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Substitutions/solving equations
1. Suppose that http://stuff.daniel15.com/cgi-bin/mathtex.cgi?a,b,c,d are real numbers such that http://stuff.daniel15.com/cgi-bin/ma...0b%5E2%20=%201 http://stuff.daniel15.com/cgi-bin/ma...0d%5E2%20
=%201 http://stuff.daniel15.com/cgi-bin/mathtex.cgi?ac+bd=0 Show that http://stuff.daniel15.com/cgi-bin/ma...0c%5E2%20=%201 http://stuff.daniel15.com/cgi-bin/ma...0d%5E2%20=%201 http://
stuff.daniel15.com/cgi-bin/ma...+%20cd%20=%200 (Problem can get messy but there is an elegant and complete solution) 2. Find all integer solutions http://stuff.daniel15.com/cgi-bin/mathtex.cgi?
%28n,m%29 to http://stuff.daniel15.com/cgi-bin/ma...5E2+2n+1=m%5E2 3. Find the smallest positive integer whose cube ends in 888.
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Probability problem using a constant
May 31st 2010, 07:04 PM #1
May 2010
Probability problem using a constant
Hello! I'm taking a probability course this summer and am having a lot of trouble with this problem:
You have:
g(x,y) = {g^(x+y-1) boundary: |x-y| <= 1}
and {0 boundary: |x-y| > 1}
where g is a constant.
Find P[ M+N < 3 ].
I understand how to set up the boundaries, but I'm confused as to how to interpret g as a constant. If anyone can help, it would be greatly appreciated! Thanks!
1 g is the name of the function, you shouldn't use it as a constant
2 Is M,N really X and Y??? Where did they come from?
The total probability is one, so that's how you will compute the constant.
May 31st 2010, 07:54 PM #2
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After using manipulatives to introduce the division algorithm for multi-digit numbers, full development of the concept should be carefully taught. It is important to give students plenty of time to
master division of multi-digit numbers. Do not rush the development of this concept.
Materials: Overhead base ten blocks, overhead projector, base ten blocks for students
Preparation: Be sure to provide at least one set of base ten blocks for each pair of students.
Ask: How can we write 276 divided by 6?
Ask: Which notation will you use to find the quotient of 276 divided by 6?
Preference should be
Say: Use your base ten blocks to represent 276.
Ask: Let's begin with the hundreds. Since we are dividing by 6, we need to make groups containing 6 hundreds. Can this be done if we only have 2 hundreds?
No. When you cannot make groups from the current place, you will need to regroup and make groups from the next place.
Ask: If we regroup the 2 hundreds for tens, how many tens would we get? If we include the 7 tens, how many tens would that be altogether?
20 tens is equivalent to 2 hundreds. If we combine the 20 tens with 7 tens, we get 27 tens.
Ask: Since we are working with tens now, how many groups of 6 tens can we make from 27 tens? Be sure to use your base ten blocks.
Notice that there are 4 groups of 6 tens with 3 tens left over.
Say: Since we have 4 groups of 6 tens, we place a 4 over the tens place in 276.
Ask: If one group of 6 tens is 60, what is 4 groups of 6 tens worth?
240. Encourage students to use their base ten blocks if necessary to count the value.
Say: Remember that we began with 276 and want to divide it by 6. Since we have made four groups of 6 tens, we can take 240 away from 276.
Ask: How many tens and ones are left over when we take away the 4 groups of 6 tens?
3 tens and 6 ones are left over.
Say: We can do this by writing 240 below 276 in our division problem and subtracting.
Ask: What is 276 240? What is the value of the base ten blocks that you have left over? What do you notice about the two values?
36. This allows students to see the connection and validation between using the base ten blocks and the algorithm they are learning to use.
Ask: Since we cannot make any more groups of 6 tens with the remaining base ten blocks, we can regroup the 3 tens for how many ones?
30 ones. Be sure to show the students the regrouping of 3 tens for 30 ones.
Ask: How many ones will we now have?
We will have 36 ones.
Ask: How many groups of 6 ones can we make from 36 ones?
We can make 6 groups.
Ask: Where do you think we will write the 6 that represents the 6 groups?
The 6 is written above the ones place in 276.
Ask: Are there any ones left over?
Ask: What is the quotient of 276
Continue this activity using different numbers. Be sure to use numbers that will not use remainders at first. Remember to have the students check their answers using multiplication.
Wrap-Up and Assessment Hints
Students need a great deal of practice when learning to divide multi-digit numbers. Do not be in a rush for students to put away their manipulatives when learning this difficult concept. This can be
a trying time in many students' mathematical development. One of the keys to success is the opportunity to spend ample time practicing this skill. As a teacher, do not be discouraged with slow
progress. Remember, this is the first time most of the students have ever encountered the concept. Your task is to take the needed time and effort to encourage students to learn this process.
Continual assessment when teaching division is a prudent tool. Be sure to provide continual assessment of division once the topic is introduced. Extra practice and assessment later in the year is an
excellent tool to be sure that students have mastered this sometimes difficult topic. When assessing students, try to remember back to when you learned how to divide large numbers. This can sometimes
help put this concept in better perspective.
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Institute for Mathematics and its Applications (IMA)
Metamaterials, which are engineered composite media with unconventional electromagnetic and optical properties, can be formed by embedding sub-wavelength inclusions as artificial molecules in host
media in order to exhibit specific desired response functions. They can have exciting characteristics in manipulating and processing RF, microwave, IR and optical signal information. Various features
of these media are being investigated and some of the fundamental concepts and theories and modeling of wave interaction with a variety of structures and systems involving these material media are
being developed. From our analyses and simulations, we have found that the devices and components formed by these media may be ultracompact and subwavelength, while supporting resonant and
propagating modes. This implies that in such structures RF, microwave, IR and optical signals can be controlled and reshaped beyond the diffraction limits, leading to the possibility of
miniaturization of optical interconnects and design and control of near-field devices and processors for the next generation of information technology. This may also lead to nano-architectures
capable of signal processing in the near-field optics, which has the potential for significant size reduction in information processing and storage. Furthermore, the nanostructures made by pairing
these media can be compact resonant components, resulting in either enhanced wave signatures and higher directivity or in transparency and scattering reduction. We are also interested in nano-optics
of metamaterial structures that effectively act as lumped nano-circuit-elements. These may provide nano-inductors, nano-capacitors, nano-resistors, and nanodiodes as part of field nanocircuits in the
optical regimes or optical-field nanoelectronics--, and can provide roadmaps to more complex nanocircuits and systems formed by collection of such nanostructures. All these characteristics may offer
various potential applications in high-resolution near-field imaging and microscopy, enhancement or reduction of wave interaction with nano-particles and nano-apertures, nanoantennas and arrays,
far-field sub-diffraction optical microscopy (FSOM), nano-circuit-filters, optical data storage, nano-beam patterning and spectroscopy, optical-molecular signaling and optical coupling and
interfacing with cells, to name a few. In this talk, we present an overview of the concepts, salient features, recent developments, and some of the potential applications of these metamaterials and
structures, and will forecast some futures ideas and directions in this area.
Negative index of refraction materials (NIMs) are promising for several applications including near-field imaging and steering of EM radiation. Although NIMs have been demonstrated using hybrid
metamaterials at microwave frequencies, high losses and narrow bandwidths are presently limiting their wide application. We are developing a novel approach to fabricating low-loss high density NIM
semiconductor-metal nanocomposites, which consists of alternating sequences of focused-ion beam nanopatterning of metallic droplet arrays and film growth using molecular-beam epitaxy. We will discuss
the formation and ordering of Ga and In droplets and droplet motifs on a variety of semiconductor surfaces. In addition, we will discuss the extension of this approach to 3D. In particular,
information from scattering measurements of 1D and 2D droplet motifs will be input into theoretical NIMs calculations to guide the fabrication of 3D arrays of appropriate motifs.
Simulations have been performed on a novel metamaterial structure generated by periodic placement of identical high dielectric cubic resonators, in a low dielectric background. These resonators have
degenerate modes, which implies that the TE and TM modes are resonant at the same frequency. Negative index behavior is deduced from these simulations near their resonant frequency. The periodic
cubic structure with these high dielectric resonators results in a metamaterial, without any plasmonic metallic material, and should be low loss.
This talk will describe negative refractive index metamaterials that are based on transmission-line networks. It will focus on microwave structures that consist of transmission lines loaded with
reactive elements. Both planar and volumetric negative refractive index metamaterials will be presented and their operation explained. Finally, ways to push these transmission-line based structures
to optical frequencies using plasmonic materials will be described.
We will review the analytic and computational foundations of Green's function-based methods for electromagnetic scattering, including high order integral representations, fast solvers, and
quasi-periodicity. We will then discuss the development of easy-to-use numerical simulation environments, and present some applications to photonic crystals, random microstructures, and negative
index materials.
A twisting and turning tale promises unimaginable gains for the savvy investor of time and effort in metamaterials research.
In this paper, we develop both semi-discrete and fully-discrete mixed finite element methods for modeling wave propagation in three-dimensional double negative metamaterials. Optimal error estimates
are proved for Nedelec spaces under the assumption of smooth solutions. To our best knowledge, this is the first error analysis obtained for Maxwell's equations when metamaterials are involved.
A variational approach is developed for the design of defects within a two-dimensional lossless photonic crystal slab to create and manipulate the location of high Q transmission spikes within band
gaps. This phenomena is connected to the appearance of resonant behavior within the slab for certain crystal defects. The methodology is applied to design crystals constructed from circular
dielectric rods embedded in a contrasting dielectric medium. This is joint work with Stephen Shipman and Stephanos Venakides.
We show how a slightly lossy superlens of thickness d cloaks collections of polarizable line dipoles or point dipoles or finite energy dipole sources that lie within a distance of d/2 of the lens. In
the limit as the loss in the lens tends to zero, these become essentially invisible from the outside through the cancelling effects of localized resonances generated by the interaction of the source
and the superlens. The lossless perfect Veselago lens has attracted a lot of debate. It is shown that as time progresses the lens becomes increasingly opaque to any physical dipole source located
within a distance d/2 from the lens and which has been turned on at time t=0. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks
the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is an exact correspondence between the response of the perfect lens in the
long time constant limit and the response of lossy lenses in the low loss limit. This is joint work with Nicolae Nicorovici and Ross McPhedran.
We develop a new approach to negative index materials and subwavelength imaging in the far field based on strong anisotropy of the dielectric response. In contrast to conventional negative refraction
systems, our method does not rely on magnetic resonance and does not require periodic patterning--leading to lower losses and high tolerance to fabrication defects.
Since the spatial extent of nanoparticles is not negligible compared to the wavelength of light, non-local effects may be expected in the electric and magnetic response of nanoparticles at optical
frequencies. It has been suggested that such spatially non-local response may be taken into account via the bianisotropic formalism for the constitutive equations. We have calculated the
susceptibilities of pairs of nanowires as a function of orientation relative to the incident fields using the discrete dipole approximation. We compare the results of our simulations with predictions
of the bianisotropic description, and summarize our observations.
We outline recent achievements in creating structural composite materials with controlled electromagnetic properties, as an integral part of a multifunctional material system. The electromagnetic
response is tailored by incorporating within the material small amounts of suitably configured, periodically distributed, electric conductors to produce distributed electric inductance and
capacitance. The small-scale response of the conductors can be homogenized to give overall macroscopic EM material properties at wavelengths that are orders of magnitude larger than the dimensions of
the periodicity of the structure. Periodic arrays of inductive elements such as thin straight wires, loop-wires, coils, and other conductive thin metallic structures can modify the effective electric
permittivity and the effective magnetic permeability of a composite and make it negative. I will discuss the process of design, analysis, manufacturing, and measurement of such composites. In
particular, I will review the UCSD's work on the design, production, and experimental characterization of a 2.7 mm thick composite panels having negative refractive index between 8.4 and 9.2 GHz. I
will also examine our work on a flat lens having a gradient variation of negative index of refraction that can focus in the 10GHz range, showing excellent agreement with full-wave simulations.
Nanocomposites made of Ag nanowires imbedded in a sol-gel host have been morphologically and optically investigated. Sonication during solidification significantly improved nanowire dispersal. The
data from the nanocomposites were compared to the data from pure sol-gels in order to determine the effects of the nanowires. Reflectometry data at 1064 nm show that the presence of ~5% nanowires (by
volume) results in a decrease from 1.17 to ≈1.1 in the real part of the index of refraction accompanied by an increase in the imaginary part. Transmission loss in the pure sol-gel is mainly due to
scattering from inhomogeneities, and the inclusion of nanowires (or the process of doing so) results in a reduction of optical loss at VIS-NUV wavelengths in several samples.
We explore the perspectives of a new type of materials with negative index of refraction - non-magnetic NIMs. In contrast to conventional NIMs, based either on magnetism or on periodicity, our design
is non-magnetic and relies on the effective-medium response of anisotropic meta-materials in waveguide geometries. Being highly-tolerable to fabrication defects, anisotropic systems allow a versatile
control over the magnitude and sign of effective refractive index and open new ways to efficiently couple the radiation from micro-scale optical fibers to nm-sized waveguides followed by
sub-diffraction light manipulation inside sub-critical waveguiding structures. Specific applications include photonic funnels, capable of transferring over 25% of radiation from conventional telecom
fiber to the spots smaller than 1/30-th of a wavelength, and NIM-based lenses with a far-field resolution of the order of 1/10-th of a wavelength. We also investigate the perspectives of active
nanoscale NIMs and demonstrate that material gain can not only eliminate problems associated with absorption, but is also a powerful tool to control the group velocity from negative to "slow"
positive values.
Metamaterials, i.e. artificial engineered structures with properties not available in nature are expected to open a gateway to unprecedented electromagnetic properties and functionality unattainable
from naturally occurring materials. Negative-refractive index metamaterials create entirely new prospects for guiding light on the nanoscale, some of which may have revolutionary impact on
present-day optical technologies. We review this new emerging field of metamaterials and recent progress in demonstrating a negative refractive index in the optical range, where applications can be
particularly important. We also discuss strategies how to push the wavelength region of negative refractive index into the visible range by using plasmon resonant metal nanostructures.
This poster studies the scattering resonance problem associated with a waveguide consisting of an infinite slab with 2-D microstructure embedded in a homogeneous material. The main goal is to
understand how resonances are affected by the presence of the microstructure in the slab. Our method is similar to the prior work of S. Moskow, F. Santosa and M. Vogelius, as the investigation
concentrates on the first order correction to the homogenized resonance. The outgoing radiation condition at infinity makes the problem non-selfadjoint. Furthermore, there are boundary layers on the
edges of the slab, due to the presence of rapidly vaying coefficients in the highest order term of the underlying equation. Our main result is a formula for the first order correction. The formula
indicates strong influence of the way microstructure hits the edges of the slab.
The challenge in engineering negative index materials in the optical frequency range involves designing sub-wavelength building blocks that exhibit both electric and magnetic activity. Achieving
strong magnetic response is particularly challenging because magnetic moment of a structure scales as the square of the unit cell size. We address this challenge by employing higher order (multipole)
electrostatic resonances that have a non-vaishing magnetic moment for a finite unite cell size. This approach provides a natural starting point for a perturbation theory that uses the ratio of the
building block size to vacuum wavelength as the smallness parameter. Perturbative calculation yields the effective parameters of the metamaterial: effective epsilon and mu tensors. Those can be
compared with the effective parameters extracted from fully electromagnetic simulations. Examples are given for two and three dimensional structures.
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Projective objects in the category of chain complexes
up vote 5 down vote favorite
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object $P$ in the category of chain complexes over an abelian category is projective if and only it is a split
exact complex of projectives.
I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help. This is no homework!
What have I a tried so far ? Given an epimorphism $\pi: X \to Y$ and a morphism $f: P \to Y$, it has to be shown that there is a morphism $g: P \to X$ s.t. $\pi \circ g=f$.
Weibel hints to consider the special case $0 \to P_1 \cong P_0 \to 0$. It's easy to construct $g$ in this case: $\pi$ epi means that each $\pi_i:X_i \to Y_i$ is epi. By projectivity of $P_1$ there is
a hom. $g_1: P_1 \to X_1$ s.t. $\pi_1 \circ g_1 = f_1$. If $d^P$ resp. $d^X$ denotes the differential in $P$ resp. $X$, set $$g_0 := d^X_1 \circ g_1 \circ (d^P_1)^{-1}: P_0 \to X_0,\qquad g_i = 0:
P_i \to X_i\; (i\neq 0,1)$$ Then $g=(g_i): P \to X$ is a morphisms s.t. $\pi \circ g=f$.
But I have no idea how to generalize this procedure to the general case where $d^P$ can not be expected to be an isomorphism.
There is a paper on projective objects in the category of chain complexes: dml.cz/bitstream/handle/10338.dmlcz/120545/…. Maybe it's of help. – tj_ Dec 4 '12 at 23:02
1 See also: On the difference between a projective chain complex and a level-wise projective chain complex: mathoverflow.net/questions/103584 – Martin Dec 4 '12 at 23:17
I seem to recall that the trick is to take an arbitrary split exact complex of projectives $Q$ and turn it into one like $0\to P_1\to P_0\to 0$ by setting $P_1 = P_0 = \bigoplus_i{Q_i}$, and
choosing $d^P$ in an appropriate way – David White Dec 5 '12 at 0:21
You'll also have to use the fact that the identity map on your split exact complex of projectives is nullhomotopic. – David White Dec 5 '12 at 0:33
add comment
5 Answers
active oldest votes
The trick with Weibel's hint is to decompose $P$ as direct sum of complexes of type $$\cdots \to 0 \to P_1 \xrightarrow{\cong} P_0 \to 0 \to \cdots$$ Since $P$ is split exact, we can
write $P_n=P_n^{'}\oplus P_n^{''}$ where $P_n^{'}=\text{ker}(d_n)$ and $d_n^{''} =d_n|P_n^{''}:P_n^{''} \to \text{im}(d_n)=P_{n-1}^{'}$ is an isomorphism. Note that since $P_n$ is
projective, the direct summands $P_n^{'},P_n^{''}$ are projective as well. If we define a complex
up vote 4 $$P(n):\quad \cdots \to 0 \to P_{n}^{''} \xrightarrow{d_n^{''}} P_{n-1}^{'} \to 0 \to \cdots$$ then $P = \bigoplus_{n \in \mathbb{Z}}P(n)$. Now let's consider the extension problem $$\
down vote begin{array}{ccl} & & P \newline & & \;\downarrow f \newline X & \overset{\pi}{\twoheadrightarrow} & Y \end{array}$$ $f$ induces by restriction a morphism $f(n): P(n) \to Y$ with $f=\
accepted sum_n f(n)$ (the sum is finite in each degree). As already observed by the OP, there is a morphism $g(n): P(n) \to X$ with $\kappa \circ g(n)=f(n)$. Hence $g := \sum_n g(n): P \to X$
satisfies $\pi \circ g=f$.
1 Indeed, this decomposition is mentioned in the link user49437 provided in the comments to the OP. A reference is Dwyer-Spalinski, Homotopy Theories and Model Categories, and in 7.10
of that paper they construct the decomposition, using the language of boundaries and cycles. – David White Dec 5 '12 at 1:01
Hmm, I think their construction requires the complex to be bounded below. At least they obtain a decomposition $P=\oplus_{k \ge 0}D_k$ and $(D_k)_n=0$ for $n\neq k,k-1$ (also note
that they only require $P$ to be acyclic and not contractible as Weibel does). – Ralph Dec 5 '12 at 1:23
add comment
The question as asked has been answered, but to understand where bounded below enters the picture, it is helpful to think model categorically (as in Dwyer and Spalinsky or, more recently,
chapter 18 of More Concise Algebraic Topology, by Kate Ponto and myself). With the usual model structure (there are others in the latter reference), a chain complex is acyclic and cofibrant
if and only if it is a projective object. If it is cofibrant (not necessarily acyclic) then it is degreewise projective. If it is degreewise projective and bounded below, then it is
cofibrant. However, it can be acyclic and degreewise projective and yet not cofibrant if it is not bounded below. There is a nice example in the paper [K] that TJ refers to: work over the
ring $Z/4$ and take all $P_n$ to be free on one generator, with all differentials given by multiplication by $2$: $P$ is acyclic and degreewise free, but it is not cofibrant and not a
up vote projective object. Split exactness rules out such examples and is automatic when $P$ is exact, degreewise projective, and bounded below.
5 down
vote Incidentally, the role of $R$-split exactness becomes really interesting model theoretically when $R$ is commutative and not a field and one considers model structures on DG modules over a DG
$R$-algebra. There are (at least) six different interesting projective type model structures, and the usual one is arguably not the most useful one (this is a shameless advertisement for a
paper in the writing stage by Tobi Barthel, Emily Riehl, and myself).
add comment
As another solution I want to offer a closed formula for the sought-after morphism $g=(g_i):P \to X$:
up vote 4 Since $P$ is split exact, it's contractible, i.e. there are maps $s_i : P_i \to P_{i+1}$ with $s_{i-1}d_i^P + s_i d_{i+1}^P=id_{P_i}$. Moreover, since each $P_i$ is projective we can
down vote choose $h_i: P_i \to X_i$ such that $\pi_i \circ h_i = f_i$. Now $$g_i := d_{i+1}^X h_{i+1}s_i + h_i s_{i-1}d_i^P: P_i \to X_i$$ does the trick.
add comment
In the following [K] refers to the paper http://dml.cz/bitstream/handle/10338.dmlcz/120545/ActaOstrav_07-1999-1_3.pdf.
That a split exact complex of projectives $(P,d)$ is a projective object can be seen as follows:
1. $im(d_n)$ is projective since it is a direct summand of $P_{n-1}$
up vote 1 down vote 2. By When is an acylic chain complex contractible a split exact complex is contractible, so $P$ is contractible.
3. By [K], Lemma 4.4 a contractible complex (like $P$) is isomorphic to the mapping cone of the boundary subcomplex $$ \cdots \to im(d_{n+1}) \xrightarrow{0} im(d_n) \to \cdots$$
4. By [K], Theorem 3.1, the mapping cone of a complex of projectives with zero differentials is a projective object. Hence $P$ is a projective object by 1. and 3.
add comment
You can check out in Rotman's Book AIHA for a clear explanation, on the part of Cartan-Eilenberg resolutions.
up vote 1 down vote
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Not the answer you're looking for? Browse other questions tagged homological-algebra or ask your own question.
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Introduction to Difference Equations
This is a well-written and extremely leisurely introduction to difference equations that includes a wealth of simple applications in the social sciences. The book assumes only high-school algebra and
trigonometry as prerequisites. It includes numerous exercises; most of these are drill and are answered by a number or formula, but a few problems in each section explore more advanced concepts.
Answers to all problems are in the back of the book. The present publication is a corrected 1986 reprint of a 1958 work.
The book carefully develops all the mathematical background it needs, starting by introducing the concepts of functions and sequences, and proving all the theorems on sequences that would be covered
in a careful calculus course. The first major discussion covers the concepts and techniques of finite differences, leading to the observation that many common sequences satisfy simple difference
equations. The book then reverses its viewpoint to consider difference equations as the starting point, and proves the existence of sequences satisfying them. The existence theorems are handled in
great generality, but after this point the book deals mostly with linear difference equations with constant coefficients, and solves these by using powers of the roots of the auxiliary equation.
There is a very thorough treatment of the second-order cases, including the handling of repeated roots and the limiting behavior of solutions to the homogeneous equations (i.e., whether the solution
goes to infinity or a finite value, or is oscillatory). The last chapter covers some mathematically more advanced techniques such as stability, generating functions, and Markov processes, but does
not go very deeply into these.
The book’s big weakness is that the set of techniques it develops so carefully are not the ones that people use in everyday practice. Working mathematicians and engineers would nearly always use
generating functions to solve the types of problems handled here. Generating functions give a uniform treatment of these problems without dividing them into cases based on the roots of the auxiliary
equation and the properties of the non-homogeneous part of the equation. Generating functions can even be used in a cookbook fashion analogous to using Laplace transforms to solve differential
equations (because of this analogy, engineers use the term Z-transform for the process of forming the generating function). The present book covers these techniques on pp. 189–207, but because it
requires some knowledge of calculus it is an optional “starred” section and is not in the mainstream of the development.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical
Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.
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This unique application is for all students across the world. It covers 114 topics of Graph Theory in detail. These 114 topics are divided in 4 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to Graphs
2. Directed and Undirected Graph
3. Basic Terminologies of Graphs
4. Vertices
5. The Handshaking Lemma
6. Types of Graphs
7. N-cube
8. Subgraphs
9. Graph Isomorphism
10. Operations of Graphs
11. The Problem of Ramsay
12. Connected and Disconnected Graph
13. Walks Paths and Circuits
14. Eulerial Graphs
15. Fluery's Algorithm
16. Hamiltonian Graphs
17. Dirac's Theorem
18. Ore's Theorem
19. Problem of seating arrangement
20. Travelling Salesman Problem
21. Konigsberg's Bridge Problem
22. Representation of Graphs
23. Combinatorial and Geometric Graphs
24. Planer Graphs
25. Kuratowaski's Graph
26. Homeomorphic Graphs
27. Region
28. Subdivision Graphs and Inner vertex Sets
29. Outer Planer Graph
30. Bipertite Graph
31. Euler's Theorem
32. Three utility problem
33. Kuratowski’s Theorem
34. Detection of Planarity of a Graph
35. Dual of a Planer Graph
36. Graph Coloring
37. Chromatic Polynomial
38. Decomposition theorem
39. Scheduling Final Exams
40. Frequency assignments and Index registers
41. Colour Problem
42. Introduction to Tree
43. Spanning Tree
44. Rooted Tree
45. Binary Tree
46. Traversing Binary Trees
47. Counting Tree
48. Tree Traversal
49. Complete Binary Tree
50. Infix, Prefix and Postfix Notation of an Arithmatic Operation
51. Binary Search Tree
52. Storage Representation of Binary Tree
53. Algorithm for Constructing Spanning Trees
54. Trees and Sorting
55. Weighted Tree and Prefix Codes
56. Huffman Code
57. More Application of Graph
58. Shortest Path Algorithm
59. Dijkstra Algorithm
60. Minimal Spanning Tree
61. Prim’s algorithm
62. The labeling algorithm
63. Reachability, Distance and diameter, Cut vertex, cut set and bridge
64. Transport Networks
65. Max-Flow Min-Cut Theorem
66. Matching Theory
67. Hall's Marriage Theorem
68. Cut Vertex
69. Introduction to Matroids and Transversal Theory
70. Types of Matroid
71. Transversal Theory
72. Cut Set
73. Types of Enumeration
74. Labeled Graph
75. Counting Labeled tree
76. Rooted Lebeled Tree
77. Unlebeled Tree
78. Centroid
79. Permutation
80. Permutation Group
81. Equivalance classes of Function
82. Group
83. Symmetric Graph
84. Coverings
85. Vertex Covering
86. Lines and Points in graphs
87. Partitions and Factorization
88. Arboricity of Graphs
89. Digraphs
90. Orientation of a graph
91. Edges and Vertex
92. Types of Digraphs
93. Connected Digraphs
94. Condensation, Reachability and Oreintable Graph
95. Arborescence
96. Euler Digraph
97. Hand Shaking Dilemma and Directed Walk path and Circuit
98. Semi walk paths and Circuits and Tournaments
99. Incident, Circuit and Adjacency Matrix of Digraph
100. Nullity of a Matrix
101. Chromatic number
102. Calculating a Chromatic number
103. Brooks Theorem
104. Brooks Theorem
105. Matrix Representation of Graphs
106. Cut Matrix
107. Circuit Matrix
108. Matrices over GF(2) and Vector Spaces of Graphs
109. Introduction to Graph Coloring
110. Planar Graphs
111. Euler’s formula
112. Kruskal’s algorithm
113. Heuristic algorithm for an upper bound
114. Heuristic algorithm for an lower bound
This software helps you deal with your daily problems in which are involved graphs.From now on, you won't have to draw all your graphs on the paper, and struggling to apply some algorithms on them.
With Graph Theory you can manipulate all sorts of graphs directly from your mobile phone.
This application is also very useful for school children for a better understanding of graphs.
In the near future i will add new algorithms to it,but please click the adds, you would help me alot.
Graph 89 is an emulator for the TI-83, TI-83 Plus, TI-83 Plus Second Edition, TI-84 Plus, TI-84 Plus Second Edition, TI89, TI89 Titanium, TI92 Plus and Voyage 200 calculators.
*Please remember to read the ROM section below before downloading this application!
It will turn your phone or tablet into an exact replica of your calculator. The emulator will provide the same functionality and generate the same results as your real calculator. Being ported to
Android means that it will always fit in your pocket, have a backlight, be rechargeable and also run faster.
You would be able to install applications by copying the App file to the internal memory of your phone, pressing the 'Back' button and selecting 'Install Application/Send File'.
Graph89 would be great tool for math, science and engineering courses in high school, college and beyond. Some of these calculators feature Computer Algebra System (CAS) having the capability to
simplify and symbolically solve mathematical expressions.
Graph89 combines two powerful emulation engines which make it the only app in the Android Play Store to support the full range of TI graphing calculators.
1) TiEmu - http://lpg.ticalc.org/prj_tiemu providing support for the Motorola 68K family: TI89, TI89 Titanium, TI92 Plus, Voyage 200
2) TilEm - http://lpg.ticalc.org/prj_tilem providing support for the Z80 family: TI 83, TI 83+, TI 83+ SE, TI 84+, TI 84+ SE
!!! IMPORTANT !!!
Emulators are computer software which simulate a specific hardware. In order for the emulator to do anything useful it needs some software to run. The software that runs in your calculator (ROM) is
copyrighted by TI, and as such, it can not be distributed by Graph89 or any other emulator for that fact.
This means that you will have to provide the ROM file yourself by extracting it from your own calculator. Transfer it to your phone, and then tell Graph89 where to find it. To extract the ROM you can
follow the instructions from http://www.ticalc.org/programming/emulators/romdump.html and by using TiLPII from http://sourceforge.net/projects/tilp/files Google and youtube are also great sources of
tutorials and help.
Wabbitemu http://wabbit.codeplex.com/ is also a great tool for extracting the ROM from your TI83/TI84
Supported ROM files:
TI89, TI89 Titanium, TI92 Plus and Voyage 200:
*.rom, *.89u, *.v2u, *.9xu, *.tib
TI83 Plus, TI83 Plus SE, TI84 Plus and TI84 Plus SE:
*.rom, *.8Xu
Firmware updates (*.89u, 9xu, *.v2u, *.8Xu) which are normally used to restore the operating system of your calculator can also be used as a ROM image.
Needless to say, you will be very disappointed if you purchase Graph89 without having the ROM file ready. You will just see some instructions and a blank screen.
Graph89 needs permission to look at your Android Account in order to generate a unique ID shown under F1/About. This works only for TI89/V200. Note that there is no internet connection required for
this App.
TiEmu, TilEm and Graph89 have been developed independently of Texas Instruments and are not affiliated with TI.
Texas Instruments and TI are trademarks of Texas Instruments Incorporated.
Revision History:
An 8Xu (firmware update) file can now be used as a ROM for TI84+, TI84+SE, TI83+ and TI83+SE
Added support for: TI-83, TI-83 Plus, TI-83 Plus SE, TI-84 Plus and TI-84 Plus Second Edition using the TilEm2.00 engine.
Bug fixes on 'State Save' and 'Out of Memory' errors on some older phones.
Backup Manager
Dot Matrix LCD simulation
Click Screen to Zoom
Reset RAM
Landscape mode for TI89, TI89T
TI92+ skin
Bug fixes
Emulates Voyage 200 and TI92 Plus
Multiple calculator instances
Take screenshots
Generate an ID under F1/About
Sync clock
Acoustic feedback on keypress
Automatic overclock
Grayscale support
Send group files (*.89g, *.tig)
Receive files, (var-link/F4/F3/send)
Performance improvements
Customizable LCD colors
Input any function, and the app will draw graph for you.
You can input functions like sin, cos, inverse, log, exponential.
You can also input complex functions like - sin(x)/x and so on..
Features -
1. Draw maximum of 5 different graphs at a time.
2. You can find intersection point of two or more graphs as well.
3. Save graph in PNG file on your SD card
This app can be used by Students, Mathematicians, Physicists.
Keywords: graph, plot, x y axis, functions, intersection, maths, mathematics
Learn about linear graphs and vectors simply by just a swipe. Select graphs or vectors on intro page.
Find the relationship between lines, gradients, vectors and equations by drawing a graph with your finger while this app does the rest.
No input of values is necessary. This is an automatic graph app.
Math Graph app – you draw graph, it works out the equation for you.
Trace the graph with your finger. When done, sit back and
study your graph.
The app will draw the line and calculate gradient.
It will also write down the graph equation at bottom left of screen.
On vectors screen, you draw vectors with your finger, and this app analyzes them for you. It is an easy way to learn about simple vectors including addition of vectors.
This native math app is meant for beginners in graphical methods, the first 2 years of learning graphs.
If you have studied complex graphical methods but would still like to remind yourself about the basics, this app will do just that.
You can work with the equations produced at your leisure, re-arranging them to discover more about graphical maths.
The program allows draw functions graphs in specified area. The area is defined by the X min, X max, Y min, Y max values and division values for X and for Y. Functions are defined by the expression
string and color. You should click on function string in the table to edit it. Only "x" symbol should be used as a varible. After area and functions data input click "Redraw" button to draw it. On
phones graph is drawn on a full screen. Via the menu You can maximize graph on the full screen, get help about functions, about program, save the graph as a picture or sent e-mail with it (with help
of mail client app,such as gmail). The advertisement will be shown after the 5 redraws, and may be closed via the menu (or shown). And please, sometimes click advertisement - it may help for
SimpleGraph is useful application for all pupils and students. Ease interface will help you to build any graph in few seconds. Also you can build two graphics in one time.
Graph-X is a scientific tool computing 4 modes in one application: '
1) Scientific calculator: basic and advanced scientific calculations with many functions:
* General Arithmetic Functions
* Trigonometric Functions
* Power & Root Functions
* Log Functions
* Modulus Function
* Integer and Fractional parts Functions
It is able to report any kind of mathematical errors, like: 0^0 is undefined,
division by zero...
2) Graph Maker:
* multiple functions graphing
* precision control
* limits control
* scrollable and resizable graphs
* fullscreen graphs in landscape orientation
* function tables.
3) Converter: allows to convert all your favourite units in categories:
* Length
* Area
* Temperature
* Volume
* Weight
* Time.
It contains more than 200 units, including Biblical and Country-Specific Units and constants.
4) Currency: converts every world currency
* Stores the last updated rates
* Convert prices without internet access
Please read the help for more information.
For suggestions & bug reports:
Developer: Morosan Gabriel, e-mail: morosan.ag@gmail.com
Graphic designer: Morosan Maria, e-mail: me_mmg@yahoo.com
A 100% free course that gives you workouts & health tips to completely transform your body with no weights or equipment. The U20 goal is to teach you how to incinerate body fat and build lean muscle
with easy-to-follow 20 Minute Workouts.
Impossible? Think again.
What else can you do in 20 minutes that has such a lasting impact?
Ok, yeah, you can watch a sitcom or pick up dinner from a drive-thru.
However, will that help you live a longer, happier, healthier life?
This isn’t just a workout this is a lifestyle shift. Welcome to the future of home workout routines. We believe that the solution to building incredible health, melting body fat and creating an all
round better life is this: Stop doing things that don’t work - Do more things that work
Let's do this!
*YOU ARE GOING TO GET FROM THIS COURSE*
- Over 16 lectures and 1.5 hours of content!
- Free workout & nutrition videos updated every month
- Change your life - melt fat and build your body
- Learn how in just 20 minutes, 3 times per week you will get the body you deserve
- Find out about the secret fat burning foods available at your local store
- Hours of content, a lifetime of benefits
*WHAT YOU WILL LEARN*
SECTION 1: Why The Under 20 Works
SECTION 2: Start Here: 10 Minute Beginner's Workout
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SECTION 5: Unusual Nutrition and Weight Loss Videos - Stuff You Don't Know
- Lifetime access to 16 lectures
- A community of 3700+ people trying to learn the same thing!
- Watch courses on the go: video lectures, audio lectures, presentations, articles and anything inside your course.
- Watch courses in offline: Save courses for offline viewing so you can watch them while you're on a plane or subway!
* WHAT PEOPLE ARE SAYING ABOUT THIS COURSE*
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walls with quick energy bursts, crashing, and then getting back up and doing it again. Thanks for the great course Justin! Looking forward to more from Under 20."
- (Trainer Jack Wilson) ★★★★★
Instructed By: Justin O'Connor
Justin O’Connor has built his life around training. After years of 5-8 hour a week short term "burn-out" workouts leaving him injured, tired and the worst shape of his life, he dedicated himself to
finding a sustainable workout that everyone could succeed at and sustain forever.
Install the "Twenty Minute Workout" app today and join over 2,000,000 people who are already learning on Udemy.
A very simple and naive app for creating graphs. Use the bottom button to switch between vertex and edges.When in vertex mode you can add vertices and move them. When in edge mode you can create a
line from one vertex to another.
Some known issues:
* moving vertices does not move edges
* if you connect to a vertex that are already connected, edge counter will increment (will change this in future update)
Math Graph est un traceur de fonctions et de courbes paramétrées avec des équations sous forme cartésienne.
Les équations peuvent autant être de la forme "y=" que de la forme "x=".
La fonction racine carrée s'obtient à l'aide de "sqrt()", la valeur absolue avec "abs()" et la fonction exponentielle avec "e^x".
Les différentes équations sont à séparer par un point virgule dans le champ de saisie.
Voici quelques exemples :
Application implements some simple algorithms for nonoriented graphs, e.g. search of shortest way, search of graph frame, search of bridges and cutpoints and so on.
- Frame search in width
- Frame search in depth
- Shortest way search
- Connected components count
- Graph bridges
- Graph cutpoints
Program interface is accessible in two languages: english and russian.
LearnLight is a science app for visible light analysis. It allows you to compare two spectral image files to graph the intensity, transmittance, and absorbance of their visible light wavelengths.
Note!!!!!!: There is a startup crash in Android 4.4 I am looking at. Sorry for this, introduced by The system, so beyond my control. Looking for solutions.
Bug fix in version 1.5: Now all levels of Android should be able to use your own photos.
The intent of the app is for high school, college, or "lifelong" students to learn about visible light, spectrometry, spectroscopy, and spectrophotometry.
The iPad version, search the Apple App Store for LearnLight
This app was built by Dave Bomberg for flappit.com. It was inspired by, is designed to follow, the layout and educational materials developed by Dr. Alexander Scheeline at the University of Illinois.
Dr. Scheeline developed a Windows Desktop application and supporting materials called "A Guided Inquiry Approach to Teaching How to Think About Analytical Instrumentation". HIs work was featured on
Wired.com in an article titled: " In High School Chem Labs, Every Cameraphone Can Be a Spectrometer " His instructional materials (pdfs of teaching modules, student modules, Windows executables, and
more) are available for free download at: http://www.asdlib.org/onlineArticles/elabware/Scheeline_Kelly_Spectrophotometer/index.html
Please DO NOT email Dr. Scheeline regarding questions about the LearnLight application.
Questions about LearnLight are welcomed at: apps@flappit.com! There is also a list of FAQs and a discussion group at https://groups.google.com/forum/?fromgroups#!forum/learnlight
Instructions for how to build a photospectrometer with an LED light and diffraction grating, and materials for teachers and students are also linked in the apps HELP section. If you are unable to
build your own spectrometer, a few example spectral images are included with this app. Have fun and learn about spectrometry!
1. Import photos taken on the Android camera, or downloaded from email from any digital camera.
2. Crop, name, save images
3. Select any 2 images to compare
4. Set spectrum width and blue/red endpoints
5. Plot intensity of both sample and reference
6. Plot only reference intensity
7. Plot only sample intensity
8. Plot transmittance
9. Plot absorbance
10. Capture and save Screenshots of any plot
11. email spectrum images or screenshots
12. email csv files for Excel(or any other spreadsheet program)
GOOGLE GROUP at http://groups.google.com/group/learnlight
Brought to you by flappit.com, Copyright 2010, All Rights Reserved
The program allows draw functions graphs in specified area. The area is defined by the X min, X max, Y min, Y max values and division values for X and for Y. Functions are defined by the expression
string and color. You should click on function string in the table to edit it. Only "x" symbol should be used as a varible. After area and functions data input click "Redraw" button to draw it. Via
the menu You can maximize graph on the full screen, get help about functions, about program or get the full version. On phones graph is drawn on a full screen. In a full program version You may save
the graph as a picture or sent e-mail with it (full version is free, it includes the advertisement).
More from developer
This unique application is for all students across the world. It covers 280 topics of Electrical Instrumentation and Process Control in detail. These 280 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to AC Electricity
2. Circuits with R, L, and C
3. RC Filters
4. AC Bridges
5. Magnetic fields
6. Analog meter
7. Electromechanical devices
8. Introduction to Basic Electrical Components
9. Resistance
10. Capacitance
11. Inductance
12. Introduction to Electronics
13. Discrete amplifiers
14. Operational amplifiers
15. Current amplifiers
16. Differential amplifiers
17. Buffer amplifiers
18. Nonlinear amplifiers
19. Instrument amplifier
20. Amplifier applications
21. Digital Circuits
22. Digital signals & Binary numbers
23. Logic circuits
24. Analog-to-digital conversion
25. Circuit Considerations
26. Introduction to Process control
27. Process Control
28. Definitions of the Elements in a Control Loop
29. Process Facility Considerations
30. Units and Standards
31. Instrument Parameters
32. Introduction to Level
33. Level Formulas
34. Direct level sensing
35. Indirect level sensing
36. Application Considerations
37. Introduction to Pressure
38. Basic Terms
39. Pressure Measurement
40. Pressure Formulas
41. Manometers
42. Diaphragms, capsules, and bellows
43. Bourdon tubes
44. Other pressure sensors
45. Vacuum instruments
46. Application Considerations
47. Introduction to Actuators and Control
48. Pressure Controllers
49. Flow Control Actuators
50. Power Control
51. Magnetic control devices
52. Motors
53. Application Considerations
54. Introduction to flow
55. Flow Formulas of Continuity equation
56. Bernoulli equation
57. Flow losses
58. Flow Measurement Instruments of Flow rate
59. Total flow and Mass flow
60. Dry particulate flow rate and Open channel flow
61. Application Considerations
62. Humidity
63. Humidity measuring devices
64. Density and Specific Gravity
65. Density measuring devices
66. Viscosity
67. Viscosity measuring instruments
68. pH Measurements, pH measuring devices and pH application considerations
69. Position and Motion Sensing
70. Position and motion measuring devices
71. Force, Torque, and Load Cells
72. Force and torque measuring devices
73. Smoke and Chemical Sensors
74. Sound and Light
75. Sound and light measuring devices
76. Sound and light application considerations
77. Introduction to Signal Conditioning
78. Conditioning
79. Linearization
80. Temperature correction
81. Pneumatic Signal Conditioning
82. Visual Display Conditioning
83. Electrical Signal Conditioning
84. Strain gauge sensors
85. Capacitive sensors
86. Capacitive sensors
87. Magnetic sensors
88. Thermocouple sensors
89. Introduction to Temperature and Heat
90. Temperature definition
91. Heat definitions
92. Thermal expansion definitions
93. Temperature and Heat Formulas
94. Thermal expansion
95. Temperature Measuring Devices
96. Thermometers
97. Pressure-spring thermometers
98. Resistance temperature devices
99. Thermistors
100. Thermocouples
101. Semiconductors
102. Application Considerations
103. Installation, Calibration & Protection
104. System Documentation
105. Pipe and Identification Diagrams
106. Functional Symbols
107. P and ID Drawings
108. Introduction to Instrument types and performance characteristics
109. Active and passive instruments
110. Null-type and deflection-type instruments
111. Analogue and digital instruments
112. Indicating instruments and instruments with a signal output
All topics are not listed because of character limitations set by the Play Store.
!!!!!! Now upgraded Free app of Basic Electrical Engineering is available named Basic Electrical Engineering-1
This unique application is for all students across the world. It covers 108 topics of Basic Electrical in detail. These 108 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Few topics Covered in this application are:
1. Introduction of electrical engineering
2. Voltage and current
3. Electric Potential and Voltage
4. Conductors and Insulators
5. Conventional versus electron flow
6. Ohm's Law
7. Kirchoff's Voltage Law (KVL)
8. Kirchoff's Current Law (KCL)
9. Polarity of voltage drops
10. Branch current method
11. Mesh current method
12. Introduction to network theorems
13. Thevenin's Theorem
14. Norton's Theorem
15. Maximum Power Transfer Theorem
16. star-delta transformation
17. Source Transformation
18. voltage and current sources
19. loop and nodal methods of analysis
20. Unilateral and Bilateral elements
21. Active and passive elements
22. alternating current (AC)
23. AC Waveforms
24. The Average and Effective Value of an AC Waveform
25. RMS Value of an AC Waveform
26. Generation of Sinusoidal (AC) Voltage Waveform
27. Concept of Phasor
28. Phase Difference
29. The Cosine Waveform
30. Representation of Sinusoidal Signal by a Phasor
31. Phasor representation of Voltage and Current
32. AC inductor circuits
33. Series resistor-inductor circuits: Impedance
34. Inductor quirks
35. Review of Resistance, Reactance, and Impedance
36. Series R, L, and C
37. Parallel R, L, and C
38. Series-parallel R, L, and C
39. Susceptance and Admittance
40. Simple parallel (tank circuit) resonance
41. Simple series resonance
42. Power in AC Circuits
43. Power Factor
44. Power Factor Correction
45. Quality Factor and Bandwidth of a Resonant Circuit
46. Generation of Three-phase Balanced Voltages
47. Three-Phase, Four-Wire System
48. Wye and delta configurations
49. Distinction between line and phase voltages, and line and phase currents
50. Power in balanced three-phase circuits
51. Phase rotation
52. Three-phase Y and Delta configurations
53. Measurement of Power in Three phase circuit
54. Introduction of measuring instruments
55. Various forces/torques required in measuring instruments
56. General Theory Permanent Magnet Moving Coil (PMMC) Instruments
57. Working Principles of PMMC
58. A multi-range ammeters
59. Multi-range voltmeter
60. Basic principle operation of Moving-iron Instruments
61. Construction of Moving-iron Instruments
62. Shunts and Multipliers for MI instruments
63. Dynamometer type Wattmeter
64. Introduction to Power System
66. Magnetic Circuit
67. B-H Characteristics
68. Analysis of Series magnetic circuit
69. Analysis of series-parallel magnetic circuit
70. Different laws for calculating magnetic field-Biot-Savart law
71. Amperes circuital law
72. Reluctance & permeance
73. Introduction of Eddy Current & Hysteresis Losses
74. Eddy current
75. Derivation of an expression for eddy current loss in a thin plate
76. Hysteresis Loss
77. Hysteresis loss & loop area
78. Steinmetzs empirical formula for hysteresis loss
79. Inductor
80. Force between two opposite faces of the core across an air gap
81. ideal transformer
82. Practical transformer
83. equivalent circuit
84. Efficiency of transformer
85. Auto-Transformer
86. Introduction of D.C Machines
87. D.C machine Armature Winding
88. EMF Equation
89. Torque equation
90. Generator types & Characteristics
91. Characteristics of a separately excited generator
92. Characteristics of a shunt generator
93. Load characteristic of shunt generator
94. Single-phase Induction Motor
All topics are not listed because of character limitations set by the Play Store.
