The algebras $$Q_{n,k}(E,\tau )$$ introduced by Feigin and Odesskii as generalizations of the 4-dimensional Sklyanin form a family quadratic parametrized coprime integers $$n>k\ge 1$$ , complex elliptic curve E, point $$\tau \in E$$ . main result in this paper is that has same Hilbert series polynomial ring on n variables when $$ not torsion point. We also show Koszul algebra, hence global dime...

: The object of this paper is to obtain a common fixed point theorem for four continuous random operators by considering a sequence of measurable functions satisfying certain contractive condition in separable Hilbert space. Mathematics Subject Classification: 54H25,47H10.

We establish a bilinear framework for elliptic soliton solutions which are composed by the Lam\'e-type plane wave factors. $\tau$ functions in Hirota's form derived and vertex operators that generate such presented. Bilinear identities constructed an algorithm to calculate residues equations is formulated. These investigated detail KdV equation sketched KP hierarchy. Degenerations periods of in...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...

We investigate the universal nonequilibrium dynamics of superradiant phase transition in anisotropic quantum Rabi model. By introducing position and momentum operators, we find generators displaced operators to diagonalize Hamiltonian, then obtain ground states their excitation gaps. According Kibble-Zurek mechanism, that gap near critical point vanishes as $\ensuremath{\omega}\ensuremath{\sim}...

 A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

In the present work we study existence and non-existence of nonnegative solutions to a class deterministic KPZ system with nonlocal gradient term. More precisely will consider system$ \begin{equation*} \left\{ \begin{array}{rcll} (-\Delta)^{s} u & = &|\mathbb{D}_{s} v|^q + \rho f\,, \quad {\rm{in }}\; \Omega,\\ v |\mathbb{D}_{s} u|^p \tau g\,, v& 0 &\quad {\text{in }} \mathbb{R}...

The present paper discusses the relations between regularity, Dirichlet, and Neumann problems. Among other results, we prove that the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem for general elliptic operators with complex bounded measurable coefficients. This is strikingly different from the case of real operators, for which such an implica...

In the genus expansion of the HOMFLY polynomials their representation dependence is naturally captured by symmetric group characters. This immediately implies that the Ooguri–Vafa partition function (OVPF) is a Hurwitz tau-function. In the planar limit involving factorizable special polynomials, it is actually a trivial exponential taufunction. In fact, in the double scaling Kashaev limit (the ...

We benefit from a recent lattice determination of the full set vector, axial and tensor form factors for ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595)\ensuremath{\tau}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625)\ensuremath{\tau}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ semil...