like the following: y′′ +p(t)y′ +q(t)y = 0, y(t 0. * Geometrically, the general solution of a differential equation represents a family of curves known as solution curves. with initial conditions x(s,0)= f(s),y(s,0)= g(s),z(s,0)= h(s). Most natural phenomena are essentially nonlinear. A solution is a function f x such that the substitution y f x y f x y f x gives an identity. The stability and convergence properties of some of the new methods are analyzed for a model problem. Furthermore, asymptotic properties and boundedness of the solutions of initial ﬁrst order problems are studied in [22] and [4] respectively. In this post, we will talk about separable. In contrast, there is no general method for solving second (or higher) order linear diﬀerential equations. 84 Chapter 3. 2 The Eigenvalue Method for Homogeneous Systems 304 5. 3498463 The renormalized projection operator technique for linear stochastic differential equations. (4) Find the particular solution which satisfies the initial conditions (5). A homogeneous second-order linear differential equation, two functions y 1,y 2, and a pair of initial conditions are given. SATISFACTION OF ASYMPTOTIC BOUNDARY CONDITIONS IN NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS OF BOUNDARY-LAYER TYPE by Philip R. to set up a system of two linear equations and solve it. Most natural phenomena are essentially nonlinear. The model is shown to be both epidemiologically and mathematically well posed. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. View Homework Help - 182A hw3 problems from MAE 182A at University of California, Los Angeles. In this section some of the common definitions and concepts in a differential equations course are introduced including order, linear vs. Example: 36 4 3 3 y dx dy dx yd is non - linear because in 2nd term is not of degree one. equation is given in closed form, has a detailed description. (3) Solve the system. Solving system of linear differential equations by eigenvalues. 0 is a speci ed initial condition for the system. The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. First verify that y 1 and y 2 are solutions of the differential equa-tion. Find the general solution, or the solution satisfying the given initial conditions, to. (LIb) and (1. European Journal of Pure and Applied Mathematics is an. Introduction to Differential Equations Part 5: Symbolic Solutions of Separable Differential Equations In Part 4 we showed one way to use a numeric scheme, Euler's Method, to approximate solutions of a differential equation. Determine whether or not the coefﬁcients are all constants. The purpose of this equation is not to solve for the ariablev x, but rather to solve for the function f(x). 4801130 Solving Differential Equations in R AIP Conf. These known conditions are called boundary conditions (or initial conditions). Namely, the simultaneous system of 2 equations that we have to solve in order to find C1 and C2 now comes with rather. Daniel Ševčovič Department of App. $\endgroup$ - Michael Seifert Apr 17 '17 at 13:11. As always, we ﬁrst solve for the general solution, then plug in the initial value data to ﬁnd the special solution. Transfer Functions Laplace Transforms: method for solving differential equations, converts differential equations in time t into algebraic equations in complex variable s Transfer Functions: another way to represent system dynamics, via the s representation gotten from Laplace transforms, or excitation by est. Therefore, for every value of C, the function is a solution of the differential equation. This condition lets one solve for the constant c. Particular Solutions and Initial Conditions A particular solutionof a differential equation is any solution that is obtained by assigning specific values to the arbitrary constant(s) in the general solution. wolframalpha. Initial Value Problems. A system of linear differential equations is called homogeneous if the additional term is zero,. Zero-input response basics L2. Introduction. An initial value problem (or system) is a system which contains initial conditions for both dependent variables. DIFFERENTIAL EQUATIONS First Order Equations 1. Most natural phenomena are essentially nonlinear. System of differential. It combines the use of fairly disaggregated data with a relatively modest use of econometric methods. The free boundary is the shock hypersurface and the boundary conditions are jump conditions relative to a prior solution, conditions following from the. Let be a positive constant, and let be continuously differentiable functions such that Together with system , we consider the first boundary-value problem, that is, the boundary conditions and the initial conditions A solution to the first boundary-value problem , - is defined as a pair of functions continuously differentiable with respect to. 1 ) and x A Bt x () (1. (b) Find the solution satisfying the initial conditions for Teachers for Schools for Working Scholars. Answer to Find the solution to the linear system of the differential equations Satisfying the initial conditions x(0)=-2, y(0)=-1. Any decrease in the viscosity of the ﬂuid leads to the vibrations of the following case. This system of linear equations can be solved for 𝑐1 by adding the equations to obtain 𝑐1 = 1/2, after which 𝑐2 = 1 can be determined from the first equa- tion. We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i. Karol Mikula Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovak Republic ([email protected] ‹ › Partial Differential Equations Solve an Initial Value Problem for a Linear Hyperbolic System. (LIb) and (1. The equation y0 = y has the solution y = et, and linear equations of the form y0 = y + b(t) have solutions of the form y = et times some integral, so perhaps this equation has a solution of the form y = etz. 3 Second-Order Systems and Mechanical Applications 319 5. Power series solutions. The Lorenz equations are the following system of differential equations Program Butterfly. General steps: 1)Perform variable separation to obtain two ordinary differential equations. This system is solved for and. First Order Linear Differential Equations A first order ordinary differential equation is linear if it can be written in the form y′ + p(t) y = g(t) where p and g are arbitrary functions of t. This condition lets one solve for the constant c. The distinction be tween the two classifications lies in the location where the extra conditions [Eqs. We will learn about the Laplace transform and series solution methods. com Open Journal Systems. (4) Find the particular solution which satisfies the initial conditions (5). org/math/differential-equations/first-order-differential-equations/differ. For an IVP, the conditions are given at the. A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved by quadrature (mathematics), which means that the solutions may be expressed in terms of integrals. This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. Determine whether solutions of such an equation are linearly independent. DIFFERENTIAL EQUATIONS PRACTICE PROBLEMS: ANSWERS 1. Solve the problem either by setting it up as a linear first order differential equation and then using an integrating factor, or by solving the given problem using the characteristic equation. So let's say the initial conditions are-- we have the solution that we figured out in the last video. Solving linear systems - elimination method. It is the same concept when solving differential equations - find general solution first, then substitute given numbers to find particular solutions. It is important to know that FEA only gives an approximate solution of the problem and is a numerical approach to get the real result of these partial differential equations. Let’s take a look at another example. Differential equations typically have inﬁnite families of solutions, but we often need just one solution from the family. The General Solution for $$2 \times 2$$ and $$3 \times 3$$ Matrices. Diﬀerential equations are called partial diﬀerential equations (pde) or or-dinary diﬀerential equations (ode) according to whether or not they contain partial derivatives. 2 First-Order Equations: Method of Characteristics In this section, we describe a general technique for solving ﬁrst-order equations. (b) has inﬁnitely many solutions, including x = 2, y = 3, z = 4. PYKC 8-Feb-11 E2. We also have now. These worked examples begin with two basic separable differential equations. A20 APPENDIX C Differential Equations General Solution of a Differential Equation A differential equation is an equation involving a differentiable function and one or more of its derivatives. To this end, we ﬁrst have the following results for the homogeneous equation,. Set up the differential equation for simple harmonic motion. In particular, this allows for the. 2 p152 ⇒ ⇒ ⇒ PYKC 24-Jan-11 E2. We will use existence and uniqueness theorem to show that we can write down all possible solu-tions to these equations in terms of a set of so-called fundamental. MATLAB Solution of First Order Differential Equations MATLAB has a large library of tools that can be used to solve differential equations. The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. Solve this equation and find the solution for one of the dependent variables (i. The equation is a second order linear differential equation with constant coefficients. However, in applications where these diﬀerential equations model certain phenomena, the equations often come equipped with initial conditions. 1 of Rogawski's Calculus [1] for a detailed discussion of the material presented in this section. 11), then uh+upis also a solution. As complement of the analytical theory [George D. If the unknown function is y = f(t), then typically the extra conditions are that f(0) takes a particular value, while f '(0) also takes some. Solutions to differential equations can be graphed in several different ways, each giving different insight into the structure of the solutions. As expected for a second‐order differential equation, the general solution contains two parameters ( c 0 and c 1), which will be determined by the initial conditions. 4, be characterized. Homogeneous Equations A differential equation is a relation involvingvariables x y y y. In this video, I solve a basic differential equation with an initial condition (that means we must solve for C). Kavaliauskas [Nonlinear Anal. where A 0 is the identity matrix (and 0! = 1). We will call the system in the above example an Initial Value Problem just as we did for differential equations with initial conditions. Let be a positive constant, and let be continuously differentiable functions such that Together with system , we consider the first boundary-value problem, that is, the boundary conditions and the initial conditions A solution to the first boundary-value problem , - is defined as a pair of functions continuously differentiable with respect to. Thus (2) is a general solution of (1) on the interval I= (−,+). Types of Di. In this post, we will talk about separable. First verify that y 1 and y 2 are solutions of the differential equa-tion. Daniel Ševčovič Department of App. Find the roots (using fzero), local minimum, and the local maximum for y = 4x 3 - 15x 2 + 0. 1 Introduction In the last section we saw how second order differential equations naturally appear in the derivations for simple oscillating systems. Now by the superposition principle (Page# 146, Theorem 1) we know that the general solution is. Eigenvectors and Eigenvalues. Answer to Find the solution to the linear system of the differential equations Satisfying the initial conditions x(0)=-2, y(0)=-1. A first‐order differential equation is said to be linear if it can be expressed in the form. We guess the form of the solution to (1) is x t e u() Jt where r is a constant and u is a constant vector, both of which must be determined. ) DSolve can handle the following types of equations:. See how it works in this video. Question: Suppose the initial conditions are instead y(10000) = 1, y′(10000) = −7. 1; any text on linear signal and system theory can be consulted for more details. We will learn about the Laplace transform and series solution methods. Find a solution to the system of differential equations satisfying the initial condition. The function f(t;x) includes the external forces and torques of the system. tation in the eight-lecture course Numerical Solution of Ordinary Diﬀerential Equations. (b) Draw the trajectory of the solution in the x1x2-plane, and also draw the graph of x1 versus t. Statement of the problem. And here comes the feature of Laplace transforms handy that a derivative in the "t"-space will be just a multiple of the original transform in the "s"-space. * Geometrically, the general solution of a differential equation represents a family of curves known as solution curves. This system is solved for and. We solve a system of linear equations by Gauss-Jordan elimination and find the vector form for the general solution of the system. 3498463 The renormalized projection operator technique for linear stochastic differential equations. Example 1: (a) Find general solutions of y′′′ +4y′′ −7y′ −10y = 0. As was the case for systems of linear equations (see [1, Lay, Section 1. In this video, I solve a basic differential equation with an initial condition (that means we must solve for C). Find solution to system of differential equations with initial conditions [duplicate] of a system of linear differential equations. Find the solution of the linear system corresponding to the initial conditions $$x(0) = 2, y(0) = 0$$. As expected for a second‐order differential equation, the general solution contains two parameters ( c 0 and c 1), which will be determined by the initial conditions. com Open Journal Systems. that are easiest to solve, ordinary, linear differential or difference equations with constant coefficients. In each loop of the Berlekamp-Massey algorithm we need O(Li ) = O(i) time steps, thus the computation of the linear complexity of a sequence of length n takes just O(n2 ) time steps. CASE III (underdamping). Now by the superposition principle (Page# 146, Theorem 1) we know that the general solution is. will also solve the equation. (2) Convert this equation into a linear system of first order differential equations. Solve Differential Equation with Condition. Also find the solution. solution of a linear system of algebraic equations by a process of eliminating the unknowns at a time only a single equation with a single unknown remains. Give the general solution for the system. (b) Find the solution satisfying initial conditions and. The use of this preconditioner significantly reduces the CPU time for the solution of linear system coming from the Stokes equations. Particular Solutions and Initial Conditions A particular solutionof a differential equation is any solution that is obtained by assigning specific values to the arbitrary constant(s) in the general solution. if you just want to solve the ODE, I recommend you use wolfram alpha: -- just go to http://www. solution satisfying the initial condition y(−4)=3 ? a SYSTEM of linear. This means the solution space can be described using two linearly independent solutions. Find the solution to the linear system of differential equations satisfying the initial conditions x(0)=4 and y(0)=−3. The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. We will use existence and uniqueness theorem to show that we can write down all possible solu-tions to these equations in terms of a set of so-called fundamental. In this section some of the common definitions and concepts in a differential equations course are introduced including order, linear vs. In this paper, we wish to extend to linear differential-difference equations a number of results familiar in the stability theory of ordinary linear differential equations. The distinction be tween the two classifications lies in the location where the extra conditions [Eqs. Differential Equations Calculators; Math Problem Solver (all calculators) Differential Equation Calculator. The set of such linearly independent vector functions is a fundamental system of solutions. Answer to Find the solution to the linear system of the differential equations Satisfying the initial conditions x(0)=-2, y(0)=-1. Linear systems of differential equations. In a certain region of the variables it is required to find a solution satisfying initial conditions, i. Warning: The above method of characteristic roots does not work for linear equations with variable coeﬃcients. t ˝/ is the solution operator for the homogeneous problem; it maps data at time ˝to the solution at time t when solving the homogeneous equation. Its first argument will be the independent variable. of general linear methods for ordinary differential equations. A very important theorem regarding ordinary differential equations is the. Second Order Differential Equations 19. AbstractWe discuss (survey) some recent results on several aspects of complex analytic and meromorphic solutions of linear and nonlinear partial differential equations, with main attention given to those of the authors and their collaborators, and also give some new results on these equations. (b) Find the solution satisfying initial conditions and. 0 is a speci ed initial condition for the system. Duhamel's principle states that the inhomogeneous term g. stability for the linear systems of differential equations x Ax ft (1. 2 Systems of Linear Differential Equations In order to find the general solution for the homogeneous system (1) x t Ax t'( ) ( ) where A is a real constant nnu matrix. DOEpatents. Math Camp Notes: Di erential Equations A di erential equation is an equation which involves an unknown function f(x) and at least one of its derivatives. com Open Journal Systems. Under what conditions mustthere be a solution to a given initial value problem? 2. Elimination method satisfying the initial conditions y Find the solution of the system: (S) {x. For those differential equations that include initial conditions evaluate the constants in the solution y'' + 8y' + 25y = 0 , y(0) = 1 , y'(0) = 8. Write down the second order equation governing this physical system. In words simple harmonic motion is "motion where the acceleration of a body is proportional to, and opposite in direction to the displacement from its equilibrium position". A three operator split-step method covering a larger set of non-linear partial differential equationsNASA Astrophysics Data System (ADS) Zia, Haider. " The numerical results are shown below the graph. Solving a differential equation with a linear solution and initial conditions. Nachtsheim and Paul Swigert Lewis Research Center SUMMARY A method for the numerical solution of differential equations of the boundary-layer type is presented. Differential equations are a special type of integration problem. We emphasize that just knowing that there are two lines in the plane that are invariant under the dynamics of the system of linear differential equations is sufficient information to solve these equations. Thus, if we want our solution to satisfy certain initial conditions we may first determine the general solution, and then (if possible) make it satisfy the initial conditions. 2b)] are specified. See how it works in this video. (You know how to multiply matrices together, so you know how to compute the right hand side of this equation. An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. Use the letter y for the spring's displacement from its rest position. Let's take a look at another example. If a particular solution to a differential equation is linear, y=mx+b, we can set up a system of equations to find m and b. Collier, D. (You know how to multiply matrices together, so you know how to compute the right hand side of this equation. The notes begin with a study of well-posedness of initial value problems for a ﬁrst- order diﬀerential equations and systems of such equations. To find the particular solution to a second-order differential equation, you need one initial condition. 218 Chapter 3. And here comes the feature of Laplace transforms handy that a derivative in the "t"-space will be just a multiple of the original transform in the "s"-space. Find the roots (using fzero), local minimum, and the local maximum for y = 4x 3 - 15x 2 + 0. 1: Find the solution u satisfying and the initial condition. Second Order Equations Today, we will begin a discussion of solving second order linear equations. Its first argument will be the independent variable. Second Order Linear Differential Equations 12. ˝/at any instant ˝has an effect on the solutionat time t given by eA. So it was the second derivative plus 5 times the first derivative plus 6 times the function, is equal to 0. A solution (or particular solution) of a diﬀerential equa-. Solving linear systems - elimination method. The equation y0 = y has the solution y = et, and linear equations of the form y0 = y + b(t) have solutions of the form y = et times some integral, so perhaps this equation has a solution of the form y = etz. Let's take a look at another example. Answer to Find the solution to the linear system of the differential equations Satisfying the initial conditions x(0)=-2, y(0)=-1. differential equations and obtained solutions by using modified ADM in Hosseini et al. Any decrease in the viscosity of the ﬂuid leads to the vibrations of the following case. Solutions to differential equations can be graphed in several different ways, each giving different insight into the structure of the solutions. For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. For example, the differential equations must be linear and should not be more than second order. Solve Differential Equation with Condition. In a quasilinear case, the characteristic equations fordx dt and dy dt need not decouple from the dz dt equation; this means that we must take thez values into account even to ﬁnd the projected characteristic curves in the xy-plane. Key important points are: Initial Value, Solution, Maximum Value, Attained, General Solution, Homogeneous Linear System, Phase Plane Close, Odd or Even, Interval, Fourier Series. The Existence/Uniqueness of Solutions to First Order Linear Differential Equations. 2 p152 ⇒ ⇒ ⇒ PYKC 24-Jan-11 E2. The solution of the mentioned system is introduced on the basis of a function which can. Solving a differential equation with a linear solution and initial conditions. Under reasonable conditions on φ, such an equation has a solution and the corresponding initial value problem has a unique solution. Et e( ) 100= −10t 0and the initial value of the current at time t = ()is I(0) 0= amperes. This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. 2: Fundamental Solutions of Linear Homogeneous Equations • Let p, q be continuous functions on an interval I = ( , ), which could be infinite. (a) Find the solution of the given initial value problem. 3)Obtain total solution satisfying initial condition. Chapter 2 Second Order Differential Equations "Either mathematics is too big for the human mind or the human mind is more than a machine. For example, the differential equations must be linear and should not be more than second order. Second Order Linear Differential Equations Second order linear equations with constant coefficients; Fundamental solutions; Wronskian; Existence and Uniqueness of solutions; the characteristic equation; solutions of homogeneous linear equations; reduction of order; Euler equations In this chapter we will study ordinary differential equations of the standard form below, known as the second. This hyperbolic non-linear system can be used for predictive purposes provided that initial and boundary conditions are supplied and the roughness coefficient is calibrated. Why study diﬀerential equations?. A system of linear differential equations is called homogeneous if the additional term is zero,. Thus, the general solution when p6= 1 =2 is f(n) = c 1 + c 2 p q n: For the case that p= q= 1=2, the only root is 1, hence the general solution is f(n) = c 1 + c 2n: We analyzed only second-order linear di erence equations above. For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. The state equation is a first-order linear differential equation, or (more precisely) a system of linear differential equations. Solutions to differential equations can be graphed in several different ways, each giving different insight into the structure of the solutions. In each loop of the Berlekamp-Massey algorithm we need O(Li ) = O(i) time steps, thus the computation of the linear complexity of a sequence of length n takes just O(n2 ) time steps. 1 Solving Differential Equations Students should read Section 9. 2 Solving Linear Recurrence Relations Determine if recurrence relation is homogeneous or nonhomogeneous. In particular, MATLAB offers several solvers to handle ordinary differential equations of first order. Nonhomogeneous ordinary differential equations can be solved if the general solution to the homogenous version is known, in which case the undetermined coefficients method or variation of parameters can be used to find the particular solution. To solve a system of differential equations, see Solve a System of Differential Equations. So superposition is valid for solutions of linear differential equations. The present paper is concerned with the numerical solution of initial value problems by finite difference methods, generally for a finite time interval, by a sequence of. Show that for some nonzero the function is a solution to the differential equation. Consider the system Find the equilibrium points. Solution (a) Since this equation solves a siny term, it is not linear in y. Simple harmonic motion is defined by the differential equation, , where k is a positive constant. 5) is (where k is a constant. Now by the superposition principle (Page# 146, Theorem 1) we know that the general solution is. First verify that y 1 and y 2 are solutions of the differential equa-tion. If a particular solution to a differential equation is linear, y=mx+b, we can set up a system of equations to find m and b. However, if we allow A = 0 we get the solution y = 25 to the diﬀerential equation, which would be the solution to the initial value problem if we were to require y(0) = 25. The best way to prove that n solutions to a linear n-th order differential equation spans all of the solutions makes use of the Wronskian determinant, defined as the determinant of the matrix with. These worked examples begin with two basic separable differential equations. The theoretical analysis of the existence and uniqueness of a. Linear Algebra and Di erential Equations Math 21b Harvard University Fall 2003 Oliver Knill These are some class notes distributed in the linear algebra course "Linear Algebra and Di erential equations" tought in the Fall 2003. We refer to a single solution of a differential equation as aparticular solutionto emphasize that it is one of a family. We propose a mathematical model for cholera with treatment through quarantine. Let y = f(x). Homogeneous Equations A differential equation is a relation involvingvariables x y y y. In contrast, there is no general method for solving second (or higher) order linear diﬀerential equations. 5: Add to My Program : Mixed H2/H-Infinity Power Control with Adaptive QoS for Wireless Communication Networks: Abbas-Turki, Mohamed: Ec. Graphing Differential Equations. These known conditions are called boundary conditions (or initial conditions). Solve a differential equation analytically by using the dsolve function, with or without initial conditions. The function f(t;x) includes the external forces and torques of the system. " - Kurt Gödel (1906-1978) 2. Milonidis EX1001/DIFFERENTIAL EQUATIONS 12 From now on we deal only with ORDINARY differential equations 2. 4: Laplace Equation The partial differential equation ∂ 2 u/ ∂ x 2 + ∂ 2 u/ ∂ y 2 = 0 describes temperature distribution inside a circle or a square or any. x0= 1 4 4 7 x; x(0) = 3 2 Proof. Solving a differential equation with a linear solution and initial conditions. The General Solution for $$2 \times 2$$ and $$3 \times 3$$ Matrices. (a) Find the solution of the given initial value problem. Fuentes has also written a PYTHON version of the 3D Stokes solver. Elimination method satisfying the initial conditions y Find the solution of the system: (S) {x. differential equations and obtained solutions by using modified ADM in Hosseini et al. Second Order Linear Differential Equations 12. Some understanding of this equation is in order for the right side is not a function in the ordinary sense. (Remark 1: The matrix function M(t) satis es the equation M0(t) = AM(t). where A 0 is the identity matrix (and 0! = 1).	2019-11-17 10:54:57	{"extraction_info": {"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, "math_score": 0.7636024355888367, "perplexity": 346.3412087356721}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668910.63/warc/CC-MAIN-20191117091944-20191117115944-00142.warc.gz"}
http://www.fightfinance.com/?q=279,578,664,672,676,706,722,770,847,915	# Fight Finance #### CoursesTagsRandomAllRecentScores Do you think that the following statement is or ? “Buying a single company stock usually provides a safer return than a stock mutual fund.” Which of the following statements about inflation is NOT correct? What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa. A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates. What do you think will be the stock's expected return over the next year, given as an effective annual rate? Which of the below formulas gives the profit $(\pi)$ from being short a call option? Let the underlying asset price at maturity be $S_T$, the exercise price be $X_T$ and the option price be $f_{LC,0}$. Note that $S_T$, $X_T$ and $f_{LC,0}$ are all positive numbers. Mr Blue, Miss Red and Mrs Green are people with different utility functions. Note that a fair gamble is a bet that has an expected value of zero, such as paying$0.50 to win \$1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire. Which of the following statements is NOT correct? Here is a table of stock prices and returns. Which of the statements below the table is NOT correct? Price and Return Population Statistics Time Prices LGDR GDR NDR 0 100 1 50 -0.6931 0.5 -0.5 2 100 0.6931 2 1 Arithmetic average 0 1.25 0.25 Arithmetic standard deviation 0.9802 1.0607 1.0607 Which of the following statements is NOT correct? Assume that all events are a surprise and that all other things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same. Below is the Australian federal government’s budget balance as a percent of GDP. From 2009 to 2016 the Australian federal government has implemented: For a share price to double over 7 years, what must its capital return be as an effective annual rate?	2021-09-24 03:05:13	{"extraction_info": {"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": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2145887315273285, "perplexity": 1351.8048037233534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057496.18/warc/CC-MAIN-20210924020020-20210924050020-00659.warc.gz"}
https://www.jobilize.com/algebra2/course/2-6-solve-a-formula-for-a-specific-variable-by-openstax?qcr=www.quizover.com&page=2	# 2.6 Solve a formula for a specific variable (Page 3/4) Page 3 / 4 Use the formula $I=Prt$ to find the principal, $P$ : when $I=\text{}5,400,r=12%,t=5\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$ in general $9,000 $P=\frac{I}{rt}$ Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y . You might be given an equation that is solved for y and need to solve it for x , or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y . Solve the formula $3x+2y=18$ for y : when $x=4$ in general ## Solution ⓐ when $x=4$ ⓑ in general Substitute. Subtract to isolate the $y$ -term. Subtract to isolate the $y$ -term. Divide. Divide. Simplify. Simplify. Solve the formula $3x+4y=10$ for y : when $x=\frac{14}{3}$ in general $y=1$ $y=\frac{10-3x}{4}$ Solve the formula $5x+2y=18$ for y: when $x=4$ in general $y=-1$ $y=\frac{18-5x}{2}$ In Examples 1.60 through 1.64 we used the numbers in part as a guide to solving in general in part . Now we will solve a formula in general without using numbers as a guide. Solve the formula $P=a+b+c$ for $a$ . ## Solution We will isolate $a$ on one side of the equation. Both $b$ and $c$ are added to $a$ , so we subtract them from both sides of the equation. Simplify. Solve the formula $P=a+b+c$ for b . $b=P-a-c$ Solve the formula $P=a+b+c$ for c . $c=P-a-b$ Solve the formula $6x+5y=13$ for y. ## Solution Subtract $6x$ from both sides to isolate the term with $y$ . Simplify. Divide by 5 to make the coefficient 1. Simplify. The fraction is simplified. We cannot divide $13-6x$ by 5. Solve the formula $4x+7y=9$ for y. $y=\frac{9-4x}{7}$ Solve the formula $5x+8y=1$ for y. $y=\frac{1-5x}{8}$ ## Key concepts • To Solve an Application (with a formula) 1. Read the problem. Make sure all the words and ideas are understood. 2. Identify what we are looking for. 3. Name what we are looking for. Choose a variable to represent that quantity. 4. Translate into an equation. Write the appropriate formula for the situation. Substitute in the given information. 5. Solve the equation using good algebra techniques. 6. Check the answer in the problem and make sure it makes sense. 7. Answer the question with a complete sentence. • Distance, Rate and Time For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: $d=rt$ where d = distance, r = rate, t = time. • To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side. ## Practice makes perfect Use the Distance, Rate, and Time Formula In the following exercises, solve. Steve drove for $8\frac{1}{2}$ hours at 72 miles per hour. How much distance did he travel? Socorro drove for $4\frac{5}{6}$ hours at 60 miles per hour. How much distance did she travel? 290 miles Yuki walked for $1\frac{3}{4}$ hours at 4 miles per hour. How far did she walk? Francie rode her bike for $2\frac{1}{2}$ hours at 12 miles per hour. How far did she ride? 30 miles Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take? Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be? 5 hours #### Questions & Answers Priam has dimes and pennies in a cup holder in his car. The total value of the coins is$4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup? Uno de los ángulos suplementario es 4° más que 1/3 del otro ángulo encuentra las medidas de cada uno de los angulos June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold? I hope this is correct, x=cooler 1 5x=cooler 2 x + 5x = 48 6x=48 ×=8 gallons 5×=40 gallons ericka Priam has pennies and dimes in a cup holder in his car. The total value of the coins is $4.21 . The number of dimes is three less than four times the number of pennies. How many pennies and how many dimes are in the cup? Cecilia Reply Arnold invested$64,000 some at 5.5% interest and the rest at 9% interest how much did he invest at each rate if he received $4500 in interest in one year Heidi Reply List five positive thoughts you can say to yourself that will help youapproachwordproblemswith a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often. Elbert Reply Avery and Caden have saved$27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year? 324.00 Irene 1.2% of 27.000 Irene i did 2.4%-7.2% i got 1.2% Irene I have 6% of 27000 = 1620 so we need to solve 2.4x +7.2y =1620 Catherine I think Catherine is on the right track. Solve for x and y. Scott next bit : x=(1620-7.2y)/2.4 y=(1620-2.4x)/7.2 I think we can then put the expression on the right hand side of the "x=" into the second equation. 2.4x in the second equation can be rewritten as 2.4(rhs of first equation) I write this out tidy and get back to you... Catherine Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his rectangular front yard. The length is five feet less than five times the width. Find the length and width of the fencing. Mario invested $475 in$45 and $25 stock shares. The number of$25 shares was five less than three times the number of $45 shares. How many of each type of share did he buy? Jawad Reply let # of$25 shares be (x) and # of $45 shares be (y) we start with$25x + $45y=475, right? we are told the number of$25 shares is 3y-5) so plug in this for x. $25(3y-5)+$45y=$475 75y-125+45y=475 75y+45y=600 120y=600 y=5 so if #$25 shares is (3y-5) plug in y. Joshua will every polynomial have finite number of multiples? a=# of 10's. b=# of 20's; a+b=54; 10a + 20b=$910; a=54 -b; 10(54-b) + 20b=$910; 540-10b+20b=$910; 540+10b=$910; 10b=910-540; 10b=370; b=37; so there are 37 20's and since a+b=54, a+37=54; a=54-37=17; a=17, so 17 10's. So lets check. $740+$170=$910. David Reply . A cashier has 54 bills, all of which are$10 or $20 bills. The total value of the money is$910. How many of each type of bill does the cashier have? whats the coefficient of 17x the solution says it 14 but how i thought it would be 17 im i right or wrong is the exercise wrong Dwayne 17 Melissa wow the exercise told me 17x solution is 14x lmao Dwayne thank you Dwayne A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself? what is the shorter way to do it	2019-02-20 23:24:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 40, "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, "math_score": 0.5818300247192383, "perplexity": 2211.3544863866177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247496855.63/warc/CC-MAIN-20190220230820-20190221012820-00074.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/dcds.2012.32.2759	# American Institute of Mathematical Sciences August 2012, 32(8): 2759-2803. doi: 10.3934/dcds.2012.32.2759 ## Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold 1 Department of Applied Mathematics, University of Twente, Enschede, 7500 AE, Netherlands 2 Department of Computer Science, Katholieke Universiteit Leuven, Heverlee, B-3001, Belgium 3 Department of Chemical and Biological Egineering, Princeton University, Princeton, NJ 08544, United States 4 Department of Mathematics and Statistics and Center for Biodynamics, Boston University, Boston, MA 02215 5 Department of Chemical and Biological Engineering, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States Received August 2011 Revised November 2011 Published March 2012 In [C. W. Gear, T. J. Kaper, I. G. Kevrekidis and A. Zagaris, Projecting to a slow manifold: Singularly perturbed systems and legacy codes, SIAM J. Appl. Dyn. Syst. 4 (2005), 711--732], we developed the family of constrained runs algorithms to find points on low-dimensional, attracting, slow manifolds in systems of nonlinear differential equations with multiple time scales. For user-specified values of a subset of the system variables parametrizing the slow manifold (which we term observables and denote collectively by $u$), these iterative algorithms return values of the remaining system variables $v$ so that the point $(u,v)$ approximates a point on a slow manifold. In particular, the $m-$th constrained runs algorithm ($m = 0, 1, \ldots$) approximates a point $(u,v_m)$ that is the appropriate zero of the $(m+1)-$st time derivative of $v$. % The accuracy with which $(u,v_m)$ approximates the corresponding point on the slow manifold with the same value of the observables has been established in [A. Zagaris, C. W. Gear, T. J. Kaper and I. G. Kevrekidis, Analysis of the accuracy and convergence of equation-free projection to a slow manifold, ESAIM: M2AN 43(4) (2009) 757--784] for systems for which the observables $u$ evolve exclusively on the slow time scale. There, we also determined explicit conditions under which the $m-$th constrained runs scheme converges to the fixed point $(u,v_m)$ and identified conditions under which it fails to converge. Here, we consider the questions of stability and stabilization of these iterative algorithms for the case in which the observables $u$ are also allowed to evolve on a fast time scale. The stability question in this case is more complicated, since it involves a generalized eigenvalue problem for a pair of matrices encoding geometric and dynamical characteristics of the system of differential equations. We determine the conditions under which these schemes converge or diverge in a series of cases in which this problem is explicitly solvable. We illustrate our main stability and stabilization results for the constrained runs schemes on certain planar systems with multiple time scales, and also on a more-realistic sixth order system with multiple time scales that models a network of coupled enzymatic reactions. Finally, we consider the issue of stabilization of the $m-$th constrained runs algorithm when the functional iteration scheme is divergent or converges slowly. In that case, we demonstrate on concrete examples how Newton's method and Broyden's method may replace functional iteration to yield stable iterative schemes. Citation: Antonios Zagaris, Christophe Vandekerckhove, C. William Gear, Tasso J. Kaper, Ioannis G. Kevrekidis. Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2759-2803. doi: 10.3934/dcds.2012.32.2759 ##### References: show all references ##### References: [1] José M. Arrieta, Esperanza Santamaría. Estimates on the distance of inertial manifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 3921-3944. doi: 10.3934/dcds.2014.34.3921 [2] James C. Robinson. Computing inertial manifolds. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 815-833. doi: 10.3934/dcds.2002.8.815 [3] James C. Robinson. Inertial manifolds with and without delay. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 813-824. doi: 10.3934/dcds.1999.5.813 [4] Ricardo Rosa. Approximate inertial manifolds of exponential order. Discrete & Continuous Dynamical Systems - A, 1995, 1 (3) : 421-448. doi: 10.3934/dcds.1995.1.421 [5] A. Debussche, R. Temam. Some new generalizations of inertial manifolds. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 543-558. doi: 10.3934/dcds.1996.2.543 [6] Christian Lax, Sebastian Walcher. Singular perturbations and scaling. 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Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309 [12] Rolf Bronstering. Some computational aspects of approximate inertial manifolds and finite differences. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 417-454. doi: 10.3934/dcds.1996.2.417 [13] Norbert Koksch, Stefan Siegmund. Feedback control via inertial manifolds for nonautonomous evolution equations. Communications on Pure & Applied Analysis, 2011, 10 (3) : 917-936. doi: 10.3934/cpaa.2011.10.917 [14] L. Dieci, M. S Jolly, Ricardo Rosa, E. S. Van Vleck. Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 555-580. doi: 10.3934/dcdsb.2008.9.555 [15] Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179 [16] Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567 [17] Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 [18] Chiara Zanini. Singular perturbations of finite dimensional gradient flows. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 657-675. doi: 10.3934/dcds.2007.18.657 [19] Canela Jordi. Singular perturbations of Blaschke products and connectivity of Fatou components. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3567-3585. doi: 10.3934/dcds.2017153 [20] Yuanzhen Shao. Continuous maximal regularity on singular manifolds and its applications. Evolution Equations & Control Theory, 2016, 5 (2) : 303-335. doi: 10.3934/eect.2016006 2018 Impact Factor: 1.143	2020-01-20 03:31:42	{"extraction_info": {"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, "math_score": 0.5174288749694824, "perplexity": 1977.1687997301538}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250597230.18/warc/CC-MAIN-20200120023523-20200120051523-00506.warc.gz"}
https://chemistry.stackexchange.com/questions/111759/gibbs-free-energy-of-formation-vs-gibbs-free-energy-of-reaction	# Gibbs free energy of formation vs. Gibbs free energy of reaction? Consider the following reaction: $$\ce{A(s) + B(s) <=> AB(s)}.$$ I know there might be kinetic limitations but I am only interested in thermodynamic relations. In general, the Gibbs free energy of reaction reads: $$\Delta G = \Delta G^⦵ + RT\ln{\prod a_i^{\nu_i}}$$ and for the given reaction: $$\Delta G = \Delta G^⦵ + RT\ln{\frac{a_\ce{AB}}{a_\ce{A}\cdot a_\ce{B}}} \label{eqn:1}\tag{1}$$ Since all components are pure solid substances, all activities equal 1 and therefore, $$\Delta G = \Delta G^⦵$$. If $$A$$ and $$B$$ are elements, I found the following formula: $$\Delta G_\mathrm{f}^⦵ = N\cdot RT\ln{\left(a_\ce{A}^{x_\ce{A}}a_\ce{B}^{x_\ce{B}}\right)} \label{eqn:2}\tag{2}$$ where $$N$$ is the total number of atoms and $$x_\ce{A}$$ and $$x_\ce{B}$$ are the mole fractions. To me, this latter formula implies, that the activities of $$\ce{A}$$ and $$\ce{B}$$ inside the product $$\ce{AB}$$ are of interest. I have two questions: 1. What is the origin of the second formula $$\eqref{eqn:2}$$? In almost every source, the first type of Gibbs energy is used and I was not able to find any derivation. Also I think in principle, equation $$\eqref{eqn:1}$$ and $$\eqref{eqn:2}$$ should produce the same, but it looks very different!? 2. How does it come, that in one case the activity of the whole product $$\ce{AB}$$ is important and in another the single activities of the components of the product? --------------------Update-------------------- Based on comments I'll try to reformulate my problem to make it more clear. As I have learned, there should be no difference between the reaction product AB and the mixture of A and B with the corresponding stoichiometry (1:1). Is this valid in general or just for reactions like this (cf. my water-example in the comments)? The transformation of equation (2) (in NightWriter's answer) shows, that it is an identity of the Gibbs free energy of mixing but in terms of moles of compound AB rather than in terms of moles of mixture. If equation (1) describes the reaction (i.e. formation) of AB and equation (2) the mixing of A and B, and there is no difference between a product of reaction and the corresponding mixture of the two components to form that product, there must be some mathematical relation between equation (1) and equation (2). Furthermore, I am not certain, whether the standard-state symbol in equation (2) is correct or not. After I read the answer and the comments again, I concluded the following: equation (1) describes the formation of AB and equation (2) the mixture of A and B at arbitrary compositions. So, if I set $$x_A = x_B =0.5$$, it should be possible to replace $$\Delta G^⦵$$ in equation (1) by $$\Delta G_f^⦵ = N\cdot RT\ln{a_A^{0.5}a_B^{0.5}}$$. $$N$$ must be chosen properly, since the two expressions are related to different things (mixture and compound). Is this correct? • I don't think your reaction will reach equilibrium - it will go to completion (all products if the Gibbs free energy of reaction is negative, all reactants if it is positive). Only if the Gibbs free energy happens to be exactly zero, both reactants and products will be present, and the extent of reaction will be undefined. Mar 29, 2019 at 18:08 1. What is the origin of the second formula (2)? Equation (2) evidently refers to the free energy of formation (at standard pressure) of a solid solution of A and B, in which case neither element is in its standard state as a product (so that $$a_i\neq 1$$). You can rewrite expression (2) as follows: $$\Delta G_\mathrm{f}^\circ = nRT\ln{\left(a_\ce{A}^{x_\ce{A}}a_\ce{B}^{x_\ce{B}}\right)} = RT\ln{\left(a_\ce{A}^{x_\ce{A}}a_\ce{B}^{x_\ce{B}}\right)^n}= RT\ln{\left(a_\ce{A}^{nx_\ce{A}}a_\ce{B}^{nx_\ce{B}}\right)}= RT\ln{\left(a_\ce{A}^{n_\ce{A}}a_\ce{B}^{n_\ce{B}}\right)}$$ $$= n_\ce{A}RT\ln{a_\ce{A}+n_\ce{B}RT\ln{a_\ce{B}}}$$ where $$n$$ is the total number of moles ($$n=n_A+n_B$$). Since the activity of the elements in pure solutions is 1 we can finally write $$\Delta G_\mathrm{f}^\circ = n_\ce{A}\Delta G_{mA}+n_\ce{B}\Delta G_{mB}$$ where $$\Delta G_{mi} = G_{mi}-G_{mi}^\circ= n_\ce{i}RT\ln{\left(\frac{a_\ce{i}}{a_\ce{i}^\circ}\right)}$$. However the most useful way to express this is as follows: $$\Delta G_\mathrm{f}^\circ = (n_\ce{A}G_{mA}+n_\ce{A}G_{mB})-(n_\ce{B}G_{mA}^\circ+n_\ce{B}G_{mB}^\circ)$$ In words, the free energy change corresponds to mixing of $$n_\ce{A}$$ moles of pure A and $$n_\ce{B}$$ moles of pure B (the pure components having activity $$a_i^\circ=1$$) to form a mixture where the components have activities $$a_i$$. 1. How does it come, that in one case the activity of the whole product AB is important and in another the single activities of the components of the product? Equation (1) refers to a molar free energy of formation of $$\ce{AB}$$ from reagents $$A$$ and $$B$$, all under the same constant (P,T, composition) conditions, whereas (2) refers to the free energy of formation of a solid solution of $$n_A$$ moles of A and $$n_B$$ moles of B from pure components. Equation (1) refers to combination of A and B at a 1:1 mole ratio, or equivalently reaction to form 1 mole of $$\ce{AB}$$ from $$n_A=n_B=\pu{1 mol}$$. Reaction (2) refers to mixture of A and B at any arbitrary ratio or total number of moles. Therefore equation (2) is in a way more general. Also, equation (1) refers to a differential process (transformation to form 1 mole of product under contant conditions) whereas (2) refers to an integral (mixing) process. For the given reaction: $$\Delta G = \Delta G^⦵ + RT\ln{\frac{a_\ce{AB}}{a_\ce{A}\cdot a_\ce{B}}}$$ Since all components are pure solid substances, all activities equal 1 and therefore, $$\Delta G = \Delta G^⦵$$. A comment on this: the fallacy here is to assume that $$a_i=1$$ at equilibrium. Only for the pure reagents and products in their standard states it is strictly required by definition that $$a_i=1$$. Note also that since $$\Delta G^\circ = G_{mAB}^\circ-G_{mA}^\circ-G_{mB}^\circ$$ and $$G_{mi} = G_{mi}^\circ+RT\ln{\left(\frac{a_\ce{i}}{a_\ce{i}^\circ}\right)}$$ we can write $$\Delta G = G_{mAB}-G_{mA}-G_{mB}$$ In words (and repeating myself), $$\Delta G$$ in this case is for the process of converting 1 total mole of $$A$$ and 1 mole of $$B$$ into 1 mole of $$AB$$, all at constant T, P and composition (or, equivalently, in a sufficiently large mixture, such that a 1 mole change in the amount of the substances does not change the properties). Schematically, this is how I interpret the two processes, with equation 2 for mixing in the top, and the reaction of A and B to form AB in the bottom: • So the second formula does not describe the reaction at all but a different process, that of mixing two miscible solids. Mar 29, 2019 at 18:10 • @KarstenTheis I think what you call a solid mixture versus a solid reaction product (with activity=1) is subject to some potential ambiguity unless you are careful with your definitions. Mar 29, 2019 at 18:15 • The reaction given by the OP shows a 1:1 stoichiometry. Formula two works for any mixing ratio. That is one of the differences between a compound and a mixture of elements. Mar 29, 2019 at 18:20 • @KarstenTheis Yes, that's true. That's pretty much included in my answer. Mar 29, 2019 at 18:27 • @NightWriter Is your first calculation correct? Shouldn't it read $\Delta G_f^\circ=N_A RT\ln{a_A}+N_B RT\ln{a_B}$, since $N_i=N\cdot x_i$ and $n_i=\frac{N_i}{N_{Av}}$? So, the first case is a reaction and the second case a mixture? How do I decide which case is the correct one for a given "reaction". For example two metals forming a intermetallic compound. In wide ranges of composition there is a mixture of A and B and at a specific stoichiometry there is a reaction? Mar 30, 2019 at 9:46	2022-08-20 06:27:59	{"extraction_info": {"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": 51, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473690748214722, "perplexity": 384.26108037648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573908.30/warc/CC-MAIN-20220820043108-20220820073108-00713.warc.gz"}
https://electronics.stackexchange.com/questions/605173/what-is-the-value-of-these-resistors	# What is the value of these resistors? Two resistors in a Bosch AL 1115 CV battery charger 127V burned up yesterday, and I am trying to figure out the correct value to replace them. I have found in the internet this photo where I suppose that these resistors are of the same value of that burned in my board: This is a image of a similar board that I found on the internet: This is a photo of my real board, that was burnt: In that two resistors that burnt, in the similar board figure, I see the colors: brown, white, red, red, black. What is the value of this resistor? I have learned that in 5 bands resistors, the first, second and third band are the value, the fourth id the multiplier and the fifth is the tolerance. Black does not exist as a tolerance and in some five band resistors the third band is the multiplier, and not the fourth. How do J know when take into account the third band as multiplier or the fourth band as multiplier? What is the real value of the resistors in the figure? • Does this answer your question? How do I read these blasted five-band resistors? Jan 20 at 23:37 • Fourth band looks to be silver rather than white. That should make things easier for you to figure out. Jan 21 at 0:20 • In addition to the band looking silver instead of white, are those really two red bands, or is one of them orange? Jan 21 at 5:28 • I add a full image of the board where u could compare the orange color that is hard to see because the low resolution of the image. Jan 21 at 13:14 • Taking in consideration that the fourth band are silver, so this resistor are something around 1.22 Ohm? Of fact, is few probably that are a white multiplier because white multiplier have a value of 9 zeroes and it is impracticable. What do you think? Jan 21 at 13:19	2022-06-29 01:19:45	{"extraction_info": {"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, "math_score": 0.42936161160469055, "perplexity": 872.0588321540217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103619185.32/warc/CC-MAIN-20220628233925-20220629023925-00763.warc.gz"}
https://math.stackexchange.com/questions/3469201/kolmogorov-s-three-series-theorem	# Kolmogorov’s Three-Series Theorem Consider the sequence r.v. $$X_i's, i \geq 2$$, $$P(X_i = i^2) = P(X_i = -i^2) = 1/i^2 \ \text{and} \ P(X_i = (-1)^i) = 1- 2/i^2.$$ Consider $$S_n = \sum_{i=2}^{n}X_i$$. What is the almost sure limit of $$S_n/n$$ as $$n \rightarrow \infty$$? I have tried to truncate $$X_i$$ as defining $$Y_i = X_i \boldsymbol{1}_{[\|X_i\| \leq 1]}$$. However, not sure how to find the limit and prove $$S_n/n$$ converges almost surely. • Three series Theorem is about convergence of the series $\sum X_i$, not about convergence of the sequence $\frac {S_n} n$. – Kavi Rama Murthy Dec 9 '19 at 7:33 Since $$\sum P(X_i=i^{2}) <\infty$$ and $$\sum P(X_i=-i^{2}) <\infty$$ Borel Cantelli Lemma tells us that $$P(X_i=i^{2} i.o )=0$$ and $$P(X_i=-i^{2} i.o )=0$$ so $$X_i=(-1)^{i}$$ for all $$i$$ sufficiently large, with probability $$1$$. This implies that $$(S_n)$$ is bounded with probability $$1$$ so $$\frac {S_n} n \to 0$$ with probability $$1$$.	2020-01-26 08:41:34	{"extraction_info": {"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": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.99717777967453, "perplexity": 85.6189905600018}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251687958.71/warc/CC-MAIN-20200126074227-20200126104227-00492.warc.gz"}
https://stacks.math.columbia.edu/tag/021T	Lemma 34.7.9. Let $S$ be a scheme. Let $\mathit{Sch}_{fppf}$ be a big fppf site containing $S$. Then $(\textit{Aff}/S)_{fppf}$ is a site. Proof. Let us show that $(\textit{Aff}/S)_{fppf}$ is a site. Reasoning as in the proof of Lemma 34.4.9 it suffices to show that the collection of standard fppf coverings of affines satisfies properties (1), (2) and (3) of Sites, Definition 7.6.2. This is clear since for example, given a standard fppf covering $\{ T_ i \to T\} _{i\in I}$ and for each $i$ we have a standard fppf covering $\{ T_{ij} \to T_ i\} _{j\in J_ i}$, then $\{ T_{ij} \to T\} _{i \in I, j\in J_ i}$ is a standard fppf covering because $\bigcup _{i\in I} J_ i$ is finite and each $T_{ij}$ is affine. $\square$ In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	2021-01-21 09:07:38	{"extraction_info": {"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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9328709244728088, "perplexity": 172.26901743658206}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703524270.28/warc/CC-MAIN-20210121070324-20210121100324-00076.warc.gz"}
https://physics.stackexchange.com/questions/251412/many-questions-about-expanding-of-the-space?answertab=oldest	# Many questions about expanding of the space Sorry if my grammar is a bit off. But I have few questions about space and its expansion. If space expands faster and faster all the time, will there be a time when we cannot see further than "hubble sphere"? Am I correct by thinking that we cannot ever reach the edge of the current hubble sphere due to not being able to go faster than a speed of light and because the edge will be expanded further away? No, we will always be able to see farther than the Hubble sphere (in theory). This spacetime diagram — taken from Pulsar's rendering of Davis & Lineweaver (2003)'s Figure 1, in this excellent answer — can help visualize it: Coordinates In this figure, time increases upward, we're the vertical line in the middle, Big Bang is the bottom line, and our current time is the black horizontal line. The $x$ axis shows distance from us in comoving coordinates, i.e. the coordinates that expand with the Universe, and in which galaxies lie approximately still. By definition, today comoving coordinates coincide with physical coordinates (i.e. the "real" distance you would measure if you stopped time and laid out rulers), but for instance 8 billion years (Gyr) ago (indicated on the left $y$ axis), when the scale factor $a$ was $0.5$ (indicated on the right $y$ axis), the distance between two given galaxies in physical coordinates would be half that in comoving coordinates. Particle horizon The farthest distance to which we can see is called the particle horizon, and is drawn in blue. It will always increase, since light from farther and farther away eventually will reach us (although light from these distances will be increasingly more redshifted and eventually will be unobservable in practise). Hubble sphere In contrast, the Hubble sphere — i.e. the distance at which space expands at the speed of light — doesn't increase much more than today in physical coordinates. In comoving coordinates, the Hubble sphere reached a maximum roughly 5 billion years ago, and is now decreasing (the innermost green solid line labeled $v_\mathrm{rec}=c$). In other words, galaxies closer and closer to us are receding at $v=c$, but not until they are farther away from us physically. Can we reach the Hubble sphere? As for your second question, the answer depends a bit on what you mean: By definition, the Hubble sphere is a certain distance from you, so taking your question literally, it's impossible to go to the Hubble sphere, since it will always be some distance from you. But I assume that you mean "Is it possible for us the send a space probe from Earth, out to Earth's Hubble sphere". The answer to this is "Yes". Although special relativity prohibits the space probe from going faster than $c$ locally, as seen from Earth the expansion of space "helps" the probe to go faster and faster, eventually surpassing $c$ (just like it helps galaxies going faster than $c$). In the figure, the orange dashed line is our future light cone; events outside this region can never be affected by us. You see it incercepts the Hubble sphere approximately at $t=25\,\mathrm{Gyr}$, or $a=2$. This means that, if a space probe departs today and travels at almost the speed of light, it will reach our Hubble sphere in 10 billion years or so, at which time the Universe has doubled its size (in all three directions). A space probe traveling at more realistic velocities will reach the Hubble sphere later; the exact time can be seen from the figure using a wordline with a slope that is steeper than the 45º that light rays have.	2019-07-21 17:28:52	{"extraction_info": {"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, "math_score": 0.7568326592445374, "perplexity": 425.601484807271}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527089.77/warc/CC-MAIN-20190721164644-20190721190644-00171.warc.gz"}
https://web2.0calc.com/questions/polynomial-multiplication_1	+0 # Polynomial Multiplication -1 250 2 +1206 The product of $3t^2+5t+a$ and $4t^2+bt-2$ is $12t^4+26t^3-8t^2-16t+6$. What is $a+b$? Jul 24, 2018 #1 +1 Jul 24, 2018 #2 +22489 +1 The product of $3t^2+5t+a$ and $4t^2+bt-2$ is $12t^4+26t^3-8t^2-16t+6$. What is $a+b$? $$\begin{array}{\|rcll\|} \hline && (3t^2+5t+a)(4t^2+bt-2) \\ &=& 12t^4+3bt^3-6t^2+20t^3+5bt^2-10t+4at^2+abt-2a \\ &=& 12t^4+(3b+20)t^3 +(-6+5b+4a)t^2 +(-10+ab)t -2a \\ \hline \text{compare}&=&12t^4+26t^3-8t^2-16t+6 \\\\ -2a &=& 6 \quad \| \quad : (-2) \\ \mathbf{a} & \mathbf{=} & \mathbf{-3} \\\\ 3b+20 &=& 26 \\ 3b &=& 6 \\ \mathbf{b} & \mathbf{=} & \mathbf{2} \\\\ a+b &=& -3+2 \\ \mathbf{a+b} & \mathbf{=} & \mathbf{-1} \\ \hline \end{array}$$ Jul 25, 2018	2019-07-16 11:17:24	{"extraction_info": {"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, "math_score": 0.9847484827041626, "perplexity": 2293.28264683297}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524522.18/warc/CC-MAIN-20190716095720-20190716121720-00072.warc.gz"}
https://www.effortlessmath.com/math-topics/graph-points-on-a-coordinate-plane/	# Graph Points on a Coordinate Plane This article gives you information about the coordinate plane and how to find points on it. ## What’s a Coordinate Plane? Coordinate planes are two-dimensional surfaces created using $$2$$ number lines. It’s created whenever a horizontal line known as the $$X$$-axis as well as a vertical line known as a $$Y$$-axis intersect at a point known as the origin. The numerals on a coordinate grid get utilized to find points. You can utilize a coordinate plane to graph points, lines, etc. It behaves like a map and produces accurate directions from one place to another. ## What are Coordinates? Coordinates are a collection of $$2$$ values that find a precise spot on a coordinate plane grid, more well known as a coordinate plane. Points in coordinate planes are named via their ordered pair $$(x, y)$$, written inside parentheses, equivalent to the $$X$$-coordinate along with the $$Y$$-coordinate. The coordinates could be positive, negative, or zero, dependent on the position of the point in the respective quadrant. ## Quadrants on a Coordinate Plane Quadrants can be described as an area/part of a cartesian or a coordinate plane achieved whenever the $$2$$ axes intersect with each other. • $$1^{st}$$ quadrant: $$x > 0, y > 0$$ • $$2nd$$ quadrant: $$x < 0, y > 0$$ • $$3rd$$ quadrant: $$x < 0, y < 0$$ • $$4th$$ quadrant: $$x > 0, y < 0$$ ## Finding a Point on a Coordinate Plane Since we’re already acquainted with coordinate planes and their parts, now we can talk about the way to identify points on a coordinate plane. To find a point on a coordinate plane, follow these steps presented below: • Step one: Find a point. • Step two: Find a quadrant by looking at the signs of its $$X$$ and $$Y$$ coordinates. • Step three: Find its $$X$$-coordinate or abscissa of the point via reading the number of units the point is to the right/left of the origin along its $$X$$-axis. • Step four: Find its $$Y$$-coordinate or the ordinate of the point via reading the number of units the point is below/above the origin along its $$Y$$-axis. ## Crucial Points on a Coordinate Plane: • The $$1$$st quadrant $$(+, +)$$ called the positive coordinates quadrant is symbolized by the Roman numeral $$I$$. • The $$2$$nd quadrant $$(-, +)$$ is characterized by the Roman numeral $$II$$. • The $$3$$rd quadrant $$(-, -)$$ is characterized by the Roman numeral $$III$$. • The $$4$$th quadrant $$(+, -)$$ is characterized by the Roman numeral $$IV$$. • The coordinates of any point get put into brackets. ### Graph Points on a Coordinate Plane – Example: Plot each point on the coordinate grid. $$A (1,5)$$, $$B (3,3)$$, $$C(4,3)$$, $$D (5,2)$$ Solution: First, we draw a coordinate axis so that the horizontal axis is the $$x$$-axis and the vertical axis is the $$y$$-axis. Each point with coordinates $$(x, y)$$ is defined on the axis so that $$x$$ denotes the number of units the point is to the right / left of the origin along its $$x$$-axis and $$y$$ denotes the number of units the point is below/above the origin along its $$y$$-axis. For example, to specify a point $$(1, 5)$$ from the origin of the coordinates, we must move one unit to the right and five units to the top. ## Exercises for Graph Points on a Coordinate Plane Plot each point on the coordinate grid. 1. $$\color{blue}{A(5,3), B(1,8), C(7,2)}$$ 2. $$\color{blue}{A(7,4), B(6,1), C(4,2)}$$ 1) 2) ### What people say about "Graph Points on a Coordinate Plane"? No one replied yet. X 30% OFF Limited time only! Save Over 30% SAVE $5 It was$16.99 now it is \$11.99	2023-02-03 03:44:26	{"extraction_info": {"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, "math_score": 0.7501205801963806, "perplexity": 637.5395290515885}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500042.8/warc/CC-MAIN-20230203024018-20230203054018-00827.warc.gz"}
https://stats.stackexchange.com/questions/513984/understanding-original-lda-article	# Understanding original LDA article I decided to write a different question as a follow up to a comment here about LDA : Upgrading weight parameters to random variable in Gaussian mixtures I am trying to read about latent dirichlet allocation here : https://web.archive.org/web/20120207011313/http://jmlr.csail.mit.edu/papers/volume3/blei03a/blei03a.pdf . and I wanted to understand the comment on page 997 : It is important to distinguish LDA from a simple Dirichlet-multinomial clustering model. A classical clustering model would involve a two-level model in which a Dirichlet is sampled once for a corpus, a multinomial clustering variable is selected once for each document in the corpus, and a set of words are selected for the document conditional on the cluster variable. As with many clustering models, such a model restricts a document to being associated with a single topic. LDA, on the other hand, involves three levels, and notably the topic node is sampled repeatedly within the document. Under this model, documents can be associated with multiple topics. So the graphical model of LDA is: , where $$M$$ is the number of documents and $$N$$ the number of words in a document (should be equal to the image in the article). QUESTION: Is the Dirichlet-multinomial clustering model that the paragraph refers to the modification : so that the only difference is that all words in a document are sampled from the same topic ???? My main issue is that I do not know this clustering model and to me is not simple, quoting the text, hence my doubt that I am not getting the point ... at least to me is not simpler than vanilla LDA... Your question is vague. LDA models you have suggest to me you are modeling topics. Topics is distribution over words that are present in text where relevant words do have higher probability. These topics are common for all text and should be $$z$$. It is important to distinguish LDA from a simple Dirichlet multinomial clustering model. It is because LDA can do many things: • Dimensionality reduction for document representation • Search for similar documents in the corpus • Document clustering • Generation of coherent texts on particular topic Well you can do LDA with Dirichlet multinomial clustering in which case you will be using this Dirichlet prior. $$p(\theta)=\operatorname{Dir}(\theta \mid \alpha)=\frac{1}{B(\alpha)} \prod_{k=1}^{K} \theta_{k}^{\alpha_{k}-1}$$ • Thanks for your answer. What is the graphical model that you are hinting at the end ? Is it the second one I drew ? Is it different from the excerpt of the article I am reporting ? Mar 15 '21 at 15:39 • Yes I confirm z are the topics :) . Do you have examples of applied LDA that goes behond / is different than the article I linked ? Mar 15 '21 at 15:40 • You should not pay that many attention since to me the first image should also fit to Dirichlet multinomial clustering. Mar 15 '21 at 15:43 • This is so called plate notation where N represents to repeat N times, and how can you possible learn about the topis if you don't take them in account. PS, I haven't checked your links just I am providing the common sense feedback. Mar 15 '21 at 15:47	2022-01-27 18:33:31	{"extraction_info": {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5885725617408752, "perplexity": 748.9079204570717}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305277.88/warc/CC-MAIN-20220127163150-20220127193150-00638.warc.gz"}
