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Cobalt phthalocyanine (Na_2.8CoPc) organic molecular ferromagnets with a Curie temperature higher than room temperature were synthesized. By means of EXAFS spectroscopy the nearest coordinational environment of the Co ion was examined in both Na_2.8CoPc and pristine β-CoPc as well as in standard substances containing metallic cobalt. The nearest coordinational environment of the Co ion in ferromagnetic Na_2.8CoPc is shown to remain virtually invariable as compared with that in pristine β-CoPc. This environment is conditioned by the nitric and carbonic coordination spheres of the phthalocyanine and differs essentially from the nearest coordinational environment of Co in metallic cobalt. The results of EXAFS studies serve as direct structural evidence that the nature of the ferromagnetism in Na_2.8CoPc is conditioned by the organic matrix, namely by (CoPc)²⁻ and (CoPc)³⁻ anions with unpaired π-electrons in the 7e_g doubly degenerate MO of the conjugated phthalocyanine macro-ring.

In this paper we consider spectral representation of infinite dimensional stationary random fields over an abelian locally compact (or LCA) group, and then extend the results of earlier authors who consider wide sense Markov random fields over a Euclidean group ℝⁿ to the general LCA group context and obtain minimality properties. We also indicate possibilities of some extensions of these results to certain nonstationary classes.

This paper presents an approach to the registration of individual images to one another to produce a larger composite mosaic. The approach is based on the use of the moments of Zernike orthogonal polynomials to compute the relative scale, rotation and translation between the images. A preliminary stage involves the use of an attention-like operation to estimate potential approximate correspondence points between the images based on extrema of local edge element density. Experimental results illustrate that the technique is effective in a range of environments and over a broad range of image registration parameters. In particular, our method makes few assumptions regarding the image content and yet, unlike several alternative approaches, can perform registration for images with only a limited amount of overlap.

We examine the stability of a class of continuous age-structured models. Stability borders are established for the different parameters in the model, including levels required for viability. Two examples are then given, the first is a simple model for which the analysis is straightforward. An example is then shown of the cod population in the North Sea, which involves more complicated life history structures making stability analysis more difficult. The model predicts that the North Sea population will go extinct if fishing levels remain high. We show, however, that if mortality was lowered it would eventually be possible for the population to reach a point where it was stable and within safe biological limits.

We investigate the spectral asymptotic properties of the stationary dynamical system ξ_t = φ(T^t(X₀)). This process is given by the iterations of a piecewise expanding map T of the interval [0,1], invariant for an ergodic probability μ. The initial state X₀ is distributed over [0,1] according to μ and φ is a function taking values in ℝ. We establish a strong law of large numbers and a central limit theorem for the integrated periodogram as well as for Fourier transforms associated with (ξ_t : t ∈ ℕ). Several examples of expanding maps T are also provided.

The paper presents an informal review of some techniques available for signal analysis. In the interpretation of biomedical signals, the individuation of hidden transient phenomena in the spectrum can have a crucial role for diagnostic purposes. Since most biological signals are nonstationary, the Fourier transform is not sufficient to detect possible transient phenomena in the spectrum; therefore, some improvements in the Fourier transform technique have been carried out by means of window functions in the transformation kernel. Some of the most important features of recent developments in signal analysis are discussed here, with special focus on the uncertainty principle governing any time–frequency analysis.

In this paper, a general summability method of multi-dimensional Fourier transforms, the so-called $\theta$-summability, is investigated. It is shown that if $\widehat{\theta }$ is in a Herz space, then the summability means ${\sigma }_T^{\theta }f$ of a function $f\in W(L_1,{\ell }_{\infty })({ℝ}^d)$ converge to $f$ at each modified Lebesgue point, whenever $T\to \infty$ and $T$ is in a cone. The same holds for Fourier series. Some special cases of the $\theta$-summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, Cesàro, de la Vallée-Poussin, Rogosinski and Riesz summations.

By applying an integral representation for $q^{k^2}$, we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of $q$-functions and polynomials that naturally arise from combinatorics, analysis, and orthogonal polynomials corresponding to indeterminate moment problems. These functions include $q$-Bessel functions, the Ramanujan function, Stieltjes–Wigert polynomials, $q$-Hermite and $q^{-1}$-Hermite polynomials, and the $q$-exponential functions $e_q$, $E_q$ and ${{ℰ}}_q$. Their representations are in turn used to derive many new identities involving $q$-functions and polynomials. In this paper, we also present contour integral representations for the above mentioned functions and polynomials.

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity is constructed. The resulting nondimensional governing equations, together with the Laplace and double Fourier transform techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free surface. The inverses of double Fourier transforms and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of thermal conductivity has significant effects on all the studied fields.

Optical pattern recognition and neural associative memory are important research topics for optical computing. Optical techniques, in particular, those based on holographic principle, are useful for associative memory because of its massive parallelism and high information throughput. The objective of this chapter is to discuss system issues including the design and fabrication of a multi-sensory opto-electronic feature extraction neural associative retriever (MOFENAR). The innovation of the approach is that images and/or 2-D data vectors from a multiple number of sensors may be used as input via an electrically addressed spatial light modulator (SLM) and hence processing can be accomplished in parallel with high throughput. A set of Fourier transforms of reference inputs can be selectively recorded in the hologram. Unknown image/data can then be applied to the MOFENAR for recognition. When convergence is reached after iterations, the output can either be displayed or used for post-processing computations. We included experimental results that demonstrate the ability of the system to recognize and/or restore input images.

This paper presents an approach to the registration of individual images to one another to produce a larger composite mosaic. The approach is based on the use of the moments of Zernike orthogonal polynomials to compute the relative scale, rotation and translation between the images. A preliminary stage involves the use of an attention-like operation to estimate potential approximate correspondence points between the images based on extrema of local edge element density. Experimental results illustrate that the technique is effective in a range of environments and over a broad range of image registration parameters. In particular, our method makes few assumptions regarding the image content and yet, unlike several alternative approaches, can perform registration for images with only a limited amount of overlap.

Image analysis using computational Fourier transforms is here applied to radiographs of vertical vertebral bone sections. Simple variables are derived that measure gross properties of the vertebral patterns and study of these using univariate statistical analyses indicates, as would be expected, that there are differences with age and in each sex. Complex variables that characterise the transforms more completely show, when analysed using multivariate statistical methods, increased detail of difference with age and sex. Thus, in the oldest individuals of both sexes, the transforms seem to recognise osteoporosis. In middle-aged individuals, though males seem fairly normal, females have features that look like those in the old individuals, though only the older middle-aged specimens show the overt condition. Whether or not this is osteoporosis, the structural features found in the entire vertebral body in the old individuals exist in the two anterior quadrants of the middle-aged females. Even in young individuals, there is a difference between males and females. This seems to relate to the same structural features as before, but they exist in only a single quadrant, the antero-superior. Though used here for the analysis of radiographs of sections, the technique is equally applicable to non-invasive images. It is easy and inexpensive to carry out. It seems to provide information of functional importance in terms of vertebral mechanics. It may be capable of development for clinical situations to reveal incipient change long before symptomatic disease is present.