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A Method of the Precision Doppler Measurements of Transverse Velocities Previous abstract Next abstract Session 117 - Instrumentation and Techniques. Oral session, Thursday, January 18 Salon del Rey North, Hilton [117.06] A Method of the Precision Doppler Measurements of Transverse Velocities L. M. Ozernoy (CSI/GM...
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Mechanics eBook: Strain Gages and Strain Rosette MECHANICS - THEORY Strain Gage Basics It is not possible (currently) to measure stress directly in a structure. However, it is possible to measure strain since it is based on d...
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p-power roots of unity in local fields up vote 5 down vote favorite 1 Let K be a number field and suppose K contains no p-power roots of unity. Let P be a prime of K above the rational prime p. Can someone prove or disprove the assertion that the local field K_P will contain no p-power roots of unity? nt.number-theor...
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The Schrödinger equation If the elec­tron in an atom of hydrogen is a standing wave, as de Broglie had assumed, why should it be con­fined to a circle? After the insight that par­ti­cles can behave like waves, which came ten years after Bohr’s quan­ti­za­tion pos­tu­late, it took less than three years for the full-​​f...
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Does there exist an order in a number field of deg>1 with a map to F_p for all p? up vote 4 down vote favorite 1 This question is motivated by a computational issue. Suppose $R$ is a product of orders in numberfields such that there is no ring homomorphism $R \to \mathbb Z$, then can one write an algorithm that actual...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: ganeshie8 Group Title ... • one year ag...
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. B.5. TIME DELAYS Nothing compares to the measurement of the Hubble constant in bringing out the worst in astronomers. As we discussed in the previous section on lens modeling, many discussions of lens models seem obfuscatory rather than illuminating, and the tendency in this direction increases when the models are ...
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Solving equations Command disabled: backlink Table of Contents Solving equations Numerous Java packages can be used to solve linear, non-linear and differential equations. Solving linear, quadratic and cubic equations To solve linear, quadratic and cubic equations, use the jhplot.math.Numeric package. In general, ...
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Weekly Challenge 6: AP Train Copyright © University of Cambridge. All rights reserved. 'Weekly Challenge 6: AP Train' printed from http://nrich.maths.org/ This problem is based on the formula for the sum of the first $n$ natural numbers $$ 1+2+\dots + (n-1) + n =\frac{1}{2}n(n+1) $$ We have Its easier in a problem l...
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Are fundamental groups of aspherical manifolds Hopfian? up vote 19 down vote favorite 9 A group $G$ is Hopfian if every epimorphism $G\to G$ is an isomorphism. A smooth manifold is aspherical if its universal cover is contractible. Are all fundamental groups of aspherical closed smooth manifolds Hopfian? Perhaps the ...
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cleft extension Let $H$ be a Hopf algebra, a right $H$-comodule algebra $E$ is an $H$-extension of a subalgebra $U\subset E$ if $U=E^{co H}$ is precisely the subalgebra of $H$-coinvariants. The $H$-extension $U\ subset E$ is cleft if there exist a convolution-invertible $H$-comodule map $\gamma:H\to E$. If $U\hookrigh...
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Global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system Abstract In this article, we investigate the global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system. Under the...
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Proving continuity of function June 16th 2010, 11:29 AM #1 Member Joined Aug 2009 Posts 130 Proving continuity of function I would just like someone to check this proof for me. I am just learning this material so I would like to make sure I am doing the proofs properly. Question: Show that if $A \su...
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geometric quantization of symplectic groupoids under construction Context Symplectic geometry Background Basic concepts Classical mechanics and quantization $\infty$-Lie theory Background Smooth structure Higher groupoids Lie theory ∞-Lie groupoids ∞-Lie algebroids Formal Lie groupoids Cohomology Hom...
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Infinite Limits; Vertical Asymptotes - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Infinite Limits; Vertical Asymptotes - Concept 19,081 views When a Calculus limit decreases or increases without bound near certain values for the independent vari...
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Chain Rule: The General Exponential Rule - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Chain Rule: The General Exponential Rule - Concept 9,695 views The exponential rule is a special case of the chain rule. It is useful when finding the derivati...
