We adapt Sarason’s proof of the Julia-Caratheodory theorem to the class of Schur-Agler mappings of the unit ball, obtaining a strengthened form of this theorem. In particular those quantities which appear in the classical theorem and depend only on the component of the mapping in the complex normal direction have K-limits (not just restricted K-limits) at the boundary. Let B denote the open uni...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

The three-way table problem is to decide if there exists an l × m × n table satisfying given line sums, and find a table if yes. Recently, it was shown to be fixed-parameter tractable with parameters l, m. Here we extend this and show that the huge version of the problem, where the variable side n is encoded in binary, is also fixed-parameter tractable with parameters l, m. We also conclude tha...

We prove a general Borg-type result for reflectionless unitary CMV operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on the unit circle. This extends a recent result of Simon in connection with a periodic CMV operator with spectrum the whole unit circle. In the course of deriving the Borg-type result we also use exponential...

Let M be a close complex manifold and T M its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then M is a complex homogeneous manifold. It implies that every irreducible close Kähler manifold with ample tangent bundle is isomorphic to the projective space. This provides an alternative proof of Hartshore's conjecture in algebrai...

Biometrics is a science that deals with human identification on the basis of our biological features. Therefore, Biometrics belongs to Pattern Recognition and is part of it. Biometric examples are all features we are born with like facial image, finger-prints, iris of the eye, . . . or the features we learn in our life like the way we write (signature), the way we walk (gait) or any of the beha...

We establish pointwise a priori estimates for solutions in D (R) of equations of type−∆pu = f (x, u), where p ∈ (1, n), ∆p := div ( |∇u|∇u ) is the p–Laplace operator, and f is a Caratheodory function with critical Sobolev growth. In the case of positive solutions, our estimates allow us to extend previous radial symmetry results. In particular, by combining our results and a result of Damascel...

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measure-valued functions. This main result implies existence of solutions...