Hasil untuk "Analytic mechanics"

Sérgio Lopes Resende, Gonçalo Paiva Dias, Pedro Alves Correia

This study explores factors associated with resistance to digital transition in organizations, a phenomenon that has received increasing attention in recent years. While prior research has largely focused on digital transition, this study shifts attention to resistance to that process. A systematic literature review was conducted using Scopus, Web of Science, and Google Scholar to identify factors linked to resistance to change. The findings suggest four broad groups of factors: personal, technical, digital literacy related, and organizational. The study offers a conceptual contribution by proposing a model that brings together variables from established frameworks (TAM and UTAUT) and additional factors discussed in the literature. Future research may examine the relevance of these findings across different contexts.

Amal Mohammed Darweesh, Adel Salim Tayyah, Sarem H. Hadi et al.

In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics.

V. K. Oikonomou

We study a class of minimally coupled scalar field theories which leads to analytic solutions for the Hubble rate and the scalar field, where the scalar field obeys a generalized tracking law $\dotφ^2\sim H^{-m}$. The inflationary phenomenology for this class of models can be studied fully analytically. The resulting phenomenology is compatible with the ACT data and for limiting cases, the spectral index is bluer than the ACT constraints and tends to the value $n_{\mathcal{S}}=0.98$, while in the limiting case, the tensor-to-scalar ratio takes very small values, nearly zero. In addition, we prove analytically that the phenomenology is a one-parameter model, and the inflationary observables encode the scaling exponent $m$ of the generalized kinetic attractor $\dotφ^2\sim H^{-m}$. Furthermore, the tensor-to-scalar ratio and the spectral index have a simple linear and $m$-dependent relation. More importantly, the resulting cosmology describes a Universe that has a finite scale factor at $t=0$, thus non-singular, evolves and expands realizing a slow-roll inflationary era and after that it reaches classically a pressure singularity. Classically, the Universe can pass through this singularity, and a turnaround cosmology is realized with the Universe contracting after the turnaround point. However, before the singularity is realized classically, the quantum phenomena dominate the evolution, avoiding the singularity. Specifically we consider the Nojiri-Odintsov conformal anomaly mechanism and we qualitatively show that the conformal anomaly erases the classical singular evolution and at the same time it enhances particle creation, which eventually reheats the Universe. Thus in this model the scalar field oscillations and the numerous couplings of the inflaton to the Standard Model particles are not required for reheating.

Y.A. Sharifov, A.R. Mammadli

Local boundary value problems for hyperbolic differential equations have been studied in considerable detail. However, the mathematical modeling of a number of real-world processes leads to nonlocal boundary value problems involving nonlinear hyperbolic differential equations, which remain poorly understood. In this paper, we consider a system of hyperbolic equations defined by both point and integral boundary conditions in a rectangular domain. To the best of our knowledge, such a problem is studied here for the first time. We note that this formulation is quite general and encompasses several special cases. The classical Goursat-Darboux problem-a problem with integral boundary conditions in which some boundary conditions are specified as point conditions and others as integral conditions-is derived from this formulation as a particular case. Under natural conditions on the initial data, the necessary conditions for the solvability of a nonlocal boundary value problem are established. A corresponding Green‘s function for the boundary value problem is constructed and the problem is reduced to an equivalent integral equation. Using the principle of contracting Banach maps, conditions for the existence and uniqueness of a solution to the boundary value problem are established. An example is given illustrating the validity of the obtained results.

Margaret Hawton

We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of fields with norm 1 describing physical photons and the Poincare operators are extended to include position to represent observables. A photon continuity equation is derived that describes creation, propagation and annihilation of photons in an optical circuit. The relationship to orthodox quantum mechanics is discussed.

Tao Wang, Yu Shi

We investigate the adiabatic elimination of fast variables in relativistic stochastic mechanics, which is analyzed by using the equation of motion and the distribution function, with relativistic corrections explicitly derived. A new dimensionless parameter is introduced to characterize the timescale. The adiabatic elimination is compared with the path integral coarse graining, which is more general yet computationally demanding.