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special unitary group Context Group Theory Classical groups Finite groups Group schemes Topological groups Lie groups Super-Lie groups Higher groups Cohomology and Extensions Contents Idea The special unitary group is the subgroup of the unitary group on the elements with determinant equal to 1. For $n$ a ...
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Algebraic/Categorical motivation for the Chevalley Eilenberg Complex up vote 6 down vote favorite 2 Is there a purely algebraic or categorical way to introduce the Chevalley-Eilenberg complex in the definition of Lie algebra cohomology? In group cohomology, for example, the bar resolution of a group is equal to the c...
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Binary to Hexadecimal Date: 12/08/98 at 11:15:11 From: Ian hamilton Subject: number base conversions I am a mature student on a computing HND. We have just gone through the followung question in class, but I am still clueless. Convert 110000001101 from base two to hexadecimal. Please help. Date: 12/08/98 at 12:48...
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Cosmological Dynamics - E. Bertschinger 3.3. Nonrelativistic evolution in an external gravitational field In this section we consider hot dark matter made of nonrelativistic massive neutrinos with [] << x, We can solve the Vlasov equation (3.9) approximately by replacing f / p with the unperturbed term f[0] / p. This...
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Union of a object (a set) in the Elementary Theory of the Category of Sets up vote 4 down vote favorite 6 I see the Todd Trimble article "Elementary Theory of the Category of Sets" on catlab. I ask: how make (in the categorical setting) the usual union of a set $\cup X=${$y |\exists x\in X: y\in x$}? This object is ...
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Fractional Exponents 8.4: Fractional Exponents Difficulty Level: Basic Created by: CK-12 Practice Fractional Exponents Suppose you want to find the cube root of a number, but your calculator only allows you to find square roots. However, it does allow you to find a number raised to any power, including non-integer p...
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When is taking an average (mean) an algebraic operation in the sense of monads? up vote 4 down vote favorite 2 Taking the average of a sequence of numbers is not an "algebraic" operation, in the following sense. Given sequences $X_1,X_2,\ldots,X_n$ of numbers, one could either take the average of each one, and then av...
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isomorphismes Oh! This one only took me 17 years or so to figure out. This was a “fact” I had committed to memory in school but never thought about why.   From The Symplectization of Science by Mark Gotay and James Isenberg: There are some connections to circles and homogeneous coordinates (v/‖v‖) but let’s leave th...
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Math Forum Discussions Re: Units in algebraic integers Posted: Sep 27, 2004 7:45 PM akolowski@hotmail.com (Andrzej Kolowski) wrote in message news:&lt;200409270403.i8R43fY08660@proapp.mathforum.org&gt;... &gt; On 26 Sep 2004, James Harris wrote: &gt; &gt;I've given the example of &gt; &gt; &gt; &gt;x^2 + (2s_1 + 3s_2...
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Defining Independent Events Date: 07/14/2009 at 18:03:55 From: Amy Subject: Independent events My book defines independence in the following way... Two events E and F are independent if P(E|F) = P(E). My question is, do we also have to have P(F|E) = P(F)? Or does this automatically follow? Is there any situation ...
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Bedtime mathematics Last year I worked on a interesting problem which asks about the possibility of partitioning a convex set in a plane in to ${n}$ internally disjoint convex pieces of equal area and perimeter. The problem has since been proved when ${n}$ is a prime power, by Aronov and Hubard and Roman Karasev for al...
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Negative Binomial Regression More About This Book Overview At last - a book devoted to the negative binomial model and its many variations. Every model currently offered in commercial statistical software packages is discussed in detail - how each is derived, how each resolves a distributional problem, and numerous e...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: gjhfdfg Group Title Find a rational zero o...
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Arithmetic sequence Before talking about arithmetic sequence, in math, a sequence is a set of numbers that follow a pattern. We call each number in the sequence a term. For examples, the following are sequences: 1, 4, 7, 10, 13, 16, 19, ....... 70, 62, 54, 48, 40, ............... An arithmetic sequence is a seque...
