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NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
GR.GROUP THEORY
Normal Subgroups of Prosupersolvable groups. Let G be a finite supersolvable group, and if p is the biggest prime dividing | G |. Then G has normal subgroups of order every possible power of p. Analogous statement in case of profinite: Let G be a prosupersolvable group such that only finitely many primes divide | G | and let p bethe biggest
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K ( RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → FHOMOLOGICAL ALGEBRA
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. TEACHING - HOW TO DRAW KNOTS WITH LATEX? - MATHOVERFLOW Update 2013-04-22: I've now uploaded a TikZ library to CTAN expressly for the purpose of drawing knots.It is already in MikTeX (according to CTAN), TeXLive might have to wait until TL2013 has been released. It is released as part of the spath3 library. Here's the link to CTAN.The hobby package also contains some useful code for drawing knots. For drawing braids, there's the braids package.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
GR.GROUP THEORY
Normal Subgroups of Prosupersolvable groups. Let G be a finite supersolvable group, and if p is the biggest prime dividing | G |. Then G has normal subgroups of order every possible power of p. Analogous statement in case of profinite: Let G be a prosupersolvable group such that only finitely many primes divide | G | and let p bethe biggest
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K ( RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → FHOMOLOGICAL ALGEBRA
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. TEACHING - HOW TO DRAW KNOTS WITH LATEX? - MATHOVERFLOW Update 2013-04-22: I've now uploaded a TikZ library to CTAN expressly for the purpose of drawing knots.It is already in MikTeX (according to CTAN), TeXLive might have to wait until TL2013 has been released. It is released as part of the spath3 library. Here's the link to CTAN.The hobby package also contains some useful code for drawing knots. For drawing braids, there's the braids package.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.REFERENCE REQUEST
Question: On balance, with theoretical advances in algorithmic information theory and Quantum Computation it appears that the remarkable effectiveness of mathematics is SET THEORY - DEDEKIND-"FINITENESS" FOR ARBITRARY LIMIT 1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange IS COHOMOLOGY ALWAYS RELATED TO TOPOLOGY? I am trying to understand whether there is a sense in which cohomology always relates to topology or whether this is the case only in particular examples.CT.CATEGORY THEORY
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
AC.COMMUTATIVE ALGEBRA Suppose we have commutative, unitary rings A, B and a (unit preserving) homomorphism φ: A → B which makes B an A -algebra. Suppose also we have elements f 1, , f n ∈ B which generate the unit ideal and such that B f i, namely the localisation of B with respect to f i, is a finitely generated A -algebra. Show that then B is afinitely
SOFT QUESTION
Publishing a Simple Paper as an Undergraduate. First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on. I am a (first year) undergraduate mathematics student, and I recently discovered some interesting properties hidden in certain families of sequences.PR.PROBABILITY
$\begingroup$ The ultimate reason in the case presented is that doing something even minimally smart is always better than doing something stupid in every possible respect. It is not the Laplace trick that is better here, but the estimate $\max(X,Y)\le|X|+|Y|$ that is worse. Even if you improve it to something as obvious as $\max(X,Y)\le \max(X,0)+\max(Y,0)$, you get a two-fold gain CLAIRAUT'S RELATION AND THE EQUATION OF GREAT CIRCLE IN Clairaut's relation for a great circle parametrized by t is r ( t) cos. . γ ( t) = Const where r is the distance to the z -axis and γ is the angle with the latitude. The implicit equation of great circle in spherical coordinates ( θ, ϕ) is cot. .PR.PROBABILITY
A lower and an upper bound for the Kullback-Leibler divergence between two Gaussian mixtures are proposed. The mean of these bounds provides an approximation to the KL divergence which is shown to be equivalent to a previously proposed approximation in: Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models (2007) Share.CO.COMBINATORICS
Consider the average game of Tic Tac Toe or Noughts and Crosses. The game is played on a 3 by 3 two dimentional board. The game is played by two people and each person is allowed to only add one type of piece to the board - $\bigcirc$ or $\large\times$, where the person with the crosses always starts first, the players take turns, and whoever puts three pieces in a row (either horizontally STACK EXCHANGE NETWORK Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and buildtheir careers.
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IS IT POSSIBLE TO PROVE “PRIME NUMBER THEOREM” IN FINITE FIELD WITHOUT INVOLVE USE OF WEIL CONJECTURE OR RIEMANN-ROCH? nt.number-theory linear-algebra prime-number-theoremfunction-fields
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EXAMPLES OF BACK OF ENVELOPE CALCULATIONS LEADING TO GOOD INTUITION? approximation-theory intuition gm.general-mathematicsheuristics
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