This unique Free application is for all students across the world. It covers 108 topics of Basic Electrical in detail. These 108 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Few topics Covered in this application are:
1. Introduction of electrical engineering
2. Voltage and current
3. Electric Potential and Voltage
4. Conductors and Insulators
5. Conventional versus electron flow
6. Ohm's Law
7. Kirchoff's Voltage Law (KVL)
8. Kirchoff's Current Law (KCL)
9. Polarity of voltage drops
10. Branch current method
11. Mesh current method
12. Introduction to network theorems
13. Thevenin's Theorem
14. Norton's Theorem
15. Maximum Power Transfer Theorem
16. star-delta transformation
17. Source Transformation
18. voltage and current sources
19. loop and nodal methods of analysis
20. Unilateral and Bilateral elements
21. Active and passive elements
22. alternating current (AC)
23. AC Waveforms
24. The Average and Effective Value of an AC Waveform
25. RMS Value of an AC Waveform
26. Generation of Sinusoidal (AC) Voltage Waveform
27. Concept of Phasor
28. Phase Difference
29. The Cosine Waveform
30. Representation of Sinusoidal Signal by a Phasor
31. Phasor representation of Voltage and Current
32. AC inductor circuits
33. Series resistor-inductor circuits: Impedance
34. Inductor quirks
35. Review of Resistance, Reactance, and Impedance
36. Series R, L, and C
37. Parallel R, L, and C
38. Series-parallel R, L, and C
39. Susceptance and Admittance
40. Simple parallel (tank circuit) resonance
41. Simple series resonance
42. Power in AC Circuits
43. Power Factor
44. Power Factor Correction
45. Quality Factor and Bandwidth of a Resonant Circuit
46. Generation of Three-phase Balanced Voltages
47. Three-Phase, Four-Wire System
48. Wye and delta configurations
49. Distinction between line and phase voltages, and line and phase currents
50. Power in balanced three-phase circuits
51. Phase rotation
52. Three-phase Y and Delta configurations
53. Measurement of Power in Three phase circuit
54. Introduction of measuring instruments
55. Various forces/torques required in measuring instruments
56. General Theory Permanent Magnet Moving Coil (PMMC) Instruments
57. Working Principles of PMMC
58. A multi-range ammeters
59. Multi-range voltmeter
60. Basic principle operation of Moving-iron Instruments
61. Construction of Moving-iron Instruments
62. Shunts and Multipliers for MI instruments
63. Dynamometer type Wattmeter
64. Introduction to Power System
66. Magnetic Circuit
67. B-H Characteristics
68. Analysis of Series magnetic circuit
69. Analysis of series-parallel magnetic circuit
70. Different laws for calculating magnetic field-Biot-Savart law
71. Amperes circuital law
72. Reluctance & permeance
73. Introduction of Eddy Current & Hysteresis Losses
74. Eddy current
75. Derivation of an expression for eddy current loss in a thin plate
76. Hysteresis Loss
77. Hysteresis loss & loop area
78. Steinmetzs empirical formula for hysteresis loss
79. Inductor
80. Force between two opposite faces of the core across an air gap
81. ideal transformer
82. Practical transformer
83. equivalent circuit
84. Efficiency of transformer
85. Auto-Transformer
86. Introduction of D.C Machines
87. D.C machine Armature Winding
88. EMF Equation
89. Torque equation
90. Generator types & Characteristics
91. Characteristics of a separately excited generator
92. Characteristics of a shunt generator
93. Load characteristic of shunt generator
94. Single-phase Induction Motor
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 143 topics of Refrigeration and AirConditioning in detail. These 143 topics are divided in 4 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
5. DESIGN DOCUMENTS
7. PSYCHROMETRICS (MOIST AIR)
9. PSYCHROMETRICS (SPECIFIC HEAT)
10. PSYCHROMETRIC CHART
11. DETERMINING THE DEW-POINT TEMPERATURE OF A MOIST AIR SAMPLE
20. BASIC AIR-CONDITIONING CYCLE - SUMMER MODE
21. DESIGN SUPPLY VOLUME FLOW RATE
22. BASIC AIR-CONDITIONING CYCLE - WINTER MODE
24. REFRIGERANTS, COOLING MEDIUMS, AND ABSORBENTS
34. INDOOR TEMPERATURE, RELATIVE HUMIDITY, AND AIR VELOCITY
36. CONVECTIVE HEAT AND RADIATIVE HEAT
37. AIR HANDLING UNITS AND PACKAGED UNITS
38. PACKAGED UNITS
39. COILS USED IN REFRIGERATION
40. AIR FILTERS
43. ROTARY/ SCREW COMPRESSORS
45. AIR-COOLED CONDENSERS
49. EVAPORATIVE COOLING
52. AIR CONDITIONING SYSTEMS
54. GAS CYCLE REFRIGERATION
55. STEAM JET REFRIGERATION SYSTEM
59. ROTARY/ SCREW COMPRESSORS
65. HEAT AND WORK
68. FIRST LAW OF THERMODYNAMICS
69. SECOND LAW OF THERMODYNAMICS
70. HEAT ENGINES
71. EFFICIENCY OF HEAT ENGINES
72. ENTROPY
73. THIRD LAW OF THERMODYNAMICS
76. PROPERTIES OF PURE SUBSTANCE
77. T-S AND P-H DIAGRAMS FOR LIQUID-VAPOUR REGIME
81. THROTTLING (ISENTHALPIC) PROCESS
82. FLUID FLOW IN REFRIGERATION
83. CONSERVATION OF MOMENTUM
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 97 topics of Basic Electronics in detail. These 97 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to Electronic Engineering
2. Basic quantities
3. Passive and active devices
4. Semiconductor Devices
5. Current in Semiconductors
6. P-N Junction
7. Diodes
8. Power Diode
9. Switching
10. Special-Purpose Diodes
11. Tunnel diode and Optoelectronics
12. Diode Approximation
13. Applications of diode: Half wave Rectifier and Full Wave Rectifier
14. Bridge Rectifier
15. Clippers
16. Clamper Circuits
17. Positive Clamper
18. Voltage Doubler
19. Zener Diode
20. Zener Regulator
21. Design of Zener regulator circuit
22. Special-Purpose Diodes-1
23. Transistors
24. Bipolar Junction Transistors (BJT)
25. Beta and alpha gains
26. The Common Base Configuration
27. Relation between different currents in a transistor
28. Common-Emitter Amplifier
29. Common Base Amplifier
30. Biasing Techniques for CE Amplifiers
31. Biasing Techniques: Emitter Feedback Bias
32. Biasing Techniques: Collector Feedback Bias
33. Biasing Techniques: Voltage Divider Bias
34. Biasing Techniques: Emitter Bias
35. Small Signal CE Amplifiers
36. Analysis of CE amplifier
37. Common Collector Amplifier
38. Darlington Amplifier
39. Analysis of a transistor amplifier using h-parameters
40. Power Amplifiers
41. Power Amplifiers: Class A Amplifiers
42. Power Amplifiers: Class B amplifier
43. Power Amplifiers: Cross over distortion(Class B amplifier)
44. Power Amplifiers: Biasing a class B amplifier
45. Power Calculations for Class B Push-Pull Amplifier
46. Power Amplifiers: Class C amplifier
47. Field Effect Transistor (FET)
48. JFET Amplifiers
49. Transductance Curves
50. Biasing the FET
51. Biasing the FET: Self Bias
52. Voltage Divider Bias
53. Current Source Bias
54. FET a amplifier
55. Design of JFET amplifier
56. JFET Applications
57. MOSFET Amplifiers
58. Common-Drain Amplifier
59. MOSFET Applications
60. Operational Amplifiers
61. Depletion-mode MOSFET
62. Enhancement-mode MOSFET
63. The ideal operational amplifier
64. Practical OP AMPS
65. Inverting Amplifier
66. The Non-inverting Amplifier
67. Voltage Follower (Unity Gain Buffer)
68. The Summing Amplifier
69. Differential Amplifier
70. The Op-amp Integrator Amplifier
71. The Op-amp Differentiator Amplifier
72. History of The Numeral Systems
73. Binary codes
74. conversion of bases
75. Conversion of decimal to binary ( base 10 to base 2)
76. Octal Number System
77. Hexadecimal Number System
78. Rules of Binary Addition and Subtraction
79. Sign-and-magnitude method
80. Sign-and-magnitude method:2s complement Representation
81. Boolean algebra
82. Basic Theorems & Properties of Boolean algebra
83. Logic gate
84. Symbols of logic Gates
85. Universal Gates
86. No associativity of NAND and NOR Gates: universal gates
87. Introduction of minimization using K-map
88. Two variable maps
89. Don't Cares condition
90. 5 variable Karnaugh Maps
91. Binary coded decimal codes(bcd)
92. Principle and types digital instruments
93. digital voltmeter
94. Cathode ray oscilloscope(CRO)
95. Cathode ray tube: CRO
96. Channel: CRO
97. Measurements with the cathode ray oscilloscope C
All topics not listed due to character limitations set by Google Play.
This ultimate unique application has more than 300,000+ topics of engineering covered across five major engineering disciplines - Electronics & Communication, Electrical, Mechanical, Civil and
Computer Science Engineering. With the unique integration with the online version of this application, users can access their saved notes from any where. The USP of this application is
ultra-portability of your engineering education.
All topics are neatly arranged under subjects and units. Users can also use the search option to find any topic of relevance within 2 clicks!
Each topic is not more than 600 words and is complete with equations, diagrams and functional graphs.
The content is more than enough to study and clear any engineering examination held by most Indian Engineering Colleges & Universities.
Go-Ahead! Download it & Make your Studies Simpler and Easier!!
This ultimate unique application is for all students of Automobile Engineering across the world. It covers 188 topics of Automobile Engineering in detail. These 188 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from any where they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
2. The expansion valve system
3. THE FIXED ORIFICE VALVE SYSTEM (CYCLING CLUTCH ORIFICE TUBE)
4. THE COMPRESSOR
5. THE CONDENSER
6. THE CONDENSER
9. THE EVAPORATOR
10. ANTI-FROSTING DEVICES
11. BASIC CONTROL SWITCHES
12. THE BASIC THEORY OF COOLING
14. ALTERNATIVES CYCLES
17. PRESSURE GAUGE READINGS
18. CYCLE TIME TESTING
19. A/C SYSTEM LEAK TESTING
20. SIGHT GLASS
21. GLOBAL WARMING
22. THE OZONE LAYER
23. INTRODUCTION TO TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
26. TYPES OF AUTOMOBILES
27. LAYOUT OF AN AUTOMOBILE CHASSIS
28. MAJOR COMPONENTS OF AN AUTOMOBILE
31. USE OF THE ENGINES
36. ADVANTAGES OF A MULTI-CYLINDER ENGINE FOR THE SAME POWER
37. ENGINE CONSTRUCTION
38. CYLINDER BLOCKS
39. CYLINDER LINER
40. CRANK CASE
41. CYLINDER HEAD
42. GASKETS
43. PISTON
44. PISTON RINGS
45. PISTON PIN
46. CONNECTING ROD
47. CRANKSHAFT
48. VALVES
49. PORT-TIMING DIAGRAM
50. FLYWHEEL
51. MANIFOLDS
52. ROLLING RESISTANCE
53. AIR RESISTANCE.
54. GRADIENT RESISTANCE
55. TRACTIVE EFFORT
56. GEAR BOX
57. TYPES OF THE GEAR BOX
58. MERITS AND DEMERITS OF GEAR BOX
59. GEAR SHIFTING MECHANISM
60. Transmission in Automobile
62. FUNCTION OF CLUTCH
63. MAIN PARTS OF CLUTCH
64. TYPES OF THE CLUTCH
65. UNIVERSAL JOINT
67. FUNCTION OF STEERING SYSTEM
68. FRONT AXLE
69. CASTER ANGLE
70. CASTER ANGLE
71. CAMBER
72. TOE-IN
73. TOE-OUT
74. ACKERMAN MECHANISM
75. FUNCTIONS OF A BRAKE
76. CLASSIFICATION OF BRAKES
77. DISC BRAKES
78. FLOATING CALIPER BRAKE
79. POWER BRAKES
80. AIR BRAKE SYSTEM
81. HYDRAULIC BRAKES
82. TYPES OF THE STARTING MOTORS
83. GENERATOR
84. ALTERNATOR
85. LIGHTING SYSTEM
86. IGNITION SYSTEM
87. IGNITION TIMING
88. IGNITION ADVANCE
89. SPARK PLUGS
91. AUTOMOBILE BATTERY
93. HORNS
94. CLUTCH OPERATION
95. Types of clutch
96. Gearbox operation
97. Gear change mechanisms
98. Gears and components
102. DIRECT SHIFT GEARBOX
104. WHEEL BEARINGS
105. FOUR-WHEEL DRIVE
106. TIRE DESIGN
107. TIRE PLY AND BELT DESIGN
108. Tire Tread Design
109. TIRE RATINGS AND SIDEWALL INFORMATION
110. SPECIALTY TIRES
111. REPLACEMENT TIRES
112. Tire Valves
113. COMPACT SPARE TIRES
114. Run-Flat Tires
115. Tire Pressure Monitoring Systems
116. TIRE CONTACT AREA
117. Wheel Rims
118. Static Wheel Balance Theory
119. Dynamic Wheel Balance Theory
120. On-Car Wheel Balancing
This ultimate unique application is for all students across the world. It covers 113 topics of Discrete Mathematics in detail. These 113 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Set Theory
2. Decimal number System
3. Binary Number System
4. Octal Number System
5. Hexadecimal Number System
6. Binary Arithmetic
7. Sets and Membership
8. Subsets
9. Introduction to Logical Operations
10. Logical Operations and Logical Connectivity
11. Logical Equivalence
12. Logical Implications
13. Normal Forms and Truth Table
14. Normal Form of a well formed formula
15. Principle Disjunctive Normal Form
16. Principal Conjunctive Normal form
17. Predicates and Quantifiers
18. Theory of inference for the Predicate Calculus
19. Mathematical Induction
20. Diagrammatic Representation of Sets
21. The Algebra of Sets
22. The Computer Representation of Sets
23. Relations
24. Representation of Relations
25. Introduction to Partial Order Relations
26. Diagrammatic Representation of Partial Order Relations and Posets
27. Maximal, Minimal Elements and Lattices
28. Recurrence Relation
29. Formulation of Recurrence Relation
30. Method of Solving Recurrence Relation
31. Method for solving linear homogeneous recurrence relations with constant coefficients:
32. Functions
33. Introduction to Graphs
34. Directed Graph
35. Graph Models
36. Graph Terminology
37. Some Special Simple Graphs
38. Bipartite Graphs
39. Bipartite Graphs and Matchings
40. Applications of Graphs
41. Original and Sub Graphs
42. Representing Graphs
43. Adjacency Matrices
44. Incidence Matrices
45. Isomorphism of Graphs
46. Paths in the Graphs
47. Connectedness in Undirected Graphs
48. Connectivity of Graphs
49. Paths and Isomorphism
50. Euler Paths and Circuits
51. Hamilton Paths and Circuits
52. Shortest-Path Problems
53. A Shortest-Path Algorithm (Dijkstra Algorithm.)
54. The Traveling Salesperson Problem
55. Introduction to Planer Graphs
56. Graph Coloring
57. Applications of Graph Colorings
58. Introduction to Trees
59. Rooted Trees
60. Trees as Models
61. Properties of Trees
62. Applications of Trees
63. Decision Trees
64. Prefix Codes
65. Huffman Coding
66. Game Trees
67. Tree Traversal
68. Boolean Algebra
69. Identities of Boolean Algebra
70. Duality
71. The Abstract Definition of a Boolean Algebra
72. Representing Boolean Functions
73. Logic Gates
74. Minimization of Circuits
75. Karnaugh Maps
76. Dont Care Conditions
77. The Quine MCCluskey Method
78. Introduction to Lattices
79. The Transitive Closure of a Relation
80. Cartesian Product of Lattices
81. Properties of Lattices
82. Lattices as Algebraic System
83. Partial Order Relations on a Lattice
84. Least Upper Bounds and Latest Lower Bounds in a Lattice
85. Sublattices
86. Lattice Isomorphism
87. Bounded, Complemented and Distributive Lattices
88. Propositional Logic
89. Conditional Statements
90. Truth Tables of Compound Propositions
91. Precedence of Logical Operators and Logic and Bit Operations
92. Applications of Propositional Logic
93. Propositional Satisfiability
94. Quantifiers
95. Nested Quantifiers
96. Translating from Nested Quantifiers into English
97. Inference
98. Rules of Inference for Propositional Logic
99. Using Rules of Inference to Build Arguments
100. Resolution and Fallacies
101. Rules of Inference for Quantified Statements
102. Introduction to Algebra
103. Rings
104. Properties of rings
105. Subrings
106. Homomorphisms and quotient rings
107. Groups
108. Properties of groups
109. Subgroups
All topics not listed due to character limitations set by Google Play.
This unique application is for all students across the world. It covers 143 topics of Material Science in detail. These 143 topics are divided in 3 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. Classification of engineering materials
4. Organic and inorganic materials
5. Semiconductors
6. Biomaterials
8. Advanced materials
9. Smart materials (materials of the future)
10. Nanostructured materials and nanotechnology
11. Quantum dots
12. Spintronics
13. Level of material structure examination and observation
14. Material structure
15. Engineering metallurgy
16. Selection of the materials
17. Atomic concepts in physics and chemistry
18. Atomic Structure: FUNDAMENTAL CONCEPTS
19. Atomic Structure: FUNDAMENTAL CONCEPTS
20. ELECTRONS IN ATOMS
21. THE PERIODIC TABLE
22. BONDING FORCES AND ENERGIES
23. Ionic Bonding
24. Covalent Bonding
25. Metallic Bonding
26. SECONDARY BONDING OR VAN DER WAALS BONDING
27. Crystal Structures: FUNDAMENTAL CONCEPTS
28. The Face-Centered Cubic Crystal Structure
29. The Body-Centered Cubic Crystal Structure
30. The Hexagonal Close-Packed Crystal Structure
32. CRYSTAL SYSTEMS
33. POINT COORDINATES
35. Hexagonal Crystals
36. Atomic Arrangements
39. IMPURITIES IN SOLIDS
40. DISLOCATIONS - LINEAR DEFECTS
41. INTERFACIAL DEFECTS
42. Microscopic Examination
43. Optical Microscopy
44. Electron Microscopy
45. GRAIN SIZE DETERMINATION
46. Introduction to mechanical properties
47. CONCEPTS OF STRESS AND STRAIN
48. Compression Tests
49. STRESS-STRAIN BEHAVIOR
50. ANELASTICITY
52. Plastic Deformation
53. Yielding and Yield Strength
54. Tensile Strength
55. Ductility
56. Resilience
57. Toughness
58. TRUE STRESS AND STRAIN
60. HARDNESS
61. Rockwell Hardness Tests
62. Brinell Hardness Tests
63. Knoop and Vickers Microindentation Hardness Tests
64. Hardness Conversion
65. Correlation Between Hardness and Tensile Strength
67. Computation of Average and Standard Deviation Values
68. DESIGN/SAFETY FACTORS
69. Phase diagrams-introduction
70. SOLUBILITY LIMIT
71. PHASES
72. PHASE EQUILIBRIA
73. ONE-COMPONENT (OR UNARY) PHASE DIAGRAMS
74. Binary Phase Diagrams
76. Determination of Phase Compositions
77. Determination of Phase Amounts
78. Equilibrium Cooling
79. Nonequilibrium Cooling
81. BINARY EUTECTIC SYSTEMS
86. THE GIBBS PHASE RULE
87. THE IRON-IRON CARBIDE (Fe-Fe3C) PHASE DIAGRAM
89. Hypoeutectoid Alloys
90. Hypereutectoid Alloys
91. THE INFLUENCE OF OTHER ALLOYING ELEMENTS
92. FERROUS ALLOYS
93. Low-Carbon Steels
94. Medium-Carbon Steels
95. High-Carbon Steels
96. Stainless Steels
97. Cast Irons
98. Gray Iron
99. Ductile (or Nodular) Iron
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 86 topics of Engineering Geology in detail. These 86 topics are divided in 6 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
4. Geological Materials
5. Description of Geological materials
6. Porosity and Permeability
7. Deformation
10. BRANCHES OF GEOLOGY
11. INTRODUCTION TO SOILS
12. INTRODUCTION TO ROCKS
13. GEOLOGICAL MASSES
14. Standard Weathering Description Systems
15. Ground Mass Description
16. Rock Mass Classification
17. SCHISTS AND GNEISSES
18. GEOLOGICAL MAPS
19. Understanding Geological Maps
20. Interpretation of Geological Maps
21. DRILLING TOOLS
22. MAPPING AT SMALL SCALE
23. MAPPING AT LARGE SCALE
24. Engineering Geological Maps
25. GIS in Engineering Geology
27. DRILLING PROCESS
28. DRILLING AND SAMPLING IN SOIL
29. Boring and Sampling over Water
30. Field Tests and Measurements
31. Strength and Deformation Tests
32. Measurements in Boreholes and Excavations
33. Engineering Geophysics
34. Properties of Minerals
35. ROCK-FORMING MINERALS
36. FELDSPAR - FAMILY
37. Quartz family
38. The Mineral AUGITE
39. Rhyolite Family
40. Fundamentals of process of formation of ore minerals
41. COAL AND PETROLEUM
42. Coal- Its origin and occurrence in India
43. Phyllite
44. GARNET AND MISCELLANEOUS ROCKS
45. Classification of Rocks
46. Difference Between Igneous, Sedimentary and Metamorphic Rocks
47. MAGMA
48. Gabbro(rock)
49. PEGMATITE
50. Igneous rock types
51. LIMESTONE
52. Metamorphic Rocks
53. GRANITE
54. Syenite
55. Larvikite,ijolite and Carbonatite
56. Phonolite, Ultramafic Rocks and Pyroxenite
57. Conglomerate and breccia
58. METAMORPHIC ROCKS
59. SLATE
60. Beds in 3D space
61. Strike and Dip
62. Inclined Bedding on Maps
63. FOLDS
64. FAULTS
65. JOINTS
66. Seismic Surveys
67. Electrical Resistivity Surveys
68. Electromagnetic Conductivity Surveys
69. Magnetic Surveys
70. REMOTE SENSING TECHNIQUES
71. Aerial Photographs
72. Satellite Images
73. Design and Construction of Road Tunnels
74. Factors that Influence Tunnel Seismic Performance
75. PREVENTIONS OF DAM CONSTUCTION
76. Sea erosion and coastal Protection
77. Internal Structure of the Earth
78. Building stones occurrences and characteristics
79. Origin of Sedimentary Rock
80. Earthquakes
81. causes of Earthquakes
82. Classification of Earthquake
83. Classification of Seismic Waves
84. Fault Types
85. Seismic Zones of India
86. Construction of Earthquake Resistant Buildings and Infrastructure
This ultimate application is useful for all students of Artificial Intelligence across the world. It covers 142 topics of Artificial Intelligence in detail. These 142 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
The USP of this application is "ultra-portability". Students can access the content on-the-go from any where they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Turing test
2. Introduction to Artificial Intelligence
3. History of AI
4. The AI Cycle
5. Knowledge Representation
6. Typical AI problems
7. Limits of AI
8. Introduction to Agents
9. Agent Performance
10. Intelligent Agents
11. Structure Of Intelligent Agents
12. Types of agent program
13. Goal based Agents
14. Utility-based agents
15. Agents and environments
16. Agent architectures
17. Search for Solutions
18. State Spaces
19. Graph Searching
20. A Generic Searching Algorithm
21. Uninformed Search Strategies
22. Breadth-First Search
23. Heuristic Search
24. A∗ Search
25. Search Tree
26. Depth first Search
27. Properties of Depth First Search
28. Bi-directional search
29. Search Graphs
30. Informed Search Strategies
31. Methods of Informed Search
32. Greedy Search
33. Proof of Admissibility of A*
34. Properties of Heuristics
35. Iterative-Deepening A*
36. Other Memory limited heuristic search
37. N-Queens eample
38. Adversarial Search
39. Genetic Algorithms
40. Games
41. Optimal decisions in Games
42. minimax algorithm
43. Alpha Beta Pruning
44. Backtracking
45. Consistency Driven Techniques
46. Path Consistency (K-Consistency)
47. Look Ahead
48. Propositional Logic
49. Syntax of Propositional Calculus
50. Knowledge Representation and Reasoning
51. Propositional Logic Inference
52. Propositional Definite Clauses
53. Knowledge-Level Debugging
54. Rules of Inference
55. Soundness and Completeness
56. First Order Logic
57. Unification
58. Semantics
59. Herbrand Universe
60. Soundness, Completeness, Consistency, Satisfiability
61. Resolution
62. Herbrand Revisited
63. Proof as Search
64. Some Proof Strategies
65. Non-Monotonic Reasoning
66. Truth Maintenance Systems
67. Rule Based Systems
68. Pure Prolog
69. Forward chaining
70. backward Chaining
71. Choice between forward and backward chaining
72. AND/OR Trees
73. Hidden Markov Model
74. Bayesian networks
75. Learning Issues
76. Supervised Learning
77. Decision Trees
78. Knowledge Representation Formalisms
79. Semantic Networks
80. Inference in a Semantic Net
81. Extending Semantic Nets
82. Frames
83. Slots as Objects
84. Interpreting frames
85. Introduction to Planning
86. Problem Solving vs. Planning
87. Logic Based Planning
88. Planning Systems
89. Planning as Search
90. Situation-Space Planning Algorithms
91. Partial-Order Planning
92. Plan-Space Planning Algorithms
93. Interleaving vs. Non-Interleaving of Sub-Plan Steps
94. Simple Sock/Shoe Example
95. Probabilistic Reasoning
96. Review of Probability Theory
97. Semantics of Bayesian Networks
98. Introduction to Learning
99. Taxonomy of Learning Systems
100. Mathematical formulation of the inductive learning problem
101. Concept Learning
102. Concept Learning as Search
103. Algorithm to Find a Maximally-Specific Hypothesis
104. Candidate Elimination Algorithm
105. The Candidate-Elimination Algorithm
106. Decision Tree Construction
107. Splitting Functions
108. Decision Tree Pruning
109. Neural Networks
110. Artificial Neural Networks
111. Perceptron
112. Perceptron Learning
113. Multi-Layer Perceptrons
114. Back-Propagation Algorithm
115. Statistical learning
All topics not listed here because of character limit set by Play Store
This unique application is for all students across the world. It covers 157 topics of Strength Of Materials in detail. These 157 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. TENSILE STRESS
3. SHEAR STRESS
6. SHEAR STRAIN
8. TENSILE STRAIN
9. STRESS STRAIN DIAGRAM
10. THERMAL STRESS
11. POISSON RATIO
12. THREE MODULUS
13. Temperature Stress In Composite Bar
14. STRAIN ENERGY
15. MODULUS OF RESSILINCE AND TOUGHNESS
16. STRAIN ENERGY IN GRADUAL AND SUDDEN LOAD
17. STRAIN ENERGY IN IMPACT LOAD
18. HOOK'S LAW
19. STRESS, STRAIN AND CHANGE IN LENGTH
20. CHANGE IN LENGTH WHEN ONE BOTH ENDS ARE FREE
21. CHANGE IN LENGTH WHEN ONE BOTH ENDS ARE FIXED
22. Composite bar in tension or compression
23. Principal Stress And Principal Plane
24. Maximum Shear Stress
25. Theories Of Elastic Failure
26. Maximum Principal Stress Theory
27. Maximum Shear Stress Theory:
28. Maximum Principal Strain Theory
29. Total Strain Energy Per Unit Volume Theory
30. Maximum Shear Strain Energy Per Unit Volume Theory
31. Mohr’s Rupture Theory For Brittle Materials
32. Mohr’s Circle
33. Introduction to Bending Moment And Shearing Force
34. Shearing Force, And Bending Moment In A Straight Beam
35. Sign Conventions For Bending Moments And Shearing Forces
36. Bending Of Beams
37. Procedure For Drawing Shear Force And Bending Moment Diagram
38. SFD & BMD Of Cantilever Carrying Load At Its One End
39. SFD And BMD Of Simply Supported Beam Subjected To A Central Load
40. SFD And BMD Of A Cantilever Beam Subjected To U.D.L
41. Simply Supported Beam Subjected To U.D.L
42. Simply Supported Beam Carrying UDL & End Couples
43. Points Of Inflection
44. Theory Of Bending : Assumption And General Theory
45. Elastic Flexure Formula
46. Beams Of Composite Cross Section
47. Flexural Buckling Of A Pin-Ended Strut
48. Rankine-Gordon Formula
49. Comparison Of The Rankine-Gordon And Euler Formulae
50. Effective Lengths Of Struts
51. Struts And Columns With One End Fixed And The Other Free
52. Thin Cylinder
53. Members Subjected to Axisymmetric Load
54. ANALYSIS: Pressurized thin walled cylinder
55. Longitudinal Stress: Pressurized thin walled cylinder
56. Change in Dimensions: Pressurized thin walled cylinder
57. Volumetric Strain or Change in the Internal Volume
58. Cylindrical Vessel with Hemispherical Ends
59. Thin rotating ring or cylinder
60. Stresses in thick cylinders
61. Stresses in thick cylinders
62. Representation of radial and circumferential strain
63. A thick cylinder with both external and internal pressure
64. The stress distribution within the cylinder wall
65. Methods of increasing the elastic strength of a thick cylinder by pre-stressing
66. Composite cylinders
67. Combined stress distribution in a composite cylinder
68. Multilayered or Laminated cylinder
69. Autofrettage
70. Derivation of the hoop and radial stress equations for a thickwalled circular cylinder
71. Lame line
72. Plastic deformation of thick tubes
73. Lame line for elastic zone
74. Portion of the cylinder is plastic
75. Stress in thin cylinders
76. Horizontal diametrical plane
77. Strains in thin cylinders
78. Change in Volume of Cylinder
79. Compound Cylinders
80. Press Fits
81. Analysis of Press Fits
82. Castigliano's first theorem
83. Castigliano’s Second Theorem
84. Torsion of a thin circular tube
85. Torsion of solid circular shafts
86. Torsion of a hollow circular shaft
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 217 topics of Advanced Welding Technology in detail. These 217 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. WELDING WITH PRESSURE
4. FUSION WELDING
10. INTRODUCTION TO HEAT FLOW IN FUSION WELDING
12. PARAMETRIC EFFECTS OF HEAT FLOW IN FUSION WELDING
15. GAS TUNGSTEN ARC WELDING
17. GAS METAL ARC WELDING
18. Submerged Arc Welding
19. INTRODUCTION TO TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
20. HEAT TRANSFER IN GAS-METAL ARC WELDING
21. PROCEDURE DEVELOPMENT TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
22. INTRODUCTION TO ARC PHYSICS OF GAS-TUNGSTEN ARC WELDING
23. ELECTRODE REGIONS AND ARC COLUMN IN GTAW
24. ARC WELDING POWER SOURCES
25. POWER SOURCE SELECTION
26. PULSED POWER SUPPLIES
27. Resistance Welding Power Sources
28. ELECTRON-BEAM WELDING POWER SOURCES
33. EFFECT OF WELDING RATE ON WELD POOL SHAPE AND MICROSTRUCTURE
34. BRAZING
35. SOLDERING
36. PHYSICAL PRINCIPLES OF BRAZING
37. ELEMENTS OF THE BRAZING PROCESS
38. HEATING METHODS FOR BRAZING
40. FUNDAMENTALS OF SOLDERING
41. GUIDELINES FOR FLUX SELECTION
42. TYPES OF FLUXES
43. JOINT DESIGN
45. SOLDER APPLICATION
47. SOLDERING EQUIPMENT
49. SHIELDING GAS SELECTION
52. DIFFUSION BONDING PROCESS
54. OUTPUT LEVEL, SEQUENCE AND FUNCTION CONTROL
55. MMAW CONSUMABLES
57. FILLER WIRES FOR GMAW AND FCAW
59. DIRECT DRIVE WELDING
60. INERTIA-DRIVE WELDING
61. JOINING OF SIMILAR METALS
62. JOINING OF DISSIMILAR METALS
65. MECHANISM OF DIFFUSION BONDING
66. BONDING PRACTICE
67. FLYER PLATE ACCELERATION
68. IMPACT ENERGY IN EXPLOSION WELDING
70. JET FORMATION IN EXPLOSION WELDING
72. BOND MORPHOLOGY AND PROPERTIES
74. TENSILE LOADING OF SOFT-INTERLAYER WELDS
75. THE SMAW PROCESS
77. ELECTRODES IN SMAW
78. WELD SCHEDULES AND PROCEDURES
79. VARIATIONS OF THE SMAW PROCESS
80. SPECIAL APPLICATIONS OF THE SMAW PROCESS
81. SAFETY CONSIDERATIONS IN SMAW
82. INTRODUCTION TO GAS-METAL ARC WELDING
83. PROCESS FUNDAMENTALS IN GMAW
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 232 topics of Power Plant Engineering in detail. These 232 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. FUEL SYSTEM OF THE DIESEL POWER PLANT
3. POWER
4. ENERGY
5. SOURCES OF ENERGY
7. CARNOT CYCLE
8. RANKINE CYCLE
9. EFFICIENCY OF THE RANKINE CYCLE
10. REHEAT CYCLE
11. REGENERATIVE CYCLE
12. BINARY VAPOUR CYCLE
13. EFFICIENCY OF BINARY VAPOUR POWER CYCLE
14. REHEAT REGENERATIVE CYCLE
15. INDIAN ENERGY SCENARIO
16. COAL ANALYSIS
17. STEAM POWER PLANT
18. NUCLEAR POWER PLANT
19. DIESEL POWER PLANT
20. FUELS AND COMBUSTION
21. STEAM GENERATORS
22. STEAM PRIME MOVERS
23. STEAM CONDENSERS
24. SURFACE CONDENSERS
25. JET CONDENSERS
26. TYPES OF JET CONDENSERS
27. HYDRAULIC TURBINES
28. IMPULSE AND REACTION TURBINES
29. SCIENCE VERSUS TECHNOLOGY
30. SCIENTIFIC RESEARCH
32. FACTS VERSUS VALUES
33. ATOMIC ENERGY
37. INTRODUCTION OF STEAM POWER PLANT
38. STEAM POWER STATION DESIGN
39. COAL HANDLING
40. DEWATERING OF COAL
42. TYPES OF FUEL BURNING SURFACES
43. METHOD OF FUEL FIRING
44. AUTOMATIC BOILER CONTROL
45. PULVERIZED COAL
46. BALL MILL
47. BALL AND RACE MILL
48. SHAFT MILL
49. PULVERISED COAL FIRING
50. CYCLONE FIRED BOILERS
51. WATER WALLS
52. ASH DISPOSAL
53. ASH HANDLING EQUIPMENT
54. SMOKE AND DUST REMOVAL
55. TYPES OF THE DUST COLLECTOR
56. FLY ASH SCRUBBER
57. FLUIDISED BED COMBUSTION
58. TYPES OF FBC SYSTEMS
60. CLASSIFICATION OF THE BOILERS
61. COCHRAN BOILER
62. LANCASHIRE BOILERS
63. LOCOMOTIVE BOILER
64. BABCOCK WILCOX BOILER
65. INDUSTRIAL BOILERS
67. REQUIREMENTS OF A GOOD BOILER
68. LA MONT BOILER
69. BENSON BOILER
70. LOEFFLER BOILER
71. SCHMIDT-HARTMANN BOILER
72. VELOX-BOILER
74. THE SIMPLE IMPULSE TURBINE
75. COMPOUNDING OF IMPULSE TURBINE
79. IMPULSE-REACTION TURBINE
80. ADVANTAGES OF STEAM TURBINE OVER STEAM ENGINE
81. STEAM TURBINE GOVERNING
82. STEAM TURBINE PERFORMANCE
83. STEAM TURBINE TESTING
85. STEAM TURBINE GENERATORS
87. INTRODUCTION OF NUCLEAR POWER PLANT
88. STRUCTURE OF ATOM
89. LAYOUT OF NUCLEAR POWER PLANT
90. NUCLEAR WASTE DISPOSAL
91. SITE SELECTION OF NUCLEAR POWER PLANT
92. PERFORMANCE OF NUCLEAR POWER PLANTS
93. NUCLEAR STABILITY
94. NUCLEAR BINDING ENERGY
95. NUCLEAR FISSION
96. NUCLEAR REACTORS
97. NUCLEAR CHAIN REACTION
99. NEUTRON LIFE CYCLE
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 213 topics of Soil Mechanics in detail. These 213 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. BASIC GEOLOGY
4. Composition of the Earth’s Crust
5. COMPOSITION OF SOILS
6. Surface Forces and Adsorbed Water
8. Particle Size of Fine-Grained Soils
11. PHASES OF A SOILS INVESTIGATION
12. SOILS EXPLORATION PROGRAM
13. Soil Identification in the Field
14. Soil Sampling
15. Groundwater Conditions
16. Types of In Situ or Field Tests
17. PHASE RELATIONSHIPS
19. DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS
21. Importance of soil compaction
23. FIELD COMPACTION
24. HEAD AND PRESSURE VARIATION IN A FLUID AT REST
25. DARCY’S LAW
26. FLOW PARALLEL TO SOIL LAYERS
28. Falling-Head Test
29. Pumping Test to Determine the Hydraulic Conductivity
31. STRESSES AND STRAINS
32. IDEALIZED STRESS - STRAIN RESPONSE AND YIELDING
34. Axisymmetric Condition
35. ANISOTROPIC, ELASTIC STATES
36. Mohr’s Circle for Stress States
37. Mohr’s Circle for Strain States
38. The Principle of Effective Stress
39. Effective Stresses Due to Geostatic Stress Fields
40. Effects of Capillarity
41. Effects of Seepage
42. LATERAL EARTH PRESSURE AT REST
43. STRESSES IN SOIL FROM SURFACE LOADS
44. Strip Load
45. Uniformly Loaded Rectangular Area
46. Vertical Stress Below Arbitrarily Shaped Areas
47. STRESS AND STRAIN INVARIANTS
48. Hooke’s Law Using Stress and Strain Invariants
49. STRESS PATHS
50. Plotting Stress Paths Using Two-Dimensional Stress Parameters
51. BASIC CONCEPTS
52. Consolidation Under a Constant Load Primary Consolidation
53. Void Ratio and Settlement Changes Under a Constant Load
54. Primary Consolidation Parameters
56. Procedure to Calculate Primary Consolidation Settlement
58. Solution of Governing Consolidation Equation Using Fourier Series
59. Finite Difference Solution of the Governing Consolidation Equation
61. Oedometer Test
62. Determination of the Coeffi cient of Consolidation
63. Determination of the Past Maximum Vertical Effective Stress
65. TYPICAL RESPONSE OF SOILS TO SHEARING FORCES
67. Effects of Increasing the Normal Effective Stress
68. Effects of Soil Tension
69. Coulomb’s Failure Criterion
70. Taylor’s Failure Criterion
71. Mohr - Coulomb Failure Criterion
72. INTERPRETATION OF THE SHEAR STRENGTH OF SOILS
74. Conventional Triaxial Apparatus
75. Unconfi ned Compression (UC) Test
76. Consolidated Undrained (CU) Compression Test
79. Hollow-Cylinder Apparatus
80. FIELD TESTS
81. BASIC CONCEPTS
82. Soil Yielding
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 113 topics of Electrical System Design and Estimation in detail. These 113 topics are divided in 6 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Types of lighting schemes
2. Electrical Symbols
3. Lists of Electrical symbols
4. Salient Features of Electricity Act, 2003
5. Consequences of Electricity Act, 2003
6. Indian Electricity Rules (1956)
7. General safety precautions
8. Role and Scope of National Electric Code
9. Components of National electric code
10. Classification of Supply Systems - TT system
11. Classification of Supply Systems - TN system
12. Classification of Supply Systems - IT system
13. Selection criteria for the TT, TN and IT systems
14. Load break switches
15. Switch Fuse Units & Fuse Switches
16. Circuit Breakers - MCB
17. Circuit Breakers - MCB Selection & Characteristics
18. Circuit Breakers - RCCB
19. Circuit Breakers - MCCB
20. Circuit Breakers - ELCB
21. Circuit Breakers - Voltage Base ELCB
22. Circuit Breakers - Current-operated ELCB
23. Circuit Breakers - ACB
24. Operation of ACB
25. Air Blast Circuit Breaker
26. Different Types of Air Blast Circuit Breaker
27. Circuit Breakers - OCB
28. Bulk Oil Circuit Breaker
29. Single & Double Break Bulk Oil Circuit Breaker
30. Circuit Breakers - Minimum Oil
31. Circuit breakers - VCB
32. Electrical Switchgear
33. SF6 Circuit Breaker
34. Types and Working of SF6 Circuit Breaker
35. Vacuum Arc or Arc in Vacuum
36. Different types of fuses
37. Protection against over load
38. Delay curves
39. Service connections
40. Electrical Diagrams
41. Methods for representation for wiring diagrams
42. Systems of House Wiring
43. Neutral and earth wire
44. Load Factor for Electrical Installations
45. Earth bus- Design of earthing systems
46. Demand Factor for electrical installations
47. Diversity Factor for electrical installations
48. Utilization factor & Maximum Demand for electrical installations
49. Coincidence factor for electrical installations
50. Demand Factor & Load Factor according to Type of Buildings
51. Design of LT panels
52. Current Rating of single core XLPE Un-armoured INSULATED Cables
53. Current Rating of single core XLPE Armoured INSULATED Cables
54. Current Rating of Two core XLPE Un-armoured INSULATED Cables
55. Current Rating of Two core XLPE Armoured INSULATED Cables
56. Current Rating of Three core XLPE Un-Armoured Insulated Cables
57. Current Rating of Three core XLPE Armoured INSULATED Cables
58. Current Rating of Three & Half core XLPE Un-Armoured INSULATED Cables
59. Current Rating of Three & Half core XLPE Armoured INSULATED Cables
60. Current Rating of Four core XLPE Un-Armoured INSULATED Cables
61. Current Rating of Four core XLPE Armoured INSULATED Cables
62. Qualities of good lighting schemes
63. Luminous flux
64. Luminous intensity
65. Illuminance
66. Luminance
67. Reflection and Reflection Factor
68. Laws of illumination
69. Necessity of Illumination
70. Photometry & Luminaire
71. Photometric Bench
72. Incandescent Lamps
73. Characteristics of Incandescent Lamps
74. Discharge Lamps
75. Mercury Vapor Lamp
76. Sodium Vapor Lamp
77. Fluorescent Lamp
78. Luminaries in Illumination Schemes
79. Mounting of Luminaries
80. Glare
81. Evaluation of Glare
82. Color
83. Color Specification Systems - Munsell system
84. Color Specification Systems
85. Interior Lighting
86. Trends and finishing of Interior Lightning
87. Sports Lighting
All topics are not listed because of character limitations set by the Play Store.
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Kurt Gödel
1. Though of course Gödel disagreed with many aspects of the Hilbert program, most notably with the thought that mathematics could be formally reconstructed in a content free manner.
2. Reprinted with a facing English translation in Gödel 1986. Henceforth all references to Gödel's papers will be to those as appear in his Collected Works, Volumes I to V. In particular all page
references, as well as the numbering scheme for Gödel's papers, refer to that of the Collected Works. (So for example Gödel's paper "On intuitionistic arithmetic and number theory" is referred to
below as 1933e, the number of it in volume I of the Collected Works, Gödel 1986.) In relevant cases the bibliography will cite original publication data as well.
3. According to the documents, the Ministry for Domestic and Cultural Affairs recommended against granting Gödel the Dozentur, on grounds of his having a political stance they termed "doubtful." See
Sigmund 2006.
4. Though according to Menger, Leibniz was an important interest of Gödel's already in the 1930s.
5. See below for a discussion of Gödel's adoption of the phenomenological world view. For the relation between phenomenology and Leibniz as Gödel saw it see van Atten and Kennedy 2003.
6. Though some credit Bolzano's "Wissenschaftslehre" (Bolzano 1992) with the first statement of the question. See the introduction by Wang to Skolem's Selected Works in (Skolem 1970).
7. For the history of this theorem see Zach 1999.
8. Skolem himself referred to the fact that set theory has countable models as the‘relativity in set theory.’
9. See von Neumann 2005. Von Neumann is referring to the meeting on Logicism, Finitism and Intuitionism which took place in Königsberg in September of 1930, at which Gödel announced his First
Incompleteness Theorem during a roundtable discussion on foundations.
10. Gödel uses the word ‘recursive’ in place of primitive recursive. For a definition of the terms ‘recursive’ and ‘primitive recursive’ see Rogers 1967. The use of recursive functions apparently
goes back to Grassman, see p. 147 of Wang 1957.
11. Gödel uses the notation B(x,y) for Prf(x,y).
12. Gödel uses the notation Bew(y) for Prov(y).
13. ‘Jetzt, Mengenlehre!’—and now, [on to] set theory!—Gödel is alleged to have said around that time (see p.128 of Wang 1993, as well as Dawson 1997.) Gödel's interest in set theory may have begun
to develop as early as 1928 when he requested at the library the volume containing Skolem's Helsinki lecture. Dawson mentions that in 1930 Gödel requested works by Fraenkel (Einleitung in die
Mengenlehre, in which Gödel will have noticed Fraenkel's skepticism about Hilbert's attempted proof of the continuum hypothesis), von Neumann, and the paper in which Hilbert had put the problem of
deciding the continuum hypothesis on the agenda of twentieth century mathematics.
14. For example, Bezboruah and Sheperdson proved (1976) the second incompleteness theorem for Q (essentially induction free arithmetic), and Wilkie & Paris proved (1987) that even the much stronger
theory IΔ[0] + exp does not prove its standard formulation of Q's consistency. But neither of these consistency statements can be said to be intensionally correct. And therefore it is not clear that
the second theorem holds in its general form for Q. In fact, Q is such a weak theory, it is not clear that a semantically contentful statement of consistency can be formulated for Q at all.
A surprising result of Pavel Pudlák's undercuts this view. As a response to the Bezboruah and Sheperdson result, Pudlák gives (1996) an intensionally correct consistency statement for Robinson's
theory Q, which Q fails to prove. The theorem states that for every consistent theory T extending Q, and for every cut J(x) in T, T ⊬ ConJT. Moreover, the arithmetization of syntax relativized to J
satisfies all the relevant intensionality criteria. Therefore the second theorem can be said to hold for Q after all.
More recently, Curtis Franks takes up the issue of the second incompleteness theorem for weak arithmetic theories in his 2009, challenging Pudláak's argument that an intensionally adequate proof
predicate can be given for Q. Any proof predicate which aspires to intensional correctness, he argues, should be formulated along the lines of Kreisel's no-counterexample construction, and therefore
must involve the concept of Herbrand provability. Herbrand proofs are propositional proofs, and these are computationally simpler; also a game semantics can be given which relativizes in a natural
way to the computational strength of the theory in question. But because the concepts of Herbrand provability and provability separate in weak theories, the question whether there is an intensionally
adequate version of the Second Incompleteness Theorem for Robinson's Q remains open.
15. For Gödel's reaction to Cohen's result see his September 1966 letter to Church in Gödel 2003a.
16. Of course Hilbert attempted to prove the CH, not just prove its consistency with the axioms of ZF or ZFC.
17. Such as: α < β implies L[α] ⊆ L[β]
18. For a discussion of Gödel's views on the absolute consistency of the Axiom of Constructibility see Kennedy and van Atten 2004.
19. Gödel's study of Leibniz took place principally from 1943 to 1946, see below.
20. There is some difficulty in making the notion "the largeness of V" precise. This is because adding sets can either collapse cardinals or increase the continuum; so adding sets in itself may lead
to self-contradictory information about the continuum. See for example Foreman 1998.
21. Gödel remarks in a footnote to this passage that the notion of provability by any means imaginable is perhaps ‘too sweeping.’ Nevertheless, this does not affect the basic distinction that Gödel
wishes to make, between the formal and informal notions of provability.
22. But see Troelstra's critical remarks in his introduction to the paper in Gödel 1995, having to do with the question whether, for the intuitionist, the Dialectica interpretation represents a
genuine epistemological advance over the so-called Heyting/Kolmogorov proof interpretation.
23. Gödel was to find support for this view in Husserl, who also rejected the notion that a science of concepts should be mathematical in nature, or similar to any empirical science. As Husserl
remarked in Ideen, about the project of developing phenomenology, "We are at the beginning…no science can help us."
24. The question whether its truth or falsity can be verified by a person is a separate one, and in fact Gödel often expressed the thought that we have only a "partial view" of sets and their
25. Gödel is very much following Husserl here. The matter is discussed in some detail in pp. 443-446 of van Atten and Kennedy 2003.
26. Gödel readily drew philosophical conclusions from the First Incompleteness Theorem. He he seems to have been slower in applying the Second Theorem.
27. Regarding the acceptability of inductive methods Gödel remarks in the Gibbs lecture, for example, that, if one is a realist about mathematical objects then inductive methods become not less but
more acceptable. See p. 313 of Gödel 1995.
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Provably computable functions and the fast growing hierarchy
Results 1 - 10 of 11
- ANNALS OF PURE AND APPLIED LOGIC, 53 (1991), 199-260 , 1991
"... This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Kruskal’s tree theorem, and in particular the connection with the
ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, an ..."
Cited by 43 (3 self)
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This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Kruskal’s tree theorem, and in particular the connection with the
ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Veblen hierarchies, some subsystems of second-order logic,
slow-growing and fast-growing hierarchies including Girard’s result, and Goodstein sequences. The central theme of this paper is a powerful theorem due to Kruskal, the “tree theorem”, as well as a
“finite miniaturization ” of Kruskal’s theorem due to Harvey Friedman. These versions of Kruskal’s theorem are remarkable from a proof-theoretic point of view because they are not provable in
relatively strong logical systems. They are examples of so-called “natural independence phenomena”, which are considered by most logicians as more natural than the metamathematical incompleteness
results first discovered by Gödel. Kruskal’s tree theorem also plays a fundamental role in computer science, because it is one of the main tools for showing that certain orderings on trees are well
founded. These orderings play a crucial role in proving the termination of systems of rewrite rules and the correctness of Knuth-Bendix completion procedures. There is also a close connection between
a certain infinite countable ordinal called Γ0 and Kruskal’s theorem. Previous definitions of the function involved in this connection are known to be incorrect, in that, the function is not
monotonic. We offer a repaired definition of this function, and explore briefly the consequences of its existence.
- PROC. AMER. MATH. SOC , 2003
"... Let f be a number-theoretic function. A finite set X of natural numbers is called f-large if card(X) ≥ f(min(X)). Let PHf be the Paris Harrington statement where we replace the largeness
condition by a corresponding f-largeness condition. We classify those functions f for which the statement PHf i ..."
Cited by 16 (5 self)
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Let f be a number-theoretic function. A finite set X of natural numbers is called f-large if card(X) ≥ f(min(X)). Let PHf be the Paris Harrington statement where we replace the largeness condition by
a corresponding f-largeness condition. We classify those functions f for which the statement PHf is independent of first order (Peano) arithmetic PA.Iffis a fixed iteration of the binary length
function, then PHf is independent. On the other hand PHlog ∗ is provable in PA. More precisely let fα(i):=|i | H −1 α (i) where | i |h denotes the h-times iterated binary length of i and H−1 α
denotes the inverse function of the α-th member Hα of the Hardy hierarchy. Then PHfα is independent of PA (for α ≤ ε0) iffα = ε0.
- SETS AND PROOFS. PROCEEDINGS OF THE LOGIC COLLOQUIUM '97 , 1997
"... A central theme running through all the main areas of Mathematical Logic is the classification of sets, functions or theories, by means of transfinite hierarchies whose ordinal levels measure
their `rank' or `complexity' in some sense appropriate to the underlying context. In Proof Theory this is ma ..."
Cited by 8 (3 self)
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A central theme running through all the main areas of Mathematical Logic is the classification of sets, functions or theories, by means of transfinite hierarchies whose ordinal levels measure their
`rank' or `complexity' in some sense appropriate to the underlying context. In Proof Theory this is manifest in the assignment of `proof theoretic ordinals' to theories, gauging their `consistency
strength' and `computational power'. Ordinal-theoretic proof theory came into existence in 1936, springing forth from Gentzen's head in the course of his consistency proof of arithmetic. To put it
roughly, ordinal analyses attach ordinals in a given representation system to formal theories. Though this area of mathematical logic has is roots in Hilbert's "Beweistheorie " - the aim of which was
to lay to rest all worries about the foundations of mathematics once and for all by securing mathematics via an absolute proof of consistency - technical results in pro...
, 1993
"... We give an analysis of classes of recursive types by presenting two extensions of the simply-typed lambda calculus. The first language only allows recursive types with built-in principles of
well-founded induction, while the second allows more general recursive types which permit non-terminating com ..."
Cited by 1 (1 self)
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We give an analysis of classes of recursive types by presenting two extensions of the simply-typed lambda calculus. The first language only allows recursive types with built-in principles of
well-founded induction, while the second allows more general recursive types which permit non-terminating computations. We discuss the expressive power of the languages, examine the properties of
reduction-based operational semantics for them, and give examples of their use in expressing iteration over large ordinals and in simulating both call-by-name and call-by-value versions of the
untyped lambda calculus. The motivations for this work come from category theoretic models. 1 Introduction An examination of the common uses of recursion in defining types reveals that there are two
distinct classes of operations being performed. The first class of recursive type contains what are generally known as the "inductive" types, as well as their duals, the "coinductive" or "projective"
types. The distingui...
"... Abstract The article starts with a brief survey of Unprovability Theory as of autumn 2006. Then, as an illustration of the subject's model-theoretic methods, we re-prove exact versions of
unprovability results for the Paris-Harrington Principle and the KanamoriMcAloon Principle using indiscernibles. ..."
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Abstract The article starts with a brief survey of Unprovability Theory as of autumn 2006. Then, as an illustration of the subject's model-theoretic methods, we re-prove exact versions of
unprovability results for the Paris-Harrington Principle and the KanamoriMcAloon Principle using indiscernibles. In addition, we obtain a short accessible proof of unprovability of the
Paris-Harrington Principle. The proof employs old ideas but uses only one colouring and directly extracts the set of indiscernibles from its homogeneous set. We also present modified, abridged
statements whose unprovability proofs are especially simple. These proofs were tailored for teaching purposes. The article is intended to be accessible to the widest possible audience of
mathematicians, philosophers and computer scientists as a brief survey of the subject, a guide through the literature in the field, an introduction to its model-theoretic techniques and, finally, a
model-theoretic proof of a modern theorem in the subject. However, some understanding of logic is assumed on the part of the readers. The intended audience of this paper consists of logicians,
logic-aware mathematicians andthinkers of other backgrounds who are interested in unprovable mathematical statements.
"... L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a "short"
strategy (he wins in a primitively recursive number of moves) and also a "long" strategy (the finiteness of ..."
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L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a "short" strategy
(he wins in a primitively recursive number of moves) and also a "long" strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the "short" and
"long" intentions (a problem suggested by J.Nesetril): After each move of Hercules (trying to kill Hydra fast) there follow k moves of Hidden Hydra Helper (making the same type of moves as Hercules
but trying to keep Hydra alive as long as possible). We prove that for k = 1 Hercules can make the game short, while for k 2 Hidden Hydra Helper has a strategy for making the game long.
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Wolfram Demonstrations Project
Natural Logarithm Approximated by Continued Fractions
Continued fractions provide a very effective toolset for approximating functions. Usually the continued fraction expansion of a function approximates the function better than its Taylor or Fourier
series. This Demonstration compares the quality of three approximations to . One is the Taylor series and the other two are continued fraction expansions. The first continued fraction expansion can
be obtained as a canonical even contraction of a continued fraction using Euler's method to transform a series to an -fraction. The other continued fraction expansion was developed by the author as
a canonical even contraction from the first one.