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Proofs That PI is Irrational The first proof of the irrationality of PI was found by Lambert in 1770 and published by Legendre in his "Elements de Geometrie". A simpler proof, essentially due to Mary Cartwright, goes like this: For any integer n and real number r we can define a quantity A[n] by the definite integra...
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An Alphanumeric Copyright © University of Cambridge. All rights reserved. Freddie Manners, of Packwood Haugh School in Shropshire, has e-mailed us about the problem "Cayley" from the February 2001 magazine. He has noticed that we had given more information than was needed to solve the problem. He is absolutely right: ...
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R Library: Introduction to bootstrapping The programs The R program (as a text file) for the code on this page. In order to see more than just the results from the computations of the functions (i.e. if you want to see the functions echoed back in console as they are processed) use the echo=T option in the ...
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elliptic curve Context Complex geometry Arithmetic geometry Elliptic cohomology Contents Idea Classically in complex geometry, an elliptic curve is a connected Riemann surface (a connected compact 1-dimensional complex manifold) of genus 1, hence it is a torus equipped with the structure of a complex manifold, or...
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Homework Help Posted by Marissa on Tuesday, August 21, 2007 at 11:20pm. 1)The area A of a triangle varies jointly as the lengths of its base b and height h. If A is 75 when b=15 and h=10,find A when b=8 and h=6 2)Determine the equation of any vertical asymtotes of the graph of f(x)=2x+3/x^2+2x-3 1) Area of a triang...
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Braingle: 'A Series of Headaches' Brain Teaser A Series of Headaches Logic puzzles require you to think. You will have to be logical in your reasoning. Puzzle ID: #49982 Fun: Difficulty: Category: Logic Submitted By: eighsse Tweet The Detroit Tigers played the Cincinnati Reds in the World Series (Maj...
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LOG ODDS RATIO Dataplot Vol 1 Auxiliary Chapter LOG ODDS RATIO Name: Type: Purpose: Compute the bias corrected log odds ratio between two binary variables. Description: Given two variables where each variable has exactly two possible outcomes (typically defined as success and failure), we define the od...
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Sierpinski Triangle Copyright © University of Cambridge. All rights reserved. 'Sierpinski Triangle' printed from http://nrich.maths.org/ The diagram shows the first three shapes in a sequence that goes on for ever and, in the limit, gives the Sierpinski triangle. How many red triangles are there at Stage $n$? If the...
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Graphing Linear Equations Introduction: We have already discussed about the various methods of solving linear equations in two variables. Let us discuss with graphing systems of linear equations in two variables. We shall also discuss solving systems of linear equations by graphing. By learning the ...
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Steiner tree methods for optimal sub-network identification: an empirical study Abstract Background Analysis and interpretation of biological networks is one of the primary goals of systems biology. In this context identification of sub-networks connecting sets of seed proteins or seed genes plays a crucial role. Giv...
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Borel Sets on $\mathbb{R}^n$ up vote 0 down vote favorite Define the Borel sigma-algebra on $\mathbb{R}^n$ as the smallest sigma-algebra containing all $n$-rectangles $(a_1, b_1) \times \cdots \times (a_n, b_n)$. Is it true that the Borel sigma algebra contains all sets of the form $A_1 \times \cdots \times A_n$, whe...
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Stochastic ant colony model | Physics of Risk Stochastic ant colony model Previously on Physics of Risk website we have presented Kirman’s ant colony agent based model [1], where each ant was represented as an agent. In this article we will move from the agent based model framework to the stochastic differential eq...
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Inductance13 Inductors and Faraday's Law We start by contemplating magnetism: there are two sources for magnetism. Ferromagnetic materials and current flowing through a wire, particularly in the shape of a solenoid. And the current can be of two sorts: AC or DC. Below shows the equation that allows you to compute the ...
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The Cave of Dragonflies Gen I Capture Mechanics Special thanks to a_magical_me, who started analyzing the algorithm, let me use his notes and then provided me with an assembly dump to pick up where he left off. The hacking genius is mostly his. If you were an avid player of Red, Blue and Yellow, you may have read the...
