Derivation of a mathematical model of oscillation processes of spatially loaded rods with account for temperature is considered in the paper. On the basis of the problem posed, using the generalized Hamilton-Ostrogradsky principle, the variations in kinetic, potential energy and work of external forces were calculated, and a nonlinear mathematical model of spatially loaded rods was derived, taking into account temperature. Based on the mathematical model, the resolving equations of spatially loaded rods with generalized natural initial and boundary conditions were derived.
In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponents for the global existence of the solution. Using the asymptotic formulas as the initial approximation for the iterative process, numerical calculations are performed.
In the present paper, we study the boundary value problem for a mixed parabolic-hyperbolic equation with fractional derivative and degeneration in time. Using the method of separation of variables, we prove theorems on the uniqueness and existence for the classical solution of this problem.
In the paper, we give the upper bounds for moments of branching processes in a varying environment starting with a random number of particles.
We explore an application from the author’s work in neuroscience. A code used to investigate neural development modeled 100 neurons with all-to-all excitatory connectivity. We used a simple ordinary differential equation system to model each neuron, and this 100-neuron model was used to produce a paper published in the Journal of Neurophysiology. Later a colleague used our code to continue this work, and found he could not reproduce our results. This lead us to thoroughly investigate this code and we discovered that it offered many different ways to thwart reproducibility that could be explained by round-off error arising from floating-point arithmetic.Numerical reproducibility is considered a task that directly follows from the determinism in computations. However, reproducibility has become an intense concern and and issue for research. In fact, the author developed an series of international workshops on numerical reproducibility and computational reproducibility that is now a regular offering at the annual international supercomputing conferences. We will show how this particular code provides a lack of reproducibility from the following three mechanisms: (i) the introduction of floating-point errors in an inner product; (ii) introduction of floating-point errors at each an increasing number of time steps during temporal refinement (ii); and (iii) differences in the output of library mathematical functions at the level of round-off error. This code’s sensitivity makes it a very powerful tool to explore many different manifestations of numerical reproducibility. However, this code is by no means exceptional, as in neuroscience these types of models are used extensively to gain insights on the functioning of the nervous system. In addition, these types of models are widely used in many other fields of study as they just nonlinear evolution equations.
It is shown any hyperfinite factor has an involutive *-antiautomorphism. It is proved that a real subfactor is irreducible if and only if its enveloping factor is irreducible. Using constructed examples in the complex case, as well as using an involutive *-antiautomorphism of a W*-algebra, examples of irreducible hyperfinite real subfactors with index larger than 4 are constructed.
In this paper, we consider a boundary value problem for a fourth-order differential equation of mixed type with involution and with Hilfer operator of fractional integro-differentiation in a rectangular domain. The mixed type differential equation under consideration is a fourth-order differential equation with respect to the second variable. Regarding the first variable, this equation is a fractional differential equation in the positive part of the segment and is a second-order differential equation in the negative part of the segment. Using the spectral method of separation of variables, the solution of the problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved.
This article describes optimization processes of functions and their solutions using quantum genetic algorithms. These are continuous heuristic optimization methods based on simulated genetic mechanisms, i.e., on dynamic processes in a population such as mutation, crossover, selection, and so on. This process leads to the emergence of a new class called quantum genetic algorithms. In this article, we have presented a discussion of new classes of quantum genetic algorithms, future capabilities, and benefits.
The paper considers the problem of assessing the quality of educational information systems in the context of the digital transformation of society. A method for determining the quality of information systems based on expert assessments is proposed. This approach differs in that it allows one to formalize qualitative assessments of the state of the system using the theory of fuzzy sets. The fuzzy quality assessment models included in the The fuzzy quality assessment models included in the methodology, as well as their corresponding algorithms, allow, on the basis of expert data, to assess the quality of educational information systems at the stage of their development, implementation and use. The implementation of the methodology makes it possible to increase the efficiency of the quality management process of educational information systems and the educational process as a whole.
In the article, using the method of computational experiments on a computer, the influence of the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid on the numerical solutions of a one-dimensional nonlinear problem of heat conduction according to explicit and implicit conservative difference schemes is investigated. The thermal conductivity is a power-law function of temperature.
In the paper, we propose a systematic approach to the development and study of the adequacy of computational models for a mixed dissipative boundary-value problem posed for symmetric t-hyperbolic systems. We consider a three-dimensional linear hyperbolic system with constant coefficients with dissipative boundary conditions. We construct a difference splitting scheme in directions for the numerical calculation of stable solutions for this system.We construct a discrete analogue of the Lyapunov function to study the stability of solutions for the considered problem. We obtain an a priori estimate for this analog, that allows us to state the exponential stability of the numerical solution. Moreover, we prove the theorem on the exponential stability of the solution of a difference splitting scheme for a linear hyperbolic system in Sobolev spaces, which gives us the opportunity to prove the convergence of the numerical solution.
In the paper, we introduce the notion of transversality for Volterra quadratic stochastic operators acting in a finite- dimensional simplex Sm−1 as the positivity condition of all principal minors of an even order of a skew-symmetric matrix A = (aki). We also study a number of properties of transversal operators that are necessary for further research. One can easily note that this definition is equivalent to the classical definition of the transversality of smooth mappings. Further, we also consider the properties of the fixed points charts of transversal operators.
