scholarly journals On the Solvability of a Class of Nonlinear Urysohn Integral Equations on the Positive Half-line

2021 ◽  
Vol 36 ◽  
pp. 57-68
Author(s):  
Kh.A. Khachatryan ◽  
◽  
H.S. Petrosyan ◽  
◽  
◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Spectral Lines ◽  
Half Line ◽  
Bounded Solutions ◽  
Qualitative Properties ◽  
Urysohn Integral Equations ◽  
Modern Natural ◽  
Special Cases ◽  
Modern Natural Science ◽  
Positive Half

The paper investigates the Urysohn’s nonlinear integral equation on the positive half-line. Some special cases of this equation have specific applications in different areas of modern natural science. In particular, such equations arise in the kinetic theory of gases, in the theory of 𝑝-adic open-closed strings, in mathematical theory of the spatiotemporal spread of the epidemic, and in theory of radiative transfer in spectral lines. The existence theorem for nonnegative nontrivial and bounded solutions is proved. Some qualitative properties of the constructed solution are studied. Specific applied examples of the Urysohn’s kernel satisfying all the conditions of the approved theorem are provided.

scholarly journals On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of p-adic strings

2020 ◽  
Vol 16 (4) ◽  
pp. 423-436
Author(s):  
Khachatur A. Khachatryan ◽  
◽  
Haykanush S. Petrosyan ◽  
◽  
◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Dynamic Theory ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Half Line ◽  
Qualitative Properties ◽  
Bounded Functions ◽  
The Difference ◽  
Total Difference ◽  
Positive Half

The article considers a boundary value problem for a class of singular integral equations with an almost total-difference kernel and convex nonlinearity on the positive half-line. This problem arises in the dynamic theory of p-adic open-closed strings. It is proved that any nonnegative and bounded solution of a given boundary value problem is a continuous function and the difference between the limit and the solution is itself an integrable function on the positive half-line. For a particular case, it is proved that the solution is a monotonically non-decreasing function. A uniqueness theorem is established in the class of nonnegative and bounded functions. At the conclusion of the article, a specific applied example of this boundary problem is given.

WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE

2013 ◽  
Vol 06 (01) ◽  
pp. 1350007 ◽  
Author(s):  
Vikram Sharma ◽  
P. Manchanda
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packets ◽  
Half Line ◽  
State University ◽  
Spectral Pairs ◽  
Funct Anal ◽  
Positive Half

Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

scholarly journals Further Results about Seeking for the Exact Solutions of the Nonlinear 2 + 1 -Dimensional Jaulent-Miodek Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jingsen Hu ◽  
Jianming Qi
Keyword(s):  
Nonlinear Equation ◽  
Exact Solutions ◽  
Nonlinear Equations ◽  
Natural Science ◽  
Expansion Method ◽  
Advantages And Disadvantages ◽  
Modern Natural ◽  
Modern Natural Science ◽  
Nonlinear Science ◽  
Formula Method

Nonlinear science is a great revolution of modern natural science. As a result of its rise, the various branches of subjects characterized by nonlinearity have been developed vigorously. In particular, more attention to acquiring the exact solutions of a wide variety of nonlinear equations has been paid by people. In this paper, three methods for solving the exact solutions of the nonlinear 2 + 1 -dimensional Jaulent-Miodek equation are introduced in detail. First of all, the exact solutions of this nonlinear equation are obtained by using the exp − ϕ z -expansion method, tanh method, and sine-cosine method. Secondly, the relevant results are verified and simulated by using Maple software. Finally, the advantages and disadvantages of the above three methods listed in the paper are analyzed, and the conclusion was drawn by us. These methods are straightforward and concise in very easier ways.

scholarly journals Asymptotic solution of Sturm-Liouville problem with periodic boundary conditions for relativistic finite-difference Schrödinger equation

