The pedunculopontine nucleus (PPN) is part of the Reticular Activating System, and active during waking and REM sleep. Previous results showed that all PPN cells plateau at gamma frequencies and intrinsic membrane oscillations in PPN neurons are mediated by high-threshold N- and P/Q-type Ca(2+) channels. The present study was designed to determine whether some PPN cells have only N-, only P/Q-,...

We study several related extremal problems for analytic functions in a finitely connected domain $$G$$ with rectifiable Jordan boundary $$\Gamma$$ . A sharp inequality is established between values of function and weighted means its on two measurable subsets $$\gamma_{1}$$ $$\gamma_{0}=\Gamma\setminus\gamma_{1}$$ the boundary: $$|f(z_{0})|\leq\mathcal{C}\,\|f\|^{\alpha}_{L^{q}_{\varphi_{1}}(\ga...

The Veneziano amplitude for the tree-level scattering of four tachyonic scalar of open string theory has an arithmetic analogue in terms of the p-adic gamma function. We propose a quantum extension of this amplitude using the q-extended p-adic gamma function given by Koblitz. This provides a one parameter deformation of the arithmetic Veneziano amplitude. We also comment on the dificulty in gen...

This paper deals with the study of global analysis following $(1,2)-$type system non-linear difference equations:\[ u_{n+1}=\frac{\alpha v_{n-1}}{\beta +\gamma v_{n}^{p}v_{n-2}^{q}},\ \ v_{n+1}=\frac{\alpha _{1}u_{n-1}}{\beta _{1}+\gamma _{1}u_{n}^{p}u_{n-2}^{q}},\ n=0,1,... \] where parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1,}p,q$ and initial conditions $u_{i},v_{i},$...

We theoretically propose and numerically demonstrate that perfect feeding of a polaritonic system with full electromagnetic energy under one-port beam incidence, referred to as critical coupling, can be achieved in hybrid dielectric metasurface--${\mathrm{WS}}_{2}$ monolayer structure. Polaritonic where coupling strong are simultaneously attained, is determined by the relative damping rates cav...

Michael Knapp, in a previous work, conjectured that every additive sextic form over $\mathbb{Q}_2(\sqrt{-1})$ and $\mathbb{Q}_2(\sqrt{-5})$ seven variables has nontrivial zero. In this paper, we show conjecture is true, establishing $\Gamma^*(6, \mathbb{Q}_2(\sqrt{-1})) = \Gamma^*(6, \mathbb{Q}_2(\sqrt{-5})) 7 $.

In 1962, Gallagher proved a higher-dimensional version of Khintchine’s theorem on Diophantine approximation. Gallagher’s states that for any non-increasing approximation function ψ: ℕ → (0, 1/2) with $$\sum\nolimits_{q = 1}^\infty {\psi \left( q \right)} $$ and γ γ′ 0 the following set $$\left\{ {\left( {x,y} \right) \in {{\left[ {0,\,1} \right]}^2}:\left\| {qx - \gamma } \right\|\left\| {qy {\...