Indian Journal of Pure and Applied Mathematics最新文献

Recent soliton advances in Indian J. Pure Appl. Math. have been impressive, while as to the dynamical pathology, etc., aortic dissection has been seen as a catastrophic disease influencing the aorta. Hereby, symbolic computation is implemented on a (3+1)-dimensional Jadaun-Singh equation for the dynamical pathology in aortic dissection. Via the singular manifold, etc., auto-Bäcklund transformation, bilinear forms and M-soliton solutions are obtained, for the amplitude of the relevant wave, where M is a positive integer. Our results might assist some studies on the dynamical pathology in aortic dissection and cardiothoracic physicians in pinpointing the latent cases and working on such preventive regimens as the control of hypertension and restriction on physiological activity.

In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the tracking in short time and with high accuracy. We then use a single valued weighted running average with a tunable parameter for the case when transition times are unknown and establish deviation bounds for the tracking accuracy. Our result has applications in choosing the optimal rewards for the multiarmed bandit scenario.

For nonnegative integers n and k, one defines the quadrinomial coefficient (left( {begin{array}{c}n kend{array}}right) _{3}) as the coefficient of (x^k) in the polynomial expansion of (left( 1+x+x^2+x^3right) ^{n}.) In this paper, we establish congruences (mod (p^2)) involving the quadrinomial coefficients (genfrac(){0.0pt}0{np-1}{p-1}_{3}) and (genfrac(){0.0pt}0{np-1}{frac{p-1}{2}}_{3}.) This extends some known congruences involving the binomial and trinomial coefficients.

Let f and g be two distinct primitive holomorphic cusp forms of even integral weights (k_{1}) and (k_{2}) for the full modular group (Gamma =SL(2,mathbb {Z})), respectively. Denote by (lambda _{fotimes fotimes cdots otimes _{l} f}(n)) and (lambda _{gotimes gotimes cdots otimes _{l} g}(n)) the nth normalized coefficients of the l-fold product product L-functions attached to f and g, respectively. In this paper, we establish a lower bound for the analytic density of the set

where (lgeqslant 4) is any fixed integer. By analogy, we also establish some similar density results of the above supported on certain binary quadratic form.

Menon’s identity is a classical identity involving gcd sums and the Euler totient function (phi ). We derived the Menon-type identity (sum limits _{begin{array}{c} m=1 (m,n^s)_s=1 end{array}}^{n^s} (m-1,n^s)_s=Phi _s(n^s)tau _s(n^s)) in [Czechoslovak Math. J., 72(1):165-176 (2022)] where (Phi _s) denotes the Klee’s function and ((a,b)_s) denotes a a generalization of the gcd function. Here we give an alternate method to derive this identity using the properties of the Cohen-Ramanujan sum defined by E. Cohen.

This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting from the space of continuous functions to the space of essentially bounded functions with a boundary condition involving integral terms. We investigates the solvability and uniqueness of the equation under certain conditions on the coefficients. The paper utilizes techniques of Vallée-Poussin theorem, and Green’s function sign constancy to establish the main results. Choosing a corresponding function within the context of the Vallée-Poussin theorem results in explicit criteria presented as algebraic inequalities. These inequalities, as we illustrate through examples, cannot be further improved.

In this paper, convexifactors of product and quotient of functions are computed. Generalized convexity of these functions in terms of convexifactors is studied. The obtained results are then applied to develop optimality conditions for fractional programming problem.

By combining the shrinking projection method with the parallel splitting-up technique and the inertial term, we introduce a new inertial parallel iterative method for finding common solutions of a finite system of generalized mixed equilibrium problems and common fixed points of a finite family of Bregman totally quasi-asymptotically nonexpansive mappings. After that, we prove a strong convergence result for the proposed iteration in reflexive Banach spaces. By this theorem, we obtain some convergence results for generalized mixed equilibrium problems in reflexive Banach spaces. In addition, we give a numerical example to illustrate the proposed iterations. The obtained results are improvements and extensions to some known results in this area.

In this paper, we first attempt to study sums of powers and to obtain some divisibility properties of the Stirling numbers of the first kind based on Newton-Girard’s identity. Then, using the obtained results, we study the divisibility properties of Wolstenholme’s theorem for the generalized harmonic numbers. Finally, we answer some open questions raised in 1992 by Y.Matiyasevich.

This paper uses a new fractal-fractional operator with a power law-type kernel in the Riemann-Liouville sense to formulate the new fractal-fractional model of hepatitis B virus (HBV) transmission with asymptomatic carriers. The existence of the model’s solutions is demonstrated using Schuder’s fixed point theorem. The Banach fixed point theorem is utilized to prove the uniqueness of the solutions. Solutions’ stability behaviors in the Ulam concept are also discussed. Further, using the newly created numerical scheme based on Newton’s polynomial, the new numerical scheme for HBV is created. Numerical simulations show the accuracy of the approximate solutions of the new numerical method, along with the clear effect of the fractal dimension and fractional order on the spread of the HBV disease.