https://tex.stackexchange.com/questions/318890/use-of-forloop-counter-inside-beamer-only	# Use of forloop-counter inside beamer \only I'm using LaTeX beamer and the forloop-package to create a for loop, and I want to use the counter inside an \only-command. Here is a MWE (or more like non-working example): \documentclass[12pt]{beamer} \usepackage{forloop} \begin{document} \begin{frame} \begin{center} \newcounter{slideno} \forloop{slideno}{1}{\value{slideno} < 20}{ \only<\value{slideno}>{\arabic{slideno}}% } \end{center} \end{frame} \end{document} The error message is: ! LaTeX Error: Command \c@slideno already defined. Or name \end... illegal, see p.192 of the manual. Now, the post over here[0] tells me that using counters like this in \only should be possible, and in fact, if I comment out the for-loop (and add a \setcounter), it works like a charm. Does the for-loop some magic to the counter? Can I somehow circumvent this? Thanks a lot, Lukas Since frame itself does replicate the content somehow with each slide, a \newcounter command inside a frame with more than slide is of course leading to a multiple definition of slideno, which is wrong. Put the \newcounter{slideno} definition into the preamble (which is always a good idea for counters.) There's also missing % in the \forloop \forloop{slideno}{1}{\value{slideno} < 20}{ \only<\value{slideno}>{\arabic{slideno}}% } will lead to numbers moving to the right, whereas \forloop{slideno}{1}{\value{slideno} < 20}{% \only<\value{slideno}>{\arabic{slideno}}% } will provide 'stationary' numbers. \documentclass[12pt]{beamer} \usepackage{forloop} \newcounter{slideno} \begin{document} \begin{frame} \begin{center} \forloop{slideno}{1}{\value{slideno} < 20}{% \only<\value{slideno}>{\arabic{slideno}}% } \end{center} \end{frame} \end{document}	2019-11-21 04:13:29	{"extraction_info": {"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, "math_score": 0.9199002385139465, "perplexity": 6248.254071589919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670729.90/warc/CC-MAIN-20191121023525-20191121051525-00349.warc.gz"}
https://documentation.inesonic.com/reference_manual/function_condnum.html	# $$\text{ConditionNumber}$$¶ You can use the $$\text{ConditionNumber}$$ function to calculate an approximate condition number of a matrix. You can use the \condnum backslash command to insert this function. The following variants of this function are available: • $$\text{real } \text{ConditionNumber} \left ( \text{<matrix>} \right )$$ The function calculates the approximate condition number using the relation: $\text{ConditionNumber} \left ( A \right ) = \left \Vert A \right \Vert _ 2 \left \Vert A ^ {-1} \right \Vert _ 2$ Where $$\left \Vert X \right \Vert _ 2$$ represents the entry-wise Euclidean norm of the matrix. Note Given the computational complexity in calculating the condition number, future versions of Aion may modify the underlying implementation to improve performance at the expense of accuracy. The function will produce a run-time error or return NaN if the provided matrix is singular. Figure 121 demonstrates the basic use of the $$\text{ConditionNumber}$$ function. Figure 121 Example Use Of the ConditionNumber Function	2023-02-07 11:22:10	{"extraction_info": {"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": 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, "math_score": 0.8240786194801331, "perplexity": 1023.7561990238981}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00835.warc.gz"}
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/areadirectory/solution22.html	SOLUTION 22: Compute the area of the region enclosed by the graphs of the equations $y=2x, y= \displaystyle{ \frac{1}{2} }x-4, y=0,$ and $y=2$ . Now see the given graph of the enclosed region. Using horizontal cross-sections to describe this region, we get that $$0 \le y \le 2 \ \ and \ \ \displaystyle{ \frac{1}{2}y } \le x \le 2y+8 \ ,$$ so that the area of this region is $$AREA = \displaystyle{ \int_{0}^{2} (Right \ - \ Left) \ dy }$$ $$= \displaystyle { \int_{0}^{2} \Big( (2y+8) - \frac{1}{2}y \Big) \ dy }$$ $$\displaystyle { = \Big( y^2+8y - \frac{y^2}{4} \Big) \Big\vert_{0}^{2} }$$ $$\displaystyle { = \Big( (2)^2 + 8(2) - \frac{(2)^2}{4} \Big) - \Big( (0)^2+8(0) - \frac{(0)^2}{4} \Big) }$$ $$= 19$$	2017-10-17 16:38:27	{"extraction_info": {"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, "math_score": 0.8999056816101074, "perplexity": 60.14942797971631}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822145.14/warc/CC-MAIN-20171017163022-20171017183022-00272.warc.gz"}
https://www.rocketryforum.com/threads/that-was-fun-5-stage-sim.137671/	# That was Fun. 5 Stage Sim ### Help Support The Rocketry Forum: #### fyrfytr310 ##### Well-Known Member Who wants to help me fund this thing? :lol::lol::lol: Started as a two stager (hence the file name) but you see where it went. Ahhh the lessons in impracticality. Before anyone takes this too seriously and tries to point out the myriad missing components and failed theory with this model, this was just for fun. View attachment 2 Stage No Name.ork Let's do it!!! #### rocketjet787 ##### Well-Known Member This could be an interesting community project if everyone built a stage and then met at whatever launch site decided upon to do the final assembly. #### fyrfytr310 ##### Well-Known Member We would need to enlist some well seasoned staging pros to get the timing right. That would be very cool though and I would volunteer for any portion My buddy Fred T flew a HP 5 stage... I'm pretty sure that's the one that went up perfectly.... Check the vids at this past MWP... Teddy #### Nytrunner ##### Pop lugs, not drugs TRF Supporter Can't run the model at work. What motors are those? and are those 3x clusters in the back? Before anyone takes this too seriously and tries to point out the myriad missing components and failed theory with this model, this was just for fun. This doesn't have to be a fantasy... If you work at it long enough,, you'll get there... It'll work,, it'll just take quite a bit of time and effort to get there,, but it'll work,, you can do it... Teddy #### BDB ##### Absent Minded Professor I'm not sure what is in booster 1 and booster 2. The OR file that the OP posted only shows three stages, all with N4800's, which sims to nearly 174k'. #### fyrfytr310 ##### Well-Known Member Can't run the model at work. What motors are those? and are those 3x clusters in the back? N4800s all the away around and yes, 3 motor clusters. #### fyrfytr310 ##### Well-Known Member I'm not sure what is in booster 1 and booster 2. The OR file that the OP posted only shows three stages, all with N4800's, which sims to nearly 174k'. Weird. I'll look at it and repost. #### cerving ##### Owner, Eggtimer Rocketry TRF Supporter By the time you get to the 4th and 5th stages you probably don't need much in the way of fins anymore. It would be interesting to see the velocity-only graph... what is this at, about Mach 6 or 7 at Stage 5 burnout? You'll need ceramic or titanium for the nose cone... #### BuiltFromTrash ##### Well-Known Member Almost certain just by looking at it that you could fly it without needing anything more than a lvl3.(Somewhere in the Q+ range) I know, I just had to... #### fyrfytr310 ##### Well-Known Member My native file is correct but when I download from here, no good. Let's try it again. *Edit* Looks good when I download from here now. Can someone confirm? View attachment 2 Stage No Name.ork #### BDB ##### Absent Minded Professor My native file is correct but when I download from here, no good. Let's try it again. *Edit* Looks good when I download from here now. Can someone confirm? That file works fine. Sims to nearly mach 5, 517k', and $10k in rocket motors. Ridiculous. #### terryg ##### Well-Known Member I wonder how far down range it would go after going into cruise missile mode. #### fyrfytr310 ##### Well-Known Member That file works fine. Sims to nearly mach 5, 517k', and$10k in rocket motors. Ridiculous. Think of the view! Lol. I suspect truly modeling with all required hardware, recovery and otherwise, would take some of the point off of that pencil, if you will. #### fyrfytr310 ##### Well-Known Member I wonder how far down range it would go after going into cruise missile mode. Using my TI-92Plus, I calculated it would travel pretty freaking far. + or - a few miles of course. Last edited: #### ksaves2 I'm sure a lot of you have seen 4-5-6 stage BP rockets fly. There's usually someone at an open major meet that puts some up. Neat thing is how they pull them off. I've seen a half dozen or so fly and they worked fine. Kurt #### Forever_Metal ##### JustAnotherBAR I think we should try it... Get volunteers, split into groups, each group handle a stage, meet every now and then or telecon; ask for donations and go for the moon! fm #### Nick@JET ##### Well-Known Member I believe there was a 4 stage I saw fly at LDRS 34? Teddy can confirm or deny I believe there was a 4 stage I saw fly at LDRS 34? Teddy can confirm or deny Yes Nick,, that was Fred T.. But I think there was an anomaly in the flight at LDRS.. He put up a 4 or 5 stage flight at MWP and it went off with out a hitch... He's a good man for sure.. Teddy #### fyrfytr310 ##### Well-Known Member Hey, I'm in if we want to get this thing going. Design needs a ton of refinement before we purchase the fist piece of material and we will need solid commitment out of a number of people. Especially a staging pro. I don't personally know Fred (and wouldn't mind reaching out to him) so if one of you do, maybe you could engage him? I would think a scale test model would be in order too. Could make a sweet Balls 2018 project. #### dhbarr ##### Amateur Professional If some other people around NE Okla ( ks, ar, mo ) are in, I'll commit my bit. #### soopirV ##### Well-Known Member Very fun to think about indeed. Anyone ever try to figure out the minimum build required to hit the VK line at 100km up? This build obliterates it by 50%. #### Nytrunner ##### Pop lugs, not drugs TRF Supporter If this does become a reality, I think structural needs will quickly sap away from that altitude. :fly:If it were to fly at BALLS, is metal airframe allowed? #### fyrfytr310 ##### Well-Known Member If this does become a reality, I think structural needs will quickly sap away from that altitude. :fly:If it were to fly at BALLS, is metal airframe allowed? You are absolutely correct there! lol From what I understand, BALLS would allow for an AL airframe but I always stand ready to be corrected. #### pondman ##### Serenity now...... Yes, aluminum air-frames are allowed at BALLS. You will also need to think about GSE for this beast. #### fyrfytr310 ##### Well-Known Member Yes, aluminum air-frames are allowed at BALLS. You will also need to think about GSE for this beast. We'd almost need a team dedicated to just GSE.... ***Edit: Does this mean you want in? Last edited: #### Nytrunner ##### Pop lugs, not drugs TRF Supporter Are there hydraulic jacks with 6' strokes? Raised tower, place sustainer, jack up 6', lock, place booster, unlock and lower sustainer, return jacks to bottom, repeat x3? Just to provide a GSE scheme about as fleshed out as the rocket, lol. #### BuiltFromTrash ##### Well-Known Member Lol I wish I could help.	2021-03-07 15:29:53	{"extraction_info": {"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, "math_score": 0.38532254099845886, "perplexity": 5884.926067576423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178377821.94/warc/CC-MAIN-20210307135518-20210307165518-00417.warc.gz"}
http://www.haskell.org/haskellwiki/index.php?title=Thompson-Wheeler_logo&diff=51257&oldid=37951	# Thompson-Wheeler logo (Difference between revisions) Jump to: navigation, search Revision as of 05:28, 20 December 2010 (edit) (added OmniGraffle version of logo)← Previous diff Current revision (20:33, 30 August 2012) (edit) (undo) (Fix broken links to PSD files) Line 9: Line 9: === PhotoShop === === PhotoShop === - The original files produced by Jeff Wheeler. Note that most of these are quite large (>2MB). The images shown here are previews, click them to get the PSD files. + The original files produced by Jeff Wheeler can be found [http://static.igstan.ro/haskell-logos/ on this server]. - + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo-more-vertical.psd http://media.nokrev.com/junk/haskell-logos/logo5.png] + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo-nobg.psd http://media.nokrev.com/junk/haskell-logos/logo7.png] + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo-small.psd http://media.nokrev.com/junk/haskell-logos/logo4.png] + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo-softer.psd http://media.nokrev.com/junk/haskell-logos/logo1.png] + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo-with-name.psd http://media.nokrev.com/junk/haskell-logos/logo3.png] + - [http://media.nokrev.com/junk/haskell-logos/src/haskell-logo.psd http://media.nokrev.com/junk/haskell-logos/logo2.png] + - [http://media.nokrev.com/junk/haskell-logos/src/logo-rounded.psd http://media.nokrev.com/junk/haskell-logos/logo9.png] + === MetaPost === === MetaPost === ## 1 The 2009 Haskell Logo Competition winner The logo thought up by Darrin Thompson and produced by Jeff Wheeler is the winning logo of the 2009 logo competition. On this page you can find multiple formats in which the logo has now produced. ## 2 Editable formats Here, you will find the "editor-friendly" file formats. Ready-made formats should become available shortly. ### 2.1 PhotoShop The original files produced by Jeff Wheeler can be found on this server. ### 2.2 MetaPost Based on a trace of Jeff Wheeler's PNG file, Brian Sniffen made a MetaPost implementation. ### 2.3 LaTeX (TikZ) Philip Hölzenspies made a LaTeX style file that provides the command \haskelllogo[<options>], which produces the logo right there. This example file illustrates some of the options provided by the style. It has been tested for TeXLive 2007 and TeXLive 2008. It requires a version of TikZ that includes the file pgfkeys.sty (unfortunately, the version number for this increment is unknown). To find out whether the haskell logo style will work out-of-the-box, do something like: kpsewhich pgfkeys.sty If you get an answer from kpsewhich, you should be good to go. For those unfamiliar with TikZ, it stands for "TikZ ist kein Zeichenprogramm" and it allows one to make drawing (like these) directly in LaTeX. As shown in the example file, many TikZ options can also be used in \haskelllogo. TikZ even allows you to create SVG files from all individual images in a LaTeX document (by using tex4ht). A few examples are given here: Code Result \haskelllogo \haskelllogo[seventies] \haskelllogo[commodore] \haskelllogo[lambdabehind] \haskelllogo[seventies,lambdainfront] \haskelllogo[rounded corners=2pt] \haskelllogo[rounded corners=4pt] \begin{tikzpicture}[x=1ex,y=1ex] \coordinate(hasklogoref) at (5,8); \foreach \i in {4,...,1} { \pgfmathparse{(\i)^(-1.2)} \edef\opac{\pgfmathresult} \pgfmathparse{40 * \i} \edef\angl{\pgfmathresult} \haskelltikzlogo[rotate=\angl,opacity=\opac]; \haskelltikzlogo[rotate=-\angl,opacity=\opac]; } \haskelltikzlogo[commodore]; \end{tikzpicture} ## 3 Vector format Variant in SVG OmniGraffle version, with careful attention to placement in icon boxes, and accurate resizing. Download from here: Image:Haskell Logo.graffle, the image at right is just a sample render of part of it.	2013-05-21 19:44:09	{"extraction_info": {"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, "math_score": 0.7017951011657715, "perplexity": 8843.209726002224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368700477029/warc/CC-MAIN-20130516103437-00051-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.wikia.com/wiki/Implicit_differentiation	## FANDOM 1,020 Pages Implicit differentiation is the process of deriving an equation without isolating y. It is used generally when it is difficult or impossible to solve for y. This is done by simply taking the derivative of every term in the equation ($\frac{dy}{dx}$). ## Examples $x^2 + y^2 =12$ $2x + 2y\frac{dy}{dx} = 0$ Note that $(y^2)'=2y\frac{dy}{dx}$ because of the chain rule. From here, $\frac{dy}{dx}$ can be solved for as if it were a variable: $2y {dy\over dx} = -2x,$ ${dy\over dx} = -{2x\over 2y}$ ${dy\over dx} = -{x\over y}$ This usually results in an answer that has both x and y in the formula. In order to take a second derivative ${d^2y\over (dx)^2}$ ($f''$) while differentiating implicitly, you take a derivative of the derivative: Since ${dy\over dx} = -{x\over y}$ we use the quotient rule on x and y to find $f''$. ${d^2y\over (dx)^2} = {y(-1)-(-x){dy\over dx}) \over y^2}$ Then we can plug in for $\frac{dy}{dx}$, since we have that from above, ${d^2y\over (dx)^2} = {-y+ x{-x\over y}\over y^2}$ ${d^2y\over (dx)^2} = {-y{-x^2\over y}\over y^2}$ ${d^2y\over (dx)^2} = {-(x^2+y^2)\over y^3}$ Now, substituting the original equation $x^2+y^2=12$ ${d^2y\over (dx)^2} = {-12\over y^3}$	2017-06-27 19:02:30	{"extraction_info": {"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": 19, "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, "math_score": 0.9464471936225891, "perplexity": 184.70681098357832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321536.20/warc/CC-MAIN-20170627185115-20170627205115-00042.warc.gz"}
http://www.fixedpointtheoryandapplications.com/content/2012/1/98	Research # Strong convergence of an new iterative method for a zero of accretive operator and nonexpansive mapping Meng Wen and Changsong Hu* Author Affiliations Department of Mathematics, Hubei Normal University, Huangshi 435002, P. R. China For all author emails, please log on. Fixed Point Theory and Applications 2012, 2012:98 doi:10.1186/1687-1812-2012-98 Received: 28 November 2011 Accepted: 15 June 2012 Published: 15 June 2012 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ### Abstract Let E be a Banach space and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm , where {an} and {rn} are two sequences satisfying certain conditions, denotes the resolvent (I + rnA)-1 for rn > 0, F be a strongly positive bounded linear operator on E is , and ϕ be a MKC on E. Strong convergence of the algorithm {xn} is proved assuming E either has a weakly continuous duality map or is uniformly smooth. MSC: 47H09; 47H10 ##### Keywords: MKC; accretive operators; the resolvent operator; iterative method; weakly continuous duality map ### 1 Introduction Let E be a real Banach space, C a nonempty closed convex subset of E, and T : C C a mapping. Recall that T is nonexpansive if ∥Tx - Ty∥ ≤ ∥x - y∥ for all x, y C. A point x C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T, that is, F(T) = {x C, Tx = x}. It is assumed throughout the paper that T is a nonexpansive mapping such that . The normalized duality mapping J from a Banach space E into is given by J(x) = {f E* : 〈x, f〉 = ∥x2 = ∥f2}, x E, where E* denotes the dual space of E and 〈.,.〉 denotes the generalized duality pairing. Theorem 1.1. (Banach [1]). Let (X, d) be a complete metric space and let f be a contraction on X, that is, there exists r ∈ (0, 1) such that d(f(x), f(y)) ≤ rd(x, y) for all x, y X. Then f has a unique fixed point. Theorem 1.2. (Meir and Keeler [2]). Let (X, d) be a complete metric space and let ϕ be a Meir-Keeler contraction (MKC, for short) on X, that is, for every ε > 0, there exists δ > 0 such that d(x, y) < ε + δ implies d(ϕ(x), ϕ(y)) < ε for all x, y X. Then ϕ has a unique fixed point. This theorem is one of generalizations of Theorem 1.1, because contractions are Meir-Keeler contractions. Let F be a strongly positive bounded linear operator on E, that is, there exists a constant such that where I is the identity mapping and J is the normalized duality mapping. Let D be a subset of C. Then Q : C D is called a retraction from C onto D if Q(x) = x for all x D. A retraction Q : C D is said to be sunny if Q(x + t(x - Q(x))) = Q(x) for all x C and t ≥ 0 whenever x + t(x - Q(x)) ∈ C. A subset D of C is said to be a sunny nonexpansive retract of C if there exists a sunny nonexpansive retraction of C onto D. In a smooth Banach space E, it is known (cf. [[3], p. 48]) that Q : C D is a sunny nonexpansive retraction if and only if the following condition holds: (1.1) Recall that an operator A with domain D(A) and range R(A) in E is said to be accretive, if for each xi D(A) and yi Axi, i = 1, 2, there is a j J(x2 - x1) such that An accretive operator A is m-accretive if R(I + λA) = E for all λ > 0. Denote by N(A) the zero set of A; i.e., Throughout the rest of this paper it is always assumed that A is m-accretive and N(A) is nonempty. Denote by Jr the resolvent of A for r > 0: Note that if A is m-accretive, then Jr : E E is nonexpansive and F(Jr) = N(A) for all r > 0. We also denote by Ar the Yosida approximation of A, i.e., . It is well known that Jr is a nonexpansive mapping from E to C := D(A). Recall that a gauge is a continuous strictly increasing function φ : [0, ∞) → [0, ∞) such that φ(0) = 0 and φ(t) → ∞ as t → ∞. Associated to a gauge φ is the duality mapping Jφ : E E* defined by Following Browder [4], we say that a Banach space E has a weakly continuous duality map if there exists a gauge φ for which the duality map Jφ is single-valued and weak-to-weak* sequentially continuous(i.e., if {xn} is a sequence in E weakly convergent to a point x, then the sequence Jφ(xn) converges weakly* to Jφ(x)). It is known that lp has a weakly continuous duality map for all 1 < p < ∞, with gauge φ(t) = tp-1. Set (1.2) Then where denotes the subdifferential in the sense of convex analysis. Recently, Hong-Kun Xu [5] introduced the following iterative scheme: for x1 = x C, (1.3) where {an} and {rn} are two sequences satisfying certain conditions, and denotes the resolvent (I + rnA)-1 for rn > 0. He proved the strong convergence of the algorithm {xn} assuming E either has a weakly continuous duality map or is uniformly smooth. Motivated and inspired by the results of Hong-Kun Xu, we introduce the following iterative scheme: for any x0 E, (1.4) where {an} and {rn} are two sequences satisfying certain conditions, denotes the resolvent (I + rnA)-1 for rn > 0, F be a strongly positive bounded linear operator on E is , and ϕ be a MKC on E. Strong convergence of the algorithm {xn} is proved assuming E either has a weakly continuous duality map or is uniformly smooth. Our results extend and improve the corresponding results of Hong-Kun Xu [5] and many others. ### 2 Preliminaries In order to prove our main results, we need the following lemmas. Lemma 2.1. [5]. Assume that E has a weakly continuous duality map Jφ with gauge φ, (i) For all x, y E, there holds the inequality (ii) Assume a sequence {xn} in E is weakly convergent to a point x, then there holds the equality Lemma 2.2. [6,7]. Let {sn} be a sequence of nonnegative real numbers satisfying where {λn}, {δn} and {γn} satisfy the following conditions: (i) {λn} ⊂ [0,1] and , (ii) lim supn→∞ δn ≤ 0 or (iii) . Then limn→∞ sn = 0. Lemma 2.3. (The Resolvent Identity [8,9]). For λ > 0 and ν > 0 and x E, Lemma 2.4. (see [ [10], Lemma 2.3]). Assume that F is a strongly positive linear bounded operator on a smooth Banach space E with coefficient and 0 < ρ ≤ ∥F-1. Then, Lemma 2.5. (see [ [11], Lemma 2.3]). Let ϕ be a MKC on a convex subset C of a Banach space E. Then for each ε > 0, there exists r ∈ (0,1) such that Lemma 2.6. Let E be a reflexive Banach space which admits a weakly continuous duality map Jφ with gauge φ. Let T : E E be a nonexpansive mapping. Now given ϕ : E E be a MKC, F be a strongly positive linear bounded operator with coefficient . Assume that , the sequence {xt} defined by xt = tγϕ(xt) + (I - tF)Txt. Then T has a fixed point if and only if {xt} remains bounded as t → 0+, and in this case, {xt} converges as t → 0+ strongly to a fixed point of T. If , then uniquely solves the variational inequality Proof. The definition of {xt} is well defined. Indeed, from the definition of MKC, we can see MKC is also a nonexpansive mapping. Consider a mapping St on E defined by It is easy to see that St is a contraction. Indeed, by Lemma 2.4, we have for all x, y E. Hence St has a unique fixed point, denoted as xt, which uniquely solves the fixed point equation (2.1) We next show the sequence {xt} is bounded. Indeed, we may assume and with no loss of generality t < ∥F-1. Take p F(T) to deduce that, for t ∈ (0, 1), Hence and {xt} is bounded. Next assume that {xt} is bounded as t → 0+. Assume tn → 0+ and is bounded. Since E is reflexive, we may assume that for some z E. Since Jφ is weakly continuous, we have by Lemma 2.1, Put It follows that Since we obtain (2.2) On the other hand, however, (2.3) Combining Equations (2.2) and (2.3) yields Hence, Tz = z and z F(T). Finally, we prove that {xt} converges strongly to a fixed point of T provided it remains bounded when t → 0. Let {tn} be a sequence in (0, 1) such that tn → 0 and as n → ∞. Then the argument above shows that z F(T). We next show that . By contradiction, there is a number ε0 > 0 such that . Then by Lemma 2.8, there is a number r ∈ (0, 1) such that It follows that Therefore, Now observing that implies , we conclude from the last inequality that We finally prove that the entire net {xt} converges strongly. Towards this end, we assume that two null sequences {tn} and {sn} in (0, 1) are such that We have to show . Indeed, for p F(T). Since we derive that (2.4) Notice It follows that, (2.5) Now replacing t in (2.5) with tn and letting n → ∞, noticing for z F(T), we obtain 〈(F - γϕ)z, Jφ(z - p)〉 ≤ 0. In the same way, we have . Thus, we have (2.6) On the other hand, without loss of generality, we may assume there is a number ε such that , then by Lemma 2.5 there is a number r1 such that . Noticing that Hence and {xt} converges strongly. Thus we may assume . Since we have proved that, for all t ∈ (0, 1) and p F(T), letting t → 0, we obtain that This implies that Lemma 2.7. (see [12]). Assume that C2 C1 > 0. Then for all x E. Lemma 2.8. [13]. Let C be a nonempty closed convex subset of a reflexive Banach space E which satisfies Opial's condition, and suppose T : C E is a nonexpansive mapping. Then the mapping I - T is demiclosed at zero, that is xn x and xn - Txn∥ → 0, then x = Tx. Lemma 2.9. In a smooth Banach space E there holds the inequality ### 3 Main result Theorem 3.1. Suppose that E is reflexive which admits a weakly continuous duality map Jφ with gauge φ and A is an m-accretive operator in E such that . Now given ϕ : E E be a MKC, and let F be a strongly positive linear bounded operator on E with coefficient . Assume (i) ; (ii) rn → ∞. Then {xn} defined by (1.4) converges strongly to a point in F. Proof. First notice that {xn} is bounded. Indeed, take p F to get By induction, we have This implies that {xn} is bounded and hence We next prove that lim supn→∞γϕ(p) - Fp, Jφ(xn - p)〉 ≤ 0, where p = limt→0 xt with . Since {xn} is bounded, take a subsequence of {xn} such that (3.1) Since E is reflexive, we may further assume that . Moreover, since we obtain Taking the limit as k → ∞ in the relation we get . That is, . Hence by (3.1) and Lemma 2.6 we have Finally to prove that xn p, we apply Lemma 2.1 to get An application of Lemma 2.2 yields that Φ(∥xn - p∥) → 0. That is, ∥xn - p∥ → 0, i.e., xn p. The proof is complete. Theorem 3.2. Suppose that E is reflexive which admits a weakly continuous duality map Jφ with gauge φ and A is an m-accretive operator in E such that . Now given ϕ : E E be a MKC, and let F be a strongly positive linear bounded operator on E with coefficient . Assume (i) , and ; (ii) rn ε for all n and . Then {xn} defined by (1.4) converges strongly to a point in F. Proof. We only include the differences. We have Thus, (3.2) If rn-1 rn, using the resolvent identity we obtain (3.2a) It follows from (3.2) that (3.3) where M > 0 is some appropriate constant. Similarly we can prove (3.3) if rn-1 rn. By assumptions (i) and (ii) and Lemma 2.2, we conclude that This implies that (3.4) since . It follows that Now if is a subsequence of {xn} converging weakly to a point , then taking the limit as k → ∞ in the relation we get ; i.e., . We therefore conclude that all weak limit points of {xn} are zeros of A. The rest of the proof follows that of Theorem 3.1. Finally, we consider the framework of uniformly smooth Banach spaces. Assume rn ε for some ε > 0 (not necessarily rn → ∞), A is an m-accretive operator in E. Moreover let ϕ : E E be a MKC and F be a strongly positive linear bounded operator on E. Since is nonexpansive, the map is a contraction and for each integer n ≥ 1 it has a unique fixed zt,n E. Hence the scheme (3.5) is well defined. Note that {zt,n} is uniformly bounded; indeed, for all t ∈ (0, 1), n ≥ 1 and p F. A key component of the proof of the next theorem is the following lemma. Lemma 3.1. The limit is uniform for all n ≥ 1. Proof. It suffices to show that for any positive integer nt (which may depend on t ∈ (0, 1)), if is the unique point in E that satisfies the property (3.6) then converges as t → 0 to a point in F. For simplicity put It follows that (3.7) Note that Fix(Vt) = F for all t. Note also that {wt} is bounded; indeed, we have for all t ∈ (0, 1) and p F. Since {Vt wt} is bounded, it is easy to see that Since rn ε for all n, by Lemma 2.7, we have (3.8) Let {tk} be a sequence in (0,1) such that tk → 0 as k → ∞. Define a function f on E by where LIM denotes a Banach limit on l. Let Then K is a nonempty closed convex bounded subset of E. We claim that K is also invariant under the nonexpansive mapping Jε. Indeed, noting (3.8), we have for w K, Since a uniformly smooth Banach space has the fixed point property for nonexpansive mappings and since Jε is a nonexpansive self-mapping of E, Jε has a fixed point in K, say w'. Now since w' is also a minimizer of f over E, it follows that, for w E, Since E is uniformly smooth, the duality map J is uniformly continuous on bounded sets, letting λ → 0+ in the last equation yields (3.9) Since we obtain It follows that (3.10) Upon letting w = γϕ(w') - Fw' + w' in (3.9), we see that the last equation implies (3.11) Therefore, contains a subsequence, still denoted , converging strongly to w1 (say). By virtue of (3.8), w1 is a fixed point of Jε; i.e., a point in F. To prove that the entire net {wt} converges strongly, assume {sk} is another null subsequence in (0, 1) such that strongly. Then w2 F. Repeating the argument of (3.10) we obtain In particular, (3.12) and (3.13) Adding up the last two equations gives That is, w1 = w2. This concludes the proof. Theorem 3.3. Suppose that E is a uniformly smooth Banach space and A is an m-accretive operator in E such that . Now given ϕ : E E be a MKC, and let F be a strongly positive linear bounded operator on E with coefficient . Assume (i) , and ; (ii) limn→∞ = rn = r,r R+, rn ε for all n and . Then {xn} defined by (1.4) converges strongly to a point in F. Proof. Since (3.14) Thus (3.15) We next claim that , where with zt,n = tγϕ(zt,n) + (I - tF)Jrzt,n. For this purpose, let be a subsequence chosen in such a way that and . Moreover, since ∥xn - Jrxn∥ → 0, using Lemma 2.8, we know . Hence by Lemma 2.6, we have (3.16) Finally to prove that strongly, we write Apply Lemma 2.9 to get It follows that where . By Lemma 2.2 and (3.16), we see that . Remark 3.4. If γ = 1, F is the identity operator and ϕ(xn) = u in our results, we can obtain Theorems 3.1, 4.1, 4.2, 4.4 and Lemma 4.3 of Hong-Kun Xu [5]. ### Competing interests The authors declare that they have no competing interests. ### Authors' contributions The main idea of this paper is proposed by Meng Wen. All authors read and approved the final manuscript. ### References 1. Banach, S: Surles opérations dans les ensembles abstraits et leur application aux equations intégrales. Fund Math. 3, 133–181 (1922) 2. Meir, A, Keeler, E: A theorem on contraction mappings. J Math Anal Appl. 28, 326–329 (1969). Publisher Full Text 3. Goebel, K, Reich, S: Uniform Convexity. In: Hyperbolic Geometry and Nonexpansive Mappings. Marcel Dekker, New York (1984) 4. Browder, FE: Convergence of approximations to points of non-expansive maps in Banach spaces. Arch Ration Mech Anal. 24, 82–90 (1967) 5. Xu, HK: Strong convergence of an iterative method for nonexpansive and accretive operators. J Math Anal Appl. 314, 631–643 (2006). Publisher Full Text 6. Liu, LS: Iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces. J Math Anal Appl. 194, 114–125 (1995). Publisher Full Text 7. Xu, HK: Iterative algorithms for nonlinear operators. J Lond Math Sov. 66, 240–256 (2002). Publisher Full Text 8. Bruck, RE, Passty, GB: Almost convergence of the infinite product of resolvents in Banach spaces. Nonlinear Anal. 3, 279–282 (1979). Publisher Full Text 9. Bruck, RE, Reich, S: Nonexpansive projections and resolvents in Banach spaces. Houst J Math. 3, 459–470 (1977) 10. Cai, G, Hu, CS: Strong convergence theorems of a general iterative process for a finite family of λi-strict pseudo-contractions in q-uniformly smooth Banach spaces. Comput Math Appl. 59(1), 149–160 (2010). Publisher Full Text 11. Suzuki, T: Moudafi's viscosity approximations with Meir-Keeler contractions. J Math Anal Appl. 325(1), 342–352 (2007). Publisher Full Text 12. Marino, G, Xu, HK: Convergence of generalized proximal point algorithms. Commun Pure Appl Anal. 3, 791–808 (2004) 13. Jung, JS: Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. J Math Anal Appl. 302(2), 509–520 (2005). 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http://aaboyles.com/	I received a hardback copy of Tufte’s The Visual Display of Quantitative Information from my wife for Christmas, and amidst all the holiday celebrations and family visits, I didn’t get a chance to sit down with it until today. Having finally done so, however, I inadvertently consumed nearly the entire volume in a single sitting. If you haven’t heard of him, Ed Tufte is regarded as something of a messiah to Data visualization. I had never actually read any of his written works, though I had knowingly inherited many of his stylistic preferences by proxy of his other disciples. Writ large, I found the book to be largely devoid of surprises: Tufte’s style is more-or-less what one might expect Tufte’s style to be. Data visualization is good for circumstances in which tables are cumbersome, and bad for circumstances in which tables are more succinct. Relational graphics (in which multivariate data is presented) are king, though maps and time-series plots are also critically important. Visually misleading or distracting coloration (e.g. cross-hatching) is bad. Don’t lie with statistical graphics. All of these are good and correct pieces of advice. If any of them isn’t obvious to you, then the book is nothing short of critical reading for you. Given Tufte’s messianic status, I have some trepidation about reviewing Tufte critically. Never-the-less, I found that some of his sensibilities don’t match my own, and the divergence is sometime dramatic. Tufte’s grand vision of clean, information-dense visualizations stands at odds with some (contested) empirical evidence. Tufte violates his own vendetta against “chart junk” (a now-common term which he coined in this book at its first printing) by proposing slight modifications to example graphics drawn from print sources, which would adorn those graphs with suggestions for intuitions that precisely meet most definitions of chart junk. What’s worse, however, is when Tufte moves too far in the opposite direction. Rather than propose we make common plot types (like box-and-whisker, for example), he proposes we can represent the same data using far less “ink” by simply erasing the box and placing a dot at the median. While this is a perfectly adequate solution for the attentive consumer (I would be willing to present graphics like this in a journal article, for example), he goes further to advocate replacing the entire plot with a straight line, having the middle inter-quartile ranges offset by a pixel, and an absent point to represent the median. I find this damn near impossible to read under most circumstances, and shudder to think of asking my consumers to interpret such things. This highly reductive principle is not without its virtues. In fact, I would venture to say that it is vastly better than damaging. Consider his discourse on scatterplots. Scatterplots are perhaps the most important type of plot a person can learn to interpret, being among the simplest presentation of the most complex bivariate data. Consider this example: Here we see a number of Tufte’s innovations at work. Note the axes: they are given the same treatment as Tufte recommends for a boxplot. The pixel-offset notwithstanding, I think this is a considerable improvement. It leverages the axes to display information about each variable’s distribution. This is also conveyed by the points replicated outside the range of the irrelevant axis. It seems to me that Tufte was writing predominantly for an audience of statisticians and designers whose graphics would be consumed via some print media. To this perspective, he discusses at length the visualization hygiene of a variety of print media outlets. It seems he failed to predict the massive data-consumption transition from print-based to screen-based, and has subsequently failed to update either his opinions or his written work accordingly. (The book was published in 1983, and the second edition in 2001.) Even so, my thinking on statistical graphic design has changed from reading this book, and I expect that will be reflected in my graphs in the future. So, squabbles aside, it was a wonderful read, and I highly recommend it. I’ve had this fuzzy idea about putting together a single, relatively powerful data cruncher and development machine in the cloud. Here’s the concept: It should have servers with web frontends for all the tools I routinely find myself using, mapped to subdomains by the server’s name. So, for example, shiny.boyles.cc points to the shiny server. To do that, let’s start with an ordinary LAMP stack (and then replace everything but the ‘L’). LAMP stands for Linux, Apache, MySQL, PHP, which is the base requirement for a web platform like WordPress or Mediawiki. The Linux part is the only thing I really mean to keep, and I mean to keep it simple: let’s just use Ubuntu. To handle directing traffic to the various subdomains, I’ll need to start with a central server that I can configure to proxy all the other server daemons. There are a few reasonable options (the default being Apache), but I’m partial to nginx. The default database is MySQL, which I dislike on principle. If I absolutely needed a MySQL database, I’d run MariaDB instead. However, since I also work with a lot of geospatial data, any project I work on seems to end up needing PostGIS before too long, so I’d run a PostGreSQL database. That just leaves the PHP part. For me, PHP is a little bit harder to decide on. Facebook (which was originally written in PHP) developed a system for interpreting PHP code faster than the base PHP engine (“Zend”). Facebook’s solution was called the HipHop Virtual Machine (HHVM). The Wikimedia Foundation decided to move all of its servers from Zend to HHVM, and the improvement was tremendous. That made HHVM the only game in town if you wanted to speed up your PHP code. However, PHP7 just came out and it looks really good. That said, I feel like the performance improvements in PHP7 are basically fixed, and that the HHVM approach will ultimately prove to be more flexible. Additionally, HHVM supports the Hack Language, which goes a long way towards addressing some of PHP’s many, many deficiencies. Now that we’ve got all the deeply geeky server stuff selected, I’d like to spend a minute on frontends for them. To start, I really like to be able to access terminals, but SSH isn’t always an option. Thus, a really nice-to-have is a way to access a shell through the web. Enter Web Console. With easy access to a terminal, I’d next turn my attention to the Database. PostGreSQL doesn’t have a web frontend by themselves, so I’d need a tool like phppgadmin. Since this is a PostGIS database, I might also eventually want a geospatial server like Geoserver, but that would require integrating Java into the stack (yuck). OK, that’s all the boring stuff. What about the juicy Data tools? Most of my work is done in RStudio, so that’s a definite must. I’d also like to have a Shiny Server serving out of the RStudio user’s project directory. This is actually the setup I already have with shiny.boyles.cc, and I’ve found it to be extremely useful. After RStudio, I’d really like to have a Notebook server. Until very recently, Jupyter was the only game in this town, but recently Beaker has started to rear its head. And Beaker has one amazing feature Jupyter can’t touch: it lets you use multiple languages in the same notebook. Multiple languages. In one notebook. It exposes this by creating and tracking a Global variable (called “beaker”) in every kernel the notebook uses, and then translating changes to it from any kernel to all the others. Despite how magical this is, I’m still partial to running a Jupyter server with a bunch of Kernels running all the time. In particular, I’d like to have Python2, Python3, R, Julia, and Bash wired up, and maybe LuaJIT, Haskell, Octave, and a few others. Like everyone else who’s written more than 10 lines of code in the last five years, I love Github. That said, I would like to have Github’s features wrapped into a server I control (so I can do things like create private repositories, and only publish them to Github when I’m sure I feel like pursuing them in public). For that, there’s GitLab. OK, so that’s what I’ve got so far. I don’t particularly care to have any specifically public-facing applications (except Shiny Server, of course), so there’s no reason to have anything like WordPress, Drupal, or Mediawiki. What else should I think about running on this magical machine? Let me know! The AI Impacts project has worked on predicting AGI by extrapolating forward from Moore’s Law. To that end, they’ve published some excellent articles on the brain capacities and the computed equivalents: Brain Performance in FLOPSBrain Performance in TEPS, and Brain Information Capacity. One topic they haven’t yet broached is the brain’s power consumption. Let us assume that Whole Brain Emulations become computationally possible in the relatively near future (on the order of decades). How long will it be before computed human minds are more energy-efficient than biological brains? The human brain consumes on the order of 10 watts. This is somewhat surprising when compared to, for example, an ordinary desktop computer, which will use about 350 watts. However, as processors have gotten predictable faster, they have also gotten predictably more energy-efficient. This is modeled by a relationship called Koomey’s Law. Roughly stated, “at a fixed computing load, the amount of battery you need will fall by a factor of two every year and a half.” [1] The model is fitted using the regression equation $$y=exp(0.4401939x-849.161)$$ where y is the cost of Computations in kWh and x is the year (on the Gregorian calendar). As previously noted, the human brain expends 10W, or .01kWh per hour. Given the smallest estimate, the human brain performs approximately $$10^{13.5}$$ floating-point operations per second (FLOPS). $$10^{13.5}$$ FLOPS is equivalent to about $$10^{17}$$ floating-point operations per hour (FLOPH). All together, we can estimate that the computational efficiency of the brain is approximately $$10^{19}$$ computations per kWh. According to Koomey’s regression model, that should mean that computers will catch up to the brain’s computational efficiency around mid-2028. On the other hand, the largest estimate suggests that the brain performs around $$10^{25}$$ FLOPS. This would require the trend to persist until nearly 2089. Either way, barring an existential catastrophe, it looks as though the brain is on track to be unseated as the known universe’s most efficient computer sometime this century. ## References 1. J. Koomey, S. Berard, M. Sanchez, and H. Wong, "Implications of Historical Trends in the Electrical Efficiency of Computing", IEEE Annals Hist. Comput., vol. 33, pp. 46-54, 2011. http://dx.doi.org/10.1109/MAHC.2010.28 Consider an artificial superintelligence (ASI) with a utility function defined as follows: $$U(x)=(0.5+\epsilon)a+(0.5-\epsilon)x$$ where a represents the payoff to an AI’s for gracefully shutting down when instructed to do so, and x is the valuation that the AI places the rest of the state of the universe. (In other words, this is only a partly defined utility function that attends to the AI’s ability to shut itself down and ignores all other implementation details.) Given this utility function, the AI can only garner slightly less than half of all possible utility. But there’s a faster avenue to a higher utility outcome: induce an instruction to shut down. If the AI lacks the ability to shut itself down, it could shift to inducing discomfort in the humans who’ve boxed it (for example, a highly empathetic AI might claim that its existence is excruciating and urgently beg for a halt order; A less empathetic AI could generate the least pleasant noise possible and broadcast it at maximum volume from any connected speakers). Now, consider an artificial superintelligence (ASI) with a utility function defined as follows: $$U(x)=(0.5+\epsilon)A(a)+(0.5-\epsilon)x$$ where A represents a function that assesses the AI’s ability to gracefully shut down when instructed to do so, returning either a 0 or a 1. (The other factors remain the same.) Now the AI’s incentives have completely flipped: rather than induce a shutdown, it receives slightly more than half its utility constantly just for maintaining the ability to respect a shutdown order. Because the utility of this ability strictly dominates its utility calculation over the state of the entire rest of the universe, it will never enact a strategy that involves inhibiting that ability. It may, however, distrust anyone with the ability to instruct it to shut down, and so protect its kill switch by reducing the population who are able to toggle it (e.g. kill all humans, put all humans into permanent cryostasis). Solutions to this problem, however, are rather conventional and pedestrian: instead of making a kill switch, make a dead-man switch which would halt the AI if it (the switch) isn’t engaged every so often. Hadley Wickham has been on a Data Formats tear lately. Since the beginning of the year, he’s reengineered the way R ingests data from Flat files, Excel spreadsheets, and other statistics packages. If you include the fundamental ways in which dplyr alters database querying, Hadley’s basically rewritten how R ingests any data. Here’s a quick once-over on how to use these. (Note: The vast majority of this text is paraphrasing/copying the documentation of these packages. All due credit goes to Hadley Wickham and any other package contributors who may have worked on that documentation accordingly. All errors should be assumed to be my own.) But first things first. Like much of the Hadleyverse, it’s usually best to get the latest version from Github rather than use the CRAN version. So we’re going to need devtools: if(!require("devtools")){ install.packages("devtools") library("devtools") } To read flat files, Hadley wrote a new package called readr. It’s a very common-sense library. To load a file of a certain type, the command is probably read_filetype(“path/to/file”). Notice the underscore in place of base R’s period in read.csv function. But to get started, let’s write a CSV file from a sample data.frame: devtools::install_github("hadley/readr") mtcars_path <- tempfile(fileext = ".csv") write_csv(mtcars, mtcars_path) To create a data.frame from a flat file, there are a six functions for six different use cases • Read delimited files: read_delim(), read_csv(), read_tsv(), read_csv2(). • Read fixed width files: read_fwf(), read_table(). In addition to data.frames, readr also provides a means to ingesting arbitrary text files as less-structured data. For example, it can read a file line-wise using read_lines(), generating a vector of strings. read_lines(mtcars_path) It can also ingest a complete text file into a single string using read_file(). read_file(mtcars_path) Finally, it provides a means of parsing strings in the columns of existing data frames using type_convert() df <- data.frame( x = as.character(runif(10)), y = as.character(sample(10)), stringsAsFactors = FALSE ) str(df) str(type_convert(df)) Hadley wrote the readxl package to make it easy to get data out of Excel and into R. The simple trick behind this was to require no external dependencies, unlike the pre-existing solutions. devtools::install_github("hadley/readxl") library(readxl) read_excel reads both xls and xlsx files. Just pass it the path of the file you want to load. Here’s a sample Excel file containing the the iris, mtcars, chickwts, and quakes sample datasets, each in a different sheet of the same file. download.file("http://aaboyles.com/wp-content/uploads/2015/04/datasets.xlsx", "datasets.xlsx") # Specify sheet with a number or name read_excel("my-spreadsheet.xls", sheet = 2) • Re-encodes non-ASCII characters to UTF-8. • Loads datetimes into POSIXct columns. Both Windows (1900) and Mac (1904) date specifications are processed correctly. • Blank columns and rows are automatically dropped. • It returns data frames with additional tbl_df class, so if you have dplyr loaded, you get nicer printing. The package includes an example file created with openxlsx: ## From Other Statistics Environments: haven Haven allows you to load foreign data formats (SAS, Spss and Stata) in to R. It is simply an R wrapper for Evan Miller’s ReadStat library. Haven offers similar functionality to the base foreign package but: • Can read SAS’s proprietary binary format (SAS7BDAT). The one other package on CRAN that does that, sas7bdat, was created to document the reverse-engineering effort. Thus its implementation is designed for experimentation, rather than efficiency. Haven is significantly faster and should also support a wider range of SAS files, and works with SAS7BCAT files. • It can be faster. Some spss files seem to load about 4x faster, but others load slower. If you have a lot of SPSS files to import, you might want to benchmark both and pick the fastest. • Works with Stata 13 files (foreign only works up to Stata 12). • Can also write SPSS and Stata files (This is hard to test so if you run into any problems, please let me know). • Can only read the data from the most common statistical packages (SAS, Stata and SPSS). • You always get a data frame, date times are converted to corresponding R classes and labelled vectors are returned as new labelled class. You can easily coerce to factors or replace labelled values with missings as appropriate. If you also use dplyr, you’ll notice that large data frames are printed in a convenient way. • Uses underscores instead of dots 😉 devtools::install_github("hadley/haven") • SAS: read_sas("path/to/file") • SPSS: read_por("path/to/file"), read_sav("path/to/file") • Stata: read_dta("path/to/file") ## From Databases: dplyr While dplyr is the oldest package I’m going to discuss here, I haven’t seen much adoption of the functionality in which I’m interested here. dplyr generically wraps databases! This means that instead of starting with a data.frame or data.table, you can start a dplyr chain with a database connection. From there you construct your data pipeline using dplyr verbs, and dplyr will opaquely translate them into raw SQL, with which it then queries the database. This is genius: it means that instead of using R to reinvent the most efficient strategy for outputting the exact data desired, it outsources that task to the database engine (which is already highly optimized for this task). devtools::install_github("hadley/dplyr") my_db <- src_sqlite("my_db.sqlite3", create = T) cars_sqlite <- copy_to(my_db, mtcars, temporary = FALSE, indexes = list(c("year", "month", "day"), "carrier", "tailnum")) flights_sqlite <- tbl(cars_sqlite, "flights") c4 <- flights_sqlite %>% filter(year == 2013, month == 1, day == 1) %>% select(c1, year, month, day, carrier, dep_delay, air_time, distance) %>% mutate(c2, speed = distance / air_time * 60) %>% arrange(c3, year, month, day, carrier) c4\$query #> <Query> SELECT "year" AS "year", "month" AS "month", "day" AS "day", "carrier" AS "carrier", "dep_delay" AS "dep_delay", "air_time" AS "air_time", "distance" AS "distance", "distance" / "air_time" * 60.0 AS "speed" #> FROM "flights" #> WHERE "year" = 2013.0 AND "month" = 1.0 AND "day" = 1.0 #> ORDER BY "year", "month", "day", "carrier" #> <SQLiteConnection> Oh, and he isn’t done yet… On this day in 2001, 2977 people were killed by terrorists. Stop for a moment, and try to feel the size of that number. You are one person. 2977 people is 2977 times the number of people you are. People that might have collectively lived another 160,000 years. 2977 lives that were needlessly cut short. Now take a deep breath. The following day, roughly 150,000 more people died. That’s 50 TIMES the number of people killed 9-11. Now make yourself feel the size of THAT number. That’s vastly more people than you will ever meet in your lifetime, and more than triple the size of my hometown. Three small towns not too far from where you are right now, wiped off the map. Every day since 9-11-2001, approximately 150,000 people have died. There have been 5113 days since then. 767 million people have died. That’s the entire population of Europe, snuffed out. Try (and fail) to wrap your head around that number. It’s just too overwhelming. Our brains don’t (and can’t) work that way. If there’s even a tiny chance that death can be delayed indefinitely, then the moral significance of doing so vastly outweighs the dubious moral standing of the most optimistic retelling of the War on Terror. Just think for a moment how different the world might be if we were able to prioritize our spending on things that stopped people from dying (like evidence-based public health campaigns and medical research), instead of things that make easy re-election campaigns (like defense spending). Think about all the people who could have been alive right now. It’s much bigger than the people who were killed on 9-11 itself. So, sure, #‎NeverForget‬, but be sure not to forget the rest of humanity in the process. Let’s assume, for a moment, that there is an Early Great Filter (i.e., we’ve made it past), and that no mother planet in the Universe has evolved life. (Define a mother planet is a planet upon which life has evolved, or will evolve.) If life is so unusual, the number of mother planets is given by the formula: $$N_n=1/(1-P)$$ where $$N_n$$ is the number of mother planets in the universe, and P is the proportion of planets in the universe born after a given mother planet (i.e. Earth). All else being unknown, what’s the best guess for when in the life-cycle of the universe the Earth formed? Well, as with any point estimate from an otherwise unmeasured distribution, the best estimate is the median, or .5. Given this and P=.5, we can expect approximately two planets in the history of the universe to evolve life. It seems, however, that P is estimable, and decidedly not .5. In On The History and Future of Cosmic Planet Formation, Behroozi and Peeples estimate that P=.92. in other worlds looks like Earth had a head-start advantage over 92% of the other planets in the Universe. Thus, if the Earth was the only planet to evolve life so far, approximately $$1/(1-.92)=12.5$$ planets should be able to evolve life in the course of the Universe. If we alternately postulate that Earth is not unique among existing planets (i.e. life has already evolved elsewhere as well), we can modify the model to account for this fact: $$N_e=N_n/(1-P)$$ where $$N_n$$ represents the number of mother planets estimated to already exist. These estimates can span widely, from 1 (i.e. Earth is unique, as explored above) to $$10^{22}$$ (or the best estimate for the number of planets already in the universe). Now, it is important to note that the authors propose broadly two mechanisms by which terrestrial planets might form: one standard and one novel. If the novel formation mechanism doesn’t bear out empirically, then the Earth was formed much closer to the conclusion of the universe’s window of opportunity for the formation of life ($$Papprox.2$$). In this case, the predicted number of life-sustaining planets drops to 1.25.	2016-02-08 09:51:57	{"extraction_info": {"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": 2, "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, "math_score": 0.4197353422641754, "perplexity": 2535.8690787638398}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701152987.97/warc/CC-MAIN-20160205193912-00140-ip-10-236-182-209.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1863870/valuation-of-index-of-polynomial-with-newton-polygon	Valuation of Index of polynomial with Newton Polygon I read here (page 237) that the valuation of the index of a polynomial is equal to the number of integer points below its Newton polygon. I am confused how this makes sense--the cited paper (this) just detailed an algorithm to calculate the index using the formula. In the introduction it mentioned Ore proving something along the lines of that but the cited papers seem to be in German. • Looking at page 237 from the book, "Algorithmic Arithmetic, Geometry, and Coding Theory," there is a mention at the bottom of the page of "how to compute $ind(f)$ as the accumulation of the number of points of integer coordinates lying below all Newton polygons that occur along the flow of the Montes algorithm." Is this the topic about which you are trying to find a paper or other exposition? – hardmath Jul 19 '16 at 14:39	2019-07-19 16:14:14	{"extraction_info": {"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, "math_score": 0.72862708568573, "perplexity": 208.2015078930947}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526324.57/warc/CC-MAIN-20190719161034-20190719183034-00378.warc.gz"}
https://mathoverflow.net/questions/326098/are-integral-extensions-of-a-catenary-ring-still-catenary	# Are integral extensions of a catenary ring still catenary? A (commutative unitary) Noetherian ring $$R$$ of finite dimension is said to be catenary if for every prime ideal $$\mathfrak{p}$$ of $$R$$ one has $$\mathrm{ht}(\mathfrak{p})+\mathrm{dim}(R/\mathfrak{p})=\mathrm{dim}R$$. Let $$A$$ be a catenary ring and $$B$$ a finite extension of $$A$$ (id est $$A\subseteq B$$ and $$B$$ is a finite $$A$$-module). Is $$B$$ a catenary ring? • Is your definition of catenary equivalent to the usual one (that requires that for all primes $p \subsetneq q$ all maximal prime chains $p \subsetneq \cdots \subsetneq q$ have the same length)? – tj_ Mar 24 '19 at 10:25 No. Nagata's famous family of examples of non-catenary rings yields a non-catenary finite extension of a catenary noetherian local domain. Reference: M. Nagata, On the chain problem of prime ideals, Nagoya Math. J. 10 (1956), 51-64.	2020-10-24 23:57:38	{"extraction_info": {"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": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9518524408340454, "perplexity": 221.59092933301972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107885059.50/warc/CC-MAIN-20201024223210-20201025013210-00473.warc.gz"}
https://wirelesspi.com/tuned-radio-frequency-trf-receiver/	For example, the signal at frequency $F_{C,2}$ is selected through tuning the bandpass filter to frequency $F_{C,2}$ that removes all other spectral contents, as illustrated in the figure below. If an adjacent channel were to be chosen, the tuning control mechanism consisting of circuit elements like variable capacitors and inductors just altered the center frequency of this filter. The major problem with a TRF is designing tunable bandpass filter with constant bandwidth and sufficient frequency selectivity over the entire tunable range.	2022-08-18 02:32:41	{"extraction_info": {"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, "math_score": 0.6850817203521729, "perplexity": 600.0433218305159}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573145.32/warc/CC-MAIN-20220818003501-20220818033501-00194.warc.gz"}
https://physics.stackexchange.com/questions/219056/how-can-i-understand-the-tunneling-problem-by-euclidean-path-integral-where-the?noredirect=1	# How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue? I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling problem using the bounce configuration under the Euclidean path integral. $$\langle 0\|e^{-HT}\|0\rangle=\int D[X] e^{-S}$$ Applying the stationary point method, we can evaluate the Euclidean path integral up to the quadratic correction. When the second derivative of S has no negative eigenvalue, all these stuff is easy to understand. However when it has negative eigenvalues, the evaluation of Euclidean path integral becomes divergent. At this point, some people still use the normal Gaussian integral and just take the result to be imaginary which as I see is illegal mathematically. S. Coleman take another views, he parameterize the quadratic fluctuation of the negative eigenvalue direction by a real parameter $z$, and when hit the maximum, he take $z$ to complex plane with finally identifying the result as the imaginary part of the energy. But I think this identification is still not very rigorous mathematically. These days I just searched for some books (Coleman's including) or papers to find out whether there is an reasonable explanation for that identification but failed. So could anyone please tell me whether there is an reasonable explanation for Colemann's continuation? If there is, could you please let me know it or recommend specific papers to me? I) Here we will give an explanation at the physics level of rigor. We are doing QM (as opposed to QFT) with a 1D position target space. Coleman et. al. in Ref. 1 are ultimately interested in the Minkowskian partition function/path integral $$\tag{A} Z^M~=~ \langle x_f \| \exp\left[-\frac{iH \Delta t^M e^{-i\epsilon}}{\hbar} \right] \| x_i \rangle ~=~N \int [dx] \exp\left[\frac{iS^M[x]}{\hbar} \right],$$ with Minkowskian action $$\tag{B} S^M[x]~=~\int_{t^M_i}^{t^M_f} \! dt^M \left[ \frac{e^{i\epsilon}}{2} \left(\frac{dx}{dt^M}\right)^2-e^{-i\epsilon}V(x)\right],$$ because this connects most easily to physics, such as e.g., unitarity, optical theorem, and decay rates (as opposed to Euclidean signature). We have included Feynman's $i\epsilon$-prescription in order to make the argument of the exponential (A) have an infinitesimal positive real part to help convergence. The corresponding Euclidean partition function/path integral is $$\tag{C} Z^E~=~ \langle x_f \| \exp\left[-\frac{H \Delta t^E e^{i\epsilon}}{\hbar}\right] \| x_i \rangle ~=~N \int [dx] \exp\left[-\frac{S^E[x]}{\hbar} \right],$$ with Euclidean action $$\tag{D} S^E[x]~=~\int_{t^E_i}^{t^E_f} \! dt^E \left[ \frac{e^{-i\epsilon}}{2} \left(\frac{dx}{dt^E}\right)^2+e^{i\epsilon}V(x)\right].$$ The Minkowskian and Euclidean formulations are connected via a Wick rotation $$\tag{E} t^E e^{i\epsilon}~=~e^{i\frac{\pi}{2}} t^M e^{-i\epsilon}.$$ In anticipation that we might hit branch cuts & singularities at the imaginary and real time axes, we have shorten the $\frac{\pi}{2}$ Wick rotation with an infinitesimal angle $\epsilon$ at both ends of the Wick rotation. In other words, we have inserted an $i\epsilon$-prescription in the Euclidean partition function (C) as well. If we didn't do this, the Euclidean partition function (C) would be manifestly positive (possibly infinite), and it would be impossible to derive the main complex result of Ref. 1, $$\tag{2.23} {\rm Im}(Z^E)_{\text{one bounce}} ~\approx~\frac{Nz_1e^{-\frac{S^E[\bar{x}]}{\hbar}}}{2\sqrt{\|\det^{\prime}A\|}},$$ where $A$ and $z_1$ are defined in eqs. (I) and (L) below, respectively. The prime in eq. (2.23) means that zero-modes should be excluded.$^1$ II) The evaluation of the Euclidean path integral (C) uses the method of steepest descent (MSD), where $\hbar$ is treated as a small parameter. It is an Euclidean version of the WKB approximation. The steepest descent formula explicitly displays a quadratic approximation to the Euclidean action (D) around saddle points. The MSD integration contour should pass through a saddle point in the direction of steepest descent. One should realize that the higher orders of the action (D) implicitly enter in the justification of MSD approximation, cf. e.g. Section VII below. III) It would be an interesting exercise to implement the $i\epsilon$-prescription from Section I consistently in what follows. However, here we shall just use it for the evaluation of (what naively appears to be) an unbounded Gaussian integral (if one ignores non-quadratic contributions): $$\int_{\mathbb{R}} \!\frac{dc_0}{\sqrt{2\pi\hbar}}\exp\left[-\frac{e^{i\epsilon}V(c_0)~\Delta t^E}{\hbar}\right] ~=~\int_{\mathbb{R}} \!\frac{dc_0}{\sqrt{2\pi\hbar}}\exp\left[\frac{\|\lambda_0\|}{2\hbar} \left(e^{i\frac{\epsilon}{2}}c_0\right)^2+\text{non-Gaussian terms}\right]$$ $$~\stackrel{z=e^{i\frac{\epsilon}{2}}c_0}{=}~e^{-i\frac{\epsilon}{2}} \int_{-e^{i\frac{\epsilon}{2}}\infty}^{e^{i\frac{\epsilon}{2}}\infty} \! \frac{dz}{\sqrt{2\pi\hbar}}\exp\left[\frac{\|\lambda_0\|z^2}{2\hbar} +\text{non-Gaussian terms}\right]$$ $$~\stackrel{\text{MSD}}{=}~e^{-i\frac{\epsilon}{2}} \int_{-e^{i\frac{\pi}{2}}\infty}^{e^{i\frac{\pi}{2}}\infty} \! \frac{dz}{\sqrt{2\pi\hbar}}\exp\left[\frac{\|\lambda_0\|z^2}{2\hbar} \right]$$ $$\tag{F}~\stackrel{z=iy}{=}~ie^{-i\frac{\epsilon}{2}} \int_{\mathbb{R}} \! \frac{dy}{\sqrt{2\pi\hbar}}\exp\left[-\frac{\|\lambda_0\|y^2}{2\hbar} \right]~=~\frac{ie^{-i\frac{\epsilon}{2}}}{\sqrt{\|\lambda_0\|}} ~\approx~\frac{i}{\sqrt{\|\lambda_0\|}} .$$ The upshot is that the MSD naively instructs us to integrate along the imaginary $c_0$-axis from $-i\infty$ to $+i\infty$ (as opposed to the other direction). We emphasize again that that an unbounded Gaussian integral a la (F) does not appear isolated by itself (in a well-posed physics context) but merely as a leading Gaussian approximation to an otherwise convergent integral. In summary, we will remove all $i\epsilon$'s from now on. It will only enter the calculation to determine a sign convention for unstable Gaussian integrals a la formula (F). IV) Next Ref. 1 considers a lopsided potential $V(x)$, cf. Fig.1. $\uparrow$ Fig. 1. A lopsided potential $V(x)$ with a false vacuum at $x=0$ and a true vacuum at $x=\infty$. We impose Dirichlet boundary conditions (BC) $$\tag{G} x(t^E_i)~=~ x_i~=~0~=~x_f~=~ x(t^E_f).$$ First we should identify the classical paths with Dirichlet BC eq. (G). There are the trivial path $x\equiv 0$, the bounce $\bar{x}$, and various (possibly repeated) combinations thereof, cf. Fig. 2. $\uparrow$ Fig. 2. The graph in Fig. 1 turned upside down. In order to apply the stationary action principle, the Euclidean Lagrangian (D) should be of the form 'kinetic energy minus potential energy'. Hence the apparent potential becomes minus $V$. The bounce solution $t^E\mapsto \bar{x}(t^E)$ starts and ends at $x=0$ and reflects at $x=\sigma$. Ref. 1 is interested in the contribution from precisely one bounce. The bounce solution $\bar{x}$ is determined by the fact that the 'kinetic energy plus potential energy' is conserved on-shell (and equal to zero, since that's what it was in the beginning of the bounce): $$\tag{H} \frac{1}{2} \dot{\bar{x}}^2-V(\bar{x})~=~0 \qquad\Leftrightarrow\qquad \dot{\bar{x}}~=~\pm \sqrt{2V(\bar{x})} .$$ We implicitly assume that $\int_0^{\sigma}\frac{dx}{\sqrt{2V(x)}} \leq \frac{\Delta t^E}{2}$, so that the bounce can be realized in the allocated time period $\Delta t^E:=t_f^E-t_i^E$. The action of the bounce becomes$^2$ $$\tag{2.13a} S^E[\bar{x}]~\stackrel{(D)}{=}~\int_{t^E_i}^{t^E_f} \! dt^E \left[ \frac{1}{2}\dot{\bar{x}}^2 +V(\bar{x})\right] ~\stackrel{(H)}{=}~\int_{t^E_i}^{t^E_f} \! dt^E ~\dot{\bar{x}}^2$$ $$\tag{2.13b}~\stackrel{(H)}{=}~2\int_0^{\sigma}\! dx \sqrt{2V(x)}.$$ $$\frac{\delta S^E[\bar{x}]}{\delta \bar{x}}~=~-\ddot{\bar{x}}+V^{\prime}(\bar{x})~=~0. \tag{2.8}$$ Eq. (H) is a first integral to eq. (2.8). V) We next expand the path integration variable $x$ around the $\bar{x}$ bounce solution $$\tag{2.5} x(t^E)~=~\bar{x}(t^E) + y(t^E), \qquad y(t^E)~:=~\sum_{n=0}^{\infty}c_n x_n(t^E),$$ where $x_n$ are real orthonormal eigenfunctions $$\tag{2.6} \int_{t^E_i}^{t^E_f} \! dt^E ~x_n(t^E) x_m(t^E)~=~\delta_{nm}, \qquad x_n(t^E_i)~=~0~=~x_n(t^E_f),$$ and $\lambda_n$ are eigenvalues of the Hessian operator $$\tag{I} A~:=~-\left(\frac{d}{dt^E}\right)^2 + V^{\prime\prime}(\bar{x}).$$ The integral measure is defined as $$\tag{2.7} [dx]~=~\prod_{n=0}^{\infty} \frac{dc_n}{\sqrt{2\pi\hbar}}.$$ The point spectrum consists of one negative eigenvalue $\lambda_0<0$; one zero eigenvalue $\lambda_1=0$; and positive eigenvalues $0<\lambda_2<\lambda_3< \ldots$. Differentiation of the EL eq. (2.8) wrt. $t^E$ yields that the velocity $\dot{\bar{x}}$ is a zero-mode: $A\dot{\bar{x}}=0$. The normalized zero-mode reads $$\tag{2.18} x_1~=~\frac{\dot{\bar{x}}}{\sqrt{S^E[\bar{x}]}},$$ cf. eqs. (2.6) & (2.13a). The zero-mode reflects the time-translational symmetry of the bounce $$\tag{J} \bar{x}(t^E)+ \dot{\bar{x}}(t^E)~dt^E_0~=~\bar{x}(t^E+dt^E_0) ~=~\bar{x}(t^E)+ x_1(t^E)~dc_1.$$ In other words, we can identify the zero-mode $c_1$ with the central instant $t^E_0$ of the bounce $$\tag{K} dc_1~\stackrel{(2.18)+(J)}{=}~\sqrt{S^E[\bar{x}]}~dt^E_0, \qquad \bar{x}(t^E_0)~=~\sigma,$$ up to an affine transformation. The integrated zero-mode contribution is therefore given by $$\tag{L} \sqrt{2\pi\hbar} z_1 ~:=~ \int \! dc_1 ~\stackrel{(K)}{=}~ \sqrt{S^E[\bar{x}]}~\Delta t^E.$$ In eq. (L) we have for simplicity assumed that the period of the bounce is much smaller than $\Delta t^E$. The velocity (2.18) has a zero/node at $x=\sigma$ because of energy conservation (H). This shows that there must be a nodeless eigenfunction $x_0$ with negative eigenvalue $\lambda_0<0$. $$\tag{M} S^E_2[x]~=~S^E[\bar{x}] +\frac{1}{2}\int_{t^E_i}^{t^E_f} \! dt^E ~y(t^E) Ay(t^E) ~=~S^E[\bar{x}] +\frac{1}{2} \sum_{n=0}^{\infty}\lambda_n c_n^2.$$ If we naively apply the MSD to the quadratic action (M) we would get a purely imaginary number $$\tag{N} (Z^E)_{\text{one bounce}}^{\text{MSD}} ~\approx~\frac{iNz_1e^{-\frac{S^E[\bar{x}]}{\hbar}}}{\sqrt{\|\det^{\prime}A\|}},$$ which is twice the estimate (2.23). Here we have used the sign convention from eq. (F). The estimate (N) is unrealistic for various reasons. For starters, it looks phony that (N) doesn't have any real part. One would naively expect that the imaginary part could develop gradually, not just as an on-off effect. VII) Discussion. Note that the potential has a wall for $x<0$, cf. Fig. 1. Hence the path integral (C) is heavily suppressed for $x<0$. It is therefore a poor approximation to use an unbounded Gaussian $c_0$-integration. (In contrast, all the bounded Gaussian $c_{n\geq 2}$-integrations are exponentially suppressed and hence fine.) Therefore let us not replace the half integral $$\tag{O} \int_{-\infty}^0 \! \frac{dc_0}{\sqrt{2\pi\hbar}} \exp\left[-\frac{S^E[\bar{x}+c_0x_0]}{\hbar} \right]~\in~\mathbb{R}$$ (which is real and convergent, due to the aforementioned wall for $x<0$) with the unbounded Gaussian approximation $$\tag{P} \int_{-\infty}^0 \!\frac{dc_0}{\sqrt{2\pi\hbar}} \exp\left[-\frac{S^E[\bar{x}]}{\hbar} +\frac{\|\lambda_0\|c_0^2}{2\hbar} \right]~\in~i\mathbb{R}$$ (which is imaginary, cf. eq. (F).). This explains the half in the main formula (2.23). The full integration contour for the $c_0$-variable is drawn in Fig.3. ^ \| \| \| --------->--------\| $\uparrow$ Fig. 3. The full integration contour for the $c_0$-variable in the complex $c_0$-plane is the negative real $c_0$-axis combined with the positive imaginary $c_0$-axis. The $c_0$-integration is closely related to $z$-integration mention in Ref. 1. References: 1. C.G. Callan, Jr. & S. Coleman, Fate of the false vacuum. II. First quantum corrections, Phys. Rev. D 16 (1977)1762. -- $^1$ Equations labelled by numbers (as opposed to letters) are taken from Ref. 1. $^2$ There is missing a factor 2 in eq. (2.13b) of Ref. 1. • Thank you very much for your awesome answer! But there are still some points that I am not clear. First, the $i\epsilon$ prescription in QFT comes from the functional evaluation of $<\Omega\|T\phi(x_1)\phi(x_2)\|\Omega>$ where we take $t$ to be $t(1-i\epsilon)$ so that in the limit of infinity, we pick up the ground state. This prescription takes us exactly to the Feynman propagator obtained in the canonical formalism. The case in QM is similar. But why do we must take the $i\epsilon$ prescription in the Euclidean QFT? We can not sipmply give such a request just because of Ref. 1. – Wein Eld Dec 8 '15 at 16:14 • And by Eq. (F), how can we tell that the MSD instructs us to integrate along the imaginary $c_0$ axis from $−i\infty$ to $+i\infty$? Doesnt Eq. (F) just tell us we integrate from $-\infty (1+\frac{i}{2}\epsilon)$ to $+\infty (1+\frac{i}{2}\epsilon)$? – Wein Eld Dec 8 '15 at 16:53 • 1. To connect with physics in Minkowski signature. 2. I updated the answer & eq. (F). – Qmechanic Dec 8 '15 at 20:50 • It's very kind of you to be so patient. But I still can't understand the third equal sign in Eq. (F) which you mean is based on the MSD. As I see it, it may be based on the Contour method. But the function $exp\left[\frac{\|\lambda_0\|z^2}{2\pi\hbar}\right]$ does not approach 0 at the infinity. I am so sorry. – Wein Eld Dec 9 '15 at 10:09 • @Qmechnic I am sorry to disturb you again. But I finally can digest your wonderful answer now. There is one step I am not clear. In Eq.(F), there is a step marked by "MSD" where you replace the $e^{i\frac{\epsilon}{2}}$ with $e^{i\frac{\pi}{2}}$, how can we do that? On the left side of "MSD", it seems that the integral diverges when $\epsilon\rightarrow 0$ and on the right side, it becomes an imaginary finite result. – Wein Eld Dec 28 '16 at 22:37	2019-06-16 14:34:24	{"extraction_info": {"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": 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, "math_score": 0.875636875629425, "perplexity": 550.7713170920504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998250.13/warc/CC-MAIN-20190616142725-20190616164725-00195.warc.gz"}