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my slice of pizza Puzzle Undone I had a great time when Michael Rabin visited for the past few months. As he was leaving, he said "I did not get to hear a good puzzle", and I am ashamed. It has indeed been a dry season. Anyway, here is a setting. n people go to dine at an Ethiopian restaurant, are seated on a circle...
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Plotting Magnetization Curves Here is a circuit you can use to measure the B -H characteristics of a ferromagnetic component. It works best with ring cores (toroids) but should be usable with other shapes having a closed magnetic path. The circuit, as shown, will plot the hysteresis loop for a half-inch diameter, hig...
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localization Idea Descent for the abelian categories may be given in two standard ways: one by using transition functors, and another to pack all the transition functors in a single comonad. We shall deal here with a family of flat localizations which are jointly a conservative family (cover by flat localization). If...
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Set Talk6 871pages on this wiki A set is a collection of distinct,symbols unordered objects. Sets are typically collections of numbers, though a set may contain any type of data (including other sets).The objects in a set are called the members of the set or the elements of the set. A set should satisfy the followi...
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MOSFET Current Limit Description This circuit provides a current-limited DC output voltage. As shown, the circuit limits the output current to a maximum of 1.2A and includes a visual indicator of a current-limit condition. During normal operation (i.e., load current is less than the limit value) the MOSFET should be ...
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Is this an embedding of $S^{[2]}$? up vote 1 down vote favorite The intersection of 3 quadrics in $P^5$ is a K3 surface $S$. There is a natural map $S^{[2]} \to G(1,5)$ well defined everywhere, because a generic K3 doesn't contain any line and this family is maximal. This is moreover injective, because a line can meet...
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action groupoid Context Homotopy theory Background Variations Definitions Paths and cylinders Homotopy groups Theorems Representation theory Contents Idea Given an action $\rho$ of a group $G$ on a set $S$, the action groupoid $S//G$ is a bit like the quotient set $S/G$ (the set of $G$-orbits). But, instead ...
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Unusual Simultaneous Equations Date: 02/06/2003 at 15:01:43 From: Khursheed Subject: Solving an Equation I don't know how to solve this. I have A = a*(b+c)/(a+b+c) B = b*(a+c)/(a+b+c) C = c*(a+b)/(a+b+c) A, B, and C are known. I don't know how to solve for a, b, and c. I just need a little direction. I tried to pu...
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Invariant Vector Fields for Homogenous Spaces up vote 6 down vote favorite 1 As we all know, the space of invariant vector fields on a Lie group can be identified with the tangent space at the identity (or any other point for that matter). My question is: How does this generalize to homogeneous spaces? My guess would ...
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Valence atom with bohmian quantum potential: the golden ratio approach Abstract Background The alternative quantum mechanical description of total energy given by Bohmian theory was merged with the concept of the golden ratio and its appearance as the Heisenberg imbalance to provide a new density-based description of...
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GMAT Tip: A Tricky Probability Question This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep. For many GMAT test-takers, probability looms as one of the more daunting concepts on the exam. While the majority of the skills tested on the GMAT—particularly arithmetic, algebra, and geometry—a...
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∞-quantity Idea The duality of space and quantity is usefully refined to a higher category theoretical context: while the idea of ∞-space is well established in terms of the notion of ∞-stack, under an $\infty$-quantity we here understand the corresponding dual notion. As so • an $\infty$-quantity is modeled as ...
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ixed Fixed Point Theory and Applications Volume 2006 (2006), Article ID 018909, 10 pages doi:10.1155/FPTA/2006/18909 Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces ^1Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia...
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Observing Fundamentals Here you will find explanations of the terms used elsewhere Angles Angles are used to measure the difference in two directions, or apparent distances on the celestial sphere. The usual unit is the degree, 1/360 of a circle. 90° is a right angle. Angles may also be measured in time units, with ...
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Polynomial of degree N with integer coefficient for a given root. up vote 0 down vote favorite Is it possible to construct a polynomial of degree N, with all of them as integer coefficient have a root as the given value. The root value provided is not necessarily a rational number. For example, if the root is 28.5526...