The agriculture sector has been the backbone of economy especially for producing agricultural products, food security, and the employment generation. However, sadly the intake patent for agriculture field in the public university in Malaysia shows the lowest number. Most youths are not interested in agriculture education in university due to their perception that agriculture courses are not as attractive as other courses. This study is aimed at determining the factors influencing the perception towards the agriculture field in high level education among public university students from across the East Coast Region, in Malaysia. Data that were collected through a questionnaire were analysed using descriptive analysis to achieve the aim of the study. The findings demonstrated that attitude was the most significant factor influencing the perception towards agriculture in high level education. Hopefully, this study can help other research to gain the perception of the students towards agriculture in the future.
The mathematical statement of a problem about potential movement of a liquid for dependent variables is given, features of numerical algorithm for the decision of a spatial eaday, the system of the difference equations for potential is offered, the order of calculation of sizes in a single-step method is described, the method of construction of a grid is considered.
In the present paper, using the discrete analogue of the operator d8/dx8 + 2d4/dx4 + 1, an interpolation spline that minimizes the quantity ∫01(φIV(x)+φ(x))2dx in the Hilbert space W2(4,0) is constructed. Explicit formulas for the coefficients of the interpolation spline are obtained. The obtained interpolation spline is exact for the exponential-trigonometric functions e22xcos(22x),e22xsin(22x),e−22xcos(22x)and e−22xsin(22x). At the end of the paper we give some numerical results which confirm our theoretical results.
The pivotal aim of the present work is to obtain analytical and approximate solution for nonlinear time-fractional Swift-Hohenberg equations (FS-HEs) using the conformable residual series method (CRSM). The fractional derivative is proposed within a conformable concept. The proposed method is graceful amalgamations of the conformable residual error functions and generalized Talyor series in the sense of conformable operator. The truncated approximate solution is substituted in the nonlinear fractional model where the conformable derivative to the residual function is equal to zero. The convergence analysis is discussed to show the accuracy and efficiency of the CRSM to obtain approximate solutions for the FS-HEs. Numerical simulation with graphical representation is also given to validate and illustrate the proposed method. The obtained results indicate that the CRS technique is effective, simple, and systematic for analyzing the behavior of nonlinear partial differential equations of fractional order arisen in many areas of physics and science.
The main area of application of various spaces of generalized functions lies in the theory of differential equations and in the theory of quadrature and cubature formulas. Therefore, it becomes necessary to study spaces of generalized functions, one way or another connected with various areas in Rn. The theory of differential equations in the space of generalized functions differs from the theory of these equations in the space of ordinary functions. Deriving these equations and finding their solutions are important in applications. The discrete analogue Dm,n [β] of the polyharmonic operator Δm=(∂2∂x21+∂2∂x22+⋯+∂2∂xn2)m plays an important role in constructing optimal quadrature and cubature formulas in the spaces W2(m)(Rn) and L2(m)(Rn). In the first in the space L2(m)(Rn) by constructing and studying the properties of the inversion of the convolution operator with the function Gm,n [β], where Gm,n (x) - is the fundamental solution of the polyharmonic operator, i.e. properties of such a function of discrete argument Dm,n [β], which satisfies the equality Dm,n[β]*Gm,n[β] = δ[β], where δ [β] is equal to one at β = 0, equal to zero at β ≠ = 0, S.L. Sobolev [1]. The theory of quadrature and cubature formulas was developed in periodic spaces by S.L. Sobolev W˜2(m)(Rn) and L˜2(m)(Rn), and for non-periodic space S.L. Sobolev W2m results are comparatively small. The main goal is that until 2 now in our 2 studies to find the discrete analogue of Dm [β], the fundamental solution Vm(x) was used, but the explicit form of the differential operator, which was Dm [β], was not known. It can be especially noted that the problem of constructing a differential operator and improving the fundamental solution of which, a discrete analogue of this operator Dm [β] is used to find the optimal coefficients of quadrature, cubature and interpolation formulas for a non-periodic space of S.L. Sobolev W2m is actual.
Steganography develops tools and methods for hiding the fact of message transmission. The first traces of stegano-graphic methods are lost in ancient times. From detective works, various methods of secret writing between the lines of ordinary text are well known: from milk to complex chemical reagents with subsequent processing. Digital steganography is based on hid- ing or embedding additional information in digital objects while causing some distortion of these objects. In this case, text, images, audio, video, network packets, and so on can be used as objects or containers. To embed a secret message, steganographic methods rely on redundant container information or properties that the human perception system cannot distinguish. Recently, there has been a lot of progress in hiding information in a text container, since text documents are used in many organizations. Based on this, here the MS Word document is considered as a data carrier, which has various parameters, changing these parameters can achieve data integration. In the same article, we present steganography using invisible Unicode characters of the Space type, but with a different encoding.
We figure out geometric properties of the Julia setJ a of cubic complex polynomialC a(z) =z 3 +az(a ∈ ℂ) and the smallest ellipse which surroundsJ a.
