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159,037 questions
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Why does the power series expressing e^x have the form of a constant raised to x ? [closed]
This question is probably very basic, but I've been away from school for a while and the answer eludes me.
I was tempted to prove that d/dx(e^x) = (e^x) for old times sake and that was easy enough. I ...
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Intuitive Example of a Jacobson Radical
Can anyone explain what a Jacobson radical is using an intuitive example? I can't quite understand Wikipedia's explanation.
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What are the most important Open Access Mathematics journals at present? [closed]
I'm asking this question from the perspective of someone who just wants to read journals rather than contribute to them. For the purpose of this question I'm using the definition of Open Access in the ...
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What is the most compelling reason to believe Church's thesis? [closed]
Church's thesis states that the Turing machine is a universal model of computation. What is the most compelling argument supporting this assertion?
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What kind of operations does the Tall-Wraith monoid encode?
According to the nLab page, for an algebraic theory V a Tall–Wraith V-monoid is "the kind of thing that acts on V-algebras". Well, it certainly does act on V-algebras, but in which sense is it "the ...
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Equivariant Derived Categories via their properties.
There are some ways to define equivariant derived categories of all sorts. But all the ways i know of involve giving a concrete construction. Is the other way around possible? Is there some universal ...
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Is there a version of Temperley-Lieb using sl(3) rather than sl(2)?
This question is a spin-off from Sammy Black's question on super Temperley-Lieb. Please see there for the background. The short version is that Sammy defines the Temperley-Lieb at index d as the ...
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Closed form solution to x^(x+1)=(x+1)^x [closed]
From an elementary question in differential entropy for decision sequences...
Numerical solutions is: x = 2.293166287408052...
The equality is only well defined (with respect to its origination) in ...
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Vector spaces of singular planar cubics
What is the largest dimensional linear space of singular planar cubics? Is this known?
Think of the space of planar cubics as a PP^9 (parametrized by the coefficients). The discriminant \Delta is ...
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What are Gromov-Witten invariants in terms of physics?
What do Gromov-Witten invariants (of say a Calabi-Yau 3-fold) represent, or what are they supposed to represent, in terms of string theory? When I compute GW invariants, am I actually computing some ...
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Recovering a monoidal category from its category of monoids
What kind of additional properties and/or structures one needs to impose on the category
of (commutative or noncommutative) monoids of some monoidal category
so that one can recover the original ...
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How does one intersect non-transverse divisors on Mg-bar.
Let Mg-bar be the Deligne-Mumford compactification of genus g curves, and let δ1 be the divisor of degenerate curves of the form `genus 1 meeting a genus g-1 transversely".
Question 1: What ...
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What kind of geometric operations "scale up" cohomology?
There's an obvious operation on the category of graded rings, given by "scaling up," multiplying the grading of every element by some fixed constant.
Does anyone know of an operation on the level of ...
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Projective Curves which are Principal Bundles
I have a very specific question: does anyone know of a (non-trivial) example of a projective curve which is also a homogenous space (or just a principal bundle)? The trivial example being CP^1 = SU(2)/...
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Variant of binomial coefficients
I've recently come across a variant of the binomial polynomials, and I'm curious if anyone has seen these before. If so, I'd love a reference, a name, etc.
First recall the following. If z is a ...
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For which spaces is homology (or cohomology) determined by the Eilenberg-Steenrod axioms
This is a spinoff of Can anyone give me a good example of two interestingly different ordinary cohomology theories? . By an ordinary homology theory, I mean a functor on topological spaces which ...
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internal homs and adjunctions?
This is probably an easy question. Let C be a category with (finite) products.
An internal hom in C category is an object uhom(X, Z) which represents the functor:
Y |-----> hom(Y x X, Z)
here "...
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Bound on cardinality of a union
Suppose I have n finite sets A1 through An contained in some fixed set S, and I am given non-negative integers N and N1 through Nn such that each Ai has cardinality N, and each k-tuple intersection ...
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limits of algebraic varieties
I'm looking for a reference which deals with limits of families of algebraic varieties as the degree increases (or at least keywords from this subject).
For the kind of example I have in mind, ...
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What is the homology of the real coordinate ring of SO(n,R)? Other compact matrix groups?
As someone whose knowledge of cohomology is patchy and picked up on a need-to-know basis, and whose algebraic geometry is even worse, I wondered if someone could help with this question. (I ran into ...
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Examples of well-displayed mathematics on the internet [closed]
I'm interested in hearing of examples of mathematical (or, at a pinch, scientific) websites with serious content where the design of the website actually makes it easy to read and absorb the material. ...
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Finiteness of Obstruction to a Local-Global Principle
Say that a projective variety V over Q satisfies the local-global principle up to finite obstruction (#) if there are only finitely many isomorphism classes of projective varieties over Q that are not ...
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Cone shaped solutions to wave equation
When I studied physics, we learned how to write down planar waves and spherical waves. But, when I turn on my flashlight, I see a cone of light. How can I see that there is a solution to the wave ...
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What is Eisenstein series?
There are several related questions here, the latter being especially interesting. We know the classical Eisenstein series.
What are the Eisenstein series on a group G and why they are interesting?