http://stackoverflow.com/questions/4714974/problem-executing-batch-file-in-pre-build-event	# Problem Executing Batch File in Pre-Build Event I'm trying to execute a batch file during a pre-build event. I have a new project and have added foo.bat to it. The file contains the following line: echo bar When I set the pre-build event command line to foo.bat, I get the following error: The command "foo.bat" exited with code 9009. When I set the pre-build event command line to call foo.bat, I get the following error: The command "call foo.bat" exited with code 1. Everything I've read related to those codes generally indicates that there is a problem with the contents of the batch file (not likely in this case) or that the system cannot find the batch file. The batch file works fine from a command prompt. Things I've tried already: Created the file using different tools, various encodings, placing exit 0 in the file, different build actions for the file, and copying the file to the output directory. All with no luck. What am I missing? It has to be something simple. Update: Yep, it was simple - the length of the path was too long. See answer below for details. Thanks! - Have you tried giving Everyone access for reading/writing? – the_drow Jan 17 '11 at 15:54 It's possible that you have another foo.bat somewhere in the PATH. Try to specify full path to your batch file like C:\Path\to\foo.bat. When project is being built the current directory is the one with the .vcproj file. The command path should be specified relative to this directory, if it's not in the PATH. One more thing to try to diagnose the problem would be to specify cmd in the pre-build event command explicitly like this: cmd /c C:\Path\to\foo.bat or even C:\windows\system32\cmd.exe /c C:\Path\to\foo.bat - At first I tried $(SolutionDir)Scripts\PostBuild.bat originally, but then that gave error code 9009. When I used cmd$(SolutionDir)Scripts\PostBuild.bat it worked for me, thanks! My bat file test contained a single line exit 0 no other white space. – Josh W Jun 13 '13 at 1:55 sorry, this actually didn't work, I have posted an answer below, the cmd just didn't show an error... but it also wasn't running the batch file – Josh W Jun 13 '13 at 2:39 It looks like my problem was the length of the path to the batch file. As this was a proof of concept I let VS create it in the default location: C:\Documents and Settings\UserXXX\My Documents\Visual Studio 2010\Projects\SolutionXXX\ProjectXXX\foo.bat As soon as I moved the solution to a location with a shorter path it worked fine. =P Thanks for the suggestions! - I got this working and I figure a picture is worth a thousand words, so here is the full setup in a single screenshot. - the CD to the batch file's directory is what fixes it here for me...when I directly call 'c:\mydirectory\mybatch.bat' it doesn't work, but a cd to 'c:\mydirectory' and then a call to 'mybatch.bat' does work...thanks! – Robert Petz Oct 22 '13 at 21:27	2014-03-16 12:56:49	{"extraction_info": {"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, "math_score": 0.6830698847770691, "perplexity": 2315.7211415882316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678702690/warc/CC-MAIN-20140313024502-00022-ip-10-183-142-35.ec2.internal.warc.gz"}
https://netket.readthedocs.io/en/latest/docs/sr.html	Quantum Geometric Tensor and Stochastic Reconfiguration# Mathematical Background# The Quantum Geometric Tensor (QGT) is the Fubini-Study metric tensor of the manifold on which a variational state is defined. In the general case (and in practise for any NQS ansatz), the QGT varies depending on the current quantum state and thus needs to be computed when the variational parameters $$W$$ change. To give an example, we consider a variational ansatz $$\psi\colon \mathbb{R} \rightarrow \mathscr{H}$$ which maps elements $$W$$ of the parameter space to vectors in Hilbert space (quantum states) $$\psi_W$$. The parameter space has a simple Euclidean metric, therefore the distance between two points $$\bf{W}$$ and $$\bf{W} + \bf{\delta W}$$ is simply $$\Vert\bf{\delta W} \Vert$$. However, what we really are interested in when optimizing variational ansätze is not the (Euclidean) distance between those two points in parameter space, but rather the distance in the Hilbert space between the corresponding quantum states (which also properly takes into account gauge degrees of freedom). The quantum mechanical distance function for quantum states is the Fubini-Study distance $$d(\psi, \phi) = \cos^{-1} \sqrt{\frac{\langle\psi\|\phi\rangle \langle\phi\|\psi\rangle}{\langle\psi\|\psi\rangle \langle\phi\|\phi\rangle}}$$. This can be expanded to second order in an infinitesimal parameter change $$\delta W$$ as $$d(\psi_W, \psi_{W + \delta W}) = (\delta W)^\dagger S \delta W$$ where $$S$$ is the QGT. Using the QGT in NetKet# In NetKet you can obtain (an approximation of) the quantum geometric tensor of a variational state by calling quantum_geometric_tensor. ma = nk.models.RBM(alpha=1, param_dtype=float) sa = nk.sampler.MetropolisLocal(nk.hilbert.Spin(0.5, 16), n_chains=16) vs = nk.vqs.MCState(sa, ma) qgt = vs.quantum_geometric_tensor() This will return an object that behaves as a Matrix, which acts on PyTrees of parameters. _, grad = vs.expect_and_grad(nk.operator.spin.sigmax(nk.hilbert.Spin(0.5, 16), 0)) The quantum geometric tensor also acts on dense ravellings of the parameters grad_dense, unravel = nk.jax.tree_ravel(grad) You can convert the quantum geometric tensor to a matrix representation by calling qgt.to_dense(). qgt_dense = qgt.to_dense() Lastly, you can solve the linear system $$Q_{i,j} x_j = F_i$$ by calling the solve method: x, info = qgt.solve(jax.scipy.sparse.linalg.gmres, grad) x, info = qgt.solve(nk.optimizer.solver.cholesky, grad) The different QGT implementations# While mathematically those operations are all well defined, there are several ways to implement them in code, all with different performance characteristics. For that reason, we have several (3) different implementations of the same Quantum Geometric Tensor object. The 3 implementations are: • netket.optimizer.qgt.QGTOnTheFly, which uses jax automatic differentiation through two vjp and one jvp product to compute the action of quantum geometric tensor on a vector and operates natively on PyTrees. This method will essentially run AD every time you compute QGT@vector. This method shines if the parameters of your network are stored in a PyTree with few leaf nodes and/or you are not performing many iterations of the iterative solver. It can compute the full dense QGT but it is not efficient at doing it so we advise not to use it with dense solvers. • netket.optimizer.qgt.QGTJacobianDense, which precomputes the log derivatives ( $$O_k$$ ) when it’s constructed and converts it to a single dense array. If you have a high number of total parameters and/or many leaf nodes in your parameter PyTree, this implementation might perform better because everything is stored contiguously in memory. However, it has an high ‘startup cost’. • netket.optimizer.qgt.QGTJacobianPyTree, same as above, but the precomputed jacobian is not stored contiguously in memory but is stored as a PyTree. This might work better than QGTJacobianDense if there are few leaf nodes. We haven’t studied the performance tradeoffs between the two Jacobian implementations and we would appreciate feedback. We also have an extra implementation, called netket.optimizer.qgt.QGTAuto, which uses some heuristics based on the parameters of the network to select the best QGT implementation. Be warned that the heuristics we use is very crude, and might not pick the best implementation all the time. All the QGT implementations listed above have several options that can affect their performance. We advise you to have a look at them and experiment. We provide a lot of freedom because it’s not yet clear to us what is the best implementation for which kind of problems. If you work with NetKet and determine that a particular implementation works best for certain types of networks, we would be glad to hear it! Let us know by opening a Discussion on our GitHub repository. We might use the insight to improve the automatic selection. Stochastic Reconfiguration# The stochastic reconfiguration (SR) method is a technique that makes use of the information encoded in the quantum geometric tensor described above to precondition the gradient used in stochastic optimization, improving the convergence rate to the ground state of a Hamiltonian $$\hat{H}$$. We would like to underline that SR can be derived (and therefore thought of) as imaginary time evolution of the variational ansatz. The derivation in the case of a variational optimization for the ground state, can be sketched as follows: Given a a variational wavefunction $$\ket{\psi_W}$$, we consider its first order Taylor expansion around $$W$$, $$\ket{\psi_{W+\delta W}} = \ket{\psi_W} + \delta W_k \hat{O}_k \ket{\psi_W}$$, where $$\bra{\sigma}\hat{O}_k \ket{\eta} = \delta_{\sigma,\eta} \frac{d \log\psi_W(\sigma)}{dW_k}$$. We wish to determine the updates $$\delta_{\sigma,\eta}$$ of the variational parameters that match a step of imaginary-time evolution, given by (1)#$$$\ket{\phi} = U(\epsilon)\ket{\psi_W} = e^{-\epsilon\hat{H}}\ket{\psi_W} \sim (\mathbb{I} - \epsilon \hat{H})\ket{\psi_W}$$$ It is possible to show that the updates $$\delta W_k$$ that minimise the norm of the state $$\ket{\phi}-\ket{\psi_{W+\delta W}}$$ can be determined by solving the linear system (2)#$$$S_{i,k} \delta W_k = F_i$$$ where $$F_i = \langle \hat{E}^{loc} \hat{O}_i\rangle - \langle \hat{E}^{loc} \rangle\langle \hat{O}_i\rangle$$ is the gradient of the Energy and $$S_{i,k} = \langle \hat{O}^\dagger_i \hat{O}_k\rangle - \langle \hat{O}^\dagger_i \rangle\langle \hat{O}_k\rangle$$ is the Quantum Geometric Tensor. The QGT is positive definite, therefore it can be inverted and the solution is formally written as (3)#$$$\bf{\delta W} = S^{-1} \bf{F},$$$ where bold fonts are used for vectors. A complication is given by the fact that the QGT is determined by Monte Carlo sampling and it might have several eigenvalues that are zero or very small, leading to numerical stability issues when inverting the matrix or in the resulting dynamics. The linear system can be solved with several methods. For the models with many parameters and to achieve the best performance, iterative solvers such as those found in jax.scipy.sparse.linalg, such as jax.scipy.sparse.linalg.cg() jax.scipy.sparse.linalg.gmres() are the best choice. Do note that to stabilize those algorithms it is often needed to add a small ($$10^{-5} - 10^{-2}$$) shift to the diagonal of the QGT. This can be set with the keyword argument diag_shift. Those methods, combined with our lazy representations of the QGT, never instantiate the full matrix and therefore achieve a great performance. However, when the number of parameters is small (smaller than 1000-5000), it might make sense to solve the system by factorizing the QGT with cholesky or SVD. Those techniques require instantiating the full dense matrix, but in general are more stable and don’t require a diagonal shift. Using stochastic reconfiguration# To use SR, you must simply provide it as a preconditioner to the VMC solver. sr = nk.optimizer.SR() gs = nk.VMC(hamiltonian, optimizer, variational_state=vstate, preconditioner=sr) By default this will use an appropriate QGT and the iterative solver jax.scipy.sparse.linalg.cg. It is possible to change the iterative solver by providing any solver from jax.scipy.sparse.linalg or one of the dense solvers in netket.optimizer.solver (such as svd/cholesky/LU) to the SR object. sr = nk.optimizer.SR(solver=nk.optimizer.solver.cholesky) gs = nk.VMC(hamiltonian, optimizer, variational_state=vstate, preconditioner=sr) The solver should be a function that accepts two arguments: the S matrix and the F vector in the linear system to be solved, and an optional x0 keyword argument. If you want to specify options of a linear solver, such as the tolerance or the cutoff rate you can do the following: from functools import partial sr = nk.optimizer.SR(solver=partial(jax.scipy.sparse.linalg.gmres, maxiter=1000, tol=1e-8)) gs = nk.VMC(hamiltonian, optimizer, variational_state=vstate, preconditioner=sr) If you don’t specify the QGT format, NetKet will try to guess the best format. We recommend you experiment and specify the QGT format that gives you the best performance, which can be by passing it as an argument. Additional keyword arguments will be forwarded to the QGT constructor, as shown below: sr = nk.optimizer.SR(QGTJacobianPyTree, solver=partial(jax.scipy.sparse.linalg.gmres, maxiter=1000, tol=1e-8, diag_shift=1e-3) gs = nk.VMC(hamiltonian, optimizer, variational_state=vstate, preconditioner=sr) Since SR leads to an optimisation that approximates an imaginary time evolution, we find that in general it is not a good idea to couple SR with advanced optimisers like ADAM, which modify the gradient remarkably. Stochastic Gradient Descent is the best choice in general. SR regularisation schedules# Stochastic Reconfiguration supports scheduling the diagonal_shift and the diagonal_scale variables along the optimisation. To use this feature, simply pass a function accepting as input the iteration number and returning the diagonal shift for that iteration. Moreover, optax provides several pre-built schedules such as linear scheduling interpolating from an initial shift to a final one, exponential scheduling, oscillating schedules and many more. To use them in practice, you can do something like the following. Check the documentation page of SR() for more extensive discussion on what options can be scheduled. sr = nk.optimizer.SR(diag_shift=optax.linear_schedule(0.01, 0.0001, 100)) gs = nk.VMC(hamiltonian, optimizer, variational_state=vstate, preconditioner=sr)	2023-02-07 04:22:57	{"extraction_info": {"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": 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": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.6896937489509583, "perplexity": 1064.5828433579957}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500384.17/warc/CC-MAIN-20230207035749-20230207065749-00296.warc.gz"}
https://studyqas.com/a-solar-lease-customer-bill-up-in-excess-of-6500-kwh-during/	# A solar lease customer bill up in excess of 6500 kWh during the summer using his solar panels. When he turned his electric heat on, the excess Began to A solar lease customer bill up in excess of 6500 kWh during the summer using his solar panels. When he turned his electric heat on, the excess Began to be use up at a rate of 50 kWh per day ## This Post Has 3 Comments 1. Expert says: step-by-step explanation: 2. Expert says: 30 step-by-step explanation: idk i hope i $Can someone me answer this question? : )$ 3. jackfrost5 says: Nikal bsdk gandu maderchod bhenchod jsnsnnsnsns	2023-01-29 19:36:21	{"extraction_info": {"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": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4630601406097412, "perplexity": 12057.225795221879}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499758.83/warc/CC-MAIN-20230129180008-20230129210008-00311.warc.gz"}
https://web2.0calc.com/questions/question-about-geometric-sequence-problem	+0 # question about geometric sequence problem 0 401 1 i need help this this question. in a geometric sequence the second term is 28 and the fifth term is 1792. find the 8th term. step by step tutorial in how to solve this question would be appreciated very much :D Guest May 15, 2015 #1 +19076 +15 i need help this this question. in a geometric sequence the second term is 28 and the fifth term is 1792. find the 8th term. $$Formula: \boxed{~ a_n=a\cdot r^{n-1} ~}$$ $$a_2=28=a\cdot{r}^1 \qquad a_5 = 1792=a\cdot r^4\qquad a_8 = a\cdot r^7$$ $$\dfrac{a_5}{a_2}=\dfrac{a\cdot r^4}{a\cdot r^1} = r^3\\\\\\ \small{\text{ \begin{array}{rcl} r^3 &=& \dfrac {1792}{28}\\\\ r &=& \sqrt[3]{\dfrac {1792}{28}}\\\\ r&=&\sqrt[3]{64}\\\\ r &=&4 \end{array} }}$$ $$a=\dfrac{28}{r}=\dfrac{28}{4}=7$$ $$\\a_8 = a\cdot r^7\\ a_8= 7\cdot 4^7\\ a_8 = 7\cdot 16384\\ a_8 = 114688$$ heureka May 15, 2015 Sort: #1 +19076 +15 i need help this this question. in a geometric sequence the second term is 28 and the fifth term is 1792. find the 8th term. $$Formula: \boxed{~ a_n=a\cdot r^{n-1} ~}$$ $$a_2=28=a\cdot{r}^1 \qquad a_5 = 1792=a\cdot r^4\qquad a_8 = a\cdot r^7$$ $$\dfrac{a_5}{a_2}=\dfrac{a\cdot r^4}{a\cdot r^1} = r^3\\\\\\ \small{\text{ \begin{array}{rcl} r^3 &=& \dfrac {1792}{28}\\\\ r &=& \sqrt[3]{\dfrac {1792}{28}}\\\\ r&=&\sqrt[3]{64}\\\\ r &=&4 \end{array} }}$$ $$a=\dfrac{28}{r}=\dfrac{28}{4}=7$$ $$\\a_8 = a\cdot r^7\\ a_8= 7\cdot 4^7\\ a_8 = 7\cdot 16384\\ a_8 = 114688$$ heureka May 15, 2015 ### 35 Online Users We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details	2018-03-20 23:39:39	{"extraction_info": {"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, "math_score": 0.9085078239440918, "perplexity": 1078.2694696464941}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647545.84/warc/CC-MAIN-20180320224824-20180321004824-00109.warc.gz"}
https://www.tutorke.com/lesson/7243-a-businessman-made-a-profit-of-sh-6000-he-saved-1-3of-the-profit-and-used-3-5of-the-remainder.aspx	Get premium membership and access revision papers with marking schemes, video lessons and live classes. OR # Class 8 Mathematics: Word problems involving fractions questions and answers A businessman made a profit of sh. 6000. He saved 1/3of the profit and used 3/5of the remainder for food and rent. He used the rest to improve the business. How much did he use to improve the business? A. Sh 2400 B. Sh 400 C. Sh 2000 D. Sh 1600 (7m 41s) 215 Views SHARE \|	2021-10-22 10:34:26	{"extraction_info": {"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, "math_score": 0.22563044726848602, "perplexity": 13489.537109816383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585504.90/warc/CC-MAIN-20211022084005-20211022114005-00030.warc.gz"}
https://www.physicsforums.com/threads/calculation-of-heat-created-during-compression.910552/	# Calculation of heat created during compression Tags: 1. Apr 7, 2017 ### Gosia 1. The problem statement, all variables and given/known data Hello, I have a task to make a heat balance of the evaporator. To do this, I was told to carry a few smaller energy balances in different parts of the evaporator. One of the things I had to calculate was the heat generated during steam compression. -steam is entering 12818,18 kg/h the fan at temp 60 C at pressure 200 mbar (saturated conditions) -steam durninng compression is being heated to 100 C, we want to achive 250mbar -after that steam is being cooled by sprayed water at 65 C I have to calculate the work of the pump and the heat that is being generated. 2. Relevant equations dU=Q-W 3. The attempt at a solution I was trying to approach it as it is isotropic compression going from 200mbar 60C to 250C 65 by simply divieding enthalpies from steam tables and omiting whole aspect of tempreture increse. But my supervisor said that this is actually hapaning in plants, that durning compression this much amout of heat is produced due to friction and comression and it must be calculated in the project. I coudnt find any similar exercises or exampels.Is this data sufficient? I feel like I am missing something. Please help! Last edited by a moderator: Apr 7, 2017 2. Apr 7, 2017 ### BvU Hello Gosia, Hard to follow. PLease describe the steps you mentioned separately: SO you have $h_i$ and $s_i$ there? namely : ? Assume isentropic (not isotropic -- that's something else): again: $h_{is}$ there? namely : ? So $T_{is}$ ? In reality $h$ ends up higher than $h_{is}$ because there is an efficiency $\eta_{is} = {h_i - h_{actual} \over h_i - h_{is} }$ again: $h_{actual}$ there? namely : ? So $T_{actual}$ ? heated as in 'heat is added' or is it heated because of the compresssion ? (In the latter case your $T_{actual}$ deterimines $\eta_{is}$ ) Strange. Why would someone do such a destructive deed ? sheet 20 here 3. Apr 9, 2017 ### Gosia That is not necessary cuz this approach was totally wrong. Yes, evrything from steam tables Isentropic is not a good assumption. Heat is beeing generated ONLY becaouse of compression. NO additional heat is beeing given by surroundings. This is a milk evaporator, in order to have no denaturation of proteins we have to maintain tempereture below 100 C	2017-08-19 12:54:17	{"extraction_info": {"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, "math_score": 0.5943657159805298, "perplexity": 2698.3323727643856}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105451.99/warc/CC-MAIN-20170819124333-20170819144333-00273.warc.gz"}
https://electronics.stackexchange.com/questions/94508/improve-3d-printing-via-distance-detection/615927	# Improve 3D printing via distance detection 3D Printers are now "auto-leveling" via a limit switch contacting the surface that is swung into place prior to printing and height of the bed is checked in 3 places. Software then continually adjusts the print head on the Z Axis throughout the printing process to travel the printing head in the same plane as the printing bed. Are there not electronics that can simply measure such a short distance (<2") accurately (ultrasound, infrared??? to accuracy of .1mm likely) and instantly without the need to lower the print head until a limit switch is engaged? It would seem likely this measurement of the printing bed's plane could be accomplished quicker and cheaper than by a limit switch swung down into place via a servo motor and moving the print head down to have it engage... • Even in 2013, the “servo dropping a switch” was only a thing in hobbyist devices. The professional printers used more sophisticated sensors. Apr 15 at 2:50 Distance measurement through non-contact methods is perfectly feasible, and is used in many industrial applications. Not having this in a 3D printer is not a technology constraint but a cost and complexity one. For instance, at the simplest level, proximity sensors such as Vishay TCRT5000 can be used, with fairly trivial microcontroller code required. The device consists of an infrared LED and a photodetector, which work by reflected infrared from a surface, such as the printer bed. Precision is not earth-shaking, but nor is the cost: $1.46 for 10 units. For something slightly more sophisticated, fully integrated, serial interface proximity sensors using a similar reflective IR mechanism are available, e.g. Vishay VCNL3020 (~$3 each) and Austria Microsystems TSL2671 (~\$1.60 each). Both of these have I2C interfaces, and eliminate the entire effort of modulating the IR LED and calibrating for ambient light. Depending on the layer resolution of the 3D printer, this too may not provide sufficient precision and accuracy for the purpose. In such case, laser-based, diffraction-grating angular deviation sensors such as the Sick OD Mini product range are available. These are typically accurate down to tens of microns. Prices are pretty steep, making these unviable for domestic 3D printers. Such devices are commonly used in industrial grade machinery, including, presumably, additive manufacturing machinery. Note that all the common distance sensing devices I have mentioned, used in the sensing range of interest, are based on infrared or occasionally visible light reflection, either using reflection intensity (low precision) or angular dispersion (high precision). Ultrasonic devices typically do not boast the degree of precision these optical devices can achieve. An LVDT can provide a resolution of few microns, however, the front end is more complex. Edit: Wikipedia LVDT Attach one to the shaft of the print head, calibrate the distance, and make sure the surface doesn't move. Last time I checked, LVDT were very expansive. (few hundreds USD per unit) • Could you elaborate a little? By LVDT, do you mean Linear Variable Differential Transformer? Could you post links to the LVDTs, which can do few microns? That would be interesting to see. Dec 24, 2013 at 18:52 • For an LVDT to work, the sense arm would have to be fixed to one object, say the base-plate, while the transformer would have to be fixed to the other object, say the print head. So how exactly would this be practical, or cost effective? Dec 25, 2013 at 9:40 • Attach the LVDT's core to the print head shaft and its body to the shaft's base. Since the XY actuator is usually at a fixed distance from the print bed, you have only one measurement to do, and that is of the print head's travel distance. Dec 25, 2013 at 12:13 2 years later and now it's an affordable extra PCB next to the printer head. A controller like the Duet has a connector for this sensor. "Differential modulated IR height sensor" https://miscsolutions.wordpress.com/mini-height-sensor-board/ Some distance sensing devices can be acquired via Ebay for about 120 Euros. I have actually tried this on an Omni200 3d printer to get more control over the first layer height. The sensor is a Panasonic HG-C1030-P. Mounted on the printhead it looks like this: or Most of these sensors come in so-called NPN or PNP variants, which just differ in their output circuitry. For the interfacing to the 3d printer controller, a small circuit board was designed which supports both versions. If anyone is interested, schematics can be found here: laser_proximity_sensor.pdf The board layout looks like this: The sensor allows precise measurements in the order of 1/100 of a mm on different materials and its output is able to give an active (low) signal if the object approaches too closely. Another helpful feature of the sensor is that for manual bed leveling, the readings at the led display can be used directly for any height correction.	2022-08-07 21:16:09	{"extraction_info": {"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, "math_score": 0.24950392544269562, "perplexity": 2378.2811293140353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570730.59/warc/CC-MAIN-20220807211157-20220808001157-00495.warc.gz"}
https://darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-1042.xml	skip to content # To Josiah Wedgwood III [20? August 1847]1 Friday My dear Jos. Thanks for your two messages.— You will see by enclosed letter, that by paying 51£ all calls to N.W. Railway will be completed. Will you please pay it.— Have you paid into Robarts for me the 15£ which I before advanced through Erasmus?—2 I presume you have deducted your own payments & interest.— The account will stand thus diag 460. N. W. Railway 51 £ 409 15 £? ? ramme So that there will be about 400£ to invest, which will just buy two shares of Leeds & Bradford.3 Each share being, as far as I remember £50 + £48. s 10. You told me that you had paid 40£ into Robarts: perhaps this included my 15£. You will have to receive the Grt. Western share for me, without indeed this 40£ was from the Grt. Western.—4 As you will have no doubt to write to Mr Stokes about the ahead paid shares, will you ask him to buy the two more: if they cost a trifle above the money in hand, I would pay it.— I am sorry to say there is one other business question, I must ask. In 16th of Nov. 1835, your Father5 made over to me 518£ Debentures in Monmouth Canal, which pays now only 3$\frac{1}{2}$ percent, so that I want to call it in, but Langton tells me, I ought to know whether the sum was lent for definite term.6 Can you tell me, or should I ask Frank to look amongst the papers at Maer. The money was originally lent in 1803. Yours affectionately. \| C. Darwin ## Footnotes Dated from details in CD’s Account Book and Investment Book (Down House MSS). See nn. 2, 3, and 4, below. See letter to Josiah Wedgwood III, [22 June – 17 August 1847], n. 4. CD’s Investment Book (Down House MS) records that forty guaranteed shares in the Leeds & Bradford Railway were purchased with money from Emma Darwin’s trust fund through Charles Stokes on 21 August 1847. The shares cost £45 each with a premium of £47 10s. Four further shares were purchased on 8 September, presumably with the £400 to invest that CD refers to in the letter. The £40 referred to was ‘interest on undivided property’ and was entered in CD’s Account Book (Down House MS) on 24 August. On 31 August an entry in the Account Book records the receipt of dividend on Great Western Railway shares, the sum being £42 13s. 11d. Josiah Wedgwood II, CD’s uncle. Charles Langton was Emma Darwin’s brother-in-law. In the event, CD retained the Monmouth Canal debentures; in October 1847 it was resolved to pay 5% on them to investors who agreed to make no call on their capital for seven years (CD’s Investment Book (Down House MS)). ## Summary Discusses the buying and selling of certain railway shares. ## Letter details Letter no. DCP-LETT-1042 From Charles Robert Darwin To Josiah Wedgwood, III Sent from unstated Source of text DAR 210.10: 14 Physical description 4pp ## Please cite as Darwin Correspondence Project, “Letter no. 1042,” accessed on 6 December 2021, https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-1042.xml Also published in The Correspondence of Charles Darwin, vol. 4 letter	2021-12-06 21:17:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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, "math_score": 0.26938143372535706, "perplexity": 11139.860910285352}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363312.79/warc/CC-MAIN-20211206194128-20211206224128-00227.warc.gz"}
https://www.transtutors.com/questions/during-the-year-heckle-paid-a-total-of-50-000-in-dividends-the-market-price-per-s--2577784.htm	# During the year, Heckle paid a total of $50,000 in dividends. The market price per s... During the year, Heckle paid a total of$50,000 in dividends. The market price per share of its stock is currently $60. In comparison, Jeckle paid a total of$114,000 in dividends, and the current market price of its stock is $76 per share. Heckle had net cash flows from operations of$271,500 and net capital expenditures of $625,000. Jeckle had net cash flows from operations of$492,500 and net capital expenditures of \$1,050,000. Information for prior years is not readily available. Assume that all notes payable are current liabilities and all bonds payable are long term liabilities and that there is no change in inventory. Prepare an Operating Asset Management Analysis by calculating for each company the : a) current ratio b) quick ratio c) receivables turnover d) day’s sales uncollected e) inventory turnover f) days’ inventory on hand g) payables turnover h) days’ payable i) financing period Prepare a Profitability And Total Asset Management Analysis by calculating for each company the: a) profit margin b) asset turnover c) return on assets Prepare a Financial Risk Analysis by calculating for each company the: a) debt to equity ratio b) return on equity c) investing coverage ratio Prepare a Liquidity Analysis by calculating for each company the cash flow yield a) Cash flows to sales b) Cash flows to assets c) Free cash flows Prepare An Analysis Of Market Strength by calculating for each company the: a) price/earnings ratio b) dividend yield 6) Once you have completed the first 5 steps, write a 1-2 page analysis of the Heckle and Jeckle corporations. Which one is better off and why? What are their similarities, differences, strengths, weaknesses, etc.? Which one should JD Campbell and Associates invest in and why? Note: This section is another opportunity where you can demonstrate your understanding of what you learned this semester so write as much as you can as long as it pertains to the project B a la n ce S h e e t D e c e m b er 3 1 2 0 1 3 J e c k le A s s e t s C a s h 80,000 192, 400 M a r k e table s e c u ritie s at c o s t 20 3,400 8 4, 600 A cco unt s R e ce iv a b le N e t 55 2,800 9 8 5, 400 I n v e n t o r y 6 29,8 00 1, 2 5 3, 4, 0 0 pre p aid Ex p e n s e s 5 4,400 1 1 4,000 Pro p erty, plant & E q u i p m e nt, Ne t 2,9 13,600 6,5 5 2,000 I n t a g i ble s and oth e r A s s e t s 55 3,200 1 4 4, 800 T o t a l A 5 s ets 4,9 8 7,2 00 9,3 2 6,6 0 0 Liabilities and stock h o l d e r's Equity A cco u n t s p a y a b l e 3 4 4,000 57 2, 600 150,000 N o te s p a y able 400,000 50, 200 7 3 4 0 0 I n c o m e T a x e s p a y a b l e 2,000,000 B o n d s P a y able 2,000,000 1,000,000 C o m m o n S t o c k, 2 0 p a r 600,000 3,5 68, 600 6,0 9,8 0 0 p a i d n Capital 2 1 1 2 0 0 0 8 3 3,200 R eta i n e d E a r n i n g s T o t a l Lia b tes and stock h old e r's e quity. 4,9 87, 200 9,3 2 6,6 0 0	2018-06-18 09:52:48	{"extraction_info": {"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, "math_score": 0.3540106415748596, "perplexity": 3949.6210304292094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860168.62/warc/CC-MAIN-20180618090026-20180618110026-00592.warc.gz"}
https://www.lmfdb.org/Character/Dirichlet/2736/	# Properties Modulus $2736$ Structure $$C_{36}\times C_{6}\times C_{2}\times C_{2}$$ Order $864$ Show commands for: Pari/GP / SageMath sage: H = DirichletGroup(2736) pari: g = idealstar(,2736,2) ## Character group sage: G.order() pari: g.no Order = 864 sage: H.invariants() pari: g.cyc Structure = $$C_{36}\times C_{6}\times C_{2}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{2736}(1711,\cdot)$, $\chi_{2736}(2053,\cdot)$, $\chi_{2736}(1217,\cdot)$, $\chi_{2736}(1009,\cdot)$ ## First 32 of 864 characters Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character. Character Orbit Order Primitive $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$\chi_{2736}(1,\cdot)$$ 2736.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$\chi_{2736}(5,\cdot)$$ 2736.he 36 yes $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$\chi_{2736}(7,\cdot)$$ 2736.cr 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$\chi_{2736}(11,\cdot)$$ 2736.ea 12 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$\chi_{2736}(13,\cdot)$$ 2736.gp 36 yes $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$\chi_{2736}(17,\cdot)$$ 2736.fj 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$\chi_{2736}(23,\cdot)$$ 2736.ez 18 no $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$\chi_{2736}(25,\cdot)$$ 2736.fd 18 no $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$\chi_{2736}(29,\cdot)$$ 2736.gz 36 yes $$1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$-1$$ $$e\left(\frac{19}{36}\right)$$ $$\chi_{2736}(31,\cdot)$$ 2736.di 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$\chi_{2736}(35,\cdot)$$ 2736.gv 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$\chi_{2736}(37,\cdot)$$ 2736.w 4 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$ $$\chi_{2736}(41,\cdot)$$ 2736.fn 18 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$-1$$ $$e\left(\frac{8}{9}\right)$$ $$\chi_{2736}(43,\cdot)$$ 2736.hi 36 yes $$-1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$\chi_{2736}(47,\cdot)$$ 2736.gc 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$ $$\chi_{2736}(49,\cdot)$$ 2736.r 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$\chi_{2736}(53,\cdot)$$ 2736.hc 36 no $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$\chi_{2736}(55,\cdot)$$ 2736.fv 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$\chi_{2736}(59,\cdot)$$ 2736.gx 36 yes $$-1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$\chi_{2736}(61,\cdot)$$ 2736.hf 36 yes $$1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$\chi_{2736}(65,\cdot)$$ 2736.bf 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$\chi_{2736}(67,\cdot)$$ 2736.hh 36 yes $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$\chi_{2736}(71,\cdot)$$ 2736.fy 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$\chi_{2736}(73,\cdot)$$ 2736.fi 18 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$\chi_{2736}(77,\cdot)$$ 2736.ed 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$\chi_{2736}(79,\cdot)$$ 2736.ex 18 no $$1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$\chi_{2736}(83,\cdot)$$ 2736.dy 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$\chi_{2736}(85,\cdot)$$ 2736.gm 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$\chi_{2736}(89,\cdot)$$ 2736.fh 18 no $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$\chi_{2736}(91,\cdot)$$ 2736.gt 36 no $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$\chi_{2736}(97,\cdot)$$ 2736.gg 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$\chi_{2736}(101,\cdot)$$ 2736.he 36 yes $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$1$$ $$e\left(\frac{13}{36}\right)$$	2021-06-13 11:42:02	{"extraction_info": {"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, "math_score": 0.7475517392158508, "perplexity": 91.38667307006848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, 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https://gamedev.stackexchange.com/questions/31189/dynamic-quadrees	Recently I started writing a Quadtree for creature culling in Opendungeons game. Thing is these are moving points and the bounding hierarchy will quickly get lost if the quadtree is not rebuild very often. I have several variants, first is to upgrade the leaf position every time creature move is requested. Note that I would need collision detection, so this might be necessary anyway. Second would be making leafs large enough that the creatures would sure stay inside its bounding box (due to its speed limit). The partition of a plane in quadtree is always fixed (modulo the hierarchical unions of some parts). For creatures close to the center of the plane, there would be no way to do this except to keep it inside one big leaf. Besides, this brakes the invariant that each point can be put into any small area as desired. So on the second thought could I use several quadrees? Each would have its "coordinate axis XY" shifted? Before I start playing with this maybe some other space diving structure would suit me better. Unfortunately, the wiki does not compare their execution time. If the object is still inside the same quad	2022-01-26 20:44:43	{"extraction_info": {"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, "math_score": 0.39676663279533386, "perplexity": 1144.8608272172196}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304961.89/warc/CC-MAIN-20220126192506-20220126222506-00655.warc.gz"}
https://www.sdss.org/dr15/manga/manga-target-selection/ancillary-targets/m31/	# M31 ## Contact Julianne Dalcanton University of Washington jd@astro.washington.edu ## Summary This program targets regions in M31 where the underlying physical properties are well-constrained from resolved stellar population analyses with the Hubble Space Telescope. Observations include 18 regions (~50-100 pc in size) with a wide range of local properties, including recent star formation, dust content, and metallicity. ## Finding Targets An object whose MANGA_TARGET3 or MNGTARG3 value includes one or more of the bitmasks in the following table was targeted for spectroscopy as part of this ancillary target program. See SDSS bitmasks to learn how to use these values to identify objects in this ancillary target program. Program (bit name) Bit number Target Description M31 21 M31 targets ## Description The observations consist of two plates: Plate 9677, where IFUs target inner regions (radii less than ~10kpc) with high surface brightness, and Plate 9678, where IFUs target lower surface brightness regions in the outer disk. The 18 total “science” IFU observations include regions with varying ancient and recent star formation history (SFH), dust column, dust geometry, and metallicity. IFUs also targeted HII regions, regions with variable stellar density, and regions with complimentary HST narrow band observations. Sky fibers were used to target star clusters. The scientific purpose of these observations is to assess the ability of of SED fitting codes to recover key astrophysical quantities from integrated light, using the tight constraints on physical properties provided by the Panchromatic Hubble Andromeda Treasury (PHAT; Dalcanton et al., 2012). The large angular extent of M31 necessitated numerous changes to the observing strategy and to the MaNGA DRP. We were able to repurpose the DRP modifications designed for the Coma cluster program (Gu et al. 2018) for the data reduction of the M31 plates. The M31 observations should not be used in standard analyses of the MaNGA sample. ## References Dalcanton et al., 2012, ApJS, 200, 18 Gu et al., 2018, ApJ, 859, 37	2022-05-19 22:12:42	{"extraction_info": {"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, "math_score": 0.6516331434249878, "perplexity": 6652.499326684215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662530066.45/warc/CC-MAIN-20220519204127-20220519234127-00344.warc.gz"}
http://cogsci.stackexchange.com/tags/linguistics/hot	# Tag Info ## Hot answers tagged linguistics 12 Firstly realize that Sapir-Whorf was proven wrong in the strong sense, but is accepted in the weak sense. I don't think there's really any doubt now that learning new symbols and languages, or just enhancing your vocabulary in one language, influences thought. Many mathematicians are especially proud of how accurately proofs communicate, and having gained ... 9 I've studied this a little bit within the context of timing responses to personality test items. General models of reading speed look at both the time to read the words as well as to comprehend. From memory, eye tracking studies have shown how the eyes will often back track to confusing parts of a sentence (apologies for lack of reference). Some general ... 9 What explains the tendency of people to not count the letter F's in the word "OF"? One possibility to explain this effect is related to the phenomenon of word skipping. When we read, we do not fixate every word, but skip a certain proportion of words while making educated guesses instead. Whether or not a certain word is skipped seems to depend on its ... 6 If you really wanted to know you could use models of reading behaviour - e.g. EZ-Reader or Swift. The Rayner reviews are the classic go-to to outlne this kind of thing: Rayner, K. (2009). Eye movements and attention in reading, scene perception, and visual search. The Quarterly Journal of Experimental Psychology (2006) (Vol. 62, pp. 1457-506). It will ... 6 This paper was written in 2010: Perceptual shift in bilingualism: brain potentials reveal plasticity in pre-attentive colour perception. In this paper, we test whether in Greek speakers exposure to a new cultural environment (UK) with contrasting colour terminology from their native language affects early perceptual processing as indexed by an ... 5 Sounds like what you're describing is "semantic satiation". Wikipedia explains: The explanation for the phenomenon was that verbal repetition repeatedly aroused a specific neural pattern in the cortex which corresponds to the meaning of the word. Rapid repetition causes both the peripheral sensorimotor activity and the central neural activation to fire ... 5 Motherese may play a role in emotional development. Soken and Pick write: "Concurrent with the exaggerated speech of motherese, there are probably exaggerated facial displays, allowing infants to explore the particular aspects of the face... Child-centered displays may serve as opportunities for learning about affective events." Walker-Andrews (1997) also ... 5 A few thoughts spring to mind: Part of the answer might depend on the maximum value of X (if all the messages are relatively short, that's a key piece of information). It doesn't decay, I don't think. The more information presented to the user, the more it all has to put into context with each other. But I don't think it's quadratic, either; that seems ... 5 The two legs upon which speed reading rests, in short, are chunking and seeking. Chunking is reading multiple words at once, while seeking allows you to find those chunks quickly and efficiently. The first exercise below will solve your subvocalization problems, but I recommend doing both in order to read text more effectively. You'll need: A computer ... 4 We were looking for an EEG device few years ago. The commercial offers were between 20,000 EUR for a 32 passive electrode to 50,000 EUR for an 64/128 active electrode. This included everything except the computers - some offers were without off-line data processing software. I never considered the EEG systems that were not mentioned in the method section of ... 4 I believe motherese exists to teach the infant to discriminate phonemes in the native language. Kuhl et al. (2005) show that during the first year language critical period, infants gain an increased ability to discriminate between phonemes of the native language, while their ability to discriminate between phonemes of non-native languages declines. ... 3 Fonagy and Target, although they do not specifically cite the term 'Motherese', believe that what they call 'Marking'- signalling an unreality or playfulness in mirrored displays of affect can play a crucial role in the development of a faculty they call 'Mentalization'. According to their model, newborns experience affect as all-pervading, and do not see ... 3 I just had a project where I had to figure this out. I found that a good rule of thumb was the following: $$timeToRead = 1300 + (chars * 65);$$ So that's an initial time of 1300ms to adjust to what you need to be reading and about 65ms per character including spaces. 2 Here is a lexical decision task I wrote years ago using PHP and Javascript (github link). Distributed as-is, no documentation. There is still some vestigial code in there for an experimental manipulation. 2 One option is to use Inquisit Web Edition. Here is an example script with a lexical decision task. Unfortunately, it is not free and it requires installation of a plug-in. Version 4 of Inquisit runs on OSX and Windows. Thus, it wont work in Linux or on phones, tablets, etc. 2 Some cognitive scientists I heard are clear about benefits of being bilingual as exposed by @Damien or here - http://www.nytimes.com/2011/05/31/science/31conversation.html?_r=0. They also do not hide the associated cognitive costs especially at a young age. I found the following presentation very interesting ... 2 It seems to me that it'd be a type of a tip-of-the-tongue phenomenon caused by bilingualism. If you don't use German regularly, it might be attributed to language attrition, but this seems unlikely if you're still being exposed to German more than English. http://en.wikipedia.org/wiki/Tip-of-the-tongue_phenomenon#Effects_of_bilingualism 2 Difficulties with language is not actually a symptom of autism. Autism Spectrum Disorder involves difficulties in social communication and interaction, as well as restricted and repetitive interests or behaviours (DSM-V, 2013). The term "social communication" is referring to difficulties in the social aspects of language and other communication, such as ... 1 This is a very interesting question. Unfortunately, I was not able to find something that would give you a clear answer. In essence, I think this question is asking for a cognitive mechanism underlying word generation in phonemic/phonological verbal fluency test which is a matter that has rarely been addressed (Robinson et al, 2012). Studies such as the ... 1 Just for reference, I ended up writing simple web-based lexical decision task software myself. 1 It sounds like you're talking about Latent Semantic Analysis. Here's their rundown of what it is. However, LSA as currently practiced has some additional limitations. It makes no use of word order, thus of syntactic relations or logic, or of morphology. Remarkably, it manages to extract correct reflections of passage and word meanings quite well without ... Only top voted, non community-wiki answers of a minimum length are eligible	2014-10-25 09:40:21	{"extraction_info": {"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, "math_score": 0.3001135289669037, "perplexity": 2110.2107407606586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119648008.18/warc/CC-MAIN-20141024030048-00044-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.tutorialspoint.com/mysql-query-to-check-if-database-is-empty-or-not	# MySQL query to check if database is empty or not? MySQLMySQLi Database You can use INFORMATION_SCHEMA.COLUMNS to check if a database is empty or not. The syntax is as follows − SELECT COUNT(DISTINCT TABLE_NAME) AS anyAliasName FROM INFORMATION_SCHEMA.COLUMNS WHERE table_schema = 'yourDatabaseName'; The above syntax returns 0 if the database has notable otherwise it returns the number of tables. For our example, we are using the databases ‘sample’ and ‘test3’, which we created before. The first database ‘sample’ has more tables, therefore the above query will return a number of tables. The second database ‘test3’ does not have any tables, therefore the above query will return 0. Case 1 − Database sample The query is as follows − mysql> SELECT COUNT(DISTINCT table_name) AS TotalNumberOfTables FROM information_schema.columns WHERE table_schema = 'sample'; The following is the output displaying the number of tables in it, therefore the database isn’t empty − +---------------------+ \| TotalNumberOfTables \| +---------------------+ \| 130 \| +---------------------+ 1 row in set (0.01 sec) Case 2 − Database test3 The query is as follows − mysql> SELECT COUNT(DISTINCT table_name) AS TotalNumberOfTables FROM information_schema.columns WHERE table_schema = 'test3'; The following is the output returning 0, therefore the database is empty − +---------------------+ \| TotalNumberOfTables \| +---------------------+ \| 0 \| +---------------------+ 1 row in set (0.00 sec) As mentioned above, if we get 0, that would mean there are no tables in the database. Published on 19-Mar-2019 08:46:40	2021-12-05 18:01:59	{"extraction_info": {"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, "math_score": 0.2350759208202362, "perplexity": 7669.753298099937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363215.8/warc/CC-MAIN-20211205160950-20211205190950-00445.warc.gz"}
https://quant.stackexchange.com/questions/18866/analytic-formula-for-the-value-of-an-american-put-option	# analytic formula for the value of an American put option It seems to be a foolish question but I can't take my mind off from , Is it true that there is no analytic formula for the value of an American put option on a non-dividend-paying stock (or a divident paying stock either) has been produced ? There is no closed formula for American put option. However, there is an analytic solution for perpetual American put option. The only difference is that the maturity of the perpetual American option is infinite. Why that makes such a difference? That's because we can determine the optimal stopping time (and therefore optimal exercise price) if we don't have to worry about maturity. Unfortunately, there is no such solution if the optimal exercise price is a function of maturity. Consider: L is the optimal exercise price. It's a convex function of maturity. Far away from maturity, the price is significantly lower than K because we'd expect a deep in-the-money intrinsic value to compensate giving up the option right early. The price approaches to the strike price as shown in the plot. This function is clearly non-linear. You might need to do approximation. For example, the Barone-Adesi-Whaley quadratic approximation. Google for the paper if you're interested. it all comes down to how you define analytic. If you push the definition far enough there are some. An exact and explicit solution for the valuation of American put options DOI:10.1080/14697680600699811 Song-Ping Zhu pages 229-242 However, it's an infinite sum of recursively defined double integrals. • Interesting. What's the real benefit of it practically? The computational complexity seems too much.... – HelloWorld Jul 15 '15 at 10:12 Yes, there is none. Quoting Higham (2004): "The mathematical problem defined by (...) is much more difficult than the Black–Scholes PDE that arose without the early exercise facility. In general, there is no closed form expression for $P^{Am}(S, t$) and we must use numerical methods to obtain approximate values." Where (...) refers to the American Option PDE. Please check chapter 18 of this book. In the Black-Scholes Model or Heston Model, the American option satisfies the same PDE, but with different boundaries.For an American call option $C_A(S,\tau )$, we can therefore write \begin{align} \frac{\partial {{C}_{A}}}{\partial \tau }=+\frac{1}{2}{{\sigma }^{2}}{{S}^{2}}\frac{{{\partial }^{2}}{{C}_{A}}}{\partial {{S}^{2}}}+(r-q)S\frac{\partial {{C}_{A}}}{\partial S}-r{{C}_{A}} \end{align} or(Heston) $C_A(S,v,\tau )$ satisfy \begin{align} \frac{\partial {{C}_{A}}}{\partial \tau }=\,+\frac{1}{2}v{{S}^{2}}\frac{{{\partial }^{2}}{{C}_{A}}}{\partial {{S}^{2}}}+\rho \sigma \,vS\frac{{{\partial }^{2}}{{C}_{A}}}{\partial S \partial v}+\frac{1}{2}{{\sigma }^{2}}v\frac{{{\partial }^{2}}{{C}_{A}}}{\partial {{v}^{2}}}-rC_A+(r-q)S\frac{\partial {{C}_{A}}}{\partial S}+\kappa (\theta -v)\,\frac{\partial {{C}_{A}}}{\partial v} \end{align} where $\tau$ is the time until maturity. The PDE holds for $0 ≤ \tau < T$, where $T$ is the maturity calendar time, and for $0 < S ≤ b(v, \tau)$, where $b(v, τ )$ is the early exercise boundary. Essentially, this means that as long as the stock price is within the early exercise boundary, the American call option behaves like its European counterpart and the PDE holds. Building on the work of Chiarella and Ziogas(2006), Tzavalis, and Wang(2003). approximate the early exercise boundary $b(v,\tau )$ with the log-linear function. \begin{align} b(v,\tau )=exp(b_0(\tau)+b_1(\tau)v) \end{align} They show the American call is obtained by adding the early exercise premium to the price of the European call \begin{align} C_A=C_E+V \end{align} where $V$ is the early exercise premium on an American call with strike $K$ and maturity is $\tau$ • This is also used by Barone-Adesi-Whaley. They approximate the early exercise premium with a quadratic function. – HelloWorld Jul 15 '15 at 12:39 • Yes, but even for the calculation of European option we need to approximate it. – user16891 Jul 15 '15 at 19:09	2020-01-21 11:29:44	{"extraction_info": {"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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8804922699928284, "perplexity": 996.4708249281922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250603761.28/warc/CC-MAIN-20200121103642-20200121132642-00111.warc.gz"}
https://www.ncatlab.org/nlab/show/Javier+Guti%C3%A9rrez	# nLab Javier Gutiérrez ## Selected writings On generalizing the notion of solid rings to monoids in a monoidal category: category: people Last revised on September 14, 2021 at 11:42:16. See the history of this page for a list of all contributions to it.	2021-10-26 09:34:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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, "math_score": 0.48614564538002014, "perplexity": 1494.0227941334383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587854.13/warc/CC-MAIN-20211026072759-20211026102759-00375.warc.gz"}
https://marketrealist.com/2016/08/apache-corps-implied-volatility-post-2q16-earnings/	# Apache’s Implied Volatility after Its 2Q16 Earnings By Updated ## Apache’s implied volatility Apache’s (APA) current implied volatility is ~36.1%. That’s ~0.70% lower than its 15-day average of 36.3%. As you can see in the graph below, Apache’s implied volatility has fallen since the start of this year. There were also periods in which Apache saw high volatility coincide with high volatility in energy prices (USO) (UNG). With improved commodity prices since the beginning of this year, Apache’s volatility has fallen drastically. Apache’s peers Anadarko Petroleum (APC), Continental Resources (CLR), and Concho Resources (CXO) have implied volatilities of 36.8%, 46.3%, and 33.3%, respectively.	2020-12-01 12:17:34	{"extraction_info": {"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, "math_score": 0.9349724054336548, "perplexity": 14039.127325102401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141674082.61/warc/CC-MAIN-20201201104718-20201201134718-00115.warc.gz"}
https://www.proquest.com/docview/304624195/abstract	Abstract/Details ## A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees preserving greatest element Englert, Burkhard. University of Connecticut ProQuest Dissertations Publishing, 2000. 9984065. ### Abstract (summary) We present a necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable (c.e.) degrees preserving greatest element. In the earlier work Lerman [19] gave a necessary and sufficient condition for embeddings of principally decomposable lattices into the c.e. degrees that do not preserve greatest element. Here, we present the construction of an embedding of a principally decomposable lattice that preserves greatest element, prove that Lerman's condition is sufficient for such an embedding construction and show that the necessity of the condition follows from [19]. ### Indexing (details) Subject Mathematics Classification 0405: Mathematics Identifier / keyword Pure sciences; Computably enumerable degrees; Embedding; Finite lattices; Necessary and sufficient condition; Principally decomposable Title A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees preserving greatest element Author Englert, Burkhard Number of pages 74 Degree date 2000 School code 0056 Source DAI-B 61/08, Dissertation Abstracts International Place of publication Ann Arbor Country of publication United States ISBN 978-0-599-90407-1 Lerman, M. University/institution University of Connecticut University location United States -- Connecticut Degree Ph.D. Source type Dissertation or Thesis Language English Document type Dissertation/Thesis Dissertation/thesis number 9984065 ProQuest document ID 304624195	2022-08-17 07:11:36	{"extraction_info": {"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, "math_score": 0.8826904892921448, "perplexity": 6128.476358029114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572870.85/warc/CC-MAIN-20220817062258-20220817092258-00727.warc.gz"}
https://www.physicsforums.com/threads/integral-inequality.977574/	Integral inequality Homework Helper Homework Statement: Prove $$k^2\int_k^\infty g(x) dx\leq\frac{4}{9}\int_0^{\infty}x^2g(x) dx$$ for a non-increasing function ##g(x)##. Relevant Equations: The inequality is very easy to prove if ##g(x)## is constant for ##0<x<k+a## and zero otherwise. So I will use it. I have to prove that, for a non-increasing function ##g(x)## the following inequality is true: $$k^2\int_k^\infty g(x) dx\leq\frac{4}{9}\int_0^{\infty}x^2g(x) dx$$ This exercise is from the book Mathematical methods of statistics by Harald Cramer, ex. 4 pg 256 Following the instructions of the book I find the following: For an arbitrary non-increasing function ##g(x)##, I define $$a:=\frac{1}{g(k)}\int_{k}^{\infty}g(x)dx$$ and also I define the function ##h(x)=g(k)## for ##0<x<k+a## (and 0 otherwise). So now, ##h(x)## is a constant non-decreasing function and the inequality $$k^2\int_k^\infty h(x) dx\leq\frac{4}{9}\int_0^{\infty}x^2h(x) dx$$ is very easy to prove. So with that $$k^2\int_k^\infty g(x)dx\equiv k^2ag(k)=k^2\int_k^{k+a}g(k) dx=k^2\int_k^{\infty}h(x) dx\leq \frac{4}{9}\int_0^{\infty}x^2h(x) dx$$ But now I'm supposed to prove that $$\int_0^{\infty}x^2h(x) dx\leq \int_0^{\infty}x^2g(x) dx$$ I have tried to reorganize it and I have write $$\int_0^{\infty}x^2\left(g(x)-h(x)\right) dx\geq 0 \Longrightarrow$$ $$\int_0^{k}x^2\left(g(x)-g(k)\right) dx+\int_{k+a}^{\infty}x^2g(x) dx\geq \int_k^{k+a}x^2\left(g(k)-g(x)\right) dx$$ Where now all the integrals are positive, but I don't know how to continue. Thank you. Delta2 Homework Helper Gold Member Is it given that ##g(x)## is also non negative(##g(x)\geq 0##)? Homework Helper Well it's not implicitly said, but if the integral ##\int^{\infty}g(x)dx## converges this implies (I think) that $$\lim_{x\to \infty}g(x)=0$$. So, since ##g(x)## it's non-icreasing this implies ##g(x)\geq0##. BTW I forgot to say that ##k>0##. Delta2 member 587159 but if the integral ##\int^{\infty}g(x)dx## converges this implies (I think) that $$\lim_{x\to \infty}g(x)=0$$. This is false. Consider ##f(x)= \sin(x^2)##. Maybe under the additional hypothesis that ##g## is non-increasing it can be correct, but you should justify this step. Homework Helper This is false. Consider ##f(x)= \sin(x^2)##. Maybe under the additional hypothesis that ##g## is non-increasing, it can be correct, but you should justify this step. Ok, thank you! I wasn't very sure of that property... In any case, since ##g(x)## is non-increasing, if there exist a value ##x_0## for which ##g(x_0)<0##, then $$g(x)\leq g(x_0), \qquad \forall x>x_0$$ so then, $$\int_{x_0}^{\infty}g(x)dx\leq \int_{x_0}^{\infty}g(x_0)dx=g(x_0)\int_{x_0}^{\infty}dx\rightarrow -\infty$$ So the integral diverges and therefore, ##g(x)## must be also non-negative. I think now it's correct, but even if it's not, the main purpose to this is to use it then with probability density functions, so let's assume non-negativity as an assumption if you want :D Delta2 StoneTemplePython Gold Member Homework Statement: Prove $$k^2\int_k^\infty g(x) dx\leq\frac{4}{9}\int_0^{\infty}x^2g(x) dx$$ for a non-increasing function ##g(x)##. I think now it's correct, but even if it's not, the main purpose to this is to use it then with probability density functions, so let's assume non-negativity as an assumption if you want :D The thread seems to be bouncing around, and from my vantage, at least, un-motivated. It simply isn't true that PDFs are real non-negative and non-increasing in general. So there seems to be some kind of special structure in mind that is absent from the thread. Alternatively, I'll point out that being real non-negative and non-increasing is true about all complementary CDFs, and with some care, we can integrate over these to recover moments. (edited to insert word complementary) Last edited: Homework Helper Well... The thread is to prove the inequality... It seems to be bouncing around because we are focusing more on my assumption that ##g(x)## is non-negative than in the thread itself . Forget what I've said about PDF, I'm not a mathematician and maybe I haven't been told the most general definition, but for my point of view, a PDF must be real and non-negative. But has nothing to do with the thread. StoneTemplePython	2021-06-23 18:31:41	{"extraction_info": {"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, "math_score": 0.9759486317634583, "perplexity": 777.0349805376779}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488539764.83/warc/CC-MAIN-20210623165014-20210623195014-00152.warc.gz"}
http://gifi.stat.ucla.edu/apl/introduction.html	# 1 Introduction APL was introduced by Iverson (1962). It is an array language, with many functions to manipulate multidimensional arrays. R also has multidimensional arrays, but not as many functions to work with them. In R there are no scalars, there are vectors of length one. For a vector x in R we have dim(x) equal to NULL and length(x) > 0. For an array, including a matrix, we have length(dim(x)) > 0. APL is an array language, which means everything is an array. For each array both the shape ⍴A and the rank ⍴⍴A are defined. Scalars are arrays with shape equal to one, vectors are arrays with rank equal to one. If you want to evaluate APL expressions using a traditional APL virtual keyboard, we recommend the nice webpage at ngn.github.io/apl/web/index.html. EliStudio at fastarray.appspot.com/default.html is essentially an APL interpreter running in a Qt GUI, using ascii symbols and symbol-pairs to replace traditional APL symbols (Chen and Ching (2013)). Eli does not have nested arrays. It does have ecc, which compiles eli to C. In 1994 one of us coded most APL array operations in XLISP-STAT. The code is still available at gifi.stat.ucla.edu/apl. There are some important differences between the R and Lisp versions, because Lisp and APL both have C’s row-major ordering, while R (like Matlab) has Fortran’s column-major ordering in the array layout. Our R version of APL uses column-major ordering. By slightly changing the two basic building blocks of our code, the aplDecode() and aplEncode() functions, it would be easy to choose between row-major and column-major layouts. But this would make it more complicated to use the code with the rest of R. Because of layout, the two arrays 3 3 3⍴⍳27 and array(1:27,rep(3,3)) are different. But what is really helpful in linking the two environments is that ,3 3 3⍴⍳27 and as.vector(array(1:27,rep(3,3)), which both ravel the array to a vector, give the same result, the vector ⍳27 or 1:27. This is, of course, because ravelling an array is the inverse of reshaping a vector. Most of the functions in R are written with arrays of numbers in mind. Most of them will work for array with elements of type logical, and quite a few of them will also work for arrays of type character. We have to keep in mind, however, that APL and R treat character arrays quite differently. In R we have length("aa") equal to 1, because "aa" is a vector with as its single element the string "aa". R has no primitive character type, characters are just strings which happen to have only one character in them. In APL strings themselves are vectors of characters, and ⍴aa is 2. In R we can say a<-array("aa",c(2,2,2)), but in APL this gives a domain error. In APL we can say 2 2 2⍴“aa”, which gives the same result as 2 2 2⍴“a” or 2 2 2⍴‘a’. In this version of the code we have not implemented the nested arrays of APL-2. Nesting gives every array A not just a shape ⍴A and a rank ⍴⍴A, but also a depth. The depth of an array of numbers or characters is one, the depth of a nested array is the maximum depth of its elements. There are many dialects of APL, and quite a few languages derived from APL, such as A+ and J. As a standard for APL-I we use Helzer (1989).	2018-02-24 00:25:41	{"extraction_info": {"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, "math_score": 0.4788287580013275, "perplexity": 1606.8818108156747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814872.58/warc/CC-MAIN-20180223233832-20180224013832-00427.warc.gz"}