Vary the number of terms used in the expansions to see that the Taylor series makes hardly any progress. The terms in the Taylor polynomial become progressively more complicated; higher terms have
huge numbers in the numerator, the denominator, and the exponent, but the contribution of this "expense" becomes quite stale. In fact, in the base-10 log plot the green curve is mostly above the
The continued fraction expansion approximates the natural logarithm by several orders of magnitude better, as can be seen in the log-plot of the relative errors. It is generally a shortcoming of
polynomials that for large they cannot approximate functions well that converge to constants or do not have zeros, as polynomials tend to for large . Rational function approximation—for example
continued fractions or Padé approximations—or certain special functions are much better.
The original continued fraction is
The continued fraction resulting from the author's canonical even contraction (using HornerForm for all polynomials) is
Additional Information:
The algorithm uses the backward recurrence method to compute the continued fraction expansion. This method has been shown to be extremely stable for most continued fraction expansions, which is
extremely important on numerical platforms that incur truncation/round-off error due to the limitations of machine precision. It can be shown that the backward recurrence method ("from tail to
head") is vastly more stable (even self-correcting) than the forward recurrence method ("from head to tail") for two important classes of continued fractions: the Stieltjes continued fractions
(which includes the -fractions) and those that fulfill the parabolic convergence region theorem. Several function classes with known Stieltjes continued fraction expansions include: exponential
integrals, incomplete gamma functions, logarithms of gamma functions, the error function, ratios of successive Bessel functions of the first kind, Euler's hypergeometric function, as well as various
elementary transcendental functions. The forward recurrence method (which solves a second-order linear difference equation), however, can be computationally more efficient due to the carry-over of
results from one step to the next, which is a property the backward recurrence method does not possess.
The backward recurrence method of the continued fraction expansion is also more stable than its conversion to a Padé approximation (even when several forms of the Horner form of the numerator and
denominator polynomials are used), which is very important on strictly numerical platforms.
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Here's the question you clicked on:
Calculate the amount of zirconium produced (in kg) if a reactor were charged with 310.0 kg ZrCl4 and 29.0 kg Na.
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Similar question: Calculate the amount of zirconium produced (in kg) if a reactor were charged with 491.0 kg ZrCl4 and 49.0 kg Na. ZrCl4+4Na→4NaCl+Zr mw (ZrCl4) =91.22 + 4(35.45) =233.02 gm/mole
mw (Na) = 22.44 gm/mole 491.0 x〖10〗^23 gm / 233.02 gm/mole = 2107.11 mole ZrCl4 49.0 x 〖10〗^23 gm / 22.44 gm/mole = 2183.60 mole Na =>Require 2183.60/4 = 545.75 mole limiting reagent ZrCl4
545.75 x 91.22 = 49783.315 gm Zr = 49.78 kg Zr.
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Programming contests
From HaskellWiki
(Difference between revisions)
Andriy (Talk | contribs) Sbahra (Talk | contribs)
m (Corrected hyperlink to Project Euler)
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== International Obfuscated Haskell Code Contest == == International Obfuscated Haskell Code Contest ==
− The IOHCC as been held three times. + The IOHCC has been held three times.
* [[Obfuscation]] * [[Obfuscation]]
Latest revision as of 06:59, 5 October 2008
There are a number of online programming contests of interest to Haskell programmers. This page attempts to document and help coordinate the efforts of the Haskell community.
[edit] 1 The ICFP Programming Contest
A yearly contest run by the functional programming community, open to all comers. Haskell has been highly successful over the years, winning several times.
[edit] 2 Great Language Shootout
A highly visible language performance contest.
We have a separate page to track the Haskell submissions and discuss improvements.
[edit] 3 The Ruby Quiz
Haskell implementations of the ruby quiz problems are collected here:
[edit] 4 Sphere Online Judge
[edit] 5 Project Euler
"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve."
[edit] 6 International Obfuscated Haskell Code Contest
The IOHCC has been held three times.
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Math Placement and Quantitative Literacy Exam
All entering students must take the combined Math Placement and Quantitative Literacy Exam. Fall 2013 incoming freshman and transfer students can access the online test at www.ithaca.edu/orientation
For students who did not take the exam during their orientation or want to retake the Math Placement exam: The exam is typically administered twice each semester, once at the beginning at the
semester and once during the advance registration period mid-way through the semester. Students can register for the exam by contacting Arlene Dende at (607) 274-3107 or via e-mail at
• Next Math Placement Exam is scheduled for Tuesday, April 15, 2014 at 5:30 PM in Williams Hall room 309.
Placement Group
Based on the results of the exam, students are initially assigned to one of the four placement groups. This determines where they can enter the mathematics curriculum. Students can move from one
group to another as follows:
Group 1 - The student may take any course in the mathematics offerings other than MATH 10000, MATH 11000, MATH 13100, and MATH 18000 provided the course prerequisites are met. Students in Group 1 are
encouraged to take courses with Group 1 or Group 2 prerequisites.
Group 2 - The student may take any course that a Group 3 student may take, except MATH 13100, and in addition may take, and is encouraged to take, at least one of MATH 10800, MATH 14400, MATH 14500,
and MATH 16100. Completion of MATH 13200 with a C- or better places the student in Group 1.
Group 3 - The student may take MATH 10500, MATH 10600, MATH 10700, MATH 13100, MATH 13500, MATH 15200, and MATH 15500. Completion of MATH 10700 or MATH 13100 with a C- or better places the student in
Group 2.
Group 4 - The student must take MATH 10000 Mathematics Fundamentals or MATH 18000 Mathematics Fundamentals with Computers before any other mathematics. Passing MATH 10000 or MATH 18000 with a C- or
better places the student in Group 3.
Readiness for Quantitative Literacy
In addition, students are deemed QL-ready or not based on results from the Math Placement - QL exam. If a student receives a passing score (9 or higher) on the QL-readiness portion of the exam, that
student may enroll in QL-designated courses for which they meet the prerequisites. QL-designated courses are part of the Integrative Core Curriculum.
If students fail the QL portion of exam, they may retake the QL portion of the exam. Otherwise, Group 4 students must take MATH 10000 or MATH 18000; others must take any math course at the 10000
level for which their placement qualifies them. Once students pass the appropriate course with C- or better, they become eligible to take QL-designated courses.
Mathematics Placement Exam Guide
Sample Mathematics Placement Exam
Math Placement Instructions - this document describes how to log into Sakai to access the Math Placement Exam.
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Haverford Algebra 2 Tutor
...I de-emphasize memorization while encouraging students to fully grasp the material via these methods. Proficient problem-solving is the key to succeeding in Chemistry. Therefore, I include
various types of problems and problem-solving techniques associated with the concepts being taught.
6 Subjects: including algebra 2, chemistry, algebra 1, prealgebra
...Each teacher received special training on how to aide students with a variety of differences, including ADD and ADHD. There and since I have worked with several students with ADD and ADHD both
in their math content areas and with executive skills to help them succeed in all areas of their life. I have tutored test taking for many tests, including the Praxis many times.
58 Subjects: including algebra 2, reading, chemistry, calculus
...I always try to make learning as enjoyable as I possibly can for the student too. Music theory is not hard to understand when it is studied in an orderly way, one small step at a time. Here is
the sequence I use in teaching music theory.
15 Subjects: including algebra 2, reading, English, geometry
...Here are some testimonials from some of my students and their parents: "Jonathan was able to work with my son and decode what he needed to know to put him on par with the other students in his
class" R.B (Mother of a 5th grader) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...
22 Subjects: including algebra 2, calculus, writing, geometry
...I am also available for SAT preparation. I can come to your home, or we can meet at a mutually convenient location. I am currently on a leave of absence from a high-school math position in
southern Maryland while my wife finishes her master's degree, so my available hours are very flexible!
8 Subjects: including algebra 2, calculus, geometry, algebra 1
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188 helpers are online right now
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?'s [Archive] - Car Audio Forum - CarAudio.com
05-21-2003, 12:47 PM
My friend abcdefg got me these port dimensions ( and I am not questioning his abilities) but was wondering if these were right. The box is 7 cubic ft and the port is 18.5x6 and I want it to be tuned
to 50hz. he got depth as 11.84. Just wondering if that was right.
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This unique application is for all students across the world. It covers 114 topics of Graph Theory in detail. These 114 topics are divided in 4 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to Graphs
2. Directed and Undirected Graph
3. Basic Terminologies of Graphs
4. Vertices
5. The Handshaking Lemma
6. Types of Graphs
7. N-cube
8. Subgraphs
9. Graph Isomorphism
10. Operations of Graphs
11. The Problem of Ramsay
12. Connected and Disconnected Graph
13. Walks Paths and Circuits
14. Eulerial Graphs
15. Fluery's Algorithm
16. Hamiltonian Graphs
17. Dirac's Theorem
18. Ore's Theorem
19. Problem of seating arrangement
20. Travelling Salesman Problem
21. Konigsberg's Bridge Problem
22. Representation of Graphs
23. Combinatorial and Geometric Graphs
24. Planer Graphs
25. Kuratowaski's Graph
26. Homeomorphic Graphs
27. Region
28. Subdivision Graphs and Inner vertex Sets
29. Outer Planer Graph
30. Bipertite Graph
31. Euler's Theorem
32. Three utility problem
33. Kuratowski’s Theorem
34. Detection of Planarity of a Graph
35. Dual of a Planer Graph
36. Graph Coloring
37. Chromatic Polynomial
38. Decomposition theorem
39. Scheduling Final Exams
40. Frequency assignments and Index registers
41. Colour Problem
42. Introduction to Tree
43. Spanning Tree
44. Rooted Tree
45. Binary Tree
46. Traversing Binary Trees
47. Counting Tree
48. Tree Traversal
49. Complete Binary Tree
50. Infix, Prefix and Postfix Notation of an Arithmatic Operation
51. Binary Search Tree
52. Storage Representation of Binary Tree
53. Algorithm for Constructing Spanning Trees
54. Trees and Sorting
55. Weighted Tree and Prefix Codes
56. Huffman Code
57. More Application of Graph
58. Shortest Path Algorithm
59. Dijkstra Algorithm
60. Minimal Spanning Tree
61. Prim’s algorithm
62. The labeling algorithm
63. Reachability, Distance and diameter, Cut vertex, cut set and bridge
64. Transport Networks
65. Max-Flow Min-Cut Theorem
66. Matching Theory
67. Hall's Marriage Theorem
68. Cut Vertex
69. Introduction to Matroids and Transversal Theory
70. Types of Matroid
71. Transversal Theory
72. Cut Set
73. Types of Enumeration
74. Labeled Graph
75. Counting Labeled tree
76. Rooted Lebeled Tree
77. Unlebeled Tree
78. Centroid
79. Permutation
80. Permutation Group
81. Equivalance classes of Function
82. Group
83. Symmetric Graph
84. Coverings
85. Vertex Covering
86. Lines and Points in graphs
87. Partitions and Factorization
88. Arboricity of Graphs
89. Digraphs
90. Orientation of a graph
91. Edges and Vertex
92. Types of Digraphs
93. Connected Digraphs
94. Condensation, Reachability and Oreintable Graph
95. Arborescence
96. Euler Digraph
97. Hand Shaking Dilemma and Directed Walk path and Circuit
98. Semi walk paths and Circuits and Tournaments
99. Incident, Circuit and Adjacency Matrix of Digraph
100. Nullity of a Matrix
101. Chromatic number
102. Calculating a Chromatic number
103. Brooks Theorem
104. Brooks Theorem
105. Matrix Representation of Graphs
106. Cut Matrix
107. Circuit Matrix
108. Matrices over GF(2) and Vector Spaces of Graphs
109. Introduction to Graph Coloring
110. Planar Graphs
111. Euler’s formula
112. Kruskal’s algorithm
113. Heuristic algorithm for an upper bound
114. Heuristic algorithm for an lower bound
This software helps you deal with your daily problems in which are involved graphs.From now on, you won't have to draw all your graphs on the paper, and struggling to apply some algorithms on them.
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In the near future i will add new algorithms to it,but please click the adds, you would help me alot.
Graph 89 is an emulator for the TI-83, TI-83 Plus, TI-83 Plus Second Edition, TI-84 Plus, TI-84 Plus Second Edition, TI89, TI89 Titanium, TI92 Plus and Voyage 200 calculators.
*Please remember to read the ROM section below before downloading this application!
It will turn your phone or tablet into an exact replica of your calculator. The emulator will provide the same functionality and generate the same results as your real calculator. Being ported to
Android means that it will always fit in your pocket, have a backlight, be rechargeable and also run faster.
You would be able to install applications by copying the App file to the internal memory of your phone, pressing the 'Back' button and selecting 'Install Application/Send File'.
Graph89 would be great tool for math, science and engineering courses in high school, college and beyond. Some of these calculators feature Computer Algebra System (CAS) having the capability to
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Graph89 combines two powerful emulation engines which make it the only app in the Android Play Store to support the full range of TI graphing calculators.
1) TiEmu - http://lpg.ticalc.org/prj_tiemu providing support for the Motorola 68K family: TI89, TI89 Titanium, TI92 Plus, Voyage 200
2) TilEm - http://lpg.ticalc.org/prj_tilem providing support for the Z80 family: TI 83, TI 83+, TI 83+ SE, TI 84+, TI 84+ SE
!!! IMPORTANT !!!
Emulators are computer software which simulate a specific hardware. In order for the emulator to do anything useful it needs some software to run. The software that runs in your calculator (ROM) is
copyrighted by TI, and as such, it can not be distributed by Graph89 or any other emulator for that fact.
This means that you will have to provide the ROM file yourself by extracting it from your own calculator. Transfer it to your phone, and then tell Graph89 where to find it. To extract the ROM you can
follow the instructions from http://www.ticalc.org/programming/emulators/romdump.html and by using TiLPII from http://sourceforge.net/projects/tilp/files Google and youtube are also great sources of
tutorials and help.
Wabbitemu http://wabbit.codeplex.com/ is also a great tool for extracting the ROM from your TI83/TI84
Supported ROM files:
TI89, TI89 Titanium, TI92 Plus and Voyage 200:
*.rom, *.89u, *.v2u, *.9xu, *.tib
TI83 Plus, TI83 Plus SE, TI84 Plus and TI84 Plus SE:
*.rom, *.8Xu
Firmware updates (*.89u, 9xu, *.v2u, *.8Xu) which are normally used to restore the operating system of your calculator can also be used as a ROM image.
Needless to say, you will be very disappointed if you purchase Graph89 without having the ROM file ready. You will just see some instructions and a blank screen.
Graph89 needs permission to look at your Android Account in order to generate a unique ID shown under F1/About. This works only for TI89/V200. Note that there is no internet connection required for
this App.
TiEmu, TilEm and Graph89 have been developed independently of Texas Instruments and are not affiliated with TI.
Texas Instruments and TI are trademarks of Texas Instruments Incorporated.
Revision History:
An 8Xu (firmware update) file can now be used as a ROM for TI84+, TI84+SE, TI83+ and TI83+SE
Added support for: TI-83, TI-83 Plus, TI-83 Plus SE, TI-84 Plus and TI-84 Plus Second Edition using the TilEm2.00 engine.
Bug fixes on 'State Save' and 'Out of Memory' errors on some older phones.
Backup Manager
Dot Matrix LCD simulation
Click Screen to Zoom
Reset RAM
Landscape mode for TI89, TI89T
TI92+ skin
Bug fixes
Emulates Voyage 200 and TI92 Plus
Multiple calculator instances
Take screenshots
Generate an ID under F1/About
Sync clock
Acoustic feedback on keypress
Automatic overclock
Grayscale support
Send group files (*.89g, *.tig)
Receive files, (var-link/F4/F3/send)
Performance improvements
Customizable LCD colors
Input any function, and the app will draw graph for you.
You can input functions like sin, cos, inverse, log, exponential.
You can also input complex functions like - sin(x)/x and so on..
Features -
1. Draw maximum of 5 different graphs at a time.
2. You can find intersection point of two or more graphs as well.
3. Save graph in PNG file on your SD card
This app can be used by Students, Mathematicians, Physicists.
Keywords: graph, plot, x y axis, functions, intersection, maths, mathematics
Learn about linear graphs and vectors simply by just a swipe. Select graphs or vectors on intro page.
Find the relationship between lines, gradients, vectors and equations by drawing a graph with your finger while this app does the rest.
No input of values is necessary. This is an automatic graph app.
Math Graph app – you draw graph, it works out the equation for you.
Trace the graph with your finger. When done, sit back and
study your graph.
The app will draw the line and calculate gradient.
It will also write down the graph equation at bottom left of screen.
On vectors screen, you draw vectors with your finger, and this app analyzes them for you. It is an easy way to learn about simple vectors including addition of vectors.
This native math app is meant for beginners in graphical methods, the first 2 years of learning graphs.
If you have studied complex graphical methods but would still like to remind yourself about the basics, this app will do just that.
You can work with the equations produced at your leisure, re-arranging them to discover more about graphical maths.
The program allows draw functions graphs in specified area. The area is defined by the X min, X max, Y min, Y max values and division values for X and for Y. Functions are defined by the expression
string and color. You should click on function string in the table to edit it. Only "x" symbol should be used as a varible. After area and functions data input click "Redraw" button to draw it. On
phones graph is drawn on a full screen. Via the menu You can maximize graph on the full screen, get help about functions, about program, save the graph as a picture or sent e-mail with it (with help
of mail client app,such as gmail). The advertisement will be shown after the 5 redraws, and may be closed via the menu (or shown). And please, sometimes click advertisement - it may help for
SimpleGraph is useful application for all pupils and students. Ease interface will help you to build any graph in few seconds. Also you can build two graphics in one time.
Graph-X is a scientific tool computing 4 modes in one application: '
1) Scientific calculator: basic and advanced scientific calculations with many functions:
* General Arithmetic Functions
* Trigonometric Functions
* Power & Root Functions
* Log Functions
* Modulus Function
* Integer and Fractional parts Functions
It is able to report any kind of mathematical errors, like: 0^0 is undefined,
division by zero...
2) Graph Maker:
* multiple functions graphing
* precision control
* limits control
* scrollable and resizable graphs
* fullscreen graphs in landscape orientation
* function tables.
3) Converter: allows to convert all your favourite units in categories:
* Length
* Area
* Temperature
* Volume
* Weight
* Time.
It contains more than 200 units, including Biblical and Country-Specific Units and constants.
4) Currency: converts every world currency
* Stores the last updated rates
* Convert prices without internet access
Please read the help for more information.
For suggestions & bug reports:
Developer: Morosan Gabriel, e-mail: morosan.ag@gmail.com
Graphic designer: Morosan Maria, e-mail: me_mmg@yahoo.com
A 100% free course that gives you workouts & health tips to completely transform your body with no weights or equipment. The U20 goal is to teach you how to incinerate body fat and build lean muscle
with easy-to-follow 20 Minute Workouts.
Impossible? Think again.
What else can you do in 20 minutes that has such a lasting impact?
Ok, yeah, you can watch a sitcom or pick up dinner from a drive-thru.
However, will that help you live a longer, happier, healthier life?
This isn’t just a workout this is a lifestyle shift. Welcome to the future of home workout routines. We believe that the solution to building incredible health, melting body fat and creating an all
round better life is this: Stop doing things that don’t work - Do more things that work
Let's do this!
*YOU ARE GOING TO GET FROM THIS COURSE*
- Over 16 lectures and 1.5 hours of content!
- Free workout & nutrition videos updated every month
- Change your life - melt fat and build your body
- Learn how in just 20 minutes, 3 times per week you will get the body you deserve
- Find out about the secret fat burning foods available at your local store
- Hours of content, a lifetime of benefits
*WHAT YOU WILL LEARN*
SECTION 1: Why The Under 20 Works
SECTION 2: Start Here: 10 Minute Beginner's Workout
SECTION 3: 2 of our Famous Under 20 Minute Workouts - (**Full Routines)
SECTION 4: Metabolism Boosting 5 Minute Workouts
SECTION 5: Unusual Nutrition and Weight Loss Videos - Stuff You Don't Know
- Lifetime access to 16 lectures
- A community of 3700+ people trying to learn the same thing!
- Watch courses on the go: video lectures, audio lectures, presentations, articles and anything inside your course.
- Watch courses in offline: Save courses for offline viewing so you can watch them while you're on a plane or subway!
* WHAT PEOPLE ARE SAYING ABOUT THIS COURSE*
"Super course! "
- (Rasa Sauciuniene) ★★★★★
"I've seen your work Justin and you are amazing! I've been a trainer myself for over 15 years and I think your concept is fantastic! Thanks for this!"
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"I have been doing this workout for awhile now and absolutely love it! Justin has put together a killer program that has got me in shape and kept me that way."
- (Blake Whitaker) ★★★★★
"Justin not only really knows his stuff when it comes to healthy eating habits and exercise, he is getting us back to the way our body was meant to move. When we were kids, we were bouncing off the
walls with quick energy bursts, crashing, and then getting back up and doing it again. Thanks for the great course Justin! Looking forward to more from Under 20."
- (Trainer Jack Wilson) ★★★★★
Instructed By: Justin O'Connor
Justin O’Connor has built his life around training. After years of 5-8 hour a week short term "burn-out" workouts leaving him injured, tired and the worst shape of his life, he dedicated himself to
finding a sustainable workout that everyone could succeed at and sustain forever.
Install the "Twenty Minute Workout" app today and join over 2,000,000 people who are already learning on Udemy.
A very simple and naive app for creating graphs. Use the bottom button to switch between vertex and edges.When in vertex mode you can add vertices and move them. When in edge mode you can create a
line from one vertex to another.
Some known issues:
* moving vertices does not move edges
* if you connect to a vertex that are already connected, edge counter will increment (will change this in future update)
Math Graph est un traceur de fonctions et de courbes paramétrées avec des équations sous forme cartésienne.
Les équations peuvent autant être de la forme "y=" que de la forme "x=".
La fonction racine carrée s'obtient à l'aide de "sqrt()", la valeur absolue avec "abs()" et la fonction exponentielle avec "e^x".
Les différentes équations sont à séparer par un point virgule dans le champ de saisie.
Voici quelques exemples :
Application implements some simple algorithms for nonoriented graphs, e.g. search of shortest way, search of graph frame, search of bridges and cutpoints and so on.
- Frame search in width
- Frame search in depth
- Shortest way search
- Connected components count
- Graph bridges
- Graph cutpoints
Program interface is accessible in two languages: english and russian.
LearnLight is a science app for visible light analysis. It allows you to compare two spectral image files to graph the intensity, transmittance, and absorbance of their visible light wavelengths.
Note!!!!!!: There is a startup crash in Android 4.4 I am looking at. Sorry for this, introduced by The system, so beyond my control. Looking for solutions.
Bug fix in version 1.5: Now all levels of Android should be able to use your own photos.
The intent of the app is for high school, college, or "lifelong" students to learn about visible light, spectrometry, spectroscopy, and spectrophotometry.
The iPad version, search the Apple App Store for LearnLight
This app was built by Dave Bomberg for flappit.com. It was inspired by, is designed to follow, the layout and educational materials developed by Dr. Alexander Scheeline at the University of Illinois.
Dr. Scheeline developed a Windows Desktop application and supporting materials called "A Guided Inquiry Approach to Teaching How to Think About Analytical Instrumentation". HIs work was featured on
Wired.com in an article titled: " In High School Chem Labs, Every Cameraphone Can Be a Spectrometer " His instructional materials (pdfs of teaching modules, student modules, Windows executables, and
more) are available for free download at: http://www.asdlib.org/onlineArticles/elabware/Scheeline_Kelly_Spectrophotometer/index.html
Please DO NOT email Dr. Scheeline regarding questions about the LearnLight application.
Questions about LearnLight are welcomed at: apps@flappit.com! There is also a list of FAQs and a discussion group at https://groups.google.com/forum/?fromgroups#!forum/learnlight
Instructions for how to build a photospectrometer with an LED light and diffraction grating, and materials for teachers and students are also linked in the apps HELP section. If you are unable to
build your own spectrometer, a few example spectral images are included with this app. Have fun and learn about spectrometry!
1. Import photos taken on the Android camera, or downloaded from email from any digital camera.
2. Crop, name, save images
3. Select any 2 images to compare
4. Set spectrum width and blue/red endpoints
5. Plot intensity of both sample and reference
6. Plot only reference intensity
7. Plot only sample intensity
8. Plot transmittance
9. Plot absorbance
10. Capture and save Screenshots of any plot
11. email spectrum images or screenshots
12. email csv files for Excel(or any other spreadsheet program)
GOOGLE GROUP at http://groups.google.com/group/learnlight
Brought to you by flappit.com, Copyright 2010, All Rights Reserved
The program allows draw functions graphs in specified area. The area is defined by the X min, X max, Y min, Y max values and division values for X and for Y. Functions are defined by the expression
string and color. You should click on function string in the table to edit it. Only "x" symbol should be used as a varible. After area and functions data input click "Redraw" button to draw it. Via
the menu You can maximize graph on the full screen, get help about functions, about program or get the full version. On phones graph is drawn on a full screen. In a full program version You may save
the graph as a picture or sent e-mail with it (full version is free, it includes the advertisement).
More from developer
This unique application is for all students across the world. It covers 280 topics of Electrical Instrumentation and Process Control in detail. These 280 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to AC Electricity
2. Circuits with R, L, and C
3. RC Filters
4. AC Bridges
5. Magnetic fields
6. Analog meter
7. Electromechanical devices
8. Introduction to Basic Electrical Components
9. Resistance
10. Capacitance
11. Inductance
12. Introduction to Electronics
13. Discrete amplifiers
14. Operational amplifiers
15. Current amplifiers
16. Differential amplifiers
17. Buffer amplifiers
18. Nonlinear amplifiers
19. Instrument amplifier
20. Amplifier applications
21. Digital Circuits
22. Digital signals & Binary numbers
23. Logic circuits
24. Analog-to-digital conversion
25. Circuit Considerations
26. Introduction to Process control
27. Process Control
28. Definitions of the Elements in a Control Loop
29. Process Facility Considerations
30. Units and Standards
31. Instrument Parameters
32. Introduction to Level
33. Level Formulas
34. Direct level sensing
35. Indirect level sensing
36. Application Considerations
37. Introduction to Pressure
38. Basic Terms
39. Pressure Measurement
40. Pressure Formulas
41. Manometers
42. Diaphragms, capsules, and bellows
43. Bourdon tubes
44. Other pressure sensors
45. Vacuum instruments
46. Application Considerations
47. Introduction to Actuators and Control
48. Pressure Controllers
49. Flow Control Actuators
50. Power Control
51. Magnetic control devices
52. Motors
53. Application Considerations
54. Introduction to flow
55. Flow Formulas of Continuity equation
56. Bernoulli equation
57. Flow losses
58. Flow Measurement Instruments of Flow rate
59. Total flow and Mass flow
60. Dry particulate flow rate and Open channel flow
61. Application Considerations
62. Humidity
63. Humidity measuring devices
64. Density and Specific Gravity
65. Density measuring devices
66. Viscosity
67. Viscosity measuring instruments
68. pH Measurements, pH measuring devices and pH application considerations
69. Position and Motion Sensing
70. Position and motion measuring devices
71. Force, Torque, and Load Cells
72. Force and torque measuring devices
73. Smoke and Chemical Sensors
74. Sound and Light
75. Sound and light measuring devices
76. Sound and light application considerations
77. Introduction to Signal Conditioning
78. Conditioning
79. Linearization
80. Temperature correction
81. Pneumatic Signal Conditioning
82. Visual Display Conditioning
83. Electrical Signal Conditioning
84. Strain gauge sensors
85. Capacitive sensors
86. Capacitive sensors
87. Magnetic sensors
88. Thermocouple sensors
89. Introduction to Temperature and Heat
90. Temperature definition
91. Heat definitions
92. Thermal expansion definitions
93. Temperature and Heat Formulas
94. Thermal expansion
95. Temperature Measuring Devices
96. Thermometers
97. Pressure-spring thermometers
98. Resistance temperature devices
99. Thermistors
100. Thermocouples
101. Semiconductors
102. Application Considerations
103. Installation, Calibration & Protection
104. System Documentation
105. Pipe and Identification Diagrams
106. Functional Symbols
107. P and ID Drawings
108. Introduction to Instrument types and performance characteristics
109. Active and passive instruments
110. Null-type and deflection-type instruments
111. Analogue and digital instruments
112. Indicating instruments and instruments with a signal output
All topics are not listed because of character limitations set by the Play Store.
!!!!!! Now upgraded Free app of Basic Electrical Engineering is available named Basic Electrical Engineering-1
This unique application is for all students across the world. It covers 108 topics of Basic Electrical in detail. These 108 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Few topics Covered in this application are:
1. Introduction of electrical engineering
2. Voltage and current
3. Electric Potential and Voltage
4. Conductors and Insulators
5. Conventional versus electron flow
6. Ohm's Law
7. Kirchoff's Voltage Law (KVL)
8. Kirchoff's Current Law (KCL)
9. Polarity of voltage drops
10. Branch current method
11. Mesh current method
12. Introduction to network theorems
13. Thevenin's Theorem
14. Norton's Theorem
15. Maximum Power Transfer Theorem
16. star-delta transformation
17. Source Transformation
18. voltage and current sources
19. loop and nodal methods of analysis
20. Unilateral and Bilateral elements
21. Active and passive elements
22. alternating current (AC)
23. AC Waveforms
24. The Average and Effective Value of an AC Waveform
25. RMS Value of an AC Waveform
26. Generation of Sinusoidal (AC) Voltage Waveform
27. Concept of Phasor
28. Phase Difference
29. The Cosine Waveform
30. Representation of Sinusoidal Signal by a Phasor
31. Phasor representation of Voltage and Current
32. AC inductor circuits
33. Series resistor-inductor circuits: Impedance
34. Inductor quirks
35. Review of Resistance, Reactance, and Impedance
36. Series R, L, and C
37. Parallel R, L, and C
38. Series-parallel R, L, and C
39. Susceptance and Admittance
40. Simple parallel (tank circuit) resonance
41. Simple series resonance
42. Power in AC Circuits
43. Power Factor
44. Power Factor Correction
45. Quality Factor and Bandwidth of a Resonant Circuit
46. Generation of Three-phase Balanced Voltages
47. Three-Phase, Four-Wire System
48. Wye and delta configurations
49. Distinction between line and phase voltages, and line and phase currents
50. Power in balanced three-phase circuits
51. Phase rotation
52. Three-phase Y and Delta configurations
53. Measurement of Power in Three phase circuit
54. Introduction of measuring instruments
55. Various forces/torques required in measuring instruments
56. General Theory Permanent Magnet Moving Coil (PMMC) Instruments
57. Working Principles of PMMC
58. A multi-range ammeters
59. Multi-range voltmeter
60. Basic principle operation of Moving-iron Instruments
61. Construction of Moving-iron Instruments
62. Shunts and Multipliers for MI instruments
63. Dynamometer type Wattmeter
64. Introduction to Power System
66. Magnetic Circuit
67. B-H Characteristics
68. Analysis of Series magnetic circuit
69. Analysis of series-parallel magnetic circuit
70. Different laws for calculating magnetic field-Biot-Savart law
71. Amperes circuital law
72. Reluctance & permeance
73. Introduction of Eddy Current & Hysteresis Losses
74. Eddy current
75. Derivation of an expression for eddy current loss in a thin plate
76. Hysteresis Loss
77. Hysteresis loss & loop area
78. Steinmetzs empirical formula for hysteresis loss
79. Inductor
80. Force between two opposite faces of the core across an air gap
81. ideal transformer
82. Practical transformer
83. equivalent circuit
84. Efficiency of transformer
85. Auto-Transformer
86. Introduction of D.C Machines
87. D.C machine Armature Winding
88. EMF Equation
89. Torque equation
90. Generator types & Characteristics
91. Characteristics of a separately excited generator
92. Characteristics of a shunt generator
93. Load characteristic of shunt generator
94. Single-phase Induction Motor
All topics are not listed because of character limitations set by the Play Store.
This unique Free application is for all students across the world. It covers 108 topics of Basic Electrical in detail. These 108 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Few topics Covered in this application are:
1. Introduction of electrical engineering
2. Voltage and current
3. Electric Potential and Voltage
4. Conductors and Insulators
5. Conventional versus electron flow
6. Ohm's Law
7. Kirchoff's Voltage Law (KVL)
8. Kirchoff's Current Law (KCL)
9. Polarity of voltage drops
10. Branch current method
11. Mesh current method
12. Introduction to network theorems
13. Thevenin's Theorem
14. Norton's Theorem
15. Maximum Power Transfer Theorem
16. star-delta transformation
17. Source Transformation
18. voltage and current sources
19. loop and nodal methods of analysis
20. Unilateral and Bilateral elements
21. Active and passive elements
22. alternating current (AC)
23. AC Waveforms
24. The Average and Effective Value of an AC Waveform
25. RMS Value of an AC Waveform
26. Generation of Sinusoidal (AC) Voltage Waveform
27. Concept of Phasor
28. Phase Difference
29. The Cosine Waveform
30. Representation of Sinusoidal Signal by a Phasor
31. Phasor representation of Voltage and Current
32. AC inductor circuits
33. Series resistor-inductor circuits: Impedance
34. Inductor quirks
35. Review of Resistance, Reactance, and Impedance
36. Series R, L, and C
37. Parallel R, L, and C
38. Series-parallel R, L, and C
39. Susceptance and Admittance
40. Simple parallel (tank circuit) resonance
41. Simple series resonance
42. Power in AC Circuits
43. Power Factor
44. Power Factor Correction
45. Quality Factor and Bandwidth of a Resonant Circuit
46. Generation of Three-phase Balanced Voltages
47. Three-Phase, Four-Wire System
48. Wye and delta configurations
49. Distinction between line and phase voltages, and line and phase currents
50. Power in balanced three-phase circuits
51. Phase rotation
52. Three-phase Y and Delta configurations
53. Measurement of Power in Three phase circuit
54. Introduction of measuring instruments
55. Various forces/torques required in measuring instruments
56. General Theory Permanent Magnet Moving Coil (PMMC) Instruments
57. Working Principles of PMMC
58. A multi-range ammeters
59. Multi-range voltmeter
60. Basic principle operation of Moving-iron Instruments
61. Construction of Moving-iron Instruments
62. Shunts and Multipliers for MI instruments
63. Dynamometer type Wattmeter
64. Introduction to Power System
66. Magnetic Circuit
67. B-H Characteristics
68. Analysis of Series magnetic circuit
69. Analysis of series-parallel magnetic circuit
70. Different laws for calculating magnetic field-Biot-Savart law
71. Amperes circuital law
72. Reluctance & permeance
73. Introduction of Eddy Current & Hysteresis Losses
74. Eddy current
75. Derivation of an expression for eddy current loss in a thin plate
76. Hysteresis Loss
77. Hysteresis loss & loop area
78. Steinmetzs empirical formula for hysteresis loss
79. Inductor
80. Force between two opposite faces of the core across an air gap
81. ideal transformer
82. Practical transformer
83. equivalent circuit
84. Efficiency of transformer
85. Auto-Transformer
86. Introduction of D.C Machines
87. D.C machine Armature Winding
88. EMF Equation
89. Torque equation
90. Generator types & Characteristics
91. Characteristics of a separately excited generator
92. Characteristics of a shunt generator
93. Load characteristic of shunt generator
94. Single-phase Induction Motor
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 143 topics of Refrigeration and AirConditioning in detail. These 143 topics are divided in 4 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
5. DESIGN DOCUMENTS
7. PSYCHROMETRICS (MOIST AIR)
9. PSYCHROMETRICS (SPECIFIC HEAT)
10. PSYCHROMETRIC CHART
11. DETERMINING THE DEW-POINT TEMPERATURE OF A MOIST AIR SAMPLE
20. BASIC AIR-CONDITIONING CYCLE - SUMMER MODE
21. DESIGN SUPPLY VOLUME FLOW RATE
22. BASIC AIR-CONDITIONING CYCLE - WINTER MODE
24. REFRIGERANTS, COOLING MEDIUMS, AND ABSORBENTS
34. INDOOR TEMPERATURE, RELATIVE HUMIDITY, AND AIR VELOCITY
36. CONVECTIVE HEAT AND RADIATIVE HEAT
37. AIR HANDLING UNITS AND PACKAGED UNITS
38. PACKAGED UNITS
39. COILS USED IN REFRIGERATION
40. AIR FILTERS
43. ROTARY/ SCREW COMPRESSORS
45. AIR-COOLED CONDENSERS
49. EVAPORATIVE COOLING
52. AIR CONDITIONING SYSTEMS
54. GAS CYCLE REFRIGERATION
55. STEAM JET REFRIGERATION SYSTEM
59. ROTARY/ SCREW COMPRESSORS
65. HEAT AND WORK
68. FIRST LAW OF THERMODYNAMICS
69. SECOND LAW OF THERMODYNAMICS
70. HEAT ENGINES
71. EFFICIENCY OF HEAT ENGINES
72. ENTROPY
73. THIRD LAW OF THERMODYNAMICS
76. PROPERTIES OF PURE SUBSTANCE
77. T-S AND P-H DIAGRAMS FOR LIQUID-VAPOUR REGIME
81. THROTTLING (ISENTHALPIC) PROCESS
82. FLUID FLOW IN REFRIGERATION
83. CONSERVATION OF MOMENTUM
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 97 topics of Basic Electronics in detail. These 97 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Introduction to Electronic Engineering
2. Basic quantities
3. Passive and active devices
4. Semiconductor Devices
5. Current in Semiconductors
6. P-N Junction
7. Diodes
8. Power Diode
9. Switching
10. Special-Purpose Diodes
11. Tunnel diode and Optoelectronics
12. Diode Approximation
13. Applications of diode: Half wave Rectifier and Full Wave Rectifier
14. Bridge Rectifier
15. Clippers
16. Clamper Circuits
17. Positive Clamper
18. Voltage Doubler
19. Zener Diode
20. Zener Regulator
21. Design of Zener regulator circuit
22. Special-Purpose Diodes-1
23. Transistors
24. Bipolar Junction Transistors (BJT)
25. Beta and alpha gains
26. The Common Base Configuration
27. Relation between different currents in a transistor
28. Common-Emitter Amplifier
29. Common Base Amplifier
30. Biasing Techniques for CE Amplifiers
31. Biasing Techniques: Emitter Feedback Bias
32. Biasing Techniques: Collector Feedback Bias
33. Biasing Techniques: Voltage Divider Bias
34. Biasing Techniques: Emitter Bias
35. Small Signal CE Amplifiers
36. Analysis of CE amplifier
37. Common Collector Amplifier
38. Darlington Amplifier
39. Analysis of a transistor amplifier using h-parameters
40. Power Amplifiers
41. Power Amplifiers: Class A Amplifiers
42. Power Amplifiers: Class B amplifier
43. Power Amplifiers: Cross over distortion(Class B amplifier)
44. Power Amplifiers: Biasing a class B amplifier
45. Power Calculations for Class B Push-Pull Amplifier
46. Power Amplifiers: Class C amplifier
47. Field Effect Transistor (FET)
48. JFET Amplifiers
49. Transductance Curves
50. Biasing the FET
51. Biasing the FET: Self Bias
52. Voltage Divider Bias
53. Current Source Bias
54. FET a amplifier
55. Design of JFET amplifier
56. JFET Applications
57. MOSFET Amplifiers
58. Common-Drain Amplifier
59. MOSFET Applications
60. Operational Amplifiers
61. Depletion-mode MOSFET
62. Enhancement-mode MOSFET
63. The ideal operational amplifier
64. Practical OP AMPS
65. Inverting Amplifier
66. The Non-inverting Amplifier
67. Voltage Follower (Unity Gain Buffer)
68. The Summing Amplifier
69. Differential Amplifier
70. The Op-amp Integrator Amplifier
71. The Op-amp Differentiator Amplifier
72. History of The Numeral Systems
73. Binary codes
74. conversion of bases
75. Conversion of decimal to binary ( base 10 to base 2)
76. Octal Number System
77. Hexadecimal Number System
78. Rules of Binary Addition and Subtraction
79. Sign-and-magnitude method
80. Sign-and-magnitude method:2s complement Representation
81. Boolean algebra
82. Basic Theorems & Properties of Boolean algebra
83. Logic gate
84. Symbols of logic Gates
85. Universal Gates
86. No associativity of NAND and NOR Gates: universal gates
87. Introduction of minimization using K-map
88. Two variable maps
89. Don't Cares condition
90. 5 variable Karnaugh Maps
91. Binary coded decimal codes(bcd)
92. Principle and types digital instruments
93. digital voltmeter
94. Cathode ray oscilloscope(CRO)
95. Cathode ray tube: CRO
96. Channel: CRO
97. Measurements with the cathode ray oscilloscope C
All topics not listed due to character limitations set by Google Play.
This ultimate unique application has more than 300,000+ topics of engineering covered across five major engineering disciplines - Electronics & Communication, Electrical, Mechanical, Civil and
Computer Science Engineering. With the unique integration with the online version of this application, users can access their saved notes from any where. The USP of this application is
ultra-portability of your engineering education.
All topics are neatly arranged under subjects and units. Users can also use the search option to find any topic of relevance within 2 clicks!
Each topic is not more than 600 words and is complete with equations, diagrams and functional graphs.
The content is more than enough to study and clear any engineering examination held by most Indian Engineering Colleges & Universities.
Go-Ahead! Download it & Make your Studies Simpler and Easier!!
This ultimate unique application is for all students of Automobile Engineering across the world. It covers 188 topics of Automobile Engineering in detail. These 188 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from any where they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
2. The expansion valve system
3. THE FIXED ORIFICE VALVE SYSTEM (CYCLING CLUTCH ORIFICE TUBE)
4. THE COMPRESSOR
5. THE CONDENSER
6. THE CONDENSER
9. THE EVAPORATOR
10. ANTI-FROSTING DEVICES
11. BASIC CONTROL SWITCHES
12. THE BASIC THEORY OF COOLING
14. ALTERNATIVES CYCLES
17. PRESSURE GAUGE READINGS
18. CYCLE TIME TESTING
19. A/C SYSTEM LEAK TESTING
20. SIGHT GLASS
21. GLOBAL WARMING
22. THE OZONE LAYER
23. INTRODUCTION TO TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
26. TYPES OF AUTOMOBILES
27. LAYOUT OF AN AUTOMOBILE CHASSIS
28. MAJOR COMPONENTS OF AN AUTOMOBILE
31. USE OF THE ENGINES
36. ADVANTAGES OF A MULTI-CYLINDER ENGINE FOR THE SAME POWER
37. ENGINE CONSTRUCTION
38. CYLINDER BLOCKS
39. CYLINDER LINER
40. CRANK CASE
41. CYLINDER HEAD
42. GASKETS
43. PISTON
44. PISTON RINGS
45. PISTON PIN
46. CONNECTING ROD
47. CRANKSHAFT
48. VALVES
49. PORT-TIMING DIAGRAM
50. FLYWHEEL
51. MANIFOLDS
52. ROLLING RESISTANCE
53. AIR RESISTANCE.
54. GRADIENT RESISTANCE
55. TRACTIVE EFFORT
56. GEAR BOX
57. TYPES OF THE GEAR BOX
58. MERITS AND DEMERITS OF GEAR BOX
59. GEAR SHIFTING MECHANISM
60. Transmission in Automobile
62. FUNCTION OF CLUTCH
63. MAIN PARTS OF CLUTCH
64. TYPES OF THE CLUTCH
65. UNIVERSAL JOINT
67. FUNCTION OF STEERING SYSTEM
68. FRONT AXLE
69. CASTER ANGLE
70. CASTER ANGLE
71. CAMBER
72. TOE-IN
73. TOE-OUT
74. ACKERMAN MECHANISM
75. FUNCTIONS OF A BRAKE
76. CLASSIFICATION OF BRAKES
77. DISC BRAKES
78. FLOATING CALIPER BRAKE
79. POWER BRAKES
80. AIR BRAKE SYSTEM
81. HYDRAULIC BRAKES
82. TYPES OF THE STARTING MOTORS
83. GENERATOR
84. ALTERNATOR
85. LIGHTING SYSTEM
86. IGNITION SYSTEM
87. IGNITION TIMING
88. IGNITION ADVANCE
89. SPARK PLUGS
91. AUTOMOBILE BATTERY
93. HORNS
94. CLUTCH OPERATION
95. Types of clutch
96. Gearbox operation
97. Gear change mechanisms
98. Gears and components
102. DIRECT SHIFT GEARBOX
104. WHEEL BEARINGS
105. FOUR-WHEEL DRIVE
106. TIRE DESIGN
107. TIRE PLY AND BELT DESIGN
108. Tire Tread Design
109. TIRE RATINGS AND SIDEWALL INFORMATION
110. SPECIALTY TIRES
111. REPLACEMENT TIRES
112. Tire Valves
113. COMPACT SPARE TIRES
114. Run-Flat Tires
115. Tire Pressure Monitoring Systems
116. TIRE CONTACT AREA
117. Wheel Rims
118. Static Wheel Balance Theory
119. Dynamic Wheel Balance Theory
120. On-Car Wheel Balancing
This ultimate unique application is for all students across the world. It covers 113 topics of Discrete Mathematics in detail. These 113 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Set Theory
2. Decimal number System
3. Binary Number System
4. Octal Number System
5. Hexadecimal Number System
6. Binary Arithmetic
7. Sets and Membership
8. Subsets
9. Introduction to Logical Operations
10. Logical Operations and Logical Connectivity
11. Logical Equivalence
12. Logical Implications
13. Normal Forms and Truth Table
14. Normal Form of a well formed formula
15. Principle Disjunctive Normal Form
16. Principal Conjunctive Normal form
17. Predicates and Quantifiers
18. Theory of inference for the Predicate Calculus
19. Mathematical Induction
20. Diagrammatic Representation of Sets
21. The Algebra of Sets
22. The Computer Representation of Sets
23. Relations
24. Representation of Relations
25. Introduction to Partial Order Relations
26. Diagrammatic Representation of Partial Order Relations and Posets
27. Maximal, Minimal Elements and Lattices
28. Recurrence Relation
29. Formulation of Recurrence Relation
30. Method of Solving Recurrence Relation
31. Method for solving linear homogeneous recurrence relations with constant coefficients:
32. Functions
33. Introduction to Graphs
34. Directed Graph
35. Graph Models
36. Graph Terminology
37. Some Special Simple Graphs
38. Bipartite Graphs
39. Bipartite Graphs and Matchings
40. Applications of Graphs
41. Original and Sub Graphs
42. Representing Graphs
43. Adjacency Matrices
44. Incidence Matrices
45. Isomorphism of Graphs
46. Paths in the Graphs
47. Connectedness in Undirected Graphs
48. Connectivity of Graphs
49. Paths and Isomorphism
50. Euler Paths and Circuits
51. Hamilton Paths and Circuits
52. Shortest-Path Problems
53. A Shortest-Path Algorithm (Dijkstra Algorithm.)
54. The Traveling Salesperson Problem
55. Introduction to Planer Graphs
56. Graph Coloring
57. Applications of Graph Colorings
58. Introduction to Trees
59. Rooted Trees
60. Trees as Models
61. Properties of Trees
62. Applications of Trees
63. Decision Trees
64. Prefix Codes
65. Huffman Coding
66. Game Trees
67. Tree Traversal
68. Boolean Algebra
69. Identities of Boolean Algebra
70. Duality
71. The Abstract Definition of a Boolean Algebra
72. Representing Boolean Functions
73. Logic Gates
74. Minimization of Circuits
75. Karnaugh Maps
76. Dont Care Conditions
77. The Quine MCCluskey Method
78. Introduction to Lattices
79. The Transitive Closure of a Relation
80. Cartesian Product of Lattices
81. Properties of Lattices
82. Lattices as Algebraic System
83. Partial Order Relations on a Lattice
84. Least Upper Bounds and Latest Lower Bounds in a Lattice
85. Sublattices
86. Lattice Isomorphism
87. Bounded, Complemented and Distributive Lattices
88. Propositional Logic
89. Conditional Statements
90. Truth Tables of Compound Propositions
91. Precedence of Logical Operators and Logic and Bit Operations
92. Applications of Propositional Logic
93. Propositional Satisfiability
94. Quantifiers
95. Nested Quantifiers
96. Translating from Nested Quantifiers into English
97. Inference
98. Rules of Inference for Propositional Logic
99. Using Rules of Inference to Build Arguments
100. Resolution and Fallacies
101. Rules of Inference for Quantified Statements
102. Introduction to Algebra
103. Rings
104. Properties of rings
105. Subrings
106. Homomorphisms and quotient rings
107. Groups
108. Properties of groups
109. Subgroups
All topics not listed due to character limitations set by Google Play.
