In this paper, an extension of DIFFERENTIAL Transformation Method (DTM) which is an analytical-numerical method for solving the fuzzy PARTIAL DIFFERENTIAL EQUATION (FPDE) by using the strongly generalized differentiability concept is investigated. The proposed algorithm is illustrated by numerical example.

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using PARTIAL DIFFERENTIAL EQUATIONs (PDEs). It combines a non-linear Fourth-order PDE method with the Locally Adaptive Zooming (LAZ) algorithm. The proposed method uses high-resolution image obtained from LAZ algorithm to construct zoomed image by Fourth-order PDE. This proposed method preserves edges and minimizes blurring and staircase effects in the zoomed image. In order to evaluate image quality obtained from the proposed method, this paper focuses on both subjective and objective assessments. The results of these measures on a variety of images show that the proposed method is superior over the other image zooming methods.

In this paper, the Goursat problem of a general form for a linear PARTIAL DIFFERENTIAL EQUATION is investigated with the help of the Riemann function method. Some results are given concerning the existence and uniqueness for the solution of the suggested problem.

In this paper, a novel device, namely heterojunction electron-hole bilayer tunnel field effect transistor (HJ-EHBTFET), is proposed which outperforms conventional tunnel field effect transistor (TFET) in terms of electrical performance. The use of lattice matched InAs/Al0.6Ga0.4Sb material combination results in a broken band gap configuration, making it highly suitable for high speed ultra-low applications, as it requires smaller gate bias for the onset of tunneling. The impact of critical design parameters on the device performance is comprehensively investigated. The proposed device utilizes electrical doping instead of physical doping for the creation of tunneling junction, which effectively addresses the problem of low solubility of dopants in heavily doped III-V materials. The top gate and bottom gate workfunction are critical design parameters that effectively modulated the electrically induced charges at the tunneling junction and consequently, affect the tunneling rate. In order to obtain the lowest possible transition voltage for the onset of tunneling, a variation matrix of threshold voltage variation is computed as a function of gate electrode workfunction. Through this process, a step-like behavior from off-state to on-state has been achieved, with a subthreshold swing of 3 mV/dec and on/off current ratio of 5.8×1012, thereby paving the way for the design of low-power high-speed digital computing systems.

In this paper, the Goursat problem of a third order EQUATION on cases of explicit solvability is investigated, with the help of the Riemann function. Some results and one theorem are given concerning the existence and uniqueness for the solution of the suggested problem.