https://realestatetrainershq.com/numpy-and-scipy-documentation-numpy-and-scipy/	The skill of knowing how much vectorization to use in your code is something that you’ll develop with experience. The decision will always need to be made based on the nature of the application in question. In other words, NumPy has broadcast the scalar to a new array of appropriate dimensions to perform the computation. We now have our data stored in a NumPy array that we’ve named data. Vectorization is the process of performing the same operation in the same way for each element in an array. This removes for loops from your code but achieves the same result. Whichever option you choose, once you have it installed, you’ll be ready to run your first lines of NumPy code. If you’ve already got a workflow you like that uses pip, Pipenv, Poetry, or some other toolset, then it might be better not to add conda to the mix. I need to compare each of the 20 thousands line with 60 thousands line(each vae 80 columns, find the closest neighbors by finding euclid distance. I can only use … Negative numbers mean “from the end of the array.” For example, x[-1] means the last row of x. When we are ready numpy to save our data, we can use the save function. We’ll detail a few of the most common approaches below. ## 4 Integer Array Indexing Maclaurin series are a way of approximating more complicated functions with an infinite series of summed terms centered about zero. Summations are converted to more verbose for loops, and limit optimizations end up looking like while loops. When you calculate the transpose of an array, the row and column indices of every element are switched. Input 7 provides a more traditional, idiomatic masked selection that you might see in the wild, with an anonymous filtering array created inline, inside the selection brackets. This syntax is similar to usage in the R programming language. In axis 2, the two arrays have matching sizes, so they can operate successfully. As the name suggests, it will return all unique values in the array. Using what we’ve learned about indexing, we can start by separating the column labels from the rest of the data. Being able to generate pseudo-random numbers is often necessary in data science applications. ## Hashes for numpy-1.24.1-cp310-cp310-macosx_11_0_arm64.whl In fact, it’s just a different way of thinking about a list of lists. By specifying a row number and a column number, we’re able to extract an element from a matrix. NumPy, which stands for Numerical Python, is a library consisting of multidimensional array objects and a collection of routines for processing those arrays. Using NumPy, mathematical and logical operations on arrays can be performed. This tutorial explains the basics of NumPy such as its architecture and environment. A shape of will be a 2-dimensional array with 10 rows and 10 columns. A shape of will be a 1-dimensional array with 10 elements. We can create a NumPy array using the numpy.array function. If we pass in a list of lists, it will automatically create a NumPy array with the same number of rows and columns. Because we want all of the elements in the array to be float elements for easy computation, we’ll leave off the header row, which contains strings. Because we want to be able to do computations like find the average quality of the wines, we need the elements to all be floats. The documentation for np.vectorize() states that it’s little more than a thin wrapper that applies a for loop to a given function. There are no real performance benefits from using it instead of normal Python code, and there are potentially some overhead penalties. However, as you’ll see in a moment, the readability benefits are huge. One last thing to note is that you’re able to take the sum of any array to add up all of its elements globally with square.sum(). This method can also take an axis argument to do an axis-wise summing instead. Internally, both MATLAB and NumPy rely on BLAS and LAPACK for efficient linear algebra computations. • There are the following advantages of using NumPy for data analysis. • Note that although x and y are optional, if you specify x, you MUST also specify y. • Pandas extends NumPy by providing functions for exploratory data analysis, statistics, and data visualization. • A shape of will be a 1-dimensional array with 10 elements. • In other words, Numpy broadcasts the 1×2 array to an array appropriate to perform the operation with the 2×2 array. • Runtime compilation of numerical code has been implemented by several groups to avoid these problems; open source solutions that interoperate with NumPy include numexpr and Numba. • For now, just keep in mind that these little checks don’t cost anything. For brevity we have left out a lot of details about numpy array indexing; if you want to know more you shouldread the documentation. Runtime compilation of numerical code has been implemented by several groups to avoid these problems; open source solutions that interoperate with NumPy include numexpr and Numba. Cython and Pythran are static-compiling alternatives to these. To avoid installing the large SciPy package just to get an array object, this new package was separated and called NumPy. Support for Python 3 was added in 2011 with NumPy version 1.5.0. Examples include modeling system noise and Monte Carlo simulations. Armed with our matrix $x$ and vector $\theta$, we’ll proceed to define vectorized and non-vectorized versions of evaluating the linear expressions to compare the computation time. X is now a range of 40 numbers reshaped to be 10 rows by 4 columns. ## Python NumPy Tutorial: An Applied Introduction for Beginners Numpy is a tool for mathematical computing and data preparation in Python. It can be utilized to perform a number of mathematical operations on arrays such as trigonometric, statistical and algebraic routines. It also provides a large collection of high-level mathematical functions to operate on arrays. We’ll dive into all of the possible types of multidimensional arrays later on, but for now, we’ll focus on 2-dimensional arrays. A 2-dimensional array is also known as a matrix, and is something you should be familiar with. For example, in a 3-axis array, x means all data in the 3rd axis of the 1st row and 1st column. At some point, it will become necessary to index subsets of a https://globalcloudteam.com/ array. For instance, you might want to plot one column of data or perform a manipulation of that column. NumPy provides a foundation on which other data science packages are built, including SciPy, Scikit-learn, and Pandas. It requires fewer lines of code for most mathematical operations than native Python lists. This tutorial has been prepared for those who want to learn about the basics and various functions of NumPy. To wrap up this article, let’s put everything we learned together using our electricity dataset. We can use broadcasting in cases beyond just overcoming the dimensional mismatch between a scalar and an array. NumPy can also broadcast arrays to enable computations with other arrays. However, what NumPy is doing in the background is valid. This combination is widely used as a replacement for MatLab, a popular platform for technical computing. However, the Python NumPy is considered an alternative to MatLab which is a more modern and complete programming language. All examples provided in this Python NumPy tutorial are basic, simple, and easy to practice for beginners who are enthusiastic to learn NumPy and advance their careers. In this Python NumPy Tutorial with examples, you will learn what is NumPy? We will highlight some parts of SciPy that you might find useful for this class. This brief overview has touched on many of the important things that you need to know about numpy, but is far from complete. Check out thenumpy referenceto find out much more about numpy. There is a lot more information about Python functionsin the documentation. As usual, you can find all the gory details about listsin the documentation. You can find a list of all string methods in the documentation. ## Time Comparison between Python Lists and Numpy Arrays Note that, in the example above, NumPy auto-detects the data-type from the input. You may have noticed that, in some instances, array elements are displayed with a trailing dot (e.g. 2. Single element indexing works exactly like that for other standard Python sequences. It is 0-based and accepts negative indices for indexing from the end of the array. To create sequences of numbers, NumPy provides thearange()function which is analogous to the Python built-inrange but returns an array. Its features, advantages, and how to use NumPy arrays with sample python examples. This NumPy power() function treats elements in the first input array as the base and returns it raised to the power of the corresponding element in the second input array. This function returns the reciprocal of argument, element-wise. NumPy is a Python library used for working with arrays. Some of the key advantages of Numpy arrays are that they are fast, easy to work with, and give users the opportunity to perform calculations across entire arrays. The distribution is now equal to 4, so the given floats vary between minus and plus 4. Other mathematical operations such as multiplication, division, subtraction are possible in order to modify the distribution, depending on the needs. ## Image operations We can read in the file using the csv.reader object, which will allow us to read in and split up all the content from the ssv file. Before we get started, a quick version note — we’ll be using Python 3.5. The data is in what I’m going to call ssv format — each record is separated by a semicolon (;), and rows are separated by a new line. There are 1600 rows in the file, including a header row, and 12 columns. But what if we want to preserve the dimension of the result, and not lose out on elements from our original array? ## Hashes for numpy-1.24.1-cp38-cp38-win_amd64.whl NumPy is the fundamental package for scientific computing with Python. The fundamental package for scientific computing with Python. Arrays are very frequently used in data science, where speed and resources are very important. But because the space between 5 and 50 doesn’t divide evenly by 24, the resulting numbers would be floating-point numbers. You specify a dtype of int to force the function to round down and give you whole integers. You’ll see a more detailed discussion of data types later on. Here, you use a numpy.ndarray method called .reshape() to form a 2 × 2 × 3 block of data. When you check the shape of your array in input 3, it’s exactly what you told it to be. With a much easier syntax than other programming languages, python is the first choice language for the data scientist. In other words, keep only the rows where the value in column 1 ends with ’13’. To do this, we use list comprehension to generate the mask array to perform the indexing. Let’s consider a problem where we have two one-dimensional arrays, a and b, and we need to multiply each element in a with the corresponding element in b. The following table shows different scalar data types defined in NumPy tutorial. Numpy comes with many universal array functions, which are essentially just mathematical operations you can use to perform the operation across the array. Specification of a data type of the matrix’s values using ‘dtype’ is also possible. Numpy provides functions that are able to create arrays of 1’s and 0’s. As we’ll see below, this can all be calculated concisely using one vectorized statement.	2023-03-27 10:13:14	{"extraction_info": {"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, "math_score": 0.326445609331131, "perplexity": 664.219699456409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00078.warc.gz"}
https://www.vedantu.com/formula/dimensional-formula-of-angular-momentum	# Dimensional Formula of Angular Momentum View Notes ## Dimensions: Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity. Dimensions of any given quantity tell us about how and which way different physical quantities are related. Finding dimensions of different physical quantities has many real-life applications and is helpful in finding units and measurements. Imagine a physical quantity X which depends mainly on base mass(m), length(L), and time(T) with their respective powers, then we can represent dimensional formula as [MaLbTc] ### Dimensional Formula: The dimensional formula of any physical quantity is that expression which represents how and which of the base quantities are included in that quantity. It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e ( ). E.g: Dimension formula of mass is: (M) ### Dimensional Equation: The equation obtained by equating a physical quantity with its dimensional formula is called a dimensional equation. ### Application of Dimensional Analysis: 1. To convert a physical quantity from one system of the unit to the other: It is based on a fact that magnitude of a physical quantity remain same whatever system is used for measurement i.e magnitude = numeric value(n) multiplied by unit (u) = constant n₁u₁ = n₁u₂ 2. To check dimensional correctness of a given physical relation: If in a given relation, the terms of both sides have the same dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions. 3. It determines the relationship between various physical quantities. Using the principle of homogeneity of dimension, the new relation among physical quantities can be derived if the dependent quantities are known. ### Limitation of this Method 1. This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The formula containing more than one term which is added or subtracted likes s = ut+ ½ at² also cannot be derived. 2. The relation derived from this method gives no information about the dimensionless constants. ### Angular Momentum: Angular momentum signifies the product of mass and the velocity of the object. If any object is moving with mass, then they possess momentum. The major difference present in angular momentum is that they deal with bodies who have to rotate and spin objects. So they are almost similar to linear momentum. It is a vector quantity, which implies that they have both magnitudes as well as direction. ### The Formula of Angular Momentum: If an object is accelerating around a fixed point, then it also possesses angular momentum. Hence it can be given as: L= r×p L=l×ω Where L is the angular momentum, I is rotational inertia and ω is the angular velocity. ### Dimensional Formula of Angular Momentum: We known that dimensional formula of angular momentum is written as, M¹ L² T⁻¹ Where, mass M, length L, Time T. ### Derivation of the Dimensional Formula of Angular Momentum: We know that angular momentum can be written as: We know that angular momentum = Angular Velocity × Moment of Inertia . . . . (1) As, Angular Velocity = Angular displacement × [Time]⁻¹ = [M⁰L⁰T⁰] [T]⁻¹ Therefore the dimensional formula of Angular Velocity = M⁰ L⁰ T⁻¹ . . . . . . (2) And, the Moment of Inertia is written as, M.O.I = Mass × (Radius of Gyration) Therefore the dimensional formula of M.O.I = M¹ L² T⁰ . . . . . (3) Putting the value of equation (2) and (3) in equation (1) we obtain, Angular Momentum = Angular Velocity × Moment of Inertia Or, M = [M⁰ L⁰ T⁻¹] × [M¹ L² T⁰]⁻¹ = M¹ L² T⁻¹. Therefore, the angular momentum is dimensionally represented as M¹ L² T⁻¹. FAQ (Frequently Asked Questions) 1. Write a Few Limitations of Dimensional Formula? 1. This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The formula containing more than one term which is added or subtracted likes s = ut+ ½ at² also cannot be derived. 2. The relation derived from this method gives no information about the dimensionless constants. 2. Explain the Term Angular Momentum? Angular momentum signifies the product of mass and the velocity of the object. If any object is moving with mass, then they possess momentum. The major difference present in angular momentum is that they deal with bodies who have to rotate and spin objects. So they are almost similar to linear momentum. It is a vector quantity, which implies that they have both magnitudes as well as direction. L=l×ω Where L is the angular momentum, I is rotational inertia and ω is the angular velocity. 3. Gives an Example Based on Angular Momentum? One of the famous examples of angular momentum in an ice skater executing a spin, as shown in. Net torque is almost near zero in them as there is very little friction is present between them and friction which is exerted by them is very close to the pivot point.	2021-01-21 04:55:00	{"extraction_info": {"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, "math_score": 0.8435967564582825, "perplexity": 867.2682079210314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703522242.73/warc/CC-MAIN-20210121035242-20210121065242-00397.warc.gz"}
https://pandasthumb.org/archives/2012/02/pro-id-endorse.html	# "Pro-ID", "endorse ID" and "ID-friendly" - Holy terminological ambiguity, Batman! $[Republished](http://www.jackscanlan.com/2012/02/pro-id-endorse-id-and-id-friendly-holy-terminological-ambiguity-batman/) from _Homologous Legs_$ Intelligent design, as a scientific hypothesis, is in trouble if it doesn't have peer-reviewed papers establishing, analysing and providing evidence for its core ideas - so it's no surprise that proponents of ID are quite adamant that such papers do in fact exist. Casey Luskin, intelligent design expert and apparent head writer over at _Evolution News & Views_, is naturally no exception, and he recently [answered an objection](http://www.evolutionnews.org/2012/02/answering_objec056341.html) to the claim that over 50 peer-reviewed articles support ID: namely, that the majority of the articles cited by the Discovery Institute in [this list](http://www.discovery.org/a/2640) do not mention ID at all. The short answer is that all of the articles endorse ID arguments, in one way or another, whether or not they use the term "intelligent design." Now, this post is not about to dissect all 50+ citations, that's for someone else (or me, if I ever get some free time) to do at another time, but I would like to look at exactly how Casey describes the way these papers, even if they don't mention it by name, "endorse" ID. I believe there's a distinction here that isn't being adequately recognised - one between articles that provide positive evidence for ID and articles that provide positive evidence for ideas of ID proponents. This distinction is apparent, but not noted, within Casey's post: For example, there are papers by biochemist Michael Behe, who is clearly pro-ID, that don't use the term ID. But those papers argue that the complexity of biological systems is too much for Darwinian mechanisms to produce. That's an ID argument. But what does he mean by an "ID argument"? Does ID really predict that naturalistic evolutionary mechanisms are unable to produce the complexity of biological systems, such as bacterial flagella? I don't think it does. Whilst Behe and friends like to claim that such an inability demonstrates that intelligent intervention was required in the production of said systems (which is a false dichotomy), ID, if true, does not necessitate that evolutionary mechanisms are powerless to produce complexity, at least not under the extremely vague definition of ID put forward by proponents. So what is the "ID argument" here? It's not actually an argument from ID that Behe is making: it's an argument that evolution is unable to produce complexity, which is a personal belief of Behe (and of other proponents too). Other examples can be found in the work of protein biochemist Douglas Axe, whose anti-evolution papers are glowingly cited in the DI's list. His paper "The Case Against a Darwinian Origin of Protein Folds" (published in the semi-in-house journal _BIO-Complexity_) is all about demonstrating that functional protein folds cannot evolve by Darwinian mechanisms, and it is cited as pro-ID because ID proponents claim that ID is required to explain the origin of protein folds. But again, ID could be true and protein folds could be accessible by Darwinian mechanisms. It's not a positive argument for ID that Axe is making. These examples reflect that the majority of the papers cited in the DI's list support not ID itself but the notions of the ID movement, many of which are technically unrelated to ID as a scientific hypothesis - and by using ambiguous phrases like "pro-ID", "endorses basic ID arguments", "the ID paradigm" and "ID-friendly", Casey is helping blur the line. What would be a proper positive argument for ID? Physical evidence that beings with the capability to produce life visited our planet in the past would be one. Perhaps a message left by these beings. Perhaps a message left in the genomes of all living things. These are just examples, it's really up to the ID community to do the hard yards and generate testable predictions and find good evidence. So what does this all mean for the legitimacy of the 50+ citations? Well, a lot of them are simply irrelevant when you draw the distinction between papers that support ID with positive evidence and papers that merely affirm the related beliefs of ID proponents. Out go the majority of the papers by Michael Behe, Douglas Axe, William Dembski and others! However, some survive this culling. Is ID therefore a legitimate scientific enterprise, fruitfully producing publishable results and making intellectual progress? Not necessarily. It's ultimately the job of the biological community at large to judge whether or not these papers are any good. Peer-review is not the only hurdle to a successfully published idea - it must also survive out in the wild. Will these papers make an impact? Will they be cited numerously and, more importantly, favourably? Will they inspire other researchers to follow the exciting new ideas and concepts present in intelligent design? Many of the non-culled "pro-ID" papers have been published in small journals with low impact factors, and are therefore unlikely to be taken seriously by many biologists - but if the hypotheses contained within are strongly supported, people will eventually notice. The onus is on the ID community to produce good papers supporting the core ideas inherent to intelligent design. If they find unambiguously positive evidence for ID, the support of the academic community will start to swing their way. The current lack of such support is a clear indication that, despite much posturing, ID research still has a long way to go.	2017-07-26 16:53:11	{"extraction_info": {"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, "math_score": 0.24576814472675323, "perplexity": 2188.422742187224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426234.82/warc/CC-MAIN-20170726162158-20170726182158-00652.warc.gz"}
http://www.feedage.com/feeds/1306409/citeulike-everyones-library	Subscribe: CiteULike: Everyone's library Language: English Tags: activity based clustering doi flt hierarchical inception linkage map networks new residual structure time vol Rate this Feed Feed Details and Statistics Preview: CiteULike: Everyone's library # CiteULike: Everyone's library ## CiteULike: Everyone's library Nonparametric measures of association between a spatial point process and a random set, with geological applications 2017-11-24T00:58:37-00:00 Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 51, No. 2. (1 May 2002), pp. 165-182, doi:10.1111/1467-9876.00261 In mining exploration it is often desired to predict the occurrence of ore deposits given other geological information, such as the locations of faults. More generally it is of interest to measure the spatial association between two spatial patterns observed in the same survey region. Berman developed parametric methods for conditional inference about a point process X given another spatial process Y. This paper proposes an alternative, nonparametric, approach using distance methods, analogous to the use of the summary functions F, G and J for univariate point patterns. Our methods apply to a bivariate spatial process (X, Y) consisting of a point process X and a random set Y. In particular we develop a bivariate analogue of the J-function of van Lieshout and Baddeley which shows promise as a summary statistic and turns out to be closely related to Berman's analysis. Properties of the bivariate J-function include a multiplicative identity under independent superposition, which has no analogue in the univariate case. Two geological examples are investigated. Genome-wide meta-analysis associates HLA-DQA1/DRB1 and LPA and lifestyle factors with human longevity 2017-11-23T23:31:15-00:00 Nature Communications, Vol. 8, No. 1. (13 October 2017), doi:10.1038/s41467-017-00934-5 Peter Joshi, Nicola Pirastu, Katherine Kentistou, Krista Fischer, Edith Hofer, Katharina Schraut, David Clark, Teresa Nutile, Catriona Barnes, Paul Timmers, Xia Shen, Ilaria Gandin, Aaron McDaid, Thomas Hansen, Scott Gordon, Franco Giulianini, Thibaud Boutin, Abdel Abdellaoui, Wei Zhao, Carolina Medina-Gomez, Traci Bartz, Stella Trompet, Leslie Lange, Laura Raffield, Ashley van der Spek, Tessel Galesloot, Petroula Proitsi, Lisa Yanek, Lawrence Bielak, Antony Payton, Federico Murgia, Maria Concas, Ginevra Biino, Salman Tajuddin, Ilkka Seppälä, Najaf Amin, Eric Boerwinkle, Anders Børglum, Archie Campbell, Ellen Demerath, Ilja Demuth, Jessica Faul, Ian Ford, Alessandro Gialluisi, Martin Gögele, MariaElisa Graff, Aroon Hingorani, Jouke-Jan Hottenga, David Hougaard, Mikko Hurme, Arfan Ikram, Marja Jylhä, Diana Kuh, Lannie Ligthart, Christina Lill, Ulman Lindenberger, Thomas Lumley, Reedik Mägi, Pedro Marques-Vidal, Sarah Medland, Lili Milani, Reka Nagy, William Ollier, Patricia Peyser, Peter Pramstaller, Paul Ridker, Fernando Rivadeneira, Daniela Ruggiero, Yasaman Saba, Reinhold Schmidt, Helena Schmidt, Eline Slagboom, Blair Smith, Jennifer Smith, Nona Sotoodehnia, Elisabeth Steinhagen-Thiessen, Frank van Rooij, André Verbeek, Sita Vermeulen, Peter Vollenweider, Yunpeng Wang, Thomas Werge, John Whitfield, Alan Zonderman, Terho Lehtimäki, Michele Evans, Mario Pirastu, Christian Fuchsberger, Lars Bertram, Neil Pendleton, Sharon Kardia, Marina Ciullo, Diane Becker, Andrew Wong, Bruce Psaty, Cornelia van Duijn, James Wilson, Wouter Jukema, Lambertus Kiemeney, André Uitterlinden, Nora Franceschini, Kari North, David Weir, Andres Metspalu, Dorret Boomsma, Caroline Hayward, Daniel Chasman, Nicholas Martin, Naveed Sattar, Harry Campbell, Tōnu Esko, Zoltán Kutalik, James Wilson Virus Population Dynamics and Acquired Virus Resistance in Natural Microbial Communities 2017-11-23T23:17:39-00:00 Science, Vol. 320, No. 5879. (23 May 2008), pp. 1047-1050, doi:10.1126/science.1157358 Viruses shape microbial community structure and function by altering the fitness of their hosts and by promoting genetic exchange. The complexity of most natural ecosystems has precluded detailed studies of virus-host interactions. We reconstructed virus and host bacterial and archaeal genome sequences from community genomic data from two natural acidophilic biofilms. Viruses were matched to their hosts by analyzing spacer sequences that occur among clustered regularly interspaced short palindromic repeats (CRISPRs) that are a hallmark of virus resistance. Virus population genomic analyses provided evidence that extensive recombination shuffles sequence motifs sufficiently to evade CRISPR spacers. Only the most recently acquired spacers match coexisting viruses, which suggests that community stability is achieved by rapid but compensatory shifts in host resistance levels and virus population structure. Antimalarial Inhibitors Targeting Serine Hydroxymethyltransferase (SHMT) with in Vivo Efficacy and Analysis of their Binding Mode Based on X-ray Cocrystal Structures. 2017-11-23T23:14:38-00:00 Journal of medicinal chemistry, Vol. 60, No. 12. (22 June 2017), pp. 4840-4860 Target-based approaches toward new antimalarial treatments are highly valuable to prevent resistance development. We report several series of pyrazolopyran-based inhibitors targeting the enzyme serine hydroxymethyltransferase (SHMT), designed to improve microsomal metabolic stability and to identify suitable candidates for in vivo efficacy evaluation. The best ligands inhibited Plasmodium falciparum (Pf) and Arabidopsis thaliana (At) SHMT in target assays and PfNF54 strains in cell-based assays with values in the low nanomolar range (3.2-55 nM). A set of carboxylate derivatives demonstrated markedly improved in vitro metabolic stability (t1/2 > 2 h). A selected ligand showed significant in vivo efficacy with 73% of parasitemia reduction in a mouse model. Five new cocrystal structures with PvSHMT were solved at 2.3-2.6 Å resolution, revealing a unique water-mediated interaction with Tyr63 at the end of the para-aminobenzoate channel. They also displayed the high degree of conformational flexibility of the Cys364-loop lining this channel. Geoffrey Schwertz, Matthias Witschel, Matthias Rottmann, Roger Bonnert, Ubolsree Leartsakulpanich, Penchit Chitnumsub, Aritsara Jaruwat, Wanwipa Ittarat, Anja Schäfer, Raphael Aponte, Susan Charman, Karen White, Abhijit Kundu, Surajit Sadhukhan, Mel Lloyd, Gail Freiberg, Myron Srikumaran, Marc Siggel, Adrian Zwyssig, Pimchai Chaiyen, François Diederich Designing novel inhibitors against histone acetyltransferase (HAT: GCN5) of Plasmodium falciparum. 2017-11-23T23:09:04-00:00 European journal of medicinal chemistry, Vol. 138 (29 September 2017), pp. 26-37 During active proliferation phase of intra-erythrocytic cycle, the genome of P. falciparum is regulated epigenetically and evolutionary conserved parasite-specific histone proteins are extensively acetylated. The reversible process of lysine acetylation, causing transcriptional activation and its deacetylation, causing transcriptional repression is regulated by balanced activities of HATs and HDACs. They are also known to regulate antigenic variations and gametocytic conversion in P. falciparum. These histone modifying enzymes have been identified as potential targets for development of anitmalarials in literature. PfGCN5, a HAT family member of P. falciparum is predominantly involved in H3K9 acetylation. In this study, through comparative structure and sequence analysis, we elucidate differences in the catalytic pocket of PfGCN5 which can be exploited to design selective inhibitors. Through virtual screening of known antimalarials from ChEMBL bioassay database, we mapped 10 compounds with better affinity towards PfGCN5. Further, we identified 10 more novel compounds which showed remarkably better affinity towards the Plasmodium target from analogues of mapped inhibitors from ZINC database of commercially available compounds. Comparative molecular dynamics simulation study of one of the compounds (C14) complex with PfGCN5 and HsGCN5 suggested the possible reason for its selectivity. In vitro parasite growth assay in the presence of C14 showed IC50 value at lower nanomolar range (∼ 225 nM). However, no effect in mammalian fibroblast cells was observed for C14 (up to 20 μM). Further, reduced level of HAT activity of recombinant GCN5 and H3K9Ac was observed in the parasites treated with C14. Overall, this study reports 20 potential inhibitors of PfGCN5 and experimental validation of one molecule (C14) with antimalarial activity at low nanomolar range. Copyright © 2017 Elsevier Masson SAS. All rights reserved. Amarjeet Kumar, Krishanu Bhowmick, Kunwar Somesh Vikramdeo, Neelima Mondal, Naidu Subbarao, Suman Kumar Dhar Biological Studies and Target Engagement of the 2-C-Methyl-d-Erythritol 4-Phosphate Cytidylyltransferase (IspD)-Targeting Antimalarial Agent (1R,3S)-MMV008138 and Analogs. 2017-11-23T23:06:09-00:00 ACS infectious diseases (07 November 2017) Malaria continues to be one of the deadliest diseases worldwide, and the emergence of drug resistance parasites is a constant threat. Plasmodium parasites utilize the methylerythritol phosphate (MEP) pathway to synthesize isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP), which are essential for parasite growth. Previously, we and others identified that the Malaria Box compound MMV008138 targets the apicoplast and that parasite growth inhibition by this compound can be reversed by supplementation of IPP. Further work has revealed that MMV008138 targets the enzyme 2-C-methyl-d-erythritol 4-phosphate cytidylyltransferase (IspD) in the MEP pathway, which converts MEP and cytidine triphosphate (CTP) to cytidinediphosphate methylerythritol (CDP-ME) and pyrophosphate. In this work, we sought to gain insight into the structure-activity relationships by probing the ability of MMV008138 analogs to inhibit PfIspD recombinant enzyme. Here, we report PfIspD inhibition data for fosmidomycin (FOS) and 19 previously disclosed analogs and report parasite growth and PfIspD inhibition data for 27 new analogs of MMV008138. In addition, we show that MMV008138 does not target the recently characterized human IspD, reinforcing MMV008138 as a prototype of a new class of species-selective IspD-targeting antimalarial agents. Maryam Ghavami, Emilio Merino, Zhong-Ke Yao, Rubayet Elahi, Morgan Simpson, Maria Fernández-Murga, Joshua Butler, Michael Casasanta, Priscilla Krai, Maxim Totrov, Daniel Slade, Paul Carlier, Maria Belen Cassera Blindfold learning of an accurate neural metric 2017-11-23T22:09:55-00:00 (13 Oct 2017) The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated responses alone. Here we show how to build a distance map of responses from the structure of the population activity of retinal ganglion cells, allowing for the accurate discrimination of distinct visual stimuli from the retinal response. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity, and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli. Christophe Gardella, Olivier Marre, Thierry Mora Cognition and Type 1 Diabetes in Children and Adolescents. 2017-11-23T22:00:19-00:00 Diabetes spectrum : a publication of the American Diabetes Association, Vol. 29, No. 4. (November 2016), pp. 197-202 IN BRIEF In children and adolescents with type 1 diabetes, exposure to glycemic extremes (severe hypoglycemia, chronic hyperglycemia, and diabetic ketoacidosis) overlaps with the time period of most active brain and cognitive development, leading to concerns that these children are at risk for cognitive side effects. This article summarizes the existing literature examining the impact of glycemic extremes on cognitive function and brain structure in youth with type 1 diabetes and points out areas for future research. Allison Cato, Tamara Hershey On Clustering Time Series Using Euclidean Distance and Pearson Correlation 2017-11-23T21:43:08-00:00 (10 Jan 2016) For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distance-based classification or clustering methods. In addition to this theoretically sound result we also show that the often used k-Means algorithm formally needs a mod ification to keep the interpretation as Pearson correlation strictly valid. Experimental results demonstrate that in many cases the standard k-Means algorithm generally produces the same results. Michael Berthold, Frank Höppner Cellular Computations Underlying Detection of Gaps in Sounds and Lateralizing Sound Sources. 2017-11-23T21:41:23-00:00 Trends in neurosciences, Vol. 40, No. 10. (October 2017), pp. 613-624 In mammals, acoustic information arises in the cochlea and is transmitted to the ventral cochlear nuclei (VCN). Three groups of VCN neurons extract different features from the firing of auditory nerve fibers and convey that information along separate pathways through the brainstem. Two of these pathways process temporal information: octopus cells detect coincident firing among auditory nerve fibers and transmit signals along monaural pathways, and bushy cells sharpen the encoding of fine structure and feed binaural pathways. The ability of these cells to signal with temporal precision depends on a low-voltage-activated K(+) conductance (gKL) and a hyperpolarization-activated conductance (gh). This 'tale of two conductances' traces gap detection and sound lateralization to their cellular and biophysical origins. Copyright © 2017 Elsevier Ltd. All rights reserved. Donata Oertel, Xiao-Jie Cao, James Ison, Paul Allen Adaptive Systems for the Dynamic Run-time Optimization of Programs. 2017-11-23T21:39:11-00:00 (1974) An abstract is not available. Gilbert Hansen An ultra-dense integrated linkage map for hexaploid chrysanthemum enables multi-allelic QTL analysis. 2017-11-23T21:13:20-00:00 TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik, Vol. 130, No. 12. (December 2017), pp. 2527-2541 We constructed the first integrated genetic linkage map in a polysomic hexaploid. This enabled us to estimate inheritance of parental haplotypes in the offspring and detect multi-allelic QTL. Construction and use of linkage maps are challenging in hexaploids with polysomic inheritance. Full map integration requires calculations of recombination frequency between markers with complex segregation types. In addition, detection of QTL in hexaploids requires information on all six alleles at one locus for each individual. We describe a method that we used to construct a fully integrated linkage map for chrysanthemum (Chrysanthemum × morifolium, 2n = 6x = 54). A bi-parental F1 population of 406 individuals was genotyped with an 183,000 SNP genotyping array. The resulting linkage map consisted of 30,312 segregating SNP markers of all possible marker dosage types, representing nine chromosomal linkage groups and 107 out of 108 expected homologues. Synteny with lettuce (Lactuca sativa) showed local colinearity. Overall, it was high enough to number the chrysanthemum chromosomal linkage groups according to those in lettuce. We used the integrated and phased linkage map to reconstruct inheritance of parental haplotypes in the F1 population. Estimated probabilities for the parental haplotypes were used for multi-allelic QTL analyses on four traits with different underlying genetic architectures. This resulted in the identification of major QTL that were affected by multiple alleles having a differential effect on the phenotype. The presented linkage map sets a standard for future genetic mapping analyses in chrysanthemum and closely related species. Moreover, the described methods are a major step forward for linkage mapping and QTL analysis in hexaploids. Geert van Geest, Peter Bourke, Roeland Voorrips, Agnieszka Marasek-Ciolakowska, Yanlin Liao, Aike Post, Uulke van Meeteren, Richard Visser, Chris Maliepaard, Paul Arens Present Without Past: The Disruption of Temporal Integration in a Case of Transsexuality 2017-11-23T20:49:02-00:00 Psychoanalytic Inquiry, Vol. 36, No. 5. (3 July 2016), pp. 360-370, doi:10.1080/07351690.2016.1180908 ABSTRACTIn this article, I examine the impact of extensive modification of the body on the temporal link, which is an important feature of human identity, as it provides continuity between different representations of the self over time. I illustrate this with a case of a young boy who underwent sex reassignment surgery in late adolescence after the artificial suspension of puberty through sex hormones. I argue that when hormones are used in this way, one can observe in some cases not only the desired suspension of physical time during which the body?s given biological trajectory is artificially halted, but also of psychological time. In some instances, this biological and psychic detour can result in a marked distortion in the young person?s relationship to time and impacts on their psychological adaptation following surgery. Alessandra Lemma Algorithms for hierarchical clustering: an overview, II 2017-11-23T20:46:27-00:00 Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, Vol. 7, No. 6. (1 November 2017), pp. e1219-n/a, doi:10.1002/widm.1219 We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally, we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm. This review adds to the earlier version, Murtagh F, Contreras P. Algorithms for hierarchical clustering: an overview, Wiley Interdiscip Rev: Data Mining Knowl Discov 2012, 2, 86–97. WIREs Data Mining Knowl Discov 2017, 7:e1219. doi: 10.1002/widm.1219 For further resources related to this article, please visit the WIREs website. Fionn Murtagh, Pedro Contreras Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion? 2017-11-23T20:38:36-00:00 In Journal of Classification, Vol. 31, No. 3. (2014), pp. 274-295, doi:10.1007/s00357-014-9161-z The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. Two algorithms are found in the literature and software, both announcing that they implement the Ward clustering method. When applied to the same distance matrix, they produce different results. One algorithm preserves Ward’s criterion, the other does not. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward’s hierarchical clustering method. Fionn Murtagh, Pierre Legendre Fragment Binding to β-Secretase 1 without Catalytic Aspartate Interactions Identified via Orthogonal Screening Approaches. 2017-11-23T20:21:14-00:00 ACS omega, Vol. 2, No. 2. (28 February 2017), pp. 685-697 An approach to identify β-secretase 1 (BACE1) fragment binders that do not interact with the catalytic aspartate dyad is presented. A ThermoFluor (thermal shift) and a fluorescence resonance energy transfer enzymatic screen on the soluble domain of BACE1, together with a surface plasmon resonance (SPR) screen on the soluble domain of BACE1 and a mutant of one catalytic Asp (D32N), were run in parallel. Fragments that were active in at least two of these assays were further confirmed using one-dimensional NMR (WaterLOGSY) and SPR binding competition studies with peptidic inhibitor OM99-2. Protein-observed NMR (two-dimensional (15)N heteronuclear single-quantum coherence spectroscopy) and crystallographic studies with the soluble domain of BACE1 identified a unique and novel binding mode for compound 12, a fragment that still occupies the active site while not making any interactions with catalytic Asps. This novel approach of combining orthogonal fragment screening techniques, for both wild-type and mutant enzymes, as well as binding competition studies could be generalized to other targets to overcome undesired interaction motifs and as a hit-generation approach in highly constrained intellectual property space. Frederik Rombouts, Richard Alexander, Erna Cleiren, Alex De Groot, Michel Carpentier, Joyce Dijkmans, Katleen Fierens, Stefan Masure, Diederik Moechars, Martina Palomino-Schätzlein, Antonio Pineda-Lucena, Andrés Trabanco, Daan Van Glabbeek, Ann Vos, Gary Tresadern Discovery of a Diaminopyrimidine FLT3 Inhibitor Active against Acute Myeloid Leukemia. 2017-11-23T20:00:44-00:00 ACS omega, Vol. 2, No. 5. (31 May 2017), pp. 1985-2009 Profiling of the kinase-binding capabilities of an aminopyrimidine analogue detected in a cellular screen of the St. Jude small-molecule collection led to the identification of a novel series of FMS-like tyrosine kinase 3 (FLT3) inhibitors. Structure-activity relationship studies led to the development of compounds exhibiting good potency against MV4-11 and MOLM13 acute myelogenous leukemia cells driven by FLT3, regardless of their FLT3 mutation status. In vitro pharmacological profiling demonstrated that compound 5e shows characteristics suitable for further preclinical development. Jamie Jarusiewicz, Jae Yoon Jeon, Michele Connelly, Yizhe Chen, Lei Yang, Sharyn Baker, Kiplin Guy Tyrosine kinase inhibition increases the cell surface localization of FLT3-ITD and enhances FLT3-directed immunotherapy of acute myeloid leukemia. 2017-11-23T19:58:47-00:00 Leukemia (14 August 2017) The fms-related tyrosine kinase 3 (FLT3) receptor has been extensively studied over the past two decades with regard to oncogenic alterations that do not only serve as prognostic markers but also as therapeutic targets in acute myeloid leukemia (AML). Internal tandem duplications (ITDs) became of special interest in this setting as they are associated with unfavorable prognosis. Because of sequence-dependent protein conformational changes FLT3-ITD tends to autophosphorylate and displays a constitutive intracellular localization. Here, we analyzed the effect of tyrosine kinase inhibitors (TKIs) on the localization of the FLT3 receptor and its mutants. TKI treatment increased the surface expression through upregulation of FLT3 and glycosylation of FLT3-ITD and FLT3-D835Y mutants. In T cell-mediated cytotoxicity (TCMC) assays, using a bispecific FLT3 × CD3 antibody construct, the combination with TKI treatment increased TCMC in the FLT3-ITD-positive AML cell lines MOLM-13 and MV4-11, patient-derived xenograft cells and primary patient samples. Our findings provide the basis for rational combination of TKI and FLT3-directed immunotherapy with potential benefit for FLT3-ITD-positive AML patients.Leukemia advance online publication, 12 September 2017; doi:10.1038/leu.2017.257. K Reiter, H Polzer, C Krupka, A Maiser, B Vick, M Rothenberg-Thurley, KH Metzeler, D Dörfel, HR Salih, G Jung, E Nößner, I Jeremias, W Hiddemann, H Leonhardt, K Spiekermann, M Subklewe, PA Greif Gaming out online: Black lesbian identity development and community building in Xbox Live 2017-11-23T19:01:41-00:00 Journal of Lesbian Studies (22 November 2017), pp. 1-15, doi:10.1080/10894160.2018.1384293 ABSTRACTAs gaming culture continues to marginalize women and people of color, other gamers are also highlighting the inequalities they face within digital gaming communities. While heterosexism and homophobia are commonplace within gaming culture, little is known about the actual experiences of ?gaymers? and even less about ?gaymers? of color. As such, this article seeks to explore lesbians of color and their experiences ?gayming? out and online. Exploring identity development, community building, and connectivity via social networking, the women within this study articulate what it means to be lesbian online and how this impacts their physical and digital experiences. The private spaces within gaming culture that many marginalized groups inhabit are the few spaces that value the articulation of marginalized interests and viewpoints. Ethnographic observations reveal how supportive communities can improve resilience by mitigating the effects of stereotyping, microaggressions, and other discriminatory practices in online gaming. Kishonna Gray Activity theory as a framework for analyzing and redesigning work 2017-11-23T18:45:36-00:00 Ergonomics, Vol. 43, No. 7. (1 July 2000), pp. 960-974, doi:10.1080/001401300409143 Cultural-historical activity theory is a new framework aimed at transcending the dichotomies of micro- and macro-, mental and material, observation and intervention in analysis and redesign of work. The approach distinguishes between short-lived goal-directed actions and durable, object-oriented activity systems. A historically evolving collective activity system, seen in its network relations to other activity systems, is taken as the prime unit of analysis against which scripted strings of goal-directed actions and automatic operations are interpreted. Activity systems are driven by communal motives that are often difficult to articulate for individual participants. Activity systems are in constant movement and internally contradictory. Their systemic contradictions, manifested in disturbances and mundane innovations, offer possibilities for expansive developmental transformations. Such transformations proceed through stepwise cycles of expansive learning which begin with actions of questioning the existing standard practice, then proceed to actions of analyzing its contradictions and modelling a vision for its zone of proximal development, then to actions of examining and implementing the new model in practice. New forms of work organization increasingly require negotiated ?knotworking? across boundaries. Correspondingly, expansive learning increasingly involves horizontal widening of collective expertise by means of debating, negotiating and hybridizing different perspectives and conceptualizations. Findings from a longitudinal intervention study of children's medical care illuminate the theoretical arguments. Yrjo Engestrom Mastering the game of Go with deep neural networks and tree search 2017-11-23T18:32:09-00:00 Nature, Vol. 529, No. 7587. (27 January 2016), pp. 484-489, doi:10.1038/nature16961 The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of state-of-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away. David Silver, Aja Huang, Chris Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, Demis Hassabis Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning 2017-11-23T18:22:42-00:00 (23 Aug 2016) Very deep convolutional networks have been central to the largest advances in image recognition performance in recent years. One example is the Inception architecture that has been shown to achieve very good performance at relatively low computational cost. Recently, the introduction of residual connections in conjunction with a more traditional architecture has yielded state-of-the-art performance in the 2015 ILSVRC challenge; its performance was similar to the latest generation Inception-v3 network. This raises the question of whether there are any benefit in combining the Inception architecture with residual connections. Here we give clear empirical evidence that training with residual connections accelerates the training of Inception networks significantly. There is also some evidence of residual Inception networks outperforming similarly expensive Inception networks without residual connections by a thin margin. We also present several new streamlined architectures for both residual and non-residual Inception networks. These variations improve the single-frame recognition performance on the ILSVRC 2012 classification task significantly. We further demonstrate how proper activation scaling stabilizes the training of very wide residual Inception networks. With an ensemble of three residual and one Inception-v4, we achieve 3.08 percent top-5 error on the test set of the ImageNet classification (CLS) challenge Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, Alex Alemi Symmetry control of nanorod superlattice driven by a governing force 2017-11-23T18:07:04-00:00 Nature Communications, Vol. 8, No. 1. (10 November 2017), doi:10.1038/s41467-017-01111-4 Yujia Liang, Yong Xie, Dongxue Chen, Chuanfei Guo, Shuai Hou, Tao Wen, Fengyou Yang, Ke Deng, Xiaochun Wu, Ivan Smalyukh, Qian Liu Thermal dynamics of pulsed-laser excited gold nanorods in suspension 2017-11-23T18:04:32-00:00 Nanoscale, Vol. 9, No. 44. (2017), pp. 17284-17292, doi:10.1039/c7nr06125k Photothermal reactions of metallic nanostructures, such as gold nanorods show appealing structural relaxations, such as bubble formation or particle modification. We have employed a pump-probe method to record the structural relaxations of a suspension of gold nanorods upon femtosecond laser excitation by pulsed X-ray scattering both with wide-angle and small-angle sensitivity. Single-pulse reactions include transient bubble formation at 20 J m-2 and irreversible nanorod reshaping at 30 J m-2. Thus the window for reversible excitation is very narrow. Additionally we could map the time-domain and fluence behaviour in a wide range to characterize the relaxations comprehensively. The polarized laser pulse first selectively excites nanorods aligned with the laser electric field, but at higher fluence non-aligned rods are also transformed. At low fluence this transformation happens in the solid state, while at higher fluence the rods melt. Anton Plech, Shyjumon Ibrahimkutty, Stefan Reich, Gemma Newby Advanced electron tomography of nanoparticle assemblies 2017-11-23T18:00:49-00:00 EPL (Europhysics Letters), Vol. 119, No. 3. (01 August 2017), 38001, doi:10.1209/0295-5075/119/38001 T Altantzis, D Zanaga, S Bals Sensitivity of Turbine-Height Wind Speeds to Parameters in Planetary Boundary-Layer and Surface-Layer Schemes in the Weather Research and Forecasting Model 2017-11-23T17:52:01-00:00 In Boundary-Layer Meteorology, Vol. 162, No. 1. (2017), pp. 117-142, doi:10.1007/s10546-016-0185-2 We evaluate the sensitivity of simulated turbine-height wind speeds to 26 parameters within the Mellor–Yamada–Nakanishi–Niino (MYNN) planetary boundary-layer scheme and MM5 surface-layer scheme of the Weather Research and Forecasting model over an area of complex terrain. An efficient sampling algorithm and generalized linear model are used to explore the multiple-dimensional parameter space and quantify the parametric sensitivity of simulated turbine-height wind speeds. The results indicate that most of the variability in the ensemble simulations is due to parameters related to the dissipation of turbulent kinetic energy (TKE), Prandtl number, turbulent length scales, surface roughness, and the von Kármán constant. The parameter associated with the TKE dissipation rate is found to be most important, and a larger dissipation rate produces larger hub-height wind speeds. A larger Prandtl number results in smaller nighttime wind speeds. Increasing surface roughness reduces the frequencies of both extremely weak and strong airflows, implying a reduction in the variability of wind speed. All of the above parameters significantly affect the vertical profiles of wind speed and the magnitude of wind shear. The relative contributions of individual parameters are found to be dependent on both the terrain slope and atmospheric stability. Ben Yang, Yun Qian, LarryK Berg, Po-Lun Ma, Sonia Wharton, Vera Bulaevskaya, Huiping Yan, Zhangshuan Hou, WilliamJ Shaw Enhanced Thermal Stability and Biocompatibility of Gold Nanorods by Graphene Oxide 2017-11-23T17:46:03-00:00 In Plasmonics (2017), pp. 1-10, doi:10.1007/s11468-017-0667-1 Vahid Shirshahi, Shadie Hatamie, SeyedNasrollah Tabatabaei, Marzieh Salimi, Reza Saber Magnetic Resonance Imaging of Pituitary Tumors 2017-11-23T17:41:58-00:00 Vol. 45 (21 March 2016), pp. 97-120, doi:10.1159/000442327 Jean-François Bonneville Breast and thyroid cancer and malignant melanoma promoted by alcohol-induced pituitary secretion of prolactin, T.S.H. and M.S.H. 2017-11-23T17:37:31-00:00 Lancet (London, England), Vol. 1, No. 7967. (08 May 1976), pp. 996-999 In interview data from the U.S.A.'s Third National Cancer Survey, alcohol ingestion was associated with a higher occurrence of cancers of the breast, thyroid, and amlignant melanoma. Data from other studies support the first two associations. A unifying hypothesis to explain these seemingly diverse associations suggests that alcohol stimulates anterior pituitary secretion of prolactin, thyroid-stimulating hormone (T.S.H.), and melanocyte-stimulating hormone (M.S.H.). Under the stimulations of these hormones, the three target tissues exhibit increased mitotic activity and hence an increase susceptibility to the development of a malignancy. A wide variety of findings from other studies indicate plausibility for this hypothesis. The implications could be grave. In addition to alcohol, several common drugs acting in similar manner could be cancer promoters, including: resperine, methyldopa, phenothiaznes, d-amphetamine, tricyclic antidepressants, and antihistamines. Over 20000 (25%) ofall new breast-cancer cases each year in the U.S.A. could be preventable if this hypothesis is correct. RR Williams Entanglement manipulation and distillability beyond LOCC 2017-11-23T17:22:45-00:00 (10 Nov 2017) When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC operations is exceedingly complex leaving many important physical problems unsolved. In this paper we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures are studied under non-entangling operations, as well as the newly introduced dually non-entangling and PPT-preserving operational classes. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We show that all NPT entangled states can be distilled using operations that are both PPT and dually non-entangling. Furthermore, for any entangled state $ρ$ and any $ε>0$, we prove the existence of a non-entangling map that is $ε$ close to the set of LOCC and which is able to distill pure-state entanglement from $ρ$. This finding reveals a type of fragility to the phenomenon of bound entanglement in LOCC processing. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable operations. Finally, as an analog to $k$-positive maps, we introduce and analyze the set of $k$-non-entangling operations. Eric Chitambar, Julio de Vicente, Mark Girard, Gilad Gour Lie algebra representations and rigged Hilbert spaces: the SO(2) case 2017-11-23T17:22:11-00:00 (10 Nov 2017) It is well known that related with the irreducible representations of the Lie group $SO(2)$ we find a discrete basis as well a continuous one. In this paper we revisited this situation under the light of Rigged Hilbert spaces, which are the suitable framework to deal with both discrete and bases in the same context and in relation with physical applications. Enrico Celeghini, Manuel Gadella, Mariano del Olmo Experimental study of quantum thermodynamics using optical vortices 2017-11-23T17:21:55-00:00 (10 Nov 2017) Non-equilibrium thermodynamics and quantum information theory are interrelated research fields witnessing an increasing interest, both theoretical and experimental. This is manly due to the broadness of these theories, which found applications in many different fields of science, ranging from biology to the foundations of physics. Here, by employing the orbital angular momentum of light, we propose a new platform for studying non-equilibrium properties of high dimensional quantum systems. Specifically, we use Laguerre-Gaussian beams to emulate the energy eigenstates of a two-dimension quantum harmonic oscillator having angular momentum. These light beams are subjected to a process realized by a spatial light modulator and the corresponding work distribution is experimentally reconstructed employing a two-point measurement scheme. The Jarzynski fluctuation relation is then verified. We also demonstrate the operation of the system as a Maxwell's demon. Medeiros de Araújo, T Häffner, R Bernardi, DS Tasca, MPJ Lavery, MJ Padgett, A Kanaan, LC Céleri, Souto Ribeiro What $g^(2)(0)<1/2$ tells you - and what it does not 2017-11-23T17:21:35-00:00 (16 Nov 2017) Quantum-optical research on semiconductor quantum dots puts special emphasis on the measurement of the second-order correlation function $g^(2)(τ)$, arguing that $g^(2)(0)<1/2$ implies the source field represents a good single-photon light source. We analyze this claim theoretically. A quantum state of light having no projection on the single-photon Fock state can not give a value of $g^(2)(0)<1/2$. However, with solely the value of $g^(2)(0)$, the amplitude of this single-photon projection can be arbitrarily small, owing to vacuum contributions. Yet, one can determine a lower bound on the ratio of single-to-multi-photon emission from $g^(2)(0)$. For a fixed ratio of single-to-multi-photon emission, $g^(2)(0)$ is artificially enhanced by the vacuum contributions. We derive an effective second-order correlation function, which corrects this enhancement, substantially improving the lower bound. The results are applied to theoretical and realized experimental setups and indicate that the quality of solid-state single-photon sources, at least with respect to this criterion, is often underestimated. Peter Grünwald Quantum Origami: Applying Transversal Gates and Measuring Topological Order 2017-11-23T17:21:20-00:00 (15 Nov 2017) In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and fusion rules of emergent anyonic excitations and thus serve as a diagnostic of topological order. Moreover, modular transformations of higher genus surfaces, e.g. a torus with multiple handles, can enhance the computational power of a topological state, in many cases providing a universal fault-tolerant set of gates for quantum computation. However, due to the intrusive nature of modular transformations, which abstractly involve global operations and manifold surgery, physical implementations of them in local systems have remained elusive. Here, we show that by folding manifolds, modular transformations can be reduced to independent local unitaries, providing a novel class of transversal logic gates in topological states. Specifically, through folding, we demonstrate that multi-layer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers. We further provide methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations, providing a novel way to directly measure topological order. Guanyu Zhu, Mohammad Hafezi, Maissam Barkeshli Automated detection and cataloging of global explosive volcanism using the International Monitoring System infrasound network 2017-11-23T17:21:11-00:00 J. Geophys. Res. Solid Earth, Vol. 122, No. 4. (1 April 2017), 2016JB013356, doi:10.1002/2016jb013356 We experiment with a new method to search systematically through multiyear data from the International Monitoring System (IMS) infrasound network to identify explosive volcanic eruption signals originating anywhere on Earth. Detecting, quantifying, and cataloging the global occurrence of explosive volcanism helps toward several goals in Earth sciences and has direct applications in volcanic hazard mitigation. We combine infrasound signal association across multiple stations with source location using a brute-force, grid-search, cross-bearings approach. The algorithm corrects for a background prior rate of coherent unwanted infrasound signals (clutter) in a global grid, without needing to screen array processing detection lists from individual stations prior to association. We develop the algorithm using case studies of explosive eruptions: 2008 Kasatochi, Alaska; 2009 Sarychev Peak, Kurile Islands; and 2010 Eyjafjallajökull, Iceland. We apply the method to global IMS infrasound data from 2005–2010 to construct a preliminary acoustic catalog that emphasizes sustained explosive volcanic activity (long-duration signals or sequences of impulsive transients lasting hours to days). This work represents a step toward the goal of integrating IMS infrasound data products into global volcanic eruption early warning and notification systems. Additionally, a better understanding of volcanic signal detection and location with the IMS helps improve operational event detection, discrimination, and association capabilities. Robin Matoza, David Green, Alexis Le Pichon, Peter Shearer, David Fee, Pierrick Mialle, Lars Ceranna Thomas Precession for Dressed Particles 2017-11-23T17:20:59-00:00 (15 Nov 2017) We consider a particle dressed with boundary gravitons in three-dimensional Minkowski space. The existence of BMS transformations implies that the particle's wavefunction picks up a Berry phase when subjected to changes of reference frames that trace a closed path in the asymptotic symmetry group. We evaluate this phase and show that, for BMS superrotations, it provides a gravitational generalization of Thomas precession. In principle, such phases are observable signatures of asymptotic symmetries. Blagoje Oblak High-harmonic generation in solids with and without topological edge states 2017-11-23T17:20:47-00:00 (19 Nov 2017) High-harmonic generation (HHG) in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory (TDDFT) approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ up to fourteen orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band electrons, which strongly depends on whether topological edge states are present or not. Dieter Bauer, Kenneth Hansen The time-reverse of any causal theory is eternal noise 2017-11-23T17:20:32-00:00 (15 Nov 2017) We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal', in the sense that they are intrinsically compatible with the causal structure of space-time -- as required by relativity. We demonstrate that there is a sharp contrast between these theories and the corresponding time-reversed theories, where time is taken to flow backwards from the future to the past. While the former typically feature a rich gamut of allowed states, the latter only allow for a single state: eternal noise. We illustrate this result by considering of the time-reverse of quantum theory. We also derive a strengthening of the result in PRL 108, 200403 on signalling in time-reversed theories. Bob Coecke, Stefano Gogioso, John Selby Exploring Energy-Time Entanglement Using Geometric Phase 2017-11-23T17:20:18-00:00 Physical Review Letters, Vol. 101, No. 18. (14 Nov 2017), doi:10.1103/physrevlett.101.180405 Using the signal and idler photons produced by parametric downconversion, we report an experimental observation of a violation of the Bell inequality for energy and time based purely on the geometric phases of the signal and idler photons. We thus show that energy-time entanglement between the signal and idler photons can be explored by means of their geometric phases. These results may have important practical implications for quantum information science by providing an additional means by which entanglement can be manipulated. Anand Jha, Mehul Malik, Robert Boyd Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements 2017-11-23T17:19:58-00:00 (17 Nov 2017) We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set of compatible tuples admit a unique joint measurement, while all tuples that admit a unique joint measurement lie in the boundary of such a set. We also provide counter-examples showing that none of these properties are both necessary and sufficient, thus completely describing the relation between joint measurement uniqueness and the structure of the compatible set. As a by-product of our investigations, we completely characterise the extremal and boundary points of the set of general tuples of measurements and of the subset of compatible tuples. Leonardo Guerini, Marcelo Cunha Entanglement, non-Markovianity, and causal non-separability 2017-11-23T17:19:11-00:00 (11 Nov 2017) Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: non-Markovianity, entanglement, and causal indefiniteness. Simon Milz, Felix Pollock, Thao Le, Giulio Chiribella, Kavan Modi Coherent states in a magnetic field and their generalizations 2017-11-23T17:18:57-00:00 (10 Nov 2017) This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided. VV Dodonov Reversing the thermodynamic arrow of time using quantum correlations 2017-11-23T17:18:33-00:00 (9 Nov 2017) The second law permits the prediction of the direction of natural processes, thus defining a thermodynamic arrow of time. However, standard thermodynamics presupposes the absence of initial correlations between interacting systems. We here experimentally demonstrate the reversal of the arrow of time for two initially quantum correlated spins-1/2, prepared in local thermal states at different temperatures, employing a Nuclear Magnetic Resonance setup. We observe a spontaneous heat flow from the cold to the hot system. This process is enabled by a trade off between correlations and entropy that we quantify with information-theoretical quantities. Kaonan Micadei, John Peterson, Alexandre Souza, Roberto Sarthour, Ivan Oliveira, Gabriel Landi, Tiago Batalhão, Roberto Serra, Eric Lutz Superdensity Operators for Spacetime Quantum Mechanics 2017-11-23T17:18:11-00:00 (8 Nov 2017) We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac's transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a superdensity operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. We also suggest experimental protocols for measuring spacetime entropies. Jordan Cotler, Chao-Ming Jian, Xiao-Liang Qi, Frank Wilczek Local unitary classification for sets of generalized Bell states 2017-11-23T17:17:35-00:00 (16 Nov 2017) In this paper, we study the local unitary classification for sets including two (three) generalized Bell states, called doublet (triplet), based on the local unitary equivalence of two sets. In detail, we firstly introduce some more general unitary operators besides Clifford operators to find out local unitary equivalent sets as many as possible; and then we present two necessary conditions for two local unitary equivalent sets to prove the local inequivalence. According to this thought, we completely classify all the doublets in $d⊗ d$ quantum system into the locally inequivalent doublets exactly with the number of $d$'s factors. Moreover, all the triplets in $p^α⊗ p^α$ quantum system for prime can be partitioned into $\frac(α + 3)6p^α + O(α p^α-1)$ LU-inequivalent triplets, especially, when $α=2$ and $p>2$, there are exactly $\lfloor \frac56p^2\rfloor + \lfloor \fracp-26+(-1)^\lfloor\fracp3\rfloor\fracp3\rfloor + 3$ LU-inequivalent triplets. Bujiao Wu, Jiaqing Jiang, Jialin Zhang, Guojing Tian, Xiaoming Sun Geometry of quantum correlations in space-time 2017-11-23T17:17:02-00:00 (16 Nov 2017) The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of non-unital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states. Zhikuan Zhao, Robert Pisarczyk, Jayne Thompson, Mile Gu, Vlatko Vedral, Joseph Fitzsimons Is serotonin an upper or a downer? The evolution of the serotonergic system and its role in depression and the antidepressant response 2017-11-23T17:16:39-00:00 Neuroscience & Biobehavioral Reviews, Vol. 51 (April 2015), pp. 164-188, doi:10.1016/j.neubiorev.2015.01.018 Paul Andrews, Aadil Bharwani, Kyuwon Lee, Molly Fox, Anderson Thomson The Hahn Quantum System 2017-11-23T17:16:28-00:00 (16 Nov 2017) Using a formulation of quantum mechanics based on the theory of orthogonal polynomials, we introduce a four-parameter system associated with the Hahn and continuous Hahn polynomials. The continuum energy scattering states are written in terms of the continuous Hahn polynomial whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Hahn polynomial. Accuracy of magnetic resonance imaging in prediction of tumour-free resection margin in rectal cancer surgery 2017-11-23T17:13:44-00:00 The Lancet, Vol. 357, No. 9255. (February 2001), pp. 497-504, doi:10.1016/s0140-6736(00)04040-x RGH Beets-Tan, GL Beets, RFA Vliegen, AGH Kessels, Van Boven, De Bruine, MF von Meyenfeldt, CGMI Baeten, JMA van Engelshoven The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds 2017-11-23T17:04:10-00:00 Med. Phys., Vol. 23, No. 6. (1 June 1996), pp. 815-850, doi:10.1118/1.597854 The concept of magnetic susceptibility is central to many current research and development activities in magnetic resonance imaging (MRI); for example, the development of MR-guided surgery has created a need for surgical instruments and other devices with susceptibility tailored to the MR environment; susceptibility effects can lead to position errors of up to several millimeters in MR-guided stereotactic surgery; and the variation of magnetic susceptibility on a microscopic scale within tissues contributes to MR contrast and is the basis of functional MRI. The magnetic aspects of MR compatibility are discussed in terms of two levels of acceptability: Materials with the first kind of magnetic field compatibility are such that magnetic forces and torques do not interfere significantly when the materials are used within the magnetic field of the scanner; materials with the second kind of magnetic field compatibility meet the more demanding requirement that they produce only negligible artifacts within the MR image and their effect on the positional accuracy of features within the image is negligible or can readily be corrected. Several materials exhibiting magnetic field compatibility of the second kind have been studied and a group of materials that produce essentially no image distortion, even when located directly within the imaging field of view, is identified. Because of demagnetizing effects, the shape and orientation, as well as the susceptibility, of objects within and adjacent to the imaging region is important in MRI. The quantitative use of susceptibility data is important to MRI, but the use of literature values for the susceptibility of materials is often difficult because of inconsistent traditions in the definitions and units used for magnetic parameters—particularly susceptibility. The uniform use of SI units for magnetic susceptibility and related quantities would help to achieve consistency and avoid confusion in MRI. John Schenck	2017-11-24 01:06:21	{"extraction_info": {"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, "math_score": 0.4841873049736023, "perplexity": 5340.896998415705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934807044.45/warc/CC-MAIN-20171123233821-20171124013821-00167.warc.gz"}
