We construct a family of $q$ deformations $E(2)$ group for nonzero complex parameters $|q|<1$ as locally compact braided quantum groups over the circle $\mathbb{T}$ viewed quasitriangular with respect to unitary R-matrix $R(m,n):=(\zeta)^{mn}$ all $m,n\in\mathbb{Z}$. For real $0<|q|<1$, deformation coincides Woronowicz's $E_{q}(2)$ groups. As an application, we study analogue contraction proced...

We study the wave equation in exterior of a bounded domain K with dissipative boundary condition $$\partial _{\nu } u - \gamma (x) \partial _t = 0$$ on $$\Gamma $$ and $$\gamma > 0.$$ The solutions are described by contraction semi-group $$V(t) e^{tG}, \, t \ge eigenvalues $$\lambda _k$$ G $$\text{ Re }\,\lambda _k < yield asymptotically disappearing $$u(t, x) e^{\lambda t} f(x)$$ having expone...

It is well known that confluence and strong normalization are preserved when combining algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual contraction rule for η, or recursion together with the usual contraction rule for surjective pairing. We show that confluence and strong normalization are modular prop...

A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r( *) (-) and is allowed to nucleate during a finite time interval t(n), after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r( *) (+). The size-distribution of nucleated particles f(r,t) further evolves due to their dete...

It is likely that the Higgs potential of Standard Model unstable, turning negative at $\ensuremath{\phi}&lt;\mathrm{\ensuremath{\Lambda}}\ensuremath{\sim}{10}^{10}\text{ }\text{ }\mathrm{GeV}$. Here we consider whether it possible to have inflation on positive stable region $\ensuremath{\phi}&lt;\mathrm{\ensuremath{\Lambda}}$. To do this add a nonminimally coupled induced gravity sector with sc...

In this paper, we deal with the following indirect pursuit-evasion model $\begin{align} \left\{\begin{array}{ll} u_t = \Delta u-\chi\nabla\cdot(u\nabla w)+ u(\lambda-u+av), \quad x\in \Omega, t&gt;0, \\ v_t v+\xi\nabla\cdot(v\nabla z)+ v(\mu-v-bu), { }{0 w- w+v}, z- z+ u}, \end{array}\right. \ (\star) \end{align} $ under homogeneous Neumann boundary conditions in a bounded domain \Omega\subset ...

In this paper, we present the existence and stability results for a nonlinear coupled system of sequential fractional differential equations supplemented with new kind boundary conditions. Existence uniqueness are established by using Schaefer’s fixed point theorem Banach’s contraction mapping principle. We examine solutions involved in Hyers–Ulam type. A few examples presented to illustrate ma...