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Are curves with `fractional points' uniquely determined by their residual gerbes?
One makes precise the vague notion of "curve with a fractional point removed" (see for instance these slides) using stacks -- one should really consider Deligne-Mumford stacks whose coarse spaces are ...
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Do orbits and stable loci of group actions have natural scheme structures?
Suppose G is an algebraic group with an action G×X→X on a scheme. Then many of the usual constructions you make when you talk about group actions on sets can be made scheme-theoretically. ...
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simplicial deRham complex and model category structure
To every simplicial manifold is associated its simplicial deRham complex.
Is there any literature that discusses explicitly to which extent this classical construction, regarded as a (contravariant) ...
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Upper bounds on FFT complexity for arbitrary radixes
Given a signal of length $N = P^m$, $P$ prime, what is a reasonable upper bound on the number of operations (complex additions and multiplications) needed to compute the Fast Fourier Transform (FFT) ...
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How to think about model categories?
I've read about model categories from an Appendix to one of Lurie's papers.
What are the examples of model categories? What should be my intuition about them?
E.g. I understand the typical examples ...
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maximizing function (stochastic calculus)
S is a price process which follows Geometric Brownian motion with no drift:
dS=S*vol*dW, vol=const., W is a Wiener process.
Define the following ratio: R=E[Max(f(S)-S(T),0)]/E[f(S)], where S(T) is ...
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Localization(s) of Categories
I've been trying to read a paper by Krause and came across a strange (to me, of course) notion of localization. After looking around for a long time, and then finding this on his site, I see that ...
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Is there any meaning to a "nice bijective proof?"
From Zeilberger's PCM article on enumerative combinatorics:
The reaction of the combinatorial enumeration community to the involution principle was mixed. On the one hand it had the universal ...
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Division Algebras as Algebraic Groups
If I'm given a division algebra D with Z(D)=F, then how can I view Dx as an algebraic group defined over F? I'd like to see first how Dx can be given the structure of a variety defined over F, and ...
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Singularity theory references
I am looking for some good references on singularity theory. I'm interested in singularity theory in the context of mirror symmetry, so this means I'm interested in things like Picard-Lefschetz theory,...
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Computations in Knot Homology Theories
1) Relative to one another, how computable are the various knot homology theories? For example, how many crossings can we allow a knot and still hope to compute its Khovanov homology, versus its knot ...
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Over which schemes can there exist non-trivial G_a bundles?
The group scheme G_a here is the one-dimensional additive group.
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"Plateaus" to watch out for [closed]
I'm a lot earlier in my math education that most of the people on this site. Currently I'm studying computer science, and I'm interested in looking into statistical and optimization applications, as ...
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Why do I find Category Theory mostly just a way to make simple things difficult?
I have a basic working knowledge of category thoery since I do research in programming languages and typed lambda-calculus. Indeed, I have refereed many papers in my area based on category theory.
...
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One Point Compactification
Suppose X is a path-connected, locally compact, Hausdorff space and Y is its one-point compactification. Let G be the fundamental group of X and H be the fundamental group of Y. Is it true that the ...
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Non trivial colouring of the edges of an infinite complete graph
Can you build a probabilistic scheme for colouring each edge (independently of all other edges) of the complete graph G on the positive integers such that the probability that G contains an infinite ...
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Is a map that is locally fiberwise equivalent to a product a Hurewicz fibration?
The following is a result I feel like I've seen some form of before, but can't figure out how to prove or find a reference for. Suppose you have a map p:E \to B, with B paracompact, and suppose that ...
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An intuitive reason why the "Rule 30" CA is random/pseudorandom?
I'm a little bit hesitant to ask this here, so please notice the tag. My hope is that someone will have a more satisfying answer than what I've heard before...
A long time ago I read (perhaps '...
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Iwasawa Decomposition
Does anyone know where I can find a proof of the Iwasawa decomposition for reductive groups? I know that there are a couple of related results that are called the Iwasawa decomposition, but I am ...
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Lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type f(n)*delta^{n(n-1)/2}
Is there a lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type
f(n) * delta^{n(n-1)/2}? For which f(n)? How can it be proven?
n(n-1)/2 is the number of degrees of ...
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Strong Bertrand postulate
Is it known that for every epsilon there is N_0 such that all intervals of the form [N, (1+\epsilon)*N], where N > N_0, contain ...
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Lower bound on volume of minimal hypersurface contained in a unit ball with curvature bounds
I was just wondering, if I have a geodesic ball of radius one in a manifold M whose sectional curvature lies between -epsilon and epsilon for epsilon small, and the injectivity radius of my manifold ...
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Something like Yoneda's lemma
This is inspired by The Whitehead for maps question.
Consider two maps f, g: X\to Y which happen to induce the same maps (of discrete spaces) ...
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(how) are vector bundles and homotopy groups related?
Hello,
homotopic maps induce isomorphic pullback bundles, and so isomorphism classes of vector bundles over X correspond to homotopy classes of maps from the grassmannian to X. But I think, in the ...
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opposite Banach space
I heard this from Haskell Rosenthal many years ago.
If V is a complex vector space, say the opposite of V is the complex vector space with the same elements, the same operations except switch scalar ...
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