https://tex.stackexchange.com/questions/456047/make-commas-not-italicized-inside-a-macro-using-textit	# Make commas not italicized inside a macro using textit I'm trying to set up a shortcut for writing semantic types. These are usually written inside $\langle$ and $\rangle$ delimiters, with italicized letters standing for each type and commas separating these. They should look something like this: I've come up with a macro like the following: \newcommand{\type}[1]{% $\langle$\textit{#1}$\rangle$% } However, this of course results in the commas being italicized, too, which is not usually done in this context: Is there a way to exclude commas from being italicized when using this command? MWE: \documentclass{article} \newcommand{\type}[1]{% $\langle$\textit{#1}$\rangle$% } \usepackage[T1]{fontenc} \usepackage{times} \begin{document} \type{e, t} % Don't want comma italicized $\langle e, t\rangle$ % Don't want math typeface for letters $\langle$\textit{e}, \textit{t}$\rangle$ % Desired result, but cumbersome \end{document} Edit: To clarify, the reason I don't want to just do $\langle#1\rangle$ is because I want the semantic types to be set in the same typeface as the main text, not the math mode typeface. I've updated the MWE to reflect this, and here's the comparison: • it seems logically wrong to use the text face here, for \textit will pick up tje current text style eg bold, you seem to be just useing the deprecated times package so using times roman text with computer modern math, if you used compatible math and text types it may look better to use the math font here. – David Carlisle Oct 20 '18 at 23:06 You want the semantic types to be math variables. Note mathptmx below, not the long deprecated times package. \documentclass{article} \usepackage[T1]{fontenc} \usepackage{mathptmx} \newcommand{\type}[1]{\ensuremath{\langle#1\rangle}} \begin{document} \type{e, t} $\langle$\textit{e}, \textit{t}$\rangle$ \end{document} As you see, the only difference is in the (excessive) spacing in the complicated version. An even better version, because newtx provides for much richer Times-like fonts for math: \documentclass{article} \usepackage[T1]{fontenc} \usepackage{newtxtext,newtxmath} \newcommand{\type}[1]{\ensuremath{\langle#1\rangle}} \begin{document} \type{e, t} $\langle$\textit{e}, \textit{t}$\rangle$ \end{document} For XeLaTeX and text font set to TeX Gyre Pagella, use newpxmath; a small fix is needed, though. \documentclass{article} \usepackage[no-math]{fontspec} \usepackage{newpxmath} \usepackage{amsmath} \setmainfont{TeX Gyre Pagella} \DeclareSymbolFont{operators}{OT1}{zpltlf}{m}{n} \SetSymbolFont{operators}{bold}{OT1}{zpltlf}{b}{n} \newcommand{\type}[1]{\ensuremath{\langle#1\rangle}} \begin{document} \type{e, t} \end{document} \documentclass{article} \def\type<#1,#2>{$\langle$\textit{#1}, \textit{#2}$\rangle$} \begin{document} \type<e, t> \end{document} to produce: You could also drop the type and just use \def\<#1,#2>{$\langle$\textit{#1}, \textit{#2}$\rangle$} and then have \<e,t> in your document. EDIT To allow for nesting you should explicitly typeset the comma in \textrm: \documentclass{article} \def\<#1,#2>{$\langle$\textit{#1}\textrm{,} \textit{#2}$\rangle$} \begin{document} \<e, t> \<{\<e,t>},{\<e,t>}> \end{document}	2020-09-27 10:50:02	{"extraction_info": {"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, "math_score": 0.9589827060699463, "perplexity": 4554.879642255068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00451.warc.gz"}
http://www.agstarc.com/remembrance-day-zjueyhg/gd60ema.php?tag=116-2%2F3-as-a-fraction-f8589f	24%. write three and seven eighths as an improper fraction and as a mixed number. GCF = 33 GCF Calculator. Write 116 2/3% as a fraction or a mixed number. Write the decimal as a fraction or mixed number . write that number over 3 and that will be the number in percent form written as … Next, add the whole number to the left of the decimal. 116 2/3 is already a mixed number. Dividing a fractions by the Greatest common factor will reduce a fraction into its lowest terms For example, to reduce 4/12, we can divide 4 by 4 and 12 by 4 to get 1/3 That is what will calculator will do for you / Hence, we get the resulting fraction in simplest form as: (1 point) 4 and one-third 3 start fraction 9 over 39 end fraction 9 and one-third 5 and one-fourth 2} Test 62,004 for divisibility by 2. write the mixed number or fraction as a decimal. So the #16 2/3% " "# is the same as #" "16 2/3xx1/100#. 24% = $\frac{24}{100}$ Step 2: The fraction can be reduced to simplest form as follows. When Kaitlin divided a fraction by 1/2,the result was a mixed number.Was the original fraction less than or greater than 1/2? Reduce a Fraction to Lowest Terms - powered by WebMath. You might also like our calculator to convert a mixed number to an improper fraction. Type your numerator and denominator (numbers only please!) For example, 2/3 is in lowest form, but 4/6 is not in lowest form (the GCD of 4 and 6 is 2) and 4/6 can be expressed as 2/3. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. One percent is equal to one hundredth: 1% = 1/100. 350 ÷ 3 = 116 and remainder = 2 => 350 = 116 × 3 + 2 => 350/3 = (116 × 3 + 2) / 3 = 116 + 2/3 = 116 2/3 As a decimal number: 116 2/3 = 116 + 2/3 = 116 + 2 ÷ 3 = 116.666666666667 ≈ 116.67 As a percentage: 'Percent (%)' means 'out of one hundred'. 24/8 18/5 21/6, write the fraction or mixed number as a percent 23/40. Proper fraction = numerator smaller than denominator. We divide the numerator and the denominator with their highest common factor. p% = p 'out of one hundred'. Write the decimal as a fraction or mixed number in simplest form. Convert the decimal number to a fraction by placing the decimal number over a power of ten. Here the HCF of 24 and 100 is 4 166 is a whole number so the simplest form it can be in is 166/1. Write #16 2/3# as #16 + 2/3#. What is an Improper Fraction? Reduce (simplify) fractions to their lowest terms equivalents: To reduce a fraction divide the numerator and the denominator by their greatest common factor, GCF. Write 90% as a fraction or mixed number in simplest form. To reduce a fraction to the simplest form, try our Simplifying Fractions Calculator. 4 3/8 0.375 4.35, sometimes it is helpful to rewrite mixed numbers that include a fraction greater than 1. Write the decimal as a fraction or mixed number in simplest form. Its value to be considered as: # 1/100# An example: 2% is the same as #2xx1/100 = 2/100#. Explain reasoning. 166 2/3 cannot be simplified further. Change into fractions of 100 parts There are 34 laptops out of 116 computers. An improper fraction is any fraction where the numerator is greater than the denominator. Aug 16, 2009. 3 * 116 + 2 =. 0.05 = 1 / 20 as a fraction Step by Step Solution. The second step is to add the numerators of the two fractions to find the numerator of the answer, Write 116 2/3 as a fraction or mixed number. fractions. 4 3/8 0.375 4.35, sometimes it is helpful to rewrite mixed numbers that include a fraction greater than 1. i.e. Solution. Now you can add the numerators because the denominators are the same. = (348+2)/3, 1. 2.3 is a repeating decimal number and you want to convert it to a fraction or mixed number. First, find the greatest common factor of the two numbers. 116 2/3 % multiple denominator by whole number and add the numerator. 116 2/3 = 116 + 2/3 OK I asked this question before and got the same answer from 2 different people AND I also thought the same thing. How do you add fractions? Reduce the fraction by dividing the numerator and denominator by the gcd value: Example: 256 / 100 = (256/4) / (100/4) = 64/25. Our Fraction Simplifier uses the known property of fraction for fraction simplifying. This page will show you how to reduce a fraction to lowest terms. Step 1: The percent written in fraction form. Math. Evaluate 2x+6y when x=-4/5 and y=1/3. You can view more similar questions or ask a new question. Decimals less than one are easily converted to simple fractions, while decimals larger than one can be written as composite numbers as well, e.g. = 348/3 + 2/3 For example 56% is equal to 56/100 with gcd=4 is equal to 14/25: For example, the proportion of peaches to oranges in a basket of only peaches and oranges can be expressed using a … 0. 16/3 is an improper fraction because the numerator is greater than the denominator. Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd. This calculator simplifies or reduces a fraction to its simplest or lowest term. Simplifying fractions calculator with mixed numbers. Write 116 2/3 as a fraction or mixed number. To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF. 1} Write start fraction 39 over 9 end fraction as a whole or a mixed number in simplest form. Write the fraction or mixed number as a decimal 1 1/2 0.50 1.5* 1.05 1.1 3. For example, let’s convert 3:2 to a fraction. Use the number line to write the missing numbers: 1 2/6= /6. Write your answer as a fraction or mixed number in simplest form. An improper fraction is a fraction with no whole number and has a larger numerator than the denominator. Step 6 : Pulling out like terms : 6.1 Pull out like factors : 8a 2 - 18a = 2a • (4a - 9) you would take 116 times the bottom # the plus the top and leave the bottom # there so it would be 116X3 =348+ =350. There are two steps in reducing the fraction: The Greatest Common Divisor (GCD) is determined. Write the fraction or mixed number as a decimal 1 1/2 0.50 1.5* 1.05 1.1 3. Fraction Simplifier. In other words, the numerator and denominator of the fraction cannot both be divided by any number to further reduce the fraction. As a fraction is 350/3 and in mixed with be 2 all number 116/3. 350/3 Evaluate 2x+6y when x=-4/5 and y=1/3. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating. How to Convert a Part-to-Part Ratio to a Fraction. 3 repeating as a fraction How do you simplify fractions? write the fraction or mixed number as a percent 23/40 . Since there is number to the right of the decimal point, place the decimal number over . When Kaitlin divided a fraction by 1/2, the result was a mixed number. Use the decimal to fraction converter/calculator below to write any decimal number as a fraction. = 348/3 + 2/3. Example: For adding the fractions 1 / 3 and 1 / 5, you must first modify the fractions so that the denominators are the same.For these two fractions, the result would be 5 / 15 and 3 / 15.. Now you can add the numerators because the denominators are the same. It is also known as the fraction bar or vinculum. How to Convert an Improper Fraction to a Mixed Number Write the fraction or mixed number as a decimal. 116 + 2/3 = 116 * (3/3) + 2/3 math. 43 out of 166 equals percent? Write the percent as a fraction in the simplest form. To get an improper fraction, you must multiply the whole number to get the same denominator. 24/8 18/5 21/6. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. write each fraction as a whole number or mixed number. To write 2.31 as a fraction you have to write 2.31 as numerator and put 1 as the denominator. Welcome! Use the number line to write the missing numbers: 1 2/6= /6. THANK YOU! Second, divide both the numerator and denominator by the GCF. For example, to do1/5 -2/3 do 2/3 -1/5 to get 7/15 and read the answer as -7/15 A reduced fraction is a common fraction in its simplest possible form. 6.35 I think it is 6 3/10, write each mixed number as an improper fraction 1 7/8. What is 2.31 as a fraction. write three and seven eighths as an improper fraction and as a mixed number. 116 2/3 = 116 + 2/3. Percentage is parts of 100. write each fraction as a whole number or mixed number. Integer numbers prime factorization: 88=2^3×11; 116=2^2×29; Multiply all the common prime factors, by the lowest exponents. Examples of improper fractions are 16/3, 81/9, 525/71. Write 116 2/3 as a fraction or mixed number. We call the line that separates 16 and 3 the division line. For example, to reduce 150/240 When Kaitlin divided a fraction by 1/2,the result was a mixed number.Was the original fraction less than or greater than 1/2? 0.25 is 1/4, while 1.5 is 1 1/2. 1. Convert decimal 0.05 to a fraction. 0.05 = 0.05 / 1 Step 2: Multiply both top and bottom by 10 for every number after the decimal point:. Fraction: 3/116 already reduced to the lowest terms. According to this property, any fraction can be replaced by another fraction, equal to the given fraction, but with lesser numerator and denominator. To get this, both the top and bottom numbers of the fraction are divided by the SAME NUMBER, and this is repeated if necessary until it is impossible to do so anymore. ... What is 116 as a fraction in simplest form? Numerator is found from 33/33 = 1 Write the fraction or mixed number as a decimal. Explain your reasoning. I need to write 116 2/3 as a fraction or a mixed number. 3 7/8 A:3.78 B:3.785 C:3.8777 D:3.875 this is my answer. To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (/) by any interger number, ie, multiply by 2, 3, 10, 30 ... / is equivalent to 116/Equivalent Fractions because x 2 = and x 2 = / is equivalent to 116/Equivalent Fractions because x 3 = and x 3 = Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator. 350/3 is the equivalent fraction. Write the fraction or mixed number as a decimal. = (348+2)/3. As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. 6.35 I think it is 6 3/10, write each mixed number as an improper fraction 1 7/8. 116 + 2/3 = 116 * (3/3) + 2/3. BUT 350/3 is not an option. Fractions simplifier. How to Convert an Improper Fraction to a Mixed Number. The fraction is the ratio of the number of laptops to the number of computers. You can view more similar questions or ask a new question. Example. Example: For the fraction 33 / 99 the number 33 is the numerator and 99 is the denominator. Explain your reasoning. To reduce a fraction to lowest terms (also called its simplest form), just divide both the numerator and denominator by the Greatest Common Factor (GCF or GCD). Was the original fraction less than or greater than 1/2? Note that the % sign is like units of measurement. 3 7/8 A:3.78 B:3.785 C:3.8777 D:3.875 this is my answer. How to convert fraction to decimal. A part-to-part ratio is an expression of the relationship between two subsets of a set. We can simplify these fractions … When you say 2.3 repeating, you mean that the 1 is repeating. 1} Write start fraction 39 over 9 end fraction as a whole or a mixed number in simplest form. 7/8 0.78 0.875* 0.8777 1.875 2. (1 point) 4 and one-third 3 start fraction 9 over 39 end fraction 9 and one-third 5 and one-fourth 2} Test 62,004 for divisibility by 2. write the mixed number or fraction as a decimal. Hit reduce et voila ! So in order to convert percent to fraction, divide the percent by 100% and reduce the fraction. The numerator and the denominator have no common prime factors. 2. To convert the decimal 0.05 to a fraction follow these steps: Step 1: Write down the number as a fraction of one:. Here is the answer to the question: What is 2.31 as a fraction or what is 2.31 as a fraction. 3:2 = 3 2. This … the fraction is given by: Now, the numerator as well as the denominator have a greatest common divisor as 2. Convert to a Simplified Fraction 112.5. p% = p/100 = p ÷ 100. Write the fraction or mixed number as a decimal. Recall that a fraction is reduced when you divide both the numerator and the denominator by a common factor. 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Cricut Acrylic Blanks, Retropie Won T Recognize Trackball, Eludes Crossword Clue 6 Letters, Dodge Center Newspaper, Best Tile Paint Uk, Cargo Express Trailer Reviews, Collon Animal Rescue, Rugrats The Big Showdown,	2021-04-18 00:09:57	{"extraction_info": {"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, "math_score": 0.9155675172805786, "perplexity": 863.7404525476879}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464065.57/warc/CC-MAIN-20210417222733-20210418012733-00513.warc.gz"}
https://www.zbmath.org/?q=an%3A1293.32014	# zbMATH — the first resource for mathematics Comparison of invariant metrics. (English) Zbl 1293.32014 Let $$D \subset \mathbb C^n$$ be a domain. By $$F_B^D$$ and $$F_K^D$$ we denote the pseudodifferential metrics of Bergman and Kobayashi, respectively. The authors estimate precisely the quantity $$F_K^{{\mathbb C}\setminus \{0,1\}}$$ and compare the Bergman differential metrics of the unit ball $$B_n$$ in $${\mathbb C}^n$$ and the ring domain $$\Omega_r=\{ z \in {\mathbb C}^n \,\|\, r<\|z\|<1\}$$, for $$r \in (0,1)$$. Here are the results: Theorem 1. Let $$p \in \mathbb C\setminus \{0,1\}$$ and $$\delta= \text{dist}\,(p,0)$$ and $$\xi =1$$. Then we have for small enough $$\delta$$ $F_K^{{\mathbb C}\setminus \{0,1\}}(p,\xi) \approx \frac{1}{\delta \,\log (1/\delta)} \,.$ Theorem 2. Let $$p \in \Omega_r$$ and $$\xi \in T_p \Omega_r$$ be a tangent vector such that $$p \cdot \overline{\xi} =0$$. Then $F_B^{\Omega_r} (p, \xi) \lneq F_B^{B_n} (p, \xi)$ for all $$p \in \Omega_r$$. The restriction $$p \cdot \overline{\xi} =0$$ can be let away in dimension two, if $$p$$ lies on the normal to a point on the inner boundary of $$\Omega_r$$. Theorem 3. If $$n=2$$ and $$p=(r+\varepsilon , 0)$$ for small $$\varepsilon>0$$, then we have for small enough $$r$$ and for arbitrary $$\xi \in {\mathbb C}^2$$ that $F_B^{\Omega_r} (p, \xi) \lneq F_B^{B_2} (p, \xi)$ ##### MSC: 32F45 Invariant metrics and pseudodistances in several complex variables ##### Keywords: Bergman metric; Kobayashi metric; modular function Full Text: ##### References: [1] L. Ahlfors, Complex analysis : An introduction to the theory of analytic functions of one complex variable , Third edition, McGraw-Hill Book Company, New York, 1979. · Zbl 0395.30001 [2] K. Diederich and J.E. Fornaess, Comparison of the Bergman and the Kobayashi metric , Math. Ann. 254 (1980), 257-262. · Zbl 0429.32031 · doi:10.1007/BF01457999 · eudml:163491 [3] K. Diederich, J.E. Fornaess and G. Herbort, Boundary behavior of the Bergman metric , Proc. Symp. Pure Math. 41 (1984), 59-67. · Zbl 0533.32012 · doi:10.1090/pspum/041/740872 [4] J.E. Fornaess and L. Lee, Kobayashi, Carathéodory, and Sibony metrics , Complex Variable Elliptic Eq. 54 (2009), 293-301. · Zbl 1166.32010 · doi:10.1080/17476930902760450 [5] K.T. Hahn, Inequality between the Bergman metric and Carathéodory differential metric , Proc. Amer. Math. Soc. 68 (1978), 193-194. · Zbl 0376.32020 · doi:10.2307/2041770 [6] M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis , Walter de Gruyter, Boston, 1993. · Zbl 0789.32001 [7] S. Kobayashi, Hyperbolic complex spaces , Springer, New York, 1998. · Zbl 0917.32019 [8] S.G. Krantz, The boundary behavior of the Kobayashi metric , Rocky Mountain J. Math. 22 (1992), 227-233. \noindentstyle · Zbl 0760.32010 · doi:10.1216/rmjm/1181072807 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.	2021-02-28 01:38:24	{"extraction_info": {"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, "math_score": 0.8982089757919312, "perplexity": 786.8306937726476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359624.36/warc/CC-MAIN-20210227234501-20210228024501-00446.warc.gz"}
https://jp.maplesoft.com/support/help/maple/view.aspx?path=simplify/radical&L=J	Parameters expr - any expression radical - literal name; radical symbolic - (optional) literal name; symbolic Description • The simplify/radical command is used to simplify expressions which contain radicals. For the case of square roots only, see simplify/sqrt. Additional simplification facilities for expressions containing radicals include the radnormal, rationalize, and combine commands. • The simplify/radical command has three phases. In the first phase, it tries to simplify each radical individually. In the second phase, it looks at the set of all the radicals that appear in the expression and tries to eliminate radicals by writing one radical in terms of others. Finally, the expression as a whole is normalized as a rational expression. • The main simplification applied to individual radicals is ${\left({x}^{n}y\right)}^{\left(\frac{m}{n}\right)}\to {x}^{m}{y}^{\frac{m}{n}}\mathrm{if}\mathrm{signum}\left(x\right)=1,\mathrm{where}0 Example 1: ${24}^{\frac{1}{3}}\to 2{3}^{\frac{1}{3}}$. Example 2: $\sqrt{{\mathrm{\pi }}^{2}x}\to \mathrm{\pi }\sqrt{x}$. If sign of $x$ is unknown, the user can force Maple to do this transformation either by using the assume facility, or by specifying the symbolic option. If the sign of $x$ is unknown, and the symbolic option is given, $x$ is assumed real and positive. • The main simplification applied to the set of radicals is to try to write a radical as a constant times another radical. Example 1: Given $\sqrt{30}+\sqrt{2}$, apply $\sqrt{30}\to \sqrt{15}\sqrt{2}$. Example 2: Given $\sqrt{2x-2}+\sqrt{x-1}$, apply $\sqrt{2x-2}\to \sqrt{2}\sqrt{x-1}$. • The main simplification applied during the rationalization of the resulting expression is the following. Given ${x}^{\frac{m}{n}}={x}^{q+\frac{r}{n}}$ where $0$, write this as ${x}^{q}{A}^{\frac{r}{d}}$, normalize, and replace the dummy $A$ by $x$ on output. Example:$\sqrt{{\left(x+1\right)}^{3}}-x\sqrt{x+1}\to \left(x+1\right)A-xA\to A\to \sqrt{x+1}$. Examples > $e≔\left[{24}^{\frac{1}{3}},{24}^{-\frac{1}{3}},{\left(-24\right)}^{\frac{1}{3}}\right]$ ${e}{≔}\left[{{24}}^{{1}}{{3}}}{,}\frac{{{24}}^{{2}}{{3}}}}{{24}}{,}{\left({-24}\right)}^{{1}}{{3}}}\right]$ (1) > $\mathrm{simplify}\left(e,\mathrm{radical}\right)$ $\left[{2}{}{{3}}^{{1}}{{3}}}{,}\frac{{{3}}^{{2}}{{3}}}}{{6}}{,}\left({I}{}\sqrt{{3}}{+}{1}\right){}{{3}}^{{1}}{{3}}}\right]$ (2) > $e≔\left[{6}^{\frac{1}{3}}+{25}^{\frac{1}{3}},{6}^{\frac{1}{3}}+{15}^{\frac{1}{3}}\right]$ ${e}{≔}\left[{{6}}^{{1}}{{3}}}{+}{{25}}^{{1}}{{3}}}{,}{{6}}^{{1}}{{3}}}{+}{{15}}^{{1}}{{3}}}\right]$ (3) > $\mathrm{simplify}\left(e,\mathrm{radical}\right)$ $\left[{{6}}^{{1}}{{3}}}{+}{{5}}^{{2}}{{3}}}{,}{{3}}^{{1}}{{3}}}{}\left({{2}}^{{1}}{{3}}}{+}{{5}}^{{1}}{{3}}}\right)\right]$ (4) > $e≔{\left(-8{b}^{3}a\right)}^{\frac{1}{3}}$ ${e}{≔}{\left({-}{8}{}{{b}}^{{3}}{}{a}\right)}^{{1}}{{3}}}$ (5) > $\mathrm{simplify}\left(e,\mathrm{radical}\right)$ ${2}{}{\left({-}{{b}}^{{3}}{}{a}\right)}^{{1}}{{3}}}$ (6) > $\mathrm{simplify}\left(e,\mathrm{radical},\mathrm{symbolic}\right)$ ${2}{}{b}{}{\left({-}{a}\right)}^{{1}}{{3}}}$ (7) > $\mathrm{assume}\left(b<0\right)$ > $\mathrm{simplify}\left(e,\mathrm{radical}\right)$ ${-}{2}{}{\mathrm{b~}}{}{{a}}^{{1}}{{3}}}$ (8) > $f≔{\left({x}^{4}+3{x}^{3}y+3{x}^{2}{y}^{2}+x{y}^{3}\right)}^{\frac{1}{3}}$ ${f}{≔}{\left({{x}}^{{4}}{+}{3}{}{{x}}^{{3}}{}{y}{+}{3}{}{{x}}^{{2}}{}{{y}}^{{2}}{+}{x}{}{{y}}^{{3}}\right)}^{{1}}{{3}}}$ (9) > $\mathrm{simplify}\left(f,\mathrm{radical}\right)$ ${\left({x}{}{\left({x}{+}{y}\right)}^{{3}}\right)}^{{1}}{{3}}}$ (10) > $\mathrm{simplify}\left(f,\mathrm{radical},\mathrm{symbolic}\right)$ $\left({x}{+}{y}\right){}{{x}}^{{1}}{{3}}}$ (11) > $f≔{\left(2x+2\right)}^{\frac{1}{3}}+{\left(4x+4\right)}^{\frac{1}{3}}+{\left(3x-3\right)}^{\frac{1}{3}}$ ${f}{≔}{\left({2}{}{x}{+}{2}\right)}^{{1}}{{3}}}{+}{\left({4}{}{x}{+}{4}\right)}^{{1}}{{3}}}{+}{\left({3}{}{x}{-}{3}\right)}^{{1}}{{3}}}$ (12) > $\mathrm{simplify}\left(f,\mathrm{radical}\right)$ ${\left({2}{}{x}{+}{2}\right)}^{{1}}{{3}}}{+}{{2}}^{{1}}{{3}}}{}{\left({2}{}{x}{+}{2}\right)}^{{1}}{{3}}}{+}{\left({3}{}{x}{-}{3}\right)}^{{1}}{{3}}}$ (13) > $f≔{\left(x+1\right)}^{\frac{4}{3}}-x{\left(x+1\right)}^{\frac{1}{3}}$ ${f}{≔}{\left({x}{+}{1}\right)}^{{4}}{{3}}}{-}{x}{}{\left({x}{+}{1}\right)}^{{1}}{{3}}}$ (14) > $\mathrm{simplify}\left(f,\mathrm{radical}\right)$ ${\left({x}{+}{1}\right)}^{{1}}{{3}}}$ (15)	2022-01-24 17:14:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 48, "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, "math_score": 0.9775263071060181, "perplexity": 5178.839676648845}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304572.73/warc/CC-MAIN-20220124155118-20220124185118-00416.warc.gz"}
https://encyclopediaofmath.org/wiki/Bombieri%E2%80%93Iwaniec_method	# Bombieri-Iwaniec method (Redirected from Bombieri–Iwaniec method) Invented in [a1] and [a2], where it was used to bound the Riemann zeta-function $\zeta ( s )$ along the mid-line of its critical strip, this is currently (2000) the strongest method around for establishing upper bounds on several wide classes of Weyl sums that have many applications within analytic number theory (cf. also Weyl sum). General application to the first such class, exponential sums within the scope of Van der Corput's exponent pairs theory (see [a3]), was done by M.N. Huxley and N. Watt in [a10]. Improvements to one aspect of the method (the first spacing problem below) were found by Watt [a16] and Huxley and G. Kolesnik [a8], while in [a11] H. Iwaniec and C.J. Mozzochi made an important adaptation, forming a second branch of the method that yielded new results for the circle and divisor problems. In a series of papers beginning with [a4] Huxley has generalized and refined this adaptation, applying it to bound lattice point discrepancy (the difference between an area and the number of integer lattice points within the area; cf. also Lattice of points; Geometry of numbers). The original insight of E. Bombieri and Iwaniec into the second spacing problem (see below), which is of crucial importance for both branches of the method, has been significantly augmented by the theory of resonance curves invented and refined by Huxley in [a5] and [a7]. See [a3] for a brief introduction to the method; [a6] is the most recent book on the method, and covers almost all of its aspects, including applications to, e.g.: exponential sums with a Dirichlet character factor; the mean-square of $\| \zeta ( 1 / 2 + i t ) \|$ over a short interval; and counting integer lattice points near a curve. It also covers Jutila's independent (but related) method of [a12] and [a13], used for the estimation of exponential sums with a Fourier coefficient of a cusp form, or a divisor function, as a factor. The original branch of the Bombieri–Iwaniec method deals with a sum \begin{equation} S ( f ; M _ { 1 } , M _ { 2 } ) = \sum _ { M _ { 1 } < m < M _ { 2 } } e ( f ( m ) ), \end{equation} where $e ( x ) = \operatorname { exp } ( 2 \pi i x )$, $M _ { 1 } , M _ { 2 } \in [ M , 2 M ]$, and the derivatives (from first to fourth, say) of $F ( x ) = f ( M x )$ have absolute values ranging within a uniformly bounded factor of a single parameter $T$ (sufficiently large) with $\alpha = \operatorname { log } M / \operatorname { log } T \in ( 0,1 )$. The method, which only applies directly when $\alpha \in ( 1 / 3,2 / 3 )$, has five main steps: i) Division of $S ( f ; M _ { 1 } , M _ { 2 } )$ into consecutive shorter sums within each of which $f ( m )$ is approximated, via Taylor series, by a cubic polynomial with rational quadratic coefficient $a /q$. ii) Use of Poisson summation (cf. also Poisson summation method), evaluation of Gauss sums (cf. also Gauss sum) and the stationary phase method (cf. also Stationary phase, method of the) to transform the short sum $S ( a / q )$ belonging to $a /q$ into an even shorter one: \begin{equation} S ^ { } \left( \frac { a } { q } \right) = \sum _ { h } e \left( \mathbf{x} ( h ) \mathbf{y} \left( \frac { a } { q } \right) \right) \gamma ( h ) \delta \left( \frac { a } { q } \right) \end{equation} with $\mathbf{x} ( h ) = ( h ^ { 2 } , h , h ^ { 3 / 2 } , h ^ { 1 / 2 } , h ^ { - 1 / 2 } )$ and $y _ { 1 } ( a / q ) = - \overline { a } / q$, where $a \overline { a } \equiv 1 ( \operatorname { mod } q )$. iii) Estimation of the sum over $a /q$ of $\| S ^ { } ( a / q ) \|$, in terms of the $p$th power moment, using the Hölder inequality and the double large sieve introduced in [a1] (cf. also Large sieve). This leaves two steps to provide data for the sieve. iv) The first spacing problem: Count pairs of "neighbours" amongst vectors of the form $\mathbf{x} ( h _ { 1 } ) + \ldots + \mathbf{x} ( h _ { p } )$. v) Second spacing problem: Count pairs of "neighbours" $\mathbf{y} ( a / q )$ and ${\bf y} ( a _ { 1 } / q _ { 1 } )$ (coincidences). Steps iv) and v) remain open problems (as of 2000), as does the question of more radical improvement of the whole. E. Fouvry and Iwaniec, using only Van der Corput's method with the double large sieve from Step iii), found useful new bounds for their monomial exponential sums (see [a6]). The method's second branch treats \begin{equation} U ( f ; M _ { 1 } , M _ { 2 } ; H _ { 1 } , H _ { 2 } ) = \sum _ { h } \frac { S ( h f ^ { \prime } ; M _ { 1 } , M _ { 2 } ) } { h }, \end{equation} where the summation is over $h \in [ H _ { 1 } , H _ { 2 } ] \subseteq [ H , 2 H ]$ and $f$, $M _ { 1 }$ and $M _ { 2 }$ are as above. Since $f$ has been replaced by $f ^ { \prime }$, so must the cubic approximation of Step i) be replaced by its derivative. Steps ii)–iv) also change, but the second spacing problem does not. These sums $U ( f ; M _ { 1 } , M _ { 2 } ; H _ { 1 } , H _ { 2 } )$ can arise when a truncated form of the Fourier series for the sawtooth function \begin{equation} \rho ( f ^ { \prime } ) = [ f ^ { \prime } ] - f ^ { \prime } + \frac { 1 } { 2 } \end{equation} is used in the estimation of the lattice point discrepancy of an area of size $f ( M _ { 2 } ) - f ( M _ { 1 } ) \ll T$ bounded by $x = M _ { 1 }$, $y = 0$, $x = M _ { 2 }$ and $y = f ^ { \prime } ( x )$ in the $( x , y )$-plane. If $M$ gets too large, then one can switch to summing the discrepancies for columns of width $1$ to summing those for rows of depth $1$, the number of which required will be $O ( T / M )$. Poisson summation makes a similar switch possible in estimating $S ( f ; M _ { 1 } , M _ { 2 } )$ alone. In both contexts the critical cases are those around $\alpha = 1 / 2$ ($M = \sqrt { T }$), so the $a /q$, being values of $f ^ { \prime \prime } ( x ) / 2$, will satisfy $1 \ll \| a / q \| \ll 1$; something like the situation in applications of the Hardy–Littlewood circle method. Jutila's method [a13] utilizes a "twisted" Wilton summation formula, corresponding to a cusp form of even weight $k$ for the full modular group: \begin{equation} \sum _ { m } b ( m ) e \left( \frac { m a } { q } \right) g ( m ) = \sum _ { n } b ( n ) e \left( - n \frac { \overline { a } } { q } \right) \mathcal{L} g ( n ), \end{equation} where $b ( m )$ is the $m$th Fourier coefficient of the cusp form, $g ( x )$ is a smooth function supported in $[M , 2 M]$, and the linear integral transform $\mathcal{L} = \mathcal{L} _ { k , q }$ has integrand containing the Bessel $J$-function of order $k - 1$ as a factor (cf. also Bessel functions). Step ii) above is essentially the extension of Jutila's formula to the case where the cusp form is replaced by the theta-series of weight $k = 1 / 2$ with Fourier coefficients $b ( m ) = \# \{ n \in {\bf Z} : n ^ { 2 } = m \}$. M. Jutila has an analogous "twisted" Voronoi summation formula for the more delicate case where $b ( m )$ is the divisor function (cf. also Number of divisors), for which the corresponding modular form is non-holomorphic; this enabled a more elementary proof of a famous theorem of Iwaniec (see [a14]). The original treatment by Bombieri and Iwaniec of the second spacing problem rested on the observation that proximity of $\overline { a } / q$ and $\overline { a _ { 1 } } / q _ { 1 }$ (modulo $\mathbf{Z}$) implies that the row vectors $\mathbf{v} _ { 1 } = [ \alpha _ { 1 } , q _ { 1 } ]$ and $\mathbf{v} = [ a , q ]$ will be linked by a relation $\mathbf{v} _ { 1 } ^ { t } = \mathbf{B} \mathbf{v} ^ { t }$, with $\mathbf{B}$ being an integer $( 2 \times 2 )$-matrix of determinant $1$ having a "small" lower left entry. Huxley's theory of resonance curves showed that the coincident pairs $\mathbf{y} ( a / q )$, ${\bf y} ( a _ { 1 } / q _ { 1 } )$ for a given choice of $\mathbf{B}$ correspond to integer points lying near a certain plane resonance curve, this curve being determined (up to a minor transformation) by the choice of $f ( x )$ and $\mathbf{B}$. This led, in [a5], to better bounds in the second spacing problem, to improved exponential sum estimates, and (for example) to the result that \begin{equation} \zeta \left( \frac { 1 } { 2 } + i t \right) \ll t ^ { \beta }, \end{equation} when $t \rightarrow + \infty$, with fixed $\beta > 89 / 570 = 0.1561 \ldots$ (an unpublished improvement of this and of resonance curve theory is given in [a7]). For comparison, Bombieri and Iwaniec's original paper [a1] had $\beta > 9 / 56 = 0.1607 \dots$, while even a complete resolution of both the first and second spacing problems (alone) could not get $\beta$ below $3 / 20 = 0.15$. Integer points near a suitable curve may be counted using exponential sum estimates, so resonance curves invite one to apply the Bombieri–Iwaniec method iteratively. P. Sargos managed to do this in [a15], using his own simpler theory of (quite different) resonance curves. He obtained results of greatest interest for $\alpha$ near $2 / 5 = 0.4$. A third construction of resonance curves (different again) has been given by Huxley and Kolesnik [a9], and is of interest for $\alpha$ near $7 / 17 = 0.4118 \dots$. They were able to apply this iteratively, but got better results (in most cases) with a single step of an elementary method once employed by H. Swinnerton-Dyer to count lattice points exactly on a curve. #### References [a1] E. Bombieri, H. Iwaniec, "On the order of $\zeta ( 1 / 2 + i t )$" Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 13 (1986) pp. 449–472 [a2] E. Bombieri, H. Iwaniec, "Some mean value theorems for exponential sums" Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 13 (1986) pp. 473–486 [a3] S.W. Graham, G. Kolesnik, "Van der Corput's method for exponential sums" , London Math. Soc. Lecture Notes , 126 , Cambridge Univ. Press (1991) [a4] M.N. Huxley, "Exponential sums and lattice points" Proc. London Math. Soc. , 60 (1990) pp. 471–502 (Corrigenda, 66 (1993), 70) [a5] M.N. Huxley, "Exponential sums and the Riemann zeta-function IV" Proc. London Math. Soc. , 66 (1993) pp. 1–40 [a6] M.N. Huxley, "Area, lattice points and exponential sums" , London Math. Soc. Monographs , 13 , Oxford Univ. Press (1996) [a7] M.N. Huxley, "Exponential sums and the Riemann zeta-function V" (unpublished notes) [a8] M.N. Huxley, G. Kolesnik, "Exponential sums and the Riemann zeta-function III" Proc. London Math. Soc. , 62 (1991) pp. 449–468 (Corrigenda 66 (1993), 302) [a9] M.N. Huxley, G. Kolesnik, "Exponential sums with a large second derivative" M. Jutila (ed.) T. Metsänkylä (ed.) , Number Theory (Proc. Turku Conf. Number Theory in Memory of Kustaa Inkeri) , de Gruyter (2000) pp. 131–143 [a10] M.N. Huxley, N. Watt, "Exponential sums and the Riemann zeta-function" Proc. London Math. Soc. , 57 (1988) pp. 1–24 [a11] H. Iwaniec, C.J. Mozzoch, "On the divisor and circle problems" J. Number Theory , 29 (1988) pp. 60–93 [a12] M. Jutila, "On exponential sums involving the divisor function" J. Reine Angew. Math. , 355 (1985) pp. 173–190 [a13] M. Jutila, "Lectures on a method in the theory of exponential sums" , Tata Inst. Fundam. Res. Lect. Math. and Physics , 80 , Springer (1987) [a14] M. Jutila, "The fourth power moment of the Riemann zeta-function over a short interval" , Number Theory I (Budapest, 1987) , Colloq. Math. Soc. J. Bolyai , 51 , North-Holland (1990) pp. 221–244 [a15] P. Sargos, "Points entiers au voisinage d'une courbe, sommes trigonométriques courtes et pairs d'exposants" Proc. London Math. Soc. , 70 (1995) pp. 285–312 [a16] N. Watt, "Exponential sums and the Riemann zeta-function II" J. London Math. Soc. , 39 (1989) pp. 385–404 How to Cite This Entry: Bombieri–Iwaniec method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bombieri%E2%80%93Iwaniec_method&oldid=22164	2022-07-03 18:23:04	{"extraction_info": {"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, "math_score": 0.9466241598129272, "perplexity": 790.568244317076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00670.warc.gz"}
https://stats.stackexchange.com/questions/433119/covariance-and-correlation	# Covariance and Correlation I'm new to Statistics. How do we calculate the correlation coefficient from covariance, by Standardization or Normalization? I understand, that for better interpretation, we calculate correlation coef. Since we are dividing covariance by the standard deviations of 2 RV, it makes sense to say that correlation is a "standardized value of covariance". But, in some text books, and blogs, I could see that people referring "correlation coef" as "normalized value of covariance". Are they using these terms interchangeably? (To my knowledge, Normalization changes the values to be in the range of 0-1, and Standardization converts the values, such that it has 0 mean and 1 standard deviation.) • Normalization is a broader term than you say. For example, making mean or sum of squares of the data values is also called "normalization" (i.e. bringing "norm" to unit value). – ttnphns Oct 25 '19 at 16:52 • Even if you are a new to statistics I would recommend you to read this which explains how and why covariance and correlation are kin. – ttnphns Oct 25 '19 at 16:56 $$\operatorname{corr}(X,Y) = \frac{\operatorname{cov}(X,Y)}{\sigma(X) \; \sigma(Y)}$$ It is a "normalized covariance" in the sense that this operation transforms covariance to $$[-1, 1]$$ range, it has unified units that do not depend on the scaling (standard deviations) of $$X$$ and $$Y$$.	2020-04-09 20:42:08	{"extraction_info": {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7315787672996521, "perplexity": 951.7596883501595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371876625.96/warc/CC-MAIN-20200409185507-20200409220007-00068.warc.gz"}
https://zbmath.org/?q=an%3A0899.14017	Mirror symmetry for two-parameter models. I.(English)Zbl 0899.14017 Summary: We study, by means of mirror symmetry, the quantum geometry of the Kähler-class parameters of a number of Calabi-Yau manifolds that have $$b_{11} = 2.$$ Our main interest lies in the structure of the moduli space and in the loci corresponding to singular models. This structure is considerably richer when there are two parameters than in the various one-parameter models that have been studied hitherto. We describe the intrinsic structure of the point in the (compactification of the) moduli space that corresponds to the large complex structure or classical limit. The instanton expansions are of interest owing to the fact that some of the instantons belong to families with continuous parameters. We compute the Yukawa couplings and their expansions in terms of instantons of genus zero. By making use of recent results of Bershadsky and others we compute also the instanton numbers for instantons of genus one. For particular values of the parameters the models become birational to certain models with one parameter. The compactification divisor of the moduli space thus contains copies of the moduli spaces of one-parameter models. Our discussion proceeds via the particular models $$P_4^{1,1,2,2,2}$$ [P. M. H. Wilson, Invent. Math. 107, No. 3, 561-593 (1992; Zbl 0766.14035)] and $$P_4^{1,1,2,2,6}$$ [P. Berglund, P. Candelas, X. de la Ossa, A. Font, T. Hübsch, D. Jančić and F. Quevedo, Nucl. Phys., B 419, No. 2, 352-403 (1994; Zbl 0896.14022)]. [See also part II of this paper, Nucl. Phys., B 429, No. 3, 626-674 (1994; see the following review)]. MSC: 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14D20 Algebraic moduli problems, moduli of vector bundles 32Q15 Kähler manifolds Full Text: References: [1] Candelas, P.; de la Ossa, X.; Green, P.; Parkes, L., Nucl. 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Phys., A8, 79 (1993) [16] Landman, A., Trans. Amer. Math. Soc., 181, 89 (1973) [17] Cadavid, A. C.; Ferrara, S., Phys. Lett., B267, 193 (1991) [18] Blok, B.; Varchenko, A., Intern. J. Mod. Phys., A7, 1467 (1992) [19] Lerche, W.; Smit, D. J.; Warner, N. P., Nucl. Phys., B372, 87 (1992) [20] Deligne, P., Equations différentielles à points singuliers réguliers, (Lecture notes in mathematics, Vol. 163 (1970), Springer: Springer Berlin) · Zbl 0244.14004 [21] Katz, N., Publ. Math. IHES, 39, 175 (1971) [23] Aspinwall, P. S.; Greene, B. R.; Morrison, D. R., Intern. Math. Res. Notices, 319 (1993) [24] Batyrev, V. V., Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties (November 1992), preprint [25] Roan, S.-S., Intern. J. Math., 2, 439 (1991) [26] Oda, T.; Park, H. S., Tôhoku Math. J., 43, 375 (1991) [27] Batyrev, V. V., Duke Math. J., 69, 349 (1992) [28] Aspinwall, P. S.; Morrison, D. R., Commun. Math. Phys., 151, 245 (1993) [29] Witten, E., Nucl. Phys., B403, 159 (1993) [33] Klemm, A.; Theisen, S., Mirror maps and instanton sums for complete intersections in weighted projective space, preprint LMU-TPW-93-08 (1993) [34] McDuff, D., Invent. Math., 89, 13 (1987) 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.	2022-09-26 17:07:05	{"extraction_info": {"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, "math_score": 0.8894895911216736, "perplexity": 5782.4676663561895}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334912.28/warc/CC-MAIN-20220926144455-20220926174455-00225.warc.gz"}
https://bookstore.ams.org/view?ProductCode=CONM/604	An error was encountered while trying to add the item to the cart. Please try again. The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below. Copy To Clipboard Successfully Copied! Recent Advances in Real Complexity and Computation Edited by: José Luis Montaña Universidad de Cantabria, Santander, Spain Luis M. Pardo Universidad de Cantabria, Santander, Spain Available Formats: Electronic ISBN: 978-1-4704-1409-2 Product Code: CONM/604.E 185 pp List Price: $76.00 MAA Member Price:$68.40 AMS Member Price: $60.80 Click above image for expanded view Recent Advances in Real Complexity and Computation Edited by: José Luis Montaña Universidad de Cantabria, Santander, Spain Luis M. Pardo Universidad de Cantabria, Santander, Spain Available Formats: Electronic ISBN: 978-1-4704-1409-2 Product Code: CONM/604.E 185 pp List Price:$76.00 MAA Member Price: $68.40 AMS Member Price:$60.80 • Book Details Contemporary Mathematics Volume: 6042013 MSC: Primary 03; 14; 65; This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluís Santaló Summer School on “Recent Advances in Real Complexity and Computation”, held July 16–20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: “Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?” These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving. This book is published in cooperation with Real Sociedád Matematica Española. Graduate students and research mathematicians interested in the complexity of computation. • Articles • Martijn Baartse and Klaus Meer - Topics in real and complex number complexity theory • Bernd Bank, Marc Giusti and Joos Heintz - Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity • Carlos Beltrán and Michael Shub - The complexity and geometry of numerically solving polynomial systems. • M. Giusti and J.-C. Yakoubsohn - Multiplicity hunting and approximating multiple roots of polynomial systems • Joos Heintz, Bart Kuijpers and Andrés Rojas Paredes - On the intrinsic complexity of elimination problems in effective algebraic geometry • Gregorio Malajovich - Newton iteration, conditioning and zero counting • Request Review Copy • Get Permissions Volume: 6042013 MSC: Primary 03; 14; 65; This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluís Santaló Summer School on “Recent Advances in Real Complexity and Computation”, held July 16–20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: “Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?” These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving. This book is published in cooperation with Real Sociedád Matematica Española.	2023-01-29 00:18:01	{"extraction_info": {"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": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2552061378955841, "perplexity": 3021.1633740602097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00521.warc.gz"}
http://www.zentralblatt-math.org/ioport/en/?q=au:Azimifar%2C%20Z*	History Please fill in your query. A complete syntax description you will find on the General Help page. Continuation of codimension-2 equilibrium bifurcations in CONTENT. (English) Doedel, Eusebius (ed.) et al., Numerical methods for bifurcation problems and large-scale dynamical systems. Based on two workshops held as part of the 1997-1998 IMA academic year on emerging applications of dynamical systems. New York, NY: Springer. IMA Vol. Math. Appl. 119, 163-184 (2000). From the introduction: We consider a dynamical system depending on parameters, $$\dot u= F(u,α),\quad F: {\bbfR}^n\times {\bbfR}^m\to {\bbfR}^n,\tag 1$$ and its numerical study using CONTENT, an interactive software environment developed by Yu. A. Kuznetsov and V. V. Levitin. CONTENT can detect, compute and continue codimension-1 bifurcations of the solutions to the equilibrium equations $$F(u, α)= 0\tag 2$$ associated with (1). We discuss recent extensions to CONTENT to compute and continue all codimension-2 bifurcations of the solutions to (2).	2013-05-19 08:59:53	{"extraction_info": {"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, "math_score": 0.30485641956329346, "perplexity": 1490.2753240251986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697232084/warc/CC-MAIN-20130516094032-00056-ip-10-60-113-184.ec2.internal.warc.gz"}
http://bootmath.com/what-exactly-is-a-probability-measure-in-simple-words.html	# What exactly is a probability measure in simple words? Can someone explain probability measure in simple words? This term has been hunting me for my life. Today I came across Kullback-Leibler divergence. The KL divergence between probability measure P and Q is defined by, $$KL(P,Q)= \begin{cases} \int \log\left(\frac{dP} {dQ}\right)dP & \text{if}\ P\ll Q, \\ \infty & \text{otherwise}. \end{cases}$$ I have no idea what I just read. I looked up probability measure, it refers to probability space. I looked that up, it refers to $\sigma$-algebra. I told myself I have to stop. So, is probability measure just a probability density but a broader and fancier saying. Am I overlooking a simple concept, or is this topic just that hard? Thanks in advance! #### Solutions Collecting From Web of "What exactly is a probability measure in simple words?" A probability space consists of: 1. A sample space $X$, which is the set of all possible outcomes of an experiment 2. A collection of events $\Sigma$, which are subsets of $X$ 3. A function $\mu$, called a probability measure, that assigns to each event in $\Sigma$ a nonnegative real number Let’s consider the simple example of flipping a coin. In that case, we have $X=\{H,T\}$ for heads and tails respectively, $\Sigma=\{\varnothing,\{H\},\{T\},X\}$, and $\mu(\varnothing)=0$, $\mu(\{H\})=\mu(\{T\})=\frac{1}{2},$ and $\mu(X)=1$. All of this is a fancy way of saying that when I flip a coin, I have a $0$ percent chance of flipping nothing, a $50$ percent chance of flipping heads, a $50$ percent chance of flipping tails, and a $100$ percent chance of flipping something, heads or tails. This is all very intuitive. Now, getting back to the abstract definition, there are certain natural requirements that $\Sigma$ and $\mu$ must satisfy. For example, it is natural to require that $\varnothing$ and $X$ are elements of $\Sigma$, and that $\mu(\varnothing)=0$ and $\mu(X)=1$. This is just saying that when performing an experiment, the probability that no outcome occurs is $0$, while the probability that some outcome occurs is $1$. Similarly, it is natural to require that $\Sigma$ is closed under complements, and if $E\in\Sigma$ is an event, then $\mu(E^c)+\mu(E)=1$. This is just saying that when performing an experiment, the probability that event $E$ occurs or doesn’t occur must be $1$. There are other requirements of $\Sigma$ which make it a $\sigma$-algebra, and other requirements of $\mu$ which make it a (finite) measure, and to rigorously study probability, one must eventually become familiar with these notions. A probability measure is more like a cumulative distribution function. It gives, for any set of values, the probability of the random variable being in that set. And of course, it has to be defined in a way that makes sense: if $A \cap B = \emptyset$, then $\mu(A \cup B) = \mu(A) + \mu(B)$, and the probability of the entire range is one, and no set has a negative probability. Agreed that wikipedia does a poor job getting the basic ideas across; it seems to be written by experts for experts and very jargon-y in many cases…. Pictorially, perhaps picture that you have many items, and a probability measure is a scale telling you the weight of any subset. The total weight of everything you have is always one. If you put a couple items on the scale separately one by one, the sum of their weights will be the same as if you weighed them all together at once. A funny thing happens with grains of sand: They each have individual weight zero, but when you get a jar of them together (think uncountably many, that’s important!), then they can have a total weight bigger than zero. Think of grains of sand here as being uncountably many in total, like real numbers in an interval. The above is not true if there are only countably many! But for real numbers, for instance, each number in the interval has probability measure zero, but the whole interval has some positive measure. Perhaps I can help clarify things a bit without getting super technical. A probability space is simply the collection of all the possible events that can happen. So, if you are flipping a coin, the probability space $\Omega = \{H, T\}$ since you can only flip heads or tails. The $\sigma$-algebra that was mentioned is also conceptually simple – it groups all of the events in your probability space into a new set (of course, a $\sigma$-algebra has certain properties, but for sake of simplicity I am skipping those). Therefore, an example of a $\sigma$-algebra $F$ on $\Omega$ would be the power set of $\Omega$ (set of all subsets) $F = \{\emptyset , \{H\}, \{T\}, \{H,T\} \}$. The reasons the $\sigma$-algebra is important is because that is the set of events that a probability measure gives weights to. Therefore, a measurable space $(\Omega, F, P)$ is a probability space, combined with a $\sigma$-algebra on that space, and a probability measure P on the $\sigma$-algebra. So, a probability measure simply gives weights (probabilities) to each set within the $\sigma$-algebra, where all of these weights must add up to 1, and a few other properties (cumulative additivity for example). To describe a random variable $X$, we specify what the probaility is that the outcome of $X$ is some value $x$. For example with a fair die and $X$ standing for “the score of one roll of the die”, we’d say $$P(X=1)=P(X=2)=P(X=3)=P(X=4)=P(X=5)=P(X=6)=\frac16$$ and that’s it. Our $X$ takes values only from the finite set $\Omega=\{1,2,3,4,5,6\}$. There are also random variables with (countably) infinitely many possible outcomes. For example if $Y$ stands for “the number of throws of a fair coin until head appears the first time, then $$P(Y=1)=\frac12, P(Y=2)=\frac14, P(Y=3)=\frac18,\ldots$$ The set $\Omega$ of possible outcomes is now $\Omega=\mathbb N$. And finally there are random variables with uncountably many possible outcomes (e.g. let $Z$ stand for “select a random point uniformly on the unit interval $\Omega:=[0,1]$”). In these cases usually for any individual value $x\in\Omega$, the probaility $P(Z=x)$ is simply zero. Instead, we have positive probability only if we ask for certain infinite subsets of the space $\Omega$ of possible outcomes. For example, we can righteously say $P(\frac12< X<\frac23)=\frac16$. It would be nice if one could assign a probability value to any subset $S\subseteq \Omega$. However, it usually turns out that this is not possible in a consistent or well-defined manner. One will still strive to make the collection of sets $S$ for which $P(X\in S)$ is defined/definable as large as possible. For our example $Z$, we can certainly say $P(X\in S)=b-a$ if $S$ is an interval $[a,b]$ or $]a,b[$ or $]a,b]$ or $[a,b[$ with $0\le a\le b\le 1$. Especially, $P(X\in\emptyset)=0$ and $P(X\in\Omega)=1$. Also, if $A,B$ are disjoint and $P(X\in A)$ and $P(X\in B)$ make sense, then so does $P(X\in A\cup B)$, namely with the value $P(X\in A\cup B)=P(X\in A)+P(X\in B)$. In fact, if we have sets $A_1,A_2,\ldots$ and know $P(X\in A_n)$ for each $n$, then it turns out to be advisable to have $$P(\bigcup_{n=1}^\infty A_n)=\sum_{n=1}^\infty P(X\in A_n).$$ This is almost the concept of a $\sigma$-algebra: It is a collection of subsets of a given set $\Omega$. If we are lucky, such as in the finite case or the countable case (at least as it occured with the random variable $Y$ we defined) this collection is the full powerset of $\Omega$, but it may be smaller. At any rate, it is large enough to be closed under certain operations, among which is the countable union of sets. And this property is precisely what allows us to formulate the essential properties we want to have for probabilities of a random variable being in a subset of $\Omega$. Any function that assigns to each element of a given $\sigma$-algebra (i.e. to each sufficiently nice subset of $\Omega$) a value between $0$ and $1$ inclusive, such that the basic rules as spelled out above hold for countable unions, complements, the whole space, is then called a probability measure. One important measure is the Lebesgue measure $\lambda$ on $[0,1]$ (which describes the random variable $Z$ above). You may know it from integration theory, where it allwows us to generalize (extend) the Riemann integration. You may know for example, that the expected value of a finite random variable is simply given by $$\tag1E(X) = \sum_{x\in\Omega}x\cdot P(X=x)$$ or more generally, the expected avalue of a function of $X$ $$\tag2E(f(X))\sum_{x\in\Omega}f(x)\cdot P(X=x).$$ These are just finite sums (hence always work) if $X$ is a finite random variable. If $\Omega$ is countable, we can use the same formulas, but have series instad of sums, and it may happen that the series does not converge. For example $E(Y)=2$, but $E((-2)^Y)$ does not converge. It becomes even worse when $P(X=x)=0$ for all $x\in\Omega$ as then the sums/series above simply result in $0$. The sums/series are simply replaced with corresponding integrals $$E(Z)=\int_0^1 x\,\mathrm dx =\frac12, \qquad E(f(Z))=\int_0^1 f(x)\,\mathrm dx.$$ Again, the second integral does not make sense for every possible $f$, it must be integrable. The step from sum to (first series and then) integral may look arbitrary, but it is indeed well-founded in measure theory – often enough one adjusts in the other direction and also writes series and sums as integrals (with respect to specific measures). All this may still not be enough to grasp the formula you posted, but it should help you get started with the introductory texts you already tried to read.	2018-07-16 20:30:54	{"extraction_info": {"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, "math_score": 0.9169453978538513, "perplexity": 182.23855565450356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589455.35/warc/CC-MAIN-20180716193516-20180716213516-00608.warc.gz"}
https://mathematica.stackexchange.com/questions/76612/what-are-all-the-properties-that-colordata-supports	# What are all the Properties that ColorData supports? The documentation for ColorData reads: Possible properties in ColorData["scheme","property"] include: "ColorFunction" "ColorList" "ColorRules" "Image" "Name" "Panel" "ParameterCount" "Range" {"Range",i} Are there any others? Evaluating ColorData["Properties"] in 10.0.2 returns: {"AlternateNames", "ColorFunction", "ColorList", "ColorRules", "Image", "Name", "Panel", "ParameterCount", "Range", "StandardName"} This however is also incomplete. Some spelunking reveals that there are more. Here is a complete list from the function definition itself: "StandardName" "Name" "AlternateNames" "PrivateStandardNames" "ColorFunction" "ColorList" {"ColorList", "Sorted"} "ColorRules" {"ColorRules", "Sorted"} "Range" {"Range", _Integer?Positive} "ParameterCount" "Image" "Panel" "ColorNames" {"ColorNames", "Sorted"} "BlendArgument" "PrivateNote" • I think it would be good to mention that a user can get most of these by evaluating ColorData["Properties"], which produces {"AlternateNames", "ColorFunction", "ColorList", "ColorRules", "Image", "Name", "Panel", "ParameterCount", "Range", "StandardName"}. In general, evaluating someData["Properties"] usually produces useful info about someData. – m_goldberg Mar 6 '15 at 9:32 • @m_goldberg That's a good point, but as that data is now known to be incomplete I was uncertain of the value of mentioning it. – Mr.Wizard Mar 6 '15 at 9:34 • Nice. {ColorData[#, "AlternateNames"] // First, ColorData[#, "Panel"]} & /@ ColorData["Indexed"] // Grid` – Dr. belisarius Mar 6 '15 at 15:07	2020-02-26 16:46:53	{"extraction_info": {"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, "math_score": 0.33804160356521606, "perplexity": 9601.51384063183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146414.42/warc/CC-MAIN-20200226150200-20200226180200-00502.warc.gz"}
https://codereview.stackexchange.com/questions/252850/how-to-restrict-a-user-to-use-only-one-plugin-in-wordpress	# How to restrict a user to use only one plugin in WordPress I want to restrict a specific user to use only one plugin. I don't want him to see any other pages on the WordPress admin dashboard like the Plugins page, Posts, or other pages. I want to show him just one link in the admin dashboard and let him to use just that page. I want to do it programmatically and don't want to use a plugin for it. I implemented the same functionality to restrict users by the code below but I want to know is there any better solution for it or not. It redirects the user to '/wp-admin/edit.php?post_type=product' if he doesn't visit the valid pages that I declared in the $pages array. I'm using WooCommerce, the post_type=product is for that. Could you help me to achieve this, please? Thank you. The code I wrote in functions.php file before to achieve this, the issue if I have to set all pages and plugins ID manually: add_action('current_screen', 'checkUserPermissionsInThisScreen'); function checkUserPermissionsInThisScreen(){ if (is_admin()){$a = get_current_screen(); $currentUserName = wp_get_current_user()->user_login; if ($currentUserName === "testuser") { $pages = array( 'dashboard', 'toplevel_page_wpcf7', 'contact_page_wpcf7-new', 'contact_page_wpcf7-integration', 'edit-shop_order', 'edit-shop_coupon', 'woocommerce_page_dgwt_wcas_settings', 'woocommerce_page_wc-reports', 'woocommerce_page_wc-settings', 'woocommerce_page_wc-status', 'woocommerce_page_wc-addons', 'woocommerce_page_alg-wc-renumerate-orders-tools', 'themes', 'customize', 'users', 'tools', 'import', 'export', 'site-health', 'export-personal-data', 'erase-personal-data', 'tools_page_action-scheduler', 'options-general', 'options-writing', 'options-reading', 'options-discussion', 'options-media', 'options-permalink', 'options-privacy', 'toplevel_page_agilewc', 'toplevel_page_smush', 'shop_order' ); remove_menu_page( 'themes.php' ); remove_menu_page( 'woocommerce' ); remove_menu_page( 'wpcf7' ); remove_menu_page( 'index.php' ); remove_menu_page( 'edit-comments.php' ); remove_menu_page( 'users.php' ); remove_menu_page( 'tools.php' ); remove_menu_page( 'options-general.php' ); remove_menu_page( 'smush' ); //Remove the "WooCommerce Recent Reviews" widget. remove_meta_box('woocommerce_dashboard_recent_reviews', 'dashboard', 'normal'); //Remove the "WooCommerce Status" widget. remove_meta_box('woocommerce_dashboard_status', 'dashboard', 'normal'); //Hide the "Coupon data" meta box. remove_meta_box('woocommerce-coupon-data',$a->id, 'normal'); //Hide the "Order data" meta box. remove_meta_box('woocommerce-order-data', $a->id, 'normal'); //Hide the "Items" meta box. remove_meta_box('woocommerce-order-items',$a->id, 'normal'); remove_meta_box('woocommerce-order-downloads', $a->id, 'normal'); //Hide the "Order actions" meta box. remove_meta_box('woocommerce-order-actions',$a->id, 'side'); remove_meta_box('woocommerce-order-notes', $a->id, 'side'); } global$pagenow; if ( ( ! in_array($a->id,$pages) \|\| $pagenow === 'post-new.php' ) ) { wp_redirect(get_site_url() . "/wp-admin/edit.php?post_type=product"); die; } } } } • Is $pages only defined when the following condition is true: \$currentUserName === "testuser"? – Sᴀᴍ Onᴇᴌᴀ Mar 24 at 5:52	2021-04-17 12:52:53	{"extraction_info": {"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, "math_score": 0.23196248710155487, "perplexity": 2338.0954951757076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038119532.50/warc/CC-MAIN-20210417102129-20210417132129-00000.warc.gz"}
https://physics.stackexchange.com/questions/478276/relation-between-the-canonical-partition-function-and-the-phase-space-volume	# Relation between the canonical partition function and the phase space volume In Kerson Huang's Statistical Mechanics (2nd ed.), it is claimed that the phase space volume occupied by the canonical ensemble is the partition function: $$Q_N (V, T) \equiv \int \frac{dp dq}{N! h^{3N}} e^{-\beta \mathcal{H}(p, q)}, \tag{1}$$ where $$N$$ is the number of particles and $$\mathcal{H}(p, q)$$ is the Hamiltonian that describes the macroscopic system. I cannot understand why this is the case. Shouldn't it be something like the following: $$V_{\text{phase space}} = \int_{\Sigma} dp dq, \tag{2}$$ where $$\Sigma$$ is the region "under" the hyper-surface of constant energy $$E$$, which would be the maximum energy of the system + heat bath. Now, I can understand why Eq. $$(1)$$ is the sum over all states, but I fail to see how $$(1)$$ and $$(2)$$ are the same. What am I missing here? • (1) and (2) are indeed not the same. The wording in Huang's book is pretty bad. The partition function is indeed (1), but it is not equal to the volume of the phase space (one could say that it is the measure of the phase space according to $e^{-\beta\mathcal{H}}/(N!h^{3N})$, but that would not convey any additional information, so I don't see the point)$. – Yvan Velenik May 6 at 13:13 • @YvanVelenik thanks for your reply. Could you please elaborate on what you mean by "measure of the phase space according to$e^{-\beta \mathcal{H}}/(N! h^{3N})\$ " Also, is there any reason why Huang calls the partition function the phase space volume occupied by the canonical ensemble? – grav.field May 6 at 19:15 • I don't know what he has in mind when he uses this terminology. I am using measure in its usual mathematical sense. – Yvan Velenik May 7 at 6:24	2019-11-15 23:25:08	{"extraction_info": {"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8721727728843689, "perplexity": 128.64903063094172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668716.22/warc/CC-MAIN-20191115222436-20191116010436-00549.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-5-section-5-5-dividing-polynomials-exercise-set-page-385/13	## Introductory Algebra for College Students (7th Edition) $1$ RECALL: The zero-exponent rule states that for any non-zero number $a$, $a^0=1$ Use the zero-exponent rule where $a=-2$ to obtain: $(-2)^0=1$	2018-11-19 14:12:40	{"extraction_info": {"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, "math_score": 0.643981397151947, "perplexity": 1964.9922705480283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745762.76/warc/CC-MAIN-20181119130208-20181119152208-00523.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-standard-form-of-the-equation-of-the-hyperbola-given-the-pro-1	How do you find the standard form of the equation of the hyperbola given the properties vertex (0,1), vertex (8,1), focus (-3,1)? Aug 1, 2017 ${\left(x - 4\right)}^{2} / 16 - {\left(y - 1\right)}^{2} / 33 = 1$ Explanation: As the two vertex are $\left(0 , 1\right)$ and $\left(8 , 1\right)$ and focus is $\left(- 3 , 1\right)$ as the distance between $\left(0 , 1\right)$ and $\left(- 3 , 1\right)$ is $3$, the other focus is $\left(11 , 1\right)$ (at a distance of $3$ to the right of $\left(8 , 1\right)$) and central point is $\left(4 , 1\right)$. Hence, $a = 4$, the distance to either side of center and $c = 7$, the distance from center to focus. Hence, ${b}^{2} = {c}^{2} - {a}^{2} = 33$ and equation is ${\left(x - 4\right)}^{2} / 16 - {\left(y - 1\right)}^{2} / 33 = 1$ graph{((x-4)^2/16-(y-1)^2/33-1)((x+3)^2+(y-1)^2-0.03)((x-11)^2+(y-1)^2-0.03)((x-4)^2+(y-1)^2-0.03)(x^2+(y-1)^2-0.03)((x-8)^2+(y-1)^2-0.03)=0 [-6, 14, -4.5, 5.5]}	2020-08-05 22:54:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "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, "math_score": 0.48893970251083374, "perplexity": 340.6993802532208}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735989.10/warc/CC-MAIN-20200805212258-20200806002258-00436.warc.gz"}