This unique application is for all students across the world. It covers 143 topics of Material Science in detail. These 143 topics are divided in 3 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. Classification of engineering materials
4. Organic and inorganic materials
5. Semiconductors
6. Biomaterials
8. Advanced materials
9. Smart materials (materials of the future)
10. Nanostructured materials and nanotechnology
11. Quantum dots
12. Spintronics
13. Level of material structure examination and observation
14. Material structure
15. Engineering metallurgy
16. Selection of the materials
17. Atomic concepts in physics and chemistry
18. Atomic Structure: FUNDAMENTAL CONCEPTS
19. Atomic Structure: FUNDAMENTAL CONCEPTS
20. ELECTRONS IN ATOMS
21. THE PERIODIC TABLE
22. BONDING FORCES AND ENERGIES
23. Ionic Bonding
24. Covalent Bonding
25. Metallic Bonding
26. SECONDARY BONDING OR VAN DER WAALS BONDING
27. Crystal Structures: FUNDAMENTAL CONCEPTS
28. The Face-Centered Cubic Crystal Structure
29. The Body-Centered Cubic Crystal Structure
30. The Hexagonal Close-Packed Crystal Structure
32. CRYSTAL SYSTEMS
33. POINT COORDINATES
35. Hexagonal Crystals
36. Atomic Arrangements
39. IMPURITIES IN SOLIDS
40. DISLOCATIONS - LINEAR DEFECTS
41. INTERFACIAL DEFECTS
42. Microscopic Examination
43. Optical Microscopy
44. Electron Microscopy
45. GRAIN SIZE DETERMINATION
46. Introduction to mechanical properties
47. CONCEPTS OF STRESS AND STRAIN
48. Compression Tests
49. STRESS-STRAIN BEHAVIOR
50. ANELASTICITY
52. Plastic Deformation
53. Yielding and Yield Strength
54. Tensile Strength
55. Ductility
56. Resilience
57. Toughness
58. TRUE STRESS AND STRAIN
60. HARDNESS
61. Rockwell Hardness Tests
62. Brinell Hardness Tests
63. Knoop and Vickers Microindentation Hardness Tests
64. Hardness Conversion
65. Correlation Between Hardness and Tensile Strength
67. Computation of Average and Standard Deviation Values
68. DESIGN/SAFETY FACTORS
69. Phase diagrams-introduction
70. SOLUBILITY LIMIT
71. PHASES
72. PHASE EQUILIBRIA
73. ONE-COMPONENT (OR UNARY) PHASE DIAGRAMS
74. Binary Phase Diagrams
76. Determination of Phase Compositions
77. Determination of Phase Amounts
78. Equilibrium Cooling
79. Nonequilibrium Cooling
81. BINARY EUTECTIC SYSTEMS
86. THE GIBBS PHASE RULE
87. THE IRON-IRON CARBIDE (Fe-Fe3C) PHASE DIAGRAM
89. Hypoeutectoid Alloys
90. Hypereutectoid Alloys
91. THE INFLUENCE OF OTHER ALLOYING ELEMENTS
92. FERROUS ALLOYS
93. Low-Carbon Steels
94. Medium-Carbon Steels
95. High-Carbon Steels
96. Stainless Steels
97. Cast Irons
98. Gray Iron
99. Ductile (or Nodular) Iron
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 86 topics of Engineering Geology in detail. These 86 topics are divided in 6 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
4. Geological Materials
5. Description of Geological materials
6. Porosity and Permeability
7. Deformation
10. BRANCHES OF GEOLOGY
11. INTRODUCTION TO SOILS
12. INTRODUCTION TO ROCKS
13. GEOLOGICAL MASSES
14. Standard Weathering Description Systems
15. Ground Mass Description
16. Rock Mass Classification
17. SCHISTS AND GNEISSES
18. GEOLOGICAL MAPS
19. Understanding Geological Maps
20. Interpretation of Geological Maps
21. DRILLING TOOLS
22. MAPPING AT SMALL SCALE
23. MAPPING AT LARGE SCALE
24. Engineering Geological Maps
25. GIS in Engineering Geology
27. DRILLING PROCESS
28. DRILLING AND SAMPLING IN SOIL
29. Boring and Sampling over Water
30. Field Tests and Measurements
31. Strength and Deformation Tests
32. Measurements in Boreholes and Excavations
33. Engineering Geophysics
34. Properties of Minerals
35. ROCK-FORMING MINERALS
36. FELDSPAR - FAMILY
37. Quartz family
38. The Mineral AUGITE
39. Rhyolite Family
40. Fundamentals of process of formation of ore minerals
41. COAL AND PETROLEUM
42. Coal- Its origin and occurrence in India
43. Phyllite
44. GARNET AND MISCELLANEOUS ROCKS
45. Classification of Rocks
46. Difference Between Igneous, Sedimentary and Metamorphic Rocks
47. MAGMA
48. Gabbro(rock)
49. PEGMATITE
50. Igneous rock types
51. LIMESTONE
52. Metamorphic Rocks
53. GRANITE
54. Syenite
55. Larvikite,ijolite and Carbonatite
56. Phonolite, Ultramafic Rocks and Pyroxenite
57. Conglomerate and breccia
58. METAMORPHIC ROCKS
59. SLATE
60. Beds in 3D space
61. Strike and Dip
62. Inclined Bedding on Maps
63. FOLDS
64. FAULTS
65. JOINTS
66. Seismic Surveys
67. Electrical Resistivity Surveys
68. Electromagnetic Conductivity Surveys
69. Magnetic Surveys
70. REMOTE SENSING TECHNIQUES
71. Aerial Photographs
72. Satellite Images
73. Design and Construction of Road Tunnels
74. Factors that Influence Tunnel Seismic Performance
75. PREVENTIONS OF DAM CONSTUCTION
76. Sea erosion and coastal Protection
77. Internal Structure of the Earth
78. Building stones occurrences and characteristics
79. Origin of Sedimentary Rock
80. Earthquakes
81. causes of Earthquakes
82. Classification of Earthquake
83. Classification of Seismic Waves
84. Fault Types
85. Seismic Zones of India
86. Construction of Earthquake Resistant Buildings and Infrastructure
This ultimate application is useful for all students of Artificial Intelligence across the world. It covers 142 topics of Artificial Intelligence in detail. These 142 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
The USP of this application is "ultra-portability". Students can access the content on-the-go from any where they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Turing test
2. Introduction to Artificial Intelligence
3. History of AI
4. The AI Cycle
5. Knowledge Representation
6. Typical AI problems
7. Limits of AI
8. Introduction to Agents
9. Agent Performance
10. Intelligent Agents
11. Structure Of Intelligent Agents
12. Types of agent program
13. Goal based Agents
14. Utility-based agents
15. Agents and environments
16. Agent architectures
17. Search for Solutions
18. State Spaces
19. Graph Searching
20. A Generic Searching Algorithm
21. Uninformed Search Strategies
22. Breadth-First Search
23. Heuristic Search
24. A∗ Search
25. Search Tree
26. Depth first Search
27. Properties of Depth First Search
28. Bi-directional search
29. Search Graphs
30. Informed Search Strategies
31. Methods of Informed Search
32. Greedy Search
33. Proof of Admissibility of A*
34. Properties of Heuristics
35. Iterative-Deepening A*
36. Other Memory limited heuristic search
37. N-Queens eample
38. Adversarial Search
39. Genetic Algorithms
40. Games
41. Optimal decisions in Games
42. minimax algorithm
43. Alpha Beta Pruning
44. Backtracking
45. Consistency Driven Techniques
46. Path Consistency (K-Consistency)
47. Look Ahead
48. Propositional Logic
49. Syntax of Propositional Calculus
50. Knowledge Representation and Reasoning
51. Propositional Logic Inference
52. Propositional Definite Clauses
53. Knowledge-Level Debugging
54. Rules of Inference
55. Soundness and Completeness
56. First Order Logic
57. Unification
58. Semantics
59. Herbrand Universe
60. Soundness, Completeness, Consistency, Satisfiability
61. Resolution
62. Herbrand Revisited
63. Proof as Search
64. Some Proof Strategies
65. Non-Monotonic Reasoning
66. Truth Maintenance Systems
67. Rule Based Systems
68. Pure Prolog
69. Forward chaining
70. backward Chaining
71. Choice between forward and backward chaining
72. AND/OR Trees
73. Hidden Markov Model
74. Bayesian networks
75. Learning Issues
76. Supervised Learning
77. Decision Trees
78. Knowledge Representation Formalisms
79. Semantic Networks
80. Inference in a Semantic Net
81. Extending Semantic Nets
82. Frames
83. Slots as Objects
84. Interpreting frames
85. Introduction to Planning
86. Problem Solving vs. Planning
87. Logic Based Planning
88. Planning Systems
89. Planning as Search
90. Situation-Space Planning Algorithms
91. Partial-Order Planning
92. Plan-Space Planning Algorithms
93. Interleaving vs. Non-Interleaving of Sub-Plan Steps
94. Simple Sock/Shoe Example
95. Probabilistic Reasoning
96. Review of Probability Theory
97. Semantics of Bayesian Networks
98. Introduction to Learning
99. Taxonomy of Learning Systems
100. Mathematical formulation of the inductive learning problem
101. Concept Learning
102. Concept Learning as Search
103. Algorithm to Find a Maximally-Specific Hypothesis
104. Candidate Elimination Algorithm
105. The Candidate-Elimination Algorithm
106. Decision Tree Construction
107. Splitting Functions
108. Decision Tree Pruning
109. Neural Networks
110. Artificial Neural Networks
111. Perceptron
112. Perceptron Learning
113. Multi-Layer Perceptrons
114. Back-Propagation Algorithm
115. Statistical learning
All topics not listed here because of character limit set by Play Store
This unique application is for all students across the world. It covers 157 topics of Strength Of Materials in detail. These 157 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. TENSILE STRESS
3. SHEAR STRESS
6. SHEAR STRAIN
8. TENSILE STRAIN
9. STRESS STRAIN DIAGRAM
10. THERMAL STRESS
11. POISSON RATIO
12. THREE MODULUS
13. Temperature Stress In Composite Bar
14. STRAIN ENERGY
15. MODULUS OF RESSILINCE AND TOUGHNESS
16. STRAIN ENERGY IN GRADUAL AND SUDDEN LOAD
17. STRAIN ENERGY IN IMPACT LOAD
18. HOOK'S LAW
19. STRESS, STRAIN AND CHANGE IN LENGTH
20. CHANGE IN LENGTH WHEN ONE BOTH ENDS ARE FREE
21. CHANGE IN LENGTH WHEN ONE BOTH ENDS ARE FIXED
22. Composite bar in tension or compression
23. Principal Stress And Principal Plane
24. Maximum Shear Stress
25. Theories Of Elastic Failure
26. Maximum Principal Stress Theory
27. Maximum Shear Stress Theory:
28. Maximum Principal Strain Theory
29. Total Strain Energy Per Unit Volume Theory
30. Maximum Shear Strain Energy Per Unit Volume Theory
31. Mohr’s Rupture Theory For Brittle Materials
32. Mohr’s Circle
33. Introduction to Bending Moment And Shearing Force
34. Shearing Force, And Bending Moment In A Straight Beam
35. Sign Conventions For Bending Moments And Shearing Forces
36. Bending Of Beams
37. Procedure For Drawing Shear Force And Bending Moment Diagram
38. SFD & BMD Of Cantilever Carrying Load At Its One End
39. SFD And BMD Of Simply Supported Beam Subjected To A Central Load
40. SFD And BMD Of A Cantilever Beam Subjected To U.D.L
41. Simply Supported Beam Subjected To U.D.L
42. Simply Supported Beam Carrying UDL & End Couples
43. Points Of Inflection
44. Theory Of Bending : Assumption And General Theory
45. Elastic Flexure Formula
46. Beams Of Composite Cross Section
47. Flexural Buckling Of A Pin-Ended Strut
48. Rankine-Gordon Formula
49. Comparison Of The Rankine-Gordon And Euler Formulae
50. Effective Lengths Of Struts
51. Struts And Columns With One End Fixed And The Other Free
52. Thin Cylinder
53. Members Subjected to Axisymmetric Load
54. ANALYSIS: Pressurized thin walled cylinder
55. Longitudinal Stress: Pressurized thin walled cylinder
56. Change in Dimensions: Pressurized thin walled cylinder
57. Volumetric Strain or Change in the Internal Volume
58. Cylindrical Vessel with Hemispherical Ends
59. Thin rotating ring or cylinder
60. Stresses in thick cylinders
61. Stresses in thick cylinders
62. Representation of radial and circumferential strain
63. A thick cylinder with both external and internal pressure
64. The stress distribution within the cylinder wall
65. Methods of increasing the elastic strength of a thick cylinder by pre-stressing
66. Composite cylinders
67. Combined stress distribution in a composite cylinder
68. Multilayered or Laminated cylinder
69. Autofrettage
70. Derivation of the hoop and radial stress equations for a thickwalled circular cylinder
71. Lame line
72. Plastic deformation of thick tubes
73. Lame line for elastic zone
74. Portion of the cylinder is plastic
75. Stress in thin cylinders
76. Horizontal diametrical plane
77. Strains in thin cylinders
78. Change in Volume of Cylinder
79. Compound Cylinders
80. Press Fits
81. Analysis of Press Fits
82. Castigliano's first theorem
83. Castigliano’s Second Theorem
84. Torsion of a thin circular tube
85. Torsion of solid circular shafts
86. Torsion of a hollow circular shaft
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 217 topics of Advanced Welding Technology in detail. These 217 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. WELDING WITH PRESSURE
4. FUSION WELDING
10. INTRODUCTION TO HEAT FLOW IN FUSION WELDING
12. PARAMETRIC EFFECTS OF HEAT FLOW IN FUSION WELDING
15. GAS TUNGSTEN ARC WELDING
17. GAS METAL ARC WELDING
18. Submerged Arc Welding
19. INTRODUCTION TO TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
20. HEAT TRANSFER IN GAS-METAL ARC WELDING
21. PROCEDURE DEVELOPMENT TRANSFER OF HEAT AND MASS TO THE BASE METAL IN GAS-METAL ARC WELDING
22. INTRODUCTION TO ARC PHYSICS OF GAS-TUNGSTEN ARC WELDING
23. ELECTRODE REGIONS AND ARC COLUMN IN GTAW
24. ARC WELDING POWER SOURCES
25. POWER SOURCE SELECTION
26. PULSED POWER SUPPLIES
27. Resistance Welding Power Sources
28. ELECTRON-BEAM WELDING POWER SOURCES
33. EFFECT OF WELDING RATE ON WELD POOL SHAPE AND MICROSTRUCTURE
34. BRAZING
35. SOLDERING
36. PHYSICAL PRINCIPLES OF BRAZING
37. ELEMENTS OF THE BRAZING PROCESS
38. HEATING METHODS FOR BRAZING
40. FUNDAMENTALS OF SOLDERING
41. GUIDELINES FOR FLUX SELECTION
42. TYPES OF FLUXES
43. JOINT DESIGN
45. SOLDER APPLICATION
47. SOLDERING EQUIPMENT
49. SHIELDING GAS SELECTION
52. DIFFUSION BONDING PROCESS
54. OUTPUT LEVEL, SEQUENCE AND FUNCTION CONTROL
55. MMAW CONSUMABLES
57. FILLER WIRES FOR GMAW AND FCAW
59. DIRECT DRIVE WELDING
60. INERTIA-DRIVE WELDING
61. JOINING OF SIMILAR METALS
62. JOINING OF DISSIMILAR METALS
65. MECHANISM OF DIFFUSION BONDING
66. BONDING PRACTICE
67. FLYER PLATE ACCELERATION
68. IMPACT ENERGY IN EXPLOSION WELDING
70. JET FORMATION IN EXPLOSION WELDING
72. BOND MORPHOLOGY AND PROPERTIES
74. TENSILE LOADING OF SOFT-INTERLAYER WELDS
75. THE SMAW PROCESS
77. ELECTRODES IN SMAW
78. WELD SCHEDULES AND PROCEDURES
79. VARIATIONS OF THE SMAW PROCESS
80. SPECIAL APPLICATIONS OF THE SMAW PROCESS
81. SAFETY CONSIDERATIONS IN SMAW
82. INTRODUCTION TO GAS-METAL ARC WELDING
83. PROCESS FUNDAMENTALS IN GMAW
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 232 topics of Power Plant Engineering in detail. These 232 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. FUEL SYSTEM OF THE DIESEL POWER PLANT
3. POWER
4. ENERGY
5. SOURCES OF ENERGY
7. CARNOT CYCLE
8. RANKINE CYCLE
9. EFFICIENCY OF THE RANKINE CYCLE
10. REHEAT CYCLE
11. REGENERATIVE CYCLE
12. BINARY VAPOUR CYCLE
13. EFFICIENCY OF BINARY VAPOUR POWER CYCLE
14. REHEAT REGENERATIVE CYCLE
15. INDIAN ENERGY SCENARIO
16. COAL ANALYSIS
17. STEAM POWER PLANT
18. NUCLEAR POWER PLANT
19. DIESEL POWER PLANT
20. FUELS AND COMBUSTION
21. STEAM GENERATORS
22. STEAM PRIME MOVERS
23. STEAM CONDENSERS
24. SURFACE CONDENSERS
25. JET CONDENSERS
26. TYPES OF JET CONDENSERS
27. HYDRAULIC TURBINES
28. IMPULSE AND REACTION TURBINES
29. SCIENCE VERSUS TECHNOLOGY
30. SCIENTIFIC RESEARCH
32. FACTS VERSUS VALUES
33. ATOMIC ENERGY
37. INTRODUCTION OF STEAM POWER PLANT
38. STEAM POWER STATION DESIGN
39. COAL HANDLING
40. DEWATERING OF COAL
42. TYPES OF FUEL BURNING SURFACES
43. METHOD OF FUEL FIRING
44. AUTOMATIC BOILER CONTROL
45. PULVERIZED COAL
46. BALL MILL
47. BALL AND RACE MILL
48. SHAFT MILL
49. PULVERISED COAL FIRING
50. CYCLONE FIRED BOILERS
51. WATER WALLS
52. ASH DISPOSAL
53. ASH HANDLING EQUIPMENT
54. SMOKE AND DUST REMOVAL
55. TYPES OF THE DUST COLLECTOR
56. FLY ASH SCRUBBER
57. FLUIDISED BED COMBUSTION
58. TYPES OF FBC SYSTEMS
60. CLASSIFICATION OF THE BOILERS
61. COCHRAN BOILER
62. LANCASHIRE BOILERS
63. LOCOMOTIVE BOILER
64. BABCOCK WILCOX BOILER
65. INDUSTRIAL BOILERS
67. REQUIREMENTS OF A GOOD BOILER
68. LA MONT BOILER
69. BENSON BOILER
70. LOEFFLER BOILER
71. SCHMIDT-HARTMANN BOILER
72. VELOX-BOILER
74. THE SIMPLE IMPULSE TURBINE
75. COMPOUNDING OF IMPULSE TURBINE
79. IMPULSE-REACTION TURBINE
80. ADVANTAGES OF STEAM TURBINE OVER STEAM ENGINE
81. STEAM TURBINE GOVERNING
82. STEAM TURBINE PERFORMANCE
83. STEAM TURBINE TESTING
85. STEAM TURBINE GENERATORS
87. INTRODUCTION OF NUCLEAR POWER PLANT
88. STRUCTURE OF ATOM
89. LAYOUT OF NUCLEAR POWER PLANT
90. NUCLEAR WASTE DISPOSAL
91. SITE SELECTION OF NUCLEAR POWER PLANT
92. PERFORMANCE OF NUCLEAR POWER PLANTS
93. NUCLEAR STABILITY
94. NUCLEAR BINDING ENERGY
95. NUCLEAR FISSION
96. NUCLEAR REACTORS
97. NUCLEAR CHAIN REACTION
99. NEUTRON LIFE CYCLE
All topics are not listed because of character limitations set by the Play Store.
This unique application is for all students across the world. It covers 213 topics of Soil Mechanics in detail. These 213 topics are divided in 5 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
3. BASIC GEOLOGY
4. Composition of the Earth’s Crust
5. COMPOSITION OF SOILS
6. Surface Forces and Adsorbed Water
8. Particle Size of Fine-Grained Soils
11. PHASES OF A SOILS INVESTIGATION
12. SOILS EXPLORATION PROGRAM
13. Soil Identification in the Field
14. Soil Sampling
15. Groundwater Conditions
16. Types of In Situ or Field Tests
17. PHASE RELATIONSHIPS
19. DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS
21. Importance of soil compaction
23. FIELD COMPACTION
24. HEAD AND PRESSURE VARIATION IN A FLUID AT REST
25. DARCY’S LAW
26. FLOW PARALLEL TO SOIL LAYERS
28. Falling-Head Test
29. Pumping Test to Determine the Hydraulic Conductivity
31. STRESSES AND STRAINS
32. IDEALIZED STRESS - STRAIN RESPONSE AND YIELDING
34. Axisymmetric Condition
35. ANISOTROPIC, ELASTIC STATES
36. Mohr’s Circle for Stress States
37. Mohr’s Circle for Strain States
38. The Principle of Effective Stress
39. Effective Stresses Due to Geostatic Stress Fields
40. Effects of Capillarity
41. Effects of Seepage
42. LATERAL EARTH PRESSURE AT REST
43. STRESSES IN SOIL FROM SURFACE LOADS
44. Strip Load
45. Uniformly Loaded Rectangular Area
46. Vertical Stress Below Arbitrarily Shaped Areas
47. STRESS AND STRAIN INVARIANTS
48. Hooke’s Law Using Stress and Strain Invariants
49. STRESS PATHS
50. Plotting Stress Paths Using Two-Dimensional Stress Parameters
51. BASIC CONCEPTS
52. Consolidation Under a Constant Load Primary Consolidation
53. Void Ratio and Settlement Changes Under a Constant Load
54. Primary Consolidation Parameters
56. Procedure to Calculate Primary Consolidation Settlement
58. Solution of Governing Consolidation Equation Using Fourier Series
59. Finite Difference Solution of the Governing Consolidation Equation
61. Oedometer Test
62. Determination of the Coeffi cient of Consolidation
63. Determination of the Past Maximum Vertical Effective Stress
65. TYPICAL RESPONSE OF SOILS TO SHEARING FORCES
67. Effects of Increasing the Normal Effective Stress
68. Effects of Soil Tension
69. Coulomb’s Failure Criterion
70. Taylor’s Failure Criterion
71. Mohr - Coulomb Failure Criterion
72. INTERPRETATION OF THE SHEAR STRENGTH OF SOILS
74. Conventional Triaxial Apparatus
75. Unconfi ned Compression (UC) Test
76. Consolidated Undrained (CU) Compression Test
79. Hollow-Cylinder Apparatus
80. FIELD TESTS
81. BASIC CONCEPTS
82. Soil Yielding
All topics are not listed because of character limitations set by the Play Store.
This ultimate unique application is for all students across the world. It covers 113 topics of Electrical System Design and Estimation in detail. These 113 topics are divided in 6 units.
Each topic is around 600 words and is complete with diagrams, equations and other forms of graphical representations along with simple text explaining the concept in detail.
This USP of this application is "ultra-portability". Students can access the content on-the-go from anywhere they like.
Basically, each topic is like a detailed flash card and will make the lives of students simpler and easier.
Some of topics Covered in this application are:
1. Types of lighting schemes
2. Electrical Symbols
3. Lists of Electrical symbols
4. Salient Features of Electricity Act, 2003
5. Consequences of Electricity Act, 2003
6. Indian Electricity Rules (1956)
7. General safety precautions
8. Role and Scope of National Electric Code
9. Components of National electric code
10. Classification of Supply Systems - TT system
11. Classification of Supply Systems - TN system
12. Classification of Supply Systems - IT system
13. Selection criteria for the TT, TN and IT systems
14. Load break switches
15. Switch Fuse Units & Fuse Switches
16. Circuit Breakers - MCB
17. Circuit Breakers - MCB Selection & Characteristics
18. Circuit Breakers - RCCB
19. Circuit Breakers - MCCB
20. Circuit Breakers - ELCB
21. Circuit Breakers - Voltage Base ELCB
22. Circuit Breakers - Current-operated ELCB
23. Circuit Breakers - ACB
24. Operation of ACB
25. Air Blast Circuit Breaker
26. Different Types of Air Blast Circuit Breaker
27. Circuit Breakers - OCB
28. Bulk Oil Circuit Breaker
29. Single & Double Break Bulk Oil Circuit Breaker
30. Circuit Breakers - Minimum Oil
31. Circuit breakers - VCB
32. Electrical Switchgear
33. SF6 Circuit Breaker
34. Types and Working of SF6 Circuit Breaker
35. Vacuum Arc or Arc in Vacuum
36. Different types of fuses
37. Protection against over load
38. Delay curves
39. Service connections
40. Electrical Diagrams
41. Methods for representation for wiring diagrams
42. Systems of House Wiring
43. Neutral and earth wire
44. Load Factor for Electrical Installations
45. Earth bus- Design of earthing systems
46. Demand Factor for electrical installations
47. Diversity Factor for electrical installations
48. Utilization factor & Maximum Demand for electrical installations
49. Coincidence factor for electrical installations
50. Demand Factor & Load Factor according to Type of Buildings
51. Design of LT panels
52. Current Rating of single core XLPE Un-armoured INSULATED Cables
53. Current Rating of single core XLPE Armoured INSULATED Cables
54. Current Rating of Two core XLPE Un-armoured INSULATED Cables
55. Current Rating of Two core XLPE Armoured INSULATED Cables
56. Current Rating of Three core XLPE Un-Armoured Insulated Cables
57. Current Rating of Three core XLPE Armoured INSULATED Cables
58. Current Rating of Three & Half core XLPE Un-Armoured INSULATED Cables
59. Current Rating of Three & Half core XLPE Armoured INSULATED Cables
60. Current Rating of Four core XLPE Un-Armoured INSULATED Cables
61. Current Rating of Four core XLPE Armoured INSULATED Cables
62. Qualities of good lighting schemes
63. Luminous flux
64. Luminous intensity
65. Illuminance
66. Luminance
67. Reflection and Reflection Factor
68. Laws of illumination
69. Necessity of Illumination
70. Photometry & Luminaire
71. Photometric Bench
72. Incandescent Lamps
73. Characteristics of Incandescent Lamps
74. Discharge Lamps
75. Mercury Vapor Lamp
76. Sodium Vapor Lamp
77. Fluorescent Lamp
78. Luminaries in Illumination Schemes
79. Mounting of Luminaries
80. Glare
81. Evaluation of Glare
82. Color
83. Color Specification Systems - Munsell system
84. Color Specification Systems
85. Interior Lighting
86. Trends and finishing of Interior Lightning
87. Sports Lighting
All topics are not listed because of character limitations set by the Play Store.
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Question about projectile motion of a rocket
1. 97853
Question about projectile motion of a rocket
A rocket is fired at a speed of 75 m/s from ground level, at an angle of 60 degrees above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 27 m away. By how much does
the rocket clear the top of the wall?
The solution includes detailed explanations of the projectile motion of a rocket.
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Time use and hindsight
I am in the midst of revising a paper that uses a very specific question from the Fragile Families Data set about reading to children. When I began writing the paper, I started looking for evidence
with time-use surveys, such as the American Time Use Suvey (ATUS) which asks participants to record everything they do and for how many minutes on two given days (a weekday and a weekend, usually). I
noticed, particularly at the PAA meetings this Spring, that there was a lot of controversy about these surveys. What, exactly, can they tell us about general effects, when we are looking at such a
small sample of time for any given individual? More specifically, if we want to examine the effects of a particular policy, how does looking at one individual’s day give us a causal effect of a
policy? Time use surveys are incredibly useful for seeing exactly how individual spends his time on any given day, and the possibilities for understanding the dynamics of child-rearing and marriage
are far-reaching. The trade-off is that you have no way of knowing whether this is a typical day or not. On average, for the population, if we have a random sample of individuals and days are
sufficiently randomly assigned, we should get an idea of what the population does, on average. But asking if a particular impetus leads to a specific behavioral change (for instance, does an increase
in income mean you invest more in child’s education) is a little more problematic. The alternative is to ask questions in a survey setting about time-use behaviors without specifying the time. That’s
what the Fragile Families does, and the question about how many days per week you read with your child has its own problems. I have long argued that when individuals answer the question, they must do
some averaging over time. The question is not “how many days did you read with your child last week” as might be preferred or indicated by the literature on work (did you work last week?), but rather
a sort of what do you usually do? I’ve been surprised at how much pushback I’ve received on this matter from discussants and reviewers. Most say the natural model to use is a count model, like
negative binomial or Poisson, but I think it makes more sense to use an ordered probit, which allows for 4 to be more than 2, but not necessarily twice as much as 2. I don’t think the reading days
answer is as firmly countable and identifiable as something like parking tickets, where a count model is the readily apparent model. I imagine the question is a lot like exercise. Over the weekend, I
helped a friend with her match.com profile and one of the questions is how many days a week do you exercise? For some, the answer is absolutely 7, every single day. For others, zero, not lifting a
finger. For most, though, I’d guess it varies from week to week. One week, you go every day, the next week is busy at work, so you go less often. Perhaps you go on a whole-day hike and tell me two
days instead of one because you don’t want to seem lazy. Thus, when I ask you the question of how many days a week you exercise, you’re not really giving me a straight answer, through no fault of
your own. You’re averaging over the last couple of weeks, you’re perhaps adjusting your answer to reflect what you think the surveyor is looking for, and you’re partially giving an impression of how
much you value exercise. I’m having a hard time making this same argument regarding time spent with children to discussants and reviewers, and I’m not sure what I’m missing in my explanation to make
it more convincing.
One thought on “Time use and hindsight”
1. In my world, we would partially concede and tell the reviewers, “We did it our way and then we did it your way, and the results were not substantially different.” That seems to appease everyone.
Of course this is not so simple if the results are indeed different, but such a difference might help you argue on behalf of your preferred method. Good luck :-)
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Re: animateMotion - specifying a start position along a path that is not the beginning of the path
From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de> Date: Sun, 12 Dec 2010 14:59:44 +0100 To: www-svg@w3.org, ryan.arnold@gmail.com Message-Id: <201012121459.44718.Dr.O.Hoffmann@gmx.de>
the example seems to be pessimised with scripting,
therefore the example is presented as an empty file
for me ;o)
However following your explanation my idea would
1. to determine/calculate the length of the path and
the lengths of each car as a fraction of the length of
the path (if you have problems with calculation for the
path, you can use stroke-dasharray to iterate it manually)
2. to use corresponding keyPoints and keyTimes
(for each car the sum of the fractions of the cars before,
respectively behind, depending on the order, see below)
For a closed path it might be necessary to repeat
the motion path to be able to provide keyPoints for
one complete turn for every car.
For an open path you might need additional motions
(maybe discrete) to remove the cars from the path
at the right time - or whatever might happen, if they
are at the end of the path.
It is maybe a good idea to to turn around the order of cars
to get a simpler method to position the cars correctly
with the keyPoints.
There can be more complications if calcMode is
not paced or the lengths of cars change within the
active duration.
If you want to use your approach with different
begin times (what could be simpler for several
viewers/user-agents), the approach is almost
the same, first the determination of the length
of the path and the lengths of each car, then
use corresponding vales for begin (active
duration multiplied by sum for fractions of cars
If you agree to simplify the car presentation to a
basic stroke (I like abstraction ;o),
you can try to realise it with an animation
of stroke-dasharray as well, avoiding advanced
calculations of path and car lengths, fractions,
keyTimes and keyPoints ;o)
Received on Sunday, 12 December 2010 14:00:18 GMT
This archive was generated by hypermail 2.3.1 : Friday, 8 March 2013 15:54:47 GMT
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increasing/decreasing/monotone function
increasing/decreasing/monotone function
Definition Let $A$ be a subset of $\mathbb{R}$, and let $f$ be a function from $f:A\to\mathbb{R}$. Then
Theorem Let $X$ be a bounded or unbounded open interval of $\mathbb{R}$. In other words, let $X$ be an interval of the form $X=(a,b)$, where $a,b\in\mathbb{R}\cup\{-\infty,\infty\}$. Futher, let $f:X
\to\mathbb{R}$ be a monotone function.
1. 1.
2. Lebesgue
• 1 C.D. Aliprantis, O. Burkinshaw, Principles of Real Analysis, 2nd ed., Academic Press, 1990.
• 2 W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Inc., 1976.
• 3 F. Jones, Lebesgue Integration on Euclidean Spaces, Jones and Barlett Publishers, 1993.
increasing, decreasing, strictly increasing, strictly decreasing, monotone, monotonic, strictly monotone, strictly monotonic, weakly increasing, weakly decreasing, strongly increasing, strongly
decreasing, strongly monotone, weakly monotone, stronly mono
Mathematics Subject Classification
no label found
no label found
Let set A = {1,2,3}.
1. How many relations are monotone increasing funtions?
2. How many relations are monotone decreasing funtions?
3. How many relations are strictly increasing funtions?
Added: 2003-04-28 - 16:02
Attached Articles
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Cleveland, TX Math Tutor
Find a Cleveland, TX Math Tutor
...I have taught Algebra II for over 4 years with a high success rate. All of my students continued to Precalculus and were successful in both subjects. I teach several different methods so that
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Post a reply
In my opinion the question is awful. I have to make so many assumptions. Now, what the heck is that drawing? Are we supposed to assume that is the xy axis without it being labelled? Am I supposed to
assume that graph at the ends is touching the x axis, making A amd B roots.
Did they expect you to be able to get the roots to that quartic? Not an easy job without a computer. Do they want the straight line distance between A and B or the Arc length distance?
Now assuming that is the xy axis and A and B are touching it and that squiggly mess is the graph of the function, which it is not. I solve like this:
-X^4+5x^3+4X^2+6X+8 = 0 has 2 real roots thay are:
x = -1 and x = 5.89102041
So the straight line distance is 6.89102041 which is none of your choices.
The arc length distance between A and B is 327.039 also not one of your choices.
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CFI Forums | Any scientific evidence to support official WTC 7 fall theory?
The supports are made of PAPER. This has been known all along.
Yes, and you picked paper because its compressive strength is a properly scaled for your model relative to the compressive strength of structural steel, taking into account the orders of magnitudes
difference in loading bearing capacity do to simple physics of scaling.
Whoops! Silly me, I forgot you keep insisting you didn’t scale your model at all, and when I said your model isn’t scaled properly you demanded I prove you claimed it was! ROFLMFAO!!!
You heard it here folks! Psik outright admits his model is not scaled correctly, admits that mass and load bearing strength do not scale linearly with dimensions which radical alters the model’s
behavior in mass and load bearing behavior. He proves this with math and then cries “but I made it out of paper and didn’t concern myself with scaling issues!”
At this point my sides are hurting from laughter. Please psik, I want you to tell us more about your model, I can’t stop laughing over here. LMAO
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New theory/algorithms for bubble density measurement using inverse
ASA 124th Meeting New Orleans 1992 October
2pAO12. New theory/algorithms for bubble density measurement using inverse acoustic scattering techniques.
Ramani Duraiswami
DYNAFLOW, Inc., 7210 Pindell School Rd., Fulton, MD 20759
Acoustical techniques have long been used to estimate the bubble density function. The conventional technique assumes isolated (non-interacting) scatterers, and results in a Fredholm integral
equation of the first kind relating the bubble density and the measured scattering is obtained. These ill-posed equations are numerically challenging to solve, especially when the data---obtained
from experiments---inevitably contain noise/error. Usually these equations are solved by assuming resonant scattering, or by accounting approximately for off-resonance scattering. Additionally the
conventional model used for the bubble scattering, does not properly account for thermal losses in the bubble oscillations. In the present work, a multiphase model for sound propagation through
bubbly liquids (due to Caflisch et al.) is combined with Prosperetti's model for bubble oscillations, to develop two new equations for determining the bubble population function from measured
phase-velocity and attenuation data. The new theory/equations address perceived drawbacks in the conventional technique. The equations are evaluated for their potential for determining the bubble
population, by testing them with analytical data with varying artificial noise. Numerical algorithms using new regularization techniques are developed. [Work supported by NSF.]
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Geometry Textbooks
Browse New & Used Geometry Textbooks
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Results 1 - 50 of 279 for Geometry Textbooks
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Neffs, PA Algebra Tutor
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FOM: Erdos Probabilistic Method: Logical Status?
Matthew Frank mfrank at jeltz.uchicago.edu
Sun Dec 3 16:57:54 EST 2000
Robert Tragesser asked various questions about Erdos's probabilistic
> (1) Is it just drama or a genuine philosophical point that inspires
> the definite article 'the', when [Aigler and Ziegler] say 'the
> nonconstructive method'?
Just drama.
> (2) "the Probabilistic Method" does not involve any essentially new
> logical idea
I agree.
> (3) If [the probabilistic] doesn't involve any essentially novel
> logical ideas, it in any case surely involves novel methodical ideas.
I'm not sure that the method is so novel. Lebesgue worried about similar
issues by the 1910s, showing how to construct elements of sets of positive
measure, and considering an example where this was non-trivial. (I just
found out about this over the summer, so hopefully I remember it right:
Consider the set of reals between 0 and 1 whose decimal expansions contain
all decimal digits equally often in the limit. Lebesgue considered the
set of reals whose expansions have this equidistribution property not just
in base 10, but in any base.)
My impression is that Erdos's use of the probabilistic method is
remarkable for the concreteness and virtuosity of his applications.
Regardless of whether the method was new with him, many people took up
the method because of his inspiration.
> I am wondering how one ought to go about evaluating the
> foundational/philosophical significance of methodological ideas
One way, as you suggest, is to codify the principles in second-order
arithmetic and find their status in the reverse math hierarchy. But, even
if one is committed to a formal analysis of methodological significance,
this is only one approach--reverse mathematics is not the only formal
system with foundational aims! Still, the pigeonhole principle will
probably be unproblematic in any formal system.
> (4) What is the reverse mathematics of "the Pigeonhole Principle?"
Since you ask...we formalize this as:
for every n,
for every function f: [1,n+1]->[1,n]
there exist distinct a,b less than n+2 with f(a)=f(b)
The following proof by induction on n contains only bounded quantifiers,
and so stays within the base theory RCA_0.
n=1 is trivial.
For the inductive step, say f: [1,n+2] -> [1,n+1].
If for all x, f(x) < n+1, then we restrict f to [1,n+1]
and are done by inductive hypothesis
If there is exactly one x such that f(x)=n+1, then
consider f': [1,n+1] -> [1,n] defined by
f'(x) = f(x) if f(x) is not n+1
f(n+2) if f(x) = n+1
Then by applying the inductive hypothesis to f',
(and a slight analysis of cases) we can find the desired a and b.
If there are two x's such that f(x)=n+1, then we are done.
What I'd like to know about the pigeonhole principle is: when did it come
to be associated with pigeons?
More information about the FOM mailing list
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Online Dictionary of Crystallography
Twin lattice
From Online Dictionary of Crystallography
Réseau de la macle (Fr). Reticolo del geminato (It). 双晶格子 (Ja)
A twin operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent (
twinning (effects of). The (sub)lattice that is formed by the (quasi)restored nodes is the twin lattice. In case of non-zero twin obliquity the twin lattice suffers a slight deviation at the
composition surface.
Let H* = ∩[i]H[i] be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D(L[T]) the point group of the twin lattice
and D(L[ind]) the point group of the individual lattice. D(L[T]) either coincides with D(H*) (case of zero twin obliquity) or is a proper supergroup of it (case of non-zero twin obliquity): it can be
higher, equal or lower than D(L[ind]).
Related articles
The definition of twin lattice was given in: Donnay, G. Width of albite-twinning lamellae, Am. Mineral., 25 (1940) 578-586, where the case D(L[T]) ⊂ D(L[ind]) was however overlooked.
See also
Chapter 3.3 of International Tables of Crystallography, Volume D
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the first resource for mathematics
Galerkin methods based on Hermite splines for singular perturbation problems.
(English) Zbl 1107.65064
This paper is concerned with the numerical solution of singularly perturbed elliptic two point boundary value problems. The authors propose a Galerkin method with Hermite splines where the knots have
been adapted to the boundary layer behaviour of the solution. A sufficient condition on the mesh that ensures that the approximate solution has optimal order of convergence in the energy norm with
respect to the perturbation parameter is given.
These optimal meshes are constructed with the aim to have an equal distribution of the errors in the subintervals and improve the orders of convergence of N. S. Bakhvalov [Zh. Vychisl. Mat. Mat. Fiz.
9, 841–859 (1969; Zbl 0208.19103)] and G. I. Shishkin [Sov. J. Numer. Anal. Math. Model. 3, 393–407 (1988; Zbl 0825.65062)].
Further an approach for the effective construction of these optimal meshes is given. Finally, the paper includes the results of some numerical experiments to test the orders of the theoretical
65L10 Boundary value problems for ODE (numerical methods)
65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
34B15 Nonlinear boundary value problems for ODE
65L20 Stability and convergence of numerical methods for ODE
65L50 Mesh generation and refinement (ODE)
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% Depth-First Search for Constraint Functional-Logic Programs % Sebastian Fischer (sebf@informatik.uni-kiel.de) This module defines depth-first search as a strategy that can be used in constraint
functional-logic programs. It shows what definitions are necessary in order to turn an instance of the `MonadPlus` type class into a strategy for CFLP.
> {-# LANGUAGE
> FlexibleInstances
> #-}
> module CFLP.Strategies.DepthFirst where
> import CFLP
Depth-first search is implemented by the list monad. In order to make it a strategy, we need to make `[]` an instance of the `Enumerable` type class that allows to enumerate monadic values in a list.
For the list monad, this instance is trivial:
> instance Enumerable [] where enumeration = id
We define depth-first search strategies for evaluation-time choice semantics. In order to get call-time choice, this needs to be transformed with the call-time choice transformer.
> dfsWithEvalTimeChoice :: c -> Monadic (UpdateT c []) a
> dfsWithEvalTimeChoice _ = Monadic undefined
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Science News
What follows is a fairly complete transcript of a discussion about quantum physics on May 19, 1994, the last day of a workshop in Santa Fe, N.M. It begins with some technical issues, posed by John
Denker of Bell Labs, concerning projection operators, mathematical expressions involved in representing quantities that can be observed in quantum measurements. It soon evolves into a more general
discussion of the interpretation of quantum mechanics and the quantum measurement problem.
John Denker, displaying a diagram of a double-slit experiment: “Let’s be a little bit careful about what’s going on here. We start with some source of state here and there’s some amplitude to get
from the source to B. There’s some amplitude to get from the source to A. Some amplitude to get through the two slits, and there’s some amplitude to propagate all the way over to the receiver. And
you add those things up and multiply them in the right way and it’s all hunky dory. And we’ve been doing that since we were babies.
“The unit operator is basically in the appropriate space that we care about right now is this outer product, but this outer product is represented by that, and the projection operator about which I
have immoderate feelings is written like this, and it’s this outer product plus zero. And the question is, is this an OK thing to use, or is this a shorthand for something else? And in particular,
when we put a brick in front of that slit, what is the appropriate quantum mechanical representation for that brick? If we treat this as a measuring apparatus, what’s the appropriate quantum
mechanical [unintelligible] about measuring apparatus. Well, rather than put a brick in front of this slit, I’m going to put here what really you can put there. You can put an antenna there attached
to a resistor which is attached to a cold load which is attached to the rest of the universe, and it actually conserves energy. So let’s do the quantum mechanics of this thing. It’s the same
propagator and source of this thing and [unintelligible] A slit but what about the B slit? There’s some chance that the B slit is going to get tossed into the dissipation, which is represented as D,
and there’s equally something here that says a fluctuation is going to come out of this cold load due to the slit and off to the receiver. The unit operator in this enlarged space ADBF looks like
that, and by putting this block in front of the B slit we do not get a projection operator. What happens is this little blue block here gets permuted one and we get this thing here. D is the
dissipation and F is the fluctuation and they’re related by the fluctuation dissipation theorem. They’re both part of the heat bath. One is the mode going into the heat bath, the other is the mode
coming out of the heat bath. And the magnitude of the fluctuation is going to be equal to the magnitude of the dissipation times some function of temperature. The function does not go to zero even at
zero temperature, which means that I can see the fluctuation even at zero temperature, even in the ground state, I can build a quantum nondemolition voltmeter that’s sensitive enough to see the
fluctuations coming off of your brick. Notice that the upper left corner two by two piece of this thing looks exactly like the projection operator that you thought you had when you had a brick that
you didn’t really understand. But you see what this really is, is shorthand for a permutation matrix that permutes one of your modes into the heat bath and permutes the corresponding thing out of the
heat bath. This is why I sit in the back of the room and growl every time I see this formalism of the entire universe as a bunch of projection operators times projection operators times projection
operators times projection operators. They are maybe the shorthand for this, but maybe not....
“If you expand unity as a complete sum of projection operators, OK, that’s mathematics, you can do that, no problem. It’s not OK in general, even as a shorthand, for we know it went through the A
slit and not through the B slit. But the bottom line is yeah, what it really is, is a shorthand not for the projection operator, a shorthand for a rotation operator that rotates something in the heat
bath and rotates something out. And that’s OK, if you can’t tell the ground state from zero times the ground state. I’ve tried to make this point in various ways, and a lot of people say I’m wrong
about this, but I would dearly love to have somebody explain why it’s not exactly right....”
Neil Gershenfeld: “What is the conclusion you draw about building quantum computers?”
Denker: “I think that you will probably wind up using a lot of quantum nondemolition measurement techniques in your quantum computer, and you need to worry about what’s terminating the other port of
your beam splitter. So I think that certainly when you’re thinking about the foundations and probably when you’re trying to implement the foundations....”
William Unruh: “What you’re essentially saying here is that quantum mechanics has unitary transformations, not projection operators.”
Denker: “Yes, and when you use projection operators as a shorthand you might get away with it and you might not.”
Unruh: “But it’s not a shorthand, because the projection operators are a statement about the interpretation of quantum mechanics, the fact that when one goes out one finds definite things happening.
What you’re raising here is the whole quantum measurement problem. In my language, that a determination is not the same as a measurement.”
Denker: “My view of the quantum measurement problem is very different from some other people’s view of it.... A lot of times you can get what you want in the appropriate limit by making, by tracing
over a low temperature or zero temperature distribution of the heat bath. What you do is you amplify the signal you care about to the point where it’s a hell of a lot bigger than your temperature, or
a hell of a lot bigger than your ground state fluctuations, and then you average over that thing and you get a measuring device that you understand in detail without ever appealing to a projection
operator. You appeal to a rotation operator with the thing that your rotated in the [unintelligible].”
Unruh: “You still have to appeal finally to a projection operator because ultimately you have to, ultimately you have to, ultimately you have to [Zurek shaking his head] ultimately (unintelligible.)”
Denker: “He’s telling you what I have to do in order to measure a voltage, and I’m telling him that in my experience in the laboratory, I don’t have to do that, ultimately or otherwise. And that this
is, at least in the situations that I understand a sufficient analysis of the measuring apparatus, I do not need separate measurement postulates. All I need is the unitary dynamics of quantum
mechanics, the unitary dynamics of amplifiers that I know how to build, and I can do quantum measurement without any stinking quantum measurement problem.”
Simon Saunders: “You also need a partial trace over the environment….”
Denker: “Absolutely. In the limit where my voltmeter is sensitive enough to where I can see this thing, it is absolutely not equivalent.”
Seth Lloyd: “It’s certainly not equivalent to just taking a bunch of projection operators as in the decoherent histories approach. Projection operators in the decoherent histories approach are
supposed to correspond to things that you could be able to say about the universe or your system without having this sort of interaction that John was describing.”
Denker: “Postulating a projection operator is very different from postulating unitary dynamics and then tracing over the environment.”
Wojciech Zurek: “The term decoherent histories is perhaps a misnomer although as I’ve seen it used during this meeting it was essentially used in the context of ... you make an appeal to the
environment and you look for what sort of projection operators can you stick in there in order to let your history evolve nicely. What Jonathan (Halliwell) talked about and I assume what Todd talked
about was very much in this spirit. It’s very different from imposing from the outside consistency conditions [unintelligible] set of the projection operators. If you recognize these projection
operators are secondary, as emerging from within, what has happened, that’s one story. If you impose them from the outside it’s a different one.”
Gerard Milburn: “Did you say as the signal to noise ratio goes up in your measurement [unintelligible]?”
Unruh: “Just to reemphasize that the decoherence stuff, et cetera, does not address the fundamental issue that when we look at the world, our experience of the world is of definite things.”
Denker: “Is not.”
Unruh: “It can at best produce for you a set of classical probabilities. Now classical probabilities make sense.... Projection operators refer to individual events.”
Denker: “No, nope nope. Let’s actually go into the lab and we will set up the NMR experiment that corresponds to his thing and we’ll have a blip here, a little blip a little blip.... We were actually
doing this experiment once and we were remarking on how damn sharp that line was — until you look at this, the sharpness of that line almost makes you believe in eigenstates. And I believe every word
in that, including the almost. This thing is not completely definite. There’s real physics in that width, and the notion that this thing is in an exact eigenanything is an approximation. The idea we
have an experience of complete definiteness, I disagree with. It’s almost definite.”
Anton Zeilinger: “Each point of your diagram is definite.”
Unruh: “Each point on the diagram, the height of that voltage curve there, you’ve got a number there, 3.49528. At the next frequency it’s another number, it’s a definite number, it’s not some fuzz.
Whereas what quantum mechanics tells you is some fuzz.”
Denker: “Man, when I do experiments, that thing’s fuzzy, I’m sorry.”
Todd Brun: “I’d just like to speak to one very minor thing since I’ve been invoked just now to support both sides of this. I guess the word that I object to is the word impose. The idea that you are
taking these projection operators and imposing a condition on the world that the decoherence functional vanishes. This is not my interpretation of what’s going on at all. What I see it as is that you
have this system which is the universe or whatever you’re describing which is evolving, and the projection operator is a way of phrasing questions that have well-defined answers. So you are not
saying these are my projection operators, I want to get a definite answer out of these, you’re saying, what questions can I ask that have definite answers? So when one is talking about approximate
decoherence, the sorts of things that we see, one is sort of making the assumption even that obviously that there are some projection operators onto some set of variables which are somehow close
enough to this that when we look at it we say that this gives the answers that we’ve calculated.”
Jonathan Halliwell: “To reiterate the sort of thing that Todd has said, and just try to make some sort of clear statement about what decoherent histories is and what it’s trying to do, and how these
projections actually arise. Where it starts from is that it’s a formulation of quantum mechanics that’s designed for genuinely closed systems, such as the entire universe, and it does not assume the
existence of any kind of classical domain, and it does not have notions of measurement, just fundamental motions and theories. What replaces those notions of classical domain and measurement is an
emphasis on classical logic, just Boolean logic. So instead of assuming classical domains as in the Copenhagen interpretation, it tries to say let’s try and find those situations in quantum mechanics
which we can actually talk about, which we can relate to each other using the ordinary logic of everyday language. Now mathematically there is a connection between Boolean logic and probability
theory, so from there, saying that we’re going to deal with classical logic you can go very quickly to this idea of probabilities of histories because you want to be able to say things like is there
a logical connection between something that is measured and some property of the system in the past. Can we just on the grounds of pure logic deduce, given a measurement of the universe now, the past
history of the universe?
“[Unintelligible] say nothing about things happening [unintelligible], we’re just saying can we make probability context of quantum mechanics using the Hilbert [unintelligible] space formalism of
quantum mechanics, can we make logical connections between different candidate events? Then given that we can then focus on probabilistic histories, you can ask the question what is the mathematical
expression that gives those probabilities? And it was argued by Omnes, just by putting forth a list of reasonable requirements, those probabilities should satisfy that one is led more or less
uniquely to this trace formula that the probability of a history is given by the usual density matrix with a string of projections operating on it. These projections, as Todd was saying, essentially
just characterize the different types of properties that the system may exhibit at different moments of time. It is characterized from within the Hilbert space formalism of quantum mechanics.
Statements like a particle was in this range at a certain time and another range at a later time and so on, so these just enter in a purely mathematical way, it just represents classical Boolean
“Ultimately at the end of the day one actually has to make a correspondence between one of those projections and some actual event in the universe. One makes the correspondence between the final
projection and some piece of present data for example, and then conditions on that quantum event to try and find things which have probability one in the past. Which I think essentially is what Bill
was saying.”
Asher Peres: “Jonathan, you said a particle was in this domain or was in another domain, what do you mean, WAS?”
Halliwell: “It was misuse of language.... You don’t think of it as an event that actually happened.... You can phrase it all in a much more roundabout way.”
Unruh: “The first thing is that the decoherence formula, that expression for the probabilities of the various histories, that’s just basically standard quantum mechanics. There’s absolutely no
difference from that from straight quantum mechanics. The place in which the consistent histories or the decoherent histories people make a change is that they state there are only certain histories
that are in some sense legal histories. And those histories are the kinds of histories where the individual events in the histories have some sort of, one can argue that they have some sort of
objective significance whether or not you determine them in my language or measure them in other people’s language. They state that all we are only going to talk about those things which have that
kind of an objectivity where it doesn’t matter whether I go in and measure it or not. Now that’s a huge additional assumption. Without that assumption you’ve just got absolutely everyday standard
quantum mechanics that we were all taught in grade 1, and with that extra bit of stuff you’ve got a new theory that doesn’t make me feel very happy.”
Halliwell: “There’s more in that sense, but there’s less than the Copenhagen interpretation in the sense that you drop any kind of assumptions about classical domains and measurements.”
Unruh: “We learned long ago that that was Bohr’s attempt in my language to associate this determination with measurement. That was his attempt to marry those two things together. I don’t think that
one can actually ever ultimately do that.”
Denker: “Just for the record I want to emphasize that that little resistor I drew there was not classical, no implication that there was anything classical in that. I believe there’s only one
universe, it’s fully quantum mechanical. Including that [unintelligible] environment….
