We study the conformal window of asymptotically free gauge theories containing ${N}_{f}$ flavors fermion matter transforming to vector and two-index representations $SO(N),SU(N)$ $Sp(2N)$ groups. For $SO(N)$ we also consider spinorial representation. determine critical number ${N}_{f}^{\mathrm{cr}}$, corresponding lower end window, by using conjectured condition on anomalous dimension bilinear ...

We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u and x. These conditions for timelike and spacelike conformal Ricci and c...

using the electrostatic capacity of a condenser, the existence of a distance function on a finsler space is discussed. this distance function divides finsler spaces into the two classes, denoted here by i and ii. the topology generated by this distance on the finsler spaces of class ii coincides with its intrinsic topology. this work provides a natural extension of mathematical analysis tools n...

Abstract. The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other types of Killing equations, as well as to overdetermined systems c...

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conform...

In the conformal prediction literature, it appears axiomatic that transductive conformal classifiers possess a higher predictive efficiency than inductive conformal classifiers, however, this depends on whether or not the nonconformity function tends to overfit misclassified test examples. With the conformal prediction framework’s increasing popularity, it thus becomes necessary to clarify the ...

The frustrated XY model on the honeycomb lattice has drawn lots of attentions because potential emergence chiral spin liquid (CSL) with increasing frustrations or competing interactions. In this work, we study extended spin-$\frac{1}{2}$ nearest-neighbor ($J_1$), and next-nearest-neighbor ($J_2$) interactions in presence a three-spins ($J_{\chi}$) term using density matrix renormalization group...