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

**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*

**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*

**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*

**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*

**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