In this paper, we are interested in the finite-time synchronization of complex-valued BAM neural networks with time delays. Without applying Lyapunov–Krasovskii functional theory, convergence theorem, graph-theoretic method, theory complex functions or integral inequality by using quadratic analysis approach, techniques and designing two classes novel controllers, sufficient conditions achieved...

We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of matchings, extended by a binary number indicating whether the matching contains two specific edges. This polytope is associated to the quadratic matching problem with a single linearized quadratic term. We provide a complete irredundant inequality description, which settles a conjecture by Klein (Ph.D. the...

If F is a finitely generated free group and φ is an automorphism of F then F ⋊φZ satisfies a quadratic isoperimetric inequality.

Rhodopsin (Rho) is a G protein-coupled receptor that initiates phototransduction in rod photoreceptors. High expression levels of Rho in the disc membranes of rod outer segments and the propensity of Rho to form higher oligomeric structures are evident from atomic force microscopy, transmission electron microscopy, and chemical cross-linking experiments. To explore the structural and functional...

We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. prove that the superharmonicity of provides sufficient condition to obtain inequalities. Namely, if $$\rho $$ is nonnegative and $$-\varvec{\Delta } \rho \ge 0$$ in weak sense, where $$\varvec{\Delta }$$ Finsler–Laplace operator defined by \varvec{\Delta = \mathrm {div}(\varvec...

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

Abstract. A cell-population based model for tumor growth under anti-angiogenic treatment with the tumor volume and its variable carrying capacity as variables is combined with the linear-quadratic model for damage done by radiation ionization. The resulting multi-input system is analyzed as an optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric con...