Saunders: “...The point about putting the brick in front of one of the slits in your history approach, as I understand it, that whole operation of placing that brick, the description of the brick
itself, the various wires that you’re going to have ... all of that will be described in terms of a sequence of projection operators which are merely stating what are the properties, perhaps the
components of the quantum mechanical state. The whole apparatus of projection operators in decoherent histories theory is not being used as [unintelligible] anything about the dynamics, it’s a method
for transferring properties of the state, in other words associating the state or coordinating the state with subsets from the spectrum of the various kinds of dynamical variable. The way something
different from unitarity comes in the unitary dynamics in particular is entirely when you start to throw away various components of the universal state, or you can use Bill’s terminology when you say
that something definite has happened, something which is recognizable according to our experience. Now that [unintelligible] decoherent histories approach it depends on how you phrase it. Some people
... would hold that only one history is actually stochastically developing in time, and in the frame of the decoherent histories approach that would indeed be to invoke the projection postulate, now
you use projections in a rather different way. But in your own approach, if you’re going to take a partial trace, OK fine, but now to interpret the impure state that you get out as a result of that
partially traced [unintelligible] state in terms of the description of an ensemble maybe, or at least such that one or another thing has actually happened, given that interpretation, the universal
state that you will then work with following taking the partial trace and supposing that something has happened, the state that you will then work with thereafter will not be unitarily related to the
state that you began with.... It’s indicating a breakdown or a failure of unitarity. That is put it to you how are you going to take that partial trace and interpret it to mean that something has
happened, consistent with unitarity. I see no option [unintelligible]”
Denker: “Well, I do the calculation pretty much as you have described. I write down the unitary operator that describes my voltmeter, and I get out of it — there is a point where I turn a crank and
take a partial trace, and the thing that falls out of the partial trace is a number with dimensions of voltage on it. And then I interpret that by saying this is the voltage. And the voltage is big
enough that it’s classical and I know what it means and I just don’t—”
Unruh: “In the usual language you say that’s what the expectation value is. You sum out over all these probabilities times the value of the voltage in each one of the probabilities and get the
expectation value.”
Denker: “Yeah, and the action behind this expectation value is big enough that the stationary phase approximation is good and the watchyacallit theorem, the voltage that comes out of my voltmeter is
big enough to be classical and I run it to a stripchart recorder and I show it to Wigner and Wigner shows it to his friend and it’s done.”
Unruh: “You now go into the same lab, you run the same voltage and you get a different value, you do the same experiment in exactly the same way you get a different value for that voltage. How do you
interpret that different value, because your theory gives you exactly the same answer in both cases.”
Denker: “That’s not a quantum mechanics problem.”
Unruh: “Sure it is. ... It’s the quantum noise, in your language, that caused that difference....”
Zeilinger: “... I should confess that I am probably one of the few surviving Copenhagenists in this thing. I don’t see any reason why I should adopt another interpretation. Because in the lab we have
classical stuff, we have stuff which we describe with our everyday language, and definite events happen, period. There’s no way around it. And quantum mechanics is never going to [unintelligible] as
long as the formalism of a certain interpretation is isomorphic with the same as quantum mechanics formulation. If I talk about a different formulation ... as long as I have something which is
isomorphic I will never be able to explain in [unintelligible] language why events happen. I can have beautiful things like Wojciech’s beautiful demonstrations and then other people’s that you get
this coupling to the environment, you get this nearly purely diagonal density matrix, which makes sense, which is in the right places and so on and so on. But that still does not explain why events
happen. Because even if I had the density matrix I will never get an explanation by the specific result that we obtain in one round of the experiment, in another round of the experiment I get another
result. And this is quite different from classical probability. People usually say OK this is just like classical probability and so on. It is NOT the same, because I start from identically prepared
initial states and I get different final results. I get sometimes this detector clicks, sometimes this one, sometimes this one. And it’s never explained, this difference, in quantum mechanics.... So
in my opinion there will never be a solution to the measurement problem.”
Samuel Braunstein: “I don’t want to get into any kind of interpretation stuff, mostly because I’m in the young generation and the young generation tend to ignore those problems. But I want to really
thank John Denker for that brief, pretty little presentation and in particular because it gave me a new way of thinking about another problem, which is eavesdropping in quantum cryptography; when the
eavesdropper is reading some information, she’s in a sense dissipating a little bit of quantum state, of the information in the quantum state, and that invariably is going to lead to some
fluctuations on the other end, and that’s a very beautiful way of looking at it.”
Zurek: “I want to make a couple of points which are related to what was said by various participants. Let me start with Anton. I think if one wants to follow through the program that John (Halliwell)
has outlined and that has come to be known as decoherence process or decoherence program, one needs to recognize that one has to work with the wave function of the whole universe. In other words,
there’s no cop-outs, you have to give up Copenhagen interpretation. Whether it’s going to get you where you want to get Anton, I don’t know. But let me try, OK? So in other words if one does have the
whole wave function there, it’s clear that all of the other things which are not supposed to happen, or which we don’t perceive, are really happening. All of the other alternatives of measurements,
somewhere they’re in this wave function — I’m saying what Everett said what, 40 years ago now. So the issue, which I think has to be stressed, is that the problem is not to explain why there is a
single universe there, really physically, but it’s a more limited question, why do we perceive one? A single one. And I think there decoherence does help. Decoherence process makes it impossible to,
for instance, remember superpositions of things or put neurons in superpositions of different perceptions. And this will make — if you include yourself within that wave function, you will be able to
understand why you can’t see anything else, if you think of yourself as a computer, now I don’t know if you are willing to do that. So the issue is that it helps you draw that boundary between
quantum and classical that Bohr wanted to draw, or put it differently in Everett language, it helps you define what the branches are. Now I think it’s very important to start defining these branches
not by putting in projection operators from the outside, and this is the point of this transparency, but by recognizing them from within. And to do that there’s no other way but to start, yes, with a
closed universe, but then recognize at some point that in order to state that problem of measurement, we have to divvy up this universe into subsystems. Once you have divvied up the universe into
subsystems in order to pose that question, we have the right to use that division to answer that question. I think a very good demonstration of how the right sort of projection operators emerge from
within the process that John Denker has reminded us of, is for instance in a harmonic oscillator with — harmonic oscillator is coupled weakly to the environment, it turns out that the states which
are most stable and which will end up being classical states are decoherent states. They are the most stable ones, and then having obtained decoherent states, you can start looking at histories. They
are going to be the histories given [unintelligible] by classical dynamics with a bit of luck....
“The point is that just by looking at the Schrodinger equation and splitting the universe into subsystems in a natural way, you can get the right sort of projection operator rather than impose them.
Now imposing them from the outside as is done in the consistent histories approach, poses a danger. For instance, one can put in projection operators which will make it difficult or impossible to put
sensible projection operators further down the road and satisfy consistency. Especially perfect consistency. So I think in a sense there are two programs there. One of them, the consistent histories
approach which goes back to Griffiths, Omnes, Gell-Mann and Hartle to some degree, which recognizes certain conditions for mathematical additivity of probabilities of histories. And that was an
approach, with mathematics. Then there is another approach which starts with a proclamation of a closed system, but then recognizes that what we are treating is actually a collection of subsystems,
and which tries to fish out from within that approach, the right sorts of projection operators which give us classical reality. And I think most of the people which commented on including Todd and
Jonathan firmly sit on the boundary between the two approaches.”
Lloyd: “I think this discussion shows that quantum measurement is quite a horse. You can beat it for 50 years and it still isn’t dead yet.”
Gershenfeld: “Asked from a naive perspective of not understanding the details, in this discussion I’m not sure I’ve heard anything falsifiable.”
Charles Bennett: “You got the basic point of it.”
Gershenfeld: “In any one situation, people use different words but come to the same answer. Is that right?”
Zeilinger: “What is just said, this coupling to the environment, it’s very important work, because it shows how a classical world is possible, but it does not give you a classical reality. There’s
still something which is left over, which you cannot explain, which I mentioned before. Let me say one thing. I don’t want to give a false impression. You know I consider myself a Copenhagenist
because I think it’s the most economic interpretation. But I think all the interpretations are important because for two reasons. Number 1, even if they are isomorphic in terms of predictions, they
might lead our intuition in a different way. So we might invent different experiments with interpretation A or with interpretation B. And the second reason why I think it’s important to have
different interpretations is that I still feel that someday we might understand, in John’s (Wheeler’s) words, why the quantum. And we have not the foggiest idea, I think, which interpretation will
finally help us….”
©2014 by Tom Siegfried
Follow me on Twitter: @tom_siegfried
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MathGroup Archive: April 2001 [00051]
[Date Index] [Thread Index] [Author Index]
Re: C, MathLink or Java, J/Link
• To: mathgroup at smc.vnet.net
• Subject: [mg28207] Re: C, MathLink or Java, J/Link
• From: tgayley at wolfram.com (Todd Gayley)
• Date: Wed, 4 Apr 2001 04:13:28 -0400 (EDT)
• Organization: Wolfram Research, Inc.
• References: <99usl9$61j@smc.vnet.net> <9a1jfh$9o8@smc.vnet.net> <9a6dps$eo2@smc.vnet.net> <9absfe$jvl@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com
On 3 Apr 2001 03:01:02 -0400, Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:
>Hi Todd,
>yes your J/Link *is* great. It is one of the best perls of software
>that I have seen!
>And the best thing on it, that you can use Java without programming
>in Java.
Thanks for your support of J/Link. The Mathematica community is also in debt to you for
your excellent (and free) MathGL3d.
>I have two questions to the benchmark, you gave. What C-compiler ?
>On Intel boxes Intel 4.5 is usual 20-30 % faster than Microsoft's
>Visual C. Even the code generated by Borland C 5.5 is better that
I used Microsoft Visual C++. There may be compilers out there that can produce faster
code, but does it matter? The fact that Java and C are in the same ballpark on this
program is enough to make my point. What fraction of users out there are going to switch
away from Visual C++ because another compiler produces code that runs a little faster?
Certainly not me. People who care about that level of performance are not going to be
using Java. I'm much more interested in using tools that I like, am comfortable with, and
am productive with. My personal productivity is _far_ more important to me than shaving a
few points off a timing. I'll wager that this is true for the vast majority of Mathematica
users (that's why they use Mathematica).
>And how does Mathematica with the code ? using all the optimizations
>that Mathematica can do ? How fast is Mathematica itself with
>the benchmark ?
Well, I don't have the motivation to put in the effort to produce an optimized Mathematica
program for this. I did a literal translation of the C/Java code into Mathematica
(resulting in a very naive Mathematica program), and it ran 8000 times slower than the
fastest Java and C timings. It could be made much faster with a little work.
>> Are these results typical of numerical programs of the sort Mathematica programmers are
>> likely to be writing? I would say yes. I usually expect a Java program to run in a range
>> comparable to C down to perhaps 1/2 to 1/3 as fast.
>Hoops ! you mean a C program on a 1.4 GHz PC is as fast as a Java
>on a 2.8 or 4.2 GHz PC ... So where to buy the 4.2 GHz PC ??
>If this *is* not slow, what else mean "slow" ? For me it make
>a difference if I have to wait one hour or three.
>I have seen people that work hard for 5 % performance gain.
If your definition of slow is that Java runs at half the speed of C, then yes, Java is
slow. If I can work in a language where I am much more productive and can ignore the
intricacies of MathLink entirely, and the cost is only that my programs run at the same
speed that my C programs ran 18 months ago (i.e., Moore's Law), then I am happy to do
I just got a 1.2 GHz machine. It's 2.5 times as fast as my 500 MHz machine, but I would
hardly say that my old machine is suitable only for Tic Tac Toe.
People writing programs that take one hour to run will probably want to use C. People who
are willing to work hard for a 5% performance gain will probably use C. Most other people
will be happy with Java.
>> As always, "Your mileage may vary". Nevertheless, people should not rule out Java in
>> advance as a language for virtually any kind of program based on the (mostly erroneous)
>> assumption that it is "too slow".
>I agree with you that in many cases speed is a so critical point.
>Since the computer spend the most time while waiting onto a mouse click
>or a keyboard character. So for those cases Java is a lot easyer than
>C or C++.
>But you should keep in mind what happens with an application.
>If the code is fast, one find always a task that can be done also.
>Every program is extended until the program hit the limits of the
Agreed, but I am just repeating myself. Some programs stretch the limits of the machine.
Most don't.
>> As for the original question, about whether to use Java or C for an algorithm to be called
>> from Mathematica, the answer is of course "it depends". Some factors that favor C are:
>> - you already are proficient in C
>> - you just have one function to call and you don't need to have a
>> complicated interaction with Mathematica
>> - you don't need to port your program to other platforms
>> - flat-out performance is overwhelmingly important
>The easy usage for complicated interaction with Mathematica
>is your merit. And it is up to every C-programmer
>to do similar stuff in C/C++. Your Java/C source is about
>500 kByte. This is the real advantage of Java -- that you
>have done a lot of work on it. But how much of this Java
>code is used by a typical MathLink application ?
>The most MathLink programms are written for speed.
>I expect the advantage of Java in writing custom
>portable user interfaces for all those people that
>need more than some buttons and in this case speed is not
>critical and one has the Java librarys.
>I think "portability" is not more a serious problem
>of a C program. MathLink is wonderful portable and
>one finds for almost every thing a portable library.
Most MathLink C/C++ programs are very portable. But that still means that you have to have
access to machines that run every OS you want to support, you have to master the
development environments on these machines, you have to recompile on every platform every
time you make a change, etc. This is not an issue for users who are just building programs
for one machine, but for those who want to produce something useful for a variety of
platforms, it is a huge consideration.
I'm sure we are both aware that we are just rehashing a debate that has gone on about new
languages and programming styles since the dawn of programming. People said C was slow
compared to assembly language. C won out because it was more productive to work in, was
portable, and got faster as compilers improved.
I think we can just agree to disagree about the usefulness of Java for general-purpose
programming tasks. The performance of Java is considered acceptable by the huge number of
developers doing commercial and research programming with it. My opinion is that for
people who are not overwhelmingly concerned about performance, Java is the best choice for
programs that call, or are called by, Mathematica. But people shouldn't take my word for
it--try it!
--Todd Gayley
Wolfram Research
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Jacobi fields on a "bump surface"
up vote 4 down vote favorite
Consider a "bump surface" which looks like the following:
Such a surface is rotationally symmetric, $C^2$-smooth, has positive curvature in the middle and negative curvature along the ring (the orange region in the picture). I don't really care what happens
past that (it could flatten out, or oscillate, etc.)
Here are two examples, as surfaces of revolution in $\mathbb R^3$ in cylindrical coordinates:
$z(r) = e^{-r^2/2}$ and $z(r) = \tfrac{2}{\pi} \cos(\tfrac{\pi}{2} r)$.
I need to do some Riemannian geometry on a bump surface; in particular, analyze a Jacobi field along a radial geodesic $\gamma$. I don't care what bump surface I use; it only has to feature both
positive and negative curvature. For any surface of revolution, it's easy to write down a formula for the scalar curvature $K$ (see p. 142 of McCleary's Geometry from a differentiable viewpoint), and
the Jacobi equation takes the form $J'' + KJ|\dot\gamma|^2 = 0$. Thus, if the scalar curvature has a simple form, then the Jacobi equation should be easy to solve. In the case of these two examples,
the scalar curvature isn't particularly pretty, hence analyzing the Jacobi equation is difficult (though not intractable).
My question to the MathOverflow community: is there a better bump surface than the two examples I gave above, for which the scalar curvature has a particularly simple form?
Edit: The curvatures for the surfaces given above are
$K(r) = \frac{2 (1 - r)}{(e^{r^2/2} + r^2 e^{-r^2/2})^2}$ and $K(r) = \frac{\pi \sin(\pi r)}{2 r (1 + \sin^2(\pi r/2))^2}$,
respectively. As you can see, they're not the worst expressions possible, but they're also not as simple as I'd like them to be.
riemannian-geometry dg.differential-geometry differential-equations
Following Mariano's comment, I guess it's important to you that the surface be $C^2$, right? – Steve Huntsman Jan 19 '10 at 23:50
Steve: You're correct. Thanks for pointing that out. I'll edit the post. – Tom LaGatta Jan 20 '10 at 0:05
2 FYI: jstor.org/stable/2162371 – Steve Huntsman Jan 20 '10 at 0:44
Steve, that looks like an extremely useful paper. Thanks for the link! – Tom LaGatta Jan 20 '10 at 0:56
One thing you can do is pick a curvature function of your liking and integrate it to a surface; then you'll like the curvature but probably not the surface :) For a surface of revolution, the
integrability conditions might not be too hard to satisfy---but I haven't checked... – Mariano Suárez-Alvarez♦ Jan 20 '10 at 1:12
show 1 more comment
2 Answers
active oldest votes
Take a portion of a pseudosphere and cap it with a portion of a sphere in such a way that the surface is ($C^1$)-smooth.
OLD (BAD) ANSWER:
up vote 4 down
vote Take a portion of a hyperboloid and cap it with a portion of a sphere in such a way that the surface is smooth.
2 But Tom wants a surface on which the curvature has a nice form... your surface has the correct signs, but depending on how artfully (or not) you do the capping, the curvature may
be quite ugly! – Mariano Suárez-Alvarez♦ Jan 19 '10 at 22:49
You're right, I was confused about hyperbolic space vs. a hyperboloid. – Steve Huntsman Jan 19 '10 at 23:09
Now, capping the pseudosphere with a sphere cannot be made $C^2$-smoothly, for if you could the curvature function would not be continuous. – Mariano Suárez-Alvarez♦ Jan 19 '10 at
Mariano's right: while it's easy to write down many such bump surfaces, I'm struggling with finding one that has a really simple expression for the curvature. – Tom LaGatta Jan 19
'10 at 23:33
Yeah, there's a singularity at the gluing circle. – Steve Huntsman Jan 19 '10 at 23:39
show 1 more comment
ORIGINAL ANSWER DELETED
EDIT: I neglected to account for the need to parameterize by arclength. And I think I also misunderstood and thought that you wanted only the Jacobi field that fixes the center. You want
to solve for an Jacobi field, given a point (away from the center) and a vector at that point, right?
So that's definitely not as easy as I thought. Here are my thoughts:
1) I think the already proposed surface given by a spherical cap glued to a pseudosphere is already a good enough question. In my experience you never really need a $C^2$ surface, and
something with piecewise continuous curvature is almost always enough. I encourage you to try it.
2) As for the more general approach, I no longer have any easy answer, but here are some thoughts:
Let the surface be given by $(r,\theta) \mapsto X(r,\theta) = (r\cos\theta, r\sin\theta, f(r))$. If $s$ be the arclength parameter along a radial geodesic, then $s'(r) = \sqrt{1 + f'(r)^2}
up vote 3 $. One Jacobi field $J_1(r,\theta)$ is given simply by
down vote
$J_1(r,\theta) = \partial X/\partial\theta = re_\theta$, where $e_\theta = (-\sin\theta, \cos\theta, 0)$ is a unit vector field that is orthogonal to and parallel along any radial
If we view $r$ as a function of $s$, then the Jacobi equation says that $r'' + Kr = 0$, where $K$ is the Gauss curvature. It suffices to solve for one more Jacobi field $J_2 = h(s)e_\
theta$ independent of $J_1$. The Jacobi equation for $J_2$ is given by $h'' + Kh = 0$. Since $r$ is already a solution, we can try to solve for $h$ using variation of parameters.
So the goal is to find an even function $f$ with an inflection point such that the function
$s(r) = \int_0^r \sqrt{1 + f'(t)^2} dt$
can be explicitly integrated and inverted. I suggest trying something like $f(r) = 1/(1+r^2)$.
Deane: Thanks for the response. Let me clarify why I care about this this surface in particular. I am interested in length-minimizing geodesics in random Riemannian manifolds. My
strategy is to show that the radial geodesic has conjugate points, and perturb the space so that the "radial" geodesic in the perturbed space still has a conjugate point. Thus I really
am trying to study Jacobi fields on a space like this. – Tom LaGatta Jan 19 '10 at 23:31
That's fine. I'm just pointing out that you already have simple explicit formulas for both the Jacobi field and the curvature for the specific examples you give above. So there's no
need to look any further. – Deane Yang Jan 19 '10 at 23:45
Also, that if it's the Jacobi field you really care about, there's no need to compute curvature first. – Deane Yang Jan 19 '10 at 23:53
1 Could you explain further? I don't quite understand. What's the simple explicit formula for Jacobi fields along a radial geodesic in a surface of revolution? Also, this might not be
clear from the above: I am starting the geodesic at an arbitrary point, with initial velocity pointing directly toward the center. – Tom LaGatta Jan 20 '10 at 0:27
add comment
Not the answer you're looking for? Browse other questions tagged riemannian-geometry dg.differential-geometry differential-equations or ask your own question.
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Utility Function Problems
March 24th 2011, 04:02 AM #1
Junior Member
May 2009
Utility Function Problems
Hi, I’m having a lot of trouble with this question as I just can’t seem to figure out the value of Px, if it is at all possible to figure out Px, and I’m also having trouble answering the other
questions. It would be great if someone could offer some help or work me through the questions. Thanks.
3. Suppose that you have the following utility function: U(x,y)=6x^0.5+y.The price of x is Px and the price of y is 1.
a. Your income is Y = $24. Find the uncompensated demand for good x. That is, find the amount of x which maximizes the consumer’s utility, subject to affordability. You can use any method you
want. Do not worry about corner solutions.
b. What is the income elasticity of uncompensated demand for good x?
c. Now suppose that you want to attain utility U = 10. Find the compensated demand for good x. That is, find the amount of x which minimizes your expenditure, subject to attaining utility of 10.
You can use any method you want. Do not worry about corner solutions
The terminology in your question is different to the one i was taught with, but i dont think you're supposed to find the price Px.
The demand for x is a function of the price Px. You need to find what the demand would be in terms of Px.
So, for example, a simple demand function might be (this is NOT the answer): Demand = 0.5 - 2Px
Last edited by SpringFan25; March 24th 2011 at 12:55 PM.
March 24th 2011, 10:33 AM #2
MHF Contributor
May 2010
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the first resource for mathematics
Greedy function approximation: A gradient boosting machine.
(English) Zbl 1043.62034
Summary: Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive
expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for
least-squares, least absolute deviation, and Huber-M loss functions for regression [
P. Huber
, Ann. Math. Stat. 35, 73–101 (1964;
Zbl 0136.39805
)], and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for
interpreting such “TreeBoost” models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classification,
especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of
Y. Freund
R. E. Shapire
[see J. Comput. Syst. Sci. 55, 119–139 (1997;
Zbl 0880.68103
)] and
J. Friedman, T. Hastie
R. Tibshirani
[Ann. Stat. 28, 337–407 (2000;
Zbl 1106.62323
)] are discussed.
62G08 Nonparametric regression
62-07 Data analysis (statistics)
65C60 Computational problems in statistics
62K10 Statistical block designs
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Speed Worksheets
Home > Measurement > Speed
Speed Worksheets
Speed worksheets provide the best practice in converting different speed units. Simple tips provided for easy conversion. Children must be familiar with basic distance and time unit conversion such
as km to m, m to miles, hour into sec etc. Refer how to solve speed problems to learn the way to solve these worksheets.
Find Speed using Distance and Time:
Find speed in the respective units using a formula, Speed = Distance / Time.
Convert m/sec into km/hr:
To convert m/sec into km/hr, multiply by 18 and then divide the result by 5.
Convert km/hr into m/sec:
To convert km/hr into m/sec, multiply by 5 and then divide the result by 18.
Convert m/sec into miles/hr:
Multiply by 2.236936 (approx) to convert meter per second into miles per hour.
Convert miles/hr into m/sec:
To convert miles/hr into m/sec, multiply the numbers by 0.44704 (approx)
Convert miles/hr into km/hr:
1 mile = 1.609344 km. Unit of time is the same in both cases. So, go ahead and multiply the number.
Convert km/hr into miles/hr:
1 km = 0.621371192 mile (approx). In both cases unit of time is hour. Go ahead and multiply.
Conversion of Units: Mixed Review
These speed worksheets provide mixed review of all common units based on speed.
Conversion of Units: Mixed Review
These speed worksheets provide mixed review of all common units based on speed.
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May 15, 2009 1:38:02 AM (5 years ago)
• v8 v9
15 15 == Language Support ==
17 The remainder of this document is a first design draft for SAC style language support of multidimensional arrays in the context of DPH. The implementation is not completed yet, and there
are several open questions.
17 The remainder of this document is a first design draft for SaC style language support of multidimensional arrays in the context of DPH. The implementation is not completed yet, and there
are several open questions.
21 19 == The regular array type ==
… …
23 21 === SaC ===
25 29 === DPH ===
26 Regular parallel arrays are similar to arrays in SAC, with one major
27 difference: array operations in DPH are fully typed, and consequently, what
28 is called 'shape invariant programming' in SAC works differently in DPH. In particular, in DPH the dimensionality of an array (not its size, however) are encoded in its type.
30 Regular parallel arrays are similar to arrays in SaC, with one major
31 difference: SaC employs a mix of static and dynamic type checking, combined with a form of shape inference, whereas we use GHC's type checker to ensure certain domain restrictions are not
33 '''Note:''' currently, we are only able to statically check that restrictions regarding the dimensionality of and array are met, but not with respect to the size. SaC is, to a certain
extend, able to do so. I still need to check if there are some cases where the DPH approach would statically find some dimensionality bugs where SaC wouldn't - need to check that.
36 array operations in DPH are fully typed, and consequently, what
37 is called 'shape invariant programming' in SaC works differently in DPH. In particular, in DPH the dimensionality of an array (not its size, however) are encoded in its type.
30 39 An multidimensional array is parametrised with its dimensionality and its
… …
51 60 type instance Shape (Int, Int) = (((),Int), Int)
52 61 }}}
54 64 For readability, we define the following type synonyms:
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Generator to run 6000btu window ac - SailNet Community
Join Date: Apr 2007
Location: St Thomas USVI
Posts: 817
Freedom 39 Thanks: 0
Thanked 9 Times in 9 Posts
Rep Power:
Re: Generator to run 6000btu window ac
Originally Posted by
The 6000BTU unit states an energy efficiency of 9.7, so 6000/9.7 is 618 Watts. In reality losses and the inefficient thermal insulation of the boat will make the unit less efficient, so take 800W as
the constant load. Generators are rated at colder temps and their efficiency goes way down as they get warmer (and since you need AC it will be warm), so take 20% off your 2000W genset giving 1600W
then take another 20% off that for the maximum constant running output giving 1300W realistic power when running all day.
The numbers are just examples of the math you need to do, you can plug in your own estimates. Are you planning on charging the batteries or running other items off the generator? Those would need to
be added into the equation as well.
You lost me Zanshin.
The AC specs show an electrical draw of 560 watts which should be RLA or running load amps. Start up loads are usual double or more for a second or two. A 1000 watt generator would probably run it
but I would get a 2000 watt one, that way you are not pushing it so hard at start up and have more than 1000 watts free to run other things if you'd like unless you find the compressor cycling on and
off. There isn't much cost difference between a 1000 and 2000 watt generator typically.
Last edited by FarCry; 05-05-2013 at 05:19 PM.
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Graphical Analysis
October 31st 2009, 10:12 AM
Graphical Analysis
I need some help with these 2 questions, thank you
a) For this case, sketch the graph of a continuous function f(x) such that
f(0)=0, f"(x)>0 for x<0, f"(x)< 0 for x>o, lim f'(x)= +infinity (x approaches 0-) and lim f'(x)= +infinity (appraches 0+)
what would the graph look like?
b) For what real number values of 'p' does the equation
p= 3x-9 have 2 real solutions (algebraically)
November 1st 2009, 01:40 AM
I need some help with these 2 questions, thank you
a) For this case, sketch the graph of a continuous function f(x) such that
f(0)=0, f"(x)>0 for x<0, f"(x)< 0 for x>o, lim f'(x)= +infinity (x approaches 0-) and lim f'(x)= +infinity (appraches 0+)
what would the graph look like?
$f(0)=0$ and $\lim_{x \to 0_-} f'(x)= +\infty$ and $\lim_{x \to 0_+} f'(x)= +\infty$ should tell you that the curve has a cusp at $x=0$.
The other conditions tell you that the slope is increasing when $x$ is negative and decreasing when $x$ is positive.
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Bayesian Curve Fitting Using Mcmc With Applications To Signal Segmentation
Results 1 - 10 of 50
"... Abstract—This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a
linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown e ..."
Cited by 37 (26 self)
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Abstract—This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear
combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of
abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and fulladditivity
constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior
distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian
estimator is illustrated by simulations conducted on synthetic and real AVIRIS images. Index Terms—Bayesian inference, endmember extraction, hyperspectral imagery, linear spectral unmixing, MCMC
methods. I.
- In International Conference in Machine Learning , 2007
"... We show how to apply the efficient Bayesian changepoint detection techniques of Fearnhead in the multivariate setting. We model the joint density of vector-valued observations using undirected
Gaussian graphical models, whose structure we estimate. We show how we can exactly compute the MAP segmenta ..."
Cited by 31 (0 self)
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We show how to apply the efficient Bayesian changepoint detection techniques of Fearnhead in the multivariate setting. We model the joint density of vector-valued observations using undirected
Gaussian graphical models, whose structure we estimate. We show how we can exactly compute the MAP segmentation, as well as how to draw perfect samples from the posterior over segmentations,
simultaneously accounting for uncertainty about the number and location of changepoints, as well as uncertainty about the covariance structure. We illustrate the technique by applying it to financial
data and to bee tracking data. 1.
, 2007
"... Abstract—This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear
combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters a ..."
Cited by 31 (21 self)
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Abstract—This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear
combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints
are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows
one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of
spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data. Index Terms—Gibbs sampler,
hierarchical Bayesian analysis, hyperspectral images, linear spectral unmixing, Markov chain Monte Carlo (MCMC) methods, reversible jumps. I.
- IEEE Transactions on Signal Processing , 2007
"... We propose a joint segmentation algorithm for piecewise constant AR processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors
allow to introduce correlations between the change locations of the observed signals. Numerical problems ..."
Cited by 28 (16 self)
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We propose a joint segmentation algorithm for piecewise constant AR processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors
allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint
segmentation methodology provides interesting results compared to a signal-by-signal segmentation. 1.
- J. Amer. Statist. Assoc , 2005
"... In this work we consider the problem of modeling a class of nonstationary time series signals using piecewise autoregressive (AR) processes. The number and locations of the piecewise
autoregressive segments, as well as the orders of the respective AR processes, are assumed to be unknown. The minimum ..."
Cited by 25 (0 self)
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In this work we consider the problem of modeling a class of nonstationary time series signals using piecewise autoregressive (AR) processes. The number and locations of the piecewise autoregressive
segments, as well as the orders of the respective AR processes, are assumed to be unknown. The minimum description length principle is applied to find the “best ” combination of the number of the
segments, the lengths of the segments, and the orders of the piecewise AR processes. A genetic algorithm is implemented to solve this difficult optimization problem. We term the resulting procedure
Auto-PARM. Numerical results from both simulation experiments and real data analysis show that Auto-PARM enjoys excellent empirical properties. Consistency of Auto-PARM for break point estimation can
also be shown. KEY WORDS: Non-stationarity, change points, minimum description length principle, genetic algorithm
"... Abstract—This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian
noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seam ..."
Cited by 17 (8 self)
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Abstract—This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian
noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate
Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by
marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the
image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more
information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is
illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument. Index Terms—Bayesian inference, deconvolution, Markov chain Monte Carlo (MCMC)
methods, magnetic resonance force microscopy
- IEEE Trans. Signal Process
"... Abstract—Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian
priors to represent relationships between signals with various degrees of certainty, and not just rigid constr ..."
Cited by 16 (9 self)
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Abstract—Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to
represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise
constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate
the performance of the proposed algorithm. Index Terms—Gibbs sampling, hierarchical Bayesian analysis, Markov chain Monte Carlo, photon counting data, segmentation. I.
, 2011
"... Abstract—This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components
contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polyno ..."
Cited by 14 (13 self)
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Abstract—This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components
contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and
optimization methods are proposed to estimate the parameters involved in the model.Theperformanceoftheunmixing strategies is evaluated by simulations conducted on synthetic and real data. Index
Terms—Hyperspectral imagery, postnonlinear model, spectral unmixing (SU). I.
- IEEE Trans. Image Processing , 2010
"... Abstract—This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are
supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model e ..."
Cited by 13 (11 self)
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Abstract—This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are
supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction
algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian
algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs
sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology
is evaluated by comparison with other unmixing algorithms on synthetic and real images. Index Terms—Bayesian inference, hyperspectral images, Monte Carlo methods, normal compositional model, spectral
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Differential Equation - how to solve a simple equation..
June 10th 2012, 03:57 AM #1
Oct 2011
Differential Equation - how to solve a simple equation..
I am really struggling to solve this differential using the basic rules that I know.
There should be a dot above the A in the numerator on the left hand side and brackets around the fraction on the right hand side but I wasn't sure how to do that.
Any help gratefully received!!
Imagine a country that is adopting foreign technology T as shown in the following equation where A denotes the level of domestic technology and the dot over A denotes its derivative with respect
to time:
$\frac{A}{A}= \phi(E)\frac{T(t)- A(t)}{A(t)}$
a) Assume that the level of foreign technology is constant and solve the differential equation above
b) What is the effect of an increase in the level of education E?
c) What is the effect of an increase in the rate of growth of foreign technology λ?
Last edited by econolondon; June 10th 2012 at 05:51 AM.
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A system of the mathematics
A system of the mathematics: containing the Euclidean geometry, plane & spherical trigonometry ... astronomy, the use of the globes & navigation ... Also a table of meridional parts ... Together with
a large & very useful table of the latitudes & longitudes of places, Volume 1 (Google eBook)
James Hodgson
We haven't found any reviews in the usual places.
Bibliographic information
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Polynomially continuous operators
Llavona, José G. and Gutiérrez, Joaquín M. (1997) Polynomially continuous operators. Israel Journal of Mathematics , 102 . 179-187 . ISSN 0021-2172
Restricted to Repository staff only until 31 December 2020.
Official URL: http://www.springerlink.com/content/67414688531p4130/fulltext.pdf
A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. Every compact (linear) operator
is polynomially continuous. We prove that every polynomially continuous operator is weakly compact.
Item Type: Article
Uncontrolled Keywords: Space
Subjects: Sciences > Mathematics > Functional analysis and Operator theory
ID Code: 16279
References: R. Alencar, R. M. Aron and S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, Proceedings of the American Mathematical Society 90 (1984),
R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by polynomials, Bulletin of the Australian Mathematical Society 52 (1995), 475–486.
R. M. Aron, M. Lacruz, R. A. Ryan and A. M. Tonge, The generalized Rademacher functions, Note di Matematica 12 (1992), 15–25.
R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, Journal für die reine und angewandte Mathematik 313 (1980), 195–216.
T. K. Carne, B. Cole and T. W. Gamelin, A uniform algebra of analytic functions on a Banach space, Transactions of the American Mathematical Society 314 (1989), 639–659.
H. S. Collins, Completeness and compactness in linear topological spaces, Transactions of the American Mathematical Society 79 (1955), 256–280.
L. A. Harris, Bounds on the derivatives of holomorphic functions of vectors, in Colloque d'Analyse (L. Nachbin, ed.), Rio de Janeiro, 1972, pp. 145–163.
T. Jech, Set Theory, Monographs and Textbooks in Pure and Applied Mathematics 79, Academic Press, New York, 1978.
M. Lacruz, Four Aspects of Modern Analysis, Ph.D. Thesis, Kent State University, Kent, OH, 1991.
J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in L p -spaces and their applications, Studia Mathematica 29 (1968), 275–326.
J. Mujica, Complex Analysis in Banach Spaces, Math. Studies 120, North-Holland, Amsterdam, 1986.
R. A. Ryan, Holomorphic mappings on ℓ 1 , Transactions of the American Mathematical Society 302 (1987), 797–811.
Deposited On: 10 Sep 2012 08:04
Last Modified: 07 Feb 2014 09:26
Repository Staff Only: item control page
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Video Library
Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation
spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all
available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant
bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Experiments have ruled out unit-strength scalar-mediated fifth forces on scales ranging from 0.1 mm to 10,000 AU. However, allowing the scalar to have a quartic self-interaction weakens these
constraints considerably. This weakening is due to the "chameleon mechanism", which gives the scalar field an effective mass that depends on the local matter density. I will describe the chameleon
mechanism and discuss experimental constraints on self-interacting scalar fields.
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Negative numbers
I am looking for advise to add a minus sign (-) to the beginning of text in a column in our spreadsheet.
For example the column has: 123456
I would like it to be: -123456
I have thousands of lines and each line has a unique text string.
Thanks in advance
HTML Code:
Public Sub X()
Dim c As Range
'// for each cell in the range you want to edit.
'// Change A1:A500 to suit ...
For Each c In Range("A2:A2727")
'// Already got - at the beginning?
If Left$(c.Value, 1) "-" Then
'// No, add it
c.Value = c.Value & "-"
End If
End Sub
I have tried the above, however it adds it to the end. 123456-
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parametric equation question
March 25th 2009, 01:01 PM #1
Oct 2007
parametric equation question
Please explain how to do the following problem.
Graph the following parametric equation. Identify the domain and range. Eliminate the parameter.
x = sq.root of t
y = 2 – sq.root of t
Thank you very much
I did a table for
t = 0, 1, 4, 9
x = 0, 1, 2, 3
y = 2, 1, 0, -1
Positioned the dots (x,y), it's a line Domain (-infinity, +infinity), Range (-infinity, +infinity). When I eliminated the parameter, the equation is y=2-x
Does it make any sense? Thank you again.
Your work is OK except for the domain and range
$x=\sqrt{t}$ and $y=2-\sqrt{t}$ are defined only for $t \geq 0$ which means $x \geq 0$ and $y \leq 2$
Therefore the graph is not a complete line but a "semi-line" starting from the point (0,2)
The domain is not $(-\infty,\infty)$, and neither is the range.
$x=\sqrt{t}$ is only defined when $t\ge 0$, which means $x\ge 0$, so your domain is $[0,\infty)$
Likewise, $y=2-\sqrt{t}$ is only defined when $t\ge 0$, which means $y\le 2$, so the range of the function is $(-\infty,2]$.
The equation IS $y=2-x$, but we must restrict the domain to $[0,\infty)$ because of the parameters we were initially given.
Thank you
running-gag and Pinkk,
Thank you very much.
March 25th 2009, 01:16 PM #2
MHF Contributor
Nov 2008
March 25th 2009, 01:17 PM #3
March 25th 2009, 03:17 PM #4
Oct 2007
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Urgent help needed
11-16-2004, 08:00 PM
URGENT Help Needed fast :(
Can anyone here please tell me how to make a java program on JBuilder that lets you put a number in between 1 and 20 and gives you the fibonacci number?:confused:
We are supposed to have it print out like "Fibonacci(14) is 377.
I have the input ok, and the output, but I do not know how to use a "While" loop to compute the fib number.:(
My teacher and tutor are both unable to help me, and if I want to pass this class, I only need this final assignment to be passing (we have no final :))!
Anyone who can help me with how to use a while loop to compute a fibonacci number i would appreciate it.. all they have online for source codes are fibonacci series' (i just need the one number
at a time computed) and stuff, and its all too advanced for my class (Comp Sci 100) so he would know I had help and fail me.
for those who dont remember, fibonacci is...
0 1 1 2 3 5 8 13 21 etc
Thanks a Billion in advance!:(
PS: I got saddled with the worst, least helpful teacher here...!
11-16-2004, 10:30 PM
to clarify, what i need is something i believe goes like this? do you have any idea what I need? lol
int num ;
int first;
first = 0;
int second;
second = 1;
num = readint.ln(what is the number, between 1 - 20?)
while (counter < fib)
first + second = fib
second = first
fib = second
counter = counter + 1
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Prediction with Expert Advice by Following the Perturbed Leader for General Weights
││ LaTeX - PostScript - PDF - Html/Gif ││
Prediction with Expert Advice by Following the Perturbed Leader for General Weights
Authors: Marcus Hutter and Jan Poland (2004)
Comments: 16 pages
Subj-class: Learning; Artificial Intelligence
Reference: Proceedings of the 15th International Conference on Algorithmic Learning Theory (ALT 2004) pages 279-293
Report-no: IDSIA-08-04 and cs.LG/0405043
Paper: LaTeX - PostScript - PDF - Html/Gif
Slides: PostScript - PDF
Keywords: Prediction with Expert Advice, Follow the Perturbed Leader, general weights, adaptive learning rate, hierarchy of experts, expected and high probability bounds, general alphabet and
loss, online sequential prediction.
Abstract: When applying aggregating strategies to Prediction with Expert Advice, the learning rate must be adaptively tuned. The natural choice of sqrt(complexity/current loss) renders the
analysis of Weighted Majority derivatives quite complicated. In particular, for arbitrary weights there have been no results proven so far. The analysis of the alternative "Follow the
Perturbed Leader" (FPL) algorithm from Kalai & Vempala (2003) (based on Hannan's algorithm) is easier. We derive loss bounds for adaptive learning rate and both finite expert classes with
uniform weights and countable expert classes with arbitrary weights. For the former setup, our loss bounds match the best known results so far, while for the latter our results are new.
││ LaTeX - PostScript - PDF - Html/Gif ││
BibTeX Entry
author = "M. Hutter and J. Poland",
title = "Prediction with Expert Advice by Following the Perturbed Leader for General Weights",
booktitle = "Proc. 15th International Conf. on Algorithmic Learning Theory ({ALT-2004})",
address = "Padova",
series = "LNAI",
volume = "3244",
editor = "S. Ben-David and J. Case and A. Maruoka",
publisher = "Springer, Berlin",
pages = "279--293",
year = "2004",
http = "http://www.hutter1.net/ai/expert.htm",
url = "http://arxiv.org/abs/cs.LG/0405043",
ftp = "ftp://ftp.idsia.ch/pub/techrep/IDSIA-08-04.pdf",
keywords = "Prediction with Expert Advice, Follow the Perturbed Leader,
general weights, adaptive learning rate,
hierarchy of experts, expected and high probability bounds,
general alphabet and loss, online sequential prediction.",
abstract = "When applying aggregating strategies to Prediction with Expert
Advice, the learning rate must be adaptively tuned. The natural
choice of sqrt(complexity/current loss) renders the
analysis of Weighted Majority derivatives quite complicated. In
particular, for arbitrary weights there have been no results
proven so far. The analysis of the alternative ``Follow the
Perturbed Leader'' (FPL) algorithm from Kalai \& Vempala (2003) (based on
Hannan's algorithm) is easier. We derive loss bounds for adaptive
learning rate and both finite expert classes with uniform weights
and countable expert classes with arbitrary weights. For the
former setup, our loss bounds match the best known results so far,
while for the latter our results are new.",
││ LaTeX - PostScript - PDF - Html/Gif ││
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from The American Heritage® Dictionary of the English Language, 4th Edition
• n. Anatomy A muscle that stretches or tightens a body part.
• n. Mathematics A set of quantities that obey certain transformation laws relating the bases in one generalized coordinate system to those of another and involving partial derivative sums. Vectors
are simple tensors.
from Wiktionary, Creative Commons Attribution/Share-Alike License
• n. A muscle that stretches a part, or renders it tense.
• adj. Of or relating to tensors
• v. To compute the tensor product of two tensors.
from the GNU version of the Collaborative International Dictionary of English
• n. A muscle that stretches a part, or renders it tense.
• n. The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into
another. See Versor.
from The Century Dictionary and Cyclopedia
• n. In anatomy, one of several muscles which tighten a part, or make it tense, or put it upon the stretch: differing from an extensor in not changing the relative position or direction of the axis
of the part: opposed to laxator.
• n. In mathematics, the modulus of a quaternion; the ratio in which it stretches the length of a vector.
• In anatomy, noting certain muscles whose function is to render fasciæ or other structures tense.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
• n. any of several muscles that cause an attached structure to become tense or firm
• n. a generalization of the concept of a vector
New Latin tēnsor, from Latin tēnsus, past participle of tendere, to stretch; see tense^1.
(American Heritage® Dictionary of the English Language, Fourth Edition)
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hi guys i think i have implemented the NQueens problem.
but i am still confused with the unwinding of the recursive backtracking so can someone explain to me what my code is doing
1. this is not an assignment or project but rather something i am doing during the holidays
and if you think its assignment or project please don't respond.
what i don't understand
my code prints out different solutions close to 90 times, i didn't check if all were different.
but i want it stop after it has found 1 solution to the problem if any.
so can anyone tell me why its printing so many times
since i have the base case if n==size:return board
if you require more explanation me know.
thought i mention that i understand the general concepts of recursion and backtracking to some degree
here is my code
i left out one functions/method call is_Safe(board,x,y) because it looks messy and bad implementation, anyway it returns
true or false
if the x,y is a safe place to place a queen in according to the board
def solve(board,x,size):
if x==size:
print" found solution"
return board
for i in range(8):#boar is 8*8
if is_Safe(board,x,i):
solve(board,0,8)#place 8 queens on board
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
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Integral of Modified Bessel Function of the Second Type
up vote 2 down vote favorite
Given the identity $$ \int^\infty_0 K_v\left(\alpha\sqrt{x^2+z^2}\right) \frac{x^{2\mu+1}}{\left(\sqrt{x^2+z^2}\right)^v}\:\mathrm{d}x = \frac{2^\mu \Gamma(\mu+1)}{\alpha^{\mu+1}z^{v-\mu-1}} K_{v-\
mu-1}(\alpha z), \quad \alpha>0,\quad \Re[\mu]>-1$$
how can I find a closed form for the integral:
$$ \int^\infty_0 \exp\left(-\beta x^2\right) K_v\left(\alpha\sqrt{x^2+z^2}\right) \frac{x^{2\mu+1}}{\left(\sqrt{x^2+z^2}\right)^v}\:\mathrm{d}x $$
I tried using series representation of the exponential function, but I got an infinite series.
integration integral-transforms special-functions
add comment
1 Answer
active oldest votes
Here is one situation when you can give a closed-form answer. Re-write the integral as
$$ I= e^{\beta z^2}\int_0^\infty e^{-\beta(x^2+z^2)} K_\nu(\alpha\sqrt{x^2+z^2}) x^{2\mu+1}(x^2+z^2)^{-\frac{v}{2}} dx $$
( $x:=zy$
up vote 3 down vote $$ =z^{2\mu+2-v} e^{\beta z^2}\underbrace{\int_0^\infty e^{-\beta z^2(y^2+1)} K_\nu(\alpha z\sqrt{y^2+1}) y^{2\mu+1}(y^2+1)^{-\frac{v}{2}} dx}_{=:A}. $$
To compute the integral $A$ use the change in variables $t=y^2+1$, $ y=(t-1)^{\frac{1}{2}} $ to reduce it to an integral of the form
$$ A = const \underbrace{\int_1^\infty e^{-\beta z^2 t} K_\nu(\alpha z t) (t-1)^\mu t^{-\frac{v}{2}} dt.}_{=: B} $$ If $\beta z^2= \alpha z$, then you can find a description of
$B$ in Gradshteyn and Ryzhik 6th Edition, formula 6.625 (9).
add comment
Not the answer you're looking for? Browse other questions tagged integration integral-transforms special-functions or ask your own question.
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A Reality Check on Chris Bowers' "Reality Check" about Obama's Approval Among Liberals
Chris Bowers, over at Open Left, is getting a bit uncomfortable with the upcoming Public Policy Polling numbers showing
Obama's approval rating at an astounding and steady 85% among liberals
. It doesn't come as a surprise to anyone except professional agitators like Bowers whose mantra - that liberals are abandoning Obama - goes ca-put with that poll. A Gallup poll shows the president's
approval among liberals at a lower 76%, according to
Ezra Klein
So he
rained on the parade
However, there is a serious flaw in citing these numbers: they are only based on a subsample of between 125-130, which gives them a margin of error of plus or minus 8.9%. That is, they are only
based on a subsample of 125-130 registered voters if PPP's new national survey is anything like their national survey from last month, when 19% of their overall sample of 667 voters
self-identified as liberal.
By way of comparison, across the last four Gallup weekly approval polls, which have a combined sample of 14,346 respondents, President Obama's job performance among self-identified liberals has
only averaged 74%. With Gallup identifying 20% of the electorate as liberal so far in 2010, that would mean a liberal subsample of 2,869, that would mean a margin of error of only 1.8%. That
makes the Gallup numbers far, far more reliable than the PPP numbers.
Sounds smart, doesn't it? It is, if you don't know much about statistics. But he does not show his math, he just asserts the margins of error. I am willing to bet he used some online calculator to
crunch these numbers,
like this one
, putting in the sample sizes. But unfortunately for Bowers, it doesn't always work that way. For
sample sizes over 40
with a significant population, the sample size matters less and less in a survey to determine the MOE. Bowers' numbers also don't make any sense, since a subsample's margin of error cannot be smaller
than the larger sample's (for Gallup it's +/- 3.0 percentage points).
In addition, Bowers quite amateurishly compares apples to oranges - he takes an aggregated sample (adds samples from many surveys together) and compares that to one survey from PPP. You can't compare
cumulative numbers to one standing survey.
Survey to survey, the sample size for Gallup is
, to PPP's 667 (for the whole population, and they roughly find the same percentage of liberals). But that's not even the whole story. Gallup surveys "national adults", whereas PPP surveys registered
voters. According to the US Census, only
65% of the US adult population is registered to vote
. So the Gallup sample of registered voters, assuming these percentages hold, is about 975. Not that big a difference.
So I suppose Chris Bowers had a nice try. But that's all it was: nice try.
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Pascal's Triangle
Explore patterns in Pascal's Triangle!
In 1653, a french mathematician named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose n
objects from a group of m indistinguishable objects.
The first seven rows of Pascal's Triangle look like:
1 n=0
1 1 n=1
1 2 1 n=2
1 3 3 1 n=3
1 4 6 4 1 n=4
1 5 10 10 5 1 n=5
1 6 15 20 15 6 1 n=6
Note that every number in the interior of the triangle is the sum of the two numbers directly above it.
It turns out that Pascal's triangle holds many interesting numeric patterns. One way of seeing some of these patterns is to pick a number x and color all numbers in the triangle that are evenly
divisible by x with one color, and all the other numbers in the triangle with a second color. To see as much of the pattern as possible, you need to be able to see as many rows of the triangle as
possible, but coloring a large number of rows like this by hand is very boring and time consuming. A computer can color 128 rows of the triangle in only a few seconds, so we can use it to look at the
results using many different divisors. The applet below lets you choose the number that you want to use as a divisor. Then it colors the first 128 rows of Pascal's triangle, coloring a square black
if the number that square represents is evenly divisible by the divisor you have selected and red if it is not. To change the divisor, type in a new number and click the "Set Divisor" button.
If you have a large monitor, here is a version of the applet which displays 256 rows of the triangle.
Here's something to investigate:
Look at the triangle using the divisors 3, 5, and 7.
Do you see a pattern? What do 3, 5, and 7 have in common?
Now try 9. Does the pattern continue?
Can you figure out what it is about 3, 5, and 7 that causes this pattern, and why it doesn't continue at 9? Does it continue with other numbers larger than 9?
Copyright (c) 1997 Jeremy Baer
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Drexelbrook, PA Algebra 1 Tutor
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"A plane is standing on a runway. . ." No, it's not. Here's why.
March 3, 2006
Dear Cecil:
Cecil, always enjoy your column, however you've got this [airplane and conveyor belt business] absolutely wrong. . . --strafe, via the Straight Dope Message Board
It's all about the interpretation of the question. Unfortunately, Cecil commingled two different interpretations in his column.
I knew this was going to happen. Everyone else, forgive me. This week's column is for the geeks.
Here's the original question: "A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This
conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?" (The Straight Dope:
The implicit assumption is that if the conveyor belt's speed backward exactly counteracts the airplane's "speed" (whatever that means) forward, the plane remains stationary relative to the earth and,
more importantly, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can't take off.
But the assumption is false. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves
forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. Many people have a hard time grasping this (although it can be easily demonstrated in the lab), but
eventually they do, smack their foreheads, and move on. We'll call this Basic Realization #1.
