We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension d = 2 is also gi...

Given a volume-preserving homeomorphism of a smooth manifold of dimension n ≥ 5, we give a necessary and sufficient condition for uniform approximability by (volume-preserving) diffeomorphisms.

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two.

a comparison of buckling analysis of the nanoplate and nanocomposite plate with central square hole embedded in winkler foundation is presented in this article. in order to enhance mechanical properties of nanoplate with central cut out, carbon nano tubes (cnts) are applied as uniform distribution (ud) through thickness direction. in order to define the shape function of plate with square cut o...

We study the mean dimension of the moduli space of Brody curves. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension. 1. Main results 1.1. Moduli space of Brody curves. M. Gromov introduced a remarkable notion of mean dimension in [6] (see also Lindenstrauss-Weiss [8] and Lindenstrauss [7]). In this paper we study the mean dimension of the modu...

Developable surfaces possess qualities that are desirable in the manufacturing processes of CAD/CAM models. Specifically, models formed out of developable surfaces can be manufactured from planar sheets of material without distortion. This quality proves most useful when dealing with materials such as paper, leather or sheet metal, which cannot be easily stretched or deformed during production....

We solve Talagrand’s entropy problem: the L2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley’s theorem on classes of {0, 1}valued functions, for which the shattering dimension is the VapnikChervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal ...

This paper presents a computation of the Vγ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression ǫ-insensitive loss function Lǫ, and general Lp loss functions. Finiteness of the Vγ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the Lǫ ...

Isolated and purified glomerular basement membranes (GBM) of normal and aminonucleoside (PAN) nephrosis rats were observed by electron microscopy after negative staining. Although GBM of normal rats appeared as a molecular sieve with uniform pores, GBM of nephrotic rats showed enlargement and elongation of the pores. For an average of fifty pores, the long dimension was 40.4+/-10.7 A and the sh...

If S is an infinite sequence over a finite alphabet Σ and β is a probability measure on Σ, then the dimension of S with respect to β , written dimβ (S), is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension dim(S) when β is the uniform probability measure. This paper shows that dimβ (S) and its dual Dimβ (S), the strong dimension of S with...