Description

Journal of AppliedMath (JAM, eISSN: 2972-4805) is an international, peer-reviewed open access journal that is dedicated to the publication of high-quality research in the field of mathematics. With a commitment to excellence and innovation, JAM provides a platform for mathematicians, scientists, and engineers to share their findings and insights across a broad spectrum of applied mathematical disciplines. It publishes various article types including Original Research Articles, Reviews, Editorials, and Perspectives. Our aim is to encourage scientists to publish their experimental and theoretical results in as much detail as possible. There is no restriction on the length of the papers. At JAM, we believe that thorough research deserves comprehensive presentation. Therefore, we require that the full account of the research be provided, enabling other researchers to reproduce the results. 

JAM is committed to advancing the frontiers of applied mathematics and looks forward to contributing to the global scientific discourse. 

Latest Articles

  • Open Access

    Article

    Article ID: 1592

    Background seismicity and seismic correlations

    by Bogdan Felix Apostol

    Journal of AppliedMath, Vol.3, No.1, 2025;

    The law of energy accumulation in the earthquake focus is presented, together with the temporal, energy and magnitude distributions of regular, background earthquakes. The background seismicity is characterized by two parameters—the seismicity rate and the Gutenberg-Richter parameter, which can be extracted by fitting the empirical earthquake distributions. Time-magnitude and temporal correlations are presented, and the information they can provide is discussed. For foreshocks the time-magnitude correlations can be used to forecast (with limitations) the mainshock. The temporal correlations indicate a decrease of the Gutenberg-Richter parameter for small magnitudes, in agreement with empirical observations for foreshocks. On the other hand, the aftershocks may be viewed as independent earthquakes with changed seismic conditions, so they may exhibit an increase of this parameter, also in accordance with empirical observations. The roll-off effect for small magnitudes and the modified Gutenberg-Richter distribution are discussed for temporal corralations, and the derivation of the Bath’s law is briefly reviewed.

    show more
  • Open Access

    Article

    Article ID: 2043

    A water wave scattering problem: Revisited

    by Gour Das, Sudeshna Banerjea, B. N. Mandal

    Journal of AppliedMath, Vol.2, No.6, 2024;

    The problem of water wave scattering by a thin vertical wall with a gap submerged in deep water is studied using singular integral equation formulation. The corresponding boundary value problem is reduced to a Cauchy type singular integral equation of first kind in two disjoint intervals where the unknown function satisfying the integral equation has square root zero at the end points of the two intervals. In this case the solution exists if the forcing function satisfies two solvability conditions. The reflection coefficient is determined here using the solvability conditions without solving the integral equation and also the boundary value problem.

    show more
  • Open Access

    Article

    Article ID: 2209

    Multistability and organization of chaos and quasiperiodicity in a memristor-based Shimizu-Morioka oscillator under two-frequency excitation

    by Paulo Cesar Rech

    Journal of AppliedMath, Vol.2, No.6, 2024;

    In this paper we investigate the organization of chaos and quasiperiodicity in a parameter plane of a continuous-time three-dimensional nonautonomous dynamical system. More specifically, we investigate a memristor-based Shimizu-Morioka oscillator, where the external excitation is represented by the sum of two different sinusoidal functions with angular frequencies ω1 and ω2. Through a scan carried out in the (ω1, ω2) parameter plane, with the dynamical behavior of each point in the phase-space being characterized by the Lyapunov exponents spectrum, we show that this system presents chaos and quasiperiodicity regions, without presenting, however, periodicity regions. Parameter regions for which the multistability phenomenon was detected, also are observed. Basins of attraction of coexisting chaotic and quasiperiodic attractors, as well as the attractors themselves, are reported.

    show more
  • Open Access

    Article

    Article ID: 2152

    Distribution of lattice points in the shifted balls

    by Ilgar Jabbarov, Jeyhun Abdullayev

    Journal of AppliedMath, Vol.2, No.6, 2024;