М.Т. Дженалиев, А.М. Серик

In this work, we introduce a new concept of the stream function and derive the equation for the stream function in the three-dimensional case. To construct a basis in the space of solutions of the NavierStokes system, we solve an auxiliary spectral problem for the bi-Laplacian with Dirichlet conditions on the boundary. Then, using the formulas employed for introducing the stream function, we find a system of functions forming a basis in the space of solutions of the Navier-Stokes system. It is worth noting that this basis can be utilized for the approximate solution of direct and inverse problems for the Navier-Stokes system, both in its linearized and nonlinear forms. The main idea of this work can be summarized as follows: instead of changing the boundary conditions (which remain unchanged), we change the differential equations for the stream function with a spectral parameter. As a result, we obtain a spectral problem for the bi-Laplacian in the domain represented by a three-dimensional unit sphere, with Dirichlet conditions on the boundary of the domain. By solving this problem, we find a system of eigenfunctions forming a basis in the space of solutions to the Navier-Stokes equations. Importantly, the boundary conditions are preserved, and the continuity equation for the fluid is satisfied. It is also noteworthy that, for the three-dimensional case of the Navier-Stokes system, an analogue of the stream function was previously unknown.

Ariel Rapaport

We extend Hochman's work on exponentially separated self-similar measures on $\mathbb{R}$ to the real analytic setting. More precisely, let $Φ=\left\{ \varphi_{i}\right\} _{i\inΛ}$ be an iterated function system on $I:=[0,1]$ consisting of real analytic contractions, let $p=(p_{i})_{i\inΛ}$ be a positive probability vector, and let $μ$ be the associated self-conformal measure. Suppose that the maps in $Φ$ do not have a common fixed point, $0<\left|\varphi_{i}'(x)\right|<1$ for $i\inΛ$ and $x\in I$, and $Φ$ is exponentially separated. Under these assumptions, we prove that $\dimμ=\min\left\{ 1,H(p)/χ\right\} $, where $H(p)$ is the entropy of $p$ and $χ$ is the Lyapunov exponent. The main novelty of our work lies in an argument that reduces convolutions of $μ$ with measures on the (infinite-dimensional) space of real analytic maps to convolutions with measures on vector spaces of polynomials of bounded degree. The reason for this reduction is that, for the latter convolutions, we can establish an entropy increase result, which plays a crucial role in the proof. We believe that our proof strategy has the potential to extend other significant recent results in the dimension theory of stationary fractal measures to the real analytic setting.

A.R. Yeshkeyev, A.R. Yarullina, S.M. Amanbekov

The article is devoted to the study of semantic Jonsson quasivarieties of universal unars and undirected graphs. The first section of the article consists of basic necessary concepts from Jonsson model theory. The following two sections are results of using new notions of semantic Jonsson quasivariety of Robinson unars JCU and semantic Jonsson quasivariety of Robinson undirected graphs JCG, its elementary theory and semantic model. In order to prove two main results of the paper, Robinson spectra RSp(JCU) and RSp(JCG) and their partition onto equivalence classes [∆]U and [∆]G by cosemanticness relation were considered. The main results are presented in the form of theorems 11 and 13 and imply following useful corollaries: countably categorical Robinson theories of unars are totally categorical; countably categorical Robinson theories of undirected graphs are totally categorical. The obtained results can be useful for continuation of the various Jonsson algebras’ research, particularly semantic Jonsson quasivariety of S-acts over cyclic monoid.

K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov et al.

In this paper the Ginzburg-Landau equation is considered in locally periodic porous medium, with rapidly oscillating terms in the equation and boundary conditions. It is proved that the trajectory attractors of this equation converge in a weak sense to the trajectory attractors of the limit Ginzburg-Landau equation with an additional potential term. For this aim we use an approach from the papers and monographs of V.V. Chepyzhov and M.I. Vishik concerning trajectory attractors of evolution equations. Also we apply homogenization methods appeared at the end of the XX-th century. First, we apply the asymptotic methods for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional spaces with weak topology, we derive the limit (homogenized) equation and prove the existence of trajectory attractors for this equation. Then we formulate the main theorem and prove it with the help of axillary lemmas.

