This paper contains an investigation of an open exponential network with bypass of systems of multi-type messages with absolute priority in transient behavior. Messages with priority received by the node with the probability depending on the state system and the type of incoming messages are for service, forcing messages that are serviced or instant changes in the following system, and can leave the...

By the method of classical potential theory, we obtain the integral representation of the two-parameter operator semigroup that describes the inhomogeneous Feller process on a closed interval [ r1,r2 ] that is a result of pasting together two diffusion processes given on ( r1,r, ) and ( r, r2 ), respectively, where - ∞ < r1 < r < r2 <∞ .

The constructive preparation of industrial production aims at determining the physical and chemical properties, the external appearance and other elements regarding quality, which shall allow the product in question to meet the requirements of national economy in the fields of usage and consumer requirements. The starting point lies in the knowledge of the pursued goal, i.e. the product type and the...

A correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold is shown.

Research of the closed exponential queueing structure with one-type messages and the income is conducted. The differential equation in partial derivatives for an income distribution density is received. The ordinary differential equation for its expected income is constructed at particular starting conditions. The offered method of its decision in a case when the intensity of the service of messages,...

The development of mathematics stands as one of the most important achievements of humanity, and the development of the calculus, differential calculus and integral calculus is one of the most important achievements in mathematics. Differential calculus is about finding the slope of a tangent to the graph of a function, or equivalently, differential calculus is about finding the rate of change of...

Free vibration analysis of Kirchhoff plate by the Boundary Element Method is presented in the paper. The boundary integral equation are derived according to the Bettie theorem. The collocation version of BEM with non-singular approach with one and double collocation points is used. The constant type of element is introduced. Boundary suport at selected point is modelled as support in vicinity of point...

Decisions concerning the way of purchasing spare parts affect the level of the generated costs of collecting and maintaining stocks as well as the level of maintaining the continuity of production in enterprises. To learn about different situations of spare parts purchasing appearing in real economic conditions there has been conducted the simulation of different scenarios of spare parts purchase...

This article discusses the transport of chain-like structures across a pore in membrane. Such a translocation process is initiated by the first monomer captured by molecules forming the pore. This study focuses on the distribution of the position of this particular polymer’s segment. The polymer attachment process is simulated using the sequential algorithm and the influence of various physical and...

The estimation of priority vectors from pairwise comparison matrices is a core of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (EM). Despite its popularity, various shortcomings of the EM have been described in literature. In this paper a new method for deriving priority vectors is proposed. This method makes use...

M/M/n/(m,V) queueing systems with service time independent of customer volume are well known models used in computer science. In real computer systems (computer networks etc.) we often deal with the overload problem. In computer networks we solve the problem using AQM techniques, which are connected with introducing some accepting function that lets us reject in random way some part of the arriving...

In industrial practice, there are frequent cases when a performer randomly serves the machines at time intervals, which prevents the elements of carrying out the processing procedure from being predetermined. Situations of random interventions on the multiserved machines occur more often in textile industry on the spinning machines, looms, knitting machines, wire weaving and interlacing machines,...

In the present work a problem pertaining to the damped lateral vibrations of the truck crane radius change system with the developed hydraulic cylinder model that changes the radius has been formulated and solved. In the adopted model the vibration energy dissipation derives from the internal damping of the viscoelastic material (the Kelvin-Voigt rheological model) of beams that model the system....

We present the result of the theory of quaternionic Fueter regular functions. It is shown that the module of such function ||F(q)||, q := w+ix+jy+kz, cannot be an analytic function in r; r2 := ||q||2 := w2 + x2 + y2 + z2.

In this paper accuracy of a simple and effective method for tracking interfaces in two-dimensional area is investigated. The method is based on the level set method (LSM) with "brute force" reinitialization algorithm. A comparison of numerical solution with an analytical solution is presented and discussed.

The hypercomplex fractals obtained from generalizations of J- and M-sets, apart from their visual aesthetics, play an important role in the mathematical description in various fields of physics. The generalizations of J- and M-sets to the four-dimensional Euclidean space are well known and well described. However, very few studies were done for the higher-dimensional generalizations. The paper discusses...

The paper presents the results of numerical analysis of the system “ceramic head - ceramic cup” in the hip joint endoprosthesis. Applying the Al2O3 ceramics in this kind of solutions, apart from all values of this material, can lead to grinding, if a high load is used. The analysis was run on the ADINA system. The geometrical model was elaborated on real measurements of the elements of endoprosthesis...

In the article the asymptotic analysis of closed exponential queueing HM-structure with priority messages is carried out with a large total number of messages, depending on time. The number of service lines in systems, the intensity of service messages in them, the probabilities of message transitions between systems also depends on time. It is proved that the density of the income distribution in...

This paper contains an investigation of an open queueing network with positive and negative messages that can be used to model the behavior of viruses in information and telecommunication systems and networks. The purpose of research is investigation of such a network at the transient behavior. We consider the case when the intensity of the incoming flow of positive and negative messages and service...

In this paper, a solution of the heat conduction problem in a two-layered hollow cylinder by using the Green’s function method is presented. The considerations concern the heat conduction in the radial direction while taking into account time-dependent boundary conditions. The continuity condition of the temperature at the dividing surface of the layers is written in the form of a Volterra integral...