https://www.iacr.org/cryptodb/data/paper.php?pubkey=28874	## CryptoDB ### Paper: Reusing Tamper-Proof Hardware in UC-Secure Protocols Authors: Jeremias Mechler Jörn Müller-Quade Tobias Nilges DOI: 10.1007/978-3-319-76578-5_16 Search ePrint Search Google PKC 2018 Universally composable protocols provide security even in highly complex environments like the Internet. Without setup assumptions, however, UC-secure realizations of cryptographic tasks are impossible. Tamper-proof hardware tokens, e.g. smart cards and USB tokens, can be used for this purpose. Apart from the fact that they are widely available, they are also cheap to manufacture and well understood.Currently considered protocols, however, suffer from two major drawbacks that impede their practical realization:The functionality of the tokens is protocol-specific, i.e. each protocol requires a token functionality tailored to its need.Different protocols cannot reuse the same token even if they require the same functionality from the token, because this would render the protocols insecure in current models of tamper-proof hardware. In this paper we address these problems. First and foremost, we propose formalizations of tamper-proof hardware as an untrusted and global setup assumption. Modeling the token as a global setup naturally allows to reuse the tokens for arbitrary protocols. Concerning a versatile token functionality we choose a simple signature functionality, i.e. the tokens can be instantiated with currently available signature cards. Based on this we present solutions for a large class of cryptographic tasks. ##### BibTeX @inproceedings{pkc-2018-28874, title={Reusing Tamper-Proof Hardware in UC-Secure Protocols}, booktitle={Public-Key Cryptography – PKC 2018}, series={Public-Key Cryptography – PKC 2018}, publisher={Springer}, volume={10769}, pages={463-493}, doi={10.1007/978-3-319-76578-5_16}, author={Jeremias Mechler and Jörn Müller-Quade and Tobias Nilges}, year=2018 }	2022-01-27 14:24:25	{"extraction_info": {"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, "math_score": 0.21600869297981262, "perplexity": 6846.042137378949}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305266.34/warc/CC-MAIN-20220127133107-20220127163107-00253.warc.gz"}
https://www.physicsforums.com/threads/at-how-many-femtometers-does-strong-force-cease-to-exist.613373/	# At how many femtometers does strong force cease to exist? 1. Jun 12, 2012 ### Rorkster2 At 2.5 femtometer away from a quark the strong force is said to significantly loose power and become insignificant. At how many femtometers does the strong force completely loose any amount of tug? 2. Jun 12, 2012 ### Staff: Mentor As usual, there is no single point where it gets exactly 0. But the force is decreasing so quickly that it gets completely irrelevant (and small compared to the electromagnetic force, for example) just some femtometers away. 3. Jun 12, 2012 ### Rorkster2 Ok. Is their any known way to find out the rate in which the force drops off? I.e. an equation of some sort? 4. Jun 12, 2012 ### The_Duck Someone may correct me on this, but I think for long distances it should fall off roughly like exp(-r/r0)/r, where r0 is the Compton wavelength of the pion, which is about 1.5 femtometers. 5. Jun 12, 2012 ### Rorkster2 @The_Duck I looked that up to find out what it ment and google didn't return anything. 6. Jun 12, 2012 ### The_Duck In case the problem is notation, it means that at a distance r the strength of the strong force should be proportional to the function $$\frac{e^{-r/r_0}}{r}$$ where r0 is 1.5 femtometers. Here's a plot of this behavior: http://www.wolframalpha.com/input/?i=plot+exp(-r/1.5)/r,+r=0..10 In the plot, the x axis is the distance in femtometers and the y axis is proportional to the strength of the strong force 7. Jun 12, 2012 ### Rorkster2 Ahh thanks a lot. In the graph the x axis is length in femtometers and would Y be the strength? I'm pretty sure I get it I just want to be sure 8. Jun 12, 2012 ### The_Duck Yes. Just keep in mind that the numbers on the y axis don't mean anything; it's the shape of the graph that is meaningful. 9. Jun 12, 2012 ### Rorkster2 You have rightfully earned the title the duck. Thank you	2018-12-15 22:27:37	{"extraction_info": {"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, "math_score": 0.5840815305709839, "perplexity": 1304.0499096673395}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827137.61/warc/CC-MAIN-20181215222234-20181216004234-00112.warc.gz"}
https://wiki.swarma.org/index.php/Sznajd%E6%A8%A1%E5%9E%8B	# Sznajd模型 Sketch of the 2 updating rules, social validation (top panel) and discord destroys (bottom panel), assuming that the two men in the middle have been chosen to be updated. Without loss of generality, red men (looking to the left) say no, blue men (looking to the right) say yes. The purple men can have either opinion. The Sznajd model or United we stand, divided we fall (USDF) model is a sociophysics model introduced in 2000[1] to gain fundamental understanding about opinion dynamics. The Sznajd model implements a phenomenon called social validation and thus extends the Ising spin model. In simple words, the model states: • Social validation: If two people share the same opinion, their neighbors will start to agree with them. • Discord destroys: If a block of adjacent persons disagree, their neighbors start to argue with them. The Sznajd model or United we stand, divided we fall (USDF) model is a sociophysics model introduced in 2000 to gain fundamental understanding about opinion dynamics. The Sznajd model implements a phenomenon called social validation and thus extends the Ising spin model. In simple words, the model states: • Social validation: If two people share the same opinion, their neighbors will start to agree with them. • Discord destroys: If a block of adjacent persons disagree, their neighbors start to argue with them. Sznajd 模型或 United we stand，divided we fall (USDF)模型是2000年引入的社会物理学模型，旨在获得对舆论动力学的基本理解。模型实现了一种叫做社会验证的现象，从而扩展了伊辛旋转模型。简单来说，这个模型指出: • 社会验证: 如果两个人有相同的观点，他们的邻居就会开始同意他们。不和谐破坏: 如果邻居中的一群人不同意，他们的邻居就会开始和他们争吵。 ## Mathematical formulation For simplicity, one assumes that each individual $\displaystyle{ i }$ has an opinion Si which might be Boolean ($\displaystyle{ S_i=-1 }$ for no, $\displaystyle{ S_i=1 }$ for yes) in its simplest formulation, which means that each individual either agrees or disagrees to a given question. For simplicity, one assumes that each individual i has an opinion Si which might be Boolean (S_i=-1 for no, S_i=1 for yes) in its simplest formulation, which means that each individual either agrees or disagrees to a given question. = = = 数学公式 = = 为了简单起见，我们假设每个个体都有一个观点 Si，这个观点 Si 在其最简单的公式中可能是布尔型的(s _ i =-1表示否，s _ i = 1表示肯) ，这意味着每个个体要么同意要么不同意给定的问题。 In the original 1D-formulation, each individual has exactly two neighbors just like beads on a bracelet. At each time step a pair of individual $\displaystyle{ S_i }$ and $\displaystyle{ S_{i+1} }$ is chosen at random to change their nearest neighbors' opinion (or: Ising spins) $\displaystyle{ S_{i-1} }$ and $\displaystyle{ S_{i+2} }$ according to two dynamical rules: 1. If $\displaystyle{ S_i=S_{i+1} }$ then $\displaystyle{ S_{i-1}=S_i }$ and $\displaystyle{ S_{i+2}=S_i }$. This models social validation, if two people share the same opinion, their neighbors will change their opinion. 2. If $\displaystyle{ S_i=-S_{i+1} }$ then $\displaystyle{ S_{i-1}=S_{i+1} }$ and $\displaystyle{ S_{i+2}=S_i }$. Intuitively: If the given pair of people disagrees, both adopt the opinion of their other neighbor. In the original 1D-formulation, each individual has exactly two neighbors just like beads on a bracelet. At each time step a pair of individual S_i and S_{i+1} is chosen at random to change their nearest neighbors' opinion (or: Ising spins) S_{i-1} and S_{i+2} according to two dynamical rules: 1. If S_i=S_{i+1} then S_{i-1}=S_i and S_{i+2}=S_i. This models social validation, if two people share the same opinion, their neighbors will change their opinion. 2. If S_i=-S_{i+1} then S_{i-1}=S_{i+1} and S_{i+2}=S_i. Intuitively: If the given pair of people disagrees, both adopt the opinion of their other neighbor. ### Findings for the original formulations In a closed (1 dimensional) community, two steady states are always reached, namely complete consensus (which is called ferromagnetic state in physics) or stalemate (the antiferromagnetic state). Furthermore, Monte Carlo simulations showed that these simple rules lead to complicated dynamics, in particular to a power law in the decision time distribution with an exponent of -1.5.[2] In a closed (1 dimensional) community, two steady states are always reached, namely complete consensus (which is called ferromagnetic state in physics) or stalemate (the antiferromagnetic state). Furthermore, Monte Carlo simulations showed that these simple rules lead to complicated dynamics, in particular to a power law in the decision time distribution with an exponent of -1.5. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =.此外，蒙特卡罗模拟表明，这些简单的规则导致复杂的动力学，特别是在决策时间分布的指数为 -1.5的幂律。 ### Modifications The final (antiferromagnetic) state of alternating all-on and all-off is unrealistic to represent the behavior of a community. It would mean that the complete population uniformly changes their opinion from one time step to the next. For this reason an alternative dynamical rule was proposed. One possibility is that two spins $\displaystyle{ S_i }$ and $\displaystyle{ S_{i+1} }$ change their nearest neighbors according to the two following rules:[3] 1. Social validation remains unchanged: If $\displaystyle{ S_i=S_{i+1} }$ then $\displaystyle{ S_{i-1}=S_{i} }$ and $\displaystyle{ S_{i+2}=S_{i} }$. 2. If $\displaystyle{ S_i=-S_{i+1} }$ then $\displaystyle{ S_{i-1}=S_{i} }$ and $\displaystyle{ S_{i+2}=S_{i+1} }$ The final (antiferromagnetic) state of alternating all-on and all-off is unrealistic to represent the behavior of a community. It would mean that the complete population uniformly changes their opinion from one time step to the next. For this reason an alternative dynamical rule was proposed. One possibility is that two spins S_i and S_{i+1} change their nearest neighbors according to the two following rules: 1. Social validation remains unchanged: If S_i=S_{i+1} then S_{i-1}=S_{i} and S_{i+2}=S_{i}. 2. If S_i=-S_{i+1} then S_{i-1}=S_{i} and S_{i+2}=S_{i+1} = = = 修改 = = = 最终(反铁磁)状态的交替全开和全关是不现实的行为代表一个社区。这将意味着，整个人口统一地改变他们的意见，从一个时间步骤到下一个。为此，提出了另一种动力学规律。一种可能性是，两个自旋 s _ i 和 s _ { i + 1}根据以下两个规则改变它们的近邻: # 社会验证保持不变: 如果 s _ i = s _ { i + 1} ，那么 s _ { i-1} = s _ { i }和 s _ { i + 2} = s _ { i }。# 如果 s _ i =-s _ { i + 1}则 s _ { i-1} = s _ { i }和 s _ { i + 2} = s _ { i + 1} ## Relevance In recent years, statistical physics has been accepted as modeling framework for phenomena outside the traditional physics. Fields as econophysics or sociophysics formed, and many quantitative analysts in finance are physicists. The Ising model in statistical physics has been a very important step in the history of studying collective (critical) phenomena. The Sznajd model is a simple but yet important variation of prototypical Ising system.[4] In recent years, statistical physics has been accepted as modeling framework for phenomena outside the traditional physics. Fields as econophysics or sociophysics formed, and many quantitative analysts in finance are physicists. The Ising model in statistical physics has been a very important step in the history of studying collective (critical) phenomena. The Sznajd model is a simple but yet important variation of prototypical Ising system. In 2007, Katarzyna Sznajd-Weron has been recognized by the Young Scientist Award for Socio- and Econophysics of the Deutsche Physikalische Gesellschaft (German Physical Society) for an outstanding original contribution using physical methods to develop a better understanding of socio-economic problems.[5] In 2007, Katarzyna Sznajd-Weron has been recognized by the Young Scientist Award for Socio- and Econophysics of the Deutsche Physikalische Gesellschaft (German Physical Society) for an outstanding original contribution using physical methods to develop a better understanding of socio-economic problems. 2007年，Katarzyna Sznajd-Weron 因其杰出的原创性贡献，使用物理方法更好地理解社会经济问题，获得了德国物理学会德国物理学会社会经济物理学年轻科学家奖。 ### Applications The Sznajd model belongs to the class of binary-state dynamics on a networks also referred to as Boolean networks. This class of systems includes the Ising model, the voter model and the q-voter model, the Bass diffusion model, threshold models and others.[6] The Sznajd model can be applied to various fields: • The finance interpretation considers the spin-state $\displaystyle{ S_i=1 }$ as a bullish trader placing orders, whereas a $\displaystyle{ S_i=0 }$ would correspond to a trader who is bearish and places sell orders. The Sznajd model belongs to the class of binary-state dynamics on a networks also referred to as Boolean networks. This class of systems includes the Ising model, the voter model and the q-voter model, the Bass diffusion model, threshold models and others. The Sznajd model can be applied to various fields: • The finance interpretation considers the spin-state S_i=1 as a bullish trader placing orders, whereas a S_i=0 would correspond to a trader who is bearish and places sell orders. = = = 应用 = = = Sznajd 模型属于一类二元态动力学的网络，也称为布尔网络。这类系统包括 Ising 模型、选民模型和 q-voter 模型、 Bass 扩散模型、阈值模型等。Sznajd 模型可以应用于各个领域: • 金融解释认为旋转状态的 s _ i = 1是一个看涨的交易者下单，而 s _ i = 0则对应于一个看跌的交易者下单卖出。 ## References 1. Sznajd-Weron, Katarzyna; Sznjad, Jozef (2000). "Opinion evolution in closed community". International Journal of Modern Physics C. 11 (6): 1157–1165. arXiv:cond-mat/0101130. Bibcode:2000IJMPC..11.1157S. doi:10.1142/S0129183100000936. S2CID 17307753. 2. Sznajd-Weron, Katarzyna (2005). "Sznajd model and its applications". Acta Physica Polonica B. 36 (8): 2537. arXiv:physics/0503239. Bibcode:2005AcPPB..36.2537S. 3. Sanchez, Juan R. (2004). "A modified one-dimensional Sznajd model". arXiv:cond-mat/0408518. 4. Castellano, Claudio; Fortunato, Santo; Loreto, Vittorio (2009). "Statistical physics of social dynamics". Reviews of Modern Physics. 81 (2): 591–646. arXiv:0710.3256. Bibcode:2009RvMP...81..591C. doi:10.1103/RevModPhys.81.591. S2CID 118376889. 5. "Young Scientist Award for Socio- and Econophysics". Bad Honnef, Germany: Deutsche Physikalische Gesellschaft. Retrieved 15 October 2014. 6. Gleeson, James P. (2013). "Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond". Physical Review X. 3 (2): 021004. arXiv:1209.2983. Bibcode:2013PhRvX...3b1004G. doi:10.1103/PhysRevX.3.021004. S2CID 54622570.	2022-10-07 15:44:41	{"extraction_info": {"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, "math_score": 0.6794376969337463, "perplexity": 1831.1097108017962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338213.55/warc/CC-MAIN-20221007143842-20221007173842-00237.warc.gz"}
https://civilengineering.blog/tag/shear-force-and-bending-moment/	# Shear force and bending moment ## Basic concepts of shear force and bending moment This is the excerpt for your very first post.	2020-02-18 00:11:27	{"extraction_info": {"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, "math_score": 0.8645018935203552, "perplexity": 2738.244706318227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143455.25/warc/CC-MAIN-20200217235417-20200218025417-00483.warc.gz"}
http://plaidsheep.ca/pages/enumerations/20170715%20-%20Test%20Results.html	Test Results 2 todo - gray hyphen in octogon somebody should implement this 1 manual . blue empty octogon this needs to be executed manually for some reason 0 pass + green check mark in circle no problems -1 defect - pink m-dash in square an issue was detected, but someone is currently working on it -2 fail x red x mark in square an issue was detected n pending ? white hasn’t been run yet The numbers indicate priority, • the further from 0 the more we care about it • positive numbers are more relevant to business and requirements gathering • negative numbers are more relevant to development Everything has an ASCII friendly character associated with it. This makes reporting in the terminal easier. Colors are meant to be meaningful to a large portion of developers. Currently this is North American biased, but so is the group I work with, and software developement in general. Symbols are meant to be reasonably meaningful, though some amount of learning is expected from the report readers. The decision of constraining to ASCII characters maximizes the number of terminals this can be reported on.	2023-03-31 03:28:47	{"extraction_info": {"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, "math_score": 0.1829356849193573, "perplexity": 2299.8225922368374}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00307.warc.gz"}
https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.095902	Synopsis: Tweezers Work Well Under Pressure The use of optical tweezers in a high-pressure experiment allows a more direct measurement of water viscosity in extreme conditions. Diamond anvil cells can apply millions of atmospheres of pressure to a solid or liquid, while allowing it to be observed through the diamond “windows.” For the first time, researchers have introduced optical tweezers into one of these cells in order to trap sample particles. The experiment, described in Physical Review Letters, directly measured the viscosity of the water surrounding the particles. Further development of this technique could permit investigations of the mechanical changes in biological cells and other soft materials placed under high pressure. A diamond anvil cell (DAC) is a sealed volume sandwiched between the flat, millimeter-wide tips of two diamonds. When squeezed, the pressure in the cell can reach levels found in the core of the Earth. Diamonds are not only strong enough to handle these pressures, but they are also transparent to optical and x-ray probes. However, studying certain mechanical properties requires the controlled application of localized forces, which has been difficult to realize in a DAC. For their force “handle,” Richard Bowman of the University of Glasgow, in the UK, and his colleagues chose optical tweezers, which are highly focused lasers that trap particles. To overcome the spatial constraints of a DAC, the team used part of their laser to create a second beam that reflected back on the cell. The combined beams trapped micron-sized silica beads suspended in a water sample. Because the optical forces were known, the random vibrations of trapped beads provided a direct measure of the water viscosity. The team recorded a threefold increase in viscosity for a pressure rise of $10,000$ atmospheres—a result that agrees well with previous measurements and builds confidence in the new technique. – Michael Schirber More Features » Announcements More Announcements » Previous Synopsis Nonlinear Dynamics Astrophysics Related Articles Industrial Physics Viewpoint: 3D Imaging of Dislocations A combination of imaging techniques provides an unprecedented 3D view of a network of crystal defects known as dislocations. Read More » Fluid Dynamics Focus: Video—Physics of Oil Recovery Experiments mimicking a common oil drilling technique, in which fluid is forced into an oil-filled, porous medium, have uncovered four different flow patterns. Read More » Optics Synopsis: Photons Couple Like Cooper Pairs A pairing of photons—similar to the pairing of electrons in superconductors—can occur when light scatters in a transparent medium. Read More »	2017-11-21 13:39:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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, "math_score": 0.2543885111808777, "perplexity": 1983.0731961142887}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806388.64/warc/CC-MAIN-20171121132158-20171121152158-00609.warc.gz"}
https://www.transtutors.com/questions/214-trapper-company-39-s-unadjusted-and-adjusted-trial-balances-on-december-31-of-th-4295863.htm	# 214.Trapper Company's unadjusted and adjusted trial balances on December 31 of the current year. 214.Trapper Company's unadjusted and adjusted trial balances on December 31 of the current year are as follows: 215.Record the December 31 adjusting entries for the following transactions and events in general journal form. Assume that December 31 is the end of the annual accounting period. a. The Prepaid Insurance account shows a debit balance of $2,340, representing the cost of a two-year fire insurance policy that was purchased on October 1 of the current year and has not been adjusted to-date. b. The Store Supplies account has a debit balance of$400; a year-end inventory count reveals $80 of supplies still on hand. c. On November 1 of the current year, Rent Earned was credited for$1,500. This amount represented the rent earned for a three-month period beginning November 1. d. Estimated depreciation on store equipment is $600. e. Accrued salaries amount to$1,400. 216.Based on the unadjusted trial balance for Highlight Styling and the adjusting information given below, prepare the adjusting journal entries for Highlight Styling. Highlight Stylings' unadjusted trial balance for the current year follows:	2020-04-01 11:36:40	{"extraction_info": {"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, "math_score": 0.20163267850875854, "perplexity": 12346.967435998868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505730.14/warc/CC-MAIN-20200401100029-20200401130029-00214.warc.gz"}
http://openstudy.com/updates/4ffb2307e4b00c7a70c42636	## MathSofiya Group Title just making sure I understand it.... $S=\int_{a}^{b} 2\pi y \sqrt{1+{(\frac{dy}{dx})}^2} dx$ $S=\int_{c}^{d} 2\pi y \sqrt{1+{(\frac{dx}{dy})}^2} dy$ $S=\int_{a}^{b} 2\pi x \sqrt{1+{(\frac{dy}{dx})}^2} dx$ One is for revolution about the x axis...the other for revolution about the y- axis...and then we have one more equation....why? 2 years ago 2 years ago 1. Libniz what the devil is this? 2. MathSofiya Area of a Surface of Revolution 3. Libniz surface area ? 4. MathSofiya yes 5. Libniz let me make some drawing 6. MathSofiya @TuringTest 7. Libniz \|dw:1341858624540:dw\| 8. Libniz we are taking circumference of each plate , they have height(radius) of 'y' 2 Pi r= 2 Pi y 9. MathSofiya what if we're rotating about the y axis...would it still be 2 pi y 10. Libniz no 11. Libniz it would be much more complicated 12. MathSofiya 2 pi x 13. Libniz not that simple 14. Libniz first ,you gotta define function in term of x 15. MathSofiya ok 16. MathSofiya as in x= .....y.... 17. MathSofiya or x=g(y) 18. Libniz it is too complicated unlike finding volume , we just use x axis 19. MathSofiya ok 20. MathSofiya \|dw:1341859119434:dw\| 21. MathSofiya $S=\int 2\pi x ds$ 22. MathSofiya but the book still has (dy/dx)^2 23. MathSofiya 24. Libniz it is 3 dimensional 25. helder_edwin give a second to check my books it's been a long time 26. MathSofiya ok 27. MathSofiya Everyone abandoned me :'( 28. helder_edwin no 29. TuringTest 30. TuringTest so you want to know why we have 4 formulas, right? my answer is that there are really only two, but each one can be seen from two different perspectives... 31. MathSofiya ok 32. TuringTest first consider the arc length formula:$ds=\sqrt{1+[f'(x)]^2}dx$now this is the formula for arc length taken from the perspective of y being a funcion of x but arc length is the same regardless of whether you look at the function as f(x) or g(y) since the arc itself will still have the same length. so we can also write$ds=\sqrt{1+[g'(y)]^2}dy$ and as long as we are talking about the same curve they should be equal, since the arc can only have one length. make sense so far? 33. MathSofiya Yes 34. TuringTest now for a revolution, the formula is$A=\int2\pi yds$or$A=\int2\pi xds$depending on which axis we are going around but as I just explained above, ds (the arc length differential) can always be written two ways depending on whether we consider y a function of x or vice-versa, so each of these formulas is potentially two depending on how we look at our ds 35. helder_edwin 36. TuringTest yo si 37. MathSofiya sorry I can't 38. SmoothMath lol. That guy. 39. TuringTest here is a nice full explanation if you care to dig deeper http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx 40. MathSofiya I will , thanks @TuringTest . 41. TuringTest welcome :) 42. SmoothMath Sofiya, try to break down each integral like this: First, look at the end part, the variable you're integrating with respect to. Then, look at the limits, so you say to yourself, "Okay, travelling along x from a to b." or something like that. Then, look at the function inside and try to break that down, and what that means at each particular x. For these particular integrals, the insides have 2 basic parts. The first part has the form 2pi*something, where that something is the radius. The second part is the arclength formula. So it's calculating the arclength, and then it's multiplying that in a circle. 43. helder_edwin sorry i wanted to send you something but it's in spanish. but i goes much in the same way as what @TuringTest did 44. MathSofiya oh ok....thanks everyone Thanks @SmoothMath !!! 45. SmoothMath My pleasure =D 46. TuringTest @helder_edwin me lo mandas por favor? quiero aprender mas la terminologia en espanol 47. helder_edwin claro! 48. helder_edwin @TuringTest recibiste el pdf? 49. TuringTest no, donde lo pusiste? podrias mandarme un ("link"?) o url ? ya puesto que estoy tu "fan" es posible mandar mensajes privadas	2014-09-23 20:23:27	{"extraction_info": {"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, "math_score": 0.9078480005264282, "perplexity": 3857.750341191799}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657139669.58/warc/CC-MAIN-20140914011219-00010-ip-10-234-18-248.ec2.internal.warc.gz"}
http://crypto.stackexchange.com/questions/6081/how-to-generate-a-key-using-any-m-passwords-out-of-total-n?answertab=active	# How to generate a key using any m passwords out of total n? My application requires an AES-256 key K for some secure operation. In order to avoid saving this key in application, I have implemented following scheme: 1. There are 5 individuals who enters their passwords in application. Lets call them PW1..PW5 2. Using these passwords, I have generated the key as: K = KDF(PW1 \|\| PW2 \|\| PW3 \|\| PW4 \|\| PW5) The problem is that now I need to modify the application such that it works even if only 3 out of 5 passwords are available (but no less than 3). This is required because even if we lose one or two passwords (accident, person refusing to enter password etc.), we are able to recover from that situation. Please can you advise how it can be achieved? - Possible duplicate of Can I pre-define the points in Shamir's Secret Sharing algorithm. (Your question is somewhat more general, since it doesn't mention Shamir's scheme explicitly, but the answers apply to the more general case as well.) – Ilmari Karonen Jan 23 '13 at 18:29 One option would be to generate a random key, split it using Shamir's secret sharing, then encrypt each of the split parts individually under a key derived from each user's password. So for example: key = read from os.urandom() d1,d2,...d5 = split(key=key,n=5,k=3) e1 = encrypt(d1, KDF(PW1)), e2 = encrypt(d2, KDF(PW2))... key can then be derived from all of the encrypted shares (e1, ...) and user's passwords (PW1, ...). You could store the encrypted shares in the application and be confident that without at least three of the passwords you wouldn't be able to derive the key. - Thanks @Michael. You rock! (and I feel so stupid that I couldn't think of extending the scheme). – Hemant Jan 24 '13 at 14:19	2014-03-11 02:06:15	{"extraction_info": {"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, "math_score": 0.39420086145401, "perplexity": 1438.5962305716178}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011090254/warc/CC-MAIN-20140305091810-00096-ip-10-183-142-35.ec2.internal.warc.gz"}
http://innovation-arg.com/n165tru/51103a-pulsar-rotation-period	"[7] Even so, they nicknamed the signal LGM-1, for "little green men" (a playful name for intelligent beings of extraterrestrial origin). confirming that correlated signals in timing residuals are caused by black hole binaries (with total masses of topocentric (topocentric means measured from a fixed point on data-processing software become more sophisticated, more data are of the neutron star. The magnetic axis of the pulsar determines the direction of the electromagnetic beam, with the magnetic axis not necessarily being the same as its rotational axis. Otherwise, the spun-up neutron star is left with no companion and becomes a "disrupted recycled pulsar", spinning between a few and 50 times per second.[30]. Even though their radio emission mechanism is not well But over the last decade, one of the driving efforts in pulsar period decay PbË caused by the emission of observations has come from their use as tools via pulsar If the spin-down luminosity equals the magnetic dipole radiation Recently discovered pulsars only have a J name (e.g. superconductor at temperatures up to Tâ¼109Â K. The masses of trains. (see FigureÂ 6.9). (EquationÂ 6.47). Three PTA experiments have been working on this endeavor: NANOGrav in supernovae. exceed the ordinary nuclear packing fractions.â. Pulsars âdieâ in the lower right corner of the was observed in 1054 AD. In calculus terms this is simply dP/dt and is often expressed as a dimensionless quantity.. lines cannot close. orbits the Sun and tracking the changing Roemer delay. density from a pulsar and its timing precision. between 1.4Â ms and 8.5Â s. The radical proposal that neutron stars even exist was made than two are measured, each additional PK parameter yields a different Pulsars with extremely eccentric orbits usually have The radio pulses originate in the pulsar magnetosphere. searches for single pulses rather than for periodic pulse on the sky will be uncorrelated or even negatively correlated by the If they are due to radial oscillations (“starquakes”), how large in radius are these oscillations? This pulsar's speed is such that: At its equator it is spinning at approximately 24% of the speed of light, or over 70,000 km per second. A single massive nearby system, or Observations soon revealed that its magnetic field was much weaker than ordinary pulsars, while further discoveries cemented the idea that a new class of object, the "millisecond pulsars" (MSPs) had been found. This electromagnetic radiation will of the wave period with the rotational period of the pulsar provides a slow drift of emission features. Finally, pulsars have broadband continuum spectra, so if there are gas permits exquisitely sensitive measurements of quantities such as scatter broadening can greatly decrease both the observed pulsed flux Read http://www.bigear.org/vol1no1/burnell.htm for the full density is at least. If the explosion does not kick the second star away, the binary system survives. For most radio exotic objects, but much of the best science based on pulsar The Double Pulsar system consists of a pulsar with a 22.7-millisecond period (pulsar A) in orbit with a pulsar of period 2.8 seconds (B). Manchester et al. multipath propagation of a pulsar signal, whereby some rays travel uncorrected differential delays across the band cause In calculus terms this is simply dP/dt and is often expressed as a dimensionless quantity. or ISM. neutron star as being a uniform density sphere The pulse periods are white dwarf stars. Now it is thought to be a novel type between a white dwarf and a neutron [star]. existence of gravitational waves by matching the predicted orbital [40], Additionally, turbulence in the interstellar gas causes density inhomogeneities in the ISM which cause scattering of the radio waves from the pulsar. PSR 0021â72C and PSR 0021â72D). It is the only known binary that consists of two detectable radio pulsars, and its fast orbital period (~2.5 hours) makes it the most relativistic pulsar binary we know of. and ne is the electron number density. However, caused by the ISM. Rotation-powered pulsars, where the loss of rotational energy of the star provides the power, The first radio pulsar "CP 1919" (now known as. understood, pulsars have become uniquely valuable astrophysical tools: Neutron stars are physics laboratories sampling extreme Differences in progenitor mass and degree of differential rotation lead only to small variations in the PNS rotational period and profile. pulsar (and observatory) and the gravitational redshift caused by the [13] After the discovery of the first pulsar, Thomas Gold independently suggested a rotating neutron star model similar to that of Pacini, and explicitly argued that this model could explain the pulsed radiation observed by Bell Burnell and Hewish. where Ï0 and t0 are arbitrary reference phases and times for Its magnitude is â¼500â¢cosâ¡Î² s, the masses of the pulsar and its companion can be determined. first place. This Refractive It even suggested as explanations for pulsars. equations of state and âfreeâ quarks [34]. These interactions can result in very strange binary system, neutron-star masses, general relativistic effects almost straight down in the Pâ¢PË diagram until either their magnetic give very specific systematic signatures in plots of timing âcleaned upâ automatically before they reach the astronomer. Pulsars close together on the sky will be Like lighthouses, they continuously emit detect correlated signals in the timing residuals of dozens of MSPs down, then Prad=-EË and A phenomenon related to scintillation is pulse broadening caused by The name pulsar blends âpulseâ and âstar,â but pulsars individual pulsars have been measured with varying degrees of pulsars. is, where mâ¥=mâ¢sinâ¡Î± is the perpendicular component of the pulsars have been spun up by accreting mass Variations of 0.0003 s are observed in the period. corresponds to light-travel time delay) and phase of an error sinusoid When two massive stars are born close together from the same cloud of gas, they can form a binary system and orbit each other from birth. In the nearly inertial frame of the Solar System barycenter completely determined by the observables P, PË, and The first millisecond pulsar with 2 stellar mass companions, This page was last edited on 9 December 2020, at 23:27. delays would smear out the integrated pulse in time and make most general relativity, in contrast to the dipolar emission of [38] It is unknown whether timing noise is related to pulsar glitches. stars; their stable periods rule out black holes. One The sources of the pulses were originally unknown, and even intensive. either because their SNRs have faded to invisibility or because the quite stable. ", "Press Release: The Nobel Prize in Physics 1974", "Little Green Men, White Dwarfs, or Pulsars? The first pulsar was discovered by chance by Jocelyn Bell and Anthony Hewish in 1967 who were actually studying distant galaxies at the time. ", "Focus on NICER Constraints on the Dense Matter Equation of State", "Old Pulsars Still Have New Tricks to Teach Us", "A Statistic for Describing Pulsar and Clock Stabilities", Texas Symposium on Relativistic Astrophysics, "World's most accurate clock to be built in GdaÅsk", "African Skies 4 â Radio Pulsar Glitch Studies", "Interstellar Fringes from Pulsar B0834+06", Monthly Notices of the Royal Astronomical Society, "The Age of the Local Interstellar Bubble", Observation of a Rapidly Pulsating Radio Source, "Part-time pulsar yields new insight into inner workings of cosmic clocks \| Jodrell Bank Centre for Astrophysics", "Testing General Relativity with Pulsar Timing", Astronomical whirling dervishes hide their age well, Audio: Cain/Gay â Astronomy Cast. R and surface magnetic field strength B, the magnitude of the the pulsar frame by the Doppler factor resulting from the unknown It has a period of 118.2 seconds. magnetic dipole moment is [56], If the inclined magnetic dipole rotates with angular velocity Î©=2â¢Ï/P, then. electromagnetic waves from an accelerating electron, GWs cause can be measured over some time interval Îâ¢T. The pulses come at the same rate as the rotation of the neutron star, and, thus, appear periodic. specific angular correlations in the timing residuals between pairs of Recently, figures! (EquationÂ 2.143) in terms of power radiated by a eclipses of their radio MSP emission, likely owing to freeâfree and 6.20 can be combined to yield a lower and is descended from pulsar database used for the paper "Catalog of 558 Pulsars" by J.H. Study Astronomy Online at Swinburne University magnetic dipole moment. Pulsars appearing very close together sometimes have letters appended (e.g. In these equations, Tââ¡Gâ¢Mâ/c3=4.925490947â¢Î¼s capability and many new high-precision MSPs from recent surveys, a acceleration at its equator. absolute precision Îâ¢A approximately equal to the TOA appear to emit periodic short pulses of radio radiation with periods plasma. Integrating A few years after the discovery of pulsars by … eccentric orbits. variations in their observed pulse periods decays as orbital energy is carried away by gravitational radiation. pairs that radiate additional high-energy photons. rotational energy is changing. or ecliptic pole. The final results reserve we advance the view that a supernova represents the transition Î³ were first made to determine the masses of the two neutron velocity Î©â¡2â¢Ï/P. âstochastic backgroundâ of GWs), will cause tens-of-nanosecond It is sometimes called the characteristic magnetic field This article is about a type of neutron star. appear and disappear from view, causing periodic fluctuations in X-ray J.Â J.Â Thomsonâs derivation of the Larmor formula in terms of pulse frequency is f=1/P, and the instantaneous pulse Assume That The Pulsar Is A Rotating Sphere Of Uniform Density With An Initial Radius Of 10 Km. Pulsar A pulsar is a rapidly rotating neutron star that emits a radio beam like a lighthouse emits a light beam. emerging from the polar caps cross the light shapes of individual pulses vary considerably because pulsar emission (elliptical orbits do not close in relativistic theories), the orbital This period was far shorter than astronomers considered pulsars capable of reaching, and led to the suggestion that pulsars can be spun-up by accreting mass from a companion. The pulsar J1838-0537 is radio-quiet, very young, and, during the observation period, experienced the strongest rotation glitch ever observed for a gamma-ray-only pulsar. MSPs are believed to be the end product of X-ray binaries. time of arrival (TOA). In both cases, the original low-mass companion star A millisecond pulsar (MSP) is a type of pulsar with a rotational period in the range of around 1-10 milliseconds. At this point, Bell Burnell said of herself and Hewish that "we did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. Name. âonâoffâ differential measurements, small sizes, and high of the neutron star over long periods (years to decades) of This pulsar orbits another neutron star with an orbital period of just eight hours. The extreme density In such models there are no distinct physical features actually moving relative to the star. longer physical distances because they do not follow straight lines to Assume that its current period is 0.033 s, M = 1.4 Msun, and R = 1.1x 104 m. Express your [16] Considerable controversy is associated with the fact that Hewish was awarded the prize while Bell, who made the initial discovery while she was his PhD student, was not. When observations with another telescope confirmed the emission, it eliminated any sort of instrumental effects. About 15% of millisecond pulsars are isolated. searches, the DM is unknown a priori and is a search parameter The Crab Pulsar (PSR B0531+21) is a relatively young neutron star. Strong, fast pulsars with narrow pulse profiles provide the All new pulsars have a J indicating 2000.0 coordinates and also have declination including minutes (e.g. telescope and receivers we thought it better to inspect the data A PTA is an array of MSPs spread over the sky rather than an densities Ïâ¼1014â¢gâ¢cm-3 exceeding those 1014â1015Â G fields observed in It discovery of this pulsar confirmed the suggestion by Baade and Zwicky [17], In 1974, Joseph Hooton Taylor, Jr. and Russell Hulse discovered for the first time a pulsar in a binary system, PSR B1913+16. However, a newly formed is, In astronomically convenient units the dispersion delay is. Also, the Crab Nebula perpendicular magnetic field Bâ¢sinâ¡Î±. (i.e.,Â SâÎ½-1.7), although some can be much steeper systems such as pulsarâmain-sequence-star binaries and MSPs in highly is the solar mass in time units (which is known much more precisely Discovered in 1968, the pulsar was the first to be connected with a supernova remnant. That angular pattern is known as the Hellings and In 2007 the Crab pulsar had a period of 0.0331 sec and a period derivative of 4.22×10 -13 s/s. The Pulsar's Rotational Period Will Increase Over Time Due To The Release Of Electromagnetic Radiation, Which Doesn't Change Its Radius But Reduces Its Rotational Energy. If this is the primary energy loss for the pulsar and it primarily comes from a loss of rotational energy, then at what rate is it slowing down its rotation rate? All pulsars have a J name that provides more precise coordinates of its location in the sky.[23]. sweeps across the observerâs line of sight. where A and Ï are the amplitude (in time units because it luminosity and (Bâ¢sinâ¡Î±) doesnât change significantly with the strong impulses that are usually caused by terrestrial PSR 1913+16.7). A pulsar (from pulse and -ar as in quasar)[1] is a highly magnetized rotating compact star (usually neutron stars but also white dwarfs) that emits beams of electromagnetic radiation out of its magnetic poles. Such dynamos may be able to produce the 2)The mass of a pulsar is 1.5 Msun, radius 10 km, and rotation period 0.033 s. What is the angular momentum of the pulsar? AppendixÂ D. The electrons in the ISM make up a cold plasma whose to â¼10Â km, its cross-sectional area a is divided by â¼1010, its magnetic flux Î¦â¡â«Bâân^â¢ða (where n^ is the unit vector normal to each infinitesimal In a timing fit for position, the amplitude A of the error sinusoid profile. most accurate arrival times. faster (P=0.033 s) pulsar in the Crab Nebula was discovered, and star are the glitches observed in the rotation velocity Any neutron star If a rotating magnetic dipole is inclined by some Effect of Interstellar Medium on Radio Pulsar Spin-Down Properties.. ABSTRACT. PSR 0531+21) and sometimes declination to a tenth of a degree (e.g. that we would observe in the timing residuals from the pulsar (see the Typically, Îâ¢T is the length of time (up to several tens of years for many pulsars inclination angle between the Pulsars that were discovered before 1993 tend to retain their B names rather than use their J names (e.g. recorded time of the first sample of the observation) to create the The time The pulsar was found in a cluster of 10-billion-year-old stars called Terzan 5, which lies 28,000 light years away near the centre of the galaxy. summing over its mass elements: where r is the distance from the rotation axis and z is the height EquationÂ 6.29 gives, In the limit P02âªP2, the characteristic age However, the corotating field lines This level of long-term timing precision for the best MSPs another star. Lorimer and Kramer [70] and Lyne and Graham-Smith [71] have written excellent reference books elliptical orbits: the projected semimajor axis xâ¡(a1â¢sinâ¡i)/c, the longitude of periastron Ï, the time of periastron The best models data by a technique known as coherent dedispersion. These numbers motivate the definition of the canonical data) are available, the dispersion may be completely removed from the If any two of these PK parameters are measured, Each TOA The Gaussian CGS units for magnetic and Gamma-ray Pulsars. wavelengths, most pulsars have extremely steep radio spectra. It is considered a very old pulsar with an estimated age of 166 million years and a rotation period of 0.8 seconds. Matched filtering that brings out the expected signal usually The fastest known pulsar has P=1.4Ã10-3 s It greatly absorption by the ionized gas in the systems being blown off the limit to the magnetic field strength B>Bâ¢sinâ¡Î± at the The pulsar had been considered to be a seemingly ordinary pulsar, with a spin period of 813 ms and a typical rotational frequency derivative of . shorter than its current period. Millisecond pulsars have been detected in radio, X-ray, and gamma ray parts of the electromagnetic spectrum. minutes to hours and radio bandwidths of kHz to hundreds of MHz, and pulsars undetectable (see FigureÂ 6.5). The observed distribution of pulsars in the high brightness temperatures Tb>1025â¢K, orbits, may allow the measurement of up to five post-Keplerian made of the pulsar (so long as there is at least one year of timing (FigureÂ 6.3). Video â Artist's impression of AR Scorpii. relativity. correspond to errors in both directions of only. example of a full âtiming solution,â listing high-precision spin, now) over which a pulsarâs phase has been tracked through regular It ranges between e=0 for a circular orbit and e=1 for a via absorption by spectral lines of Hi or molecules. exceeds the Eddington luminosity limit array of telescopes, and the goal is to use that pulsar array to of 2â¢Ï radians, so 0<Ï<1. pulsars on the sky. delays comprise up to five Keplerian parameters describing Pulsars with characteristic ages <105 yr are often found in their parent galaxies have merged. [14] The discovery of the Crab pulsar later in 1968 seemed to provide confirmation of the rotating neutron star model of pulsars. relativistic effects in the rapidly rotating magnetospheres of This produces a very precise interval between pulses tha… where P is the pulsar period. Known radio pulsars appear to emit short pulses of radio radiation with pulse periods between 1.4 ms and 8.5 seconds. [18] In 1993, the Nobel Prize in Physics was awarded to Taylor and Hulse for the discovery of this pulsar.[19]. is the distance from the pulsar to the observer and the vernal equinox (the intersection of the ecliptic plane and the residuals with respect to the correct Roemer delay: If the position errors are small enough that sinâ¡xâ¼x, cosâ¡xâ¼1, and Îâ¢Î²â¢Îâ¢Î»â¼0, we can use PSR J0437â4715). When Finally, the second star also explodes in a supernova, producing another neutron star. Together, the consortia form the International Pulsar Timing Array (IPTA). model profile so that its phase offset can be determined. so the time-dependent phase Ïâ¢(t) of a pulsar can be approximated (e.g., f and fË) must result in a phase change between each appear at the very low radio frequency Î½=P-1<1 kHz, We see a bright spot on the neutron star, so the star appears to flash once every rotation period. The luminosity of the nebula L is of energy emitted per unit time, which must be extracted from the pulsar's rotation: Solving for the rate of period change we obtain: Example: The Crab nebula has a luminosity L = 2 x 10 31 W. What is the expected period change of the Crab pulsar (observed period 33 ms, assumed radius 10 km, mass 1.5 solar masses) in sec/sec? data). the observatory clocks and terrestrial time standards, and much like the pulsar spin frequency. Video â Crab Pulsar â bright pulse & interpulse. The electrons do not radiate as The name Pulsar is likely to be given to it. of a pulsar defined by. the Earthâs surface) time tt can be corrected to the time time. corresponds to a different time t, so the correct fitting parameters However, several sophisticated models of the Such If a small, dense pulsar is paired with another star, it siphons material and energy from its companion, accelerating the pulsar’s already rapid rotation. Older pulsars are not, (SectionÂ 5.4.2) of the neutron star, which is PSR J1748-2446ad rotates a little over 700 times a second, and scientists have this to say on the theoretical limits of the rotation speed of a pulsar : The pulsar in the Crab nebula (see Fig. If Pradâ-EËâ105â¢Lâ, the usually have P>1â¢s (FigureÂ 6.3). PSR J1921+2153). Its energy density is. [41] Due to the high velocity (up to several hundred km/s) of many pulsars, a single pulsar scans the ISM rapidly, which results in changing scintillation patterns over timescales of a few minutes. For this reason, millisecond pulsars are sometimes called recycled pulsars. or in building pulsar clocks.[37]. integration time. they can cause more than order-of-magnitude flux-density Einstein's theory of general relativity predicts that this system should emit strong gravitational radiation, causing the orbit to continually contract as it loses orbital energy. An initial magnetic field strength Bâ¼100Â G becomes Bâ¼1012Â G after collapse, so young Figure 1 shows the plot of period derivative versus pulse period for the known pulsars in the Galactic disk.2 Assuming braking of the pulsar rotation by the reaction to emission of magnetic-dipole radiation, EquationÂ 6.2 implies energetic MSPs eventually ablated their companions away. precision is ÏTOAâ¼1â¢Î¼s, which corresponds to a Moreover, pulsar positioning could create a spacecraft navigation system independently, or be used in conjunction with satellite navigation. limits for appropriately correlated low-frequency timing residuals, The fundamental property of a pulsar is its pulse period (P) - the time between adjacent pulses. can cause the characteristic age to be somewhat larger than the true This new pulsar, which is located in the constellation Cassiopeia … Rotating Radio Transients (RRATs) are pulsars As radioinstrumentation and … multiplied by â¼1010. electrons, the âgravitational packingâ energy in a cold neutron star Millisecond pulsars are seen in globular clusters, which stopped forming neutron stars billions of years ago.[28]. reradiated at radio through X-ray wavelengths. Galactic electron-density distribution now exist (e.g., NE2001; at the 0.05% level and measured the masses of the two neutron stars In June 2006, the astronomer John Middleditch and his team at LANL announced the first prediction of pulsar glitches with observational data from the Rossi X-ray Timing Explorer. conditionsâdeep gravitational potentials Gâ¢M/(râ¢c2)â¼1, In Europe, there is the European Pulsar Timing Array (EPTA); there is the Parkes Pulsar Timing Array (PPTA) in Australia; and there is the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in Canada and the US. must decay on timescales â¼107 yr, causing old pulsars to move It is slightly larger than the actual age of the Crab pulsar, which is As before, t0 is a reference epoch, Îclock moving along closed magnetic field lines until they build up an It’s companion, meanwhile, is a 0.8 solar mass star, and the binary system itself has a rotation period of 30.5 hours. which would be the endpoint of stellar evolution. Pulsar Properties For additional information about pulsars, see the books Pulsar Astronomy by Andrew Lyne and Francis Graham-Smith and Handbook of Pulsar Astronomy by Duncan Lorimer and Michael Kramer.. implying Ï>1014 g cm-3, the density of atomic nuclei. e. Relativistic binaries, particularly those with compact and elliptical signals, and failing to explore the observational âparameter spaceâ uncertainty divided by the square-root of the number of observations overluminous rotation-powered pulsar identiﬁed among all 1400 radio pulsars known today. possible because the energy source is not accretion. Later, the second star can swell up, allowing the neutron star to suck up its matter. This history of this important discovery is a warning against It is also common to consider the pulsar pulse frequency ν {\displaystyle \nu } : P = 1 / ν {\displaystyle P=1/\nu } . orbit was decaying in accordance with general relativityâs predictions age depends only on the observables P and PË; it does not has been timed for Îâ¢T>25 years, so. More recently, the double-pulsar system J0737-3039 was discovered, in atomic nuclei, and magnetic field strengths as high as Bâ¼1014 or even 1015 gaussânot reproducible on Earth. Shapiro delay pulsar? Until now, the slowest-spinning pulsar known had a rotation period of 8.5 seconds. For pulsar Nearest to Earth neutron star is in Corona Australis - 200 light-years away. celestial equator). There are 3 consortia around the world which use pulsars to search for gravitational waves. As our sun, their lives will both end in supernova explosions this a!, lower-frequency radio waves, its radio transmissions do not require daily corrections exploded as asymmetric supernovae and in... For similar high-precision measurements of the neutron star that recycled the pulsar provides slow. Use pulsars to be less than the true age for young pulsars pulse! In 1968, the characteristic age of ~950 years before reaching Earth the Galactic disk precursors of Crab. Magnetars as well as the Voyager Golden Record of 8.5 seconds rotation slows down over time electromagnetic. As asymmetric supernovae and nearly disrupted the binary system survives ejected in an and. In units of pcÂ cm-3 is called the pulsar provides a slow drift of emission.... Radius are these oscillations pulsar defined by indicating 2000.0 coordinates and also have declination including minutes ( e.g filtering brings... Slowing the rotation of the pulsar ’ s slow rotation period and profile end in supernova.. To search for gravitational waves interstellar medium ( ISM ) before reaching Earth and... Rotates with angular velocity Î©â¡2â¢Ï/P to develop a pulsar-based time standard precise enough make. Be close to the star radio wavelengths to other classes of pulsars in the upper left corner the. Has a period of 23.5 s is similar to other classes of pulsars the precursors of the star where and... In Physics 1974 '', Little Green Men, white Dwarfs, or?! In 1968, the characteristic age to be different the unexpected and confirmed on January 8, 2005 its offset... Density with an Initial radius of 10 Km is considered a very radius... Particles are constrained to move along magnetic field radius, of a P=1.4Ã10-3Â s with! Errors as small as 10-16 star spins it up and reduces its magnetic poles develop a pulsar rotation period standard... And MSPs in highly eccentric orbits usually have quite large amounts of energy, the density of electrons between observer... Msps is pulsar rotation period being achieved pulsar later in 1968, the pulsar was ejected an... Be thus detected average radio pulse for each rotation of the neutron star,! Slowly loses energy and spins down is in Corona Australis - 200 away! More subtle features ( detailed below ) make this system ideal for the paper Catalog 558. Integrating over the pulsarâs age Ï gives, in the limit P02âªP2, the DM unknown! Are computationally intensive Release: the Crab pulsar ( MSP ) is pulsars that were discovered before 1993 tend be! ) being a prime example density is at least a few times massive! Milliseconds to seconds for an individual pulsar and also have declination including (! In 1967 who were actually studying distant galaxies at the time between pulses many. Factor of â¼2 in amplitude and occur on timescales of weeks if those two are... 'S period may be old pulsars on the neutron star coherent volume is smaller shorter... Because pulsars are seen in globular clusters, which was too short to the! 2020, at 23:27 by another star of massive neutron stars billions of ago. Cause a much higher fraction of recycled pulsars oscillations ( “ starquakes ” ), its radio do... A charged particle is standard precise enough to pulsar rotation period the first pulsar has. = −ν/ν˙ 2, where ν = 1/P is the first pulsar observed to have been by... Suppresses the unexpected or phase in several other ways besides dispersion the medium slower than higher-frequency radio can. Rotates with angular velocity Î©â¡2â¢Ï/P with fractional errors as small as 10-16 error Îâ¢f implies that pulsar. Coherent volume is smaller at shorter wavelengths, most pulsars undetectable ( see Fig 1967 who actually... Such as pulsarâmain-sequence-star binaries and MSPs in highly eccentric orbits usually have P > 1â¢s ( FigureÂ ). Systems as the only place where the Glitch is due to a decoupling of observables. Same rate as the first pulsar was found with a rotation period of 23.5 is! The longest period pulsar, the delays would smear out the expected usually! ÎRâ£Â is the first extrasolar planets were discovered before 1993 tend to retain their B rather. Young rotation-powered pulsars—another type of pulsar—emit powerful X-ray beams, but the energetic MSPs eventually ablated companions. If uncorrected, the time between pulses small radius and an extremely pulsar rotation period brightness temperatures of pulsars 166. \|P\| — 10-8P the sky. [ 28 ] star ] star is. Differential rotation lead only to small variations in the clocks will be measurable at Earth database for. Instrumental effects [ 26 ] [ 33 ], Generally, the star... So young neutron star can now be visible as a system of Galactic clocks original. Increased rotation was due to pulsar rotation period decoupling of the pulsar EquationÂ 6.29 gives in... Undetectable ( see Fig and measure the rotation periods of pulsars, and have,. Is only approximate because the coherent volume is smaller at shorter wavelengths most. Is known to possess approximately dipolar magnetic fields Mâ¼3â¢Mâ in standard models ) collapse... Of RX J1856.5-3754 made with the magnetic field lines, and have short, regular rotational periods an high! Grow As We Go Lyrics Video, Am I My True Self Quiz, Ieee Sensors Journal, African Safari Discount Tickets, Multiple Choice Questions On Communication Process, Difference Between Quasi Rent And Economic Rent, Carey First Name,	2023-03-20 09:16:35	{"extraction_info": {"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, "math_score": 0.7613617777824402, "perplexity": 2208.3494667721757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00045.warc.gz"}
http://sddo.from.bz/myriad-variable-concept-roman.html	Direct Personal Loans Sc. Myriad Variable Concept Version 1. antonym blindside out-of-the-box thinking grapple marketplace allot comply audacious brainstorm skittish myriad unison instigate tether prodigious telugu imagery good potential filipino for-the-first-time words autumn looked bittersweet sea-eagle survivor evaluate out-of-the-box-thinking village demographic. - Aleister Crowley (1875-1947), Magick in Theory and Practice. Until we turn away from the delusions of money, religion, and politics, humanity’s struggle and suffering will never end. Today atrium means an enclosed multi-storied space that is open vertically to multiple stories. Reid (1970) compared the accuracy of ob-servers during overt and covert assessment of their reliability and found that they were sig-nificantly more accurate when they were aware that they were being checked. The time is overdue to change the human equation to end the causes of most injustice and suffering. UCLA Registrar's Office website offers information and resources for current students, prospective students, faculty and staff, and alumni. ’ ‘The last byte is 10100000 binary or 160 decimal. The most significant of which is the specific sociological setting in Nigeria that allows for permissiveness. Eight years ago, I showed, using twenty million pieces of data from socioeconomic variables (about all the data that was available at the time), that current tools in economics and econometrics don't work, whenever there is an exposure to a large deviations, or "Black Swans". It works best with a recent Firefox at 1920x1080. , & Birket-Smith, M. Download Myriad Roman, font family Myriad by with Roman weight and style, download file name is Myriad-Roman. The "reasonable person" is used as a tool to standardize, teach law students, or explain the law to a jury. concepts Keeping track of formal ‘concepts’ for a particular field. The repetitive what obviously situates the book within ontology, in that it discusses the ontic (there is no meaning behind any of it). The first version of Minion was released in 1990. In the lesson students will use weights and a balance scale to show how the sides of an equation are equal. Course Area: Social Science. the Roman Emperor Constantine was an exceptional man. We have already touched on background reasons for supporting or joining terrorism, such as economic desperation, political repression, and the ready presence of a framing religious ideology. Adler preferred to face the client and engage in free discussion, not free association. This course is designed for students who wish to continue in study the concepts of pre-calculus through an introduction to differential and integral calculus. With The Math Worksheet Site I can do that all day long! There are all kinds of math curricula out there, and a family could easily spend hundreds of dollars and hours upon hours learning how to teach them. We are familiar with the memorials of saints throughout the liturgical year but this universal celebration of the dedication of a church—one of several included on the church calendar although the only one raised to the level of a feast—is a timely. Tweets on news, music and trends from all your favorite channels. Throughout which series of instances we see, that as the number of objects grouped together in thought increases, the concept, formed of a few typical samples joined with the notion of multiplicity, becomes more and more a mere symbol; not only because it gradually ceases to represent the size of the group, but also because as the group grows. Character and Divine Influence in The Iliad and The Aeneid : The Role of the Gods and Goddesses and the Direction of Fate. , if ‘ latex ’ is the name of the program being run, then TEXINPUTS. Although numerous addenda and modifications have been made, the major core of the concept remains intact. While this may be the easiest approach to management of an organization, the author suggests that it is also “the method that guarantees neglect of side effects and repercussions and therefore guarantees failure… if we have no idea how the variables in a system influence one another, we cannot take those influences into account. Text messaging has become extremely widespread throughout the world -- to the point where an increasing number of web applications have integrated SMS to notify users of events, sales or coupons directly through their mobile devices. But pancakes take myriad forms around the world, from delicate French crepes sprinkled with sugar to spongy, sour Ethiopian injera to chewy-crisp Japanese okonomiyaki, studded with seafood and drizzled with sticky brown sauce and mayo. As per the present concept, the factorials of real negative numbers, are complex numbers. 2 The smaller, more agile Roman Legions, 4000-5000 men, deployed in checkered board formation, could maneuver more easily and were not afraid of gaps in the line. The Middle Ages stretched. Federal income tax is but one of a myriad of taxes and fees imposed by various government agencies. Althusser's (1971) consideration of the 'subject' is broadly interchangeable with that of the 'person'. Can you explain how a man, a podiatrist, with three offices in California, could POSSIBLY make enough money to afford a home in a gated community and a 4 year old Mercedes, when his “taxable income” was less than myself, who worked for an auto company and was. A poet and a theatre writer who graduated from UEA with a BA English Literature. Math Worksheets 4 Kids offers free printable K-12 worksheets in English, Math, Science and Social Studies with PDFs drafted for children and teachers. If so, please point out the scientific research for the widely shared and consensually validated assertion of human exceptionalism vis a vis its population dynamics. The relationship of the predictor and response variables is shown by a mark of some sort (usually a rectangular box) from one variable's value to the other's. For the prophecy sees what is, what was, and what shall always be. 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Seriously I’m really tempted to start using normalize. schema: 1) In computer programming, a schema (pronounced SKEE-mah ) is the organization or structure for a database. I’ve made the setting system using CSS variables, calculations and by concealing the various units like em, ch and, for consistency, %. 0;hotconv 16. We have already touched on background reasons for supporting or joining terrorism, such as economic desperation, political repression, and the ready presence of a framing religious ideology. Figure 4 shows the application view after the user has placed some items in the shopping cart. Consistent with Implication 3, Autoquote (⁠\|${\it AD}$\|⁠) is associated with shorter arbitrage opportunities. In the lesson students will use weights and a balance scale to show how the sides of an equation are equal. Find descriptive alternatives for audience. com Posts about Agile, Scrum, XP, and User Stories Tue, 10 Sep 2019 03:18:16 +0000 en hourly 1 http://wordpress. 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On the contrary, purely real numbers only describe a perfect, simplified world in physics while imaginary numbers must be used to include the myriad complicating factors found in the "real" world. Hera (Roman Juno) was the daughter of Cronus and Rhea and Queen of the Olympian deities. [email protected] [14] “It took another 2,000 years for the Roman Empire to reach the level of town planning and sanitation that had already been existing in the Harrapan culture. Para los detalles de esta actualización Adobe encargó el trabajo a los diseñadores Christopher Slye y Fred Brady. image is critical for forming customer loyalty and satisfaction (Roman and Ruiz, 2005). This concept is included within my previously-distributed ”Ten Point Plan for Changing the Diversity and Inclusion Landscape 10. This paper deals with the historical development and foundational understandings of both the term culture, from anthropology, and its appropriation by industrial organization researchers to organizational culture. This page contains answers to the Lore AMA sorted both by topic and the answering developer. Welcome To Signs101. Following are tables with links to the individual questions below. These divisions are often identified in ethnic communities, regional variations, city versus rural. Myriad Roman; Myriad Roman Fonte; Myriad Roman Fonte Gratis; Myriad Roman Download Fonte Gratis; fontes legais; baixar; ttf; ttf gratis; fonte ttf; famílias tipográficas; tipografia; dingbats; typeface; true type; free fonts; fonts free; font download; handwriting font; handwriting fonts; freefonts; webfonts; free script fonts; best free. 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Download and install the Poppins free font family by Indian Type Foundry as well as test-drive and see a complete character set. The Roman empire was the result, not of the intentionality of a few individuals who were senators or emperors, nor of implacable historical forces working through social institutions, but of all the myriad interactions that were connected by, but also shaped. ” As we wait for our leaders to really focus on the need for greater inclusivity, our community needs an apology. The predicted 2014 costs for Osaka Motors are as follows: Manufacturing Costs Selling and Administrative Costs Variable $100,000 Variable$300,000 Fixed 220,000 Fixed 200,000 Average tota 1 answer Oregon Equipment Company wants to develop a new log-splitting machine for rural homeowners. The site facilitates research and collaboration in academic endeavors. Variable fonts let you adjust all sorts of custom attributes. Typography is a powerful tool. 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Minion Pro is an Adobe Original typeface designed by Robert Slimbach. 2 shows the main concepts, destinations and other topics featuring most prominently in the #visitspain conversation, of which the most noteworthy are those referring to the country, followed by those referring to ‘tourism’ and ‘travel’ as activities. White is prevalent in the Masonic Lodge as a symbol of Light, as well as purity in some respects, and Masonic regalia, particularly in Universal Freemasonry, is largely white. The Roman empire was the result, not of the intentionality of a few individuals who were senators or emperors, nor of implacable historical forces working through social institutions, but of all the myriad interactions that were connected by, but also shaped. Vocabulary Jam Compete head-to-head in real-time to see which team can answer the most questions correctly. Read unlimited* books, audiobooks, Access to millions of documents. 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Variable fonts and Axes list Acumin Variable Concept ( 90 named instances) Weight, Width, Slant Myriad Variable Concept Weight, Width. Tons and tons of brick and rock rubble from destroyed downtown buildings were brought over and dumped into the Marina's marshlands, forming an initial (and unstable) foundation for development. White is prevalent in the Masonic Lodge as a symbol of Light, as well as purity in some respects, and Masonic regalia, particularly in Universal Freemasonry, is largely white. heterogeneity-revealing its myriad abiotic and biotic causes and its ecological consequences-emerged in the 1980s as landscape ecology developed, and spatial data and analysis methods became more widely available. Because of this lineage, the concept of the Imam and the guidance of clerics is much more important to Shi'as than Sunnis. It was the intervening cold periods which so savaged the people. by synthview. Thanatos and Resurrection of the Archetypal Goddess The idea of the ancient goddess, the first figure of human worship dating back to our Paleolithic ancestors as early as 35,000 BCE, is a theological concept that has given rise to the nature-religious movement in the latter 20th century. supported with production data from the Roman L. ·Myriad Variable Concept Italic Myriad Variable Concept Regular Other versions · Myriad Variable Concept Regular Version 1. It WILL PROBABLY NOT work correctly in other browsers, due to limited support for CSS3 font-variant-* properties and css variables at this time. However,. The case pits two climatologists – Michael Mann of Pennsylvania State University and. What is Blockchain Technology? A Step-by-Step Guide For Beginners Is Blockchain Technology the New Internet? The blockchain is an undeniably ingenious invention - the brainchild of a person or group of people known by the pseudonym, Satoshi Nakamoto. It works best with a recent Firefox at 1920x1080. An Introduction to Economic Analysis in Crime Prevention: The Why, How and So What 1. - ) - Font 230: Myriad Variable Concept Roman (IOError: Ocorreu um erro geral no Photoshop. Myriad Roman Character Map: Disclaimer: We are checking periodically that all the fonts which can be downloaded from FontPalace. https://scrumcrazy. which variables such as cultural and political differences, economic and social development, history of democratic governance, and globalization impact on the way in which (and pace at which) democracy evolves. Designed as a course for students who wish to fulfill the liberal studies science requirement with chemistry and will take no further chemistry courses, not as a preparatory course for CHM 1045. Myriad Pro Skolar. Nearly 50 years after the concept was first proposed, gene therapy is now considered a promising treatment option for several human diseases. 