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In this paper some properties of a special case of generalized Hölder functions, which belong to the space W γ [a, b], are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the theorem that product of two functions belonging to the space W γ [a, b] also belongs to this space.
In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to be prime.
The paper presents thermal analysis as far as tests on polymers are concerned. The obtained results, after being mathematically elaborated, differentiate thermal processes and define normal heat. It also consists of mathematical elaboration of the tests as well as an explanation of the graphical results. The paper also presents the empirical results of the tests conducted on polymers crystallinity...
Most of the mechanical failures in alloplasty are caused by material fatigue. To cut down the risk of it, we can either increase the fatigue resistance of the material or decrease the load strain. All presented numerical calculations allow to draw quality conclusions concerning the influence of some parameters of endoprostheses on the values of stress and strain that are formed in polyethylene inserts.
The paper presents the solution of a fourth order differential equation with various coefficients occurring in the vibration problem of the Euler-Bernoulli beam. The concerning equation is written as a first order matrix differential equation. To solve the equation, the power series method is proposed.
We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the...
In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified. The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been...
The mathematical model of thermal processes in the casting domain can be formulated using the fixed domain approach. The energy equation corresponding to this model contains the parameter called a substitute thermal capacity (STC), in which the alloy latent heat appears. The aim of considerations is the application of sensitivity analysis methods for estimation of temperature field changes due to...
In this paper, the mathematical and numerical model of the solidification of a cylindrical shaped casting, while taking into account the process of the mould cavity filling with molten metal, has been proposed. The feeding of the casting by a riser head during solidification and the formation of shrinkage cavity has also been taken into consideration. The shape and depth of the shrinkage cavity distribution...
In the paper the simplified model of thermal processes proceeding in the domain of biological tissue secured with protective clothing is discussed. In particular, the simplification of the mathematical model consists in the omission of the real layer of fabric for which the transient temperature field is determined by the Fourier equation and the introduction in this place of the additional thermal...
We study properties of geodesic foliations on the flat, n-dimensional torus. Using the isomorphism of the Hodge star, we obtain some facts concerning compact totally geodesic surfaces (which are the leaves of geodesic foliations). We compute the p-module of a geodesic foliation. On the basis of these results, we derive a kind of reciprocity formula for the product of modules of two orthogonal foliations...
Hardening is one of the manufacturing processes used for improving mechanical properties such as strength, hardness and wear resistances of the mechanical components for machine parts. This paper describes modelling of the processes of steel C80U hardening. The first priority was given to thermal phenomena, phase transformations in a solid state and mechanical phenomena. A numerical algorithm of thermal...
In the present paper, a problem of free vibration of a double-walled nanotubes system is considered. The nanotubes of the system are coupled by an arbitrary number of elastic rings. The Green’s functions method was used to obtain a solution to the problem. Numerical results are presented graphically.
The study presents the application of a mathematical description of a thermochemical process which consists in diffusion saturation of steel with carbon atoms. The mathematical description assumes temperature-based activation of the process of carburizing and estimates the effect of diffusion flow, which has a direct effect on the thickness of the obtained carburized layers, on the process temperature...
In this paper critical buckling loads for axially functionally graded (FG) beams are studied. It is assumed that material properties of the beam vary exponentially through the axial direction. Solutions are derived for three types of boundary conditions: a beam that is clamped at both ends, pinned at both ends and a beam that is clamped at one end and pinned at the other.
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