This paper focuses on the integrability properties of the negative-order nonlinear Schro¨dinger equation with a source. The source consists of the combination of the eigenfunctions of the corresponding spectral problem for the Dirac system which has not spectral singularities. The connection between the negative-order nonlinear Schro¨dinger equation with a self-consistent source and the Dirac system of equations is crucial, as it allows the complex dynamics of the original nonlinear model to be interpreted through the spectral theory of the Dirac operator. Building on this relationship, the evolution equations for the scattering data of the Dirac operator are derived, which is the central part in the inverse scattering transform (IST) framework. Due to the IST procedure, the rapidly decaying potential of the Dirac operator can be reconstructed from the derived differential equations for the scattering data, and this potential corresponds precisely to the solution of the problem under consideration. To illustrate the practical value of the theoretical results, the paper presents a detailed example demonstrating each stage of the method, from the formulation of the scattering data to the final reconstruction of the potential. This example clarifies the overall procedure and highlights the effectiveness of the approach in concrete applications.
We develop original flow-based methods to interrogate and manipulate out-of-equilibrium behaviour of ternary fluids systems at the small scale. In particular, we examine droplet and jet formation of ternary fluid systems in coaxial microchannels when an aqueous phase is injected into a solvent-rich oil phase using common fluids, such as ethanol for the aqueous phase, silicone oil for the oil phase and isopropanol for the solvent. Alcohols are often employed to impart oil and water properties with a myriad of practical uses as extractants, antiseptics, wetting agents, emulsifiers or biofuels. Here, we systematically examine the role of alcohol solvents on the hydrodynamic stability of aqueous–oil multiphase flows in square microchannels. Broad variations of flow rates and solvent concentration reveal a variety of intriguing droplet and jet flow regimes in the presence of spontaneous emulsification phenomena and significant mass transfer across the fluid interface. Typical flow patterns include dripping and jetting droplets, phase inversion and dynamic wetting and conjugate jets. Functional relationships are developed to model the evolution of multiphase flow characteristics with solvent concentration. This work provides insights into complex natural phenomena relevant to the application of microfluidic droplet systems to chemical assays as well as fluid measurement and characterisation technologies.
In this paper, the solvability of initial-boundary value problems for a nonlocal analogue of a hyperbolic equation in a cylindrical domain is studied. The elliptic part of the considered equation involves a nonlocal Laplace operator, which is introduced using involution-type mappings. Two types of boundary conditions are considered. These conditions are specified as a relationship between the values of the unknown function at points in one half of the lateral part of the cylinder and the values at points in the other part of the cylinder boundary. The boundary conditions specified in this form generalize known periodic and antiperiodic boundary conditions for circular domains. The unknown function is represented in the form u(x) = v(x)+w(x), where v(x) is the even part of the function and w(x) is the odd part of the function with respect to the mapping. Using the properties of these functions, we obtain auxiliary initial-boundary value problems with classical hyperbolic equations. In this case, the boundary conditions of these problems are specified in the form of the Dirichlet and Neumann conditions. Further, using the known assertions for the auxiliary problems, theorems on the existence and uniqueness of the solution to the main problems are proved. The solutions to the problems are constructed as a series in systems of eigenfunctions of the Dirichlet and Neumann problems for the classical Laplace operator.
The article is devoted to the study of a singularly perturbed initial problem for a linear differential equation with a piecewise constant argument second-order for a small parameter. This paper is considered the asymptotic expansion of the solution to the Cauchy problem for singularly perturbed differential equations with piecewise-constant argument. The initial value problem for first order linear differential equations with piecewise-constant argument was obtained that determined the regular members. The Cauchy problems for linear nonhomogeneous differential equations with a constant coefficient were obtained, which determined the boundary layer terms. An asymptotic estimate for the remainder term of the solution of the Cauchy problem was obtained. Using the remainder term, we construct a uniform asymptotic solution with accuracy O(εN+1) on the θi ≤ t ≤ θi+1, i = 0, p segment of the singularly perturbed Cauchy problem with a piecewise constant argument.
Ebrahem A. Algehyne, Abdelhalim Ebaid, Essam R. El-Zahar
et al.
The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein’s famous equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>=</mo><mfrac><msub><mi>m</mi><mn>0</mn></msub><msqrt><mrow><mn>1</mn><mo>−</mo><msup><mi>v</mi><mn>2</mn></msup><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> is the rest mass of the projectile and <i>c</i> is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to <i>c</i>. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>π</mi><mo>/</mo><mn>4</mn></mrow></semantics></math></inline-formula>. In addition, this angle lies in a certain interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mi>π</mi><mo>/</mo><mn>4</mn><mo>,</mo><mi>π</mi><mo>/</mo><mn>6</mn><mo>)</mo></mrow></semantics></math></inline-formula> for any given initial velocity (<<i>c</i>). The obtained results are discussed and interpreted. Comparisons with a similar problem in the literature are performed and the differences in results are explained.