    In this work we study the mean value of the difference between the number of integer points and the volume of a ball as a function of the center of a ball in the unit cube [0, 1]3, applying new method. This mean value is estimated by its possible exact value. Using methods of Fourier analysis, we lead the question to the estimates of double trigonometric integrals. This method allows consider the question on lattice points in domains of arbitrary nature without any symmetry.

    show more
  • Open Access

    Article

    Article ID: 1593

    Site effects in seismic motion

    by Bogdan Felix Apostol

    Journal of AppliedMath, Vol.2, No.6, 2024;

    We use the harmonic-oscillator model to analyze the motion of the sites (ground motion), seimograph recordings, and structures built on the Earth’s surface under the action of the seismic motion. The seismic motion consists of singular waves (spherical-shell P and S primary seismic waves) and discontinuous (step-wise) seismic main shocks. It is shown that these singularities and discontinuities are present in the ground motion, seismographs’ recordings and the motion of the built structures. In addition, the motion of the oscillator exhibits oscillations with its own eigenfrequency, which represent the response of the oscillator to external perturbations. We estimate the peak values of the displacement, the velocity and the acceleration of the ground motion, both for the seismic waves and the main shock, which may be used as input parameters for seismic hazard studies. We discuss the parameters entering these formulae, like the dimension of the earthquake focus, the width of the primary waves and the eigenfrequencies of the site. The width of the seismic waves on the Earth’s surface, which includes the energy loss, can be identified from the Fourier spectrum of the seismic waves. Similarly, the eigenfrequencies of the site can be identified from the spectrum of the site response. The paper provides a methodology for estimating the input parameters used in hazard studies.

    show more
  • Open Access

    Article

    Article ID: 1949

    From computer algebra to gravitational waves

    by J.-F. Pommaret

    Journal of AppliedMath, Vol.2, No.6, 2024;

    The first finite length differential sequence has been introduced by Janet (1920). Thanks to the first book of Pommaret (1978), the Janet algorithm has been extended by Blinkov, Gerdt, Quadrat, Robertz, Seiler and others who introduced Janet and Pommaret bases in computer algebra. Also, new intrinsic tools have been developed by Spencer in the study of Lie pseudogroups or by Kashiwara in differential homological algebra. The achievement has been to define differential extension modules through the systematic use of differential double duality. Roughly, if D = K[d] is the non-commutative ring of differential operators with coefficients in a differential field K, let D be a linear differential operator with coefficients in K. A direct problem is to find the generating compatibility conditions (CC) in the form of a differential operator D1 such that Dξ = η implies D1η = 0 and so on. Taking the adjoint operators, we have ad(D) ◦ ad(D1) = ad(D1 ◦ D) = 0 but ad(D) may not generate all the CC of ad(D1). If M is the D-module defined by D and N is the D-module defined by ad(D) with torsion submodule t(N), then t(N) = ext 1 (M) “measures” this gap that only depends on M and not on the way to define it. Also, R = homK(M, K) is a differential module for the Spencer operator d : R → T ⊗ R, first introduced by Macaulay with his  inverse systems (1916). When D : T → S2T : ξ → L(ξ)ω = Ω is the Killing operator for the Minkowski metric ω with perturbation Ω, then N is the differential module defined by the Cauchy = ad(Killing) operator and t(N) = ext 1 (M) = 0 because the Spencer sequence is isomorphic to the tensor product of the Poincaré sequence by a Lie algebra. The Cauchy operator can be thus parametrized by stress functions having nothing to do with Ω, like the Airy function for plane elasticity. This result is thus pointing out the terrible confusion done by Einstein (1915) while ”adapting” to space-time the work done by Beltrami (1892) for space only. both of them using the same Einstein operator but ignoring it was self-adjoint in the framework of differential double duality (1995). Though unpleasant it is, we shall prove that the mathematical foundations of General Relativity are not coherent with these new results which are also illustrated by many other explicit examples.

    show more
View All Issues