# Volume 1 (2009), Number 1-2

## Green’s Functions in Mathematical Physics

### Author(s): WILHELM KECS

**Abstract:** The determination of Green functions for some operators
allows the effective writing of solutions to some boundary problems of
mathematical physics.

## Distributions from ${D}^{\prime}({\mathbb{R}}^{n})$ Representable only with Respect to the Polar Coordinate $r\in \mathbb{R}$

### Author(s): WILHELM W. KECS

**Abstract:** The notion of distribution from ${D}^{\prime}({\mathbb{R}}^{n})$ representable only with respect to
the polar coordinate $r\in \mathbb{R}$ is defined. Some
of its properties are proved. It is shown that the distributions
$\delta x$,
$\Delta \delta (x)\in {D}^{\prime}({\mathbb{R}}^{n})$
and others are representable with respect to $r\in \mathbb{R}$ and their
expressions are given.

## A Nonlinear Fredholm Integral Equation

### Author(s): MARIA DOBRIȚOIU

**Abstract:** This paper contains several results of existence,
existence and uniqueness and continuous data dependence of the solution
of a nonlinear Fredholm integral equation with modified argument, which
appears in the 70', in some problems from turbo-reactors industry. To
obtain these results the Contraction Principle, the Schauder's theorem
and the General data dependence theorem are useful.

## Gauss-Christoffel Type Quadrature Formulas with Fixed Nodes. Gauss-Laguerre-Radau Quadrature Formula

### Author(s): DANIEL VLADISLAV

**Abstract:** We study in this paper the Gauss-Christoffel with
fixed nodes quadrature formula with their principal's properties, looking
up to construct a new Gauss-Laguerre-Radau quadrature formula with one
fixed nodes, corresponding to the Laguerre orthogonal polynomials. We gave
too an application to this formula.

## Variation of Curves Length Reported to Cone Metric in Lorentz Manifold

### Author(s): SORIN NOAGHI

**Abstract:** On Lorentz manifold $\left(M,g\right)$ we consider a timelike, parallel and unitary vector field
$Z$ with
its help we define the $Z$-length of curves and we obtain their first and the second
variation.

## Linking Devices for Wide Cables to Balance Winding Installations

### Author(s): DUMITRESCU IOSIF, JULA DUMITRU, AND ITU VILHELM

**Abstract:** Linking devices for wide balancing cables connect
between extraction vessel and wide cable to compensate for vertically
transported masses. Such a device is made up of a series of elements of
resistance that make connection between the bottom of the extraction vessel
and the exterior core, whose operational width is determined by the width of
the wide cable and a series of fixing clamps of the cable end wrapped around
the core. In the paper is present the numerical analysis with finite elements
DLCLE118 device.

## The National Conference of Mechanics of Solids

### Author(s): P.P. TEODORESCU

**Abstract:** The National Conference of Mechanics of Solids