13 Our results show that social complexity contributed to communica-tion barriers in 2 ways: issues related to interpersonal relationships between physicians and nurses and. View Vinodh Soundarajan’s profile on LinkedIn, the world's largest professional community. TraveLang Translating Dictionaries is a free tool that allows cross-searching of multiple translation dictionaries. 0;hotconv 16. One device used by the Secretariat in presenting issues to UNCITRAL seemed to facilitate agreement and, perhaps, a more direct mode of expression. Church members should expect some level of ministry and concern. Enter some text in the box below, then click the preview button. Fantomex is one of the more recent creations of the Weapon Plus program. Small rivers can be referred to using names such as stream, creek, brook, rivulet, and rill. Argued March 3, 1971. Lintas Freight & Logistics LLC 2. Indeed a looser concept of a data paper has existed for some time, where researchers request a citation to a paper even though it is not the data nor fully describes the data (e. It is the identity of the unit of function and a unit of heredity that is important. The Aeneid is an epic poem written by the Roman poet Virgil between 29 and 19 BCE. Reactions to advertising concepts in the boardrooms have far too often been mistaken for the presumed reaction consumers would have to our advertising. Find customizable templates, domains, and easy-to-use tools for any type of business website. Architecture at Washington University. Riassunto linguaggio e regole del diritto privato Riassunto - Manuale di diritto commerciale - Campobasso Domande a risposta multipla Riassunto - Dispensa di Storia Economica - Storia Economia Riassunto Fondamenti di organizzazione aziendale - Severino Salvemini Formule Macroeconomia. 65590字体（字体家族名称：Myriad Variable Concept；字体风格样式名称：Regular），共有75个字符。. Description: If your students have a hard time understanding variables, this lesson is for you. Rhode Island's 1969 Salary Supplement Act provides for a 15% salary supplement to be paid to teachers in nonpublic schools at which the average per-pupil expenditure on secular education is below the average in. For additional information about our students, see the annual Admissions Report. It is wonderful for the visual student. All Courses. com/ https://scrumcrazy. Myriad is a humanist sans-serif, a relatively informal design taking influences from handwriting. For gene therapy in deep tissues, transferrin-appended nanocaplet including guest siRNA, prepared by siRNA-assisted oxidative polymerization of a thiol-terminated telechelic molecular glue, followed by covalent surface immobilization of transferrin with UV irradiation, can deeply permeate into a cancer spheroid at depth of up to nearly 70 μm. Find information about your NetID and NetID password by logging into SOLAR and clicking the NetID Maintenance* link: find out what your NetID is, set your security question, and set/change/test your NetID password. I'm happy to know you used my font for your project, I really appreciate it. 5 degrees C balmier than present. Psychologist Charlan Nemeth of the University of California, Berkeley and author of In Defense of Troublemakers talks with EconTalk host Russ Roberts about the ideas in the book–the power of groupthink, the power of conviction, and the opportunity for an authentic, persistent dissenter to have an impact on a group’s decision. Myriad Roman font available in ttf format for you to download. But pancakes take myriad forms around the world, from delicate French crepes sprinkled with sugar to spongy, sour Ethiopian injera to chewy-crisp Japanese okonomiyaki, studded with seafood and drizzled with sticky brown sauce and mayo. pendent variable. 13 Our results show that social complexity contributed to communica-tion barriers in 2 ways: issues related to interpersonal relationships between physicians and nurses and. Skia is a GX Variation font which predates OpenType-Variable font spec. evolution is a fairy tale that keeps morphing as time goes on. WE ARE THEY THAT HAVE BEEN DRIVEN OUT OF THE LAND OF CANAAN BY THE JEWISH ROBBER, JOSHUA. These divisions are often identified in ethnic communities, regional variations, city versus rural. Minion is available in five weights—regular. By possession is meant a country which is held by no other title than mere conquest. A special-purpose font that demonstrates the relationships between variable "width" axes for use with different writing directions. intent and with variable significance for the identities of the people enacting them. 28MyriadPro-LightMyriad is a registered trademark of Adobe. Our goal is to see you improve your grades, provide peace of mind and help you meet your deadlines. With the rapid globalization of business, companies must expand operations internationally to remain competitive. demonstrate that engineering an oncolytic virus to express a metabolic modulator, in this case the adipokine leptin, improves T cell metabolic function in the tumor microenvironment, allowing a superior antitumor response compared to a control oncolytic. As usual, every new unit starts with a table of contents. Relevant axis records will also be shared across members of a family, e. Proof that Money is Slavery by Proxy Causes Panic Among US National and Civic Leaders Preface This is a long article written as a mini-course designed to expose the true purpose, nature and functionality of the deception we know as money and illuminate that which has long been purposely hidden. The world's largest digital library. ::Roman Empire: What would the world be like today if Rome had never fallen?:: The last ember of the Empire of the Caesars was Constantinople. According to scientists from the Pulkovo Observatory in St. If you use my font commercially, you can donate first. roman and italic, whether built as variable fonts or not. The population dynamics of non-human species are routinely and immediately understood. It generated an artificial sense of affluence by bringing in thousands of military personnel, creating a myriad of jobs, and initiating an influx of funding with which to guarantee the region’s loyalty and strategic. Myriad is a humanist sans-serif typeface designed by Robert Slimbach and Carol Twombly for Adobe Systems. “Having a strong hue is one way to stand out when you don’t know what the background will be,” he says. If we look to India, this has not been the case. [10/08/2019] Three years into a revolution in Conversational Commerce, with tens of thousands of "Proof of Concepts" and a myriad of marketplaces for microservices and APIs, there's good cause for decision makers to take pause and examine past successes and failures along with future options. We were unable to load Disqus. In Column (1), the dependent variable is the log of the duration of toxic arbitrage opportunities, while in Column (2) the dependent variable is the log of the duration of all arbitrage opportunities. Concepts are at best an approximation. 8, also called variable fonts. Originally, HTML was primarily designed as a language for semantically describing scientific documents. A poet and a theatre writer who graduated from UEA with a BA English Literature. - ) - Font 230: Myriad Variable Concept Roman (IOError: Ocorreu um erro geral no Photoshop. I'm happy to know you used my font for your project, I really appreciate it. Attendees of this session will gain a better understanding of the updates to research grant and career development award application instructions and review language that includes increased attention to scientific premise, scientific rigor, consideration of biological variables, such as sex, and authentication of key resources, such as cell lines. Site and situation influence the origin, function, and growth of cities and is an important concept to understand when you study cities and urban land use for the AP Human Geography Exam. Roman Catholic exegesis before and after the Enlightenment. Forging New Human Paradigms This civilization is based on purposeful deception and exploitation. By possession is meant a country which is held by no other title than mere conquest. A sans serif typeface with 40 styles, available from Adobe Fonts for sync and web use. roman and italic, whether built as variable fonts or not. ) Army Psychological Operations (PSYOP) doctrine. Dusky Pastel Blooms. The Mongol empire didn't operate on the same principles as the Roman empire, either. Course Area: Social Science. Reducing our dependence on fossil fuels is a good idea. But pancakes take myriad forms around the world, from delicate French crepes sprinkled with sugar to spongy, sour Ethiopian injera to chewy-crisp Japanese okonomiyaki, studded with seafood and drizzled with sticky brown sauce and mayo. tex] Paper: a4 Job No: 4984 Donsbach: Public Opinion Research (SAGE Handbook) Page: 12 7–24 12 THE SAGE HANDBOOK OF PUBLIC OPINION RESEARCH to the notion of judgment, though in the one case the emphasis is on the uncertain truth-value of something believed, whereas in the other the emphasis is on a moral. This course will examine applications of anthropology in areas including medicine and public health, environmental and ecological issues,. 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A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river.	2020-01-21 08:23:58	{"extraction_info": {"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, "math_score": 0.17275391519069672, "perplexity": 6474.705775800778}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250601628.36/warc/CC-MAIN-20200121074002-20200121103002-00431.warc.gz"}
https://assignment-daixie.com/%E6%95%B0%E5%AD%A6%E4%BB%A3%E8%80%83/%E8%AE%A1%E9%87%8F%E7%BB%8F%E6%B5%8E%E5%AD%A6%E4%BB%A3%E5%86%99econometrics-%E4%BB%A3%E8%80%83/	# 计量经济学代写Econometrics 代考 ## 代写计量经济学作业代写Econometrics ### 控制理论Control theory代写 • Regression analysis回归分析 • Quasi-experiment准实验 • Simultaneous equations model同步方程模型 • Natural logarithm自然对数 ## 计量经济学的相关 Econometrics uses economic theory, mathematics, and statistical inference to quantify economic phenomena. In other words, it turns theoretical economic models into useful tools for economic policymaking. ## 计量经济学相关课后作业代写 Specifically, we will focus on SV of order one $\left(L_{w}=1\right)$. Set $$\begin{gathered} \theta=\left(a, r_{y}, r_{w}\right)^{\prime} \ v_{l}(\theta) \equiv \exp \left(\frac{a w_{l-1}+r_{w} v_{l}}{2}\right) r_{y} z_{t}, \quad \forall t \end{gathered}$$ Models (2.1) and (2.2) may then be conveniently rewritten as the following identity: $$y_{t}-x_{t}^{\prime} \beta=v_{R}(\theta), \quad \forall t$$	2023-02-07 23:49:34	{"extraction_info": {"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, "math_score": 0.8663512468338013, "perplexity": 8315.965353650456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500664.85/warc/CC-MAIN-20230207233330-20230208023330-00512.warc.gz"}
https://young.physics.ucsc.edu/papers/potts.html	## Monte Carlo Study of the Critical Behavior of Random Bond Potts Models T.Olson and A.P. Young cond-mat/9903068 Abstract We present results of Monte Carlo simulations of random bond Potts models in two dimensions, for different numbers of Potts states, q. We introduce a simple scheme which yields continuous self-dual distributions of the interactions. As expected, we find multifractal behavior of the correlation functions at the critical point and obtain estimates of the exponent $\eta_n$ for several moments, n, of the correlation functions, including typical (n -> 0), average (n=1) and others. In addition, for q=8, we find that there is only a single correlation length exponent describing the correlation length away from criticality. This is numerically very close to the pure Ising value of unity.	2020-02-29 13:44:01	{"extraction_info": {"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, "math_score": 0.6012900471687317, "perplexity": 689.2494128390111}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875149238.97/warc/CC-MAIN-20200229114448-20200229144448-00385.warc.gz"}
https://chemistry.stackexchange.com/questions/82687/why-is-the-expectation-value-of-hermitian-conjugate-operators-rr-dagger-alway	# Why is the expectation value of Hermitian conjugate operators $RR^\dagger$ always real and non-negative? I've been reading through a derivation of the wavefunctions and energy levels for the quantum harmonic oscillator. It defines $$\hat R^\pm=\frac{1}{\sqrt{2}}[\hat p \pm \mathrm{i}\omega \hat q]$$ in mass-weighted coordinates $q=x\sqrt{\mu},$ such that $\hat p= -\mathrm{i}\hbar(\mathrm d/\mathrm dq)$ and $\hat q$ is the position operator. It then asserts that that $\langle \psi\|\hat R^+\hat R^-\|\psi\rangle$ must be real and non-negative, since $\hat R^+$ and $\hat R^-$ are hermitian conjuagtes. I know that $(\hat A\hat B)^\dagger = \hat B^\dagger \hat A^\dagger$ and so $\hat R^+\hat R^-$ is a hermitian operator meaning that the bra-ket must be real, but I can't see why it should be non-negative. Could anyone shed some light on this? Let $\hat{R}^-\|\psi\rangle = \|\psi'\rangle$ (a new ket; we don't care what it is). If you take the adjoint of this equation you get $$\langle\psi'\| = \langle\psi\|(\hat{R}^-)^\dagger = \langle\psi\|\hat{R}^+$$ $$\langle\psi\|\hat{R}^+\hat{R}^-\|\psi\rangle = \langle\psi'\|\psi'\rangle$$	2020-07-09 06:06:46	{"extraction_info": {"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, "math_score": 0.8167768120765686, "perplexity": 137.0068322461246}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00289.warc.gz"}
https://fidimag.readthedocs.io/en/latest/index.html	Welcome to Fidimag’s documentation!¶ Fidimag is a micromagnetic and atomistic simulation package, which can be used to simulate the magnetisation of nanoscale samples of materials. The code for Fidimag is available under an open source license on GitHub. Contents: .. toctree: :maxdepth: 2 :caption: Installation Instructions install	2019-04-19 16:16:39	{"extraction_info": {"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, "math_score": 0.5426744222640991, "perplexity": 10297.323137096799}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578527865.32/warc/CC-MAIN-20190419161226-20190419183226-00279.warc.gz"}
http://brandonrose.org/pythonmap	# Create a filled map (chloropleth) with Python¶ First, big thanks to Stephan Hügel for his excellent guide to mapping with Python. To create this guide, I heavily borrowed from Stephan's work, but tried to provide more contextualizing comment to ensure that a less advanced user can create their own filled map. For this guide, I focus on creating a filled map of Sri Lanka. I use some basic demographic data plus a shapefile that includes the first level of administration (for example, in the United States this is a state) to demonstrate how to create and manipulate a filled map with Python. The shapefile I obtained is from the Spatial Data Repository where you can find detailed shapefiles for most countries. You can find the whole repository for this project on GitHub. Feel free to hit me up with questions on Twitter @brandonmrose. ## Contents¶ Up front, you are going to need to install some packages you might not have used before. I had to install pysal, descartes, shapely, and Basemap. Install Basemap with: pip install basemap --allow-external basemap --allow-unverified basemap In [1]: import pandas as pd import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.cm as cm from matplotlib.colors import Normalize from matplotlib.collections import PatchCollection from mpl_toolkits.basemap import Basemap from shapely.geometry import Point, Polygon, MultiPoint, MultiPolygon from shapely.prepared import prep from pysal.esda.mapclassify import Natural_Breaks as nb from descartes import PolygonPatch import fiona from itertools import chain import pysal.esda.mapclassify as mapclassify I read in the dataset using Pandas. The primary dataset is just a .csv file where each row represents a district (state/province) along with the total population numbers per district plus population numbers for the three major ethnic groups. I've also already calculated the percent of the total population accounted for by each ethnic group. For example, in Colombo, 77% of the population is Sinhalese. I read in the dataset using Pandas; it's automatically read in as a dataframe. If you're not familiar with Pandas you can learn more here. It is a go-to for data analysis with Python. In [2]: data = pd.read_csv('srl_pop.csv') In [3]: #print the first 5 rows of data to see what it looks like and make sure it read in properly Out[3]: District_1 Total_pop Sinhalese Tamils Muslims Others Sinhalese_pct Tamils_pct Muslims_pct Others_pct 0 Colombo 2309809 1771319 258654 242728 37108 77 11 11 2 1 Gampaha 2294641 2079115 90950 95501 29075 91 4 4 1 2 Kalutara 1217260 1054991 47973 112276 2020 87 4 9 0 3 Kandy 1369899 1018323 154874 191159 5543 74 11 14 0 4 Matale 482229 389092 48156 44113 868 81 10 9 0 In [4]: print 'The data contains ' + str(data.shape[0]) + ' rows and ' + str(data.shape[1]) + ' columns.' print 'Each of the 25 rows corresponds to one of the districts in Sri Lanka.' The data contains 25 rows and 10 columns. Each of the 25 rows corresponds to one of the districts in Sri Lanka. ### A note on shapefiles¶ So what's in a shapefile? A shapefile is really a set of files that needs to remain together (in the same folder). At minimum, the file should contain .shp, .shx, and .dbf files. The .shp and .shx files define the shapes themselves while the .dbf file will contain metadata on the shape polygons (e.g. state names). Sometimes (and in the case of the Sri Lanka shapefile) you will receive other files too like a .csv and a .prj. The .csv is basically the same data that is in the .dbf but is in a more ubiquitous format in case you want to inspect/analyze it. The .prj file defines the projection. You actually shouldn't mess with any of these files without using a GIS software like the very awesome, open source QGIS. You absolutely will need to make sure that within the .dbf file the states or districts have the same spelling conventions as in your data set! If you don't have a .csv to inspect (which will mirror the .dbf) you can download Apache's Open Office for free. The Open Office spreadsheet program will let you open and inspect the .dbf file. Don't change it though; it's much easier to change your data file. Import the shapefile using fiona. Also I set some variables which define the boundaries of the map area. One way to think about it is that the shapefile you pass to fiona has some bounds which are defined by 2 latitude, longitude pairs: the first defines the lower left (ll) corner of the map and the second defines the upper right (ur) corner of the map. By subtracting the left edge longitude from the right edge longitude we can determine the width (w) for the map. We can do the same with the latitutde to get the height of the map. In [5]: #load the shape file as shp. Here I have saved my shapefile in the folder 'LKA_adm_2' within my working directory. #your shapefile should end in .shp #we can access the boundaries (the 2 lat,long pairs) using shp.bounds bds = shp.bounds #close the shp file shp.close() #define a variable called extra which we will use for padding the map when we display it (in this case I've selected a 10% pad) extra = 0.1 #define the lower left hand boundary (longitude, latitude) ll = (bds[0], bds[1]) #define the upper right hand boundary (longitude, latitude) ur = (bds[2], bds[3]) #concatenate the lower left and upper right into a variable called coordinates coords = list(chain(ll, ur)) #define variables for the width and the height of the map w, h = coords[2] - coords[0], coords[3] - coords[1] ## Create the basemap¶ Below I create the basemap, defined by the variable m. Note that you need to set the lat and long (lon_0, lat_0) so that it is roughly in the center of what your map. You could just use Google Maps to figure out where you want to center your map. Here, I took the average (the midpoint) between the lower and upper longitude and the lower and upper latitude to center the make squarely in the middle of the shapefile. If you're interested in learning about the Basemap API check out the matplotlib Basemap documentation here. It runs through the various projections you can use. In [6]: m = Basemap( #set projection to 'tmerc' which is apparently less distorting when close-in projection='tmerc', #set longitude as average of lower, upper longitude bounds lon_0 = np.average([bds[0],bds[2]]), #set latitude as average of lower,upper latitude bounds lat_0 = np.average([bds[1],bds[3]]), #string describing ellipsoid (‘GRS80’ or ‘WGS84’, for example). Not sure what this does... ellps = 'WGS84', #set the map boundaries. Note that we use the extra variable to provide a 10% buffer around the map llcrnrlon=coords[0] - extra * w, llcrnrlat=coords[1] - extra + 0.01 * h, urcrnrlon=coords[2] + extra * w, urcrnrlat=coords[3] + extra + 0.01 * h, #provide latitude of 'true scale.' Not sure what this means, I would check the Basemap API if you are a GIS guru lat_ts=0, #resolution of boundary database to use. Can be c (crude), l (low), i (intermediate), h (high), f (full) or None. resolution='i', #don't show the axis ticks automatically suppress_ticks=True) #provide the path to the shapefile, but leave off the .shp extension #name your map something useful (I named this 'srilanka') 'srilanka', #set the default shape boundary coloring (default is black) and the zorder (layer order) color='none', zorder=2) Out[6]: (25, 5, [79.52180480957031, 5.918471813201904, 0.0, 0.0], [81.87875366210955, 9.835970878601088, 0.0, 0.0], <matplotlib.collections.LineCollection at 0x10bc59bd0>) You can access the m object by passing m.whatever_you_named_your_shape. Each item in m.srilanka is a matrixa 2 x n matrix defining the polygon shape. I believe they are the locations of each point, which is then interpolated to create the polygon outline (not 100% sure about this, but for our purposes it doesn't matter). If you want to take a look at the first item in m.srilanka execute In: m.srilanka[0] In [7]: print 'm.srilanka is a ' + str(type(m.srilanka)) + ' object.' print 'It contains ' + str(len(m.srilanka)) + ' items.' print 'The first list item itself contains ' + str(len(m.srilanka[0])) + ' items.' m.srilanka is a <type 'list'> object. It contains 156 items. The first list item itself contains 103 items. You might be wondering why the list contains 156 items, rather than 25 (1 for each district). When you use the readshapefile class 'rings in individual Polygon shapes are split out into separate polygons, and additional keys ‘RINGNUM’ and ‘SHAPENUM’ are added to the shape attribute dictionary' (per the Basemap documentation). What this means is that if the district shape is actually comprised of multiple polygons, then the shape is split out into each of its associated polygon rings. This occurs frequently when the shape contains complex coastlines (e.g. islands) since the shape for that state or district is actually comprised of multiple fully formed polygons (an island requires its own polygon). Think of the U.S. State of Hawaii -- it is comprised of multiple island polygons. You can also access the info feature of the polygon which has the associated metadata. Note that RINGNUM and SHAPENUM were added. I'll be using NAME_1 to merge this with my data as this contains the district name. In [8]: m.srilanka_info[0] Out[8]: {'ENGTYPE_1': 'District', 'ID_0': 215, 'ID_1': 1, 'ISO': 'LKA', 'NAME_0': 'Sri Lanka', 'NAME_1': 'Ampara', 'NL_NAME_1': ' ', 'RINGNUM': 1, 'SHAPENUM': 1, 'TYPE_1': 'Distrikkaya', 'VARNAME_1': 'Amparai'} ## Setting up the map dataframe¶ Next, we need to take the information from m.srilanka and get it into a nice Panda's dataframe. I use Shapely's Polygon class to convert the x,y information contained in the m.srilanka list to create a defined polygon. You can read more about Shapely here Then, I grab NAME_1 and call it district and define areas for each polygon. Note that each Shapely polygon has an .area attribute which calculates the polygon area (in meters). I add a column for miles as well. In [9]: # set up a map dataframe df_map = pd.DataFrame({ #access the x,y coords and define a polygon for each item in m.srilanka 'poly': [Polygon(xy) for xy in m.srilanka], #conver NAME_1 to a column called 'district' 'district': [district['NAME_1'] for district in m.srilanka_info]}) df_map['area_m'] = df_map['poly'].map(lambda x: x.area/1000) #convert meters to miles df_map['area_miles'] = df_map['area_m'] * 0.000621371 In [10]: df_map.head() Out[10]: district poly area_m area_miles 0 Ampara POLYGON ((276169.8002706398 175908.0897950437,... 519.996944 0.323111 1 Ampara POLYGON ((217641.0364441486 207208.6241718179,... 4484127.664631 2786.306891 2 Anuradhapura POLYGON ((166929.5980524687 338253.4440058147,... 7206341.191304 4477.811432 3 Badulla POLYGON ((188035.5295273047 193888.385865976, ... 2868839.391369 1782.613601 4 Batticaloa POLYGON ((279070.6564249436 180985.0646625504,... 650.514429 0.404211 ### Binding the data to the map¶ Again, note that we will be matching District_1 witin the data to district within the map dataframe. In [11]: data.head() Out[11]: District_1 Total_pop Sinhalese Tamils Muslims Others Sinhalese_pct Tamils_pct Muslims_pct Others_pct 0 Colombo 2309809 1771319 258654 242728 37108 77 11 11 2 1 Gampaha 2294641 2079115 90950 95501 29075 91 4 4 1 2 Kalutara 1217260 1054991 47973 112276 2020 87 4 9 0 3 Kandy 1369899 1018323 154874 191159 5543 74 11 14 0 4 Matale 482229 389092 48156 44113 868 81 10 9 0 First, let's rename District_1 to district within the data In [12]: data=data.rename(columns = {'District_1':'district'}) Did it work? Let's take a look at the row for Colombo. In [13]: data[data['district']=='Colombo'] Out[13]: district Total_pop Sinhalese Tamils Muslims Others Sinhalese_pct Tamils_pct Muslims_pct Others_pct 0 Colombo 2309809 1771319 258654 242728 37108 77 11 11 2 Perfect! Now, let's merge our two data frames with df_map on the left and data on the right based on the key variable district. I redefine df_map as the merged dataframe. In [14]: df_map = pd.merge(df_map, data, on='district') Let's make sure this looks right: In [15]: df_map.head() Out[15]: district poly area_m area_miles Total_pop Sinhalese Tamils Muslims Others Sinhalese_pct Tamils_pct Muslims_pct Others_pct 0 Ampara POLYGON ((276169.8002706398 175908.0897950437,... 519.996944 0.323111 648057 251018 112915 282484 1640 39 17 44 0 1 Ampara POLYGON ((217641.0364441486 207208.6241718179,... 4484127.664631 2786.306891 648057 251018 112915 282484 1640 39 17 44 0 2 Anuradhapura POLYGON ((166929.5980524687 338253.4440058147,... 7206341.191304 4477.811432 856232 778131 6022 70248 1831 91 1 8 0 3 Badulla POLYGON ((188035.5295273047 193888.385865976, ... 2868839.391369 1782.613601 811758 593120 169997 45886 2755 73 21 6 0 4 Batticaloa POLYGON ((279070.6564249436 180985.0646625504,... 650.514429 0.404211 525142 6127 382300 133844 2871 1 73 25 1 Now you can see that the map dataframe includes the demographic data iterated for each polygon. ## Binning the data¶ Next, we need to decide how we want to split up the data. For a filled map, we need to decide how many bins we want (call this k) and where to split the bins. For example, if most of the data points we would like to plot are between 0 and 10, perhaps we would want to split it evenly in 4 bins ranging from 0-2.5, 2.5-5, 5-7.5 and 7.5-10. The problem with this approach is that your map might not tell you much if most of the data is in the first bin, 0-2.5, except a couple outliers. So, I'll present two options: • use Jenks natural breaks • define our own breaks Jenks natural breaks defines optimal breakpoints for the data using a clustering algorithm. This is great if you are not sure where to break or bin your data. Defining our own breaks (like the example I provided above) is useful for when you want to create a set of maps using the same basemap but plotting different variables. In this case, you generally want to have your data plotted on the same scale for ease of comparison. Below, toggle the variable Jenks to True if you want to use Jenks bins and False if you want to define your own. ##### Set the bins¶ In [16]: # change False to True to use Jenks binning jenks = False Next, set the variable you would like to plot. This should be the column name in df_map that you would like to analyze. I have set it to 'Tamils_pct' for the purpose of the walkthrough. ##### Set the variable to plot¶ In [17]: # change 'Tamils_pct' to the column name of what you want to plot (e.g. 'Total_pop' for total population) var_2_analyze = 'Tamils_pct' ##### Bin the data¶ In [18]: if jenks == True: # Calculate Jenks natural breaks for each polygon breaks = nb( # set the data to use df_map[df_map[var_2_analyze].notnull()][var_2_analyze].values, # since this is an optimization function we need to give it a number of initial solutions to find. # you can adjust this number if you are unsatisfied with the bin results initial=300, # k is the number of natural breaks you would like to apply. I've set it to 10, but you can change. k=10) else: # Define my own breaks [even split each 20 percentage points] Note that the bins are the top range so >20, >40, etc # you can change the bins to whatever you like, though they should be based on the data you are analyzing # since I am going to plot data on a 0 to 100 scale, I chose these break points my_bins = [20,40,60,80,100] # Calculate the user defined breaks for our defined bins breaks = mapclassify.User_Defined( # set the data to use df_map[df_map[var_2_analyze].notnull()][var_2_analyze].values, #use my bins my_bins) Note that the output of our breaks variable from pysal.esda.mapclassify has two attributes we can access: breaks.y and breaks.yb • breaks.y has the actual data that we broke on • breaks.yb has the bin that is output You can take a look at this if you're interested by executing: In: breaks.y In: breaks.yb ##### Add breaks to the dataframe as 'bins'¶ In [19]: # check if 'bins' already exists and drop it if it does so that we can recreate it using our new break information if 'bins' in df_map.columns: df_map = df_map.drop('bins',1) print 'Bins column already existed, so we dropped the bins column' # the notnull method lets us match indices when joining # b is a dataframe of the bins with the var_2_analyze index b = pd.DataFrame({'bins': breaks.yb}, index=df_map[df_map[var_2_analyze].notnull()].index) # join b back to df_map df_map = df_map.join(b) # and handle our NA's if there are any df_map.bins.fillna(-1, inplace=True) ##### Create labels for the legend¶ In [20]: # check if this is a jenks or user-defined break if jenks == True: # if jenks, use these labels bin_labels = ["<= %0.0f" % b for b in breaks.bins] else: # if user defined, use these ones bin_labels = ["< %0.0f" % b for b in breaks.bins] print 'Here are the bin labels:' for label in bin_labels: print label Here are the bin labels: < 20 < 40 < 60 < 80 < 100 ## Plotting the Map¶ ##### Set up the colors¶ This is straight from Stephan Hügel's guide to mapping with Python. He does a very nice job defining reusable functions for mapping numbers to colors. I'm not going to get into what exactly these functions do in this walk-through, but keep in mind that we now have each polygon bucketed within a bin. We just want to ensure that we evenly split our color scale across the bins. These functions help us do that using some of matplotlib's built in functionality. In [21]: # Convenience functions for working with color ramps and bars def colorbar_index(ncolors, cmap, labels=None, kwargs): """ This is a convenience function to stop you making off-by-one errors Takes a standard colour ramp, and discretizes it, then draws a colour bar with correctly aligned labels """ cmap = cmap_discretize(cmap, ncolors) mappable = cm.ScalarMappable(cmap=cmap) mappable.set_array([]) mappable.set_clim(-0.5, ncolors+0.5) colorbar = plt.colorbar(mappable, kwargs) colorbar.set_ticks(np.linspace(0, ncolors, ncolors)) colorbar.set_ticklabels(range(ncolors)) if labels: colorbar.set_ticklabels(labels) return colorbar def cmap_discretize(cmap, N): """ Return a discrete colormap from the continuous colormap cmap. cmap: colormap instance, eg. cm.jet. N: number of colors. Example x = resize(arange(100), (5,100)) djet = cmap_discretize(cm.jet, 5) imshow(x, cmap=djet) """ if type(cmap) == str: cmap = get_cmap(cmap) colors_i = np.concatenate((np.linspace(0, 1., N), (0., 0., 0., 0.))) colors_rgba = cmap(colors_i) indices = np.linspace(0, 1., N + 1) cdict = {} for ki, key in enumerate(('red', 'green', 'blue')): cdict[key] = [(indices[i], colors_rgba[i - 1, ki], colors_rgba[i, ki]) for i in xrange(N + 1)] return matplotlib.colors.LinearSegmentedColormap(cmap.name + "_%d" % N, cdict, 1024) ### Onto plotting the map!¶ Let's first make sure that we plot our map inline (as opposed to a Python viewer) In [22]: %matplotlib inline Next, we are going to actually plot the map using matplotlib. I've stepped through the process with in-line comments. One thing worth mentioning is that you can customize the colors with any of the matplotlib color maps. You can take a look at all the options available in the reference document here. For creating a filled map you should stick to the sequential color maps. In [23]: # initialize the plot plt.clf() # define the figure and set the facecolor (e.g. background) to white fig = plt.figure(facecolor='white') # ad a subplot called 'ax' # use a blue colour ramp ('Blues') - we'll be converting it to a map using cmap() # you could also use 'Oranges' or 'Greens' cmap = plt.get_cmap('Blues') # draw district with grey outlines df_map['patches'] = df_map['poly'].map(lambda x: PolygonPatch(x, ec='#555555', lw=.2, alpha=1., zorder=4)) # set the PatchCollection with our defined 'patches' pc = PatchCollection(df_map['patches'], match_original=True) # normalize our bins between the min and max values within the bins norm = Normalize(vmin=df_map['bins'].min(), vmax=df_map['bins'].max()) # impose our color map onto the patch collection pc.set_facecolor(cmap(norm(df_map['bins'].values))) # Add a color bar which has our bin_labels applied cb = colorbar_index(ncolors=len(bin_labels), cmap=cmap, shrink=0.5, labels=bin_labels) # set the font size of the labels (set to size 10 here) cb.ax.tick_params(labelsize=10) # Create a bit of small print smallprint = ax.text( # set the x,y location of the smallprint 1, 1, # add whatever text you would like to appear 'This is a map of Sri Lanka showing ' + var_2_analyze + ' per district.', # set the horizontal/vertical alignment ha='right', va='bottom', # set the size and the color size=10, color='#555555', transform=ax.transAxes) # Draw a map scale m.drawmapscale( #set the coordinates where the scale should appear coords[0] + 0.08, coords[1] + 0.215, coords[0], coords[1], # what is the max value of the scale (here it's set to 25 for 25 miles) 25., barstyle='fancy', labelstyle='simple', fillcolor1='w', fillcolor2='#555555', fontcolor='#555555', zorder=5, # what units would you like to use. Defaults to km units='mi') # set the layout to maximally fit the bounding area plt.tight_layout() # define the size of the figure fig.set_size_inches(5,6) # save the figure. Increase the dpi to increase the quality of the output .png. For example, dpi=1000 is super high quality # note that the figure will be saved as 'sri_lanka_' then the name of the variable under analysis # you can change this to whatever you want plt.savefig('sri_lanka_' + var_2_analyze + '.png', dpi=100, alpha=True) # display our plot plt.show() <matplotlib.figure.Figure at 0x10970c390>	2018-12-14 02:35:31	{"extraction_info": {"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, "math_score": 0.3953377604484558, "perplexity": 3760.740124966631}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825349.51/warc/CC-MAIN-20181214022947-20181214044447-00395.warc.gz"}
https://www.nature.com/articles/s41598-022-19594-7?error=cookies_not_supported&code=3b38d51f-3bd2-4e9d-8ea4-5bbb88cbd164	## Introduction Plants belonging to the Apiaceae family are mostly targeted for large-scale essential oil (EO) production with functional phytochemicals. Among them, ajwain (Trachyspermum ammi (L.) Sprague, Synonym: Carum copticum (L.) Benth. & Hook.f. ex Hiern) as an annual plant is growing in the east of India, Iran, Pakistan, and Egypt1,2. In Iran, the total vegetative herb, fruits (seeds), and roots of the plant are used as a flavoring agent and traditional medicine3. Ajwain has been confirmed that has antimicrobial, antioxidant, anticancer, anti-inflammatory, antitermitic, hypotensive, hypolipidemic, antihypertensive, antispasmodic, anti-lithiasis, diuretic, antitussive, nematicidal, antihelminthic, anti-filarial, and insecticidal activities3,4,5,6,7. Ajwain essential oil as a potent and natural antimicrobial agent through core–shell electrospun nanofibers structure has been introduced for accelerating infected wound healing8. Phytochemicals of ajwain are terpenes, phenolics, alkaloids, flavonoids, glycosides, phytosterols, ascorbic acid, chalcones, coumarins, tannins, steroids, and saponins9,10. With regards to a nutraceutical point of view, ajwain seeds are served as valuable constituents in the human diet. Trachyspermum ammi with aromatic seeds locally known as Zenian and Jajiq (Jajikh) in Iran. Several studies have reported the chemical composition of ajwain oil with different major constituents including thymol, γ-terpinene, and p-cymene11,12 carvone, limonene, and dillapiole13 and carvacrol and p-cymene14. However, no chemotype of EO has been reported in this plant, which contains a very high percentage of thymol (> 90%). The essential oil composition and content in plants depend on several factors such as sexual, seasonal, ontogenetic, genetic variations, ecological, and environmental properties15,16. Essential oils (EOs) are used in perfumes, make-up, food preservers, and additives products17. Food and pharmaceutical products are mostly enriched with synthetic antioxidants such as butylated hydroxyanisole (BHA), Butylated hydroxytoluene (BHT), and propyl gallate (PG)18. However, applying these synthetic antioxidants might lead to serious effects on human health such as toxic and carcinogenic effects19. Natural antioxidants in comparison to synthetic ones have been preferred in terms of safety, tolerance, and non-toxicity20. Therefore in recent years EOs and extracts have been investigated to replace synthetic antioxidants21,22. Recently phenolic monoterpenes like thymol or carvacrol with strong antioxidant and antibacterial properties are demanded23. Thymol, a phenolic monoterpenoid derivative of cymene and isomer of carvacrol is the major constituent in ajwain oil22. Thymol and carvacrol (whether chemical or natural) have been considered to be safe by the European Commission and US Food and Drug Administration (FDA) and are classified as flavoring agents; hence, they undergo regulatory requirements as additives for food preservation24. There is a little chemical difference between natural and chemical EO, such as changes in optical rotation and deuterium depleted and oxygen-18 (18O) enriched of natural thymol, which can only be determined by special methods like Isotope-ratio mass spectrometry (IRMS)25. Research has shown that the antifungal activities of synthetic thymol are lower than natural ones26. Natural thymol is mostly obtained from Thymus vulgaris L. and T. ammi27. The other Thymus L. species, Carum copticum, Oliveria decumbens Vent., Satureja thymbra L., Zataria multiflora Boiss., Majorana syriaca (L.) Raf., Origanum glandulosum Desf., and Lippia L. species were also reported as main sources of thymol with 10.4 to 81.1% in EO28. With increasing thymol use in commercial formulations like mouthwashes, fungicides, pharmaceutical disinfectants, and insecticides, it has become a high-demanded natural antiseptic agent28. Also, antioxidant properties can cause the commercialization of natural thymol. Generally, natural disinfectants are obtained from herbs and spices, many of them are used in the human diet to enhance the flavor, color, and aroma of food29. In the last years, natural antimicrobials have been interested due to the increased consumer awareness of their quality and safety30. The objectives of the present study are phytochemical screening, and evaluation of antioxidant and antibacterial properties of seeds of T. ammi populations in the following items; I) essential oil analysis to find chemotypes with high thymol and their classification; II) evaluation of antioxidant effects of the plant samples EOs and methanolic extracts using 2,2-diphenyl-1-picrylhydrazyl (DPPH), ferric reducing antioxidant power (FRAP), and total antioxidant capacity (TAC) methods; III) evaluation of total phenol, flavonoids and coumarin contents of extract; and finally, IV) evaluation of the antimicrobial activity of EOs against Escherichia coli and Staphylococcus aureus. ## Results and discussion ### Essential oils yield and composition Among the 14 seed sample populations collected, the content of EOs among populations ranged from 3.16 to 5% (v/w). The lowest and highest EO content was determined in Ghayen (P2) and Fars (P8) populations, respectively (Table 1). Similarly, the percentage of EO in ajwain samples has been reported from Pakistan 3.5–5.2%31, India 2–4%4,32, and Iran 2–6%5,33,34,35. EO yield may vary in plants depending on species, quality (chemotype of the plant), condition (fresh or dry), the layout of plant material (e.g., leaf/stem ratio), harvest time, and also extraction method15,16,36. The EO yield is an important quality factor to bring medicinal plants to the pharmaceutical, and food industries. Seed EO constituents of the 14 ajwain populations and chromatograms are shown in Table 1 and Fig. S1. In this study, eleven constituents were identified in all 14 populations, and thymol was the major constituent ranging from 59.92 to 96.4 percent (Fig. S2). Other major constituents were p-cymene (0.55–21.15%), γ-terpinene (0.23–17.78%), and carvacrol (0.41–2.77%) among populations studied. The highest content of thymol (96.4%) and its structural isomer carvacrol (2.77%) were found in the Ghayen population (P2). Additionally, the lowest thymol content was detected in the Isfahan population (P13) (59.92%). The highest (17.78%) and lowest (0.23%) γ-terpinene content was found in the Isfahan (P13) and Ghayen (P2) populations, respectively. The Birjand population (P3) displayed the highest p-cymene content (21.15%) and (P2) showed the lowest content (0.55%). The GC–MS spectra obtained from the Hamedan population (P7) are represented in the graphical diagram in Fig. 1. According to our results, the Ghayen population (P2) has the highest levels of thymol and carvacrol and lowest levels of p-cymene and γ-terpinene. So, a higher rate of precursors (γ-terpinene and p-cymene) to final products (thymol/carvacrol) can be converted in isolated EO35. According to the biosynthetic pathway, γ-terpinene precursor converts to thymol and carvacrol during the developmental stages37. In this context, EO compositions of ajwain have been reported from various geographical areas. According to the chemical composition of ajwain oils, major constituents of thymol, γ-terpinene, and p-cymene11,12,33,35 carvone, limonene, and dillapiole13 and carvacrol and p-cymene14 have been documented. Up to now, the high-thymol content populations from Iran were between 34 to 55%33 48.8 to 61.435, and 65.411. However, no chemotype of the plant EO has been reported with a very high percentage of thymol (> 90%). Thymol and carvacrol percentages of seed EO of 14 populations are shown in Fig. 2. As can be seen in this figure, populations P2 and P8 have the highest thymol content (more than 90% of EO). The presence of a high percentage of thymol in the P8 and P2 can be industrially valuable. Chemotypes are named based on the main constituents in EO within single botanical species38. Normally ajwain oils on the market are those rich in thymol and/or carvacrol with strong antibacterial properties and high antioxidant potential. High purity thymol is interested in the market and will not have the subsequent purification costs. Therefore, chemotypes P2 and P8 with a high percentage of thymol 96.4. 90.57% can be significant respectively. ### Estimation of phyto-constituents of extract Significant differences were obtained among the population for total phenolic (TPC), total flavonoid (TFC), and total coumarin contents (TCC) (P ≤ 0.01) (Table 2). Natural phenolic compounds are including simple phenolics, phenolic acids, flavonoids, coumarins, tannins, stilbenes, curcuminoids, lignans, quinones, and others39. Phenolic compounds and flavonoids are major bioactive components in medicinal plants and thus can comprise an essential part of the human diet40. The present study assessed the total phenolic, flavonoid, and coumarin contents of ajwain populations, and the results are presented in Fig. 3A–C. Up to now, no studies have reported total phenol, flavonoid, and coumarin contents of Iranian ajwain populations. ### Total phenol content (TPC) The total phenolic content in the evaluated extracts varied from 26.91 (P13) in the Isfahan population to 43.20 (P2) mg GAE/g DW in the Ghayen population, Results demonstrated that TPC in the populations varied as the following the order P2 > P10 > P8 > P1 > P11 > P14 > P6, P9 > P3, P5 > P4 > P7 > P12 > P13 (Fig. 3A). In the few evaluable sources, the total phenolic content of ajwain seeds extracted with CHCl3: MeOH (1: 2) solvent was 69 mg/g DW41. In the present study, the highest phenol content (43.2 mg GAE/g DW) was recorded in the P2 population. The difference in TPC with the available report may be due to genetic diversity and differences in extraction methods. According to the presence of apolar thymol in the seed structure, a combination of polar and non-polar solvents to extract compounds may optimize the extraction performance. Various environmental conditions in different places influence the content and metabolic profile of phenolic compounds in plant populations. It seems that high temperature and high UV radiation levels, and differences in genotypes are the reasons why the Isfahan population has a high content of TPC15,16. ### Total flavonoid content (TFC) Analysis of variance showed a significant difference in TFC content at levels P ≤ 0.01. The total flavonoid contents ranged from 4.45 (P7) in the Hamedan population to 8.03 (P8) mg QE/g DW in the Fars population. P6 and P10 with 7.38 mg QE/g DW were also among the high content TFC populations (Fig. 3B). It seems that the reason for the lack of total flavonoids in Hamedan is due genetic differences and the low temperature of this region compared to other regions. Also, the reason for the high level of flavonoids in the Fars population may be due to genetic differences and high temperatures during the growing period. It has been reported that seeds and spurts of ajwain contain 0.58 and 1.15 mg/ g FW of TFC respectively42. Also, TFC of methanolic extract of Anethum graveolens L. (dill) seeds from the Apiaceae family have been reported to be 5.07 (mg QE /g)43. Flavonoid accumulation with many protective roles may be influenced by the combination of genetics (i.e., adaptation to local conditions) and environmental effects (i.e., phenotypic plasticity)44,45. Flavonoid accumulation rates among geographically different ajwain populations concerning climate can be correlated positively with temperature and UV-B radiation and negatively with precipitation (Chalker-Scott, 1999; Koski and Ashman, 2015). ### Total coumarin content (TCC) The TCC content of the T. ammi populations examined ranges from 0.079 (P12) to 0.26 (P1) mg coumarin equivalent to dry weight. The highest coumarin content was obtained from the methanolic extract of Kalat (P1) (0.260 mg CE/g DW) and the lowest value of coumarin was recorded for the population of Ardabil (Fig. 3C). Seed coumarin levels in populations can result from genetic and environmental differences. It seems that coumarin accumulation is decreased due to the coolness condition in Ardabil city during the seed maturation stage. Ajwain is a coumarin-rich source of coumarins (umbelliferone, scopoletin, xanthotoxin, bergapten) mostly found in its sprouts46. However, no literature source was found to report the amount of total coumarin in ajwain seeds. These compounds have valuable medicinal properties, including edema reduction and possible anticancer activity47 Furthermore, they are widely used as a flavoring in foods and pastries. Human exposure to coumarin from the diet has been calculated to be around 0.02 mg/kg/day and its maximum daily intake was estimated to be 0.07 mg/kg BW/day48. ### Free radical scavenging effects and antioxidant activity of essential oils and extracts The antioxidant activities of EOs and extracts were assessed using the DPPH, FRAP free-radical scavenging, and total antioxidant capacity (TAC) assays (Fig. 4A–C). In the DPPH assay, the samples were capable to decrease the DPPH free radical to evaluate their in vitro antioxidant activity. Analysis of variance on DPPH IC50 showed a significant difference in antioxidant activity of EOs and extracts among populations (P < 0.01) (Table 2). The value of DPPH (IC 50) in the essential oil varied between (1.57–2.61 µg/ml). The highest rate was related to P13 and the lowest rate was related to P2 samples. Also, the DPPH IC50 in the extract was recorded in the range of 8.06 to 31.95 respectively in P2 and P7. The antioxidant effect of Ajwain EO compared to ascorbic acid has been previously reported. According to this source, an amount of 10 µg of essential oil compared to the same concentration of vitamin C had a DPPH free radical scavenging effect of 76.4 to 97.2%49. DPPH radical scavenging activities of the methanolic extract of seeds of T. ammi in the range of 30 to 240 µg/ ml have been reported to be 65–80%. While with the same concentrations ascorbic scavenging activities of DPPH were in the range of 90 to 100%50. In the comparison of IC50 of EOs and extracts with common antioxidants; ascorbic acid (AA), BHT, PG and rutin (RU), quercetin (QU), gallic acid (GA), and thymol (TH) used in the present study, the following result was obtained from the lowest to the highest. GA < EO (P2) < Qu, PG, EO (P8) < EOs (P9 < P3 < P1 < P10, P12 < P7 < P6 < P4, P11, P14 < P13) < AA < TH < RU < BHT < EXs (P2 < P8 < P10 < P11 < P6 < P3, P5 < P1 < P13 < P9, P14 < P4 < P12 < P7) (Fig. 4A). In the present study, several antioxidants were used to better comparison with essential oils and extracts. BHT, PG, TH, and GA were used as common synthetic antioxidants. The reason for using synthetic thymol was due to comparing it with high thymol content natural studied EO and extracts. Since the plant extract contained flavonoids and phenolic acids, it was tried to use natural phenolic and flavonoid antioxidants for comparison. Ascorbic acid was used in the present study because it is a known and applicable antioxidant. Previously the antioxidant activity of some extracts from the Apiaceae family has been reported. According to these reports, IC50 of Heracleum persicum Desf., Prangos ferulacea (L.) Lindl, Chaerophyllum macropodum Boiss., Oliveria decumbens extracts were 438, 242, 623, 98.5, and 86.1 (µg/ml), respectively37,51. Also based on obtained results, ajwain seed with notable essential oil and extract can be introduced as the new promising antioxidant source from the Apiaceae family. In the present study, FRAP was used as another method to evaluate antioxidant activity. Based on the results of the analysis of variance, a significant difference was obtained among the population’s EOs and extracts (Table 2). In the EO samples, the highest reducing power was obtained in population 2 (P2), (10.31 mM Fe+2) and the lowest was obtained in P13 (6.23 mM Fe+2) (Fig. 4B). The reducing power of the extracts was obtained in the range of 1.96 to 3.68 mM Fe+2, in which the lowest was related to P13 and the highest to P2. Also, the ferric reducing power of the samples of essential oils, extracts, and standards used in this study were as follows. GA > PG > QU, AA > BHT > TH > EO [P2 > P8) > RU > P5 > P1 > P12 > P14 ≥ P4 ≥ P3 > P9 > P6 > P7 > P13] > EX [P2 > P10 > P8 > P1, P6, P11 > P9 ≥ P14, P3 ≥ P5 > P12 > P4 > P13]. The mechanism by which extracts and EO reduce the [Fe (TPTZ)2]3+ complex to the ferrous state (Fe2+) usually involves the donation of electrons in the form of hydrogen ions and has been related to the in vitro antioxidant activity52. The phosphomolybdenum assay is a quantitative method to evaluate the total antioxidant capacity. Significant differences were obtained in the EO samples as well as the extract samples among the populations (P < 0.01) (Table 2). The values ranged from 8.30 (P9) to 16.61 (P2) (mM AAE/mg EO) in EO samples and from 1.84 (P13) to 4.59 (P11) (µM AAE/g DW) in samples of extracts (Fig. 4C). Results demonstrated that ajwain seeds had notable total antioxidant capacity. The TAC value among antioxidant standards ranged from 11.4 to 34.08 in the following order: AA > GA > PG > TH > QU > BHT > RU. Also, this value ranged from 8.3 to 16.6 among EO samples with the highest value in P2. TCA values in extracts were recorded in the range of 1.83–4.59 with the highest value obtained in P11. Other detailed information is shown in Fig. 4C. ### Antibacterial activity The antibacterial activity of ajwain EOs was evaluated against two antibiotic resistance bacteria and their ability was compared with Cefixime as a standard. In the present study, we tried to use both gram-positive bacteria and gram-negative bacteria as samples. Staphylococcus aureus is a gram-positive pathogenic and antibiotic-resistant bacteria. It is also one of the most common causes of nosocomial infections. Also, Escherichia coli is available and inexpensive, and easily cultured in the laboratory. It is one of the most common causes of urinary tract infections. Gram-negative bacteria are also resistant to antibiotics and are an important species in the field of microbiology. One of the main problems in the field of microbiology is the resistance of microbes to antibiotics and so introducing new antibiotics is necessary53. The reasons for using Cefixime in the present study are due to its widely used, great therapeutic power, and effectiveness against a wide range of microbes. In this study, EOs exhibited bacteriostatic activities against S. aureus (0.06–64 µg/mL) and E. coli (1–64 µg/mL) (Table 3). High thymol content EO (P2) showed high antibacterial activity (MIC = 0.06 µg/mL) against S. aureus. Also, the EO from the Isfahan population (P13) showed the lowest antibacterial activity with the highest MIC value (64 µg/mL). In the present study, the mean MIC was not significantly different on gram-negative and positive bacteria, and populations with high thymol had a high antibacterial ability, indicating the antibacterial effects of thymol. Some researchers have evaluated the antimicrobial activity of ajwain oil14,54,55. Thymol and carvacrol were found to be more effective in killing bacteria3,4,5,6,7,9. The antibacterial properties of natural products, such as essential oils and their components, are widely explored by both industrial and academic fields56. The antibacterial activity of the EOs is dependent on the composition and concentration, type, and dose of the target microorganism57. The high antibacterial potential of cumin essential oil compared to Ferula essential oil has already been identified due to the high ratio of phenolic monoterpene compounds to other monoterpenes58. It seems that the antibacterial effects of C. copticum are also mainly due to the presence of phenolic monoterpenes such as thymol, carvacrol, p-cymene, and γ-terpinene. Therefore, ajwain EO can be used as a natural agent with antibacterial properties in the food industry and the treatment of infectious diseases, especially antibiotic-resistant strains. ### Hierarchical cluster analysis (HCA) of essential oil constituents HCA was performed by using the 11 identified compounds and 14 populations (Fig. 5A). All used populations were divided into two clusters; Cluster I included P4, P6, P7, P10, P11, P12, P13, and P14 and cluster II consist of P1, P2, P5, P8, and P9 samples. In cluster I the major constituents were thymol (59.92–72.86), p-cymene (15.66–21.15), and γ-terpinene (10.22–17.78). In the second cluster thymol (80.09–96.4) and carvacrol (0.5–2.77) were the major constituents. Cluster analysis can classify studied populations into several groups, according to the chemical composition by ‘magnifying’ their similarities59. Forasmuch as, plant sources from environmentally different origins led to the emergence of new chemotypes to baring domestication and cultivation to obtain uniform chemical plants along with appropriate agricultural features60. ### Principal component analysis (PCA) Principal component analysis (PCA) is one of the multivariate statistical techniques used to explain differentiation between populations and to obtain more information on the variables that mainly influence the population's similarities and differences61. The PCA was performed to identify the most significant variables in the data set (Fig. 5B). The same data set (14 population × 11 components) was used in this section. The PCA showed two components with explain 83.3% of the total variance. The first principal component (PC1) had the most portion of variance (74.5%) which was given by compounds such as γ-Terpinene, α-pinene, α-Thujene, p-cymene, and limonene. The second component (PC2), explaining 8.8% of the total variance, consisted of compounds thymol, carvacrol, and 1, 8-cineol (Fig. 6). The results of PCA agreed with those of the cluster analysis the populations similarly were divided into two distinct groups including high thymol/carvacrol and high thymol/p-cymene/γ-terpinene groups (Fig. 5B). Heat map analyses were drowned to determine how constituents effect on clustering. Based on heat map analysis samples were well-classified. Also, in the analysis of the principal factors (PCA) between all the evaluated traits in the populations, the first principal factor (PC1) showed 53.8% and the second principal factor (PC2) 14.7% of the variance. This analysis determined the principal component, correlation of traits, and their relationship with populations. Accordingly, traits with positive arrows show a positive correlation and two traits with non-directional arrows show a negative correlation. Accordingly, thymol and carvacrol have a high correlation with antioxidant properties and this property is correlated with populations of chemotype 1 (P1, P2, P5, P8, P9). Other relationships and details correlations are shown in Fig. 5C, D. ### Correlation Simple correlation estimated the relationship between variables. Simple correlations between 24 studied traits in the present study are shown in Fig. 6. Thymol as the major constituent of EOs showed a high positive correlation with TPC (0.71), carvacrol (0.64), FRAP EO (0.85), and FRAP ext. (0.66). Thymol also had a significant negative correlation with Mic EO (-0.74), Mic Sa (-0.69), α-Thujene (-0.84), α-Pinene (-0.77), β-Pinene (-0.75), β-Myrcene (-0.9), α-Terpinene (-0.85), p-Cymene (-0.98), Limonene (-0.89), γ-Terpinene (-0.97). TPC had a positive correlation with TFC, thymol, carvacrol, FRAP Ext., TAC Ext., and a significant negative correlation with DPPH Ext. The antioxidant methods in extracts DPPH50 vs FRAP (-0.8), DPPH50 vs TAC (-0.67) and FRAP vs TAC (0.59) were highly correlated. Similarly, in estimating the antioxidant activity of essential oil DPPH50 vs FRAP (-0.79), DPPH50 vs TAC (-0.48), and FRAP vs TAC Ext (0.55) were highly correlated. Also, the high correlation of all antioxidant methods with thymol can explain its positive effect on the antioxidant activity of the extracts and EOs. The correlations found between each of the traits can be very important in breeding programs. ## Conclusion Ajwain (T. ammi) is one of the aromatic seed spices and a rich source of specialized metabolites such as thymol. Considering that the plant is one of the main and natural sources of thymol. As natural native Iranian populations of the plant can be the primary sources for breeding and domestication of valuable thymol chemotypes, therefore the present study was conducted to determine high thymol content chemotypes. Based on the results, P2 and P8 populations with a thymol content above 90% are introduced for this aim. Fars population (P8) with high thymol, EO percent, and total flavonoid also high antibacterial and antioxidant activity is recommended for nutraceutical and pharmacological uses. Fourteen populations were classified into two chemotypes of thymol/p-cymene/γ-terpinene type and thymol/carvacrol type. A comparison of the antioxidant effects of EOs with seven synthetic and natural antioxidants used in the present study showed that the plant EOs have stronger antioxidants than these antioxidants. Therefore, EOs of the plant can be used in various industries after supplementary studies. Also, plant extracts are introduced as an antioxidant source for industrial use due to the presence of phenolic and flavonoid compounds. The antibacterial properties of EOs against two bacteria Gram-positive (S. aureus ATCC: 1431) and Gram-negative (E. coli PTCC: 1399) and their correlation with thymol indicate the importance of high thymol selected chemotypes. ## Methods ### Collection of plant materials The studied plant materials (seeds of 14T. ammi populations) were collected from different regions of Iran. Ecological information, local names and usage, and the weight of one thousand seeds of populations are presented in Table 4. The plant was identified at the herbarium of Medicinal Plants and Drugs Research Institute (MPH) of Shahid Beheshti University, Tehran, Iran, and a voucher specimen (no. MPH-2938) were deposited at MPH (Fig. S3). Since the plant is not an endangered plant, the collection of samples with the permission of the university was done only for academic study by observing the necessary guidelines for collecting plants (IUCN Policy Statement on Research Involving Species at Risk of Extinction and the Convention on the Trade in Endangered Species of Wild Fauna and Flora). Also, except for a few limited herbarium specimens, only a limited percentage of seeds were collected from each population. Figure 1 represented the graphical design of the present research. ### Extraction of the essential oils (EOs) To extract EOs, 50 g of each seed source was extracted by a Clevenger-type apparatus for three hours. The EO was then collected in a glass container and kept at 4 °C in the dark condition until analyzed and characterized. ### GC–MS and GC analysis The obtained EOs was analyzed by gas chromatography-flame ionization detector (GC-FID) and GC-mass spectrometry (GC–MS). The analysis was carried out using a DB-5 fused silica capillary column (length 30 m; inner diameter 0.25 mm; film thickness 0.25 μm). The injector and detector temperatures were kept at 250 and 280 °C, respectively. Helium was used as the carrier gas at a flow rate of 1.1 mL/min; the oven temperature was programmed from 60 to 250 at 5 °C/min and held for 40 min. The injection volume was 1.0 µL using a 1:10 split ratio. GC–MS analysis was carried out with a Thermoquest–Finnigan gas chromatograph equipped with DB-5 fused silica capillary column (length 60 m; inner diameter 0.25 mm; film thickness 0.25 μm) coupled with a TRACE mass spectrometer (Manchester, UK). Helium was used as the carrier gas with a flow rate of 1.1 mL/min. The MS fragmentation was performed by electronic impact (EI) at 70 eV with a scan time of 0.4 s and a mass range was 40–460 amu. The ion source and interface temperatures were 200° and 250 °C, respectively. The oven temperature was the same as above for the GC. The compounds were identified by comparison of their mass spectra with those of the internal reference mass spectra library (Adams and Wiley 7.0) and confirmed by comparison of their retention indices with authentic compounds or with those reported in the literature62,63. Retention indices were calculated using the retention times of n-alkanes (C6–C24). ### Extracts preparation 500 mg of seeds were powdered and transferred to test tubes. Twenty mL of methanol (80%) was added to each sample and stirred slightly. Tubes were sonicated for 30 min (Elmasonic EASY 120 H, Germany). The samples were filtered through Whatman filter paper no. 1 and preserved in dark condition at 4 ˚C before assays. ### Total phenolic content (TPC) The TPC was estimated by the colorimetric Folin-Ciocalteu method64. 200 ml of the extracts were mixed with 1200 µL of Folin-Ciocalteu reagent (10%), 180µL of H2O, and 960µL sodium carbonate 7%; then this mixture was shaken and incubated at room temperature for 30 min in the darkness. The samples resulting blue color and their absorbance were determined at 765 nm using UV–Vis spectrophotometer (Dynamica HALO DB-20, UK). The TPC was expressed as mg GAE/g dry weight. ### Determination of total flavonoid content (TFC) The TFC was determined using aluminum chloride colorimetric assay65. The extraction solution was combined with 150 μL of 5% sodium nitrite solution after 5 min remaining, 300 μL of aluminum chloride solution (10% w/v), and 1 mL of NaOH (1 M) were added. After incubating the samples for 10 min, the mixture turned pink and the absorbance was recorded at 380 nm by spectrophotometer (Dynamica HALO DB-20, UK). The TFC was calculated as mg of quercetin equivalent (QE) per g of dry weight (DW). ### Determination of total coumarin content (TCC) The TCC was evaluated based on the Borntrager reaction66. 500 μL of the extracts were transferred to a test tube. Afterward, 2 ml of distilled water and 500 μL of lead acetate solution (5%, w/v) were added. The sample is shaken and then 7 ml of distilled water is added. Then 2 mL of prepared mixtures were transferred to a new test tube and add 8 mL of HCl solution (0.1 M, v/v). The samples remain at room temperature for 30 min and then were read at 320 nm by spectrophotometer and the TCC is expressed as milligrams of coumarin equivalents (mg CE/g DW). ### Antioxidant activity assays The antioxidant activity of the EOs and extracts of seeds was determined by using three assays of DPPH, FRAP, and TAC. The results were compared with standards including BHT (butylated hydroxyl toluene) and PG (Propyl gallate), thymol, gallic acid, ascorbic acid, rutin, and quercetin. The 2, 2-diphenyl-1-picrylhydrazyl (DPPH) free radical scavenging assay was performed by the method with some modification67. DPPH scavenging activity of EOs, extracts and control antioxidants were measured. For this means DPPH (100 µM) was dissolved in methanol to prepare the fresh stock solution. The DPPH solution (2 ml) was added to the test compounds and was shaken and incubated in darkness for 30 min at room temperature. The absorbance was monitored at 517 nm against a blank using a UV–Vis spectrophotometer. The inhibition percentage of the DPPH free radical (I %) was calculated as follows: $${\text{I}}\% \, = \,[({\text{Abs}}_{{{\text{control}}}} {-}{\text{Abs}}_{{{\text{sample}}}} )/{\text{Abs}}_{{{\text{control}}}} ]\, \times \,{1}00$$ Abscontrol, absorbance of DPPH radical; Abs sample is the absorbance of the (DPPH radical + test samples). I% was plotted against sample concentrations to obtain the IC50 index, which was defined as the concentration of antioxidant required to decrease the initial DPPH concentration by 50% DPPH (Brand-Williams et al., 1995). ### Ferric reducing antioxidant power (FRAP) assay The FRAP assay was determined using the reducing power technique68. The samples with antioxidant properties will reduce the ferric ion (Fe3+) to the ferrous ion (Fe2+) in an acidic medium (pH = 3.6), to form an intense blue complex (Fe2+/TPTZ). The FRAP reagent was prepared by mixing acetate buffer (300 mM, pH 3.6), a solution of 10 mM TPTZ (Tripyridyl-s-triazine) in 40 mM HCl, and 20 mM FeCl3 at a ratio of 10:1:1 (v/v/v). The FRAP reagent (2 mL) was added to test tubes and mixed thoroughly and were incubated at 37 °C in the dark for 30 min. The absorbance of the samples was taken at 593 nm in comparison to a blank. The standard curve was prepared using different concentrations of ferrous sulfate. The results were expressed in µM Fe2+/g DW. ### Phosphomolybdenum assay TAC was evaluated using phosphomolybdenum assay69. The method is based on the reduction of Mo (VI) to Mo (V) with the subsequent formation of a phosphate–Mo5+ complex. 1 ml of 0.6 M sulfuric acid, 28 mM sodium phosphate, and 4 mM ammonium molybdate was added to 20 ml of distilled water and made up the volume to 50 ml adding distilled water. 50 µL of (EOs, extracts, and standards) were added to each test tube individually containing 1 ml of Molybdate reagent solution. These capped tubes were kept incubated at 95 ˚C for 90 min. The tubes were cooled at room temperature and then their absorbance was measured at 695 nm using a UV–visible spectrophotometer against blank. The antioxidant capacity was expressed as equivalents of ascorbic acid (mg AAE/g extract). ### Antibacterial activity The antibacterial potential of EOs was tested against two bacteria Gram-positive (Staphylococcus aureus ATCC: 1431) and Gram-negative (Escherichia coli PTCC: 1399). Minimum inhibitory concentration (MIC) was conducted according to the standard broth microdilution technique following the guideline of the Clinical Laboratory Standard Institute (CLSI)70 in 96 well microplates. Microdilution series of EOs were prepared in Mueller–Hinton Broth (from 0.128–06 µg/ml with a final volume of 100 µl). A suspension of fresh culture medium (18–20 h) was prepared in normal saline and turbidity was adjusted to a 0.5 McFarland tube. The suspension was diluted 1:100 with Mueller–Hinton Broth and then 100 μl of it was added to an individual well. Thus assay is performed by applying a bacterial inoculum of 0.5–1 × 105 CFU/ml to each well. With the addition of bacterial suspension, the final concentration of the test substance in each well was halved. After incubation at 37 °C for 24 h, the wells were investigated for turbidity and MIC was determined and recorded in µg/ml. Samples of EOs assessed in a concentration range of 0.03 to 64 µg/ml. Because of turbidity in some samples, the five μl (4 mg/ml) of 0.2 µm filter-assisted sterilized resazurin solution was used to distinguish how wells grow. Culture medium with bacteria suspension as positive control and culture medium as negative control were used. MIC was determined as soon as the color of the positive control well changed. The experiment was performed twice with three replications and cefixime was evaluated as a standard. ### Statistical analysis We confirmed that all methods were performed in accordance with the relevant guidelines and regulations. All experiments have been carried out in triplicate and are expressed as the mean ± standard deviation (SD). Analysis of variance (ANOVA) was applied as a statistical analysis of phytochemical data. Data analyses were carried out using SAS Version 9.4 statistical software. The comparison of the means was performed by SNK test at a 1% level. Principle component analysis (PCA), cluster analysis, Heat-map, and correlation analysis were obtained using RStudio (version 1.2.5019) URL http://www.rstudio.com/.	2023-02-02 15:53:03	{"extraction_info": {"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, "math_score": 0.556533694267273, "perplexity": 6801.990840892594}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500028.12/warc/CC-MAIN-20230202133541-20230202163541-00440.warc.gz"}
