An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

Analysis of Extreme Rainfall Event with Different Microphysics and Parameterization Schemes in WRF Model

In the present study, the imitation of heavy rainfall event which occurred over Jharkhand during 18 August 2016 was taken as a case study. Weather Research and Forecasting (WRF) model has been utilized for this study. National Centers for Environmental Prediction (NCEP) analysis data is compared with GSMaP data with different combination of physical parameterization scheme like microphysics (MP) and cumulus parameterization (CP). In the present study, three MP schemes: Kessler scheme, Lin et al. scheme and WRF Single-moment 6-class scheme with combination of three CP schemes: Betts-Miller-Janjic scheme, Multi-scale Kain-Fritsch scheme and New simplified Arakawa-Schubert scheme have been used. The model predicted humidity, temperature and precipitation were compared with the GSMaP product. The model nicely depicted the cloud pattern and recognized the rain event spatially. The obtained result shows that the model overestimates the precipitation for all the schemes.

Trigonometric Approximation of Signals (Functions) Belonging to the <i>Lip</i>(<i>ξ</i>(<i>t</i>),<i>r</i>),(r>1)-Class by (<i>E</i>,<i>q</i>) (<i>q</i>>0)-Means of the Conjugate Series of Its Fourier Series

Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα, Lip(α,r), Lip(ξ(t),r) and W(Lr,ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to Lip(ξ(t),r) class by (E,q) summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].

Numerical study on thermal therapy of triple layer skin tissue using fractional bioheat model

This paper deals with the study of heat transfer and thermal damage in triple layer skin tissue using fractional bioheat model. Here, we consider three types of heating viz. sinusoidal heat flux, constant temperature and constant heat flux heating on skin surface. An implicit finite difference scheme is obtained by approximating fractional time derivative by quadrature formula and space derivative by central difference formula. The temperature profiles and thermal damage in the skin tissue are obtained to study the effect of fractional parameter a on diffusion process for constant temperature and heat flux boundary heating on skin surface. A parametric study for sinusoidal heat flux at skin surface has also been made.