Slavica Medic

Inequalities of Jensen and Chebyshev Type for Interval-Valued Measures Based on Pseudo-integrals

Since interval-valued measures have applications in number of practical areas, this paper is focused on two approaches to this problem as well as on the corresponding generalizations of the Jensen and the Chebyshev integral inequalities. The first approach is based on an interval-valued measure defined by the pseudo-integral of interval-valued function, while the second approach considers an interval-valued measure obtained through pseudo-integrals of real-valued functions.

Interval-valued Chebyshev, Hölder and Minkowski inequalities based on g-integrals

A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are interval-valued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of interval-valued non-additive measures, have been extensively applied in the mathematical representation of the various aspects of uncertainty, the present paper offers a generalization of Chebyshev, Hölder and Minkowski types inequalities obtained by g-integrals for non-negative real-valued functions with respect to an interval-valued ⊕-measures.

Inequalities of Hölder and Minkowski type for pseudo-integrals with respect to interval-valued ⊕-measures

Abstract In the present paper, the Holder and Minkowski type of inequality for the pseudo-integral of a real-valued function with respect to the interval-valued pseudo-additive measure is proven. Two cases of semirings are considered. In the first case, pseudo-operations (pseudo-addition and pseudo-multiplication) are set by a strictly monotone continuous function. In the second case, the pseudo-addition is the idempotent operation sup, and pseudo-multiplication is specified by a strictly monotone continuous function, as in the first case. Trivial and nontrivial examples of interval-valued pseudo-additive measures are provided, as well as Holder and Minkowski type of inequalities with respect to those measures.

Weak convergence of sequences of distorted probabilities

In this paper, the portmanteau theorem which provides the equivalent conditions of the weak convergence of a sequence of probability measures is extended on the sequence of distorted probabilities.

A premium principle based on the g-integral

ABSTRACT A novel approach of calculating an insurance premium based on g-integrals and interval-valued integrals is introduced. The characterization theorem for the g-integral-based premium principle is proven, and the relations with some well-known premium principles are discussed. The main properties of the interval-valued premium principle based on the g-integral are presented and some illustrative examples are given.

Inequalities of the Chebyshev type based on pseudo-integrals

This paper presents the Chebyshev type of pseudo-integral inequalities, with the particular emphasis on the g-semirings. With the suitable choice of the generator g, the pseudo-expectation and pseudo-moments exist for the Cauchy distribution (in general case the standard expectation and moments for the Cauchy distribution are not defined). The computation of the pseudo-expectation for the Cauchy distribution and some examples that illustrate the applicability of the introduced generalization are also given in the paper.

On measures based on the interval-valued pseudo-integrals of real functions and absolute continuity

One of the important mathematical tools that play a central role in many practical areas, such as mathematical economics, are real-valued functions and integration of real-valued functions with respect to interval-valued measure. The focus of this paper is on measures based on the pseudo-integration of real-valued function with respect to interval-valued measure. The absolute continuity of the first type and of the sixth type for the observed measure are investigated.

A dominator path scheduler for deep pipeline architectures

There are many different instruction scheduling techniques that are used in compilers today. The most frequently used one is the list scheduling. It is easy to implement and gives good results in most cases. It works on the basic block level. According to Fisher and Rau instruction level parallelism that can be achieved using this technique cannot be greater then 2. Architectures with deep pipeline can run much more instructions in the same cycle and global scheduler techniques can give better results. In our tests we used a dominator path scheduler with three different strategies for choosing the scheduling paths. Our application encoded sound to the mp3 format, and was run on a digital signal processor with a deep pipeline. Using these scheduling techniques, our C compiler generated 10% fewer NOP instructions compared to local instruction scheduling. In addition, this implementation of a dominator path scheduler was used on a C compiler for SUN Sparc processors (for testing purposes only), and it was shown that the same implementation of the scheduler can be used for different platforms.

Finite-difference method for singular nonlinear systems

This paper presents a method for solving nonlinear system with singular Jacobian at the solution. The convergence rate in the case of singularity deteriorates and one way to accelerate convergence is to form bordered system. A local algorithm, with finite-difference approximations, for forming and solving such system is proposed in this paper. To overcome the need that initial approximation has to be very close to the solution, we also propose a method which is a combination of descent method with finite-differences and local algorithm. Some numerical results obtained on relevant examples are presented.

Generalization of Portmanteau Theorem for a sequence of interval-valued pseudo-probability measures

Abstract The main result of this paper is a generalization of Portmanteau Theorem for a sequence of interval-valued pseudo-probability measures. The classical Lebesgue integral from Probability Theory had been substituted with the pseudo-integral of a real-valued function with respect to an interval-valued ⊕-measure.