The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.     

Polar decompositions and related classes of operators in spaces ∏κ

Polar decompositions with respect to an indefinite inner product are studied for bounded linear operators acting on a space. Criteria are given for existence of various forms of the polar decompositions, under the conditions that the range of a given operatorX is closed and that zero is not an irregular critical point of the selfadjoint operatorX ^[*]X. Both real and complex spaces are considered. Relevant classes of operators having a selfadjoint (in the sense of the indefinite inner product) square root, or a selfadjoint logarithm, are characterized.The work of this author was partially supported by INdAM-GNCS and MURSTThe work of this author was partially supported by NSF grant DMS-9988579.     

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

The equation of state of binary ionic mixtures of similar ions, such as nitrogen, oxygen and carbon, has been extensively studied. The study of dense asymmetric mixtures, where Z₂ >> Z₁, has primarily focused on mixtures of hydrogen and iron at solar conditions. Using molecular dynamics simulations, we examine the behavior of highly asymmetric binary ionic mixtures, where the coupling of the high‐Z species may be orders of magnitude higher than the coupling of the low‐Z species. For the conditions we have studied, we find that strong correlations and signatures of solidification occur in the high‐Z species, while the low‐Z species exists as a freely flowing fluid within the high‐Z solid matrix. Solidification of the low‐Z species is correlated with the coupling between the two components. Using the Widom expansion method, we compute the plasma screening enhancement of the nuclear reaction rates for Z = 1 in a high‐Z matrix. We also provide some estimates of the coefficient of binary diffusion in the mixture. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

     

Approximation numbers and Yamamoto's theorem in Banach algebras

Yamamoto's Theorem is an asymptotic relation between the singular values and eigenvalues of a matrix. There are formulations of this result involving generalized singular values (approximation numbers) of matrices and, more generally, bounded linear operators on Banach spaces. In this paper, we prove Yamamoto type theorems for Banach algebras.This work partially supported by NSF grant DMS 88-02836     

Stable real invariant semidefinite subspaces and stable factorizations of symmetric rational matrix functions

Stability of certain classes of invariant subspaces of a real matrix which is selfadjoint in a real indefinite inner product, is studied. The study is motivated by, and subsequently applied to, the problem of stability for minimal factorizations of real symmetric rational matrix functions.     

On the spectral structure of monic matrix polynomials and the extension problem

We consider the following problem: find a monic matrix polynomial, given its companion matrix on a fixed invariant subspace, and given also the Jordan structure of this matrix on some complimentary invariant subspace. A detailed investigation is presented for the case when the additional Jordan matrix has only one point of spectrum.