Indian Journal of Pure and Applied Mathematics最新文献

General analytical results on the azimuthal unstable modes of variable density swirling flows between coaxial cylinders are obtained in the present paper. In particular estimates for the growth rate of unstable modes and instability regions within which the complex phase velocities should lie are obtained. All the results obtained indicate an important role for the basic flow vorticity and its variation on the instability of the swirling flows. The general analytical results obtained are illustrated in figures for various basic angular velocity profiles and a family of density profiles.

We shall give a notion to obtain some adequate conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. In pursuit of this, our interest lies in presenting some invigorating results containing altering distance functions and control functions in metric spaces. Using these results, we employ some firm conditions for the existence and uniqueness of a positive definite common solution to the pair of non-linear matrix equations. We also figure out a systematic applicable area of our findings. Eventually, we give precise examples to assert one of the prominent results with a numerical approximation of convergence of iterated sequence using a diagram.

In this paper, we consider the semi-commutants of Toeplitz operators on the Fock-Sobolev space of the complex plane. This work generalizes several partial results in a novel manner.

We present a numerical method for approximating the temperature distribution and a time-dependent source function in the one-dimensional heat equation, considering integral overdetermination and non-local Wentzel-Neumann boundary conditions. Initially, we reformulate the problem as a non-classical parabolic equation with initial and homogeneous boundary conditions. We apply the (theta )-weighted finite difference method (FDM) to discretize the time derivative. Subsequently, the main problem is transformed into a system of second-order ordinary differential equations (ODEs), which is then solved using a spectral method. This approach ensures that the obtained approximation accurately satisfies the boundary conditions at each time level. Additionally, a regularization method is employed to find a stable approximation for the derivative of perturbed boundary data. We conduct stability analysis to address the solution of the considered problem, and three numerical tests are provided to demonstrate the effectiveness and accuracy of the proposed scheme.

The paper is deals with the heat transfer in the laminar flow of a viscous incompressible fluid along a plate with a small heated localized irregularity. It is well known that double- and triple-deck structures of the boundary layer arise in such flow problems. These structures make it possible, among other things, to describe the phenomenon of separation of the boundary layer behind irregularities. In this paper, we study the heat transfer in the double-deck structure of the boundary layer. The asymptotic solution with double-deck structure is constructed for the problem under consideration for large Reynolds numbers. The results of numerical simulation of heat transfer in the region near the streamlined surface are presented. In particular, the effect of the presence of a separation zone (region with vortex) on heat transfer was studied, as well as the magnitude of the heat flux from the streamlined surface. The obtained results can be used in the design of cooling systems for microsized devices.

Vinogradov’s three primes theorem indicates that, for every sufficiently large odd integer N, the equation (N=p_1+p_2+p_3) is solvable in prime variables (p_1,p_2,p_3). In this paper, it is proved that Vinogradov’s three primes theorem still holds with three prime variables constrained in the intersection of multiple Piatetski–Shapiro sequences.

Let (P_m) and (E_m) be the m-th Padovan and Perrin numbers, respectively. In this paper, we prove that for a fixed integer (delta ) with (delta ge 2) there exists finitely many Padovan and Perrin numbers that can be represented as products of three repdigits in base (delta .) Moreover, we explicitly find these numbers for (2le delta le 10) as an application.

Let X be a compact Hausdorff space. We show the existence and uniqueness of injective envelope in the category of unital (C(X))-algebras. As an application, we characterize injective objects in the category of upper semi-continuous C*-bundles.

In this article we prove in main Theorem A that any infinity type real hyperplane arrangement (mathcal {H}_n^m) with the associated normal system (mathcal {N}) can be represented isomorphically by another infinity type hyperplane arrangement (widetilde{mathcal {H}}_n^m) with a given associated normal system (widetilde{mathcal {N}}) if and only if the normal systems (mathcal {N}) and (widetilde{mathcal {N}}) are isomorphic, that is, there is a convex positive bijection between a pair of associated sets of normal antipodal pairs of vectors of (mathcal {N}) and (widetilde{mathcal {N}}). We show in Theorem 7.1 that, if two generic hyperplane arrangements (mathcal {H}_n^m) and (widetilde{mathcal {H}}_n^m) are isomorphic then their associated normal systems (mathcal {N}) and (widetilde{mathcal {N}}) are isomorphic. The converse need not hold, that is, if we have two generic hyperplane arrangements ((mathcal {H}_n^m)_1), ((mathcal {H}_n^m)_2) in (mathbb {R}^m), whose associated normal systems (mathcal {N}_1) and (mathcal {N}_2) are isomorphic, then there need not exist translates of each of the hyperplanes in the hyperplane arrangement ((mathcal {H}_n^m)_2), giving rise to a translated generic hyperplane arrangement (widetilde{mathcal {H}}_n^m), such that, (widetilde{mathcal {H}}_n^m) and ((mathcal {H}_n^m)_1) are isomorphic.

The existence, uniqueness and asymptotic behavior for one dimensional boundary blow-up problem with p-Laplace operator has been investigated. This problem arises in many fields, such as in the theory of automorphic functions and Riemann surfaces of constant negative curvature, in the study of the electric potential in a glowing hollow metal body, etc. Our result shows that the boundary blow-up solution exists provided that the Keller-Osserman condition holds true and the absorb terms satisfy a divergent condition in some neighbourhood of zero. By symmetry method, comparison theorem and the regularly varying theory, we also investigate the uniqueness of the boundary blow-up solutions, these results can be seen as the beneficial supplement to the corresponding results of elliptic equations.