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In this paper the authors propose a method of verifying formulae in normal modal logics. In order to show that a formula α is a thesis of a normal modal logic, a set of decomposition rules for any formula is given. These decomposition rules are based on the symbols of assertion and rejection of formulae.
In the present paper we derive sufficient conditions for the linear differential equation (r(t)y′(t))′+p(t)y(t) = 0 to be either oscillatory or non-oscillatory on the left and eventually on the right. Some estimations of count of zero point s for solutions to considered equation on an interval are also presented.
The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.
In this paper we present generalization of probability density of random variables. It is obvious that probability density is definite only for absolute continuous variables. However, in many practical applications we need to define the analogous concept also for variables of other types. It can be easily shown that we are able to generalize the concept of density using distributions, especially Dirac’s...
In [5] it was shown that two number fields have isomorphic Witt rings of quadratic forms if and only if there is a Hilbert symbol equivalence between them. A Hilbert symbol equivalence between two number fields K and L is a pair of maps(t,T), where t: K∗/K∗2→L∗/L∗2is a group isomorpism and T: ΩK→ΩLis a bijection between the sets of finite and infinite primes of K and L, respectively, such that the...
In the paper we present the current theoretical base of the J2FADD tool, which translates a Java program to a network of finite automata with discrite data (FADDs).The reason for building the tool is that to model check a concurrent program writ-ten in Java by means of the tools like Uppaal or VerICS (the module VerICS ), an automata model of the Java program must be build first. This is because these...
Let F be a field of characteristic p >0,S=F[[X]],S∗the unit group of S, and W a subgroup of S∗. We characterize finite groups depending on a projective (S,W)-representation type. We also give necessary and sufficient conditions for a finite group and its Sylow p-subgroups to be of the same projective (S,W) -representation type.
The paper includes a necessary condition and sufficient conditions under which two ψ -sparse topologies generated by two functions ψ1and ψ2are equal. Additionally we proved that the intersection of all ψ -sparse topologies is equal to the Hashimoto topology.
In the present paper we investigate some properties on isometric mappings between Euclidean spaces. In addition, non-isometric distance one preserving mappings are also considered.
In the present paper, we deal with the methodology of constructing modular number systems (MNS), named also residue number systems, on arbitrary mathematical structures such as finite groups, rings and Galois fields.
In the present paper, a few different notions of preponderant continuity of a real function are discussed. We study the relationship between them and give some properties of preponderant continuity.
Professor Igor Kluvánek had developed a unique course of calculus (mathematical analysis) to teach students the differential and integral calculus. In the present paper, this concept is briefly outlined. The notion of derivative is introduced via continuity. The definition of integral given in this article applies an idea of Archimedes.
We discuss a processor sharing system with non-homogeneous customers. There are resources of two types for their service: 1) resource of the first type is discrete, there are N units (servers) of the resource; 2) resource of the second type (capacity) is not-necessary discrete. The type of a customer is defined by the amount of first type resource units which is used for the customer service. Each...
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