Soft topological polygroups are defined in two different ways. First, it is defined as a usual topology. In the usual topology, there are five equivalent definitions for continuity, but not all of them are necessarily established in soft continuity. Second it is defined as a soft topology including concepts such as soft neighborhood, soft continuity, soft compact, soft connected, soft Hausdorff space and their relationship with soft continuous functions in soft topological polygroups.
Abstract We consider a class of tripartite systems for which two d-dimensional QFTs are cross-coupled via a third d + 1-dimensional “messenger” QFT. We analyse in detail the example of a pair of one-dimensional matrix quantum mechanics) coupled via a twodimensional theory of the BF-type and compute its partition function and simple correlators. This construction is extendible in higher dimensions) using a Chern-Simons “messenger” theory. In all such examples, the exact partition function acquires a form, speculated to correspond to systems dual to Euclidean wormholes and the cross correlators are sufficiently soft and consistent with analogous gravitational calculations. Another variant of the tripartite system is studied, where the messenger theory is described by a non-self-interacting (matrix)-field, reaching similar conclusions. While the Euclidean theories we consider are perfectly consistent, the two possible analytic continuations into Lorentzian signature (messenger vs. boundary QFT directions) of the tripartite models, reveal physical features and “pathologies” resembling those of the expected Lorentzian gravitational backgrounds.
Nuclear and particle physics. Atomic energy. Radioactivity
The study considers the solvability of a mixed problem for a Hilfer type partial differential equation of the even order with initial value conditions and small positive parameters in mixed derivatives in threedimensional domain. It studies the solution to this fractional differential equation of higher order in the class of regular functions. The case, when the order of fractional operator is 1 <α< 2, is examined. During this study the authors use the Fourier series method and obtain a countable system of ordinary differential equations. The initial value problem is integrated as an ordinary differential equation and the integrated constants find by the aid of given initial value conditions. Using the Cauchy-Schwarz inequality and the Bessel inequality, it is proved the absolute and uniform convergence of the obtained Fourier series. The stability of the solution to the mixed problem on the given functions is studied.
On January 25, 2022, a well-known specialist in the field of the theory of partial differential equations and its applications, Chief Researcher of the Institute of Mathematics and Mathematical Modeling of the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan, Doctor of Physical and Mathematical Sciences, Professor Muvasharkhan Tanabaevich Jenaliyev, turned 75 years old.
Mohammad Fahiminia, Hossein Jafari Mansoorian, Akbar Eskandari
et al.
Background and Objective: Visual pollution is one of the important components of the man-made environment in urban spaces. The purpose of this research was to investigate the visual pollution of workshops in Qom city using Expert Choice software and then the occupational ranking was done in terms of visual pollution.
Materials and Methods: This study was a descriptive-analytic cross-sectional study conducted in 670 trade units associated with 67 urban trade unions. The data collection tools were local visits, database preparation and completion of a questionnaire based on urban-environmental aesthetic criteria. The purpose of this study was to investigate the visual pollution caused by the occupations and workshops of Qom.
Results: The results showed that, in terms of total visual pollution, the units of oil changes with a total score of 1, materials and construction materials with 0.988, Smoothies with 0.980, Mechanics with 0.973, ceramic makers with 0.944, Chips and grills with 0.933, mosaics with 0.914, carwash with 0.885, stones cutting with 0.872, carpet with 0.870, trowel and blacksmiths with 0.857, burners with 0.830, battery makers with 0.825, iron manufacturers with 0.872 and manufacturers of general blinds and blinds with 0.753 were inadequate.
Conclusions: In order to reduce the number of visually impaired businesses in the short term, continuous inspections of businesses must be undertaken and, in the long run, by organizing the program, the polluting industries must be transferred out of the city.
The importance of energy-saving and correct design is obvious for energy efficiency. Correct design means that before construction considerable things, such as orientation or isolation decisions, need to be made. This study gives a mathematical model of the nonstationary energy consumption calculation problems. The model is well-posedness in Holder spaces of the mixed one-dimensional parabolic problem with Robin boundary conditions. In this study, an effective numerical method is also developed for energy consumption calculation which is related to this mathematical model. The three case problems are taken to test this numerical method. The dynamic model results have been compared with the previous finite-difference or steady-state solutions. The study also aims to develop a mathematical model in which the result can be found at any time.
The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau–Ginzburg kinetic equation that becomes a generic one-dimensional nonlinear iteration map for discrete time. We focus on the Renormalization Group (RG) fixed-point maps for the three routes to chaos. We show that all fixed-point maps and their trajectories have analytic closed-form expressions, not only (as known) for the intermittency route to chaos but also for the period-doubling and the quasiperiodic routes. These expressions have the form of <i>q</i>-exponentials, while the kinetic equation’s Lyapunov function becomes the Tsallis entropy. That is, all processes described by the evolution of the fixed-point trajectories are accompanied by the monotonic progress of the Tsallis entropy. In all cases the action of the fixed-point map attractor imposes a severe impediment to access the system’s built-in configurations, leaving only a subset of vanishing measure available. Only those attractors that remain chaotic have ineffective configuration set reduction and display ordinary statistical mechanics. Finally, we provide a brief description of complex system research subjects that illustrates the applicability of our approach.