Message-board discussions of this question tend to feature a lot of posters who haven't yet arrived at BR #1 talking right past those who have, insisting more and more loudly that the plane won't
take off. Then there's a whole other breed of disputants who, whether or not they've cracked the riddle as originally posed, prefer to reframe it by proposing progressively more esoteric assumptions,
refinements, analogies, etc. Often they arrive at a separate question entirely: Is there a way to set up the conveyor so that it overcomes the thrust of the engines and the plane remains stationary
and doesn't take off?
The answer is yes. Understanding why is Basic Realization #2.
The conveyor doesn't exert much backward force on the plane, but it does exert some. Everyone intuitively understands this. To return to the analogy in my original column, if you're standing on a
treadmill wearing rollerblades while holding a rope attached to the wall in front of you, and the treadmill is switched on, your feet will initially be tugged backwards. Partly this is due to
friction in the rollerblade wheel bearings, but partly--this is key--it's because the treadmill is accelerating the rollerblade wheels and in the process imparting some angular (rotary) but some
linear (backward) momentum to them. You experience the latter as backward force. Eventually the treadmill reaches a constant speed and the rollerblade wheels cease to accelerate. At this point you
can easily haul in the rope and pull yourself forward.
But what if the treadmill continues to accelerate? Different story. In principle it's possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply.
(This is a departure from the original question, which said the conveyor belt compensated for the plane's speed,, not its force.) The only mathematics needed to demonstrate this is the well-known
physics axiom F = ma--that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to
equal any forward force F generated by its engines. Result: The plane stands still and doesn't take off. Welcome to BR #2.
You may say it's impossible to build a constantly accelerating treadmill, that eventually we run into the limitation imposed by the speed of light, etc. True but irrelevant--BR #2 has an intrinsic
elegance that transcends such practical concerns. Why didn't I bring it up in the first place then? You've got to be kidding. It took an entire column to get BR #1 across, and a second one to convey
(I hope) BR #2. One fricking thing at a time.
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- Grade 2
Essential Diet for Math
Outline of a Typical Lesson: (Daily)
First, introduce the math concept to the whole group. "Today in math you're going to be learning about ____." Relate the concept to previously taught concepts and/or real life experiences.
Next, because second graders need and enjoy movement it's helpful to gather the class together in a different spot from the introduction. Sitting in a circle on the floor works well. Model the
activity using the manipulative,. It is REALLY important to model first BEFORE handing out materials. That way the children are focused on YOU, not the fun stuff they'll be using. NOTE: Be sure to
give students opportunities to use all your manipulative in free play before using them in any math lesson. This really helps them focus on the lesson rather than just playing with the manipulative.
It's also helpful to pick some children to model for the group before you let them go do it on their own just to check for understanding. Once they've got it, let them go and practice while you
circulate, redirect, and guide.
After the class has had enough time to complete the activity, bring them back together and talk about their experience. Find out from them what worked, what didn't. This is your time to informally
assess their understanding and decide where your teaching should go from there. Often you can immediately move them into paper and pencil practice of the concept. This brings a quiet close to your
lesson just before you summarize. If you are using a page from the math workbook, it works nicely to complete the front page together and save the back of the page for independent work.
Finally, take a moment to wrap up the lesson with a quick summary. "Today we learned about Fact Families. We discovered that to make a family you need to....Tomorrow we will...."
• Be sure to use homework as practice for the skills recently taught or as a way to review previously taught concepts. Be careful not to overwhelm students (or parents!) with too much homework.
• It is very important to use the correct mathematical vocabulary. Be sure to use math terms on your word wall.
• Many skills can't be taught in one day using one or two workbook pages. They need to be revisited many times, even daily, throughout the year in order for them to become concrete.
• The teacher's manual is a life saver! There are six manipulative type activities to choose from for each lesson.
• Put your parent volunteers to work making multiple copies and laminating the Multi-Use Teaching Tools that you will use the most, such as: Tens Place-Value mat, Hundreds Place-Value mat, and
Hundreds Chart. Also use parent volunteers to make any other games described below.
• It is important to have a classroom set of the same rulers with the "0" on the edge of the ruler.
• Mental Math (Use a problem of the day)
• Paper/pencil activities
Good Supplemental Resources for Teaching Second Grade Math
│A Collection of Math Lessons Grades 1-3 │Marilyn Burns │Math Solutions Publication │
│Group Solutions │Jan Goodman │GEMS │
│Measuring │Joan Westley │Creative Publications │
│Time and Money │Joan Westley │Creative Publications │
│Math Excursions 2 │Donna Burke │Heineman │
│Frog Math Predict, Ponder, Play │Jaine Kopp │GEMS │
│Math and Literature │Mailyn Burns │Math Solutions Publication │
│Math and Literature │Stephanie Sheffield│Math Solutions Publication │
│Math by All Means Gr 2 Place Value │Mailyn Burns │Math Solutions Publication │
│Math by All Means Gr 2 Geometry │Chris Confer │Math Solutions Publication │
│Young Children Continue to Reinvent Arithmetic │Constance Kamii │Teachers College Press │
│Developing Number Concepts Using Unifix Cubes │Kathy Richardson │ │
│Used Numbers Sorting and Graphs │Russell and Corwin │Dale Seymour Publications │
│The Pattern Factory │Roper and Harvey │Ideal School Supply Company│
│Elementary Problem Solving Through Patterning │ │ │
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Corbino-geometry Josephson weak links in thin superconducting films
Title Corbino-geometry Josephson weak links in thin superconducting films
Publication Journal Article
Year of 2010
Authors Clem JR
Journal Physical Review B
Volume 82
Pages 174515
Date 11
Type of Article
ISBN Number 1098-0121
Accession WOS:000293784900005
Keywords barriers, JUNCTIONS, nonlocal interaction, phase
I consider a Corbino-geometry superconducting-normal-superconducting Josephson weak link in a thin superconducting film, in which current enters at the origin, flows outward, passes
through an annular Josephson weak link, and leaves radially. In contrast to sandwich-type annular Josephson junctions, in which the gauge-invariant phase difference obeys the sine-Gordon
equation, here the gauge-invariant phase difference obeys an integral equation. I present exact solutions for the gauge-invariant phase difference across the weak link when it contains an
Abstract integral number N of Josephson vortices and the current is zero. I then study the dynamics when a current is applied, and I derive the effective resistance and the viscous drag
coefficient; I compare these results with those in sandwich-type junctions. I also calculate the critical current when there is no Josephson vortex in the weak link but there is a Pearl
vortex nearby.
DOI 10.1103/PhysRevB.82.174515
Alternate Phys. Rev. B
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New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 139123, 8 pages
Research Article
New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces
College of Science, Civil Aviation University of China, Tianjin 300300, China
Received 4 May 2013; Accepted 17 June 2013
Academic Editor: Gue Myung Lee
Copyright © 2013 Peichao Duan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited.
We propose an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo-contractive mappings and the set of solutions of an equilibrium
problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper
improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.
1. Introduction
Let be a real Hilbert space with inner product and induced norm . Let be a nonempty closed convex subset of .
Let be a nonlinear mapping; we consider the problem of finding such that It is known as the variational inequality problem (denoted by ).
Generally, is assumed to be Lipschitzian and strongly monotone. The relative definitions are listed as follows.(i)is called -Lipschitzian on , if there exists a constant such that (ii) is said to be
-strongly monotone on , if there exists a constant such that (iii)A mapping of is said to be a -strict pseudo-contraction if there exists a constant such that for all ; see [1]. (iv)A mapping of is
said to be a nonexpansive mapping if it is strictly pseudo-contractive with constant .
Obviously, the class of strict pseudo-contractions strictly includes the class of nonexpansive mappings. We denote the set of fixed points of by (i.e., ).
Let be a bifunction from to , where is the set of real numbers.
The equilibrium problem for is to determine its equilibrium points, that is, the set The set of such solutions is denoted by .
Many problems in applied sciences such as physics, optimization, and economics reduce into finding some element of . Some methods have been proposed to solve the equilibrium problem (5); see, for
instance, [2–6]. In particular, Combettes and Hirstoaga [7] proposed several methods for solving the equilibrium problem. On the other hand, Mann [8] and Shimoji and Takahashi [9] considered
iterative schemes for finding a fixed point of a nonexpansive mapping. Further, Acedo and Xu [10] projected new iterative methods for finding a fixed point of strict pseudo-contractions.
In 2006, Marino and Xu [5] proposed a general iterative method and proved that the algorithm converged strongly. Recently, Tian [11] revealed the inner contact of Yamada’s algorithm [12] and
viscosity iterative algorithm and then introduced a new general iterative algorithm combining a -Lipschitzian and -strong monotone operator. On this basis, Wang [13] considered a general composite
iterative method for infinitely many strict pseudo-contractions in 2010. However, the -mapping used in Wang’s paper requires many composite operations. Very recently, He and Sun [14] proposed a new
operator to replace the -mapping for infinite family nonexpansive mappings.
The mapping is defined as follows: where such that , , and are infinite nonexpansive mappings. Because it does not contain many composite computations, it is more simple and easy to realize.
In this paper, we combine the operator and the general iterative algorithm to propose a new explicit iterative scheme involving equilibrium problem (5) and an infinite family of strict
pseudo-contractions. Under certain assumptions, we will prove that the sequence converges strongly. Further an example will be given to demonstrate the effectiveness of our iterative scheme and
another will be given to compare numerical results and convergence rate of the algorithm in this paper and [15].
2. Preliminaries
In the sequel, we will make use of the following lemmas in a real Hilbert space .
Lemma 1. Let be a real Hilbert space. There hold the following identities:(i)(ii)
Lemma 2 (see [13]). Let be a -Lipschitzian and -strongly monotone operator on a Hilbert space with , , , and . Then is a contraction with contractive coefficient and .
Lemma 3 (see [1]). Let be a -strict pseudo-contraction. Define by for each . Then, as , is a nonexpansive mapping such that .
Lemma 4. Let be an -Lipschitz mapping with coefficient and a -Lipschitzian continuous operator and -strongly monotone operator with , . Then, for , That is, is strongly monotone with coefficient .
Proof. Since is -Lipschitz and -strongly monotone, it is easy to get
Lemma 5 (see [16]). Assume that is a sequence of nonnegative real numbers such that where is a sequence in and is a sequence such that(i)(ii)Then, .
Let be a sequence of -strict pseudo-contractions. Define , . Then, by Lemma 3, is nonexpansive. In order to find the common fixed point set of infinite mappings, -mapping is often used; see [9, 13,
15, 17, 18] and references therein. The mapping is defined by where are real numbers such that . Such a mapping is called a -mapping generated by and . As we have seen, -mapping contains many
composite computation of , and it is complicated and needs a large number of complex operations. In [14], He and Sun proposed a new hybrid steepest descent method for solving fixed point problem
defined on the common fixed point set of infinite nonexpansive mappings.
Lemma 6 (see [14]). Let be a real Hilbert and all nonexpansive mappings with . Let , where such that . Then is a nonexpansive mapping with .
Lemma 7 (see [14]). Let be a real Hilbert and all nonexpansive mappings with . Let , where such that . Assume , where . Then uniformly converges to in each bounded subset in .
For solving the equilibrium problem, let us assume that the bifunction satisfies the following conditions:(A1) for all ;(A2) is monotone; that is, for any ;(A3)for each ;(A4) is convex and lower
semicontinuous for each .
We recall some lemmas which will be needed in the rest of this paper.
Lemma 8 (see [2]). Let be a nonempty closed convex subset of , let be bifunction from to satisfying (A1)–(A4), and let and . Then there exists such that
Lemma 9 (see [7]). For , , define a mapping as follows: for all . Then, the following statements hold:(i) is single valued; (ii) is firmly nonexpansive; that is, for any , (iii); (iv) is closed and
Lemma 10 (see [19]). Let and be bounded sequences in a Banach space and a sequence of real numbers such that for all Suppose that for all and . Then .
Lemma 11 (see [6]). Let , , , and be as in Lemma 9. Then the following holds: for all and .
Lemma 12 (see [13]). Let be a Hilbert space, a nonempty closed convex subset of , and a nonexpansive mapping with . If is a sequence in weakly converging to and if converges strongly to , then .
We adopt the following notations:(1) stands for the weak convergence of to ,(2) stands for the strong convergence of to .
3. Main Result
Recall that, given a nonempty closed convex subset of a real Hilbert space , for any , there exists a unique nearest point in , denoted by , such that for all . Such a is called the metric (or the
nearest point) projection of onto . As we all know, if and only if there holds the following relation:
Throughout the rest of this paper, we always assume that is an -Lipschitzian mapping of into itself with coefficient and is a -Lipschitzian continuous operator and -strongly monotone on with , .
Assume that and .
Define a mapping . Since both and are nonexpansive, it is easy to get that is also nonexpansive. Consider the mapping on defined by where . By Lemmas 2 and 9, we have Since , it follows that is a
contraction. Therefore, by the Banach contraction principle, has a unique fixed point such that
For simplicity, we will write for provided no confusion occurs. Next we prove the sequence converges strongly to a which solves the variational inequality By the property of the projection, we can
get equivalently.
Theorem 13. Let be a nonempty closed convex subset of a real Hilbert space and a bifunction from to satisfying (A1)–(A4). Let be family -strict pseudo-contractions for some . Assume the set . Let be
an -Lipschitzian mapping of into itself with , and let be a -Lipschitzian continuous operator and -strongly monotone on with , ,, and . For every , let be the mapping generated by and with
according to (6). Given , let and be sequences generated by the following algorithm: If , and satisfy the following conditions:(i), and ;(ii); (iii) and , then, converges strongly to , which solves
the variational inequality (24).
Proof. The proof is divided into several steps.
Step1. Show first that is bounded.
Taking any , by Lemma 9, we have It follows from (25) that Further we get By induction, we obtain . Hence, is bounded, so are and . It follows from the Lipschitz continuity of and that , , and are
also bounded. From the nonexpansivity of , it follows that is also bounded.
Step2. Show that Suppose , then .
Hence, we have Observe that By the definition of , we have where
It follows from (30) and (32) that where .
Hence we get . Since is convergent, it is easy to see that is also convergent. Thus we have .
From conditions (i) and (iii) and Lemma 11, we obtain By Lemma 10, we have . Thus
By Lemma 11 and (30) and (29), we obtain
Step3. Show that where .
Observe that From condition (i) and (25), we can obtain It follows from condition (ii) that By Lemma 9, we get This implies that By nonexpansivity of , we have It follows from (25) that This implies
that From conditions (i) and (ii) and (29), we have Thus, we get
On the other hand, we have Combining (47) and Lemma 7, we obtain (37).
Step4. Show that where is a unique solution of the variational inequality (24). Indeed, take a subsequence of such that
Since is bounded, there exists a subsequence of which converges weakly to . Without loss of generality, we can assume . From (37), we obtain .
By the same argument as in the proof of Theorem 13, we have . Since , it follows that
Step5. Show that
Since It follows from (29) and (51) that This implies that where , . Put , . It is easy to see that . Hence, by Lemma 5, the sequence converges strongly to .
Remark 14. If we extend the equilibrium problem to be system of equilibrium problems, we still obtain the desired result by the similar proof of Theorem 13.
4. Numerical Result
In this section, we consider the following two simple examples to demonstrate the effectiveness, realization, and convergence of the algorithm in Theorem 13. Further, we compare convergence rates of
the algorithm in this paper and [15].
First, we give an example as follows.
Example 15. In Theorem 13, let , , , for all . Define , and let , . Take with Lipschitz constant and strongly monotone constant , , for all with Lipschitz coefficient . Give the parameters , for
every , and fix and . Then is the sequence generated by As , we have .
Let , ; then we have . Take the initial guess , using software MATLAB R2012, we obtain the numerical experiment results in Table 1.
Let be the two-dimensional Euclidean space with usual inner product and induced norm .
Next, we consider another simple example.
Example 16. In Theorem 13, let , ,, for all . Give , and let , , . Take with Lipschitz constant and strongly monotone constant , , , for all with contraction coefficient . Give the parameters , for
every , and fix and . Then is the sequence generated by As , we have .
For analysis of the rate of convergence, we use the concept introduced by Rhoades [20] as follows.
Definition 17. Let be a closed interval on the real line and a continuous function. Suppose that and are two iterations which converge to the fixed point of . Then, is said to converge faster than if
Now we turn to numerical simulation using the algorithm (57). Take the initial guess and , respectively. All the numerical experiment results are given in Tables 2(a) and 3(a). Then we realize the
algorithm in [15], and the -mapping is used in the paper. Further we obtain the corresponding numerical results which can be found in Tables 2(b) and 3(b).
It is easy to see that the approximation values obtained by the algorithm (25) in this paper are more close to the common fixed point at the same iterative number. And from the computer programming
point of view, the algorithm is easier to implement in this paper.
The author would like to thank the referee for valuable suggestions to improve the paper and the Fundamental Research Funds for the Central Universities (Grant ZXH2012K001).
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Elastic Collisions in One Dimension - Boundless Open Textbook
An elastic collision is a collision between two or more bodies in which the total kinetic energy of the bodies before the collision is equal to the total kinetic energy of the bodies after the
collision. An elastic collision will not occur if kinetic energy is converted into other forms of energy. It important to understand how elastic collisions work, because atoms often undergo
essentially elastic collisions when they collide. On the other hand, molecules do not undergo elastic collisions when they collide . In this atom we will review case of collision between two bodies.
Double-bonded atoms
Some atoms are joined by more than one pair of electrons. The oxygen atoms in an O2 molecule are joined by a double bond.
The mathematics of an elastic collision is best demonstrated through an example. Consider a first particle with mass $m_{1}$ and velocity $v_{1i}$ and a second particle with mass $m_{2}$ and velocity
$v_{2i}$. If these two particles collide, there must be conservation of momentum before and after the collision. If we know that this is an elastic collision, there must be conservation of kinetic
energy by definition. Therefore, the velocities of particles 1 and 2 after the collision ($v_{1f}$ and $v_{2f}$ respectively) will be related to the initial velocities by:
$\frac{1}{2}m_1\cdot v_{1i}^2+\frac{1}{2}m_2\cdot v_{2i}^2=\frac{1}{2}m_1\cdot v_{1f}^2+\frac{1}{2}m_2\cdot v_{2f}^2$ (due to conservation of kinetic energy)
$m_1\cdot v_{1i}+m_2\cdot v_{2i}=m_1\cdot v_{1f}+m_2\cdot v_{2f}$ (due to conservation of momentum).
Since we have two equations, we are able to solve for any two unknown variables. In our case, we will solve for the final velocities of the two particles.
By grouping like terms and canceling out the ½ terms, we can rewrite our conservation of kinetic energy equation as:
$m_1\cdot (v_{1i}^2-v_{1f}^2) = m_2\cdot (v_{2f}^2-v_{2i}^2)$. (Eq.1)
By grouping like terms from our conservation of momentum equation we can find:
$m_1\cdot (v_{1i}-v_{1f}) = m_2\cdot (v_{2f}-v_{2i})$. (Eq. 2)
If we then divide Eq. 1 by Eq. 2 and perform some cancelations we will find:
$v_{1i} + v_{1f} = v_{2f} + v_{2i}$. (Eq. 3)
We can solve for $v_{1f}$ as:
$v_{1f} = v_{2f} + v_{2i}-v_{1i}$. (Eq. 4)
At this point we see that $v_{2f}$ is still an unknown variable. So we can fix this by plugging Eq. 4 into our initial conservation of momentum equation. Our conservation of momentum equation with
Eq. 4 substituted in looks like:
$m_1\cdot v_{1i}+m_2\cdot v_{2i}=m_1\cdot(v_{2f} + v_{2i}-v_{1i})+m_2\cdot v_{2f}$. (Eq.5)
After doing a little bit of algebra on Eq. 5 we find:
$v_{2f} =\frac{2\cdot m_1}{(m_2+m_1)}v_{1i} +\frac{(m_2-m_1)}{(m_2+m_1)}v_{2i}$. (Eq.6)
At this point we have successfully solved for the final velocity of the second particle. We still need to solve for the velocity of the first particle, so let us do that by plugging Eq. 6 into Eq. 4.
$v_{1f} = [\frac{2\cdot m_1}{(m_2+m_1)}v_{1i} +\frac{(m_2-m_1)}{(m_2+m_1)}v_{2i}] + v_{2i}-v_{1i}$. (Eq. 7)
After performing some algebraic manipulation of Eq. 7, we finally find:
$v_{1f} =\frac{(m_1-m_2)}{(m_2+m_1)}v_{1i}+\frac{2\cdot m_2}{(m_2+m_1)}v_{2i}$. (Eq. 8)
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Analyzing Linear Data
Much of the work of those in financial careers is to look at data and examine the relationship to determine an equation. In many cases that equation is linear or can be simplified to be thought of as
linear. Students explore data and linear equations throughout algebra and it can be useful for students to explore situations with which they are familiar.
Highlighted Problem: Taxi!
In the city of Lineville, the taxi rates are based on a linear equation. The cost for a 4-mile ride is $3.10, while a 7-mile ride costs $4.15.
This is a nice problem for students, especially those who live in cities where taxi are common, to explore how to model the cost of using this type of transportation. To extend this problem, it may
be nice to add in a discussion of other options for transportation (buses, trains, subways, cars, carpools) and play with how to determine the cost of those forms of transportation and if any of them
are also linear.
If you have not already created a free account, you'll need to do so to access the Financial Education Problems of the Week.
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Computer Science courses 06-08
Computer Science (CSCI)
101 Introduction to Computer Science (3) A first course in computer science providing a survey of current topics as well as core programming and related problem-solving skills. Satisfies the
mathematics requirement for General Education. Students should have an acceptable score on the Mathematics Placement Test or have completed an appropriate remedial course. Cross-listed as CSCI/LIBS
101. MATH 095 is recommended. F06, S07, F07, S08
110 Introduction to Computer Programming I (2) Self-paced independent study in the fundamentals of computer programming. Each student may choose from several languages of current interest that are
not offered in other courses. Students complete several programming exercises and projects. Prerequisite: Independent study contract. Topics: Beginning Programming with LOGO, Beginning Programming
with JavaScript, Basic Web Page Development, Visual Basic.Net, Information Security. Instructor consent required. F06, S07, F07, S08
111 Introduction to Computer Programming II (2) Self-paced independent study of intermediate-level computer programming. Each student may choose from several languages of current interest that are
offered in other courses. Students complete several programming exercises and projects. Prerequisites: Independent study contract and instructor consent. Topics: Intermediate Programming with LOGO,
Intermediate Programming with JavaScript, Intermediate Programming with PASCAL, Intermediate Programming with JAVA, Intermediate Programming with C, Intermediate Programming with C++, Intermediate
Web Page Development, Linux Shell Programming. F06, S07, F07, S08
170 Programming and Technology for the Teaching of Mathematics (3) Graphing and analysis of functions using graphing calculators; structured programming; use of software packages such as Maple and
Geometer's Sketchpad. Prerequisite: Acceptable score on the Mathematics Placement Test or completion of MATH 115 with a grade of at least C-. Lecture and lab. F06, S08
201 Introduction to Programming (3) A first programming course for students with a serious interest in computing. Topics include: formal languages; data types and variables; control structures;
primitive and reference data types; methods and modular programming; introduction to abstract data types and classes; simple algorithms; and programming conventions and style. Satisfies the
mathematics requirement for General Education. Prerequisite: Acceptable score on the Mathematics Placement Test or completion of an appropriate course. MATH 102 recommended. Lecture and lab. S06,
S07, F07, S08
202 Object-Oriented Programming (3) Continuation of CSCI 201. Programming course emphasizing the methodology of programming from an object-oriented perspective and software engineering principles.
Topics include: data structure fundamentals; abstraction and encapsulation; inheritance; pointer and reference variables; memory management, operator overloading, recursion; various important
algorithms; and file processing techniques. Prerequisite: CSCI 201 with a grade of C- or better. Lecture and lab. S07, S08
250 Internet Programming (3) Internet technologies for the World Wide Web such as XHTML, DHTML, CSS, CGI, JavaScript, Java, and Serlets. Topics include: converting HTML into XHTML/XML; page layout
control with cascading style sheets, form processing and validation, working with images and JavaScript-based animation, fundamentals of CGI programming under UInix/Linux environment, server-side
programming with Perl and/or PHP and server programming; server configuration issues; working with multimedia objects; Java applets; and database access. Prerequisite: Acceptable score on the
Mathematics Placement Test or completion of an appropriate course. MATH 102, CSCI 201 recommended. Lecture and lab. S08
270 Introduction to Computer and Network Security (3) Based on the System Administration and Network Security Institute (SANS) recommendations. Offers comprehensive coverage of the essentials that
were determined by the collaborative work of security professionals and includes topics ranging from network security and perimeter defense to encryption and risk management. F07
280 Introduction to E-commerce (3) Broad coverage of topics pertaining to the current electronic commerce environment. While this course discusses the various business models via which ecommerce is
delivered, it is weighted more heavily on giving more depth to the computer science aspects of ecommerce.
303/503 Algorithms and Data Structures (4) Continuation of CSCI 202. Concepts and techniques for various algorithms and related data structures of particular interest to computer scientists. Emphasis
on proper implementation of abstract data types and analysis of the complexity of algorithms. Topics include: stacks and queues; hashing graphs and trees, data compression and encryptions; and
related algorithms. Prerequisite: CSCI 202 with grade of C- or better. Lecture. F06, F07
320/520 Discrete Structures (4) Continuation of MATH 310. Investigation of concepts of noncalculus mathematics used in computer science, operations research and other areas of applied mathematics.
Topics include: relations and functions; recurrence relations; combinatorics; graph theory; and related algorithms. Cross-listed with CSCI 320/520. Prerequisite: MATH 310. F06, F07
324/524 Assembly Language Programming (4) Fundamentals of Assembly language programming under DOS, Windows, and Linux operating systems. Topics include: data representation and fundamentals of
computer architecture; memory access and organization; arithmetic and logical operations; functions and procedures, bit and string manipulation; pattern matching, computer graphics, interrupt
handling, floating-point arithmetic and combining assembler with high-level languages. Prerequisite: acceptable score on the Mathematics Placement Test or completion of an appropriate course. MATH
102 recommended. Lecture and lab. S07, S08
331/531 Computer Graphics and 3-D Modeling (3) Data structures and algorithms used in computer graphics emphasizing programming rather than graphics design. Topics include: graphics algorithms;
design and implementation of graphics applications; 2-D and 3-D modeling; and animation. Mathematical treatment of topics requires an understanding of fundamental concepts in calculus and matrix
algebra. Prerequisite: CSCI 201. Lecture and lab. Offered on demand.
340/540 Software Development and Professional Practice (4) Best practices in the field of software development. Students complete a medium-scale software project as members of a development team.
Topics include: professional ethics and responsibilities; multi-tier systems; software life cycle; requirements analysis; system modeling; implementation and testing; re-engineering and
maintainability, secure coding, system security, and risk management techniques are integrated into all facets of the development process. Prerequisite CSCI 303. S07, S08
356/556 Data-centric Computing and Data Security (3) Discusses the representation, organization, transformation, and presentation of information, algorithms for efficient and effective access and
updating of stored information, data modeling and abstraction; information security, privacy, integrity, and protection in a shared environment. Prerequisite: CSCI 201 recommended. S08
381 Special Projects (1-4) Various individual and small-group projects carried out under the supervision of one or more instructors. Requires weekly progress reports plus a final report and/or a
final exam. May be repeated, but no more than a total of four credits may be earned from both MATH 381 and CSCI 381. Evaluation. Pass-Fail only. Instructor consent required. Prerequisites:
Preliminary project plan and an independent study contract. Topics: Independent Study, Java Certification Part 2, C++, JAVA, On-Line Curriculum Development, DNA Microarrays. F06, S07, F07, S08
390 Mathematical Sciences Internship (1-4) Work in an approved position to gain experience in solving real problems using computer science, mathematics, and statistics. Interns may receive salaried
appointments with cooperating companies. Credits do not apply to any major or minor in Mathematics and Computer Science. Evaluation: Pass-Fail only. Prerequisite: Department approval. Independent
study. F06, S07, F07, S08
399 Mathematical Sciences Seminar (1) Students carry out individual investigations in current literature and present their findings to the entire department. Taken during senior year. Pass-Fail only.
Prerequisite: Independent study contract and permission of instructor. F06, S07, F07, S08
401/601 Formal Models for Computer Security (4) A survey of formal mathematical models for computer security with in-depth examination of important features and characteristics. Includes an
investigation of mathematical properties of these models as well as related cryptographic and system implementations. The models include classical lattice-based models as well as modern policy-based
models such as the Bell-LaPadula model; noninterference models, hybrid models, integrity models, and miscellaneous formal verification techniques. Prerequisite: MATH 310, CSCI 270. S08
410/610 Programming Language Principles (4) Survey of programming languages of current interest with in-depth examination of important features and characteristics. Includes an investigation of
fundamental programming language concepts and design issues related to the procedural, functional, and object-oriented paradigms. Students conduct programming exercises to discover and experiment
with features of several languages and to implement interpreters and compilers for simple languages of their own design. Prerequisite: CSCI 303. Offered on demand.
421/621 Theory of Computation (4) Thorough introduction to automata, formal languages and compatibility. Topics include: models of computation; regular and context-free languages; finite and pushdown
automata; Turing machines; unsolvable decision problems; and fundamentals of computational complexity. Cross-listed as MATH 421/621. Prerequisites: CSCI 320. F07
425 Algorithm Design and Analysis (4) Study of the design and analysis of algorithms that are based on elementary data structures such as queues, stacks and trees. Some graph and network algorithms
(shortest paths, connectivity, coloring, flows, matchings), goemetric algorithms (convex hulls, range search, nearest neighbors), NP-complexity, approximation algorithms (vertex cover, traveling
salesman, scheduling), and introduction to randomized algorithms. Introduction to algorithm design techniques, including greedy algorithms, divide-and-conquer, and dynamic programming. Lower and
upper bounds of program complexity are analyzed. Introduction to algorithms used in the area of information security. Cross-listed as MATH 425/625. Prerequisites: CSCI 320. CSCI 202 recommended. F06
437 Cryptography (4) Study of the theory of cryptography and its use in computer security. Topics include: discrete probability spaces, Shannon's theory of information, unicity distance, perfect
secrecy, redundancy of a language, classical cryptosystems, classical cryptanalysis (frequency analysis, index of coincidence), authentication and keyexchange, public key cryptosystems, elementary
number theory, primality checking, the RSA cryptosystem. Prerequisite: CSCI 201, MATH 310. Cross-listed as MATH 437. S07
451/651 Operating Systems and System Security (4) In-depth study of the concepts, issues, and algorithms related to the design and implementation of operating systems. Topics include: process
management, process synchronization and interprocess communication; memory management; virtual memory; interrupt handling; processor scheduling; device management; I/O; file systems; and introduction
to networking and network security. Students conduct programming projects and case studies to investigate modern operating systems such as Solaris, Linux, and Windows. Prerequisite: CSCI 201. F06
461/661 Computer Architecture and Organization (4) In-depth study of fundamentals of computer hardware organization. Topics include: digital logic and circuits; finite state machines; computer
arithmetic, machine instructions and assembly language; memory management and design; storage system design; I/O modules, operating system support; structure and function of computer processors, RISC
vs. CISC architecture, microprogrammed control, input/output devices, and computer security. Prerequisite: CSCI 324. S07
470 Net-centric Computing and Network Security (4) Introduces the structure, implementation, and theoretical and underpinnings of computer networking and the applications that have been enabled by
that technology. Introduction to network security. Prerequisite: CSCI 201. F07
475/675 Numerical Analysis (4) Study of theory and applications of computational techniques for mathematical solutions emphasizing rapid approximation and error analysis. Topics include: solution to
equations in one variable; polynomial approximations to functions; error analysis; numerical solutions to ordinary differential equations; boundary value problems. Prerequisite: MATH 242. Offered
when sufficient demand exists. Cross-listed as MATH 475/675. Prerequisite: MATH 242.
481/681 Special Topics (1-4) Investigation of one or more topics of current interest not covered in other courses. Not intended for independent study projects. May be repeated, but no more than a
total of eight credits may be earned from both MATH 481 and CSCI 481. Prerequisite: Consent of instructor. Offered when sufficient demand exists.
499 Capstone Project (1-3) Group projects are carried out by students under supervision of a faculty member. Prerequisite: CSCI 340 and independent learning contract. F06, F07
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Vertical Angles and Perpendicular Lines
Vertical angles are two angles whose sides form two pairs of opposite rays. When two lines intersect, two pairs of vertical angles are formed.
Vertical angles are congruent:
Perpendicular Lines:( ^ means perpendicular)
Perpendicular lines are two lines that form right angles.
Adjacent angles formed by perpendicular lines are congruent.
If two lines form congruent adjacent angles, then the lines are perpendicular.
If the exterior sides of two adjacent acute angles are perpendicular then the angles are complementary.
If two angles are supplements of congruent angles ( or of the same angle), then the two angles are congruent.
If two angles are complements of congruent angles ( or of the same angle), then the two angles are congruent.
A line contains at least two points, a plane contains at least three points but not all in one line, and space contains at least four points, but not all on one plane.
Through any two points, there is exactly one line.
Through any three points, there is at least one plane, and through any three noncollinear point there is exactly one plane.
If two points are in a plane then the line through the points are in that plane.
The intersection of two planes is a line.
The intersection of two lines is exactly at one point.
If line and a point not on the line exist, then a plane contains both
If two lines intersect, then a plane contains both of them.
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Dr. Vasilis Pagonis- McDaniel College
The OTOR model in THERMOLUMINESCENCE
The simplest model in Thermoluminescence consists of two energy levels: the electron traps and the recombination center (RC) shown in the figure below.
N=total concentration of the electron traps in the crystal (in cm^-3).
n=concentration of the filled electron traps in the crystal (in cm^-3).
nc=concentration of the free carriers in the conduction band CB (in cm^-3).
E=activation energy of the electron traps (in eV).
s=frequency factor of the electron trap (in s^-1).
An=capture coefficient of the traps (in cm^3. s^-1).
Ah=capture coefficient of the recombination center RC (in cm^3. s^-1).
For more details on the OTOR model see, for example, the book :
Chen, R. and McKeever, S.W.S. 1997. Theory of thermoluminescence and related phenomena. World Scientific, Singapore, Chapter 4.
and also, for example, in the following paper :
Sunta, C.M., Feria, Ayta W.E., Piters, T.M., Watanabe, S., 1999. Limitation of peak fitting and peak shape methods for determination of activation energy of thermoluminescence glow peaks. Radiation
Measurements 30, 197 – 201.
The differential equations governing the traffic of electrons between the trap level, the recombination center and the conduction band are:
The first equation describes the traffic of electrons in and out of the electron trap.
The electrons can leave the traps via thermal excitation, which is described mathematically by the term [n.s.exp(-E/kT)]
The electrons can also be retrapped in the trap, an event described mathematically by the retrapping term [nc.(N-n).An].
The second equation describes the traffic of electrons in and out of the conduction band.
The electrons in the conduction band can be trapped in the recombination center RC, an event described mathematically by the term [nc.(n+nc).Ah]
The quantity (n+nc) here represents the total concentration of FILLED TRAPS in the system at any moment. Because of conservation of charge, this quantity (n+nc) is also equal to the total
concentration of FILLED HOLES in the recombination center.
The third equation above gives the observed TL, which is proportional to the amount of light measured during the thermoluminescence measurement.
Unfortunately these differential equations can not be solved in any closed form, and the solutions must be obtained numerically.
We will now present two examples of the OTOR solutions, for different values of the parameters.
EXAMPLE #1: OTOR
The parameters for the calculation shown below are:
An/Ah=0.01 and no/N=1, N=10^10, An=10^-7, heating rate=1 C.s^-1
In this example the coefficient of retrapping An is 100 times smaller than the coefficient of recombination (An/Ah=0.01), and the traps are initially full (no/N=1). The result of the OTOR calculation
produces a TL glow curve which has the shape of a 1st order kinetics curve.
In this example τ=Tmax-T1=17.3 C , δ=T2-Tm=12.5 C, and ω=T2-T1=29.9 C.
The asymmetry factor μ for this OTOR TL glow curve is equal to μ=δ/ω=12.5/29.9=0.42, which corresponds to the shape of a 1st order glow curve.
EXAMPLE #2: OTOR
The parameters for the calculation shown below are:
An/Ah=1 and no/N=1, N=10^10, An=10^-7, heating rate=1 C.s^-1
In this example the coefficient of retrapping An is equal to the coefficient of recombination (An/Ah=1), and the traps are initially full (no/N=1). The result of the OTOR calculation produces a TL
glow curve which has a shape close to the shape of a 2nd order kinetics curve.
In this example τ=Tmax-T1=20.0 C , δ=T2-Tm=20.3 C, and ω=T2-T1=42.1 C.
The asymmetry factor μ for this OTOR TL glow curve is equal to μ=δ/ω=12.5/29.9=0.48, which is close to the shape of a 2nd order glow curve (m=d/w=0.52).
The following is a Mathematica program to solve the system of differential equations for the OTOR model.
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An Introduction to Linear Algebra - Eigenvector Research
An Introduction to Linear Algebra - Eigenvector Research PDF:
reviews the basics of linear algebra and provides the reader with the foundation required for understanding most chemometrics literature.
An Introduction To Linear Algebra - Eigenvector Research :
Download PDF Find similar free ebook
Related Books to An Introduction to Linear Algebra - Eigenvector Research :
textbook is designed to teach the university mathematics student the basics of the subject of linear algebra and the techniques of formal mathematics.”
Basics of Algebra, Topology, and Di erential Calculus Jean Gallier Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104, USA
reviews the basics of linear algebra and provides the reader with the foundation required for understanding most chemometrics literature.
Properties of real numbers Solutions NAME: Basics of numbers and algebra This worksheet will try to make the properties of real numbers more meaningful and
Algebra & Logarithmic Functions Quadratic Formula: Example: If p(, x) =ax2 +bx+c a ≠0and 0 ≤b2 −4ac, then the real zeroes of p are a b b ac x 2
Algebra5.com does not store or upload any files on its server. It just links to files (like Google) which is available on the internet. DMCA
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Capital Asset Pricing Model - Arbitrage Portfolio
Capital Asset Pricing Model
What is Capital Asset Pricing Model or CAPM?
As an arbitrageur, you should always be well aware of the way bankers value their assets and what rate of return they expect from them. The Capital Asset Pricing Model or CAPM is the industry
standard for pricing the future market return of an investment security.
The value of the Formula CAPM is that; internally accounts for the many market risks that investors are exposed to, like systematic risks because when the market goes down all correlations (beta)
goes to one (1). The framework of the return of investment of the Capital Asset Pricing Model equation is that the individual investor can compare the future performance of a single equity name or
fund versus the risk free return of treasury bills (^TNX).
What is Capital Asset Pricing Model/
CAPM Spreadsheet Calculator
Risk Free Rate vs. Market Return
William Sharpe formulated the equation to compare the risk relationship of expected market returns of a diversified portfolio; and is the fundamental base for Arbitrage Pricing Theory ATP. But we are
only going to focus on single names stocks that pay a high dividend yield. In order to explain the changes we are going to apply; to the commonly used modern portfolio theory formula, we need to
explain the original equation:
Capital Asset Pricing Model Formula
- First Step: you have to begin with the risk-free rate (Rf) the yield of a ten years government bond. Now in the Arbitrageur Capital Asset Pricing Model Instead using the coupon rate of the bond we
are going to use the effective saving which is calculated by subtracting(^TNX- consumer price index CPI)
- Second Step: input the Market Beta (B): beta assess the stock market risk correlation. It measures the relative volatility of how stocks may go “bullish”, a positive +1 or higher correlation; or
“bearish” a negative -1 or lower correlation towards the whole flow of the S&P 500 index. But since we are going to arbitrage with a single name security we are going to use the beta of the specific
- Third Step: research the expected market return (Erm). Market investing exposes you to the risk of losing your original capital. We must demand a higher compensation for our exposure, a “risk
premium”. But in the new application we are going to use the yield of our fund as the risk premium value.
The Arbitrageur System Capital Asset Pricing Model Formula
The Bottom Line
As part of your investing process you should always account for market risk. Using the Capital Asset Pricing Model can give you an advantage at the time of making your buy and sell decisions because
it gives you the opportunity of predicting your future return on investment ROI.
Case Study Time
Develop a spreadsheet where you can calculate the expected market return for the biggest holding in one’s portfolio; using the new application of the Arbitrageur System for Capital Asset Pricing
Facebook Thoughts
What is the expected return of your largest position?
Wow 13.49% return on PSEC - Prospect Capital Corporation. You can take a look at the rest of my portfolio in the income
reports page.
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Hilbert C*-Modules Home Page
Hilbert C*-modules are an often used tool in operator theory and in operator algebra theory. They serve as a major class of examples in operator C*-module theory. Beside this, the theory of Hilbert
C*-modules is very interesting on its own. Interacting with the theory of operator algebras and including ideas from non-commutative geometry it progresses and produces results and new problems
attracting attention. During the last couple of years many interesting applications of Hilbert C*-module theory have been found.
At the contrary, the pieces of Hilbert C*-module theory are still rather scattered through the literature. Most publications explain only as many definitions and results as necessary for the striven
for applications in the fields considered there in the main. However, there are some papers, chapters in monographs and lecture notes that give comprehensive representations of parts of the theory.
The purpose of this webpage is to give a literature list containing about 1707 items of preprints, papers, books, lecture notes, books wherein Hilbert C*-modules and their properties are described or
they are successfully applied to solve problems in other research fields. The literature list starts with two guides to Hilbert C*-modules: the first one refers to mayor sources by the type of
source, the second one by subject. Since the notion ''Hilbert ... modules'' is in use for at least five more or less different mathematical concepts we list basic references to the other definitions
as well.
The reader has to take into account that the choice of the sources is limited by the author's research interests and linguistic profiency, as well as by the availability of sources. He apologizes for
a probable insufficient representation of the work of some colleagues in the present overview. All suggestions, corrections and supplements are welcome.
I am grateful to B. Kirstein, M. A. Rieffel and E. V. Troitsky for valuable comments and suggestions complemeting this list.
Bibliography on Hilbert C*-module literature (.PDF, 01.04.2013) - contains about 1707 references, a comprehensive guide through publications on the theory and the application fields, historical
remarks, statistics. Suggestions, additions and corrections are welcome.
For a quite complete literature list on operator spaces see:
What are Operator Spaces? (in German), a online lexicon on operator spaces with bibliography maintained by G. Wittstock and his colleagues at Universität des Saarlandes, Saarbrücken, Germany.
Some mayor open problems in Hilbert C*-module theory:
• Does every Hilbert C*-module M over a unital C*-algebra A possess a normalized tight frame? I.e., does M admit a set of elements x[i] indexed by a set I such that the equality x=SUM[i in I] (x,x
[i]) x[i] is valid for every x of M?
Equivalently, for every Hilbert C*-module M over a unital C*-algebra A, does there exist an isometric embedding into a standard Hilbert C*-module l[2](A,I) as an orthogonal direct summand for
some index set I? Partial answer obtained by Hanfeng Li, see paper.
• Characterize those C*-algebras with the property that for every Hilbert C*-module over them and for each of its Hilbert C*-submodules which coincides with its biorthogonal completion therein, the
latter is always a topological direct summand of the former.
• Whether each kernel of a surjective bounded module operator between Hilbert C*-modules is a toplogical direct summand of the domain of this operator, or not?
• Prove or disprove: Each injective bounded C*-linear orthogonality-preserving mapping T on a Hilbert C*-module over a given C*-algebra A is of the form T= tU for some C*-linear isometric mapping U
on the Hilbert C*-module and for some element t of the center Z(M(A)) of the multiplier C*-algebra of A which does not admit zero divisors therein.
Michael Frank, last changes: April 1, 2013
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[Solved] Multiple Conditional Formatting for Pivot Tables
Thanks for your response. I was trying to add an additional column because every conditional formatting option I have tried does not work within the pivot table. However if I can work within the
table, this would be preferable. I have even considered going back to the Access database and trying to bundle the dates together, but I'm relatively new at Pivot Tables and Access.
My columns are as such:
Column L = P1, P2 or P3 (Stands for Priority type)
Column M = Used a formula to turn column L into numerical value such as P1 = 3, P2 = 7, P3 = 14 (number represents days)
Column N = Date 1 - Date Project is presented
Column O = Date 2 - Date of Completion
I want to conditionally format either one cell or the entire row if Date 2 (O) - Date 1 (N), is greater than Column M's different numerical values corresponding with their priority.
Ultimately I want to show when we have surpassed our deadline to complete a project based on it's priority. For example, If I have a project that is P1 (L), which represents in 3 days due (M), the
difference between my completion date (O) and my start date (N) should not be greater than 3 days (M).
I have tried to conditionally format with the formula as described above, but it has not worked. Do I need to select the data in a particular way?
PRICING_PRIORITY P1-4 IN DAYS PRICE_EFFECTIVE_DT PRICING_COMPLETED_DT
P3 14 7/13/2012 7/23/2012 16:53
P1 3 11/29/2012 11/30/2012 13:32
P3 14 8/15/2012 8/17/2012 15:43
P2 7 7/27/2012 8/8/2012 13:06
P3 14 10/9/2012 10/23/2012 13:38
P3 14 9/24/2012 9/27/2012 14:18
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Exploring Software: Scientific Python and Image Processing - Open Source For You
Exploring Software: Scientific Python and Image Processing
By Anil Seth on April 30, 2012 in Coding, Columns · No Comments
Discover what a beautiful language Python is for image processing.
A substantial part of the human brain is dedicated to vision and the processing of images. Social sites are full of images that friends share with each other. The sheer number of images from various
sites is so huge that aggregation sites like Pixable hope to consolidate them for you, and help you find the ones you want from among all the clutter and noise. Another site, Scalado, created an
application that allows you to remove unwanted people from your photographs, apart from various other things.
These examples illustrate that algorithms for the better classification or improvement of images and their content is a hot area. Python is a superb tool for exploring ideas and algorithms very
quickly. While Python may seem unsuitable for computationally expensive tasks, the Scientific Python (SciPy) community has built tools for fast numerical computation while retaining the power,
versatility and flexibility of Python.
A common option for image processing in Python has been the Python Imaging Library (PIL). However, implementing and exploring image-processing algorithms is better done in SciPy or NumPy. There are
utility functions that convert a PIL image into a SciPy array and back:
im = Image.open('image.png')
A = scipy.array(im)
im2 = Image.fromarray(A)
But there is an ndimage module in SciPy, which makes it unnecessary to move between the two environments. The advantage of SciPy is that you can manipulate arrays in elegant ways, and not have to
manipulate each element in a loop. Getting the sine of each element in an array, A, is as simple as what follows:
sinA = scipy.sin(A)
As you explore the possibilities with an image, you may find numerous uses for it in other areas as well, including financial modelling (read this, and this)!
Fancy indexing
The fancy indexing of NumPy/SciPy arrays provides a powerful abstraction tool. You can think about implementing algorithms at a higher level than manipulating elements of an array. The best approach
is for you to actually try these in some simple but realistic examples, and judge for yourself.
You may want to try implementing a threshold on an image, by using a reference image included in SciPy:
lena = scipy.lena()
# create an array with zeros of the same size
A = scipy.zeros(lena.shape, dtype='uint8')
# find the elements in lena above the threshold, e.g. 120
mask = lena > 120
# set these to white (255)
A[mask] = 255
The use of a mask as an index creates a very flexible and powerful way to manipulate arrays.
You could try a simple method to find a gradient in an image. One such relatively unused method would be to take the difference with the adjacent pixel in the same axis, like for a row. For example:
deltaA = A[1: , :] - A[:-1, :]
Indices are zero-relative, so the first term means a slice of the array starting with the second row, and all the columns. The second term represents a slice of the array starting with the 1st row
till the last-but-one row, and all the columns. Both slices are of the same size, and can thus be subtracted. You get speed as well, because the element-wise operations are done by the C library.
Now, let’s assume that you wish to convolute an image with a 3×3 mask, M. This operation corresponds to element-by-element multiplication of the values in a 3×3 window around a pixel with
corresponding mask elements, and then summing the result. For the sake of simplicity, you may ignore the border elements.
NR, NC = A.shape
Result = [ [ (M*A[i-1:i+2, j-1:j+2]).sum()
for j in range(1, NC-1)]
for i in range(1, NR-1)]
You can use the Laplacian mask to get another image of the edges.
You will find a rich set of routines for filtering, morphology, segmentation and feature extraction in the ndimage module. To know more, just look at the section on image processing, analysis and
face recognition (an example of machine learning).
New applications in image processing are waiting to be created. One wishes that Matlab would be replaced by SciPy in colleges — only then is it likely that a clever student will create a killer app.
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Tags: Exploring Software Column, Image processing, LFY April 2012, matlab, NC, NumPy, PIL, Pixable, python, Python Imaging Library, SciPy
Article written by:
The author works as a consultant. Prior to consulting, Anil was a professor at Padre Conceicao College of Engineering (PCCE) in Goa, managed IT and imaging solutions for Phil Corporation Limited
(Goa), supported domestic customers for Tata Burroughs/TIL, and was a researcher with IIT-K and the Indian Institute of Geomagnetism (Mumbai).
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Unpublished doctoral dissertation, University of Montana. Thompson, D. R., Senk, S. L., Witonsky, D., Usiskin, Z., and Kaeley, G. (2001). An evaluation of the second edition of UCSMP advanced
algebra. (Unpublished manuscript). Thompson, D. R., Witonsky, D., Senk, S. L., Usiskin, Z., and Kaeley, G. (2003). An evaluation of the second edition of UCSMP geometry. (Unpublished manuscript).
U.S. Department of Education. (2001). No Child Left Behind Act of 2001. Available: http://www.ed.gov/legislation/ESEA02/107-110.pdf [11/18/03]. Usiskin, Z. (1997). The evaluation of new curricula.
(Unpublished manuscript). Walker, R. K. (1999). Students’ conceptions of mathematics and the transition from a standards-based reform curriculum to college mathematics. Unpublished doctoral
dissertation, Western Michigan University. Wasman, D. (2000). An investigation of algebraic reasoning of seventh- and eighth-grade students who have studied from the Connected Mathematics curriculum.
Unpublished doctoral dissertation, University of Missouri, Columbia. Webb, N. L., and Dowling, M. (1995a). Impact of the Interactive Mathematics Program on the retention of underrepresented students:
Class of 1993 transcript report for school 1, Brooks High School. Project Report 95-3. Madison: University of Wisconsin–Madison, Wisconsin Center for Education Research.
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On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations Webb, N. L., and Dowling, M. (1995b). Impact of the Interactive Mathematics Program on the retention of
underrepresented students: Class of 1993 transcript report for school 2, Hill High School. Project Report 95-4. Madison: University of Wisconsin–Madison, Wisconsin Center for Education Research.
Webb, N. L., and Dowling, M. (1995c). Impact of the Interactive Mathematics Program on the retention of underrepresented students: Class of 1993 transcript report for school 3, Valley High School.
Project Report 95-5. Madison: University of Wisconsin–Madison, Wisconsin Center for Education Research. White, P., Gamoran, A., and Smithson, J. (1995). Math innovations and student achievement in
seven high schools in California and New York. Madison: Consortium for Policy Research (CPRE) and Wisconsin Center for Education Research, School of Education, University of Wisconsin–Madison. Zahrt,
L. T. (2001). High school reform math programs: An evaluation for leaders. Unpublished doctoral dissertation, Eastern Michigan University. CHAPTER 6 Baxter, J., Woodward, J., and Olson, D. (2001).
Effects of reform-based mathematics instruction on low-achievers in five third-grade classrooms. The Elementary School Journal, 101(5), 529-547. Bay, J. M. (1999). Middle school mathematics
curriculum implementation: The dynamics of change as teachers introduce and use standards-based curricula. Unpublished doctoral dissertation, University of Missouri, Columbia. Bickman, L. (1987).
