Filament sets and homogeneous continua

New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.     

Recognition of the structural-functional organization of genetic sequences

The analysis problem for genetic sequences is formulated from the viewpoint of modern mathematical and information approaches. Statistical, correlative, entropic, and spectral approaches are considered. A brief introduction into the background of the problem is given. Genesis of a new interdisciplinary subject area, bioinformatics, a science considering application of computer methods in biological studies, is analyzed. New approaches to studying macromolecular systems on the basis of combined spectral-analytic technologies are proposed. Estimates of the algorithmic complexity of implementation of the proposed approaches are presented.     

Structural and electrical characterization of PZT on gold for micromachined piezoelectric membranes

Piezoelectric membranes have been fabricated that incorporate a gold bottom electrode with an adhesion layer of titanium–tungsten (10:90 wt. %). For solution-deposited acetic acid based lead zirconate titanate (HoAc-PZT) with a Zr:Ti ratio of 40:60, the film’s average piezoelectric coefficient, e₃₁, is -5.31 C/m², with a dielectric constant of 814 at 200 Hz, which is similar to values for platinum bottom electrodes. The PZT structure remains columnar on both types of bottom electrodes. Initial fabrication attempts resulted in cracking that initiated in the PZT layer of the structure. X-ray photoelectron spectroscopy was utilized to establish how processing affects diffusion throughout the composite membrane structure. Crack-free membranes were fabricated and tested. This paper discusses the performance properties and piezoelectric fatigue results for these membranes. PACS 77.84.-s; 77.84.Lf     

Synthesis and conformational study of 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines

A new class of endocyclic enamines, 1,6-disubstituted 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines, was synthesized from 4-piperidone imines by successive subjecting the latter to lithiation with lithium diethylamide, to alkylation with 1-bromo-3-chloropropane, and to intramolecular cyclization. All stages were carried out as a unique process without isolation of the intermediate compounds. A thorough optimization of the process conditions, workup, and product storage was carried out. The conformational study of 1,6-disubstituted 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines was performed.     

Evidence for complex magnetic order in U2Zn17: A μ+ SR studySR study

μ⁺ SR-measurements in transversally applied magnetic fields of 2000 G and 4000 G on heavy-electron single crystal U₂Zn₁₇ are presented. They reveal that at least two types of interstitial sites are occupied by the positive muons. One of these sites (1/3, 2/3, 5/6) could be identified via induced local dipolar fields which aboveT _N=9.7 K can exactly be derived from the magnetic susceptibility. The corresponding component of the μ⁺-signal exhibits a steplike decrease by about 40% atT _N which is caused by the onset of a very broad distribution of static internal magnetic fields (ΔB≈1000 G) with zero average. Such a field distribution is in distinct contrast to dipolar-field calculations performed for the simple antiferromagnetic structure deduced from neutron diffraction. The remaining 60% of the muons contributing to this component belowT _N are subject to a narrow static field distribution (ΔB≈1 G). The induced dipolar fields at the site (1/3, 2/3, 5/6) are temperature-independent belowT _N. A weak dipolar coupling to the U-moments renders similar observations for muons occupying the second type of interstitial impossible.     

Rational functions of best uniform approximation and holomorphic continuation of functions

Let f be a function, continuous and real valued on the segment Δ, Δ ⊂ (−∞, ∞) and {R_n} be the sequence of the rational functions of best uniform approximation to f on Δ of order (n, n). In the present work, the convergence of {R_n} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {R_n} accumulate in the terms of weak convergence of measures to acompact set of zero capacity. As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of f are given. The work is supported by Project 69 with Ministry of Science and Education, Bulgaria.     

Quantitative EPR — Sensitivity to experimental conditions and optimal setting of recording parameters

This is the proportionality of the area under undistorted absorption curve to the spin number contributing to the resonance phenomena which makes the electron paramagnetic resonance spectrometry a method of quantitative analysis. However, quantitative EPR (Q-EPR) is not so simple as the relation is. Direct quantitative measurements are practically excluded, the comparison of both standard and unknown sample EPR signals (indirect determination) is rather used, as a rule. The accuracy of spin number determination is an essential problem of quantitative EPR. The experimental conditions and instrumental variables influencing the signal shape and intensity may lower the accuracy of quantitative determinations. There is different sensitivity of various line parameters to the instrumental distortions and experimental conditions. Thus, the optimal setting of instrumental variables controlling the distortions depends on the procedure being used for quantitative determinations. The aspects of sensitivity of different Q-EPR procedures to instrumental distortions, as well as the rules of optimal setting of these parameters are the subject of this review.