This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.
Heppy Ridhatul Aula, Dewi Kurniasih, Farizi Rachman
Introduction: A steam power plant company is an electric energy production company, utilizing main energy sources such as coal, biomass, and other energies that are related to production process. This company is a big industry that operates 24 hours and have many various steps of production process. It is also supported by a variety of high-risk system equipment such as confined spaces, working at height, hot work, ergonomics, mechanics, and others. This type of work can lead to workers’ unsafe conditions and unsafe acts. One of the causes is the psychological aspects of workers, namely the lack of workers’ awareness and understanding in implementing occupational safety aspects. Workers’ psychology in this study is Psychological Capital (PsyCap) with self-efficacy, hope, optimism, and resilience dimensions. This study aims to analyze PsyCap impacts on safety behavior of contractor workers. Methods: this study was an observational analytic research using cross-sectional approach. The population was all workers in a steam power plant company in units 7&8, totalling 400 contractors. This study was conducted by distributing questionnaires to 101 respondents of contractor workers. The questionnaires consisted of items about self-efficacy, hope, optimism, and resilience dimension of PsyCap and safety compliance and safety participation dimension of safety behavior. The analysis used a Structural Equational Modeling (SEM) method and AMOS software. Results: PsyCap dimensions that impacted on safety behavior was optimism. Conclusion: optimism dimension was the factor that had the strongest impact on safety behavior especially workers’ safety compliance. Meanwhile, other PsyCap dimensions which did not have not impact on safety behavior were safety compliance and safety participation dimensions.
Keywords: contractor worker, psychological capital, safety behavior, steam power plant company, structural equational modelling
This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a serrated leading edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a modal expansion in the spanwise coordinate; however, for low- and mid-range incident frequencies only the zeroth-order mode is seen to contribute to the far-field acoustics, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated leading edges compared to those with straight edges, and predicts a logarithmic dependence between the tip-to-root serration height and the decrease of far-field noise. The two mechanisms behind the noise reduction are proposed to be an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes as the tip-to-root serration height is increased. The analytic results show good agreement in comparison with experimental measurements. The results are also compared against nonlinear numerical predictions where good agreement is also seen between the two results as frequency and tip-to-root ratio are varied.
We pose and investigate the first boundary value problem using a model second order equation of parabolic - hyperbolic type with A.M. Nakhushev’s conditions violated relative to coefficients. Despite these conditions are violated an a priori estimate similar to the a priori estimate obtained by A.M. Nakhushev takes place for solving the first boundary - value problem under study.
In this paper we consider the eigenvalue problem for the Cauchy - Riemann operator with homogeneous Dirichlet type boundary conditions. The statement of the problem is justified to the theorem of M. Otelbaev and A.N. Shynybekov, which implies the correctness of the considered problem. As an example, non - local boundary conditions and Bitsadze - Samarskii type boundary conditions are given. It is taken into account that the above spectral problem for a differential Cauchy - Riemann operator with homogeneous boundary conditions of the Dirichlet type type is reduced to a singular integral, also reduces to a linear integral equation of the second kind with a continuous kernel. And it is also taken into account that the index of the singular integral equation is zero and the Noetherian condition is obtain. It is proved that the considered spectral problem does not have eigenvalues, that is, for any complex ?, has only the zero solution and thus the Cauchy - Riemann spectral problem is a Volterra problem.
The aim of the study is to develop an algorithm for constructing an integer random variable representing
random components of the keys of the RSA cryptosystem, and determining the table for the distribution
of its probabilities. The constructed random variable can be used to estimate the hypothesis that a given
generator generates its values with the same probability with which a random variable takes these values.
A hypothesis testing algorithm is provided, which is accompanied by a calculation table for a uniformly
distributed random variable that takes primes from a given half-open interval.
In article considered the problem of curved rod fluctuation with Jungs module. Shown the civility of the problem formulation. For solution used integro - interpolation method. Constructed implicit differential scheme, which realized by five - point sweep method. Conducted numerical calculations showed coincidence of theoretical calculation values of solution. Calculations conducted on the system of computer algebra Wolfram Mathematica. Results of calculations are given for two cases of fixing ends of the rod: both ends are fixed and one end is fixed other is free.
The article presents the calculation of rectangular plates by a variational method. For considered rectangular plate the research was conducted by the equilibrium conditions of the elementary strip isolated from the plate, by the method that was used in the works of V.Z.Vlasov. To illustrate the above variational method were given specific examples of the calculation of a square plate, hinged along the contour and loaded equally by distributed loading of given intensity, as well as a square plate, rigidly clamped along the contour. A comparative analysis of the results was carried out.