Using program theory in evaluation. San Francisco: Jossey-Bass. Campbell, D. T. (1994). Foreword. In R. K. Yin (Ed.), Case study research: Design and methods (2nd ed., pp. ix-xi). Thousand Oaks, CA:
Sage. Carroll, W. M., and Isaacs, A. (2002). Achievement of students using the University of Chicago School Mathematics Project’s Everyday Mathematics. In S. L. Senk and D. R. Thompson (Eds.),
Standards-oriented school mathematics curricula: What are they? What do students learn? (pp. 79-108). Mahwah, NJ: Lawrence Erlbaum Associates. Cobb, P., Boufi, A., McClain, K., and Whitenack, J.
(1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258-277. Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., and Trigatti, B.
(1991). Assessment of a problem-centered second grade mathematics project. Journal for Research in Mathematics Education, 22(2), 3-29. Collins, A. M. (2002). What happens to student learning in
mathematics when a multi-faceted, long-term professional development model to support standards-based curricula is implemented in an environment of high stakes testing? Unpublished doctoral
dissertation, Boston College, Boston, MA. Dapples, B. C. (1994). Teacher-student interactions in SIMMS and non-SIMMS mathematics classrooms. Unpublished doctoral dissertation, Montana State
University. de Groot, C. (2000). Three female voices: The transition to high school mathematics from a reform middle school mathematics program. Unpublished doctoral dissertation, New York
University. Easley, J. A. Jr. (1977). On clinical studies in mathematics education. Washington, DC: U.S. Department of Education. Available: ERIC #: ED146015 [11/20/03]. Fuson, K. C., Diamond, A.,
and Fraivillig, J. L. (Unknown). Implementation of reform norms in Everyday Mathematics classrooms. (Unpublished manuscript). Greeno, J., and Goldman, S. (1998). Thinking practices in mathematics and
science learning. Mahwah, NJ: Lawrence Erlbaum Associates.
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On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations Herbel-Eisenmann, B. (2000). How discourse structures norms: A tale of two middle school mathematics
classrooms. Unpublished doctoral dissertation, Michigan State University, East Lansing, MI. Hetherington, R. A. (2000). Taking collegial responsibility for implementation of standards-based
curriculum: A one-year study of six secondary school teachers. Unpublished doctoral dissertation, Michigan State University. Keiser, J., and Lambdin, D. (2001). The clock is ticking: Time constraint
issues in mathematics teaching reform. The Journal of Educational Research, 90(1), 23-31. Kett, J. R. (1997). A portrait of assessment in mathematics reform classrooms. Unpublished doctoral
dissertation, Western Michigan University. Kramer, S., and Keller, R. (2003). Tale of synergy: The joint impact of 4 × 4 block scheduling and an NCTM standards-based curriculum on high school
mathematics achievement (DRAFT). (Unpublished manuscript). Lehrer, R., Jacobson, C., Kemeny, V., and Strom, D. (1999). Building on children’s intuitions to develop mathematical understanding of
space. In E. Fennema and T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 63-87). Mahwah, NJ: Lawrence Erlbaum Associates. Lott, J. W., Hirstein, J., Allinger, G., Walen, S.,
Burke, M., Lundin, M., Souhrada, T., and Preble, D. (2002). Curriculum and assessment in SIMMS Integrated Mathematics. In S. L. Senk and D. R. Thompson (Eds.), Standards-oriented school mathematics
curricula: What are they? What do students learn? (pp. 399-423). Mahway, NJ: Lawrence Erlbaum Associates. Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An
exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454-482. Manouchehri, A., and Goodman, T. (1998). Mathematics curriculum reform and teachers:
Understanding the connections. The Journal of Educational Research, 92(1), 27-41. Manouchehri, A., and Goodman, T. (2000). Implementing mathematics reform: The challenge within. Educational Studies
in Mathematics, 42, 1-34. Murphy, L. (1998). Learning and affective issues among higher- and lower-achieving third-grade students in math reform classrooms: Perspectives of children, parents, and
teachers. Unpublished doctoral dissertation, Northwestern University. National Research Council. (2002). Scientific research in education. Committee on Scientific Principles for Education Research.
R. J. Shavelson and L. Towne (Eds.). Center for Education. Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press. Nicholls, J., Cobb, P., Wood, T.,
Yackel, E., and Ptashnick, M. (1990). Dimension of success in mathematics: Individual and classroom differences. Journal for Research in Mathematics Education, 21, 109-122. Romberg, T. A. (1997).
Mathematics in context: Impact on teachers. In E. Fennema and B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 357-380). Mahwah, NJ: Lawrence Erlbaum Associates. Schoen, H. L., Finn, K.
F., Griffin, S. F., and Fi, C. (2003). Teacher variables that relate to student achievement in a standards-oriented curriculum. Journal for Research in Mathematics Education, 34(3), 228-259. Senk,
S., and Thompson, D. (2002). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah, NJ: Lawrence Erlbaum Associates. Shafer, M. C. (in press). Expanding
classroom practices. In T. A. Romberg (Ed.), Insight stories: Assessing middle school mathematics. New York: Teachers College Press. Smith, S. Z. (1998). Impact of curriculum reform on a teacher’s
conception of mathematics. Unpublished doctoral dissertation, University of Wisconsin, Madison.
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On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations Thompson, A. G., Philipp, R. A., Thompson, P. W., and Boyd, B. A. (1994). Calculational and conceptional
orientations in teaching mathematics. In A. Coxford (Ed.), 1994 yearbook of the NCTM (pp. 79-92). Reston, VA: National Council of Teachers of Mathematics. Woodward, J., and Baxter, J. (1997). The
effects of an innovative approach to mathematics on academically low-achieving students in inclusive settings. Exceptional Children, 63(3), 373-388. Yackel, E., and Cobb, P. (1996). Sociomathematical
norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-476. CHAPTER 7 National Council of Teachers of Mathematics. (2000). Principals and
standards for school mathematics. Reston, VA: Author. National Research Council. (2002). Scientific research in education. Committee on Scientific Principles for Education Research. R. J. Shavelson
and L. Towne (Eds.). Center for Education. Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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Two congruent equilateral triangles have sides of 34 mm and 6x-2 mm. Find the value of x.
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I'm assuming that the sides are corresponding? If so, then the sides are congruent since the triangle is congruent. 34 = 6x -2 Add 2 to each side. 36 = 6x Divide 6 from each side. x = 6
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Calculate power consumption/ life times
1. 29th January 2005, 13:15 #1
Full Member level 4
Join Date
May 2004
4 / 4
Calculate power consumption/ life times
I found that the datasheet of electronic device have the power consumption details. But I not clear that how the manufacturer calculate the life times for the devices.
For example:
Operating Voltage: 5V or 3.3V
• TX consumption: 300mA (Max)
• RX consumption: 200mA (Max)
• Sleep Mode: 50mA
If we are using the normal 5Volt battery. How can we calculate the life times?
If possible, please show the example or the relevant resource to answer this question.
Thanks you.
2. 29th January 2005, 13:53 #2
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Nov 2001
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Calculate power consumption/ life times
i hope u r asking for battery life time...
well in the worst case..the max current is 300mA (Assuming the chip is semi duplex operation)
obviously if the chip is in sleep mode for long(ie no tx or rx) the power consumed is totally different..
so u can say the battery life time corresponds to 50mA when no call is made and corresponds to 250mA(average) when a call is going on
3. 29th January 2005, 14:48 #3
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Re: Calculate power consumption/ life times
Usually rechargeables come with charge-storage capacities, something like 2100mAh. Non-rechargeable batteries typically have larger capacities than rechargeable ones, but they are normally
not stated. You'll have to give an estimate.
Now, mAh stands for milliAmpere hours. So 2100mAh translates to 2.1x60x60C of charges.
Now assuming 50mA current drawn, since I = dQ/dt, you can roughly compute the dt.
Note that these figures are normally gross estimates, and losses are usually significant. So use these figures with a pinch of salt. The best way is still to do a lifetime test.
4. 29th January 2005, 16:16 #4
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Calculate power consumption/ life times
for example if there are 3 ICs in my circuit. to calculate the total power consumption, is it right to add all of the IC's power consumption directly?
5. 29th January 2005, 20:35 #5
Re: Calculate power consumption/ life times
Yes, of course you add all the currents drawn by all devices in your circuit.
The current drawn from the battery can be the same if there is no regulator between the battery and your circuit. If there is a linear regulator you ave to add its quiescent current to the
circuit current to get the battery current.
If there is a switching regulator between the battery and the circuit, then this will draw a constant POWER from the battery. Its input current (=battery current) can be calculated if you
know its efficiency and output voltage and current:
Ibat=(Vcircuit*Icircuit)/η/Vbat, where η is the efficiency of the regulator. This current is an approximation, since it increases as the battery discharges. Plus, the efficiency of the
regulator can also change as the battery voltage or output current change. But it should give you a fair ESTIMATE of the input current.
Once you have established the current the battery needs to supply, just use the formula given by checkmate to calculate the time.
If the circuit current varies, which it probably will, you have to use a best estimate as to how much average current it draws.
6. 30th January 2005, 20:23 #6
Full Member level 4
Join Date
May 2004
4 / 4
Re: Calculate power consumption/ life times
Thanks you for quick and nice reply.
But I still not clear about the standard that used for manufacture to do the calculation for the life times.
Can help me?
7. 2nd February 2005, 17:11 #7
Re: Calculate power consumption/ life times
If you are referring to lifetime of a product, there are standards for calculating the expected life from failure rates of different components, based on their ratings and the stresses in the
circuit. It is pretty much a statistical calculation, based on numerous data sets collected over a number of years to establish these failure rates. One of the companies that does this kind
of work is Telcordia.
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[SOLVED] High School Quadratic Inequalities
October 1st 2009, 09:13 AM
[SOLVED] High School Quadratic Inequalities
Q) Use the discriminant 'b^2=-4ac' to solve the following:
i) Find the values of ' k ' for which the following equations have two separate roots.
a) $kx^2+kx+2=0$
Answer is 0>k>8
I solved the above to get
Now my question is that we know that k>8 but how do we figure k<0?
Is it because we are 100% that if k>8 from my final step then the other value must be smaller? (k<0)
ii) Find the values of ' k ' for which the following equations have no roots.
a) $k^2x^2+2kx+1=0$
I solved this and got:
Answer is k=0
How is the answer k=0? I mean shouldn't 0<0 mean no solution or something?
iii) Sketch, on the same diagram, the graphs of $y=1/x$ and $y=x-3/2$. Find the solution set of the inequality $x-3/2>1/x$
Please tell me step by step on how to solve this question.
Thanks in advance!
October 1st 2009, 10:54 AM
Q) Use the discriminant 'b^2=-4ac' to solve the following:
i) Find the values of ' k ' for which the following equations have two separate roots.
a) $kx^2+kx+2=0$
Answer is 0>k>8
I solved the above to get
Now my question is that we know that k>8 but how do we figure k<0?
Is it because we are 100% that if k>8 from my final step then the other value must be smaller? (k<0)
ii) Find the values of ' k ' for which the following equations have no roots.
a) $k^2x^2+2kx+1=0$
I solved this and got:
Answer is k=0
How is the answer k=0? I mean shouldn't 0<0 mean no solution or something?
iii) Sketch, on the same diagram, the graphs of $y=1/x$ and $y=x-3/2$. Find the solution set of the inequality $x-3/2>1/x$
Please tell me step by step on how to solve this question.
Thanks in advance!
for the first question
k(k-8)>0 you want the values of k that make this inequality true just draw the real number line and plot 0 and 8 (zero of k(k-8)) then take a value between 0,8 and sub it in k(k-8) if the sign is
negative ignore the interval between 0,8 take a number more than 8 and sub if it is positive take this interval and take a number less than 0 and sub if it is positive take the interval
(-infinity , 0)
ii) if $b^2-4ac < 0$ there is no solution right but here
$b^2-4ac = 4k^2 - 4k^2 = 0$ for all k real number so always there is a equal roots and the root is
$\frac{-b \mp \sqrt{4k^2-4k^2}}{2a} = \frac{-b}{2a} = \frac{-2k}{2k^2}=\frac{-1}{k}$ repeated root so there is no value of k that make no solution
iii) draw the two curve and take the region where $x-\frac{3}{2}$ is above $\frac{1}{x}$ and find the points where the two curve intersect 2,-1/2 and zero since at zero 1/x change see this pic
take the intervals where x-3/2 is above 1/x
Attachment 13156
October 3rd 2009, 07:43 AM
Thanks for your reply but I did not understand the first part at all.
The second part I understood somewhat. I didn't get what why you included 0 as an intersection point for the line and the curve and I didn't understand how we are supposed to shade/select the
required region to fulfill the inequality.
October 3rd 2009, 09:17 AM
Thanks for your reply but I did not understand the first part at all.
The second part I understood somewhat. I didn't get what why you included 0 as an intersection point for the line and the curve and I didn't understand how we are supposed to shade/select the
required region to fulfill the inequality.
I did not say it is a point of intersection but as you can see at zero 1/x have a disconnect point , 1/x is not continues at 0 , 1/x at 0 change it is graph as you can see .
in general you want the interval where the line is above the curve .
as in graph at the interval (-infinity , -1/2 ) the curve is above the line this interval dose not fulfill the inequality
in the interval (-1/2 , 0 ) the line is above the curve and this fulfill the inequality .
the interval (0 ,2) the curve is above the line this dose not fulfill
(2, infinity ) line is above this fulfill .
what I want to say in the first question , to solve this k(k-8)>0 we should study the sign of k(k-8) where this function is positive and where is negative after we determine this we take the
interval where the function is positive , to determine this first we should find the point where is function equal zero and where it is dose not exist the zeros of the denominator , since usually
the function change it is sign at these points , ok in our function we have 0,8 zero of it , we will take a number in each interval here we have three intervals (-infinity , 0) , (0,8) and (8,
infinity ) ok take -1 in first interval and substitute it in the function is the sign is positive that mean the function is positive in all the first interval , do the same thing to the other
intervals .
I wish it is clear now .
October 3rd 2009, 10:20 AM
Thanks much appreciated ;)
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Winter 2014
Math 42 Winter 2014
Math 42 Winter 2014
This sheet is not a complete syllabus -- instead find everything online at http://math42.stanford.edu, along with our first assignment of Daily Discussion Problems for this Tuesday's sections.
Home Schedule Section Assignments Office Hours Homework Exams
Math 42 is a 5-unit second-term course in calculus with an accelerated pace -- the class covers techniques of integration, applications of integration, differential equations, infinite sequences and
series, and Taylor polynomials. Although everyone is welcome in the course, it is aimed primarily to students who took Math 41 last quarter (or have equivalent preparation) and will continue taking
more advanced quantitative classes which require a strong calculus background. There are at least two other math courses which may be appropriate for students considering Math 42, so you should be
deciding in the first week or so whether Math 42 is the right class for you.
If you successfully took Math 41 last quarter and wish to continue studying calculus, either as background for other subjects or purely out of interest, then Math 42 should be the best class for you.
However, be warned that Math 42 moves just as quickly as Math 41 but covers more difficult material. So you can expect Math 42 to be more work than Math 41 was, especially if you had calculus in high
school and that background helped you through Math 41.
If you didn't take Math 41 last quarter, you should consider taking Math 20 instead. This is especially true if you are taking math purely out of interest or to satisfy a GER and don't plan to take
Math 51 or other more advanced classes -- even if you did well in calculus in high school. The sequence Math 19-20-21 covers the same material as Math 41-42, but at the more traditional year-long
pace (ending with Math 21 in the spring quarter). The non-accelerated pace of Math 20 makes it easier for students who have been away from calculus for a while to get their feet under them, and the
3-unit workload may be preferable to students who don't plan to continue taking math courses. Completing Math 21 also gives you the appropriate background to take Math 51 if you choose to do so
One quick heads-up to those who didn't take Math 41 and do decide to take Math 42 this quarter: Math 41 last quarter covered a couple of topics which are not on the Calculus AB syllabus, and which
you therefore may not have seen in high school. In particular, we covered l'Hospital's Rule (which will not be discussed much in Math 42, but will come up in passing) and integration by parts (which
will be treated as a review topic at the very beginning of Math 42).
Finally, to any students who have already seen and are comfortable with most of the material in Math 42, but don't feel quite ready for Math 51: you should know that Math 42 and Math 51 cover very
different material, and seeing the material in Math 42 again will not substantially improve your preparation for Math 51. You're probably better off diving right into Math 51.
On Registrar deadlines: Please pay careful attention to all Registrar deadlines, especially the add/drop deadline at the end of the third week of classes. However, University Advising and Research
has a special provision in place to accept petitions for switches from Math 42 to 20 submitted in complete form before Friday, February 7, 2014, at 5pm. The instructions for how to properly complete
the petition is contained at the bottom of this page. You can also contact your instructor for more information.
The textbook is Single Variable Calculus: Concepts and Contexts, 4th edition, by James Stewart. This is the same textbook used in Math 41 last fall (and it is also used by Math 19, 20, and 21). We
will cover most of the material from the second half of Chapter 5 to the end of the book. Most homework exercises and reading assignments are taken from the book, so you should have access to a copy
throughout the quarter. (It is not recommended that you try to use a copy of an older edition: although the text is very similar, some examples, some of the homework problems, and most of the problem
numbers will be different.)
Each week you will attend three lectures and two discussion sections. The lectures are on Monday, Wednesday and Friday, either at 10am, 11am, or 1:15pm. The discussion sections are on Tuesday and
Thursday. See the Section Assignments page to view the choices for times and locations and instructions on the sign-up process. You will sign up for a discussion section via CourseWork, and your
available options will depend on your lecture instructor.
The lectures will be used primarily to introduce concepts and develop theory, and serve as a complement to the course textbook. You can get the most out of lecture by having first read the relevant
sections in the textbook (as set in the calendar of topics on the course schedule page). In the discussion sections, you meet with your Teaching Assistant in a smaller group. Much of the time in
section will be used for example problems based on topics developed in lecture and the textbook; you can get the most out of section by working on the posted daily discussion problems in advance
(i.e., immediately after lectures).
Attendance at all lectures and sections is required. If you miss a lecture or a section, it is your responsibility to catch up on the topics that you missed. You should keep in mind that in this
course, the material builds on itself; if you miss some of the material, subsequent lectures will be more difficult (or even unintelligible) for you.
There will be weekly homework assignments. For more information and policies, see the Homework page.
Calculators will not be used in a systematic way in Math 42. Calculators will not be allowed on any of the exams, nor should there be any need for one. Occasionally, homework problems may call for
the use of a scientific or graphing calculator.
The midterm exams will be held in the evenings on January 28 and February 20. The exact times and locations and other information will be posted on the Exam Information page. If you have a schedule
conflict with one of the midterm exams due to another course meeting, you must at least one week before the exam to arrange to take it at an alternate (early) sitting. (The same deadline holds for
OAE accomodation requests; see below for details.)
The final exam will be held on Monday, March 17, from 7-10pm. You must take the final exam at this time, which is set by the University.
All of the exams are closed book, closed notes, with no electronic aids. For each exam, if appropriate, you may be provided with a formula sheet, which will be available on the exam materials page
prior to the exam, along with other study materials.
Your grade will be based on the following components:
• Weekly Homework: 10%
• Total points earned on all exams (midterms and final): 90%
Points available on exams: The total points available on the exams will be in approximate proportion 2:2:3. That is, the first and second midterm exams will have approximately equal numbers of total
points available, and the number of points available on the final exam will be approximately 1.5 times those available on a single midterm exam.
There are no predetermined numerical cutoffs for letter grades, and the cutoffs may turn out to be rather different from what you are accustomed to from high school. In general, the grade
distribution for the class is usually (roughly) as follows: around 30% of the class receive A's, around 40% receive B's, and most of the rest receive C's.
CourseWork is a web-based program that will be used in Math 42 to allow students to check grades online. It is a secure program, so your grades will be available through CourseWork only to you. Every
student must sign into CourseWork and choose a discussion section. CourseWork will be our primary gradekeeping tool; if you do not sign up, you could lose credit for work that you have done. This is
completely independent of signing up for the course on Axess -- neither program has any knowledge of the other.
Before you sign into CourseWork, make sure you read the Section Assignments page, which contains instructions on the sign-up process for discussion sections.
Again, remember that Axess and CourseWork are different programs, and you will sign up for different course components on each -- on CourseWork, you sign up for a discussion section based on the
table on the Section Assignments page, but on Axess you sign up for a lecture.
Despite its other capabilities, in this class CourseWork will be used only for grades and possibly email announcements.
Math 41 web site, including solutions and statistics for the Final Exam.
Tips for Success in Undergraduate Math Courses by Jessica Purcell
Some very good advice for college calculus students. Read this carefully and do as it suggests.
Note: Pay particular attention to #3 under "Weekly" and #6 and #7 under "Before the exam". Students who think they're following these tips often overlook those parts, and they're the most
important ones!
Common Errors in Undergraduate Mathematics by Eric Schechter
Although this document is a bit on the long side, you should read at least some of it carefully -- you'll do better in your math classes because of it. We encourage you to pay particular
attention to the sections: bad handwriting, all of the algebra errors, stream-of-consciousness notations, and going over your work.
Math 42 Teaching Staff Office Hours
Your first resource for help outside of class meetings should be the course instructors and teaching assistants. You are encouraged to attend any of their office-hour sessions, not just those for
your lecture or section leader, and no appointment is necessary at the times posted. In office hours we welcome any kind of question; we are here to help you and ready to explain the same thing
as many times as necessary. You can also email us, but keep in mind that questions in office hours are answered more quickly and more clearly.
Free Tutoring at the Center for Teaching & Learning (runs Sunday, Jan. 12 through dead week)
Evening Tutoring by SUMO undergraduate members (free, but priority goes to Math 50-series students)
Math Department Web Page
Math 42A students are part of the ACE program, short for "Accelerated Calculus for Engineers." More information about the program can be found here.
"Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the
request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students
should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
Honor Code and Fundamental Standard
By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.
Statement from Undergraduate Advising and Research concerning the special provision for fifth-week switch to Math 20:
"Any student registered for either MATH 42 or MATH 42A who wishes to switch to MATH 20 after the Add/Drop Deadline may do so by submitting a Petition to Change Course Enrollment no later than
5:00pm on Friday, February 7, 2014. Students will receive full credit for MATH 20 (3 units) upon earning a passing grade for that course. (Students switching from MATH 42A to MATH 20 may also add
the 1-unit ACE course EE 191, before the above date.)
"Note: Because of the discrepancy in units between either MATH 42 (5 units) or MATH 42A (6 units), and MATH 20 (3 units), students should be advised to consider the possible impact this change
may have on their university enrollment requirements. For this reason, students switching from either MATH 42/42A must meet with a UAR Advisor.
"Specifically, students should complete the Petition to Change Course Enrollment form in the following manner:
1. Complete the personal information section.
2. Select 'Section change' and enter the information for both courses in the Change Requested section.
3. Obtain signature from the instructor of the new course (MATH 20). This may require advance notice of 1-2 days, so prompt attention to this is imperative. [See "additional details" below for
contacting Math 20 instructors.] (Students switching from MATH 42A may also submit a separate petition form to request a Late Add for EE 191 at 1-unit, signed by Professor Brad Osgood.)
4. Sign the form(s).
5. Meet with an Advisor from the office of Undergraduate Advising and Research to discuss the situation and obtain the Advisor's signature.
6. Submit the form to VPUE in the office of Undergraduate Advising and Research (UAR) by 5:00pm, February 7, 2014.
"Students will not need to write a statement regarding why they wish to submit the petition. But they will need to obtain the instructor's signature, as well as the signature of a UAR Advisor.
The request will be routinely approved and rather than a withdrawal with the notation of 'W,' MATH 42 or MATH 42A will be dropped from the student's record and MATH 20 (and EE 191, where
appropriate) will be added. "
Additional details concerning switch to Math 20:
When switching to Math 20, all of your grades from Math 42 will be deleted. You will be excused from all work from Math 20 that was due before you enrolled in Math 20; your final grade in Math 20
will be computed using the work turned in during the rest of the quarter. In particular, when necessary, the weight of the first midterm will be made up by increasing the weights of the
pre-quizzes, homework, second midterm, and final exam proportionally to their original weight in Math 20. Note that Math 20 does not have a discussion section. Please see the Math 20 course
website for more details on that course, and please contact the Math 20 instructors listed there if you have additional questions.
To ensure that you can receive the signature of the Math 20 instructor in time for the UAR deadline listed above, you must email the Math 20 instructor for permission by 5:00pm on Thursday,
February 6, 2014. In your email, you must include the following:
□ Your full name
□ The Math 20 lecture you wish to enroll in. To choose your lecture, you can visit the Math 20 course website for a list of lectures offered, along with the lecturer contact information. Please
note that by the fifth week some of the lectures might be full; if possible note a second choice in case your first-choice lecture is full and otherwise state clearly that this is the only
time slot you are able to attend. Make sure to send your email to the instructor of your first-choice lecture.
□ Your SUNetID (for example "gocard12") and your student ID number (for example "05555555")
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The Science of Sticky Spheres
The Science of Sticky Spheres
On the strange attraction of spheres that like to stick together
At Sixes and Sevens
Up to this point, each value of n has had a unique cluster that maximizes C[n]. Furthermore, in each case the best-connected cluster with n+1 spheres can be assembled incrementally by sticking a new
sphere somewhere on the surface of the max(C[n]) cluster. These properties come to an end at n=6. With six spheres, two cluster shapes both yield the same maximum contact number, C[6]=12. (Note that
a hypothetical six-sphere clique would have 15 contacts.) One of the max(C[6]) clusters is built incrementally from the five-sphere triangular dipyramid. But the other max(C[6]) cluster is a “new
seed”—a structure that cannot be created simply by gluing a sphere to the surface of a smaller optimum cluster. The new seed is the octahedron (which might also be described as a square dipyramid).
Beyond n=6, the problem of finding all the maximum-contact clusters becomes more daunting. For n=7, the incremental approach of adding another sphere to the surface of an n=6 cluster yields four
solutions that have 15 contact points. Three of these C[7]=15 clusters consist of four tetrahedra glued together face-to-face in various ways. The remaining product of incremental construction
consists of an octahedron with a tetrahedron erected on one face. (One of the seven-sphere solutions has both left-handed and right-handed forms, but the convention is to count these “chiral” pairs
as variants of a single cluster, not as separate structures.)
Finding this particular set of structures is not especially difficult. If you spend some time playing with Geomags or some other three-dimensional modeling device, you are likely to stumble upon
them. But having identified these four clusters with C[7]=15, how do you know there aren’t more? And how do you prove that no seven-sphere cluster has 16 or more contacts?
As it turns out, 15 is indeed the maximum contact number for seven spheres, but there is another C[7]=15 cluster. It is a new seed, called a pentagonal dipyramid. With its fivefold symmetry, it has
no structural motifs in common with any of the smaller clusters. The novelty of this object again raises the question: How can we ever be sure there aren’t still more arrangements waiting to be
A successful program for answering such questions was initiated about five years ago by Natalie Arkus, who was then a graduate student at Harvard University. (She is now at Rockefeller University.)
In a series of papers written with her Harvard colleagues Michael P. Brenner and Vinothan N. Manoharan, she enumerated all the max(C[n]) configurations for n=7 through n=10. The results were later
extended to n=11 by Robert S. Hoy, Jared Harwayne-Gidansky and Corey S. O’Hern of Yale University. (Hoy is now on the faculty of the University of South Florida.) All of the results I describe here
come from the work of these two groups.
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MTH 56
For New Students
Apply & Register
Distance Education
Course Schedule
Online Advising
Tutoring for
Online Students
Frequently Asked Questions
Have Questions?
Need Help?
Spring 2010 MTH 56 Intermediate Algebra (5 units)
Section 4483, 4484 Class Begins January 25, 2010
Course Description: Fundamental properties and operations of the set of real and complex numbers; linear and quadratic equations and inequalities; polynomials; factoring polynomials; rational
expressions; exponents and roots; relations, functions and inverse functions; the Cartesian Coordinate System and linear functions; conic sections; systems of equations and inequalities; matrices,
determinants, and Cramer's Rule; exponential and logarithmic functions; sequences and series; and the Binomial Theorem.
• Instructor: J. Edington
• Email: jedington@mendocino.edu
• Textbook Information:
□ Intermediate Algebra for College Students, 5th Edition, Bundled with MyMathLab, Blitzer.
□ Stand Alone MyMathLab Access Code (ISBN 0-13-14789-4X): Provides an electronic version of the textbook. Although this is a less expensive way to take the course, since everything needed to
complete the course is online, the downside is that you must be online to study and complete assignments.
• Estimated Time Per Week: Students can expect to spend approximately 15 to 20 hours per week reading, writing, and taking quizzes and participating in online class discussions.
• Special Requirements:
□ PC or MAC- If you have any other computer configuration, call MyMathLab Product Support at 1-800-677-6337 to be sure yours will work in this course:
□ Operating system: PC – Windows XP or Windows Vista. Mac – Macintosh OS 10.4 or 10.5. Internet connection: Cable/DSL, T1, or other high-speed for multimedia content; 56k modem (minimum) for
tutorials, homework, and testing.
□ Browsers and Plug-ins/Players: Windows XP – Firefox 2.0, Internet Explorer 6.0 or 7.0, Netscape Navigator 7.2. Windows Vista: Firefox 2.0 or Internet Explorer 7.0. Macintosh OS 10.4 – Firefox
2.0, Safari 2.0, or Netscape Navigator 7.2. Macintosh OS 10.5 – Safari 3.1. Install from the MyMathLab Installation Wizard online.
□ Pop-Up Blockers: To be able to access various features in the online content, you MUST disable any Pop-Up Blocker software (or hit Ctrl + the blocked link).
□ Calculator Policy –Basic calculators needed for lectures and to check homework, but no calculators are allowed on quizzes and tests.
CourseCompass Course: This course uses specialized math software, Course Compass. For information on orientation, you must email your instructor by Monday, 1/25 AND visit the online math page at
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Mental Methods
Mental Methods Starters:
Abundant Buses: A game based around the concept of abundant numbers.
Add Quickulations: Calculations appear on the screen every 10 seconds. This mental arithmetic starter provides pace to the start of the Maths lesson.
Ancient Mysteries: This activity requires students to memorise fifteen numbers in a three by five grid.
Countdown: How close can you get to the target by making a calculation out of the five numbers given?
Division Quickulations: Random divisions calculations appear on screen every ten seconds.
Eleventh of the Eleventh: Practise multiplying and dividing by eleven in your head.
Family Buses: Fit families onto eleven seater buses without splitting up the families.
Flabbergasted: If each number in a sequence must be a factor or multiple of the previous number what is the longest sequence that can be made from the given numbers?
Four Factors: Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question?
Four to Seven: Which of the numbers from one to twenty can you make with the digits 4, 5, 6 and 7?
Just In Time: Calculations appear on the screen every 10 seconds.
Know Your Place: Without a calculator perform some calculations requiring a knowledge of place value.
Mental Test 9: A traditional twenty question mental arithmetic test presented as a PowerPoint presentation.
Mult Sum Diff Div: For each pair of numbers multiply the sum by the difference then divide the answer by 5.
Multiply Quickulations: Random multiplications appear on screen every ten seconds.
Multiply, Add, Subtract and Divide: For each pair of numbers subtract the sum from the product then divide the result by 20 ... without a calculator.
No Partner: Find which numbers in a given list do not combine with other numbers on the list to make a given sum.
Outnumbered: Which group of four numbers, arranged in a square, has the largest total?
Percent Table: Complete the table by calculating common percentages without using a calculator.
Percentages Grid: Calculate the percentages without using a calculator.
Positions Please: Stand at the point between the classroom walls to represent a given number.
Quick: Develop a quick way of multiplying by 1001.
Six Discrimination: An activity involving a calculator which is missing the six button. Can you evaluate the given expressions without using the six?
Strange Tables: A challenge to learn an unfamiliar times table involving decimals.
Subtract Quickulations: Calculations appear on the screen every 10 seconds.
Table Legs: Learn an unusual times table from the strategic finger moving up and down the 'Table Leg'!
Table Spiders: Multiply the number on the spider's back by the numbers next to its legs.
Take Sides: Put up your right hand or left hand depending on the expressions that appears.
Team Age: Work out who is in which team from the information given.
Timed Tables: How fast can you answer 25 mixed times tables questions?
Triple Totals: Complete the sums using only the given numbers then check your calculations are correct.
Triplets: Find as many sets of three of the available numbers as possible which add up to the given total.
Tutu 5!: Which of the numbers from 1 to 20 can you make with the digits: 2, 3, 4 and 5?
Complete Index of Starters
Featured Activity
Tables Conga
Race around the screen to collect the multiples in the correct order while avoiding the Conga viruses. You can choose the times table and earn a trophy for your efforts.
Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:
"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being
able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks."
Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:
"A set of real life savers!!
Keep it up and thank you!"
Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:
"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website
and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"
Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :
"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics
before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"
Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:
"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"
Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:
"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."
Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:
"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"
Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:
"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."
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with group of studen...
42 Subjects: including SAT math, reading, ESL/ESOL, calculus
...While enjoying the classroom again, I also passed 6 actuarial exams covering Calculus (again), Probability, Applied Statistics, Numerical Methods, and Compound Interest. It's this spectrum of
mathematics, from high school through post baccalaureate, which I feel most comfortable tutoring. I also became even more proficient with Microsoft Excel, Word, and PowerPoint.
21 Subjects: including SAT math, calculus, statistics, geometry
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[Haskell-cafe] Joy Combinators (Occurs check: infinite type)
Daniel Fischer daniel.is.fischer at web.de
Tue Mar 8 10:19:18 EST 2005
Keean Schupke wrote:
> Daniel Fischer wrote:
> >And, BTW, that's why Keean et al's HList library doesn't help here either,
> > the type of an HList determines the number of elements and the type of
> > each, so there we face the same problems as with nested tuples. What we
> > need is type Stack = [ArbitraryType] (from the HList paper, I surmise
> > that [Dynamic] would be possible, but that seems to have it's own
> > problems).
> Well it depends on what you want to do... If the types of elements are
> determined by the computation then you can use an HList as is, and there
> is no problem.
The problem is that for the recursion combinators we need polymorphic
recursion functions.
For fact3 we need
rec2 :: forall l. (HCons a (HCons a l) -> HCons a l),
which is illegal in an HList (at least, I haven't found a way to make it
acceptable) and in tuples.
For the general recursion combinator it's even worse, because
rec2 may take n2 elements of certain types from the stack, does something with
them and put k2 elements of certain types determined by the types of the
consumed elements on the stack, leaving the remainder of the stack unchanged,
rec1 takes n1 elements etc. And the numbers n2, n1 . . . and the types depend
on the supplied recursion functions.
So (reverting to nested pairs notation), we would have to make linrec to
accept arguments for rec2 of the types
(a,b) -> (r,b),
(a,(a1,b)) -> (r,(r1,(r2,b))),
(a,(a1,b)) -> (r,b)
(a,(a1,(a2,b))) -> (r,b)
and so on, for arbitrary munch- and return-numbers, where we don't care what b
is. These can't be unified however, so I think it's impossible to transfer
these combinators faithfully to a strongly typed language. [Dynamic] won't
work either, I believe, because Dynamic objects must be monomorphic, as I've
just read in the doc.
The point is, in Joy all these functions would have type Stack -> Stack and we
can't make a stack of four elements the same type as a stack of six elements
using either nested pairs or HLists (correct me if I'm wrong, you know HList
better than I do).
However, Joy has only very few datatypes (according to the introduction I
looked at), so
data Elem = Bool Bool
| Char Char
| Int Integer
| Double Double
| String String
| Fun (Stack -> Stack)
| List [Elem]
| Set [Int]
type Stack = [Elem]
type Joy = State Stack (IO ())
looks implementable, probably a lot to write, but not too difficult - maybe,
I'll try.
> The only time there is a problem is if the _type_ of an element to be put
> in an HList depends on an IO action. In this case you need to existentially
> quantify the HList.
How would I do that?
What the user's guide says about existential quantification isn't enough for
> So you can use the HList in both cases, but you have to deal with
> existential
> types if the type of the HList is dependant on IO (you dont have to do this
> if only the value of an element depends on IO).
> Keean.
If you can faithfully implement Greg's code (including fact3-5) using HList,
I'd be interested to see it, I think HList suits other purposes far better.
More information about the Haskell-Cafe mailing list
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Patente US6597311 - Method and apparatus for determining time in a satellite positioning system
This application is a divisional application of U.S. patent application Ser. No. 09/684,345, filed Oct. 6, 2000, now U.S. Pat. No. 6,433,731 which is a divisional application of U.S. patent
application Ser. No. 09/062,232, filed Apr. 16, 1998, now U.S. Pat. No. 6,215,442. The application is a continuation-in-part of U.S. patent application Ser. No. 08/794,649, entitled “Method and
Apparatus for Satellite Positioning System Based Time Measurement”, filed on Feb. 3, 1997, now U.S. Pat. No. 5,812,087 and assigned to the assignee of the present invention.
1. Field of the Invention
This invention relates to satellite positioning systems (SPS), and in particular, to determining time associated with SPS signal transmission and/or reception.
2. Background Information
SPS receivers such as GPS (Global Positioning System) receivers normally determine their position by computing relative times of arrival of signals transmitted simultaneously from a multiplicity of
satellites such as GPS (or NAVSTAR) satellites. In typical satellite positioning systems, such as GPS, the multiplicity of satellites are synchronized according to a highly accurate system clock,
which may provide atomic clock accuracy. Generally, each satellite transmits navigational data (e.g., the location of the satellite) that also includes a time stamp to indicate when the data was
transmitted, according to the time as indicated by the system clock (referred to hereafter as system time), which, in the case of GPS, is referred to as (GPS) system time.
However, SPS receivers typically do not have such an accurate clock. Thus, an SPS receiver typically determines timing information by reading and timing information contained in the satellite
message. Many receivers determine position and time by using measurements from four (or more) satellites. The range to each of four satellites (i=1, 2, 3, 4) may be expressed as:
PRi={square root over ((x−xi)^2+(y−yi)^2+(z−zi)^2)}+cb(1)
x, y, and z are the coordinates/position of the receiver (unknown);
xi, yi, and zi are the ith satellite's coordinates/position (known); and
cb represents the clock bias, which is a result of the error in time between the clock of the receiver and the reference time (unknown).
Thus, there is typically a total of four unknowns in equation (1) above.
Often, PRi is referred to as a pseudorange, since it represents the actual range to the ith satellite, plus or minus an offset that may result due to the receiver's clock error, as indicated by the
cb term in equation (1). The above equation, using measurements from four satellites, may be linearized and expressed in matrix form as follows: $[ Δ PR1 Δ PR2 Δ PR3 Δ PR4 ] = [ ux1
uy1 uz1 1 ux2 uy2 uz2 1 ux3 uy3 uz3 1 ux4 uy4 uz4 1 ] × [ Δ x Δ y Δ z Δ cb ] or Z = H · x ( 2 )$
ΔPRi is the pseudorange residual for the ith satellite (i=1, 2, 3, 4), and represents a difference between the measured pseudorange and an initial estimated range to the ith satellite (known);
uxi, uyi, and uzi are the direction cosines of the line-of-sight (LOS) vector from the receiver to the ith satellite, as projected along the x, y and z coordinate axes (known);
Δx, Δy, Δz, and Δcb are the corrections to the initial estimates of coordinates/position and the clock of the receiver, which may be offset from a reference clock (unknown).
Hereinafter, the pseudorange residual vector is also referred to as Z, the n×4 element matrix H is also referred to as an observation matrix, and x represents the SPS receiver position and time
correction vector, which contains the unknowns of interest. Thus, if an inverse of the observation matrix H exists, a unique solution to unknown x in the set of linear equations represented by the
above matrix equation (2) may be determined, such that:
x=H ^−1 ·Z
{circumflex over (x)}=(H ^T ·H)^−1 H ^T ·Z(3)
H^−1 is the inverse of the observation matrix;
(H^T·H)^−1 is the pseudoinverse of the observation matrix; and
{circumflex over (x)} is the least-squares estimate of the vector of unknown parameters, x.
To determine the pseudoranges (PRi), a conventional SPS receiver typically uses an initial estimate of its position and clock bias that is known to within a millisecond. However, since signals from
satellites travel at or approximately the speed of light, even a 1 millisecond ambiguity in time may result in an error of up to 300 kilometers in the pseudorange measurement. By solving the matrix
equation (2) above, the conventional GPS receiver may compute a correction to its initial clock bias estimate, wherein the initial clock bias estimate is derived by reading the navigational message
which provides “time-alignment” information.
Unfortunately, in many situations, determining the system time by reading the navigation message of one or more satellites may be difficult, due signal quality degradation. For example, where there
is blockage of the satellite signals, the received signal level or signal-to-noise ratio (SNR) from the GPS satellites may be too low to demodulate and read the satellite data signals without error.
Such situations may arise in personal tracking and other highly mobile applications. Under such signal conditions, it is possible for a receiver to still acquire and track the GPS signals. However,
performing location and unambiguous time measurement without timing data may be best performed using alternative methods.
The present invention provides a method and apparatus for determining time in an SPS, such as the time of satellite transmission and/or time of measurement by an SPS receiver, relative to a reference
time (e.g., system time or other relatively accurate reference time) without the need to determine the reference time from processing timing information provided within the satellite navigational
data message.
A method and apparatus for determining a reference time associated with a satellite positioning system is described. Once determined, the reference time, in one embodiment, may be used to determine
other navigational information. Such navigational information may include, for example, the location/position of a satellite positioning system (SPS) receiver. In one embodiment, a relative velocity
between an SPS receiver and a set of one or more satellites is used to determine an offset between time as indicated by the SPS receiver and the reference time. According to another embodiment of the
invention, an error statistic is used to determine the reference time. According to yet another embodiment of the invention, two records, each representing at least a portion of a satellite message,
are compared to determine time. In one implementation, the SPS receiver is mobile and operates in conjunction with a basestation to determine time and/or other navigational information according to
one or a combination of the methods described.
FIG. 1A shows an example of a combined mobile GPS receiver and communication system which may be utilized according to one embodiment of the present invention;
FIG. 1B illustrates in further detail the RF to IF converter 7 and the frequency synthesizer 16 of FIG. 1A;
FIG. 2 is a flow diagram illustrating a method for utilizing relative satellite velocity for time determination in a satellite positioning system, according to one embodiment of the invention, as may
be utilized with a mobile SPS receiver which is combined with a mobile communication receiver and transmitter, such as that shown in FIG. 1A;
FIG. 3A is a flow diagram illustrating a method for utilizing an error statistic to determine time in a satellite positioning system, according to one embodiment of the invention;
FIG. 3B is a flow diagram illustrating a method for utilizing a unit variance error statistic in the method 300 of FIG. 3A to determine time in a satellite positioning system, according to one
embodiment of the invention;
FIGS. 4A and 4B depict an example of unit variance fits for a set of range estimates, according to one embodiment of the invention;
FIG. 5 shows a generalized method for determining time associated with a satellite positioning system based on comparing a first and a second record of a satellite data message, and which may be
utilized with a mobile SPS receiver which is combined with a mobile communication receiver and transmitter, such as that shown in FIG. 1A, according to one embodiment of the invention;
FIG. 6 illustrates in further detail a method 620 for measuring time related to satellite data messages for use with a satellite positioning system;
FIG. 7A illustrates a basestation according to one embodiment of the invention;
FIG. 7B illustrates a basestation according to one embodiment of the invention;
FIG. 8 illustrates a system according to one embodiment of the invention, which includes an SPS receiver, a cellular telephone site, a basestation, the Internet, and a client computer system.
Various methods and apparatuses for measuring time related to satellite data messages for use with satellite positioning systems are described below. Some of the discussion of the invention focuses
upon the United States Global Positioning Satellite (GPS) system. However, it should be evident that these methods are equally applicable to similar satellite positioning systems, such as the Russian
Glonass system. Moreover, it will be appreciated that the teachings of the present invention are equally applicable to positioning systems which utilize pseudolites or a combination of satellites and
pseudolites. Moreover, the various architectures for basestations and mobile SPS receivers are provided for illustrative purposes rather than to be construed as limitations of the present invention.
Overview of One Embodiment Utilizing Satellite Velocity for Time Determination
FIG. 2 is a flow diagram illustrating a method for utilizing relative satellite velocity for time determination in a satellite positioning system, according to one embodiment of the invention, as may
be utilized with a mobile SPS receiver which is combined with a mobile communication receiver and transmitter, such as that shown in FIG. 1A. In the method 200 shown in FIG. 2, an entity, such as a
mobile SPS receiver 100 shown in FIG. 1A, estimates its position to a set of one or more satellites in step 202. In one embodiment, the SPS receiver may determine a set of pseudoranges to the set of
satellite based on signals transmitted from the satellites. As such, any range or position estimate by the SPS receiver will typically be offset relative to an actual position or range, due to an
offset between the time of measurement as provided by the clock of the SPS receiver, and a reference time.
In step 204, a basestation, such as the basestation shown in FIG. 7A, receives estimation information from the SPS receiver. For example, the estimation information may include a representation of
pseudorange measurements, as associated with an estimate of the time of measurement by the SPS receiver. For example, the pseudorange may be determined using the time as indicated by the clock of the
SPS receiver. As mentioned above, without knowledge of satellite position at an exact instant of time, relative to an accurate reference time, the SPS receiver may only be limited to an estimate/
approximation of its position that may be offset by the actual distance due any offset/error in time.
In step 206, the basestation determines the time offset associated with the range or position estimate of the SPS receiver, as represented by the estimation information provided to the basestation by
the SPS receiver, based on an estimate of the relative velocity of the set of satellites. In one embodiment, the relative velocity of each of the set of satellites represents an approximated relative
velocity between the satellite and the mobile SPS receiver. A method, according to one embodiment of the invention, for utilizing relative satellite velocity to determine time offset between a time
of measurement by an SPS receiver and a reference time (e.g., GPS system time) is described below with reference to matrix equation (4).
Finally, in step 208, the basestation provides improved navigational information, such as time, position, velocity, etc., to the SPS receiver. The improved navigational information is based on a
determination of the offset (or an approximation thereof) to determine at what time, relative to the reference time, position, range, or other information was estimated or measured by the mobile SPS
receiver. In an alternative embodiment, the basestation may not provide the improved navigation information to the SPS receiver. For example, such information may be stored, provided to another
entity via a data communication link which may be wired or wireless, etc.
Table 1 shows how and by which device(s) some of the quantities mentioned herein are determined, according to one embodiment of the invention.
TABLE 1
receiver Basestation How Determined
PR X X Measured by method of cross-
correlation, for example, as
described below with reference
to FIG. 5-6
ΔPR X Estimated by use of the relation-
ship ΔPR = PR-{circumflex over (R)}, wherein {circumflex over (R)} is
an estimate of the true range R
TOM X Estimated, such that TOM(GPS
(Time-of- or reference)) = TOM(receiv-
Measurement) er) + clock offset
GPS Time X Known from reading satellite
navigation data message(s)
SV Range_rate X Estimated by reading satellite
navigation data message(s)
In one embodiment of the invention, a pseudorange matrix equation (4) as shown below is solved for the error/offset in time between the estimated time associated with a time of measurement at the
mobile SPS receiver and the reference time. Such a solution, in one embodiment, is based upon the relative velocity between the set of satellites used to estimate the position of the mobile SPS
receiver and the mobile SPS receiver itself. For five measurements, the modified matrix equation (4) may be expressed as follows: $[ Δ PR1 Δ PR2 Δ PR3 Δ PR4 Δ PR5 ] = [ ux1 uy1
uz1 1 sv — range — rate1 ux2 uy2 uz2 1 sv — range — rate2 ux3 uy3 uz3 1 sv — range — rate3 ux4 uy4 uz4 1 sv — range — rate4 ux5 uy5 uz5 1 sv — range — rate5 ] × [ Δ x Δ
y Δ z Δ t Δ cb ] ( 4 )$
ΔPRi is the pseudorange residual for the ith satellite (i=1, 2, 3, 4, 5), and represents a difference between the measured pseudorange and an initial estimated range to the ith satellite (known);
uxi, uyi, and uzi are the direction cosines of the line-of-sight (LOS) vector from the receiver to the ith satellite (i=1, 2, 3, 4, 5), as projected along the x, y and z coordinate axes (known);
sv_range_ratei is the relative velocity between the ith satellite (i=1, 2, 3, 4, 5) and an entity (e.g., a mobile SPS receiver) (known);
Δx, Δy, Δz, and Δcb are the corrections to the initial estimates of coordinates/position and the clock of the receiver (unknown);
Δt is the offset in the time measurement, which, in one embodiment, represents the difference (or offset) between the estimated time at which the pseudorange measurements are taken and a reference
time (e.g., GPS system time, a time based on GPS system time, etc.) (unknown).
The above matrix equation (4) may be solved to obtain a unique solution to “fit” the pseudorange measurements taken at a particular time. From the solution of the matrix equation (4), Δt provides the
coarse correction and Δcb provides the fine correction to the initial estimate of the time at which the pseudoranges are determined. Thus, an offset, which may be in the order of a submillisecond or
more, between a reference time (e.g., GPS system time) and the estimated time at which an entity estimates its location and/or that of a set of satellites may be determined based on the relative
velocity of the set of satellites.
Although not necessarily always the case, the matrix equation (4) typically includes five unknown values: Δx, Δy, ΔZ, Δcb, and Δt. Thus, unless any of these unknown values are known at the time of
measurement, five (or more) independent pseudorange measurements should typically be taken into account to solve for a unique solution for the unknown values.
In general, the accuracy of the matrix equation (4) is dependent at least in part upon the accuracy of the relative velocity of each of the satellites (sv_range_ratei). Furthermore, errors in the
initial position and time estimates, which are used to compute the line-of-sight (LOS) vectors from each satellite to an entity, such as a mobile SPS receiver, may cause errors in the velocity
estimates of each satellite. Thus, in one embodiment, cellular site location information is utilized to determine an initial estimate of the location of the SPS receive. Furthermore, in one
embodiment, the matrix equation (4) is solved iteratively by re-computing the velocities of one or more of the set of satellites with improved position estimates for the entity. As such, each
iteration may provide five improvements: three in spatial domain or position/range (Δx, Δy, Δz), and two improvements in the time domain (Δcb and Δt).
In one embodiment of the invention, wherein the velocity of the mobile SPS receiver is known, Doppler measurements may be utilized to determine time. In this embodiment, the a posteriori velocity
error is minimized using Doppler information to determine time. The velocity error represents, in this embodiment, the difference between a computed velocity for the mobile SPS receiver (which may be
calculated using several methods, including the matrix equation (4) above or the error statistic method described below) and the known velocity of the mobile SPS receiver. By minimizing such as
error, the time of interest may be determined. For example, if the mobile SPS receiver is stationary (i.e., velocity is zero), a set of solutions may be computed using several approximations for the
time of measurement, relative to a reference time. The solutions corresponding to a velocity of zero would best approximate the reference time, which could then be used to determine the position of
the mobile SPS receiver and/or other navigational information. In alternative embodiments of the invention, altitude aiding, dead reckoning (i.e., restricting velocity to a known direction), or other
techniques may also be employed to improve or simplify the use of the relative velocity of the SPS receiver and the set of one or more satellites to determine time and/or other navigational
Overview of Another Embodiment Utilizing an Error Statistic for Time Determination
In one embodiment of the invention, an error statistic is utilized to determine a reference time associated with a satellite positioning system. One situation in which this aspect of the
invention—namely, determination of time based on an error statistic-is useful is when the number of measurements (e.g., pseudorange measurements) exceeds the number of unknown values (e.g., Δx, Δy,
Δz Δcb, etc.). Furthermore, the error statistic may be utilized in conjunction with other techniques for improving determination of time and/or other navigational information.
