Nonlinear multi-parameter eigenvalue problems for systems of nonlinear ordinary differential equations arising in electromagnetics

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of nonlinear waveguides to a more general nonlinear multiparameter eigenvalue problem for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations whose roots yield the desired eigenvalues. The existence and distribution of roots are veried

Pannexin 1 facilitates arterial relaxation via an endothelium-derived hyperpolarization mechanism

AbstractPannexin 1 (Panx1) is involved in endothelium-dependent vasodilation in large arteries, but the exact mechanistic role remains poorly understood. We hypothesized that Panx1 facilitates large vessel relaxations regulating endothelium-derived hyperpolarization (EDH)-like mechanisms. The EDH-like component of acetylcholine-induced relaxation of saphenous arteries studied in isometric myograph after inhibition of NO-synthase and cyclooxygenase was significantly impaired in mice with genetically ablated Panx1 (KO) relative to that in the wild type (WT) mice. Application of P1-receptor antagonist and apyrase significantly reduced this component in WT, but not in KO mice, indicating participation of ATP released via Panx1 in the EDH-like relaxation

Resonant States and Unique Permittivity Reconstruction of Layered Dielectrics

Proceeding from the discovery of complex singularities of the scattering matrix of a multi-layered parallel-plane dielectric inclusion in a waveguide of rectangular cross section, a method is proposed for justifying unique reconstruction of the layer permittivities. The technique is extended to the analysis of more complicated dielectric inclusions placed in waveguides of arbitrary cross section

Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes

Cloaking: analytical theory for benchmark structures

Proceeding from the scattered field expansion in cylindrical harmonics, we define partial invisibility or partial cloaking as suppression of finitely many lowest-order field harmonics. We show that for benchmark structures (a dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric dielectric layer), such multiple suppression can be achieved. For this purpose, we prove the solvability and explicitly determine the solution of the corresponding equation system which provide vanishing of the lowest-order field expansion coefficients and the resulting simultaneous suppression of up to five lowest- order scattered harmonics. We investigate the character and qualitative properties of partial invisibility and partial cloaking by analyzing the scattered field patterns