we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unitweight fusion frames with these properties is the flexible a...

Objective: The objective of this study was to compare plasma concentrations of C-reactive protein between pregnant patients with preeclampsia and subjects with uncomplicated pregnancy. Subjects and Methods: We conducted a case-control study of 60 nulliparous women without preexisting medical complications. In this study, 30 patients with preeclampsia and 30 women with uncomplicated pregnancy we...

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw(φ → ψ) → (Kwφ → Kwψ). Knowing whether logic cannot define many common frame properties, and its expressive po...

This document contains supplementary materials for the paper Frames and numerical approximation by B. Adcock & D. Huybrechs [3]. SM1 Example 1. Fourier frames for complex geometries Consider the frame (3.1) over a domain Ω ⊆ (−1, 1)d. SM1.1 The kernel of G We first characterize the kernel of the Gram operator: Proposition SM1.1. Let G be the Gram operator (2.7) of the frame (3.1). Then Ker(G) =...

This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equatio...

(a) The expectation value of a component 〈α|V̂i|α〉 remains unchanged in the rotated frame (with respect to the transformed operator), i.e., 〈α′|V̂ ′ i |α′〉 = 〈α|V̂i|α〉 where |α〉 −→ D(R)|α〉 = |α′〉 and V̂ ′ i is the operator transform. The expectation value in the two bases must be the same, because we are assuming that space is isotropic, and all physical observables and physical laws must remain in...

| The Gabor transform yields a discrete representation of a signal in the phase space 1, 2]. Since the Gabor transform is non-orthogonal, eecient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so-called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, bas...