This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that sampling with well-localized frames improves both the accuracy of the numerical frame approximation as well as the robustness and efficiency of the (finite) frame...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

Motivated by the strong maximum principle for Paneitz operator in dimension 5 or higher found in [GM] and the calculation of the second variation of the Green’s function pole’s value on S3 in [HY2], we study Riemannian metric on 3 manifolds with positive scalar and Q curvature. Among other things, we show it is always possible to …nd a constant Q curvature metric in the conformal class. Moreove...

In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

In this dissertation I study the properties of singleton kinds and singleton types. These are extremely precise classi ers for types and values, respectively: the kind of all types equal to [a given type], and the type of all values equal to [a given value]. Singletons are interesting because they provide a very general and modular form of de nition, allow ne-grained control of type computation...

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes localize the information within entangled state, must enact an entanglement extraction protocol also that frame. for Gaussian ground in such construction has been shown require minimum energy and hence interesting process gravitational p...

We describe a computer program which facilitates the analysis of a series of C.T. scans made while a stereotaxic frame is fixed to the patient. The program has 2 modes of operation: a) The operator may select a region and determine the three-dimensional frame coordinate. b) The operator may select a set of frame coordinates and have the computer program display these at the appropriate sites on...