Search results for " functions"

The convolution operation on the spectra of algebras of symmetric analytic functions

2012

Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.

Linearization of holomorphic mappings on fully nuclear spaces with a basis

1994

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

Geometric Properties of Planar BV -Extension Domains

2009

We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.

Learning with confidence

1996

Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).

Enumeration of L-convex polyominoes by rows and columns

2005

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.

Cluster values of holomorphic functions of bounded type

2015

We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. Fil: Aron, Richard Martin. Kent State University; Estados Unidos Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Lassalle, S…

Transformations by diagonal matrices in a normed space

1962

Line element-less method (LEM) for beam torsion solution (truly no-mesh method)

2008

In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…

Algorithmic approaches to Siegel's fundamental domain

2017

Siegel determined a fundamental domain using the Minkowski reduction of quadratic forms. He gave all the details concerning this domain for genus 1. It is the determination of the Minkowski fundamental domain presented as the second condition and the maximal height condition, presented as the third condition, which prevents the exact determination of this domain for the general case. The latest results were obtained by Gottschling for the genus 2 in 1959. It has since remained unexplored and poorly understood, in particular the different regions of Minkowski reduction. In order to identify Siegel's fundamental domain for genus 3, we present some results concerning the third condition of thi…

Frontiers of metal-coordinating drug design

2020

INTRODUCTION: The occurrence of metal ions in biomolecules is required to exert vital cellular functions. Metal-containing biomolecules can be modulated by small-molecule inhibitors targeting their metal-moiety. As well, the discovery of cisplatin ushered the rational discovery of metal-containing-drugs. The use of both drug types exploiting metal–ligand interactions is well established to treat distinct pathologies. Therefore, characterizing and leveraging metal-coordinating drugs is a pivotal, yet challenging, part of medicinal chemistry. AREA COVERED: Atomic-level simulations are increasingly employed to overcome the challenges met by traditional drug-discovery approaches and to compleme…