Basirhat College

This study develops a novel thermoelastic model for an unbounded micropolar half-space produced by a magnetic field having constant intensity. A novel spatiotemporal nonlocal elasticity theory is proposed by taking into account one dynamical scalar nonlocal kernel. In line with the theory, an isotropic nonlocal elasticity model of the Klein-Gordon type is formulated, incorporating both a characteristic internal length scale and an essential internal time scale parameter. The Moore-Gibson-Thompson theory, which is adjacent to the memory responses, governs the micropolar medium’s heat transport mechanism. While the boundary is free of traction, the micropolar medium experiences a time-harmonic thermal loading. The solutions to the governing equations have been obtained using Laplace and Fourier transform techniques. Numerical estimates of each of the physical fields have been performed for the analysis of the effectiveness of the nonlocality parameters of space and time, the micropolar parameters and the time-delay also. The significance of various kernels involved in the heat conduction process and the influence of magnetic field have also been concluded.

Using tools from topological dynamics, H. Furstenberg introduced the notion of central sets and established the celebrated Central Sets Theorem, which simultaneously generalizes both van der Waerden’s theorem and Hindman’s theorem. Later, V. Bergelson and N. Hindman provided an equivalent description of central sets in N using the algebraic structure of the Stone–Čech compactification of discrete semigroups, and the full generality was subsequently obtained by H. Shi and H. Yang. Through ultrafilter techniques, J. McLeod further extended the concept of central sets to commutative adequate partial semigroups, with analogous definitions available for the noncommutative setting.In this article, we introduce a framework of topological dynamics for actions of partial semigroups and, within this framework, we obtain a dynamical characterization of central sets in partial semigroups that is equivalent to the ultrafilter-based definitions.111Recently, the authors of Goodrazi et al. (2024) have attempted a related characterization using a different method.

The present work develops the well-known analogy and cross-coupling between heat conduction and moisture diffusion for an infinite semiconductor with a spherical cavity in context of photothermal transport process. A linear hygrothermoelastic theory is adopted assimilating the nonlocal stress theory proposed by Eringen. The heat transport and the moisture diffusion equations have been formulated in the context of Moore–Gibson–Thompson theory defined within a sliding interval adjoining the memory-dependent derivative. The surface of the cavity is free of moisture concentration and is subjected to exponentially decaying pulse and prescribed carrier density flux. Embedding the Laplace transform, the basic equations have been derived in the transformed domain. In order to arrive at the solution in real space-time domain, the inversion of the Laplace transform is accomplished using the method of Zakian. From the graphical illustrations, impact of change of kernel function in the heat and moisture transport has been analyzed. Moreover, significant effect of nonlocal parameter and time-delay parameters have been reported in the variation of temperature, mass concentration, displacement distribution and carrier density. It is also monitored that how a nonlinear kernel can control the transport phenomena more effectively than the existing linear kernel functions.

H. Furstenberg introduced the notion of central sets in terms of topological dynamics and established the famous Central Sets Theorem. Later in [A new and stronger Central Sets Theorem, Fund. Math. 199 (2008), 155-175], D. De, N. Hindman, and D. Strauss established a stronger version of the Central Sets Theorem that uses the algebra of the Stone-\v Cech compactification of discrete semigroups. In this article, We will provide a new and combinatorial proof of the stronger Central Sets Theorem.

The ferromagnetism in Cu doped Zinc oxide (ZnO) has been investigated and the possible origin of magnetism in the system has been discussed. The Cu doped ZnO has been successfully prepared by solid state reaction method. Magnetization measurement of these Cu doped ZnO samples show ferromagnetic behavior at room temperature. Room temperature Photoluminescence spectroscopy measurements shows defect related blue emission peak together with the UV emission. Employing positron annihilation spectroscopy all the Cu doped and undoped ZnO samples has been characterized. Positron annihilation lifetime results suggest no significant increase of cation defect in Cu doped ZnO.