The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, interrelations between defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions continuous discrete transfer functions. Simple transformations presented allow ...

We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This exists for magnetic fields with nested toroidal flux surfaces} provided $ \oint\mathrm{d}l/B\:(\mathbf{j}\cdot\nabla\psi)=0$, where symbols have their usual meaning, and integral is taken along closed field lines. All quasisymmetric fields, regardless associated form equilibria, must s...

Abstract We develop a discrete counterpart of the De Giorgi–Nash–Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations second-order linear elliptic problems form $-\nabla \cdot (A\nabla u)=f-\nabla F$ with $A\in L^\infty (\varOmega ; {{\mathbb{R}}}^{n\times n})$ uniformly matrix-valued function, $f\in L^{q}(\varOmega )$, $F\in L^p(\...

We prove the continuity of bounded solutions for a wide class parabolic equations with (p, q)-growth $$\begin{aligned} u_{t}-\mathrm{div}\left( g(x,t,|\nabla u|) \,\frac{\nabla u}{|\nabla u|}\right) =0, \end{aligned}$$ under generalized non-logarithmic Zhikov’s condition $$\begin{aligned}g(x,t,\mathrm{v}/r)&\leqslant c(K)\,g(y,\tau ,\mathrm{v}/r), \quad (x,t), (y,\tau )\in Q_{r,r}(x_{0},t_{0}),...

Abstract Geo-electromagnetic forward modeling problems are ill-posed due to the low signal frequencies being used and electrically insulating air space. To overcome this numerical issue, $A - \phi $ formula using magnetic vector potentials ($\bf A$) electric scalar ($\phi $) was developed. At present, there two sets of formulae used: one has a curl–curl ($\nabla \times \nabla structure another ...

This paper deals with a three-species predator-prey system prey-taxis \begin{document}$ \begin{eqnarray*} \left\{ \begin{split}{} &u_t = d_{1}\Delta u-\chi_{1}\nabla\cdot(u\nabla w)+\gamma_{1}uw-\theta_{1}u-\beta_{1}uv,&(x,t)\in \Omega\times (0,\infty),\\ &v_t d_{2}\Delta v-\chi_{2}\nabla\cdot(v\nabla w)+\gamma_{2}vw-\theta_{2}v-\beta_{2}uv,&(x,t)\in &w_t d_{3}\Delta w-(u+v)...

Abstract Consider a double degenerate parabolic equation arising from the electrorheological fluids theory and many other diffusion problems. Let $v_{\varepsilon }$ v ε be viscous solution of equation. By showing that $|\nabla v_{\varepsilon }|\in L^{\infty }(0,T; L_{\m...

Let $\Omega\subset \mathbb{R}^3$ be a Lipschitz domain and let $S_\mathrm{curl}(\Omega)$ the largest constant such that $$ \int_{\mathbb{R}^3}|\nabla\times u|^2\, dx\geq S_{\mathrm{curl}}(\Omega) \inf_{\substack{w\in W_0^6(\mathrm{curl};\mathbb{R}^3)\\ \nabla\times w=0}}\Big(\int_{\mathbb{R}^3}|u+w|^6\,dx\Big)^{\frac13} for any $u$ in $W_0^6(\mathrm{curl};\Omega)\subset W_0^6(\mathrm{curl};\mat...