Huy T. Q. Phan, Duc M. Bui, Cong T. Than et al.

Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how the geometries of fractals can be exploited to determine their important mechanical properties, such as the first and second moments, which physically correspond to the center of mass and the moment of inertia, using a family of complex fractals known as the dragons.

Pavel Etingof, Edward Frenkel, David Kazhdan

We discuss a general framework for the analytic Langlands correspondence over an arbitrary local field F introduced and studied in our works arXiv:1908.09677, arXiv:2103.01509 and arXiv:2106.05243, in particular including non-split and twisted settings. Then we specialize to the archimedean cases (F=C and F=R) and give a (mostly conjectural) description of the spectrum of the Hecke operators in various cases in terms of opers satisfying suitable reality conditions, as predicted in part in arXiv:2103.01509, arXiv:2106.05243 and arXiv:2107.01732. We also describe an analogue of the Langlands functoriality principle in the analytic Langlands correspondence over C and show that it is compatible with the results and conjectures of arXiv:2103.01509. Finally, we apply the tools of the analytic Langlands correspondence over archimedean fields in genus zero to the Gaudin model and its generalizations, as well as their q-deformations.

Anton Jeran Ratnarajah, Sahani Goonetilleke, Dumindu Tissera et al.

Law enforcement officials heavily depend on Forensic Video Analytic (FVA) Software in their evidence extraction process. However present-day FVA software are complex, time consuming, equipment dependent and expensive. Developing countries struggle to gain access to this gateway to a secure haven. The term forensic pertains the application of scientific methods to the investigation of crime through post-processing, whereas surveillance is the close monitoring of real-time feeds. The principle objective of this Final Year Project was to develop an efficient and effective FVA Software, addressing the shortcomings through a stringent and systematic review of scholarly research papers, online databases and legal documentation. The scope spans multiple object detection, multiple object tracking, anomaly detection, activity recognition, tampering detection, general and specific image enhancement and video synopsis. Methods employed include many machine learning techniques, GPU acceleration and efficient, integrated architecture development both for real-time and postprocessing. For this CNN, GMM, multithreading and OpenCV C++ coding were used. The implications of the proposed methodology would rapidly speed up the FVA process especially through the novel video synopsis research arena. This project has resulted in three research outcomes Moving Object Based Collision Free Video Synopsis, Forensic and Surveillance Analytic Tool Architecture and Tampering Detection Inter-Frame Forgery. The results include forensic and surveillance panel outcomes with emphasis on video synopsis and Sri Lankan context. Principal conclusions include the optimization and efficient algorithm integration to overcome limitations in processing power, memory and compromise between real-time performance and accuracy.

P. E. Brandyshev, Yu. A. Budkov

In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether's first theorem for the case of fluctuating order parameter, to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and the fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects local stresses in a nonuniform Coulomb fluid. We also use previously formulated general covariant methodology [P.E. Brandyshev and Yu.A. Budkov, J. Chem. Phys. 158, 174114 (2023)] in conjunction with a functional Legendre transformation method and derive within it the same total stress tensor. We would like to emphasize that our general approaches are applicable not only to Coulomb fluids but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a functional of the relevant scalar order parameters.

Kenric P. Nelson

Nonextensive Statistical Mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. Upon the 80th birthday of the field's founder, Constantino Tsallis, a review of open problems that can stimulate future research is provided. Over the thirty-year development of NSM a variety of criticisms have been published ranging from questions about the justification for generalizing the entropy function to interpretation of the generalizing parameter q. While these criticisms have been addressed in the past and the breadth of applications has demonstrated the utility of the NSM methodologies, this review provides insights on how the field can continue to improve the understanding and application of complex system models. The review starts by grounding q-statistics within scale-shape distributions and then frames a series of open problems for investigation. The open problems include using the degree of freedom to quantify the difference between entropy and its generalization; clarifying the physical interpretation of the parameter q; improving the definition of the generalized product using multidimensional analysis; defining a generalized Fourier transform applicable to signal processing applications; and re-examination of the normalization of nonextensive entropy. The review concludes with a proposal that the shape parameter is a candidate for defining the statistical complexity of a system.