FIG. 3A is a flow diagram illustrating a method for utilizing an error statistic to determine time in a satellite positioning system, according to one embodiment of the invention. In step 302 of the
method 300 shown in FIG. 3A, an entity, such as a mobile SPS receiver, estimates its range or position relative to a set of satellites at a set of time instances, wherein one or more of the set of
time instances are associated with an estimated time of measurement that is offset from a reference time. Such an offset, as mentioned above, may be due to offset between the SPS receiver clock and
time as indicated by a reference clock, drift and/or other inaccuracies in the SPS receiver clock, etc. The reference time may correspond to a time associated with the satellite positioning system,
such as GPS system time.
In step 304, each of the set of time instances is altered by further adding or subtracting an offset. For example, in one embodiment, each estimated time of measurement associated with each range or
position estimate may be altered by an offset between −5 and +5 seconds. In alternative embodiments, other ranges of offset values may be added or subtracted to obtain various samples for the error
In step 306, an error statistic is determined for the altered set of time instances (i.e., ones having an offset added thereto or subtracted therefrom). Finally, in step 308, the reference time (or
an approximation thereof) is determined based on the behavior of the error statistic. In one embodiment, as further described below with reference to FIG. 3B, the error statistic includes determining
a unit variance distribution of pseudorange residual values. In this embodiment, a linear deviation of the unit variance typically corresponds to a linear deviation in the spatial (x, y, z) and
temporal (Δt) domains. By optimizing the error statistic used—which, in the case of unit variance would correspond to a minimum value of the unit variance—a time that approximates the reference time
sought could be determined. The use of the unit variance with respect to range or position estimate errors/offsets, according to one embodiment, is further described below with reference to FIG. 3B.
FIG. 3B is a flow diagram illustrating a method for utilizing a unit variance error statistic in the method 300 of FIG. 3A to determine a reference time in a satellite positioning system, according
to one embodiment of the invention. In particular, FIG. 3B depicts one embodiment of step 306 of FIG. 3A. In step 310, a unit variance is determined for the altered set of time instances. In one
embodiment, the unit variance is defined by: $σ 2 = v ^ T W v ^ n - m , v ^ = H · x ^ - Z ( from equation ( 3 ) above ) ( 5 )$
{circumflex over (v)}^r is the transpose vector of a posteriori pseudorange residuals;
W is a weight factor, which represents a weighting observation matrix.
In one embodiment, no weight factor is used, which is generally equivalent to setting a weight matrix to the identity matrix; and
n is the number of measurements; and
m is a number of unknowns.
Thus, the unit variance represents, in most part, the weighted (or unweighted) sum of squares of the pseudorange residual values. The denominator of the unit variance equation (5) represents the
number of degrees of freedom.
In step 312, a polynomial fit for the unit variance is determined. It can be shown that for the normally distributed pseudorange residuals, the expected value of the unit variance is unity and the
distribution is the Chi-square distribution with (n-m) degrees of freedom. However, in some cases, individual unit variance values may also equal zero, which corresponds to a perfect fit of a
position or time fix for the SPS receiver. Thus, the measurements (e.g., pseudoranges, pseudorange residuals, etc.) for statistically optimum position fix should generally minimize the unit variance,
ideally to a value close to zero. In other words, when the unit variance for a set of range or position estimates is minimized, a “best fit” (or solution) may be obtained in space and/or time.
FIGS. 4A and 4B depict an example of unit variance fits for a set of range estimates according to one embodiment of the invention. When a distribution of the unit variance error statistic (as a
function of time offset), such as the one shown in FIG. 4A, is obtained, two linear fits may be computed—one for positive offsets and one for negative. The point of inclination, where the two lines
intersect, provides an approximation to the reference time. It should be appreciated that several well-known types of polynomial fits may be utilized for the unit variance data, and also, to
determine the local minimum of the unit variance distribution, and in turn, the reference time of interest.
FIG. 4B is a zoomed depiction of the unit variance distribution example shown in FIG. 4A. As such, the time offset scale of FIG. 4B is smaller than that of FIG. 4A. It should be noted from the
example of FIG. 4B that the intersecting or minimum point of inclination of the unit variance fit may not necessarily correspond exactly to a time offset of zero. In any case, the unit variance may
provide a sufficiently accurate estimate of position of an SPS receiver and/or a reference time of interest, such as GPS system time.
It should be appreciated that other error statistics may be used to obtain a “fit” that provides an approximation to a reference time. Furthermore, the method described with reference to FIGS. 3A and
3B may be performed by a combination of a mobile SPS receiver and a basestation, or exclusively by either entity. For example, in one embodiment, the basestation receives a set of range estimates
(e.g., pseudorange values) from the mobile SPS receiver, and determines the receiver's time, position, or other navigation information based on an error statistic, such as the unit variance.
Optionally, the basestation may provide the navigation information, or information based at least in part thereon, to the mobile SPS receiver or another entity. In this case, the SPS receiver may,
based on such information and/or other information, determine its time, position, and/or other navigational information.
An Alternative Embodiment
As indicated above, relative velocity and an error statistic (e.g., unit variance associated with pseudorange residuals) may be used separately or in conjunction, according to various embodiments of
the invention, to determine time associated with a satellite positioning system. Furthermore, a selection of which method to use may be made according to a predetermined condition, such as the
available data, the quality of signals, the number/spacing of satellites, the range between one or more satellites and the receiver, etc. In one embodiment, both methods may be performed, and the
optimum result for the solution of time, position, or other navigational information may be selected based on a minimization of inaccuracy.
In yet another embodiment of the invention, one or a combination of the above-described methods and apparatuses for determining time in a satellite positioning system are combined with another method
and apparatus for time determination, as described in detail in U.S. patent application Ser. No. 08/794,649, filed on Feb. 3, 1997, and which is entitled “Method and Apparatus for Satellite
Positioning System Based Time Measurement,” and which is hereby incorporated herein by reference. As described in detail in the referenced patent, time may be determined by comparing a record of a
satellite data message received by an entity, such as a mobile SPS receiver, to another record that is assumed to be error free. From such a comparison, time may be determined as described generally
below with reference to FIGS. 5 and 6, and described in further detail in the above-referenced copending application Ser. No. 08/794,649.
FIG. 5 shows a generalized method for determining time associated with a satellite positioning system based on comparing a first and a second record of a satellite data message, and which may be
utilized with a mobile SPS receiver which is combined with a mobile communication receiver and transmitter, such as that shown in FIG. 1A, according to one embodiment of the invention. The method
described below with reference to FIGS. 5 and 6 may be combined with one or a combination of the above-described techniques of time determination based on relative velocity and/or error statistic
determination. The mobile GPS receiver 100 shown in FIG. 1A samples the satellite data message, such as ephemeris, and creates a record of the message in step 501. Next in this method 500, the remote
or mobile GPS receiver transmits this record to a basestation, such as the basestation shown in FIGS. 7A or 7B in step 503. This record is typically some representation of the satellite data message
received by the mobile SPS receiver. In step 505, the basestation compares the record transmitted from the mobile SPS receiver to another record which may be considered a reference record of the
satellite navigation message. This reference record has associated time values wherein various segments of the satellite data message have specified “reference” times associated therewith. In step
507, the basestation determines the time of sampling by the mobile GPS receiver of the satellite data message. This determination is based upon a time value which is associated with the reference
record, and will generally indicate the time when the record was received by the mobile GPS receiver.
FIG. 6 illustrates in further detail a method 620 for measuring time related to satellite data messages for use with a satellite positioning system. The mobile or remote GPS receiver acquires in step
621 GPS signals and determines pseudoranges from those acquired GPS signals. In step 623, the mobile GPS receiver removes the PN data and creates a record of the satellite data message from the
acquired GPS signals used to create or determine the pseudoranges. This record is typically some representation of the satellite navigation message in the acquired GPS signals and typically
represents an estimate of the data. In step 625, the mobile GPS receiver transmits the record and the determined pseudoranges to a basestation, such as the basestation shown in FIG. 7A or 7B.
In step 627, the basestation performs a cross-correlation of the record transmitted from the mobile GPS receiver to a reference record of the navigation message of the set of satellites. This
reference record typically includes an accurate time stamp associated with the data in the reference record (e.g. each bit of data in the reference record has an associated time value or “stamp”),
and it is this time stamp which will be used to determine the time of receipt by the mobile GPS receiver of the originally acquired GPS signals. Generally, the record transmitted from the mobile GPS
receiver and the reference record partially overlap relative to time.
In step 629, the basestation determines from the cross-correlation operation the time of acquiring by the remote GPS receiver of the received GPS signals. The basestation then uses in step 631 the
time of the acquiring by the remote GPS receiver of the GPS signals and uses the determined pseudoranges to determine a position information, which may be a latitude and longitude of the remote/
mobile GPS receiver. The basestation, in step 633, may communicate this position information of the remote GPS receiver to another entity, such as a computer system coupled through a network, such as
the Internet, or an intranet, to the basestation.
Hardware Overview
FIG. 1A shows an example of a combined mobile GPS receiver and communication system which may be used with the present invention. This combined mobile GPS receiver and communication system 100 has
been described in detail in copending U.S. patent application Ser. No. 08/652,833, which was filed May 23, 1996, and entitled “Combined GPS Positioning System and Communication System Utilizing
Shared Circuitry,” which is hereby incorporated herein by reference. FIG. 1B illustrates in further detail the RF to IF converter 7 and the frequency synthesizer 16 of FIG. 1A. These components shown
in FIG. 1B are also described in copending application Ser. No. 08/652,833.
The mobile GPS receiver and communication system 100 shown in FIG. 1A may be configured to perform a particular form of digital signal processing on stored GPS signals in such a manner that the
receiver has very high sensitivity. This is further described in U.S. Pat. No. 5,663,734, which was issued on Sep. 2, 1997, and is entitled “GPS Receiver and Method for Processing GPS Signals”, and
this patent is hereby incorporated herein by reference. This processing operation described in U.S. Pat. No. 5,663,734, typically computes a plurality of intermediate convolutions typically using
fast Fourier transformations (FFTs) and stores these intermediate convolutions in the digital memory and then uses these intermediate convolutions to provide at least one pseudorange. The combined
GPS and communication system 100 shown in FIG. 1A also may incorporate certain frequency stabilization or calibration techniques in order to further improve the sensitivity and accuracy of the GPS
receiver. These techniques are described in copending application Ser. No. 08/759,523 which was filed Dec. 4, 1996, and is entitled “An Improved GPS Receiver Utilizing a Communication Link”, and
which application is hereby incorporated herein by reference.
Rather than describing in detail the operation of the combined mobile GPS receiver and communication system 100 shown in FIG. 1A, a brief summary will be provided here. In a typical embodiment, the
mobile GPS receiver and communication system 100 will receive a command from a basestation, such as basestation 17, which may be either one of the basestations shown in either FIG. 7A or FIG. 7B.
This command is received on the communication antenna 2 and the command is processed as a digital message and stored in the memory 9 by the processor 10. In one embodiment, the memory 9 could be
expanded to be a random access memory (RAM) for storing commands, data, and/or “snapshot” information. The processor 10 determines that the message is a command to provide a position information to
the basestation, and this causes the processor 10 to activate the GPS portion of the system at least some of which may be shared with the communication system. This includes, for example, setting the
switch 6 such that the RF to IF converter 7 receives GPS signals from GPS antenna 1 rather than communication signals from the communication antenna 2. Then the GPS signals are received, digitized,
and stored in the digital memory 9, and may be processed in accordance with the digital signal processing techniques described in the U.S. Pat. No. 5,663,734. The result of this processing typically
may include a plurality of pseudoranges for a set of satellites “in view” and these pseudoranges or data based thereon may then be transmitted back to the basestation by the processing component 10
by activating the transmitter portion and transmitting the pseudoranges back to the basestation via the communication antenna 2.
The basestation 17 shown in FIG. 1A may be coupled directly to the remote through a wireless communication link or may be, as shown in FIG. 8, coupled to the remote through a cellular telephone site
which provides a wired communication link between the telephone site and the basestation. FIGS. 7A and 7B illustrate examples of these two possible basestations.
The basestation 701 illustrated in FIG. 7A may function as an autonomous unit by providing a wireless link to and from mobile GPS receivers and by processing received pseudoranges. According to one
or a combination of the embodiments described above, the basestation 701 may process the pseudoranges to determine time by utilizing relative satellite velocity, an error statistic, and/or a
comparison of satellite data message records. The basestation 701 may find use where the basestation is located in a metropolitan area and all mobile GPS receivers to be tracked are similarly located
in the same metropolitan area. For example, the basestation 701 may be employed by police forces or rescue services in order to track individuals wearing or using the mobile GPS receivers. Typically,
the transmitter and receiver elements 709 and 711, respectively, will be merged into a single transceiver unit and have a single antenna. However, these components have been shown separately as they
may also exist separately. The transmitter 709 functions to provide commands and/or navigational information to the mobile GPS receivers through transmitter antenna 710. Typically, the transmitter
709 is under control of the data processing unit 705 which may receive a request from a user of the processing unit to determine the location of a particular mobile GPS receiver. Consequently, the
data processing unit 705 would cause the command to be transmitted by the transmitter 709 to the mobile GPS receiver. In response, the mobile GPS receiver would transmit back to the receiver 711
pseudoranges and associated time estimates and/or satellite data message records (or portions thereof) in one embodiment of the present invention to be received by the receiving antenna 712. The
receiver 711 receives such information from the mobile GPS receiver and provides them to the data processing unit 705 which then performs one or more of the above-described operations to determine
time, position, and/or other navigational information associated with the pseudoranges received from the mobile GPS receiver. As mentioned above with reference to copending application Ser. No. 08/
794,649, such operations may involve the satellite data messages received from the GPS receiver 703 or other source of reference quality satellite data messages. This is further described in the
above-noted copending patent applications. The GPS receiver 703 may provide the satellite ephemeris data which may be used, in one embodiment, with the pseudoranges and the determined time in order
to calculate a position information for the mobile GPS receiver. The mass storage 707 may store satellite velocity information, a stored version of the reference record of the satellite data messages
which is used to compare against the records received from the mobile GPS receiver, error statistic analysis routines in accordance with one or more of the techniques discussed above, and/or other
information to determine time based on the pseudoranges and any other information provided by the mobile GPS receiver. The data processing unit 705 may be coupled to an optional display 715 and may
be also coupled to a mass storage 713 with GIS software which is optional. It will be appreciated that while depicted separately, the mass storage 713 may be the same as the mass storage 707 in that
they may be contained in the same hard disk or other data storage device/medium.
FIG. 7B illustrates an alternative basestation of the present invention. This basestation 725 is intended to be coupled to remote transmitting and receiving sites such as a cellular telephone site
855 shown in FIG. 8. This basestation 725 may also be coupled to client systems through a network, such as the Internet or an intranet, or other types of computer networking systems. The use of the
basestation in this manner is further described in copending application Ser. No. 08/708,176, which was filed Sep. 6, 1996 and which is entitled “Client-Server Based Remote Locator Device” and which
is hereby incorporated herein by reference. The basestation 725 communicates with a mobile GPS unit, such as the combined mobile GPS receiver and communication system 853 shown in FIG. 8 through the
cellular telephone site 855 and its corresponding antenna or antennae 857 as shown in FIG. 8. It will be appreciated that the combined GPS receiver and communication system 853 may be similar to the
system 100 shown in FIG. 1A.
The basestation 725, as shown in FIG. 7B, includes a processor 727 which may be a conventional microprocessor coupled by a bus 730 to main memory 729 which may be random access memory (RAM). The
basestation 725 further includes other input and output devices, such as keyboards, mice, and displays 735 and associated I/O controllers coupled via bus 730 to the processor 727 and to the memory
729. A mass storage device 733, such as a hard disk or CD ROM or other mass storage devices, is coupled to various components of the system, such as processor 727 through the bus 730. An input/output
(I/O) device 731 which serves to provide I/O functionality between the GPS receiver or other source of satellite data messages, is also coupled to the bus 730. This I/O device 731 may receive
satellite data messages from a GPS receiver (e.g., the GPS receiver 703 shown in FIG. 7A) and provides them through the bus 730 to the processor which, in accordance to one of the above described
embodiments of the invention, may cause a time stamp to be applied to them. The records may then be stored in the mass storage device 733, for example, for later use in comparing to records received
from mobile GPS receivers. The mass storage device 733 may also store velocity information representing relative velocity of a set of one or more satellites. Additionally, the mass storage device 733
may store routines corresponding to one or more of the above-described methods for processing satellite positioning information/signals.
Two modems 739 and 737 are shown in FIG. 7B as interfaces to other systems remotely located relative to the basestation 725. In the case of modem or network interface 739, this device is coupled to a
client computer, for example, through the Internet or some other computer network. The modem or other interface 737 provides an interface to the cellular telephone site, such as the site 855 shown in
FIG. 8 which illustrates a system 851.
The basestation 725 may be implemented with various computer architectures as will be appreciated by those skilled in the art. For example, there may be multiple busses or a main bus and a peripheral
bus or there may be multiple computer systems and/or multiple processors. It may be advantageous, for example, to have a dedicated processor to receive the satellite data message from the GPS
receiver 703 and process that message in order to provide a reference record in a dedicated manner such that there will be no interruption in the process of preparing the reference record and storing
it and managing the amount of stored data in accordance with one of the above-described embodiments of the present invention.
FIG. 8 illustrates a system according to one embodiment of the invention, which includes an SPS receiver, a cellular telephone site, a basestation, the Internet, and a client computer system. The
system 851 shown in FIG. 8 may operate, in one embodiment, in the following manner. A client computer system 863 will transmit a message through a network, such as the Internet 861 to the basestation
825. It should be appreciated that there may be intervening routers or computer systems in the network or Internet 861 which pass along the request for position of a particular mobile GPS receiver.
The basestation 825 will then transmit a message through a link, which is typically a wired telephone link 859, to the cellular telephone site 855. This cellular telephone site 855 then transmits a
command using its antenna or antennae 857 to the combined mobile SPS receiver and communication system 853. In response, the system 853 transmits back pseudoranges, records of the satellite data
messages, velocity information, and/or other information. Such information may be received by the cellular telephone site 855 and communicated back to the basestation through link 859. The
basestation then performs one or more of the operations as described above with various embodiments of the invention, such as time determination using one or a combination of relative satellite
velocity, Doppler measurements, an error statistic, and/or comparing two or more satellite data records. The basestation may then determine navigational information, such as time and/or position of
the SPS receiver, and communicate the navigational information through a network, such as the Internet 861, to the client computer system 853 which may itself have mapping software at the client
computer system, allowing the user of this system to see on a map the exact position of the mobile SPS system 853.
Alternative Embodiments
While the invention has been described in terms of several embodiments and illustrative figures, those skilled in the art will recognize that the invention is not limited to the embodiments or
figures described. In particular, the invention can be practiced in several alternative embodiments that provide a method and/or apparatus to determine time or other navigational information in
satellite positioning system by one or a combination of the following: (1) utilizing relative velocity of an entity and/or a set of satellites; (2) computing an error statistic for time or position/
range; and (3) comparison of two or more satellite data messages.
Therefore, it should be understood that the method and apparatus of the invention can be practiced with modification and alteration within the spirit and scope of the appended claims. The description
is thus to be regarded as illustrative instead of limiting on the invention.
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South Waltham, MA Geometry Tutor
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New (?) Way To Calculate ERA
I’m thinking out loud here, so I welcome your feedback on this one. I doubt I’m the first to think of this, but a Google search along these lines has turned up nothing.
Let’s start with the seventh inning of last night’s game. Jamie Moyer left the game with the bases loaded, no outs. Geoff Geary came in and let Moyer’s three runners score, along with another
runner of his own. He left with the bases loaded and one out. Mike Zagurski relieved Geary, allowing two of Geary’s runners to score. He ended the inning leaving both of his own runners on base.
Now, according to traditional ERA calculation, Moyer gets credited with 3 runs in 0 innings because the three guys he put on base scored, even if after he left the game; Geary gets credited with
3 runs in 1/3 of an inning, because he got one out but one runner of his scored when he was in the game and two runners scored after he left; and Zagurski gets credited with 0 runs in 2/3 of an
inning, even though he let up two runs, because both runners who scored on his watch were Geary’s.
But why calculate ERA this way? Why not split up the allocation of runs based on how many bases each pitcher is responsible for?
Re: New (?) Way To Calculate ERA
bigh0rt wrote:
But why calculate ERA this way? Why not split up the allocation of runs based on how many bases each pitcher is responsible for?
FULL STORY
Because it doesn't make any sense. All it does is punish the reliever for entering the game in tight situations.
Bury me a Royal.
Re: New (?) Way To Calculate ERA
bigh0rt wrote:
But why calculate ERA this way? Why not split up the allocation of runs based on how many bases each pitcher is responsible for?
FULL STORY
Because the starting pitcher had 3 open bases to use to get out of previous innings before an earned run. So should the reliever.
Re: New (?) Way To Calculate ERA
i like where your heads at hort
(phillies blog)
Shane Victorino wrote:“We keep fighting,” Victorino said. “We keep plugging along.”
Re: New (?) Way To Calculate ERA
Snakes Gould wrote:i like where your heads at hort
(phillies blog)
You know what they say... keep your friends close...
I do agree that it seems rather senseless, and punishes relievers for coming in with men on base. I was wondering if anyone had any further insight on it than that, or actually supported this notion.
Re: New (?) Way To Calculate ERA
reliever's got a real cushy job..
gives up 3 of 4 bases required to score a run and keeps his perfect era AND can use the starter's litter on the bases to GET outs...outs that might not otherwise be available at 1st base, PLUS
mutiple outs on one play..
ie the reliever's Outs are easier
always wondered about this, but guess when they voted on it, relievers outnumbered starters..
still do
Re: New (?) Way To Calculate ERA
I can see the problem. While it doesn't seem that the starter should take 100% of the blame when a reliever lets all his baserunners score, it also doesn't seem that a reliever should be penalized
for letting up a couple RBI hits when he wasn't the one who let on the runners who scored. After all, a starter can let a couple baserunners get on to lead off the inning and not get penalized as
long as he gets out of it, so why shouldn't a reliever be allowed the same cushion?
What it comes down to, in my opinion, is that ERA just isn't that great a statistic for judging the effectiveness of relievers. Starters (rightfully) have the luxury of getting into jams as long as
they can get out of them. If they let allow two baserunners an inning for six innings without allowing a run, then more power to them - they've done their job. The ERA would be 0.00, and at the end
of the day, that's really what matters. (Of course, the odds aren't too high that a starter would continue to put up a low ERA when he's allowing two baserunners an inning, but that's another story.)
With a reliever, on the other hand, the ERA doesn't really show much of the picture. The fact of the matter is that the reliever's job just isn't the same as the starter's job. Sure, there are times
when a reliever will come in to open the inning and simply finish it cleanly himself. However, there are also plenty of times when he comes in to bail out a starter or another reliever. For the
reasons that this article pointed out, ERA isn't going to be too reflective of the reliever's effectiveness. WHIP, on the other hand, is a lot more useful. The main reason why that's the case is that
when a reliever comes in with runners on base, his job is to prevent any more runners from reaching base. If he lets up two hits and allows two runs to score, then even if he walks away from the
inning without any damage to his ERA, he hasn't done his job.
There are other factors to take into account also. It's important for a reliever not to allow hits with runners on base, but it's also better to let up a single than a home run. So stats like HR
Allowed, SLG against, etc. are also useful. If there were a version of WHIP that were weighted to assign more weight to extra-base hits, then that would be that stat I'd use to evaluate relievers.
Of course, all of this doesn't change the point that it's not really fair to the starter when a reliever allows all of a starter's runs to score. Even if we were to judge relievers by WHIP rather
than ERA (meaning that the fact that the reliever's ERA comes away clean doesn't seem quite so unfair, since that's not what people would be judging him by anyway), that doesn't change the fact that
the starter got screwed. However, if you calculated the league average percentage of inherited runners scored, then you could create a version of ERA that assumes that the league average percentage
of inherited runners scored. It would be a little complicated, since the percentage would be different depending on the exact number of baserunners and outs that the reliever inherited, but it seems
like it should be pretty do-able. It still wouldn't be perfect, since it wouldn't take into account things like the ability of the hitters that the reliever had to face (although I suppose that the
average OPS of opposing hitters could be factored in there also).
Anyway, that would be my solution. I'd use a version of ERA that assumes the league average percentage of inherited runners scored to evaluate starters, and I'd use a version of WHIP that assigns
more weight to more powerful hits to evaluate relievers.
Re: New (?) Way To Calculate ERA
jswede wrote:
bigh0rt wrote:
But why calculate ERA this way? Why not split up the allocation of runs based on how many bases each pitcher is responsible for?
FULL STORY
Because the starting pitcher had 3 open bases to use to get out of previous innings before an earned run. So should the reliever.
yeah, but the starter always comes into the inning with 0 outs. is it really fair to let a reliever come in with men on and 2 outs, and allow a couple base hits before getting the out and not taking
a hit to their era?
maybe it doesn't matter anyways, because comparing starter/reliever era's is comparing apples to oranges in the first place.
Re: New (?) Way To Calculate ERA
to be perfectly equitable, can't just divy the earned run by the number of bases allowed as the article suggests.
say, the reliever comes in after the starter gives up a single, run scores.. applying to the reliever 3/4 of the run and the starter 1/4 wouldn't be fair.
while the reliever can use the runner to make any additional outs easier (double play, force at second when no out available at 1st,etc) fact is the HARDEST base to get on the way to 4, and the run,
IS the 1st base.
To get the 1st base earned against a pitcher - the pitcher has absolutely got to do something that is clearly a negative by the pitcher...allow a hit, walk a batter, hit a batter, throw a wild pitch
for a 3rd strike, etc.
Rest of the bases can be attained when the pitcher actually does his job (get outs) through base advancement on ground balls to left of shortstop, sac bunts, fly balls, weak arm of catcher on stolen
Additionally a single is often worth not 1 but 2 bases when a runner goes 1st to 3rd, 2nd to home,a double worth not 2 but 3, when runner goes 1st to home, hit and runs figure in also.
Easier outs don't balance out this HUGE disadvantage on pitcher negatives that the reliever is faced with.
But they should get SOMETHING counted against their ERA.
Right now, relievers get a free ride
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Perspective projection to orthographic and vice versa [Archive] - OpenGL Discussion and Help Forums
06-09-2012, 09:15 AM
If I know field of view angle and current view volume co-ordinates defined by left_perspective, right_perspective, top_perspective, bottom_perspective, zNear, zFar. Then is it possible to some how
find equivalent view volume in orthographic mode, that is left_ortho, right_ortho, top_ortho, bottom_ortho, zNear, zFar?
Is it possible to reverse it (to get perspective view volume if I know orthographic view volume and FOV angle?)
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problem in primitive roots
December 18th 2007, 01:13 PM
problem in primitive roots
i wish any one can hepl me with this problems
1) if p is prime , show that th product of the $\phi(p-1)$ primitive roots of p is congurent modulo p to $(-1)^\phi(p-1)$.
[hint: if r is primitive root of p , then r^k is primitive root of p provided that gcd(k,p-1)= 1 ]
2) use the fact that each prime p has a primitive root to give a different proof of Wislon's theroem.
[hint : if p has a primitive root r, then (p-1)!=r^1+2+..+(p-1)(modp)]
December 18th 2007, 01:29 PM
Post #5 might help. Assume that p>2.
Let $a_1,a_2,...,a_{\phi(p-1)}$ be the primitive roots of $p$. Let $a_1 = r$ then $a_2 \equiv r^{b_2}$ where $1< b_2 < p-1$ and $\gcd( b_2, p-1)=1$. Similarly $a_3 \equiv r^{b_3}$ and so one.
Thus, $r^{1},r^{b_2},...,r^{b_{\phi(p-1)}}$ are all the primitive roots. Now one of the exponents of $r$ are the same, and they are all relatively prime to $p-1$. By pigeonholing we see that they
are a premutation of all integers relatively prime to $p-1$ and less than it.
Thus, $r^1 \cdot r^{b_2} \cdot ... \cdot r^{ b_{\phi(p-1)}} \equiv r^{c_1+...+c_{\phi(p-1)}} (\bmod p)$.
The question now is what is a nice formula for $c_1+...+c_{\phi(p-1)}$ where $c_1,c_2,...,c_{\phi(p-1)}$ are all the positive integers less than $p-1$ and are congruent to $p-1$ written in
increasing order. Note that $c_1 - (p-1),c_2-(p-1),...,c_{\phi(p-1)} - (p-1)$ all again a permutation of all the relatively prime integers to $p-1$, thus, $c_1+...+c_{\phi(p-1)} = [c_1 - (p-1)]
+...+[c_{\phi(p-1)} - (p-1)]$, thus, $c_1+...+c_{\phi(p-1)} = (1/2)(p-1)\phi(p-1)$.
Thus, we have,
$r^{c_1+...+c_{\phi(p-1)}} \equiv r^{(1/2)(p-1)\phi(p-1)} \equiv\left( r^{(p-1)/2} \right)^{\phi(p-1)} (\bmod p)$.
But $r^{(p-1)/2} \equiv -1 (\bmod p)$ (remember that?).
Thus, $r^{c_1+...+c_{\phi(p-1)}} \equiv (-1)^{\phi(p-1)} (\bmod p)$.
January 14th 2008, 07:14 PM
really thnx man
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How to Do Break Even Analysis
Edit Article
Edited by IngeborgK, Jeff, Reneedessi, Abrogation316
Break-even analysis is a very useful cost accounting technique. It is part of a larger analytical model called cost-volume-profit (CVP) analysis, and it helps you determine how many product units
your company needs to sell to recover its costs and start realizing profit. Learning how to do a break-even analysis is a matter of following a few steps.
1. 1
Determine your company's fixed costs. Fixed costs are any costs that don't depend on the volume of production. Rent and utilities would be examples of fixed costs, because you will pay the same
amount for them no matter how many units you produce or sell. Categorize all your firm's fixed costs for a given period and add them together.
2. 2
Determine your company's variable costs. Variable costs are those that will fluctuate along with production volume. For example, a business that performs oil changes will have to purchase more
oil filters if they perform more oil changes, so the cost of buying oil filters is a variable cost. In fact, because the company can expect to buy 1 oil filter per oil change, this cost can be
allocated to each oil change performed.
3. 3
Determine the price at which you will sell your product. Pricing strategies are part of the much more comprehensive marketing strategy, and can be fairly complex. However, you know that your
price will be at least as high as your production costs (in fact, a lot of anti-trust legislation exists to outlaw selling below cost).
4. 4
Calculate your unit contribution margin. The unit contribution margin represents how much money each unit sold brings in after recovering its own variable costs. It is calculated by subtracting a
unit's variable costs from its sales price. Consider the following example using an oil change business.
□ The sales price of an oil change is $40 (note that these calculations will work equally well when expressed in other currencies). Each oil change has 3 costs associated with it: purchasing a
$5 oil filter, purchasing a $5 can of oil, and paying $10 in wages to the technician performing the oil change. These are the variable costs associated with an oil change.
□ The contribution margin for a single oil change is: 40 � (5 + 5 + 10) or $20. Providing an oil change to a customer brings the company $20 in revenue after recovering its own variable costs.
5. 5
Calculate your company's break-even point. The break-even point tells you the volume of sales you will have to achieve to cover all of your costs. It is calculated by dividing all your fixed
costs by your product's contribution margin.
□ Using the example above, imagine all of your company's fixed costs for a given month are $2000. Therefore, the break-even point is: 2000 / 20 or 100 units. When 100 oil changes have been
performed in a month, the company "breaks even."
6. 6
Determine your expected profits or losses. Once you have determined the break-even volume, you can estimate your expected profits. Remember that each additional unit sold will produce revenue
equal to its contribution margin. Therefore, each unit sold above the break-even point will produce a profit equal to its contribution margin, and each unit sold below the break-even point will
generate a loss equal to its contribution margin.
□ Using the example above, imagine your business provides 150 oil changes in a month. Only 100 oil changes were needed to break even, so the additional 50 oil changes generated a profit of $20
each, for a total of (50 * 20) or $1000.
□ Now imagine your business provided only 90 oil changes in a month. You didn't achieve your break-even volume, so you sustained a loss. Each of the 10 oil changes under your break-even volume
generated a loss of $20, for a total of (10 * 20) or $200.
• Make sure that you understand the limitations of break-even analyses. Because they rely on cost and volume estimates, they won't ever be able to produce a perfectly accurate profit or loss
Sources and Citations
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Categories: Accounting and Regulations
Recent edits by: Reneedessi, Jeff, IngeborgK
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Español: Cómo hacer un análisis del punto de equilibrio
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Quantum Physics
1112 Submissions
[9] viXra:1112.0091 [pdf] replaced on 2012-02-20 16:50:56
A Three Step Program For Return To Reality In Physics
Authors: Paul J. Werbos
Comments: 19 Pages. more details on how to do steps one and three
Modern physics has become so vast and so complicated that a deep connection between empirical technologically-oriented physics and the realm of basic theory becomes more and more a rare exercise in
crossdisciplinary cooperation. This paper will give an overview of many important developments both on the empirical side and the theoretical side, well known to both but not to each other, and give
the specifics of a way to connect them more effectively. After the initial review, it provides a three-step program for reorganizing and simplifying our fundamental assumptions about the laws of
physics, starting by linking recent progress in areas like backwards time physics, coherence phenomena in quantum optics and cavity QED to the retrieval of an updated form of Einstein’s vision of a
universe of mathematically elegant and rigorous continuous fields, addressing empirical and theoretical questions which are still open in the study of nuclear interactions and in the mathematical
study of solitons, including the Higgs boson.
Category: Quantum Physics
[8] viXra:1112.0087 [pdf] submitted on 2011-12-30 13:37:01
A Dissertation on the Origins of Quantization in the Universe (With Unification Gravity Electromagnetism as Appendix)
Authors: Leonardo Rubino
Comments: 49 Pages.
The Universe is quantized simply because its age is very long, so its cycle frequency is very small, but not zero! From this, the quantizations of all physical quantities can be derived.
Category: Quantum Physics
[7] viXra:1112.0086 [pdf] submitted on 2011-12-30 13:40:59
Laser Theory
Authors: Leonardo Rubino
Comments: 18 Pages.
In this paper you can find not only a formal LASER Theory, but also useful appendixes which help you to understand the origins of all the equations used in the paper itself.
Category: Quantum Physics
[6] viXra:1112.0084 [pdf] replaced on 2012-04-05 15:45:38
The Hilbert Book Model; in Concise Format
Authors: J.A.J. van Leunen
Comments: 195 Pages.
The Hilbert Book Model is a simple model of fundamental physics that is strictly based on the axioms of traditional quantum logic. It uses a sequence of instances of an extension of a quaternionic
separable Hilbert space that each represent a static status quo of the whole universe.
Category: Quantum Physics
[5] viXra:1112.0068 [pdf] submitted on 2011-12-20 15:31:50
Camouflaged Camouflaged Contextual Posturing in the Laws of Nature: Hidden Riches for Novel forms of Technology and Energy Generation
Authors: Donald Reed
Comments: 12 Pages.
Evidence will be presented from a wide spectrum of theoretical and empirical research to advance the thesis that the laws of nature, particularly in the astrophysical and microphysical arenas, are in
some sense contextual, possibly dependent on both location and to a certain extent, direction...
Category: Quantum Physics
[4] viXra:1112.0067 [pdf] replaced on 2013-07-31 16:38:53
Comment on “Entanglement and the Thermodynamic Arrow of Time” and Correct Reply on “Comment on "Quantum Solution to the Arrow-of-Time Dilemma"” of David Jennings and Terry Rudolph
Authors: Oleg Kupervasser
Comments: 5 Pages. "Frontiers in Science",Vol.2, No.6, December 2012
Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone’s paper "Quantum Solution to the Arrow-of-Time Dilemma". In these papers, the authors suppose that second law of
thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors
use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not
an enough condition for a system to be macroscopic. The macroscopic system must also be chaotic and has small chaotic interaction with its environment/observer resulting in decoherence
(decorrelation). We demonstrate that for relevant thermodynamic macroscopic quantum systems no objection appears.
Category: Quantum Physics
[3] viXra:1112.0059 [pdf] submitted on 2011-12-19 10:35:06
Nonlocality and Interaction
Authors: Manfred Buth
Comments: 6 Pages.
Three statements are asserted: (a) There is no contradiction between quantum mechanics and special relativity, if the role of interaction in the analysed experiments is sufficiently respected. (b)
There is no paradoxical situation in the gedankenexperiment of Einstein, Podolsky and Rosen. (c) The principles of quantum statistics describe nonlocal effects. From (b) one can infer that the whole
discussion about EPR and all that was and is dispensable. It could have been avoided, if in time the analysis of possible experiments would have been carried out a bit more carefully.
Category: Quantum Physics
[2] viXra:1112.0040 [pdf] submitted on 2011-12-14 16:26:57
Is Entanglement Signaling Really Impossible?
Authors: Jack Sarfatti
Comments: 9 Pages.
Quantum entanglement cannot be used as a communication channel without an auxiliary light speed limited classical key to unlock the message at the receiver? Hermitian observables guarantee orthogonal
sender base states that erase any nonlocal influence of the sender settings on the detection probabilities at the receiver. However, this is no longer true when the entangled whole has different
macro-quantum coherent Glauber sender states. Glauber states are non-orthogonal eigenstates of the non-Hermitian photon destruction operator. The Born probability interpretation breaks down because
of "phase rigidity" (P.W. Anderson's "More is different"). This is a new regime that is to orthodox quantum theory what general relativity is to special relativity. Antony Valentini has argued that
the breakdown of the Born probability rule entails "signal non locality" (aka entanglement signals). The space-time interval between the sending and the receiving irreversible measurements is
irrelevant depending only on the free will of the local observers. That is, this is a pre-metrical topological information effect. There is asymmetry between the sending and the receiving. Therefore,
there is no ambiguity between active (retro) cause and passive effect. In particular a message can be decoded back from the future before it is sent, but only if it will be sent in a globally
self-consistent Novikov time loop.
Category: Quantum Physics
[1] viXra:1112.0023 [pdf] submitted on 2011-12-07 13:12:04
How the World Works
Authors: Ir J.A.J. (Hans) van Leunen
Comments: 14 Pages. The paper concerns a tale that explains quantum mechanics
I wrote this for all people that hate a car load of formulas.
Category: Quantum Physics
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CSU Early Assessment of Readiness for College Mathematics -- Standards Assessed
from the Blueprint for the California Standards Test of Algebra II | Early Assessment
Program | Academic Affairs
Standard Description of Standard
AII.1.0 Students solve equations and inequalities involving absolute value.
AII.2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
AII.3.0 Students are adept at operations on polynomials, including long division.
AII.4.0 Students factor polynomials representing the the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
AII.5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
AII.6.0 Students add, subtract, multiply, and divide complex numbers.
AII.7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including
those with negative exponents in the denominator
AII.8.0 Students solve and graph quadratic equations by factaoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also
solve quadratic equations in the complex number system.
AII.9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a,
b, and c vary in the equation y = a(x-b)2 + c
AII.10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
AII.12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
AII.15.0* Stuetns determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or
never true. *If NOT about logarithms.
AII.16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation
representing it.
AII.17.0 Give a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether
the graph of the equation is a circle, an ellipse, a parabold, or a hyperbola. Students can then graph the equation.
AII.18.0 Students use fundamental counting principles to compute combinations and permutations.
AII.20.0 Students know the binomial theoreum and use it to expand binomial expressions that are raised to positive integer powers.
AII.22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
AII.24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
AII.25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
September 30, 2004
Download PDF File » (.pdf, 56K)
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Let $A$ the collection of finite unions of sets of the form
$(a,b]$$\cap$$\mathbb{Q}$, when $-\infty$$\leq$a<b $\leq$$+\infty$."
a. Show that $A$ is an algebra on $\mathbb{Q}$.
b. Show that the $\sigma$-algebra generated by $A$ is
P( $\mathbb{Q}$) (the power set of $\mathbb{Q}$).
c. Define $u$ on $A$ by $u$( $\phi$)=0 and $u$(C)= $+\infty$ for C $eq$$phi$. Show that $u$ is a premeasure on $A$ and that there is more than one measure on P( $\mathbb{Q}$) whose restriction to
$A$ is $u$.
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Computational problems of data exchange
Seminar Room 1, Newton Institute
Data Exchange is the problem of inserting data structured under a source schema into a target schema of different structure (possibly with integrity constraints), while reflecting the source data as
accurately as possible. We study computational issues related to data exchange in the setting of Fagin, Kolaitis, and Popa (PODS´03). In particular, we are interested in computing a particular
universal solution to a data exchange problem, called "the core". We present polynomial algorithms for computing the core of large classes of data exchange problems, solving relevant open problems by
Fagin et al. Our results show that data exchange with cores is feasible in a very general framework. Furthermore, we use the technique of hypertree decompositions to derive improved algorithms for
computing the core of a relational instance with labeled nulls, a problem we show to be fixed-parameter intractable with respect to the block size of the input instances. Finally, we show that
computing cores is NP-hard in presence of a system-predicate NULL(x), which is true if x is a null value.
Part of this work is joint work with Alan Nash, UCSD.
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Spreading rumors rapidly despite an adversary
- Distributed Computing , 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include
synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refe ..."
Cited by 44 (4 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include
synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent
difficulty of individual problems and in studying the power of different models of distributed computing.
- Proc. 35th Annual Symp. on Foundations of Computer Science , 2003
"... We introduce a theory of competitive analysis for distributed algorithms. The first steps in this direction were made in the seminal papers of Bartal, Fiat, and Rabani [18], and of Awerbuch,
Kutten, and Peleg [16], in the context of data management and job scheduling. In these papers, as well... ..."
Cited by 30 (5 self)
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We introduce a theory of competitive analysis for distributed algorithms. The first steps in this direction were made in the seminal papers of Bartal, Fiat, and Rabani [18], and of Awerbuch, Kutten,
and Peleg [16], in the context of data management and job scheduling. In these papers, as well...
- In Proc. 28th ACM Symp. on Theory of Computing (STOC , 2000
"... We define a novel measure of competitive performance for distributed algorithms based on throughput, the number of tasks that an algorithm can carry out in a fixed amount of work. This new
measure complements the latency measure of Ajtai et al. [3], which measures how quickly an algorithm can finish ..."
Cited by 13 (2 self)
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We define a novel measure of competitive performance for distributed algorithms based on throughput, the number of tasks that an algorithm can carry out in a fixed amount of work. This new measure
complements the latency measure of Ajtai et al. [3], which measures how quickly an algorithm can finish tasks that start at specified times. An important property of the throughput measure is that it
is modular: we define a notion of relative competitiveness with the property that a k-relatively competitive implementation of an object T using a subroutine U , combined with an l-competitive
implementation of U , gives a kl-competitive algorithm for ...
, 2001
"... The problem of performing t tasks in a distributed system on p failure-prone processors is one of the fundamental problems in distributed computing. If the tasks are similar and independent and
the processors communicate by sending messages then the problem is called Do-All . In our work the communi ..."
Cited by 6 (4 self)
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The problem of performing t tasks in a distributed system on p failure-prone processors is one of the fundamental problems in distributed computing. If the tasks are similar and independent and the
processors communicate by sending messages then the problem is called Do-All . In our work the communication is over a multiple-access channel, and the attached stations may fail by crashing. The
measure of performance is work, defined as the number of the available processor steps. Algorithms are required to be reliable in that they perform all the tasks as long as at least one station
remains operational. We show that each reliable algorithm always needs to perform at least the minimum amount t + p p t) of work. We develop an optimal deterministic algorithm for the channel with
collision detection performing only the minimum work (t + p p t). Another algorithm is given for the channel without collision detection, it performs work O(t+p p t+p minff; tg), where f < p is the
number of failures. It is proved to be optimal if the number of faults is the only restriction on the adversary. Finally we consider the question if randomization helps for the channel without
collision detection against weaker adversaries. We develop a randomized algorithm which needs to perform only the expected minimum work if the adversary may fail a constant fraction of stations, but
it has to select the failure-prone stations prior to the start of an algorithm.
- in Proceedings, 36th ACM Symposium on Theory of Computing (STOC), 2004
"... The Collect problem for an asynchronous shared-memory system has the objective for the processors to learn all values of a collection of shared registers, while minimizing the total number of
read and write operations. First abstracted by Saks, Shavit, and Woll [37], Collect is among the standard pr ..."
Cited by 4 (2 self)
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The Collect problem for an asynchronous shared-memory system has the objective for the processors to learn all values of a collection of shared registers, while minimizing the total number of read
and write operations. First abstracted by Saks, Shavit, and Woll [37], Collect is among the standard problems in distributed computing, The model consists of n asynchronous processes, each with a
single-writer multi-reader register of a polynomial capacity. The best previously known deterministic solution performs O(n 3/2 log n) reads and writes, and it is due to Ajtai, Aspnes, Dwork, and
Waarts [3]. This paper presents a new deterministic algorithm that performs O(n log 7 n) read/write operations, thus substantially improving the best previous upper bound. Using an approach based on
epidemic rumor-spreading, the novelty of the new algorithm is in using a family of expander graphs and ensuring
- In the Proceedings of the 3rd International Conference on Ad-Hoc Networks & Wireless (AD HOC NOW , 2004
"... Consider k particles, 1 red and k − 1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it “infects ” it with its color. The newly red particles are
now available to infect more white ones. When is it the case that all white will become red? It turns out t ..."
Cited by 3 (1 self)
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Consider k particles, 1 red and k − 1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it “infects ” it with its color. The newly red particles are now
available to infect more white ones. When is it the case that all white will become red? It turns out that this simple question is an instance of information propagation between random walks and has
important applications to mobile computing where a set of mobile hosts acts as an intermediary for the spread of information. In this paper we model this problem by k concurrent random walks, one
corresponding to the red particle and k − 1 to the white ones. The infection time Tk of infecting all the white particles with red color is then a random variable that depends on k, the initial
position of the particles, the number of nodes and edges of the graph, as well as on the structure of the graph. In this work we develop a set of probabilistic tools that we use to obtain upper
bounds on the (worst case w.r.t. initial positions of particles) expected value of Tk for general graphs and important special cases. We easily get that an upper bound on the expected value of Tk is
the worst case (over all initial positions) expected meeting time m ∗ of two random walks multiplied by Θ(log k). We demonstrate that this is, indeed, a tight bound; i.e. there is a graph G (a
special case of the “lollipop ” graph), a range of values k < n (such that √ n − k = Θ ( √ n)) and an initial position of particles achieving this bound. When G is a clique or has nice expansion
properties, we prove much smaller bounds for Tk. We have evaluated and validated all our results by large scale experiments which we also present and discuss here. In particular, the experiments
demonstrate that our analytical results for these expander graphs are tight. Due to lack of space, an Appendix is added, to be read at the discreetion of the Program Committee members. 1
, 1996
"... Consider a set of n processors that can communicate with each other. Assume that each processor can be either "good " or "faulty". We wish to diagnose the system. That is, we use tests between
the processors to determine the status of each processor. We suppose that good processo ..."
Cited by 2 (0 self)
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Consider a set of n processors that can communicate with each other. Assume that each processor can be either "good " or "faulty". We wish to diagnose the system. That is, we use
tests between the processors to determine the status of each processor. We suppose that good processors are accurate, but that faulty processors may be in error. We develop fast parallel diagnosis
algorithms, and also use adversary arguments to prove that our algorithms are near optimal. Our models are based upon the system diagnosis model proposed by Preparata, Metze and Chien [46]. We
consider three different models of diagnosis. First we have a static model in which each processor has a fixed status, there is an upper bound t on the number of faulty processors, and we wish to
minimize the number of rounds of testing used to perform diagnosis. We prove that 4 rounds are necessary and sufficient when (8=3)pn ^ t ^ 0:03n (for n sufficiently large). Furthermore, at least 5
rounds are necessary when t * 0:42n (for n sufficiently large), and 10 rounds are sufficient when t! 0:5n (for all n). It is well known that no general solution is possible when t * 0:5n. Second we
consider a dynamic model in which a processor may change status during the diagnosis. In each round up to t processors may break down, and we may direct that up to t processors are repaired. We show
that it is possible to limit the number of faulty processors to O(t log t), even if the system is run indefinitely. We present an adversary which shows that this bound is optimal.
- In DALT–2006 , 2006
"... Abstract. This paper discusses the problem of efficient propagation of uncertain information in dynamic environments and critical situations. When a number of (distributed) agents have only
partial access to information, the explanation(s) and conclusion(s) they can draw from their observations are ..."
Cited by 2 (2 self)
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Abstract. This paper discusses the problem of efficient propagation of uncertain information in dynamic environments and critical situations. When a number of (distributed) agents have only partial
access to information, the explanation(s) and conclusion(s) they can draw from their observations are inevitably uncertain. In this context, the efficient propagation of information is concerned with
two interrelated aspects: spreading the information as quickly as possible, and refining the hypotheses at the same time. We describe a formal framework designed to investigate this class of problem,
and we report on preliminary results and experiments using the described theory. 1
, 2004
"... Rumor spreading algorithms are a useful way to disseminate information to a group of players in the presence of faults. Rumors are either spread by pushing, in which the players knowing the
rumor call other players at random and spread the rumor, or by pulling, where players who do not know the rumo ..."
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Rumor spreading algorithms are a useful way to disseminate information to a group of players in the presence of faults. Rumors are either spread by pushing, in which the players knowing the rumor
call other players at random and spread the rumor, or by pulling, where players who do not know the rumor call other players and ask for any new rumors.
"... log n log(n log n)−log t We consider the problem of gossiping when dynamic node crashes are controlled by adaptive adversaries. We develop gossiping algorithms which are efficient with respect
to both the time and communication measured as the number of point-to-point messages. If the adversary is a ..."
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log n log(n log n)−log t We consider the problem of gossiping when dynamic node crashes are controlled by adaptive adversaries. We develop gossiping algorithms which are efficient with respect to
both the time and communication measured as the number of point-to-point messages. If the adversary is allowed to fail up to t nodes, among the total of n, where additionally n−t =Ω(n/polylog n),
then one among our algorithms completes gossiping in time O(log 2 t)andwithO(npolylog t) messages. We prove a lower � bound which � states that the time has to be at least Ω if the communication is
restricted to be O(n polylog n). We also show that one can solve efficiently a more demanding consensus problem with crash failures by resorting to one of our gossiping algorithms. If the adversary
is allowed to fail t nodes, where n − t = Ω(n/polylog n), we obtain a time-optimal solution that is away from the communication optimality by at most a polylogarithmic factor.
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Windsor, CA Math Tutor
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Compute the Eigenvalues and Eigenvectors
1. The problem statement, all variables and given/known data
Compute the Eigenvalues and Eigenvectors of A
A= [0 0 1;0 2 0;3 0 0]
2. Relevant equations
where I know the lamdas and plug them into the above equation and expand the system of equations.
3. The attempt at a solution
I have solved for the eigenvalues and got +sqrt(3), -sqrt(3) and 2.
I have solved for the eigenvectors associated with +sqrt(3), -sqrt(3), and checked them in matlab.
For lamda (eigenvalue) of sqrt(3) the eigenvector is
[ 1;0;sqrt(3)]
For lamda (eigenvalue) of -sqrt(3) the eigenvector is
[ -1;0;sqrt(3)]
But for when the eigenvalue is equal to 2 I come up to problems. where the 2nd row of my matrix is all zeroes. This confuses me because I have checked the vector in matlab and know it should be [0;1;
0]. Which is impossible based on the 2nd row being all zeroes.
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