# All Questions

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### Connected components $0-1$ matrices

Let $M$ be a $0-1$ matrix. Here a matrix has one component means we can traverse from a matrix entry $(i,j)$ which is $1$ to any other one by moving step of $(i\pm1,j),(i,j\pm1),(i\pm1,j\pm1)$ where ...
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### Complete solution set of a Convolutional Equation?

Here is a problem that am I stuck and I appreciate any help. In essence, I am trying to show that the only solutions for the described problem are the ones provided below. Best.. Setup: In what ...
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### A question on models of set theory and Lebesgue measure

In a question and an answer at MO, Joel David Hamkins showed that (if ZFC is consistent) there are models of ZFC in which $V\neq HOD$ and every $\Sigma_2$-definable set has a definable member. Let ...
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### equivalence in simplicial category

Let $(\mathcal{C},W)$ be a category with weak equivalences. One can build from $(\mathcal{C},W)$ its hammock localization $L^{H}(\mathcal{C},W)$ which is a simplicial category $\textit{ie}$ a category ...
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### automorphism of prime order for group of Lie type in

Thanks for any help. Suppose $S$ is a simple group of Lie type of prime characteristic $p$. we know that every automorphism of $S$ is composite of inner, diagonal, field and graph automorphism of ...
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### Is every projective space curve a set-theoretic intersection of two surfaces? What is known about this question?

I am sorry if this question has been already asked, couldn't find anything similar myself. I have recently recalled this long standing open problem of whether every curve in $\mathbb{P}^3(\mathbb{C})$ ...
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### Extension of homomorphism to place in quotient field, or of local ring to valuation ring in quotient field

Let be given a domain $R$ (that can be supposed to be integrally closed if this can help), and $\varphi$ an homomorphism of $R$ into a field $F$. $\varphi$ extends uniquely to a homomorphism ...
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### intuitive interpretation of analytic spread

I am studying analytic spreads from Bruns-Herzog's book. The definition is clear but calculation of the analytic spread of an ideal is hard for me in practice. I wonder if it is hard for you too. ...
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### Retractions and left-factoring morphisms

Let $\mathcal{C}$ be any category and let $A, B$ be objects. A retraction is a morphism $r: A\to B$ such that there is $s:B\to A$ such that $r\circ s:B\to B$ is the identity. A morphism $l: A\to B$ ...
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### What are interesting open problems in pseudo-differential operators?

May I ask what are some interesting open problems in the field of micro-local analysis (or classical analysis, semi-classical analysis, etc) using pseudo-differential operators? To my knowledge the ...
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### (Affine) Schemes and the point of view of morphisms with values in a field

Let $A$ be a commutative ring with unity. If $\varphi_1 : A \rightarrow K_1$ and $\varphi_2 : A \rightarrow K_2$ are ring morphisms from $A$ to fields, $\varphi_1$ and $\varphi_2$ are said to ...
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### sufficient condition of complete intersection [on hold]

According to Corollary 2.8 and the front part of Section 3 of this paper, if $X:= Q_1\bigcap Q_2\bigcap Q_3\subset \mathbb{P} _{\mathbb{C}}^{4}$ be a connected and purely $1$-dimensional intersection ...
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### Flow in graph. Proof [on hold]

Let $(S_1, \overline{S_1} ) , (S_2, \overline{S_2} )$ be minimum cuts in some network. Is it true that $(S_1 \cap S_2, \overline{S_1 \cap S_2)}$ is a minimum cut in this network?
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### show that L(X,Y)banach then Y banach

Let {Xα}α∈A be a collection of Banach spaces. It is easy to show that P={(xα):supα∥xα∥<∞} with ∥(xα)∥=supα∥xα∥ is a banach space. If the indexing set A is finite, then it is easy to show that P ...
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### Any two bivariate algebraically dependent polynomials are always in the same ring generated by some bivariate polynomial?

If $f(x,y)$ and $g(x,y)$ are two algebraically dependent polynomials over some field $k$, is it true that there exists a bivariate polynomial $p(x,y)$ such that both $f(x,y)$ and $g(x,y)$ are in the ...
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### An extension of group schemes admitting Neron models

Let $R$ be a discrete valuation ring, $K$ its field of fractions, and $$0 \rightarrow G_K' \rightarrow G_K \rightarrow G_K'' \rightarrow 0$$ a short exact sequence of smooth $K$-group schemes of ...
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### On transforming pair of bivariate polynomials to pair of univariate polynomials by applying polynomial map

We know that a polynomial map $f(x,y), g(x,y)$ is polynomial automorphism if there exists polynomials $p(x,y)$ and $q(x,y)$ such that $f(p,q)$=x and $g(p,q)=y$. Jacobian conjecture tries to ...
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### Writing an integral for a bounded volume [on hold]

Good day folks! I'm trying to write an integral which could represent the volume of the shaded area below. However my integral calculus is quite poor, so I need some help on that equation. ...
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### Graduate program applications that require questionnaires and other non-letter material

In the December 2014 AMS Notices, a letter to the editor (http://www.ams.org/notices/201411/rnoti-p1311.pdf) by Deconinck and Medlock addresses the problem of (math) graduate programs requiring letter ...
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### Is the space of real conics with a singular point an orientable manifold?

Consider the space of non zero real homogeneous degree $2$ polynomials in three variables upto scaling. This space is $\mathbb{R} \mathbb{P}^5$. The zero set of such a polynomial gives a real curve ...
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### A question in Sasakian geometry

Let $(S,\eta, \xi)$ be a Sasakian manifold with killing vector field $\xi$, then we have the following exact sequence $$0\to <\xi>\to TS\to \frac{TS}{<\xi>}\to 0$$. Can ...
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### ULU Decomposition of a matrix

Let $g \in GL_n(\mathbb{F}_q)$. Is it true that we can always write $g = u_1lu_2$, where $u_1$ and $u_2$ are upper-triangular and $l$ is lower-triangular? Note that I'm not requiring that the matrices ...
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### Gaussian Elimination for Orthogonal groups [on hold]

We known the classical Gaussian elimination algorithm where we can reduce any invertible matrix to a diagonal matrix by row-column operations. Is there row-column operations and Gaussian elimination ...
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### Roots in the solution

It is known that for a one-dimensional self-adjoint operator with periodic boundary conditions, the number of roots is directly related to the eigenstate this eigenfunction belongs to. Now it is ...
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### Hypergeometric function 2F1 convexity proof:

Suppose $F$ is the Gaussian hypergeometric function 2F1, $x\in \mathbb{N}$, $t>x \in \mathbb{N}$, $\mu \in (0,1)$. Is the function: $$f(\mu)=\mu^{x+1} F(x,-t+x,2+x,\mu),$$ convex in $\mu$? I've ...
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### Classifying set theories whose standard models sharing the same ordinals are equal

Let's say that a (recursively axiomatizable) set theory $T$ extending ZF is "ordinal-categorical" if, whenever $M$ and $N$ are standard models of $T$ sharing the same ordinals, one has $M = N$. For ...
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### p-adic Stein spaces

The higher cohomology of coherent sheaves vanish on Stein spaces (both complex and p-adic). In the case when the space ($X$) is a curve and we're working in the complex world, this shows that all ...
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### Do we need Feller condition if the process jumps?

Consider the SDE: $$dv_t = k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{v}_{t}$$ It describes a process $v_t$ which is a strictly positive if the drift is stronger enough, i.e. ...