Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

Admissible Substitutions in Sequent Calculi

For first-order classical logic a new notion of admissible substitution is defined. This notion allows optimizing the procedure of the application of quantifier rules when logical inference search is made in sequent calculi. Our objective is to show that such a computer-oriented sequent technique may be created that does not require a preliminary skolemization of initial formulas and that is efficiently comparable with methods exploiting the skolemization. Some results on its soundness and completeness are given.

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Fractional Integration and Fractional Differentiation of the M-Series

Mathematics Subject Classification: 26A33, 33C60, 44A15

A Mathematical Basis for an Interval Arithmetic Standard

Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8.

The Eccentric Connectivity Polynomial of some Graph Operations

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

On Y. Nievergelt's Inversion Formula for the Radon Transform

Mathematics Subject Classification 2010: 42C40, 44A12.

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation

2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.

Един начин за преговор на формулите по тригонометрия в средното училище

Kliment Vasilev - The trigonometry formulas are given in the form of mathematical problems. Some of these problems are solved, and it is shown how the others can be solved with the help of adequate guidance that includes the previous problems. This method is suitable for revision in the secondary school, as well as for preparation for school-leaving exams and matriculation.

Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution

Павел Т. Стойнов - В тази работа се разглежда отрицателно биномното разпределение, известно още като разпределение на Пойа. Предполагаме, че смесващото разпределение е претеглено гама разпределение. Изведени са вероятностите в някои частни случаи. Дадени са рекурентните формули на Панжер.

Approximate Model Checking of Real-Time Systems for Linear Duration Invariants

Real-time systems are usually modelled with timed automata and real-time requirements relating to the state durations of the system are often specifiable using Linear Duration Invariants, which is a decidable subclass of Duration Calculus formulas. Various algorithms have been developed to check timed automata or real-time automata for linear duration invariants, but each needs complicated preprocessing and exponential calculation. To the best of our knowledge, these algorithms have not been implemented. In this paper, we present an approximate model checking technique based on a genetic algorithm to check real-time automata for linear durration invariants in reasonable times. Genetic algorithm is a good optimization method when a problem needs massive computation and it works particularly well in our case because the fitness function which is derived from the linear duration invariant is linear. ACM Computing Classification System (1998): D.2.4, C.3.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.