Functions and Analysis

1403 Submissions

[5] viXra:1403.0977 [pdf] submitted on 2014-03-31 12:36:51

Solid Angle of the Off-Axis Circle Sector

Authors: Richard J. Mathar
Comments: 6 Pages.

The solid angle of a circular sector specified by circle radius, angle of the sector, and distance of the circle plane to the observer is calculated in terms of various trigonometric and cyclometric functions. This generalizes previous results for the full circle that have appeared in the literature.
Category: Functions and Analysis

[4] viXra:1403.0951 [pdf] submitted on 2014-03-27 10:50:26

Recent Results on Modular Convergence Theorems, Rates of Approximation and Korovkin Theorems for Filter Convergence

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 9 Pages.

We give a survey on recent results about the problem of approximating a real-valued function by means of suitable families of sampling type operators, which include both discrete and integral ones, and about the order of approximation, and abstract Korovkin-type theorems with respect to different types of test functions, in the context of filter convergence. We give a unified approach, by means of which it is possible to consider several kinds of classical operators, for instance Urysohn integral operators, in particular Mellin-type convolution integrals, and generalized sampling series. We obtain proper extensions of classical results.
Category: Functions and Analysis

[3] viXra:1403.0310 [pdf] submitted on 2014-03-20 00:14:06

Operator Exponentials for the Clifford Fourier Transform on Multivector Fields

Authors: David Eelbode, Eckhard Hitzer
Comments: Submitted to Publications of Research Institute for Mathematical Sciences (PRIMS), March 2014, 18 pages.

This paper briefly reviews the notion of Clifford's geometric algebras and vector to multivector functions; as well as the field of Clifford analysis (function theory of the Dirac operator). In Clifford Fourier transformations (CFT) on multivector signals the complex unit $i\in \mathbb{C}$ is replaced by a multivector square root of $-1$, which may be a pseudoscalar in the simplest case. For these transforms we derive, via a multivector function representation in terms of monogenic polynomials, the operator representation of the CFTs by exponentiating the Hamilton operator of a harmonic oscillator.
Category: Functions and Analysis

[2] viXra:1403.0304 [pdf] submitted on 2014-03-19 18:07:58

Nikodym-Type Theorems for Lattice Group-Valued Measures with Respect to Filter Convergence

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 3 Pages.

We present some new convergence and boundedness theorem with respect to filter convergence for lattice group-valued measures, whose techniques are based on sliding hump arguments.
Category: Functions and Analysis

[1] viXra:1403.0262 [pdf] submitted on 2014-03-14 21:51:47

A Mathematical Analysis of Crowds

Authors: Shreyak Chakraborty
Comments: 8 Pages.

Crowds are generally analyzed in the regime of sociology- where they are studied and classified on the basis of crowd psychology. This analysis arises from the study of collective behavior and treats crowds as dependent on psychology of humans in the crowd. In this introductory paper we show a generalized treatment of crowds as a set of living objects: called members of the crowd. We classify crowds based on various parameters and study some general and specific characteristics of crowd of humans and study the response of a simple crowd to an external situation or stimulus by deriving the solution of the generalized crowd equation. We also define some terminology regarding the mathematical description of crowds and hence arrive at some useful conjectures.
Category: Functions and Analysis