# All Questions

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### When is the direct product of two graph cores itself a core?

A graph homomorphism $f$ is a function $f : V(X) \to V(Y)$ such that if $uv \in E(X)$, then $f(u)f(v) \in E(Y)$. If such an $f$ exists, write $X \to Y$. $X$ and $Y$ are hom-equivalent if $X \to Y$ and ...
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### Matchings in countably infinite geometric lattices of finite height

Let $L$ be a countably infinite geometric lattice of finite height $r\ge3$. (A geometric lattice of height $r$ is an atomistic semimodular lattice such that every maximal chain has $r+1$ elements.) ...
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### A moment problem

Suppose $X, Y$ are two positive random variables such that $\mathbb{E}[X^\alpha] = \mathbb{E}[Y^\alpha]$ for all $\alpha \in (0, 1/2)$. It is also known that the first moment exists for each of them, ...
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### Studying topology: which first, algebraic or differential? [on hold]

I have recently studying the basics of topology (ideas in point set, connectedness compactness) and I want to continue my studies but i'm interested in both differential and algebraic topology. which ...
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### Prefactor of a bounded differences inequality

I have a question concerning the prefactor of a bounded difference inequality. In Corollary 1, see p.7 there is the inequality $\text{Var}[Z]\leq\frac{1}{2}\sum\limits_{i=1}^n c_i^2$. On the other ...
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### The Gherkin - equation for the curve inoder to calculate the surface area of revolution [on hold]

I am trying to calculate the surface area of revolution for The Gherkin. not sure about how to obtain the equation of the curve but i have the data points that allowed me to graph it in excel but the ...
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### The free group of a group and the kernel of a canonical morphism

Let $G$ be a group and $F_G$ the free group on the set $G$. Then there exists a canonical surjective morphism ${\rm can}: F_G \to G \to 1$ constructed as follows: let $(e_x)_{x \in G}$ be a copy as a ...
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### (co)limits in the category of diffeological spaces vs. category of smooth manifolds

I am wondering which (co)limits that exist in the category of smooth manifolds are preserved by the inclusion into the category of diffeological spaces? Are there any results that allow us to ...
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Let f and alpha be functions defined by $$f(x) = \begin{cases} x & 0 \leq x < 1\\ 2x & 1 \leq x \leq 2 \end{cases}$$ $$\alpha(x) = \begin{cases} 1 & 0 \leq x \leq 1\\ 2 ... 0answers 124 views ### What are explicit obstructions to realizability of formal group laws as complex-oriented ring spectra? Recall that a complex-oriented spectrum is a ring spectrum E with a map MU \to E. Analogously, a ring with a (1-d commutative) formal group law is (represented by) a ring R with a map L \to R ... 1answer 93 views ### Contraction semigroup Let (X, \mu) be a finite measure space and let A be a non-negative self-adjoint operator which generates a contraction semigroup e^{tA} on L^2(X, \mu). If additionally, we have that e^{tA} ... 1answer 106 views ### Fourier coefficients of real analytic functions on an n-dimension torus Let (\mathbf{R}^n,\langle\;,\; \rangle) be the n-dimensional euclidean space endowed with the standard inner product. For a lattice L\subseteq \mathbf{R}^n we let cov(L) denote the covolume of ... 0answers 95 views ### Self-avoiding random walks that always turn I am wondering if the statistics of self-avoiding random lattice-walks on \mathbb{Z}^2 that turn left or right at each step (i.e., they cannot continue the direction of the preceding step) have been ... 0answers 23 views ### Proving Unboundedness of a Martingale [on hold] Suppose I have a submartingale X_k, what results/theorems can be useful if I want to show that X_k is unbounded in the limit. There are results (basically bounding \mathbb{E}X_k) for convergence ... 0answers 32 views ### Looking for an example of a contour integral with matrix entries [on hold] Let A be a matrix (if needed assume it to be the adjacency matrix of graph). Let one be given two functions P(z) and Q(z,A) such that both are polynomials in z and A, where z is some ... 0answers 87 views ### Identifying a Hopf algebra cohomology theory Here is a cohomology theory for a Hopf algebra, which I am sure has appeared elsewhere. I met it in the van Est spectral sequence for Hopf algebras. Apologies for my being stupid here, but it would be ... 0answers 17 views ### density function time series I have a time series of density functions, say A1-A5. Each density function is defined as f(x)=\Sigma_{i=1}^{N} \beta(x-a_i), where \beta is a smoothing function (e.g., gaussian or delta), and N ... 1answer 237 views ### What's the difference between Euler systems and Kolyvagin systems? Is there a difference between Euler systems and Kolyvagin systems - or do they refer to the same thing? For example there is the Heegner point Euler system, but you don't really see a Heegner point ... 0answers 28 views ### Calculus II Function Construction [on hold] I need help please! Construct a function that is continuous and non-negative [0,1], with the property that the area under the function on [0,1] is finite yet the arc length on [0,1] is infinite. 0answers 113 views ### Fiber bundle in smooth category and topological category Let M be a smooth manifold and G be a Lie group. Denote by Bun(M,G) the set of all equivalent smooth Principal bundles on M with structural group G in smooth category. And denote by ... 0answers 46 views ### When is a 2-Calabi–Yau triangulated category the cluster category of a QP? Keller–Reiten's main theorem in Acyclic Calabi–Yau categories implies that if \mathcal{C} is a 2-Calabi–Yau (algebraic) triangulated category admitting a cluster-tilting object T such that the ... 0answers 49 views ### Existence of a Lie algebra element orthogonal to the adjoint orbit of another element Consider a compact, semi-simple, connected Lie group G and its Lie algebra \mathfrak{g}. Denote the Killing form by K. Given a single A \in \mathfrak{g} when (i.e. which groups and which A) ... 0answers 56 views ### Descriptive Complexity of Knot Equivalence I was reading a little about knots (in a popular math book that wasn't very good) and the book put forth several knot invariants like the Alexander and Jones polynomials. But these are not complete ... 0answers 37 views ### Is there an action functional for the s-dependent Floer equation? The usual Floer equation (in local coordinates) \begin{equation*} \partial_su+J(t,u)(\partial_tu-X_{H_t}(u))=0 \end{equation*} is derived as the gradient flow of the symplectic action functional ... 1answer 71 views ### Renorming into contraction In Pazy's book on semigroups he mentions (page 18) that when you have a commuting family of operators B(t), such that$$ \sup \| B(t_1) .. B(t_n) \| \le M $$for all finite choices t_1, .. t_n ... 0answers 47 views ### Are universally catenary equidimensional local rings Cohen-Macaulay? [on hold] Cohen-Macaulay rings are universally catenary, I do not choose catenary rings because we can find catenary but not universally catenary rings at wiki Catenary ring. Cohen-Macaulay local rings are ... 2answers 130 views ### Counterexample on completely distributive lattices I would like to see an example of a complete lattice C which is both a frame and a dual-frame, i.e. finite meets distribute over arbitrary joins and finite joins distribute over arbitrary meets ... 0answers 64 views ### Integer solution to the equation [migrated] Does there exists an integer solution (for every integer m\geq 1) for the following equation?$$x_1x_2...x_n+(2y+1)z+y=4m+3 where, $1\leq x_1\leq x_2\leq...\leq x_n\leq l$,$0\leq y \leq ... 0answers 69 views ### Dominating affine varieties over$k$with affine smooth varieties over$k$Given a geometrically integral affine variety$X:=\mathrm{Spec}(K[X_1,\ldots, X_n])/(f_1,\ldots, f_m)$over a possibly imperfect field$K$, does there always exist an affine variety$\tilde{X}\$ ...

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