Let X = ε n x n be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable ||X|| in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given. In [6] the second-named author calculated the distribution of a scalar Rademacher series ε n a n...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...

Using the framework provided by Clifford algebras, we consider a noncommutative quotient-difference algorithm for obtaining the elements of a continued fraction corresponding to a given vector-valued power series. We demonstrate that these elements are ratios of vectors, which may be calculated with the aid of a cross rule using only vector operations. For vector-valued meromorphic functions we...

Unit-vector fields n on a convex polyhedron P subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to minimisers and local minimisers of the Dirichlet energy, and may be regarded as S-valued harmonic maps on P . We consider unit-vector fields which are continuous away fro...

We consider Perron solutions to the Dirichlet problem for quasilinear elliptic equation divA(x,∇u)=0 in a bounded open set Ω⊂Rn. The vector-valued function A satisfies standard ellipticity assumptions with 1<p<∞ and p-admissible weight w. show that arbitrary perturbations on sets of (p,w)-capacity zero continuous (and certain quasicontinuous) boundary data f are resolutive such coincide. As con...

where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...

This paper introduces a high-order time stepping technique for solving the incompressible Navier–Stokes equations which, unlike coupled techniques, does not require solving a saddle point problem at each time step and, unlike projection methods, does not produce splitting errors and spurious boundary layers. The technique is a generalization of the artificial compressibility method; it is uncon...