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Approximation Schemes for convective term - structured grids From CFD-Wiki When we shall fill this page, I offer to make common identifications, because in different issues was used different notation. Also I beg everybody to help me with original works. Later I shall write, what is necessary. If anyone have literat...
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standard Courant algebroid Contents Idea A standard Courant Lie algebroid of a manifold $X$ is a type of Courant algebroid constructed from the tangent bundle and cotangent bundle of $X$. This is the principal algebraic structure studied in generalized complex geometry. Definition Recall from the discussion at Cour...
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principles of physical science :: Diffusion principles of physical science Article Free Pass A dissolved molecule or a small particle suspended in a fluid is constantly struck at random by molecules of the fluid in its neighbourhood, as a result of which it wanders erratically. This is called Brownian motion in the c...
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Does Zariski's Main Theorem come with a canonical factorization? up vote 17 down vote favorite 6 Zariski's Main Theorem (EGA IV, Thm 8.12.6): Suppose $Y$ is a quasi-compact and quasi-separated scheme, and $f:X\to Y$ is quasi-finite, separated, and finitely presented. Then $f$ factors as $X\ xrightarrow{g} Z\xr...
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2-categor Context 2-Category theory Definitions Transfors between 2-categories Morphisms in 2-categories Structures in 2-categories Limits in 2-categories Structures on 2-categories Higher category theory Basic concepts Basic theorems Applications Models Morphisms Functors Universal constructions Extra...
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Computer Science Seminars and Short Courses — 2004/05 You main need this to find your way... • The room is likely to be BEN LT5, which is in the Bennet building and quite straightforward to find; however... • If the room is "Ken Edwards LT3" be aware that the entrance is hidden on the left hand side when you walk...
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Multiple scattering in the Compton effect DuMond, Jesse W. M. (1930) Multiple scattering in the Compton effect. Physical Review, 36 (12). pp. 1685-1701. ISSN 0031-899X. http://resolver.caltech.edu/CaltechAUTHORS:DUMpr30e PDF See Usage Policy. 1740Kb Use this Persistent URL to link to this item: http://resolver....
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Graphing Rational Functions, n=m - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Graphing Rational Functions, n=m - Concept 8,233 views There are different characteristics to look for when creating rational function graphs. With rational function g...
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Can any one please help with this Euler's function question ? August 18th 2010, 02:38 AM #1 Newbie Joined Aug 2010 Posts 13 Can any one please help with this Euler's function question ? Determine all integers n for which Euler's function (phi) = n/2? Can anyone please help me, I'm really not su...
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Truncated Dirichlet series take their supremum on the imaginary axis up vote 0 down vote favorite 1 Hi there, I am struggling with a theorem about truncated Dirichlet series. I am trying to prove the following theorem: Let $(a_n)_n \subset \mathbb{C}$ and $N \in \mathbb{N}$. Then $\sup_{t \in \mathbb{R}} \vert \sum_{...
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A simple maximality principle • J. D. Hamkins, “A simple maximality principle,” J. symbolic logic, vol. 68, iss. 2, pp. 527-550, 2003. @article{Hamkins2003:MaximalityPrinciple, AUTHOR = {Hamkins, Joel David}, TITLE = {A simple maximality principle}, JOURNAL = {J. Symbolic Logic}, FJOURNAL = {The...
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The Saas Fee Lectures on Strong Gravitational Lensing - C.S. Kochanek B.4.6. Model Fitting and the Mass Distribution of Lenses Having outlined (in perhaps excruciating detail) how lenses constrain the mass distribution, we turn to the problem of actually fitting data. These days the simplest approach for a casual user...
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sequentially compact space ** topology ** algebraic topology ## Basic concepts * space * locale * topological space * continuous map * homeomorphism * Top * nice topological space * nice category of spaces * convenient category of topological spaces * ** homotopy theory ** * homotopy group * ...
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How Many Solutions? Copyright © University of Cambridge. All rights reserved. 'How Many Solutions?' printed from http://nrich.maths.org/ This is a 'quickie'. Ling Xiang Ning of Raffles Institution in Singapore, found two solutions, and after trying some more values of x, decided that there would be no more because: ...
