Indian Journal of Pure and Applied Mathematics最新文献

This paper is to establish new results on the zeros of (F^{(k)}-alpha (z)), where F(z) is a differential polynomial or difference polynomial of f and (alpha (z)) is a small function with respect to f in the sense of Nevanlinna theory. We also obtain that at least one of (F^{(k)}-alpha (z)) and (G^{(k)}-alpha (z)) has infinitely many zeros, where F(z) and G(z) are crossed differential polynomials or difference polynomials of f and g.

Let (mathcal {T}) be the set of spanning trees of a graph G and let L(T) be the number of leaves in a tree T. The leaf number L(G) of G is defined as (L(G)=max {L(T)|Tin mathcal {T}}). Let G be a connected graph of order n and minimum degree (delta ) such that (L(G)le 2delta -1). We show that the circumference of G is at least (n-1), and that if G is regular then G is hamiltonian.

In this paper, linear differential equations involving fractional and integer order derivatives are considered. Here fractional derivatives are defined in the Caputo–Fabrizio sense. A solution in the form of the truncated Pell series of the fractional differential equation is investigated. Firstly, the truncated Pell series solution is substituted into the fractional differential equation. Then, the collocation process leads to a system of linear equations. Finally, the unknown coefficients of the truncated Pell series are obtained by solving the linear system. The error and convergence analysis of the method is also presented. Additionally, the accuracy of the method is shown by numerical examples.

We propose and study the notion of triangles in smooth cubic hypersurfaces. We prove that for a generic cubic n-fold X ((nge 2)), the variety of triangles in X is of dimension (3n-6). We show that on a generic cubic n-fold, the triangles with a given edge can be parametrized by an open subset of a quintic hypersurface in (mathbb {P}^{n-1}). In the case of a generic cubic threefold, we show that the locus of the opposite vertices for triangles with a given edge form a curve of degree 10. As a corollary, we get an interesting enumerative result on the number of triangles satisfying some restrictions.

In this article, we aim to emphasize the critical role of extended convergence analysis in advancing research and understanding in the interdisciplinary fields of Applied and Computational Mathematics, Physics, Engineering, and Chemistry. By gaining a comprehensive understanding of the convergence behavior of numerical methods, one can make informed decisions regarding algorithm selection, optimization, and convergence domains, leading to more accurate and reliable scientific results in diverse applications. The conventional approach to assessing the convergence order of higher order methods for solving systems of non-linear equations relied on the Taylor series expansion, necessitating the computation of higher order derivatives that were typically absent in the method. This limitation not only constrained the method’s applicability but also increased the computational cost of solving the problem. In contrast, our study introduces a unique and innovative approach, where we demonstrate the improvised convergence of the method using only first order derivatives. Our new method offers several advantages over the traditional approach, providing valuable information regarding the radii of the convergence region and precise estimates of error boundaries. Furthermore, we establish the notion of semi-local convergence, which proves to be particularly significant as it allows for the identification of the specific domain in which the iterates converge. We have validated the convergence requirements through carefully selected numerical examples.

In this paper, we give weighted sum formulas of the multiple Hurwitz zeta functions (zeta (s_1, ldots , s_n;a)). As a corollary, we prove a well known explicit evaluation formula for (zeta (s, ldots , s;a)).

In this paper, we investigate the structure of finite group G by assuming that the intersections between p-sylowizers of some p-subgroups of G and (O^p(G)) are S-permutable in G. We obtain some criterions for p-nilpotency of a finite group.

In this article, we study the boundedness of generalized one-sided maximal function, ({mathcal {M}}^{+}_{g}) on one-sided weighted like Morrey space, (M^{+}_{p,alpha }) for a pair of weights (u, v). We also discuss the Fefferman-Stein’s type weighted inequalities for generalized one-sided maximal function on the same space. Finally, as a corollary, we obtain the Fefferman-Stein’s type inequalities for generalized one-sided maximal function on one-sided weighted like Morrey space for a pair of weights.