Antonela Toma

Distribution theory : with applications in engineering and physics

Preface XI 1 Introduction to the Distribution Theory 1 2 Integral Transforms of Distributions 113 3 Variational Calculus and Differential Equations in Distributions 151 4 Representation in Distributions of Mechanical and Physical Quantities 201 5 Applications of the Distribution Theory in Mechanics 241 6 Applications of the Distribution Theory to the Mechanics of the Linear Elastic Bodies 253 7 Applications of the Distribution Theory of Linear Viscoelastic Bodies 273 8 Applications of the Distribution Theory in Electrical Engineering 285 9 Applications of the Distribution Theory in the Study of Elastic Bars 301 10 Applications of the Distribution Theory in the Study of Viscoelastic Bars 343 11 Applications of the Distribution Theory in Physics 365 References 377 Index 379

Generating Functions for the Mean Value of a Function on a Sphere and Its Associated Ball in

We define two functions which determine the properties and the representation of the mean value of a function on a ball and on its associated sphere. Using these two functions, we obtain Pizzettis formula in as well as a similar formula for the mean value of a function on the ball associated to the sphere. We also give the expressions of the remainders in these two formulas, using the surface integral on a sphere.

Nonlinear optical effects used for investigations on biological samples at micro and nanoscale

In our work we present some investigations on biological samples at micro and nanoscale by using nonlinear effects in laser scanning microscopy techniques. We developed an integrated multimodal system that allows for the simultaneous image acquisition from multiple optical imaging modalities. Our system includes several microscopy techniques working in far field and in near field. The main advantage of the system is connected with the possibility to image the same area of the sample at micro and nanoscale so that a correlation between the images could be made and an explanation of the images at nanoscale can be done. By overlaying the structural images obtained from different techniques, a more comprehensive view of different biological specimens can be obtained. In addition the possibility to see the same sample area at micro and nanoscales offers the possibility to make a connection between the different elements of the biological structures.

The Univalence Conditions For A General Integral Operator

Abstract In this paper we extend a general integral operator which was introduced in the paper (Breaz, 2010) [3] . We denote this operator by H γ 1 , γ 2 , … , γ [ | η | ] , β , η . For this integral operator we show some conditions of univalence on the class of analytical functions.

Properties and Representation of the Mean Values of a Function over a Sphere and Its Associated Ball in R3

In this paper we define two functions which determine the properties and the representations of the mean values of a function over a sphere and its associated ball. The relations between these two functions and their mean values are established, as well as the similarity with the Taylor’s Series.