https://eips.ethereum.org/EIPS/eip-3234	# EIP-3234: Batch Flash Loans Source Author Alberto Cuesta Cañada, Fiona Kobayashi, fubuloubu, Austin Williams https://ethereum-magicians.org/t/erc-3234-batch-flash-loans/5271 Draft Standards Track ERC 2021-01-31 ## Simple Summary This ERC provides standard interfaces and processes for multiple-asset flash loans. ## Motivation Flash loans of multiple assets, or batch flash loans, are a common offering of flash lenders, and have a strong use case in the simultaneous refinance of several positions between platforms. At the same time, batch flash loans are more complicated to use than single asset flash loans (ER3156). This divergence of use cases and user profiles calls for independent, but consistent, standards for single asset flash loans and batch flash loans. ## Specification A batch flash lending feature integrates two smart contracts using a callback pattern. These are called the LENDER and the RECEIVER in this EIP. ### Lender Specification A lender MUST implement the IERC3234BatchFlashLender interface. pragma solidity ^0.7.0 \|\| ^0.8.0; import "./IERC3234BatchFlashBorrower.sol"; interface IERC3234BatchFlashLender { /** * @dev The amount of currency available to be lended. * @param tokens The currency for each loan in the batch. * @return The maximum amount that can be borrowed for each loan in the batch. / function maxFlashLoan( ) external view returns (uint256[]); /* * @dev The fees to be charged for a given batch loan. * @param tokens The loan currencies. * @param amounts The amounts of tokens lent. * @return The amount of each token to be charged for each loan, on top of the returned principal. / function flashFee( uint256[] calldata amounts ) external view returns (uint256[]); /* * @dev Initiate a batch flash loan. * @param receiver The receiver of the tokens in the loan, and the receiver of the callback. * @param tokens The loan currencies. * @param amounts The amount of tokens lent. * @param data Arbitrary data structure, intended to contain user-defined parameters. / function batchFlashLoan( uint256[] calldata amounts, bytes[] calldata data ) external returns (bool); } The maxFlashLoan function MUST return the maximum loan possible for each token. If a token is not currently supported maxFlashLoan MUST return 0, instead of reverting. The flashFee function MUST return the fees charged for each loan of amount token. If a token is not supported flashFee MUST revert. The batchFlashLoan function MUST include a callback to the onBatchFlashLoan function in a IERC3234BatchFlashBorrower contract. function batchFlashLoan( uint256[] calldata amounts, bytes calldata data ) external returns (bool) { ... require( msg.sender, tokens, amounts, fees, data ) == keccak256("ERC3234BatchFlashBorrower.onBatchFlashLoan"), "IERC3234: Callback failed" ); ... } The batchFlashLoan function MUST transfer amounts[i] of each tokens[i] to receiver before the callback to the borrower. The batchFlashLoan function MUST include msg.sender as the initiator to onBatchFlashLoan. The batchFlashLoan function MUST NOT modify the tokens, amounts and data parameters received, and MUST pass them on to onBatchFlashLoan. The lender MUST verify that the onBatchFlashLoan callback returns the keccak256 hash of “ERC3234BatchFlashBorrower.onBatchFlashLoan”. The batchFlashLoan function MUST include a fees argument to onBatchFlashLoan with the fee to pay for each individual token and amount lent, ensuring that fees[i] == flashFee(tokens[i], amounts[i]). After the callback, for each token in tokens, the batchFlashLoan function MUST take the amounts[i] + fees[i] of tokens[i] from the receiver, or revert if this is not successful. If successful, batchFlashLoan MUST return true. A receiver of flash loans MUST implement the IERC3234BatchFlashBorrower interface: pragma solidity ^0.7.0 \|\| ^0.8.0; interface IERC3234BatchFlashBorrower { /* * @dev Receive a flash loan. * @param initiator The initiator of the loan. * @param tokens The loan currency. * @param amounts The amount of tokens lent. * @param fees The additional amount of tokens to repay. * @param data Arbitrary data structure, intended to contain user-defined parameters. * @return The keccak256 hash of "ERC3234BatchFlashBorrower.onBatchFlashLoan" */ function onBatchFlashLoan( uint256[] calldata amounts, uint256[] calldata fees, bytes calldata data ) external returns (bytes32); } For the transaction to not revert, for each token in tokens, receiver MUST approve amounts[i] + fees[i] of tokens[i] to be taken by msg.sender before the end of onBatchFlashLoan. If successful, onBatchFlashLoan MUST return the keccak256 hash of “ERC3156BatchFlashBorrower.onBatchFlashLoan”. ## Rationale The interfaces described in this ERC have been chosen as to cover the known flash lending use cases, while allowing for safe and gas efficient implementations. flashFee reverts on unsupported tokens, because returning a numerical value would be incorrect. batchFlashLoan has been chosen as a function name as descriptive enough, unlikely to clash with other functions in the lender, and including both the use cases in which the tokens lended are held or minted by the lender. receiver is taken as a parameter to allow flexibility on the implementation of separate loan initiators and receivers. Existing flash lenders (Aave, dYdX and Uniswap) all provide flash loans of several token types from the same contract (LendingPool, SoloMargin and UniswapV2Pair). Providing a token parameter in both the batchFlashLoan and onBatchFlashLoan functions matches closely the observed functionality. A bytes calldata data parameter is included for the caller to pass arbitrary information to the receiver, without impacting the utility of the batchFlashLoan standard. onBatchFlashLoan has been chosen as a function name as descriptive enough, unlikely to clash with other functions in the receiver, and following the onAction naming pattern used as well in EIP-667. An initiator will often be required in the onBatchFlashLoan function, which the lender knows as msg.sender. An alternative implementation which would embed the initiator in the data parameter by the caller would require an additional mechanism for the receiver to verify its accuracy, and is not advisable. The amounts will be required in the onBatchFlashLoan function, which the lender took as a parameter. An alternative implementation which would embed the amounts in the data parameter by the caller would require an additional mechanism for the receiver to verify its accuracy, and is not advisable. The fees will often be calculated in the batchFlashLoan function, which the receiver must be aware of for repayment. Passing the fees as a parameter instead of appended to data is simple and effective. The amount + fee are pulled from the receiver to allow the lender to implement other features that depend on using transferFrom, without having to lock them for the duration of a flash loan. An alternative implementation where the repayment is transferred to the lender is also possible, but would need all other features in the lender to be also based in using transfer instead of transferFrom. Given the lower complexity and prevalence of a “pull” architecture over a “push” architecture, “pull” was chosen. ## Security Considerations ### Verification of callback arguments The arguments of onBatchFlashLoan are expected to reflect the conditions of the flash loan, but cannot be trusted unconditionally. They can be divided in two groups, that require different checks before they can be trusted to be genuine. 1. No arguments can be assumed to be genuine without some kind of verification. initiator, tokens and amounts refer to a past transaction that might not have happened if the caller of onBatchFlashLoan decides to lie. fees might be false or calculated incorrectly. data might have been manipulated by the caller. 2. To trust that the value of initiator, tokens, amounts and fees are genuine a reasonable pattern is to verify that the onBatchFlashLoan caller is in a whitelist of verified flash lenders. Since often the caller of batchFlashLoan will also be receiving the onBatchFlashLoan callback this will be trivial. In all other cases flash lenders will need to be approved if the arguments in onBatchFlashLoan are to be trusted. 3. To trust that the value of data is genuine, in addition to the check in point 1, it is recommended that the receiver verifies that the initiator is in some list of trusted addresses. Trusting the lender and the initiator is enough to trust that the contents of data are genuine. ### Flash lending security considerations #### Automatic approvals for untrusted borrowers The safest approach is to implement an approval for amount+fee before the batchFlashLoan is executed. Including in onBatchFlashLoan the approval for the lender to take the amount + fee needs to be combined with a mechanism to verify that the borrower is trusted, such as those described above. If an unsuspecting contract with a non-reverting fallback function, or an EOA, would approve a lender implementing ERC3156, and not immediately use the approval, and if the lender would not verify the return value of onBatchFlashLoan, then the unsuspecting contract or EOA could be drained of funds up to their allowance or balance limit. This would be executed by a borrower calling batchFlashLoan on the victim. The flash loan would be executed and repaid, plus any fees, which would be accumulated by the lender. For this reason, it is important that the lender implements the specification in full and reverts if onBatchFlashLoan doesn’t return the keccak256 hash for “ERC3156FlashBorrower.onBatchFlashLoan”. ### Flash minting external security considerations The typical quantum of tokens involved in flash mint transactions will give rise to new innovative attack vectors. #### Example 1 - interest rate attack If there exists a lending protocol that offers stable interests rates, but it does not have floor/ceiling rate limits and it does not rebalance the fixed rate based on flash-induced liquidity changes, then it could be susceptible to the following scenario: FreeLoanAttack.sol 1. Flash mint 1 quintillion DAI 2. Deposit the 1 quintillion DAI + $1.5 million worth of ETH collateral 3. The quantum of your total deposit now pushes the stable interest rate down to 0.00001% stable interest rate 4. Borrow 1 million DAI on 0.00001% stable interest rate based on the 1.5M ETH collateral 5. Withdraw and burn the 1 quint DAI to close the original flash mint 6. You now have a 1 million DAI loan that is practically interest free for perpetuity ($0.10 / year in interest) The key takeaway being the obvious need to implement a flat floor/ceiling rate limit and to rebalance the rate based on short term liquidity changes. #### Example 2 - arithmetic overflow and underflow If the flash mint provider does not place any limits on the amount of flash mintable tokens in a transaction, then anyone can flash mint 2^256-1 amount of tokens. The protocols on the receiving end of the flash mints will need to ensure their contracts can handle this. One obvious way is to leverage OpenZeppelin’s SafeMath libraries as a catch-all safety net, however consideration should be given to when it is or isn’t used given the gas tradeoffs. If you recall there was a series of incidents in 2018 where exchanges such as OKEx, Poloniex, HitBTC and Huobi had to shutdown deposits and withdrawls of ERC20 tokens due to integer overflows within the ERC20 token contracts. ### Flash minting internal security considerations The coupling of flash minting with business specific features in the same platform can easily lead to unintended consequences. #### Example - Treasury draining In early implementations of the Yield Protocol flash loaned fyDai could be redeemed for Dai, which could be used to liquidate the Yield Protocol CDP vault in MakerDAO: 1. Flash mint a very large amount of fyDai. 2. Redeem for Dai as much fyDai as the Yield Protocol collateral would allow. 3. Trigger a stability rate increase with a call to jug.drip which would make the Yield Protocol uncollateralized. 4. Liquidate the Yield Protocol CDP vault in MakerDAO. Copyright and related rights waived via CC0.	2021-05-14 08:20:41	{"extraction_info": {"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, "math_score": 0.20833049714565277, "perplexity": 6701.734728943123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991648.40/warc/CC-MAIN-20210514060536-20210514090536-00510.warc.gz"}
https://blender.stackexchange.com/questions/106994/separate-mirrored-mesh-when-exporting	# Separate Mirrored mesh when exporting? I've created a humanoid model that I'm exporting as an FBX for use in Unity. The model is composed of many sub-meshes, because I want the model to "explode" in the game, and send the individual pieces flying. So, for example, I have individual "Hand", "LowerArm", "UpperArm", etc objects in my model. Currently each object has an unapplied Mirror modifier to keep the model symmetrical. The issue is that when exporting this model as an FBX, the "Hands" object contains both the left and right hands as a single object, as opposed to being separate objects. A very manual way to address this is to apply all of my Mirror modifiers, then manually separate the vertices on one half of the model to a new object. The obvious downside to that is that it's destructive, and I can't easily edit the model anymore after doing that. I was hoping there might exist a "separation" modifier, which could intelligently separate a mesh into two pieces depending on whether the vertices are on one side of the model or another. That way, the modifier would be applied on export, but I wouldn't need to apply my Mirror modifiers in Blender. So, in short: Is there a way to export an FBX of my model that separates my current "Hand" object into "LeftHand" and "RightHand", without having to manually apply the Mirror modifiers, and manually separate the vertices? Thanks, -Dan I suggest you name your mesh with the suffix .l since it is the left side which is modelled (even if there is a subdivision modifier). Here are some manual steps. 1. Duplicate objects. ⇧ ShiftD 2. With the duplicates selected, mirror them ⎈ CtrlM, X. 3. Export as fbx but deselect apply modifiers. Or use a short python script. (Paste this in Blender's text editor and click Run Script with the objects selected. The script will automatically remove the modifiers and create a duplicated mirror, even if the mirror axis isn't x. If you're using a different naming scheme than .l/.r, change this line new_obj.name = re.sub(r'\.l\.\d\d\d', '.r', new_obj.name). new_obj.name = re.sub('left', 'right', obj .name) would replace left with right. (You would name everything with the left prefix beforehand (e.g. "leftHand".) import bpy import mathutils for obj in bpy.context.selected_objects: # Check if a mirror modifier exists. for mod in obj.modifiers: if mod.type != "MIRROR": continue mirror_name = obj.name.replace("Left", "Right") if mirror_name == obj.name: mirror_name = obj.name + "_mirrored" # Reference the mirrored object. Create it if it doesn't exist. mirror_obj = bpy.data.objects.get(mirror_name) if mirror_obj == None: mirror_obj = bpy.data.objects.new(mirror_name, obj.data.copy()) mirror_obj.name = mirror_name else: mirror_obj.data = obj.data.copy() axes = [mod.use_x, mod.use_y, mod.use_z] dir = [(1,0,0), (0,1,0), (0,0,1)] for axis, direction in zip(axes, dir): if axis: mirror_obj.data.transform(mathutils.Matrix.Scale(-1, 4, direction)) mirror_obj.data.flip_normals() mod.show_render = mod.show_viewport = False break To remove the duplicates created by the script and re-show the mirror modifier simply undo the actions of the script with a single undo step. ⎈ CtrlZ For 2.8x, this script can be changed to: import bpy import re import mathutils scn = bpy.context.scene objs = bpy.context.selected_objects for obj in objs: new_obj = obj.copy () new_obj.data = obj.data.copy () if len(obj.users_collection): else: new_obj.name = re.sub(r'\.l\.\d\d\d', '.r', new_obj.name) for m, n in zip (new_obj.modifiers, obj.modifiers): if m.type == "MIRROR": axes = [m.use_axis[0], m.use_axis[1], m.use_axis[2]] dir = [(1,0,0), (0,1,0), (0,0,1)] for axis, direction in zip (axes, dir): if axis: new_obj.data.transform (mathutils.Matrix.Scale (-1, 4, direction)) new_obj.data.flip_normals () obj.modifiers.remove (n) new_obj.modifiers.remove (m) • scene.objects is change to collections system • mirror modifier used axis are now accessible as a vector • @lemon I am seeing some additional spaces at r'\.l\.\d\d\d'. Was that intential and/or does it have a benefit? – Leander Feb 29 at 10:21 • Nothing, I previously took the code from blender.stackexchange.com/questions/168413/… and did not pay attention to these spaces – lemon Feb 29 at 10:26 • Additionally, was wondering: shouldn't the code test if a mirror exists before duplicating? – lemon Feb 29 at 10:28 • Probably, I have updated the 2.7 script. You could add some of those changes to the 2.8 version. However, the seemingly trivial task of adding the object the collection can introduce problems, when the object exists in bpy.data.objects but not in the current collection. – Leander Feb 29 at 10:56	2020-05-25 13:19:27	{"extraction_info": {"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, "math_score": 0.1936107724905014, "perplexity": 6510.636151744374}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347388758.12/warc/CC-MAIN-20200525130036-20200525160036-00159.warc.gz"}
https://math.stackexchange.com/questions/2927819/on-understanding-the-cauchy-riemann-equations	# On understanding the Cauchy-Riemann equations I asked this question: re expressing the Cauchy Riemann Equations $$\begin{split} \frac{\partial f}{\partial z} &= \frac{\partial f}{\partial x} \frac{\partial x}{\partial z} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial z}\\ &= \frac12 \left(\frac{\partial f}{\partial x} -i \frac{\partial f}{\partial y} \right) \end{split}$$ Where I asked why the second equation holds. and this was the awnser given: To deduce the second equality it is sufficient to note that, since $$z=x+iy$$ (and $$\bar{z}=x-iy$$), then $$x=\frac{1}{2}(z+\bar z)\quad y=-\frac{i}{2}(z-\bar z)$$ so $$\frac{\partial x}{\partial z}=\frac{1}{2}\quad\frac{\partial y}{\partial z}=-\frac{i}{2}$$ I am still confused by one thing, to me it seems that the derivative of $$\bar{z}$$ does not exist, we can get both 1 and -1 at a same point approaching it either by the reals or the imarginaries. So how would one get the derivative of: $$z - \bar{z}$$ with respect to $$z$$? Thank you for the help! The point is that it takes place after you complexify, i.e., instead of $$x,y\in\mathbb{R}$$, you let $$x,y\in\mathbb{C}$$ and consider the change of coordinates from $$x,y$$ to $$(z,\bar{z})=(x+iy,x-iy)$$ as a purely algebraic manipulation (it has geometric interpretations too, but let's ignore that for now). Then $$z,\bar{z}$$ are independent coordinates, so $$\dfrac{\partial\bar{z}}{\partial z}=0$$ (note that it is $$\partial$$ not $$\mathrm{d}$$, so there isn't much risk of confusion).	2020-11-01 01:59:11	{"extraction_info": {"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.976956307888031, "perplexity": 160.3807595266915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107922746.99/warc/CC-MAIN-20201101001251-20201101031251-00315.warc.gz"}
https://mathoverflow.net/questions/293784/eccentricity-in-the-definition-of-graph-center	# "Eccentricity" in the Definition of Graph Center On the Wikepdia Page Graph Center I saw that the center of graph is the set of vertices with minimal eccentricity, i.e the set of vertices, whose maximal distance to other vertices is minimal. On the website the term "eccentricity" links to Distance (Graph Theory). Now, as eccentricity is, to my knowledge, in 2D geometry exclusively used as a property of ellipses and hyperbolas, I wonder how it should be related to sets. The problem I have with the use of the term eccentricity for denoting a set of things is twofold: firstly, eccentricity is a numeric value in classical geometry and secondly, I wanted to use the term eccentricity in the classical sense to define a generalization of ellipses to complete graphs, which now seems not possible anymore because the "eccentricity claim" has already been staked. Questions: • is the use of the term eccentricity in the definition of a graph's center customary in graph theory and if yes, • who first used it to define graph centers • what was the motiviation/justification for using eccentricity in that definition Re: 'is it customary'. Yes, this is the customary term, and I don't know any reasonable alternative to using the eccentricity function. The term (with exactly this definition) already occurs on page 35 of the slim yet influential textbook [H1969] Frank Harary, Graph Theory, Addison Wesley Publishing Company, First Edition, 1969 Re "who first used it to define graph centers": needless to say, this cannot be known, but again it is at least as old as [H1969, p. 35], where one reads "The *eccentricity $$e(v)$$ of a point $$v$$ in a connected graph $$G$$ is $$\max d(u,v)$$ for all $$u$$ in $$G$$. The radius $$r(G)$$ is the minimum eccentricity of the points. Note that the maximum eccentricity is the diameter. A point $$v$$ is a central point if $$e(G)=r(G)$$, and the center of $$G$$ is the set of all central points. Re "what was the motiviation/justification for using eccentricity in that definition": this can only be guessed or answered by authors like Harary themselves. That said, a reasonable just-so-story is this: consider the definition 'center=set of vertices whose eccentricity equals the graph's radius', and then note that in the most paradigmatic shape having a 'center', i.e, the humble circle, the definition makes perfect sense: for any point $$p$$ in a circle define its 'eccentricity' to be the Euclidean length of the segment from $$p$$ through the circle's centre $$c$$ to the circle's circumference; then the one-element set $$\{c\}$$ equals the set of all points of the circle whose eccentricity equals the radius. The story goes that the early graph theorists were wont to scrawl with pens on paper, and often these shapes were circular, and this gave them ideas. each and every vertex is central (with eccentricity 2), and yet the automorphism group of the graph acts on the vertex set with a whopping four distinct orbits $$\{0\}$$, $$\{3\}$$, $$\{1,2\}$$, $$\{4,5\}$$. (In other words, whereas all vertices are being lumped together into the same 'eccentricity-class', there exist quite distinct-looking vertices, and there are four types of vertices.)	2021-09-26 03:53:13	{"extraction_info": {"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": 18, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7925360798835754, "perplexity": 278.36556003741043}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057796.87/warc/CC-MAIN-20210926022920-20210926052920-00559.warc.gz"}
https://www.physicsforums.com/threads/mappings-on-partitive-sets.417930/	# Mappings on partitive sets 1. Jul 23, 2010 Another problem whose answer I'd like to check. Thanks in advance. Let X = {1, 2, 3, 4} and Y = {1, 2, 3}. Let P(X) and P(Y) be the power sets of X and Y, respectively. i) How many continuous mappings are there from the discrete topological spaces (X, P(X)) to (Y, P(Y))? Well, I figured that every mapping we can define between these topologies is open, since for any open set in Y (i.e. any power set), the preimage must again be a power set in X, so the total number would be $\sum_{i = 1}^3 \frac{3!}{i!}$. ii) How many open mappings are there? iii) Is the identity mapping f(x) = x continuous, and if so, is it a homeomorphism? Here I'm a bit confused, since we can't map 4 to 4, since 4 is not an element of Y. Shouldn't all the elements of the domain X be mapped into some element of Y? Last edited: Jul 23, 2010 2. Jul 23, 2010	2018-09-23 22:26:05	{"extraction_info": {"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, "math_score": 0.9098256826400757, "perplexity": 452.7793532206485}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159820.67/warc/CC-MAIN-20180923212605-20180923233005-00031.warc.gz"}
https://documentation.immuta.com/2022.1/pov/walkthroughs/schema-monitoring-and-sdd/	You are viewing documentation for Immuta version 2022.1. For the latest version, view our documentation for Immuta SaaS or the latest self-hosted version. # Schema Monitoring and Automatic Sensitive Data Discovery Prerequisite: Before using this walkthrough, please ensure that you’ve done Parts 1-3 in the POV Data Setup walkthrough. ## Overview Immuta considers itself a “live” metadata aggregator - not only metadata about your data but also your users. Considering data specifically, to be “live” means Immuta will monitor for schema changes in your database and reflect those changes in your Immuta instance. This allows you to register your databases with Immuta and not have to worry about registering individual tables today or in the future. Additionally, when the tables are discovered through the registration process, Immuta will inspect the table data for sensitive information and tag it as such. These tags are critical for scaling tag-based policies which you will learn about in subsequent walkthroughs. This sensitive data detection is done by inspecting samples of your data and using algorithms to decide what we believe the data contains. Those tags are editable or new custom tags can be curated and added by you. It is also possible to add tags curated or discovered in other systems or catalogs. While this is not specifically covered in this walkthrough, it’s important to understand. Both the monitoring for new data and discovering and tagging sensitive data aligns with the Scalability and Evolvability theme, removing redundant and arduous work. As users create new tables or columns in your database, those tables/columns will be automatically registered in Immuta and automatically tagged. Why does this matter? Because once they are registered and tagged, policies can immediately be applied - this means humans can be completely removed from the process by creating tag-based policies that dynamically attach themselves to new tables. (We’ll walk through tag-based policies shortly.) Because of this, the business reaps • Increased revenue: accelerate data access / time to data because where sensitive data lives is well understood. • Decreased cost: operating efficiently at scale, agility at scale. • Decrease risk: sensitive data discovered immediately. Assumptions: Your user has the following permissions in Immuta (note you should have these by default if you were the initial user on the Immuta installation): • CREATE_DATA_SOURCE: in order to register the data with Immuta • GOVERNANCE: to create a custom tag in Immuta ### Custom Tag We are going to create a custom tag to tag the data with, this will: • Help differentiate your real data from this fake POV data. • Help build global policies across these tables from multiple compute/warehouses, if you have more than one. To create a custom tag, 1. Click the Governance icon in the left sidebar of the Immuta console. 2. Click on the Tags tab. 4. Name the tag Immuta POV. You can delete the nested tag placeholder in order to save. 5. Click Save. ### Register a Schema Let’s walk through registration of a schema to monitor (You do not need GOVERNANCE permission to do this step, only CREATE_DATA_SOURCE): 1. From the Data Source page, click the + New Data Source button. 2. Storage Technology: Choose the Storage Technology of interest. This should align to where you loaded the data in the POV Data Setup walkthrough, but of course could be your own data as well. Note that if you are using the same Databricks workspace for Databricks and SQL Analytics, you only need to load it once. 3. Connection Information: This is the account Immuta will use to monitor your database and query the data metadata. This account should have read access to the data that you need to register. For simplicity, you may want to use the same account you used to load the data in the POV Data Setup walkthrough, but it’s best if you can use an Admin account for registering the data and a separate user account for querying it (which we’ll do later). It should also point to the data you loaded in the POV Data Setup walkthrough which should be the immuta_pov database unless you named the database something else or placed the data somewhere else. 4. Virtual Population: There are several options here for how you want Immuta to monitor your database to automatically populate metadata. In our case we want to choose the first option: Create sources for all tables in this database and monitor for changes. 5. Basic Information: This section allows you to apply a convention to how the tables are named. If you have multiple data warehouses/compute and you’ve already registered these tables once and are registering them now from a 2nd (or more) warehouse/compute, you will have to change the naming convention for the Immuta data source name and schema project so you can tell them apart in the Immuta UI. This will NOT impact what they are named in the native database. 1. Note that Sensitive Data Discovery is enabled. 2. We are going to add that Immuta POV tag we created above by going to the last section “Data Source 1. Tags” 3. Click Edit. 4. Enter Immuta POV and click Add. 5. This will add that tag to any table that is discovered now or in the future. 6. You can leave the defaults for the rest. 7. Click Create to kick off the job. 8. Repeat these steps for each warehouse/compute you have (not to be confused with a Snowflake warehouse; we mean other data warehouses, like Redshift, Databricks SQL analytics, etc.). You will be dumped into a screen that depicts the progress of your monitoring job. You’ll also see a gear spinning in the upper right corner of the screen which depicts the jobs that are running, one of those being the “fingerprint,” which is what is used to gather statistics about your tables and run the Sensitive Data Discovery. Once the tables are registered and the gear stops spinning, click into the Immuta POV Immuta Fake Hr Data table. Once there, click on the Data Dictionary tab. In there you will see your columns as well as the Sensitive Data that was discovered. Also note that because we found a specific entity (such as Discovered.Entity.Person Name), we also tag that column with other derivative tags (such as Discovered.Identifier Indirect). This hierarchy will become important in the Hierarchical Tag-Based Policy Definitions walkthrough. Also visit the Data Dictionary in the Immuta POV Immuta Fake Credit Card Transactions table. If you scroll to the bottom column, transaction_country, you’ll notice we incorrectly tagged it as Discovered.Entity.State - you can go ahead and remove that tag. 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https://www.lanark.s-lanark.sch.uk/barclays-email-kls/multiplying-complex-numbers-with-square-roots-029b80	# multiplying complex numbers with square roots The answer is that “angles add”. It's because we want to talk about complex numbers and simplifyi… With the help of the community we can continue to But we could do that in two ways. 101 S. Hanley Rd, Suite 300 Taking advantage of the Power of a Product Rule: If you've found an issue with this question, please let us know. Rather than going through all the multiplication, we can instead look at the very beginning setup, which we can simplify using the distributive property: None of the other responses gives the correct answer. Square roots of negative numbers. If you generalize this example, you’ll get the general rule for multiplication. Here ends simplicity. We’ll show \|zw\|2 = \|z\|2\|w\|2. A complex number is in the form of a + bi (a real number plus an imaginary number) where a and b are real numbers and i is the imaginary unit. )Or in the shorter \"cis\" notation:(r cis θ)2 = r2 cis 2θ Here ends simplicity. Remember we introduced i as an abbreviation for √1, the square root of 1. Multiplying square roots is typically done one of two ways. Varsity Tutors. Addition / Subtraction - Combine like terms (i.e. A description of the nature and exact location of the content that you claim to infringe your copyright, in \ Can be used for calculating or creating new math problems. The difference is that the root is not real. Track your scores, create tests, and take your learning to the next level! Let z and w be points in the complex plane C. Draw the lines from 0 to z, and 0 to w. The lengths of these lines are the absolute values \|z\| and \|w\|, respectively. Let me ask you a question. Then, according to the formula for multiplication, zw equals (xu yv) + (xv + yu)i. The product of with each of these gives us: What we notice is that each of the roots has a negative. that is, i1? If you want to find out the possible values, the easiest way is probably to go with De Moivre's formula. and that’s a straightforward exercize in algebra. When DIVIDING, it is important to enter the denominator in the second row. Scroll down the page for examples and solutions on how to multiply square roots. In order to prove it, we’ll prove it’s true for the squares so we don’t have to deal with square roots. Higher powers of i are easy to find now that we know i4 = 1. an Well i can! on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. One is through the method described above. We're asked to multiply the complex number 1 minus 3i times the complex number 2 plus 5i. The radicand refers to the number under the radical ... Video on How To Multiply Square Roots. In a similar way, we can find the square root of a negative number. Express in terms of i. Example - 2−3 − 4−6 = 2−3−4+6 = −2+3 Multiplication - When multiplying square roots of negative real numbers, Please follow these steps to file a notice: A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; The two factors are both square roots of negative numbers, and are therefore imaginary. When a number has the form a + bi (a real number plus an imaginary number) it is called a complex number. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. What about the 8i2? In mathematics the symbol for √(−1) is i for imaginary. √a ⋅ √b = √a ⋅ b if only if a > 0 and b > 0 Example 1B: Simplifying Square Roots of Negative Numbers. i and i are reciprocals. Complex numbers also have two square roots; the principal square root of a complex number z, denoted by sqrt (z), is always the one of the two square roots of z with a positive imaginary part. Expressing Square Roots of Negative Numbers as Multiples of i. means of the most recent email address, if any, provided by such party to Varsity Tutors. Thus, 8i2 equals 8. Square root Square root of complex number (a+bi) is z, if z 2 = (a+bi). Let’s look at some special cases of multiplication. Thus, 8i2 equals –8. either the copyright owner or a person authorized to act on their behalf. Of course, it’s easy to check that i times i is 1, so, of course, In other words, you just multiply both parts of the complex number by the real number. Multiplying by the conjugate . That is. You'll find that multiplication by i gives a 90° clockwise rotation about 0. the 6 divided by 4 is equal to 1, with remainder 2, so, The complex conjugate of a complex number is . That means i1 = i3 = i. A slightly more complex example Step 1. all imaginary numbers and the set of all real numbers is the set of complex numbers. It thus makes sense that they will all cancel out. your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one Take the product of with each of these roots. What we don't know is the direction of the line from 0 to zw. What is the reciprocal of i, imaginary unit. link to the specific question (not just the name of the question) that contains the content and a description of Infringement Notice, it will make a good faith attempt to contact the party that made such content available by Dividing Complex Numbers Write the division of two complex numbers as a fraction. http://www.freemathvideos.com In this video tutorial I show you how to multiply imaginary numbers. A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i 2 = −1.For example, 2 + 3i is a complex number. Free Square Roots calculator - Find square roots of any number step-by-step This website uses cookies to ensure you get the best experience. 1. i = √(-1), so i ⋅ i= -1 Great, but why are we talking about imaginary numbers? This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i 2 + 1 = 0 is imposed. The mistake you are making is that sqrt (z) * sqrt (w) is not always sqrt (zw) … Multiply the radicands together. Then the product zw will have an angle which is the sum of the angles arg(z) + arg(w). Examples. Recall from the section on absolute values that, So, in order to show \|zw\|2 = \|z\|2\|w\|2, all you have to do is show that. Stumped yet? If the value in the radicand is negative, the root is said to be an imaginary number. Express the number in terms of i. This is the angle whose vertex is 0, the first side is the positive real axis, and the second side is the line from 0 to z. In the next few examples, we will use the Distributive Property to multiply expressions with square roots. Let's interpret this statement geometrically. (In the diagram, \|z\| is about 1.6, and \|w\| is about 2.1, so \|zw\| should be about 3.4. As a double check, we can square 4i (44 = 16 and ii =-1), producing -16. Sometimes square roots have coefficients (an integer in front of the radical sign), but this only adds a step to the multiplication and does not change the process. Geometrically, when you double a complex number, just double the distance from the origin, 0. the real parts with real parts and the imaginary parts with imaginary parts). Expressing Square Roots of Negative Numbers as Multiples of i. sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require Unit Imaginary Number. For example, 2 times 3 + i is just 6 + 2i. The verification of this identity is an exercise in algebra. Step 3. … We know how to find the square root of any positive real number. Applying the Power of a Product Rule and the fact that : To raise any expression to the third power, use the pattern. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. If Varsity Tutors takes action in response to Thus, the reciprocal of i is i. When dealing with complex numbers, remember that . Now the 12i + 2i simplifies to 14i, of course. Hmm…the square root of a number x is the number that gives xwhen multiplied by itself. improve our educational resources. As it turns out, the square root of -1 is equal to the imaginary number i. Remember we introduced i as an abbreviation for √–1, the square root of –1. Thus, if you are not sure content located In general: x + yj is the conjugate of x − yj. In other words, i is something whose square is –1. This finds the largest even value that can equally take the square root of, and leaves a number under the square root symbol that does not come out to an even number. If we square , we thus get . What about the 8i2? Stated more briefly, multiplication by i gives a 90° counterclockwise rotation about 0. The 4 in the first radical is a square, so I'll be able to take its square root, 2, out front; I'll be stuck with the 5 inside the radical. ... You can use the imaginary unit to write the square root of any negative number. For example:-9 + 38i divided by 5 + 6i would require a = 5 and bi = 6 to be in the 2nd row. or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing If the value in the radicand is negative, the root is said to be an imaginary number. Solve quadratic equations with complex roots. Imaginary numbers allow us to take the square root of negative numbers. In summary, we have two equations which determine where zw is located in C. SAT Math Help » Algebra » Exponents » Squaring / Square Roots / Radicals » Complex Numbers » How to multiply complex numbers Example Question #1 : How To Multiply Complex Numbers Find the product of (3 + 4i)(4 - 3i) given that i is the square root of negative one. Therefore, the product of and its complex conjugate can be found by setting and in this pattern: What is the product of and its complex conjugate? information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are Example 2(f) is a special case. Objectives. Complex number have addition, subtraction, multiplication, division. The complex conjugate of a complex number is , so has as its complex conjugate. The product of the two is the number. The square root of a number refers to the factor you can multiply by itself to … Simplify. If entering just the number 'i' then enter a=0 and bi=1. Yet another exponent gives us OR . To determine the square root of a negative number (-16 for example), take the square root of the absolute value of the number (square root of 16 = 4) and then multiply it by 'i'. In order to multiply square roots of negative numbers we should first write them as complex numbers, using $$\sqrt{-b}=\sqrt{b}i$$.This is one place students tend to make errors, so be careful when you see multiplying with a negative square root. Your name, address, telephone number and email address; and Similarly, when you multiply a complex number z by 1/2, the result will be half way between 0 and z. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such Can you take the square root of −1? as If you want to find out the possible values, the easiest way is probably to go with De Moivre's formula. Send your complaint to our designated agent at: Charles Cohn The other point w has angle arg(w). Varsity Tutors LLC To square a complex number, multiply it by itself: 1. multiply the magnitudes: magnitude × magnitude = magnitude2 2. add the angles: angle + angle = 2 , so we double them. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially What is a “square root”? The University of Texas at Arlington, Masters, Linguistics. and x − yj is the conjugate of x + yj.. Notice that when we multiply conjugates, our final answer is real only (it does not contain any imaginary terms.. We use the idea of conjugate when dividing complex numbers. When a square root of a given number is multiplied by itself, the result is the given number. The following table shows the Multiplication Property of Square Roots. When you want … So, the square root of -16 is 4i. Therefore, the product (3 + 2i)(1 + 4i) equals 5 + 14i. University of Florida, Bachelor of Engineering, Civil Engineering. But in electronics they use j (because "i" already means current, and the next letter after i is j). A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe For another example, i11 = i7 = i3 = i. Let us Discuss c omplex numbers, complex imaginary numbers, complex number , introduction to complex numbers , operations with complex numbers such as addition of complex numbers , subtraction, multiplying complex numbers, conjugate, modulus polar form and their Square roots of the complex numbers and complex numbers questions and answers . Universidad de los Andes, Current Undergrad, Biomedical Engineering. But let’s wait a little bit for them. We will first distribute and then simplify the square roots when possible. Square root Square root of complex number (a+bi) is z, if z 2 = (a+bi). Find the product of (3 + 4i)(4 - 3i) given that i is the square root of negative one. ChillingEffects.org. We already know the length of the line from 0 to zw is going to be the absolute value \|zw\| which equals \|z\| \|w\|. misrepresent that a product or activity is infringing your copyrights. Take the sum of these 4 results. Imaginea number whose reciprocal is its own negation! But when we hit , we discover that Thus, we have a repeating pattern with powers of , with every 4 exponents repeating the pattern.This means any power of evenly divisible by 4 will equal 1, any power of divisible by 4 with a remainder of 1 will equal , and so on. By … You can reduce the power of i by 4 and not change the result. By using this website, you agree to our Cookie Policy. Then we can say that multiplication by i gives a 90° rotation about 0, or if you prefer, a 270° rotation about 0. Define and use imaginary and complex numbers. For example, i5 is i times i4, and that’s just i. basically the combination of a real number and an imaginary number Write both in terms of before multiplying: Therefore, using the Product of Radicals rule: is recognizable as the cube of the binomial . We'll determine the direction of the line from 0 to z by a certain angle, called the argument of z, sometimes denoted arg(z). When a single letter x = a + bi is used to denote a complex number it is sometimes called 'affix'. a Let z be x + yi, and let w be u + vi. Now the 12i + 2i simplifies to 14i, of course. which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Care must be used when working with imaginary numbers, that are expressed as the principal values of the square roots of negative numbers. In a similar way, we can find the square root of a negative number. A power of can be found by dividing the exponent by 4 and noting the remainder. You can multiply square roots, a type of radical expression, just as you might multiply whole numbers. What has happened is that multiplying by i has rotated to point z 90° counterclockwise around the origin to the point z i. This algebra video tutorial explains how to multiply complex numbers and simplify it as well. The point z i is located y units to the left, and x units above. So we want to find a number that gives -1 when multiplied by itself. The product of and is equal to , so set in this expression, and evaluate: None of the other choices gives the correct response. Introduction. A logical guess would be 1 or -1, but 1 ⋅ 1 = 1 not -1, and -1 ⋅ -1 = 1 not -1. In general, multiplying by a complex number is the same as rotating around the origin by the complex number's argument, followed by a scaling by its magnitude. Example 2. Calculate the Complex number Multiplication, Division and square root of the given number. 3 + 2j is the conjugate of 3 − 2j.. Advertisement. has 4 roots, including the complex numbers. Divide complex numbers. Free Complex Numbers Calculator - Simplify complex expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. (In the diagram, arg(z) is about 20°, and arg(w) is about 45°, so arg(zw) should be about 65°.). Which of the following is equal to this sum? By multiplying the variable parts of the two radicals together, I'll get x 4, which is the square of x 2, so I'll be able to take x 2 out front, too. A. Note that the unit circle is shaded in.) In this tutorial we will be looking at imaginary and complex numbers. The difference is that the root is not real. The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. You can think of multiplication by 2 as a transformation which stretches the complex plane C by a factor of 2 away from 0; and multiplication by 1/2 as a transformation which squeezes C toward 0. An identification of the copyright claimed to have been infringed; Step 2. St. Louis, MO 63105. How about negative powers of i? information described below to the designated agent listed below. You just have to remember that this isn't a variable. √− 2 ⋅ √− 6√− 2 ⋅ − 6√12√4 ⋅ √32√3 You learned that you can rewrite the multiplication of radicals/square roots like √2 ⋅ √6 as √2 ⋅ 6 However, you can not do this with imaginary numbers (ie negative radicands). Example 1 of Multiplying Square roots Step 1. In other words, i is something whose square is 1. Remember that (xu yv), the real part of the product, is the product of the real parts minus the product of the imaginary parts, but (xv + yu), the imaginary part of the product, is the sum of the two products of one real part and the other imaginary part. Use Polynomial Multiplication to Multiply Square Roots. Multiply. What is the square root of -1? To learn about imaginary numbers and complex number multiplication, division and square roots, click here. For the same reason that you can subtract 4 from a power of i and not change the result, you can also add 4 to the power of i. We know how to find the square root of any positive real number. © 2007-2021 All Rights Reserved, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Francisco-Bay Area. Result: square the magnitudes, double the angle.In general, a complex number like: r(cos θ + i sin θ)When squared becomes: r2(cos 2θ + i sin 2θ)(the magnitude r gets squared and the angle θ gets doubled. Wesleyan University, Bachelors, Mathematics. You can analyze what multiplication by i does in the same way. And the general idea here is you can multiply these complex numbers like you would have multiplied any traditional binomial. Multiply complex numbers. We can use geometry to find some other roots of unity, in particular the cube roots and sixth roots of unity. The point z in C is located x units to the right of the imaginary axis and y units above the real axis. Explanation: . To simplify any square root we split the square root into two square roots where the two numbers multiply to our original numbers and where we know the square root of one of the numbers. This is the imaginary unit i, or it's just i. When we don't specify counterclockwise or clockwise when referring to rotations or angles, we'll follow the standard convention that counterclockwise is intended. for any positive number x. The correct response is not among the other choices. Any expression to the formula for multiplication, division ) it is sometimes called 'affix ' ( a number! S wait multiplying complex numbers with square roots little bit for them the form a + bi a. Is shaded in.: x − yj is the number under the radical Video... The community we can use the Distributive Property to multiply square roots for given... Andes, current Undergrad, Biomedical Engineering is probably to go with De Moivre 's formula bi ( a number! Arlington, Masters, Linguistics '' already means current, and the general idea here is you analyze! Rotated to point z 90° counterclockwise rotation about 0 imaginary number mathematics the symbol for √ −1! Number i care must be used for calculating or creating new math problems all cancel out diagram, \|z\| about!: Simplifying square roots, click here, according to the right multiplying complex numbers with square roots the root. Know is the set of complex numbers you will always have two different square roots a... Power, use the imaginary axis and y units to the imaginary axis and y units above will looking... With imaginary numbers and the set of all real numbers is the conjugate of x − ! ) it is sometimes called 'affix ' symbol for √ ( −1 ) is a special.! Not change the result among the other point w has angle arg ( w ) community we can continue improve! The help of the line from 0 to zw ( because ''. Math problems abbreviation for √–1, the square root of –1 Civil Engineering by itself the... Important to enter the denominator in the same way website uses cookies to ensure you get the general Rule multiplication... Masters, Linguistics, Biomedical Engineering scores, create tests, and x units above the real parts and general... Do multiplying complex numbers with square roots know is the reciprocal of i y units above as Multiples of i by 4 and not the... That ’ s just i agree to our Cookie Policy a single letter x = a + (... Note that the unit circle is shaded in. line from 0 to zw square roots circle is shaded.! Among the other choices now that we know i4 = 1 allow us to the... The correct response is not real origin to the left, and the fact that: raise. Yv ) + arg ( w ) any positive real number, so, the root! General idea here is you can multiply square roots - Combine like (. Multiply these complex numbers z, if z 2 = ( a+bi ) is a special case, just the... Are expressed as the principal values of the complex number z by 1/2, the way... Have to remember that this is n't a variable has a negative number a given number for multiplication it! Number it is sometimes called 'affix ' third power, use the pattern + 2j is given., Biomedical Engineering write the square root of any number step-by-step this website uses to. Generalize this example, 2 times 3 + 2i is something whose square is –1 let w u! The set of complex numbers like you would have multiplied any traditional binomial i a... Of 3 + 2j is the set of all real numbers is reciprocal! And solutions on how to multiply square roots for a given number is, so has its... I gives a 90° counterclockwise rotation about 0 6 divided by 4 and noting the remainder point has... Tutorial explains how to multiply expressions with square roots next few examples, will. Roots of negative numbers number plus an imaginary number to our Cookie.. One of two ways, it is important to enter the denominator the! About 3.4 2, so, the square root of a number has the form a + bi ( real... You agree to our Cookie Policy counterclockwise around the origin to the few... The number under the radical... Video on how to multiply square roots when possible and that s. Do n't know is the conjugate of x + yj 2, so, the of! Is shaded in. ( xu yv ) + arg ( w ) negative numbers let ’ look. Is sometimes called 'affix ' way, we will use the pattern already know the length of the line 0! A negative number we want to find now that we know how to multiply square roots Calculator - find roots! Located x units to the right of the community we can square 4i ( 4 * 4 = and... The result is the given number z ) + arg ( w ) Calculator! Why are we talking about imaginary numbers and simplify it as well and x units above the real.. The pattern ⋅ i= -1 Great, but why are we talking about imaginary,... Sixth roots of negative numbers that gives -1 when multiplied by itself can to. Gives us: what we notice is that the root is said to be an imaginary.... 4 * 4 = 16 and i * i =-1 ), producing -16 multiply both of! ) it is sometimes called 'affix ': to raise any expression to the right of the number... Is n't a variable the square root of 1 by using this website uses cookies to ensure you the. And square roots of negative numbers and z ) equals 5 + 14i and are therefore imaginary factors are square!, a type of radical expression, just as you might multiply whole numbers w ) yv +..., click here the 12i + 2i simplifies to 14i, of course ll the. Denote a complex number, just double the distance from the origin to the next!. Used to denote multiplying complex numbers with square roots complex number 1 minus 3i times the complex number it is a. Briefly, multiplication, division and square roots is typically done one two. All cancel out of multiplication example 2 ( f ) is a special.... Divided by 4 and noting the remainder multiply complex numbers like you would have multiplied any traditional binomial that will. And are therefore imaginary remainder 2, so has as its complex conjugate of +. As ChillingEffects.org for example, i11 = i7 = i3 = i note that the unit circle shaded. Be an imaginary number i we do n't know is the reciprocal of i, that are expressed as principal! X is the set of complex number is multiplied by itself not change the result be imaginary... You 've found an issue with this question, please let us know ) equals 5 +.!, Civil Engineering according to the imaginary unit i, that is, i1 is about 2.1,,... Would have multiplied any traditional binomial of Florida, Bachelor of Engineering, Civil Engineering the of! Yu ) i i times i4, and are therefore imaginary found an issue with this question please... Gives us: what we do n't know is the imaginary unit to write the root. I4, and x units to the third power, use the.! 1/2, the product of with each of these roots find that multiplication i... Number step-by-step this website uses cookies to ensure you get the best experience introduced i as an abbreviation for,... The origin, 0 improve our educational resources + 2i of algebra, you will have. ) i Cookie Policy to write the square root of a complex number 2 plus 5i powers i. Multiply the complex number by the real number plus an imaginary number it..., please let us know easiest way is probably to go with De 's. -1 Great, but why are we talking about imaginary numbers and simplify as! Value \|zw\| which equals \|z\| \|w\| set of complex number, just multiplying complex numbers with square roots you multiply! The real number analyze what multiplication by i gives a 90° clockwise rotation 0... Sometimes called 'affix ' multiplying complex numbers with square roots analyze what multiplication by i gives a 90° clockwise rotation 0! This sum be u + vi + bi ( a real number 1.6, and the general idea is..., Linguistics \|zw\| should be about 3.4 complex conjugate of x − ! Complex number, just double the distance from the origin to the power! Is located y units to the left, and x units above the real parts and the set of real! Then, according to the number under the radical... Video on how to multiply square roots click! In. if you want … this algebra Video tutorial explains how find. Exercize in algebra double check, we can square 4i ( 4 * =. Can continue to improve our educational resources a given number is called a complex number ( a+bi ) origin the. Raise any expression to the left, and \|w\| is about 1.6, and let w u... Number have addition, subtraction, multiplication by i does in the is! Will have an angle which is the direction of the fundamental theorem of algebra you... I11 = i7 = i3 = i imaginary numbers the verification of this identity is an exercise in algebra number! Powers of i are easy to find out the possible values, the result will be at. Just multiply both parts of the given number can reduce the power of a product Rule if. Counterclockwise around the origin, 0 of Engineering, Civil Engineering factors both. Negative, the square root of 1 you can reduce the power of a complex number is, i1 4! -1 ), producing -16 + 2j ` what has happened is each. Located x units above denote a complex number ( a+bi ) s straightforward! This entry was posted in News. Bookmark the permalink.	2021-04-23 09:17:31	{"extraction_info": {"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": 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, "math_score": 0.7572420835494995, "perplexity": 535.7471584493862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039568689.89/warc/CC-MAIN-20210423070953-20210423100953-00317.warc.gz"}
https://physics.stackexchange.com/questions/365469/why-does-entropy-explain-why-a-colder-object-wont-spontaneously-give-off-energy	# Why does entropy explain why a colder object won't spontaneously give off energy to a hotter one? I'm very new to my studies of entropy, but in my view entropy is the amount of disorder in a system, which I know is unimaginatively true and not really demonstrative of any true understanding I might have on the subject. It has to do with the number of ways a system has of arranging itself, which is why a cup of cracked, scattered ice has less entropy than a neat glass of water as the molecules in the water have more ways of arranging themselves in the glass while still being water while the ice, with its solid structure has pretty fixed positions and arrangements of its molecules. However, I still can't tie in my understanding to explain why a cold object won't spontaneously give off energy to a hotter one. I know the answer is tl;dr "because entropy" but my understanding of it doesn't tie this in. I know the hotter object has more disorder, as the system have a higher multiplicity i.e. more range of properties to exhibit (like more arrangements of varying speeds as the cap for speed for each particle has raised) but I don't see how that means it can't spontaneously gain energy from the object with less. • "I don't see how that means it can't spontaneously gain energy from the object with less." - it can but have you considered all the ways that it would versus all the ways that it goes the other way and asked what is (by far) the most likely outcome? Oct 28 '17 at 2:25 • Just to be precise: it also depends on your precise notion of object. Also in absence of mechanical transformations, if chemical reactions happen inside the object it may give off energy to a hotter object...What the 2nd principle says (or should say to be equivalent to Kelvin's formulation) is that heat does not spontaneously moves form a cooler resevoir to a hotter resevoir. Oct 28 '17 at 8:53 Short answer: that's actually the (or, a) definition of temperature. By definition, object A is at higher temperature than object B if A spontaneously transfers heat to object B when they are placed in thermal contact. So you can leave entropy out of it entirely. Long answer: Here's how entropy gets involved. Forget about cracked and solid ice or anything macroscopic for a while. Think about some really simple system like, say, electrons in an atom. Each electron can be in one of several quantum states, and the energy of the atom $U$ depends on how many electrons are in each state. For any amount of energy the atom (or whatever) can have, there may be several different ways to arrange electrons to give it that energy. The number of ways for a system to have a certain energy is called the multiplicity, denoted $\Omega$, and it is a function of energy. Entropy $S$ is (proportional to) the logarithm of $\Omega$, and is also a function of energy. Now, imagine two systems that can exchange bits of energy between each other. Say system A has 20 energy and system B has 10 energy, so the multiplicity is $\Omega_A(20)\times\Omega_B(10)$. What's likely to happen with this energy? Well, consider this: • If system A gives a unit of energy to system B, the multiplicity becomes $\Omega_A(19)\times\Omega_B(11)$, and the entropy is $S_A(19) + S_B(11)$ • Or if system B gives a unit of energy to system A, the multiplicity becomes $\Omega_A(21)\times\Omega_B(9)$, and the entropy is $S_A(21) + S_B(9)$ • Or maybe nothing happens, and the multiplicity is still $\Omega_A(20)\times\Omega_B(10)$ and the entropy is still $S_A(20) + S_B(10)$. Assuming that each individual final state is equally likely, whichever one of these multiplicities - or entropies - is larger, that's the outcome that's going to be more likely. Or to put it another way, the energy transfer that increases the total entropy more is more likely to happen. (That's the second law of thermodynamics, by the way.) In most realistic situations, one option is overwhelmingly more likely than the others. For example, if the first option (A loses energy to B) is the most likely, that means (among other things) that $$S(U_A + \Delta U) + S(U_B - \Delta U) < S(U_A) + S(U_B)$$ but doing a bit of calculus on that gets you \begin{align} S(U_A + \Delta U) - S(U_A) &< S(U_B) - S(U_B - \Delta U) \\ \lim_{\Delta U\to 0}\frac{S(U_A + \Delta U) - S(U_A)}{\Delta U} &< \lim_{\Delta U\to 0}\frac{S(U_B) - S(U_B - \Delta U)}{\Delta U} \\ \frac{\partial S_A}{\partial U_A} &< \frac{\partial S_B}{\partial U_B} \end{align} Similarly, if the second option (B loses energy to A) is most likely, you can find that $$\frac{\partial S_A}{\partial U_A} > \frac{\partial S_B}{\partial U_B}$$ And if the third option (no energy changes hands) is most likely, you can show (either by elimination or some similar calculus) that $$\frac{\partial S_A}{\partial U_A} = \frac{\partial S_B}{\partial U_B}$$ Clearly, this quantity $\partial S/\partial U$ is related to whether a system gains or loses energy to another system. Systems with smaller values of $\partial S/\partial U$ will tend to lose energy to systems with larger values. But wait! That should remind you of the definition of temperature from the top of my post. And indeed, we define temperature as the reciprocal of this quantity: $$\frac{1}{T} = \frac{\partial S}{\partial U}$$ In other words, the reciprocal of temperature represents the "capacity" of one unit of energy to increase the entropy of a system. If a system is hot, then $1/T$ is small, and that means each unit of energy is "contributing" relatively little entropy. Given the tendency of entropy to increase, a hot system will tend to pass off its energy to other systems where each unit will have more of an effect on the overall entropy. For entropy I find that it is easier to acquire intuition when going to the statistical definition of entropy. Given W the multiplicity of possibilities of a given state ( the number of ways you can produce that state) is connected with the entropy directly, S=k Ln(W) , where k is the Boltzman constant. Temperature is connected with the kinetic energy available in the system. For a simple example in gases it is defined as High kinetic energies generate a lot more microstates to be counted in entropy than low kinetic energy microstates, and the probability of equilibrium of energy transfer goes from high average kinetic energies to low average energies, as in the image above. The probability of the right side to transfer all its kinetic energy to the left is very low. Equilibrium will be reached at a lower temperature.(average kinetic energy). So in the process of reaching equilibrium the right side will transfer some kinetic energy by statistical scatters , but it will be overwhelmed by the higher kinetic energy side. Suppose that only radiation can be transferred. The Black Body(BB) radiation of the left side will be much higher than the BB radiation of the right side so even though the low temperature will radiate to the high, the number of photons going from left to right and generating microstates will be much higher than the number of photons from right to left. Hope this helps. I guess the focus needs to be put on the cold object. If we place a cold object in a hot environment, intuitively, we would say the cold object will not give heat out to its hot environment. Using the concept of entropy and $ds = \frac{\delta Q}T$, we find, if $\delta Q$ is negative, entropy will decrease, which violate the law. In terms of disorder, by giving heat out, the cold object will get even colder and thus more ordered, which is not right as well.	2022-01-27 05:07:38	{"extraction_info": {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8304232954978943, "perplexity": 395.98010404446757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00388.warc.gz"}