Narrow Results

We have conducted research on the presence of wormholes characterized by a logarithmic shape function within the framework of exponential $f(R,T)$ gravity. This gravity model is defined as $f(R,T)=R+2e^{\beta t}$, with $\beta$ representing an arbitrary constant. We find that the logarithmic shape function serves as expected, providing all the necessary conditions for traversable and asymptotically flat wormholes. We have examined the solutions with three distinct sets of physical constraints placed on $p_r$, $p_t$ and $\rho$. viz. Model-I: $p_r=k{p}_t$ with k being variable dependent on r and $p_t=\omega \rho$ with $\omega$ being EoS parameter, Model-II: $p_r={\omega }_1\rho$ and $p_t={\omega }_2\rho$ with ${\omega }_1$ and ${\omega }_2$ being EoS parameters, Model-III: Trace is zero i.e. $T=0$ or $\rho =p_r+2p_t$ i.e. $f(R)$ gravity model. From Model-I, we have obtained a new parametrization for EoS parameter $\omega (r)$ and from Model-III, we have obtained a new form of shape function $b(r)$ in $f(R)$ gravity theory.

This paper is an attempt to improve the quality of Gouraud shading with minimum increase in the computation requirements. It presents algorithms for intermediate quality shading i.e. the quality of shading is better than Gouraud shading and nearly comparable to the quality of bi-quadratic Phong shading, at the same time, algorithms are very fast as compared to bi-quadratic Phong shading. Three algorithms are discussed. The first algorithm uses hybrid shading in which bi-quadratic interpolation of intensity is performed on the edges of a triangle and linear interpolation of intensity is performed on the scan line. Hybrid shading, in which bi-quadratic interpolation of normals is performed on the edges and linear interpolation of intensity is performed on the scan line, has been proposed in the second algorithm. In the third algorithm, bi-cubic interpolation of intensity is performed on the edges and linear interpolation of intensity is performed on the scan line. The paper also presents an incremental method for fast calculation of area coordinates and shape functions enhancing the speed of the algorithms.

In this talk, focusing on groomed jet and quarkonium production and decay processes, we discuss the factorization and resummation of large logarithms at the level of cross section involving TMDs. For groomed jets we analyze the measurement of hadronic transverse momentum with respect to the groomed-jet-axis and show that this observable can be used for probing the non-perturbative part of the TMD (rapidity) evolution kernel. For the case of quarkonium we present a new framework for factorization of quarkonium production and decay TMD related processes. In this new approach the factorization theorems are written in terms of the new TMD quarkonium shape functions. We work in the framework of effective field theories and particularly soft collinear effective theory and non-relativistic quantum chromodynamics.