Department of Mathematics

In this study free vibrations of anti-symmetric angle-ply composite plates including shear deformation under clamped-clamped boundary conditions are presented. Two types of numerical methods are adopted to analyze the problem. The spline and radial basis functions base mesh free scheme are applied simultaneously to approximate the displacement and rotational functions. Comparative studies have been made for analyzing the frequency parameters with respect to the material properties, number of layers, fiber orientations, side-to-thickness ratio and aspect ratio. The results are depicted in terms of tables and graphs.

For a matrix A ∈ ℝn × n whose off-diagonal entries are nonpositive, there are several well-known properties that are equivalent to A being an invertible M-matrix. One of them is the positive stability of A. A generalization of this characterization to partially ordered Banach spaces is considered in this article. Relationships with certain other equivalent conditions are derived. An important result on singular irreducible M-matrices is generalized using the concept of M-operators and irreducibility. Certain other invertibility conditions of M-operators are also investigated.

Spatial pattern formation via Turing instability in the reaction–diffusion system associated with the replicator dynamics is concerned with the long-term effects of perturbations, whereas the notion of reactivity describes the transient behaviour of perturbations to an asymptotically stable equilibrium point. This article establishes the connection between these two concepts—Turing instability and reactivity—in the context of the reaction–diffusion system associated with game replicator dynamics. In particular, we show that for Turing instability to occur in the reaction–diffusion system, the smallest diffusion coefficient of the system must be strictly less than the ratio of positive reactivity of the stable equilibrium point and square of wavenumber. This connection is also explored in terms of elements of the symmetric part of the associated stability matrix.

Let K/Q be a real quadratic field. Given an automorphic representation π for GL2/K, let As±(π) denote the plus/minus Asai transfer of π to an automorphic representation for GL4/Q. In this paper, we construct a rigid analytic map from a subvariety of the universal eigenvariety of GL2/K to an eigenvariety of GL4/Q, which at nice classical points interpolate this Asai transfer.

In the present study, we develop an energetically efficient suboptimal open-loop strategy to control the wake behind a circular cylinder in the laminar regime. The open-loop suboptimal controller is designed to resemble the feedback integral controller with reference to its dynamical behaviour. Energetic efficiency is measured using the power loss coefficient. The Van der Pol model for the evolution of lift force on the cylinder is chosen as the reduced-order model for the development of an open-loop suboptimal controller. The parameter estimation of the low- dimensional model is carried out using the results from the continuum based Navier - Stokes simulations. It is shown that a subspace identification method can be used to model the relationship between the inputs to the reduced-order model and the inputs to the higher-order computational fluid dynamic model. The development of the suboptimal control is realised by means of solving suitably formulated optimal tracking and regulator problems using the Pontryagin's minimum principle. The resultant controller is found to be energetically efficient and also successful in the control of vortex shedding.

The problem of vanishing of a (generalized) Schur complement of a block matrix (corresponding to the leading principal subblock) implying that the other (generalized) Schur complement (corresponding to the trailing principal subblock) is zero, is revisited. Absorption laws for two important classes of generalized inverses are considered next. Inheritance properties of the generalized Schur complements in relation to the absorption laws are derived. Inheritance by the generalized principal pivot transform is also studied.

Current paper deals with the numerical study on steady triple diffusive mixed convection boundary layer flow for exponentially decreasing external flow velocity in presence of suction/injection. Such exponentially decreasing external flows have specific applications in diverging channel flows. The temperature of the vertical surface is assumed to be higher compared to the surrounded fluid temperature. In the triple diffusive flow, the solutal components are chosen as Sodium chloride and Sucrose and the components are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are assumed to be lower within the free stream compared to the species concentrations of NaCl-Water and Sucrose-Water near the wall. The coupled nonlinear partial differential equations governing the flow, thermal and species concentration fields are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of wall suction/injection, Richardson number, decelerating parameter, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are analyzed and discussed. Results indicate that the thickness of the momentum boundary layer is lower for suction compared to injection for the buoyancy opposing flow. The decelerating parameter has significant impact on the flow fields. Also, the species concentration boundary layer thickness decreases with the increase of Schmidt numbers and that increases with the ratio of buoyancy parameters for both the species components. Overall, the mass transfer rate is found to increase with Schmidt numbers approximately 10% and 64% for NaCl and Sucrose, respectively.

The exact distance p-power of a graph G, denoted G[#p], is a graph on vertex set V(G) in which two vertices are adjacent if they are at distance exactly p in G. Given integers k and p, we define f(k, p) to be the maximum possible order of a clique in the exact distance p-powers of graphs with maximum degree k + 1. It is easily observed that f(k, 2) ≤ k2+ k + 1. We prove that equality may only hold if a connected component of G is isomorphic to a member of the class Pk of incidence graphs of finite projective k-geometries. (These famous combinatorial structures are known to exist when k is a prime power, and are conjectured not to exist for other values of k.) We then study the case of graphs of maximum degree k + 1 with clique number k2+ k. One way to obtain such a graph is to remove a vertex from a graph in P k; we call Pk' the class of all such resulting graphs. We prove that for any graph G of maximum degree k + 1 whose exact square has a (k2+ k)-clique, either G has a subgraph isomorphic to a graph in P'k, or a connected component of G is a (k + 1)-regular bipartite graph of order 2(k2+ k). We call Okthe class of such bipartite graphs, and study their structural properties. These properties imply that (if they exist) the graphs in Okmust be highly symmetric. Using this structural information, we show that O2contains only one graph, known as the Franklin graph. We then show that O3also consists of a single graph, which we build. Furthermore, we show that O4and O5are empty. For general values of p, we prove that f(k, p) ≤ (k + 1)k[p/2]+ 1, and that the bound is tight for every odd integer p ≥ 3. This implies that f(k, 2) = f(k, 3) whenever there exists a finite projective k-geometry, however, in such a case, the bound of f(k, 3) could also be reached by highly symmetric graphs built from a finite k-geometry, which is not the case for other values of k.

For β<1, let Pγ(β) denote the class of all normalized analytic functions f in the unit disc Δ such that for some φ ε ℝ. Let script S sign*(μ), 0 ≤ μ<1, denote the usual class of starlike functions of order μ. Define script K sign (μ)={f: zf′(z) ε script S sign *(μ)}, the class of all convex functions of order μ. In this paper, we consider integral transforms of the form The aim of this paper is to find conditions on λ (t) so that each of the transformations carries script P signγ(β) into script S sign *(μ) or script K sign(μ). A number of applications for certain special choices of λ (t) are also established. These results extend the previously known results by a number of authors.

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results. Here, we consider the image of the origin and the boundary of the image of the unit disk under the function in question and let the distance between both play a central role in our theorems. Thereby we extend the refined versions of the Bohr inequality for the class of the quasi-subordinations which contains both the classes of majorization and subordination as special cases. As a consequence, we prove Bohr type theorems for functions subordinate to convex or univalent functions.