All Questions

8 views

Rational homology sphere that is not Seifert manifold

I wonder if there is an example of rational homology sphere that is not a Seifert manifold. If there is, how can one construct such a rational homology sphere from a surgery of a knot in $S^3$?
13 views

The weak-star closure of closed left ideals corresponded to pure states

I asked this question at math.stackexchange and received no comment. Let $A$ be a C*-algebra and $\phi$ be a positive linear functional on $A$. Let $\tilde{\phi}$ be its unique $w^*$-continuous ...
5 views

Problem Formulation for SGD as Applied in Non-stationary Optimziation

This post is about how to formulate a time-varying (loss) problem. Basically I am looking for a target-tracking (time-varying) model which is amenable (error can be controlled) for stochastic ...
13 views

Suggestion for books in Pertubation theory with an emphasis on the theory

As the title suggest I am looking for another good coverage of the theory of Pertubation theory. Currently I am working through Murodock's book: Pertubations: Theory and Methods. But I am rest assure ...
21 views

...
43 views

When the reduced $C^*$-algebra of $\Gamma$ admits character then $\Gamma$ is amenable

Suppose that $C^*_r(\Gamma)$ admits some character (homomorphism into $\mathbb{C}$)-here $\Gamma$ is discrete group and $C^*_r(\Gamma)$ is the closure of the image of the group ring $\mathbb{C}\Gamma$ ...
34 views

Are there any ways we can determine whether the $\Xi_x$-classes of natural numbers upto $\frac{1}{2}p^2_x -2$ exvert all non-trivial $\Xi_x$-classes? [on hold]

This question follows from the information provided below. Are there any ways we can determine whether the $\Xi_x$-classes of natural numbers up to $\frac{1}{2}p^2_x -2$ exvert all non-trivial ...
38 views

How to evaluate this equality [on hold]

I want to prove this equality $$\frac{1}{2\pi}\frac{(x-y)\cdot y}{(x_1-y_1)^2+(x_2-y_2)^2}= \frac{ab}{4\pi}\frac{1}{a^2\sin^2(\alpha+\beta)+b^2\cos^2(\alpha+\beta)}.\tag{1}$$ where $\cdot$ is the ...
134 views

Is there a consistent arithmetically definable extension of PA that proves its own consistency?

I asked this on stackexchange with no answer. The negation would be the obvious generalization of Gödel's second incompleteness from r.e. extensions of PA to any arithmetically definable extension of ...
252 views

“Set theory” founded on lists rather than sets

On a computer, sets are often represented rather "indirectly / implicitly", e.g. in terms of some properties that they or their members satisfy. But some sets can be represented more "directly / ...
21 views

minimizing sum of distances [on hold]

I have three points A(-3.5, 0), B(2,0), C(0.3). Looking for D(0,d) such that AD + BD + CD is minimal. Fermat does not work here due to D lying on the y-axis. I thought I could just minimize the sum ...
97 views

211 views

Asymptotics for the number of abelian groups of order at most $x.$

The number of abelian groups of order $n$ (call it $a(n)$ is a studied subject (see http://oeis.org/A000688), but I can't seem to find any asymptotic results. Obviously, there is no asymptotic for ...
24 views

Maximal TB number and slice genus relation of a knot in any 3-manifold

Lisca-Stipsicz say that if a knot $K\subset{S^{3}}$ satisfies $g_{s}(K)>{0}$ and $TB(K)=2g_{s}(K)-1$ then $S^{3}_r(K)$ carries positive, tight contact structures for every ...
44 views

Should I learn information technology? [on hold]

I am 18 y.o., and I want to go to university. I will study Software Engineering (Computer science), but I do not know yet what I want to be exactly. I love math, phisycs, psychology, philosophy, ...
73 views

Cells in affine Weyl groups

This may sound like a very general question, which pretty much reflects my ignorance on the subject. In the case of Weyl groups $W$, there is a notion of left/right/double cells, which is roughly ...
73 views

Weak*-closure of finite rank operators on dual space

Given a Banach space $X$, we consider the space $B(X^*)$ of bounded, linear operators on $X^*$ with the weak*-topology from its canonical predual $B(X^*)_*=X^*\hat{\otimes}X$. What is ...
85 views

Continuous non-constant function with infinite intersections with horizontal line on a compact interval?

The title might be misleading, but whether such a function exists is what boggles me about the following problem: Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a continuous function such that for all ...
38 views

Wave-like equation with 1st order time derivative and non-constant coefficients

We start with the following recurrence relation for complex coefficients $c_{n,m}$: $$i\dot{c}_{n,m}(t) = \sqrt{(n+1)(n+2)(m-1)m}c_{n-2,m-2} + \sqrt{n(n-1)(m+1)(m+2)}c_{n+2,m-2}$$ where ...
Let $X\in \mathrm{sSet}$ and $FX$ be the Milnor's construction (model for $\Omega\Sigma |X|$) - in each dimension $n$ this is the free group on $X_n$ with one relation $*=1$. I'm interested in ...