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This paper introduces some notions of e ective dimension for weighted function spaces. A space has low e ective dimension if the smallest ball in it that contains a function of variance 1, has no fu...
The way people answer this question is illuminating and can reveal deeply held beliefs about the nature of mathematics and how it is best taught and learned. This presentation considers the ex...
By proving an integral formula of the curvature tensor of E⊗detE, we observe that the curvature of E⊗detE is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Na...
In this paper we present a numerical method for solving Riemann type problem for the fifth order improperly elliptic equation in complex plane .We reduce this problem to the boundary value problems fo...
The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purp...
Abstract: Let A be a commutative domain containing Z which is finitely generated as a Z-algebra, and let a,b,c be non-zero elements of A. It follows from work of Siegel, Mahler, Parry and Lang that th...
Abstract: This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction...
Abstract: We develop an algorithm for computing the closure of a given nilpotent $G_0$-orbit in $\g_1$, where $\g_1$ and $G_0$ are coming from a $\Z$ or a $\Z/m\Z$-grading $\g= \bigoplus \g_i$ of a si...
Abstract: In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general...
Abstract: We present some extensions to singular varieties of effective membership results previously known in $\C^n$ or smooth varieties. In particular, we extend a geometric effective Nullstellensat...
Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipatio...
We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial cu...
A method to derive homogeneous effective constitutive equations for periodically layered elastic media is proposed. The crucial and novel idea underlying the procedure is that the coefficients of th...
In these notes we review some recent results concerning the derivation of effective equations from first principle quantum dynamics. In particular, we discuss the derivation of the semi-relativistic...

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