# All Questions

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### probability distribution [on hold]

X is a continous random variable of normal distribution for the length of the rulers produced in a factory. Given X has mode of 15 cm and standard deviation of 1 cm. A ruler is randomly selected from ...
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### How to show Well Founded Induction false? [on hold]

The abstract reduction system ({a,b,c,d},→) where the → is defined as: http://i.stack.imgur.com/TS0Ud.png Let Q be a monadic predicate on {a,b,c,d} such that Q(a) = Q(b) = false and Q(c) = Q(d) = ...
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### If d(“G/H”) < d(G) = 2, must H contain a primitive element?

Let $G$ be a finite group that can be generated by $2$ elements, and let $H \leq G$ be a (not necessarily normal) subgroup for which there exists some $g \in G$ such that $H \langle g\rangle = G$. ...
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### Underlying Set in Model Theory [migrated]

In model theory a structure has an underlying set. In addition to the interpreted relations, are there (implicit) assumptions made about possible operations on this set? For example, is it assumed to ...
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### Multiplication Map, Is it invariant?

Let $\pi:X\rightarrow Z$ a double cover of an elliptic curve with genus $g\geq 3$. Choose a general rank 2 and degree -1 vector bundle $F$ on $Z$, let $E=\pi^*F$ and fix $x\in X$. The involution $i$ ...
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### Upper bounds on elements of a matrix

During my research I have come across matrices this type $$C=B\left(B^T B\right)^{-1}B^T\ ,$$ where $B$ is an $m\times n$ real matrix. If $B^TB$ is not invertible, then $\left(B^T B\right)^{-1}$ ...
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### what is the computational complexity for finding SVD and pseudo inverse? [on hold]

For a given MxN matrix A and A is full rank matrix (rank=N and M>N),what is the computational complexity for finding SVD and pseudo inverse ?Which one will be having low complexity?
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### Deriving inequalities from a polynomially-bounded derivative

In this paper (p. 2, definition/remark) the following notion of ‘polynomial growth’ is defined for a non-negative real function $g(x)$ and a real constant $b\in(0;1)$: There exist positive ...
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### Piecewise linear (PL) structures on $\mathbf R^4$

One can read in Wikipedia that the 4-dimensional affine space $\mathbf R^4$ has uncountably many piecewise linear structures (in contrast with other dimensions, where it has exactly one). A reference ...
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### Who coined “mob” and “clan” and why these words?

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element. Who used these words with these meanings first and ...
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### Hyperbolic paraboloid, Analytic Geometry [on hold]

Please don't ban this question, I just need some advice on how to find the equation of the tangent plane on a point of the hyperbolic paraboloid which is perpendicular to a certain plane say ...
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### Relation between intersection and product of ideals

Let $C$ be a smooth projective (irreducible) curve in $\mathbb{P}^n$ for some $n$. Denote by $I_C$ the ideal of $C$. Let $g \in I_C\backslash I_{C}^2$, an irreducible element. Is it true that for any ...
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### An example of a non-(locally cyclic) Abelian group whose automorphism group is cyclic not of order $2$

In the wake of my curiosity on this kind of things, I was thinking if there is an example of a non-(locally cyclic) Abelian group whose automorphism group is cyclic not of order $2$. Every example I ...
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### Represention of the element of a group: A Confusion [on hold]

I am reading a paper "FAST ALGORITHMS FOR CALCULATION OF GIBBS DERIVATIVES ON FINITE GROUPS" by R. S. Stankovic (Approx. Theory & its AppL 7:2, June 1991). In Section 2, following is written about ...
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Let $(\frac{m}{n})$ denote the usual quadratic Jacobi symbol. What is the abscissa of convergence of the double Dirichlet series ? $$\sum_{\substack{m,n \in \mathbb{N} \\ \gcd(m,n)=1 \\m,n\equiv 1 ... 0answers 20 views ### Expression in theta notation [on hold] Am I right that the theta notation for the following expression is: n^2+(n^3/2) = theta (gn^3) as n^2/2 is the low order term 0answers 109 views ### On Gromov's Theorem on Symplectic Homotopy I want to understand the proof of the following theorem due to Gromov which I'll state in the context of Euclidean spaces. While I tried to read the proof from Macduff-Salamon, it turned out that my ... 0answers 61 views ### A simple question about a resolution of a conifers singularity Let X be a conifold defined by the equation xy-zw=0 in \mathbb{C}^4 and \tilde{X} its crepant resolution, which is isomorphic to \mathcal{O}_{\mathbb{P^1}}(-1)^{\oplus 2}. Then there is a ... 1answer 130 views ### When is the tensor product of two graphs planar? Given two graphs G=(V_1,E_1) and H=(V_2,E_2), the tensor product of G and H is the graph G \times H = (V,E), where V=V_1 \times V_2 is the Cartesian product of the V_i and  (u,v) \ E \ ... 1answer 91 views ### configuration spaces of real projective space Let F(\mathbb{R}P^n,k) be the k-th ordered configuration space on \mathbb{R}P^n. In http://arxiv.org/abs/1502.04258, the cohomology ring$$ H^*(F(\mathbb{R}P^n,k);R) is obtained for any ...
Let $K=\mathbb Q(\sqrt{-m})$ be a quadratic field. Let $O_K$ be ring of algebraic integers. Let $\alpha=a+b\sqrt{-m}\in O_{K}$ with gcd$(a,b)=1 .$ Then how to show that $\langle \alpha \rangle$ ...
Let $M$ be an $m$-dimensional simply connected Riemannian manifold that is not geodesically complete. Suppose $M$ has constant sectional curvature. Because the curvature is constant, locally $M$ ...