In this paper, we study the existence of normalized ground states to following lower critical fractional Choquard equation $ (-\Delta)^su = \lambda u+\gamma(I_{\alpha}*|u|^{1+\frac{\alpha}{N}})|u|^{\frac{\alpha}{N}-1}u+\mu |u|^{q-2}u\ \mbox{in}\ \mathbb R^N under L^2 $-norm constraint$ \int_{\mathbb R^N}|u|^2dx a^2, $where N \geq3 $, s\in(0,1) \alpha\in (0,N) a, \gamma, \mu>0 and 2<q\leq ...

Abstract We discuss sublinear differential equations of the Emden–Fowler type $x''=q(t) x^{\gamma }$ x ″ = q ( t ) γ under assumption that coefficient q is a rapidly va...

The presence of exotic matter for the existence wormhole geometry has been an unavoidable problem in GR. In recent studies researchers have tried to deal with this issue using modified gravity theories where WH is explained by extra curvature terms and NEC's are not violated signifying standard geometry. present article we trying find solutions traversable wormholes normal throat within framewo...

For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q d \frac{\gamma-1}\gamma$.

Abstract We derive a general expression for the absorptive part of one-loop photon polarization tensor in strongly magnetized quark-gluon plasma at nonzero baryon chemical potential. To demonstrate application main result context heavy-ion collisions, we study effect potential on emission rate. The rate and ellipticity are studied numerically as function transverse momentum (energy) several val...

have many applications in pure mathematics as in other branches of science. They are named by Karlin and Szegő in [8], Turán-type inequalities because the first of these type of inequalities was introduced by Turán in [18]. More precisely, he used some results of Szegő in [17] to prove the previous inequality for x ∈ (−1, 1), where fn is the Legendre polynomial of degree n. This classical resul...

Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the q-gamma function, Bessel and cylinder functions and the Hermite function.

This paper aims at presenting a new application of information geometry to reinforcement learning focusing on dynamic treatment resumes. In standard framework learning, Q-function is defined as the conditional expectation reward given state and an action for single-stage situation. We introduce equivalence relation, called policy equivalence, in space all Q-functions. A class divergence every s...

In this paper, we develop theorems on finite and infinite summation formulas by utilizing the q (q,h) anti-difference operators, also extend these core to q(α) (q,h)α difference operators. Several integer order based operator have been published, which gave us idea derive fractional equations for construct a function known as quantum geometric alpha-quantum function, behaves class of series. We...