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. 3. HOT DARK MATTER The previous lecture studied the evolution of an ideal collisional gas including gravity and pressure. A gas of neutrinos, or of collisionless dark matter particles, behaves differently. In this lecture we investigate the evolution of a nonrelativistic collisionless gas whose particles have signi...
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Equivalence of two definitions of sheaves on a site up vote 2 down vote favorite 1 I'd like to prove that two definitions of sheaves on a site are equivalent, but I'm having trouble proving one direction. Let $C$ be a category with pullbacks. Let $(C,T)$ be a site defined through a collection $\Phi$ of covering famil...
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Bode' Plots Why Bode' Plots? What are Bode' Plots? First Order Systems Decibels Bode' Plots for Second Order Systems Bode Plots for Larger Systems (Examples) You are at: Basic Concepts - System Models - Frequency Response - Bode' Plots Click he...
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~x + ~y == ~(x + y) is always false? up vote 148 down vote favorite 32 Does this code always evaluate to false? Both variables are two's complement signed ints. ~x + ~y == ~(x + y) I feel like there should be some number that satisfies the conditions. I tried testing the numbers between -5000 and 5000 but never achi...
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Cálculo Integral ITPA In this section we will formally define the definite integral and give many of the properties of definite integrals. Let’s start off with the definition of a definite integral. Definite Integral ┌───────────────────────────────────────────────────────────────────────────────────────────────────...
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Degree Distributions in Sexual Networks: A Framework for Eva... : Sexually Transmitted Diseases THE RAPID BUT UNEVEN GLOBAL spread of human immunodeficiency virus (HIV) has challenged researchers to better understand sexually transmitted infection (STI) transmission dynamics and their implications for prevention. The b...
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Pullbacks and Inclusions of Smooth function algebras of manifolds. up vote 1 down vote favorite 2 Let $M$ and $N$ be two smooth finite dimensional manifolds and $C^\infty(M)$ as well as $C^\infty(N)$ their smooth function algebras. Is the following true: Let $\imath: M \to N$ be an embedding. Then the algebra morphi...
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Litov's Mean Value Theorem Copyright © University of Cambridge. All rights reserved. Well done to Ken from Blessed Robert Johnson Catholic School who sent us his solution to this problem: After a while of playing with the numbers on a spreadsheet I have discovered that the formula to find the "limiting value" for $2$...
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Power of a Product: Under What Conditions Do You Use This Rule? When to Use the Power of a Product Rule Definition: (xy)^a = x^ay^b When this works: • Condition 1. Two or more variables or constants are being multiplied. (xy)^a • Condition 2. The product, or the result of the multiplication, is raised to a pow...
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measure (mathematics) measure, in mathematics, generalization of the concepts of length and area to arbitrary sets of points not composed of intervals or rectangles. Abstractly, a measure is any rule for associating with a set a number that retains the ordinary measurement properties of always being nonnegative and suc...
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Complex Numbers: What and Why? Date: 9/1/96 at 6:51:2 From: Anonymous Subject: Complex Numbers: What and Why? Dear Dr. Math: What actually is a complex number? How does it work? What sort of problems do complex numbers solve? What are some examples? Thank you very much! Martin Date: 10/19/96 at 21:45:18 From: D...
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Lie algebra Context $\infty$-Lie theory Background Smooth structure Higher groupoids Lie theory ∞-Lie groupoids ∞-Lie algebroids Formal Lie groupoids Cohomology Homotopy Examples $\infty$-Lie groupoids $\infty$-Lie groups $\infty$-Lie algebroids $\infty$-Lie algebras Contents Idea A Lie algebra is the...
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isomorphismes Commutativity is an easy property to render into English: it means order doesn’t matter. For example “three groups of five rocks” totals the same as “five groups of three rocks”. In fact a general proposition is true: “L groups of R rocks” totals the same as “R groups of L rocks” for any L,R. Which is su...
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Infinity of primes October 7, 2010 Leave a comment Q.1. Prove that there are infinitely many primes. Solution. Assume to the contrary a finite set of primes $\{p_1, p_2, ..., p_k\}$. $\ldots (1)$. Consider $n = p_1 \times p_2 \times ... \times p_k + 1$. Now, $p_i | n-1$$\forall$$1 \leq i \leq k$. $\therefore n$ ...
