Volume 5, Issue 1

Oscillations of parabolic equations with functional arguments are studied, and sufficient conditions are derived for all solutions of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional problems to one-dimensional problems for functional differential inequalities.

Numerous methods for the inversion of the Radon transformation which is the basis of computerized tomography are known: Fourier inversion, filtered backprojection or Kaczmarz's method. In the filtered backprojection method the choice of the filter function is crucial for the quality of the pictures. Here we deal with singular filter functions which have some advantages in comparison with conventional filters. An adapted method allows to handle the numerical problems caused by the singularities.

This paper presents a mathematical model for a chemical process used to machine cristal as glass or silica. A short physical description is presented from which we draw the mathematical model. We obtain a coupled parabolic equations system on a free boundary domain with a non-linear condition on the boundary. The existence and the uniqueness is proved in the one-dimensional case.

In this paper, we give a new minimax theorem and two new existence theorems of solutions for generalized quasi–variational inequalities in H -spaces. Our results improve and develop some famous results.

Let Dar stand for the Darboux Baire class 1 functions. We show that the cofinality of the meager sets in ℝ is the smallest cardinality of a set of Baire class 1 functions F such that for any finite collection of Baire class 1 functions G there is an ƒ ∈ F such that ƒ + G ⊆ Dar. Other results of this type are shown. These results are then considered as statements about additivity. The notion of super–additivity is introduced.

We consider a hyperbolic variational–hemivariational initial value problem on a vector valued functions space. Using a regularization procedure and a Barbu result we obtain an existence result for a problem independent on u ′.

It is possible to color the plane with countably many colors such that if H is the rational points of a line (i.e., H = φ [ℚ] for some rigid motion) then H gets every color exactly once.

We prove the existence of solutions to an integral equation modeling the infiltration of a fluid in an isotropic homogeneous porous medium.

Regular variation is an asymptotic property of functions and measures. The one variable theory is well–established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on multivariable regular variation for functions and measures.

Herein a sufficient condition for q to belong to Q ∩ T –1 (0) is provided, where Q is a weakly compact convex subset of a real reflexive Banach space E and is a maximal monotone operator.