We show that spin-density separation in a Bose gas is not restricted to 1D but also occurs in higher dimensions. The ratio (alpha) of the intraspecies atom-atom interaction strength to the interspecies interaction strength strongly influences the dynamics of spin-density separation and the elementary excitations. The density wave is phononlike for all values of alpha. For alpha < 1, the spin wa...

In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on parameter $\alpha$ and study their trajectory behaviors. We find all fixed points for operator finite-dimensional simplex. construct some Lyapunov functions. A complete description set limit is given, show that such have ergodic property.

We consider a formulation of gauge field theory where the $A_\alpha$ and strength $F_{\alpha\beta}$ are independent variables, as in Palatini gravity. For simplest action, this is known to be equivalent usual formulation. add non-minimal couplings between scalar field, solve for insert it back into action. This leads modified terms. slow-roll inflation show that because modifications sector, ad...

Control scheduling refers to the problem of assigning agents or actuators act upon a dynamical system at specific times so as minimize quadratic control cost, such objectives linear-quadratic-Gaussian (LQG) linear regulator problems. When budget operational constraints are imposed on schedule, this is in general NP-hard and its solution can therefore only be approximated even for moderately siz...

We use the discrete phenomenological model to study theoretically the phase diagrams in antiferroelectric liquid crystals (AFLCs) as a function of optical purity and temperature. High sensitivity of the phase sequence in the AFLCs to optical purity is attributed to the piezoelectric coupling which is reduced if optical purity is reduced. We limit our study to three topologically equal smetic (S...

We construct affine varieties over \mathbb{Q} and imaginary quadratic number fields \mathbb{K} with a finite of \alpha-lattice points for fixed \alpha\in \mathcal{O}_\mathbb{K}, where \mathcal{O}_\mathbb{K} denotes the ring algebraic integers \mathbb{K}. These arise from equations form F(y) = F(g(x_1,x_2,\ldots, x_k))+r(x_1,x_2\ldots, x_k), F is rational function, g r are polynomials \mathbb{K}...