Abstract Let $c_{kl} \in W^{1,\infty }(\Omega , \mathbb{C})$ for all $k,l \{1, \ldots d\};$ and $\Omega \subset \mathbb{R}^{d}$ be open with uniformly $C^{2}$ boundary. We consider the divergence form operator $A_p = - \sum \nolimits _{k,l=1}^{d} \partial _l (c_{kl} _k)$ in $L_p(\Omega )$ when coefficient matrix satisfies $(C(x) \xi ) \Sigma _\theta$ $x \Omega$ $\xi \mathbb{C}^{d}$ where $\Sigm...

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contr...

fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. in this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. we focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. at last, fuzzy completecongruen...

We show that if R is a compact domain in the complex plane with two or more holes and an anticonformal involution onto itself (or equivalently a hyperelliptic Schottky double), then there is an operator T which has R as a spectral set, but does not dilate to a normal operator with spectrum on the boundary of R. 0.1. Definitions. LetX be a compact, path connected subset ofC, with interior R, and...

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this letter, we employ contraction theory improve robustness of ODEs (NODEs). A dynamical system is contractive if all solutions with different initial conditions converge each other exponentially fast. As consequence, become less relevant over time. Since NODEs...

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry and anti-$\mathcal{PT}$ give rise to exceptional points (EPs) intriguing properties related to, e.g., chiral transport enhanced sensitivity, due the coalescence of eigenvectors. In this paper, we propose a powerful easily computable tool, based on Hilbert-Schmidt speed (HSS), which does not require diagonalization evolved density ...