The Benjamin Ono equation with a slowly varying potential is $$ \text{(pBO)} \qquad u_t + (Hu_x-Vu \tfrac12 u^2)_x=0 $V(x)=W(hx)$, $0 0$ are parameters. For initial condition $u_0(x)$ to (pBO) close $Q_{0,1}(x)$, it was shown in previous work by Z. Zhang that the solution $u(x,t)$ remains $Q_{a(t),c(t)}(x)$ and approximate parameter dynamics for $(a,c)$ were provided, on dynamically relevant ti...

We introduce a new signaling scheme for timeand frequencyselective channels that is a generalization of Multi-Carrier Code Division Multiple Access (MC-CDMA) signaling used in slowly time-varying channels. The Fourier basis functions used in conventional MC-CDMA systems encounter temporal distortion in rapidly time-varying channels resulting in degraded performance. The proposed scheme transmit...

Heat engines are fundamental physical objects to develop nonequilibrium thermodynamics. The thermodynamic performance of the heat engine is determined by choice cycle and time-dependence parameters. Here, we propose a systematic numerical method find optimize some target functions. We apply with slowly varying parameters show that works well. Our based on genetic algorithm which widely applied ...

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition inhomogeneous versions equations considered, case polynomial forcing terms. The involve exponential, Airy Scorer functions slowly varying analytic coefficient involving simple coefficients. approximations uniformly valid large values parameter unbounded real complex argument. ...

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that th...

We study the Dirac equation with slowly varying external potentials. Using matrix-valued Wigner functions we prove that the electron follows with high precision the classical orbit and that the spin precesses according to the BMT equation with gyromagnetic ratio g = 2.

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...