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.     

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)     

Control of de-excitation to selected vibrational levels in the ground state of NaH molecule using two broadband ultrashort pulses

We show that the de-excitation to different vibrational levels of the ground state in NaH molecule can be controlled by using two delayed ultrashort pulses (4 fs Gaussian). A vibrational wave packet generated on the excited A¹Σ⁺ state by the first pulse is de-excited back to the ground state by a second pulse after a time delay. The cross-section for de-excitation of the wave packet to different vibrational levels of the ground electronic state can be controlled by controlling the delay time between the two pulses as well as by choosing a pulse duration much shorter than the vibrational period of the molecule, such that the de-excited wave packet remains localized in the Franck–Condon region of a particular vibrational level of the ground state. Hence, the de-excitation to a particular vibrational level can be enhanced by suppressing that in others. In spite of the large bandwidth of the pulse which includes nine vibrational levels of the upper state and five vibrational levels of the ground state, one can selectively de-excite the molecule to any one or two vibrational levels of the ground state by carefully choosing the delay time between the pulses and the pulse duration. We are designing the wave packet in the ground state by two short pulses and selectively distributing the population in one or two levels at various values of the delay time. In light molecules having small vibrational period, this selectivity in de-excitation to one or two vibrational levels in the ground state can be achieved only by using ultrashort (4 fs) pulses in the presence of which the localization of the wave packet in the Franck–Condon region of the vibrational levels are particularly possible. It has been shown that the de-excitation cross-section to a particular vibrational level oscillates with delay between the pulses which can be realized as a time-dependent quantum gate.     

Luminescence characteristics of K2Ca2(SO4)3:Eu,Tb micro- and nanocrystalline phosphor

K₂Ca₂(SO₄)₃ microcrystalline pure, doped with Eu, Tb and co-doped with Eu, Tb was prepared by solid-state diffusion method. Nanoparticles of these phosphors were also prepared by the chemical co-precipitation method. The formation of the compounds was confirmed by XRD. The particle size was calculated by broadening of the XRD peaks using Scherrer's formula. The particle size of nanocrystalline powder material was approximately found to be around 20 nm. Thermoluminescence and photoluminescence were studied to see the effect of co-doping and particle size. Tb³⁺ co-doping decreases the intensity in the Eu²⁺ doped phosphor due to the energy transfer and multiple de-excitations through various radiative and non-radiative processes. The sensitivity of K₂Ca₂(SO₄)₃:Eu,Tb microcrystalline phosphor was around 15 times more than LiF-TLD 100 and 7 times more than CaSO₄:Dy. A high temperature peak (615 K) was observed in case of the nanoparticles, which was attributed to a particle size induced phase transition. This was confirmed by differential scanning calormetry measurements. The decrease in the sensitivity in case of nanoparticles is attributed to the particle size effect i.e. volume to surface ratio. Theoretical analysis of the glow curves was done by glow curve convolution deconvolution method to calculate trapping parameters of various peaks.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

A unified framework for constructing globally convergent algorithms for multidimensional coefficient inverse problems

We present a unified framework for constructing the globally convergent algorithms for a broad class of multidimensional coefficient inverse problems arising in natural science and industry. Based on the convexification approach, the unified framework substantiates the numerical solution of the corresponding problem of nonconvex optimization. A globally convergent iterative algorithm for an inverse problem of diffuse optical mammography is constructed. It utilizes the contraction property of a nonlinear operator resulting from applying the convexification approach. The effectiveness of this algorithm is demonstrated in computational experiments.     

Viable solutions of differential inclusions on closed sets

This article studies the existence of viable solutions to the Cauchy problem u′ ∈ ? (t , u) for a.e. t∈ [0,1], u (0)=x ₀ ∈ K (a closed subset of R ^N ) where the nonlinearity ? satisfies a Wintner-type growth condition.