相关论文: The Top Dimensional Singular Set $\text{sing}_{*}u…
We consider the possible sizes of large sumfree sets contained in the discrete hypercube $\{1,...,n\}^k$, and we determine upper and lower bounds for the maximal size as $n$ becomes large. We also discuss a continuous analogue in which our…
We survey some properties of homotopical and homological $Z_n$-sets in topological spaces.
We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…
For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
The Homogeneous sine-Gordon (HSG) theories are integrable perturbations of $G_k/U(1)^{r_G}$ coset CFTs, where $G$ is a simple compact Lie group of rank $r_G$ and $k>1$ is an integer. Using their T-duality symmetries, we investigate the…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
This entry for the SIGSPATIAL Special July 2010 issue on Similarity Searching in Metric Spaces discusses the notion of intrinsic dimensionality of data in the context of similarity search.
Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the…
For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.
A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
In this paper, we study and classify singular minimal translation surfaces in a Euclidean space of dimension 3 endowed with a certain semi-symmetric (non-)metric connection.
In this paper, we will define $\mathcal{I}^{*}$-sequential topology on a topological space $(X,\tau)$ where $\mathcal{I}$ is an ideal of the subset of natural numbers $\mathbb{N}$. Besides the basic properties of the…
We analyze the correspondence between finite sequences of finitely supported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on…
We construct two new one-parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss type formulas geared for points of any given homogeneity…
We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a…
The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…
The purpose of this paper is twofold. We explore higher property T as an abstract group-theoretic property. In particular, we provide new operator-algebraic characterizations of higher property T. Then we turn to lattices in semisimple Lie…