For $\mathfrak g$ a Kac-Moody algebra of affine type, we show that there is an $\text{Aut}\, \mathcal O$-equivariant identification between $\text{Fun}\,\text{Op}_{\mathfrak g}(D)$, the functions on space ${\mathfrak g}$-opers disc, and $W\subset \pi_0$, intersection kernels screenings inside vacuum Fock module $\pi_0$. This kernel $W$ generated by two states: conformal vector, state $\delta_{-...

We investigated several novel conformable fractional gamma-nabla dynamic Hardy–Hilbert inequalities on time scales in this study. Several continuous and their corresponding discrete analogues the literature are combined expanded by these inequalities. Hölder’s inequality a few algebraic used to demonstrate our findings.

In this paper, we introduce the nabla fractional derivative and integral on time scales in Riemann-Liouville sense. We also Gr\"unwald-Letnikov Some of basic properties theorems related to calculus are discussed.

In this note, we consider the large time behavior of following chemotaxis-Navier-Stokes system$ \begin{equation*} \label{AH4} \left\{ \begin{split} n_t + {\bf u}\cdot\nabla n & = \Delta n^m - \nabla \cdot\big(n\nabla c\big), \qquad x\in\Omega ,\, t>0,\\ c_t c nc, &\qquad u}_t u} \Delta{\bf +\nabla P n\nabla \phi, \cdot{\bf 0, t>0 \end{split} \right. \end{equation*} $with $ m>1 ...

In this paper, we consider the global behavior of classical solutions to following two-species predator-prey chemotaxis model with signal-dependent diffusion and sensitivity$ \left\{\begin{array}{ll} u_{1t} = \nabla\cdot(d_{1}(v)\nabla u_{1})+ \nabla\cdot(\chi_{1}(v)u_{1}\nabla{v})+\mu_{1}u_{1}(1-u_{1}-e_{1}u_{2}), \\ u_{2t} \nabla\cdot(d_{2}(v)\nabla u_{2})- \nabla\cdot(\chi_{2}(v)u_{2}\nabla{...