Take a torus with a Riemannian metric. Lift the metric on its universal cover. You get a distance which in turn yields balls. On these balls you can look at the Laplacian. Focus on the spectrum for the Dirichlet or Neumann problem. We describe the asymptotic behaviour of the eigenvalues as the...

By using the complete discrimination system for polynomials, we study the number of positive solutions in [0, 1] to the integral equation , where , are continuous functions on [0, 1], is a positive integer. We prove the following results: when = 1, either there does not exist, or there exist...

In this paper, we study the frequency response of uncertain systems using Kharitonov stability theory on complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at any fixed frequency is attained at some prescribed vertex transfer...

We study two applications of a modified Durrmeyer-Bernstein operator introduced by T.N.T. Goodmann and Sharma [11]. First a new method is proposed for the degree reduction of a Bezier curve. We give an upper bound of the error function in term of the control points of the initial curve followed...

The idea of continuous measurement asks for the concept of weight function in order for one to be able to properly construct the propagator. The main property of the weight function is its invariance property, which is exploited in present work in connection with the measurements in the phase...

The first open problem is concerned with introducing three derivation rules in predicate calculus and the second one suggests a solution for the continuum hypothesis. The conjecture says that there will always be profound questions in any significant theory, over and above those suggested by...

We propose a classification of the reliability laws in dependence from behavior a failure rate. It is offered to consider six classes of the reliability laws. It is investigated the what known laws of reliability enter in the given classes, and also them some properties. Using the given...

It is proved, under Martin's Axiom, that all (,) gaps in / fin are indestructible in any forcing extension by a separable measure algebra. This naturally leads to a new type of gap, a The results of these investigations have applications in Descriptive Set Theory. For example, it is shown that...

We obtain the necessary and sufficient conditions that guaranties the absolute stability of semi-implicit multirate linear discretizations of 2 × 2 differential systems. This result is based on the construction of a general companion matrix that characterizes the class of multirate...

Given a simple polygon with two marked vertices and the problem asks whether two guards can move on the two boundary chains of from to one clockwise and the other counterclockwise, such that they are always mutually visible. In this paper, we present a simple and straightforward solution to the...