2020 ◽  
Vol 28 (3) ◽  
pp. 230-251
Author(s):  
Ilkizar V. Amirkhanov ◽  
Irina S. Kolosova ◽  
Sergey A. Vasilyev
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Asymptotic Series ◽  
Periodic Boundary Conditions ◽  
Singularly Perturbed ◽  
Half Line ◽  
Asymptotic Convergence ◽  
Relativistic Particles ◽  
Positive Half

The quasi-potential approach is very famous in modern relativistic particles physics. This approach is based on the so-called covariant single-time formulation of quantum field theory in which the dynamics of fields and particles is described on a space-like three-dimensional hypersurface in the Minkowski space. Special attention in this approach is paid to methods for constructing various quasi-potentials. The quasipotentials allow to describe the characteristics of relativistic particles interactions in quark models such as amplitudes of hadron elastic scatterings, mass spectra, widths of meson decays and cross sections of deep inelastic scatterings of leptons on hadrons. In this paper SturmLiouville problems with periodic boundary conditions on a segment and a positive half-line for the 2m-order truncated relativistic finite-difference Schrdinger equation (LogunovTavkhelidzeKadyshevsky equation, LTKT-equation) with a small parameter are considered. A method for constructing of asymptotic eigenfunctions and eigenvalues in the form of asymptotic series for singularly perturbed SturmLiouville problems with periodic boundary conditions is proposed. It is assumed that eigenfunctions have regular and boundary-layer components. This method is a generalization of asymptotic methods that were proposed in the works of A. N. Tikhonov, A. B. Vasilyeva, and V. F Butuzov. We present proof of theorems that can be used to evaluate the asymptotic convergence for singularly perturbed problems solutions to solutions of degenerate problems when 0 and the asymptotic convergence of truncation equation solutions in the case m. In addition, the SturmLiouville problem on the positive half-line with a periodic boundary conditions for the quantum harmonic oscillator is considered. Eigenfunctions and eigenvalues are constructed for this problem as asymptotic solutions for 4-order LTKT-equation.

H. COLLINS'S PROJECT FOR DEVELOPING A RELATIVISTIC EMPIRICAL PROGRAMME IN SOCIOLOGY OF SCIENCE

2020 ◽  
pp. 40-44
Author(s):  
Nadezhda Nikolina
Keyword(s):  
Scientific Knowledge ◽  
Natural Science ◽  
Sociology Of Science ◽  
Main Idea ◽  
Special Role ◽  
Special Issue ◽  
Modern Natural ◽  
Modern Natural Science ◽  
Experimental Process ◽  
Issue Knowledge

The main idea of the project discussed in the article is that the production of scientific knowledge is not only an experimental process. Convention among scientists is played a special role in the acceptance of theory. To demon-strate this idea, H. Collins and co-authors of the relativistic empirical programme in the sociology of science publish a special issue “Knowledge and Controversy: Studies of Modern Natural Science”. The results obtained by the authors are discussed in this article.

The Materialism Controversy

After Hegel ◽  
2014 ◽  
Author(s):  
Frederick C. Beiser
Keyword(s):  
Nineteenth Century ◽  
Shock Waves ◽  
Free Will ◽  
Natural Science ◽  
Main Question ◽  
Modern Natural ◽  
Modern Natural Science ◽  
Scientific Materialism ◽  
Reason And Faith

This chapter examines the so-called “materialism controversy,” one of the most important intellectual disputes of the second half of the nineteenth century. The dispute began in the 1850s, and its shock waves reverberated until the end of the century. The main question posed by the materialism controversy was whether modern natural science, whose authority and prestige were now beyond question, necessarily leads to materialism. Materialism was generally understood to be the doctrine that only matter exists and that everything in nature obeys only mechanical laws. If such a doctrine were true, it seemed there could be no God, no free will, no soul, and hence no immortality. These beliefs, however, seemed vital to morality and religion. So the controversy posed a drastic dilemma: either a scientific materialism or a moral and religious “leap of faith.” It was the latest version of the old conflict between reason and faith, where now the role of reason was played by natural science.

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