Research
Research
Research
Research
548+ open-access research outputs.
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intr…
Let $\mathbb{K}$ be a field of characteristic different from $2$, and let $M_n(\mathbb{K})$ be the algebra of all $n\times n$ matrices over $\mathbb{K}$. We consider the corresponding special Jordan a…
A torus-covering $T^2$-link of degree $n$ is a surface-link consisting of tori, in the form of an unbranched covering of degree $n$ over the standard torus. We focus on a torus-covering $T^2$-link of …
Let $\overline\mu_\Lambda(t):=\sum\limits_{m\geq1}\mu_\Lambda(m)t^m$ be the \emph{$\mu$-series} of a finite-dimensional tame algebra $\Lambda$ over an algebraically closed field, where $\mu_\Lambda(m)…
We obtain new lower and upper bounds for the numerical radius of a bounded linear operator $A$ on a complex Hilbert space, which refine the existing ones. In particular, if $w(A)$ and $\|A\|$ denote…
Eigenvalue and eigenvector perturbation theory is a fundamental topic in several disciplines, including numerical linear algebra, quantum physics, and related fields. The central problem is to underst…
In large-scale X-ray computed tomography (CT), matrix-free iterative methods are essential due to the prohibitive cost of explicitly forming the system matrix. In practice, forward projectors and back…
We study the symmetrization of the Novikov product. Using the embedding of a free Novikov algebra into a differential algebra over a field of characteristic zero and the Euler operators (variational d…
Let $k$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $\delta$. A graph $G$ is said to have property $P(k, d)$ if it contains $k$ edge-disjoint spanning trees an…
A complete theory ${\mathcal T}$ of partial order is an FLD$_1$-theory iff some (equivalently, any) of its models ${\mathbb X}$ admits a finite lexicographic decomposition ${\mathbb X} =\sum _{{\mathb…
Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}…
Let $M_n(\mathbb{F})$ denote the algebra of $n \times n$ matrices over an algebraically closed field $\mathbb{F}$ of characteristic different from $2$. For $n \ge 2$, we classify all maps $\phi : M_n(…
Let $D$ be a finitely generated abelian group and $S$ a $D$-graded ring. We introduce a geometric semistability condition for points $x \in \Spec(S)$, characterized by maximal-dimensional orbit cones …
We begin with (densely-defined) fractional linear transformations (FLT) on (some) Banach algebras and their relatives. This leads to Wedderburn's continued fractions (recursively-defined noncommutativ…
Affine isoperimetric inequalities for the functional radial mean bodies are derived from the new affine chord Sobolev inequalities, which extend the recent affine isoperimetric inequalities of Haddad …
Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural netw…
Let $\U$ be a von Neumann algebra with a projection $P\in \U$. For any $A_1,A_2,\ldots,A_n\in\U,$ define $p_1(A_1)=A_1,$ $p_n (A_1,A_2,\ldots,A_n)=[p_{n-1} (A_1,A_2,\ldots,A_{n-1}),A_n]$ for all integ…
The Burnside process is a classical Markov chain for sampling uniformly from group orbits. We introduce the dual Burnside process, obtained by interchanging the roles of group elements and states. Thi…
We introduce a class of generalized convex functions, termed star quasiconvexity, to ensure the linear convergence of gradient and proximal point methods. This class encompasses convex, star-convex, q…
Matrix Phylogeny introduces compact spectral fingerprints (CSF/ASF) that characterize matrices at the family level. These fingerprints are low-dimensional, eigendecomposition-free descriptors built fr…
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