R.R. Ashurov, Yu.E. Fayziev

Initial boundary value problems with a time-nonlocal condition for a subdiffusion equation with the Riemann-Liouville time-fractional derivatives are considered. The elliptical part of the equation is the Laplace operator, defined in an arbitrary N−dimensional domain Ω with a sufficiently smooth boundary ∂Ω. The existence and uniqueness of the solution to the considered problems are proved. Inverse problems are studied for determining the right-hand side of the equation and a function in a time-nonlocal condition. The main research tool is the Fourier method, so the obtained results can be extended to subdiffusion equations with a more general elliptic operator.

T.K. Yuldashev, B.J. Kadirkulov, Kh.R. Mamedov

In three-dimensional domain, an identification problem of the source function for Hilfer type partial differential equation of the even order with a condition in an integral form and with a small positive parameter in the mixed derivative is considered. The solution of this fractional differential equation of a higher order is studied in the class of regular functions. The case, when the order of fractional operator is 0 <α< 1, is studied. The Fourier series method is used and a countable system of ordinary differential equations is obtained. The nonlocal boundary value problem is integrated as an ordinary differential equation. By the aid of given additional condition, we obtained the representation for redefinition (source) function. Using the Cauchy-Schwarz inequality and the Bessel inequality, we proved the absolute and uniform convergence of the obtained Fourier series.

A.T. Kasimov, G.A. Yessenbayeva, B.A. Kasimov et al.

In the article, an analytical and numerical study based on one modified refined bending theory is presented. By the finite difference method, a general numerical calculation algorithm is developed. The solution obtained by the proposed method is compared with the results of known solutions, namely, with the solution of the classical theory, the exact solution, the solution in trigonometric series, as well as with experimental data. Comparison of the results obtained by the method given in the article with the solutions determined by other methods shows sufficient accuracy, which indicates the reliability of the proposed method based on one option of the modified refined bending theory. Classical theory is not applicable to such problems under consideration.

Serhii Shuklinov, Anatoly Uzhva, Mikhail Lysenko et al.

Problem. The disadvantage of current dependences for determining the acceleration indicators at engine maximum brake power and driving tire-to-surface friction coefficients is that they are adequate only if the engine and transmission parameters provide power input to the drive wheels rolling without slipping regardless to speed. To eliminate this drawback, it is necessary to take into account that the power input to the drive wheels depends on the engine shaft speed, and therefore on the speed of the vehicle when accelerating. Goal. The purpose of the work is to further develop the theory of the automobile by improving the dependencies that allow determining the automobile acceleration rates and assessing the nature of its acceleration process from the design factors. Methodology. The approaches taken to achieve this goal are based on laws of physics, theoretical mechanics and the theory of automobile. Results. Analytic dependences for determining maximum and limiting automobile acceleration when speeding up depending on its design factors and speed have been improved. Dependences for determining the range of drive wheel slipping on the automobile speed when accelerating and the limiting automobile acceleration under the condition of its pitch stability have been obtained. When studying the automobile acceleration process theoretically it was found that the developed dependences allow determining the nature of automobile movement and assessing the influence of its design factors on the acceleration indicators. Originality. The obtained dependences for determining the maximum and limiting acceleration, the range of driving speeds with wheel slip when automobile accelerating allowed us to clarify the idea of the nature of movement during acceleration and the influence of automobile design factors on the acceleration indicators. Practical value. The obtained dependences can be used in designing new and improving racing cars such as dragsters, and analysing the dynamics of the vehicle when accelerating with full fuel delivery and determining the nature of driving tire-to-surface friction depending on the driving speed.