We show that the canonical quantifications of uniform properties such as precompactness and total boundedness, which were already studied by Kuratowski and Hausdorff in the setting of complete metric spaces, can be generalized in the setting of products of metric spaces in an intuitively appealing way. 2000 Mathematics Subject Classification. 54E15, 18B30.

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

We study the initial boundary value problem for a time-dependent Ginzburg-Landau model of superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion parameter > 0 in the case of Coulomb gauge for 2D case. Our second result is the uniqueness of axially symmetric weak solutions in 3D with L2 initial data under Lorentz gauge. Mathematics Subject Classi...

In this paper, synchronization between two Rössler Chaotic Systems with impulsively controlling is established by using the criteria on uniform equi-boundedness and equi-Lagrange stability for impulsive systems. After several theoretical derivations, some simulation results are given to demonstrate our results.

We consider a d-vnamic system containing uncertain elements. Only the set of possible values of these uncertainties is known. Based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbimrity srnnll neighborhood of the zero state. These feedback controls are continuous functions of the state.

In this work, we will introduce a fractional Duhamel principle and use it to establish the well-boundedness stability of mild solution an original stochastic equation with initial data.

We present a functional interpretation of Peano arithmetic that uses Gödel’s computable functionals and which systematically injects uniformities into the statements of finite-type arithmetic. As a consequence, some uniform boundedness principles (not necessarily set-theoretically true) are interpreted while maintaining unmoved the Π2-sentences of arithmetic. We explain why this interpretation ...

We prove that if μ is a d-dimensional Ahlfors-David regular measure in R, then the boundedness of the d-dimensional Riesz transform in L(μ) implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of μ.

Abstract. For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to L∞ norm, which generalize analogous results obtained for little qLegendre, little q-Jacobi and little q-Laguerre polynomials, b...