Zobrazeno 1 - 10
of 301
pro vyhledávání: '"13J30"'
This article studies generalizations of (matrix) convexity, including partial convexity and biconvexity, under the umbrella of $\Gamma$-convexity. Here $\Gamma$ is a tuple of free symmetric polynomials determining the geometry of a $\Gamma$-convex se
Externí odkaz:
http://arxiv.org/abs/2412.13267
We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue field. We do
Externí odkaz:
http://arxiv.org/abs/2410.10344
We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but critical component of a transformer becomes a natural development of an old
Externí odkaz:
http://arxiv.org/abs/2408.09624
This expository article gives a survey of matrix convex sets, a natural generalization of convex sets to the noncommutative (dimension-free) setting, with a focus on their extreme points. Mirroring the classical setting, extreme points play an import
Externí odkaz:
http://arxiv.org/abs/2405.07924
Autor:
Kumar, Neeraj, Venugopal, Chitra
An almost complete intersection ideal can be seen as a $d$-sequence ideal with the minimal number of generators being one more than its height. In this paper, we give exact formulas for the regularity of powers of graded almost complete intersection
Externí odkaz:
http://arxiv.org/abs/2403.15844
We present a novel, general, and unifying point of view on sparse approaches to polynomial optimization. Solving polynomial optimization problems to global optimality is a ubiquitous challenge in many areas of science and engineering. Historically, d
Externí odkaz:
http://arxiv.org/abs/2403.03560
A linear map $\Phi$ between matrix spaces is called cross-positive if it is positive on orthogonal pairs $(U,V)$ of positive semidefinite matrices in the sense that $\langle U,V\rangle:=\text{Tr}(UV)=0$ implies $\langle \Phi(U),V\rangle\geq0$, and is
Externí odkaz:
http://arxiv.org/abs/2401.17425
This paper studies Positivstellens\"atze and moment problems for sets $K$ that are given by universal quantifiers. Let $Q$ be a closed set and let $g = (g_1,...,g_s)$ be a tuple of polynomials in two vector variables $x$ and $y$. Then $K$ is describe
Externí odkaz:
http://arxiv.org/abs/2401.12359
Autor:
Yahaghi, Bamdad R.
In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. In Section 3, we show how to develop the spectral theory in
Externí odkaz:
http://arxiv.org/abs/2401.00985
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (real) quadratic form is a sum of squares of linear forms: If a form (of arbitrary even degree) is positive definite then it becomes a sum of squares of f
Externí odkaz:
http://arxiv.org/abs/2310.12853