5
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Action of left $\mathbb{C}_q[SL_2]$-crossed modules up vote 3 down vote favorite Shahn Majin and Xavier Gomez say in the beginig of their article (Noncommutative cohomology and electromagnetism on $\mathbb{C}_q [SL_2]$ at roots of unity) that tha action of left $\mathbb{C}_q [SL_2]$-crossed modules is given by: \begi...
4
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Physics Archive | October 08, 2008 | Chegg.com Physics Archive: Questions from October 08, 2008 • Anonymous asked 1 answer • Anonymous asked 1 answer • Anonymous asked 1 answer • Anonymous asked 1 answer • Anonymous asked 1 answer • Anonymous asked 1 answer • Anonymous...
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Fast Approximate Lambert W This is of questionable personal utility, after all, I've only seen Lambert's W function once in a machine learning context, and there it occurs as $W (\exp (x)) - x$ which is better to approximate directly. Nonetheless generating these fast approximate functions makes for amusing sport a...
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The Inverse of a Universal R-Matrix for Quantized Universal Enveloping Algebra of sl2 and the Dual Pairing with SUq(2) up vote 10 down vote favorite 2 I have recently begun to study quasi-triangular structures and have come across a problem I can't resolve. Let ${\cal U}_q({\mathfrak sl}_N)$ denote the quantised envel...
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Harvard Psychological Studies, Volume 1 SummaryHarvard Psychological Studies, Volume 1 Summary w(r’-r) = pr’ , pr’ w = ------- . (4) r’-r [Illustration: Fig. 5] [Illustration: Fig. 6] In Fig. 6 rod and disc are moving in opposite directions, and w = BB’, p — w t = ------- , r w t = —–­ , r’ r’(p — w) =...
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Konrad Knopp: Texts We give here the contents of three books published by Konrad Knopp. The first is Infinite Sequences and Series which contains the following publisher's information:- One of the finest expositors in the f...
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Addition and Subtraction Identities 5.3 Trigonometric Addition and Subtraction Identities Basic Identities For angles \(A\) and \(B\) it can be proven geometrically that \(\sin ( A + B ) = \sin A \cos B + \cos A \sin B\) and \(\sin ( A - B ) = \sin A \cos B - \cos A \sin B\) It can also be geometrically verified th...
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enriched category Context Category theory Concepts Universal constructions Theorems Extensions Applications Enriched category theory Background Basic concepts Universal constructions Homotopical enrichment Contents Idea The notion of enriched category is a generalization of the notion of category. Very o...
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Adams's New Arithmetic... the fraction to its equal £, which is now in its lowest terms, for no greater number than 1 will again measure them. Note 1.—Any fraction may evidently be reduced to its lowest terms by a single division, if we use the greatest common divisor of the tw...
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CURVEFIT The CURVEFIT function uses a gradient-expansion algorithm to compute a non-linear least squares fit to a user-supplied function with an arbitrary number of parameters. The user-supplied function may be any non-linear function where the partial derivatives are known or can be approximated. Iterations are perfo...
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Proof of DeMorgan's Theorem Proof of DeMorgan's Theorem For quite a while I've been looking for a purely algebraic proof of DeMorgan's theorem. I know that it can be proven simply by filling out a truth table, but that seems so... inelegant. Plus, the truth-table proof only applies to logics with values of '1' and '0...
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A multiverse perspective on the axiom of constructiblity • J. D. Hamkins, “Infinity and truth.” , 2013, vol. 25. @INBOOK{Hamkins:MultiverseOnVeqL, author = {Joel David Hamkins}, editor = {}, title = {Infinity and Truth}, chapter = {A multiverse perpsective on the axiom of constructibility}, ...
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Solving the Introduction One of the most extraordinary things about Einstein’s energy-mass equivalence equation is its simplicity. However, we still need to make sure we are using the correct units when solving the equation, and that we understand the answer. The purpose of this page is to solve the equation as it is...
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