A Parabolic Approach to Martin Boundaries for Elliptic Equations in Skew Product Form

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin compactifications and Martin kernels for a wide class of elliptic equations in skew product form by exploiting parabolic Martin kernels for associated parabolic equations.     

On height isotopy classes of embeddings in the plane of a Morse function of a circle

Let \(\mathrm{SM}_{2n}(S^1,\mathbb {R})\) be a set of stable Morse functions of an oriented circle such that the number of singular points is \(2n\in \mathbb {N}\) and the order of singular values satisfies the particular condition. For an orthogonal projection \(\pi :\mathbb {R}^2\rightarrow \mathbb {R}\), let \({\tilde{f}}_0\) and \({\tilde{f}}_1:S^1\rightarrow \mathbb {R}^2\) be embedding lifts of f. If there is an ambient isotopy \(\tilde{\varphi }_t:\mathbb {R}^2\rightarrow \mathbb {R}^2\) \((t\in [0,1])\) such that \({\pi \circ \tilde{\varphi }}_t(y_1,y_2)=y_1\) and \(\tilde{\varphi }_1\circ {\tilde{f}}_0={\tilde{f}}_1\), we say that \({\tilde{f}}_0\) and \({\tilde{f}}_1\) are height isotopic. We define a function \(I:\mathrm{SM}_{2n}(S^1,\mathbb {R})\rightarrow \mathbb {N}\) as follows: I(f) is the number of height isotopy classes of embeddings such that each rotation number is one. In this paper, we determine the maximal value of the function I equals the n-th Baxter number and the minimal value equals \(2^{n-1}\).     

Martin Boundaries of Elliptic Skew Products, Semismall Perturbations, and Fundamental Solutions of Parabolic Equations

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations.     

The Effects of Comprehensive Exercise Program on the Adjustments of Standing Balance in Community-Dwelling Elderly Persons

The objective of this study was to assess the effect of comprehensive exercise program widely accepted as a community-based physical intervention for the prevention of falling in the elderly persons on their controlling standing balance. Twenty-six community-dwelling elderly persons (13 males and females; 69.8 ± 2.8 years old) participated in this study. Daily exercise was comprised of walking for more than 30 min, stretching, muscle strengthening and balance exercise without exercise equipments. The intervention was continued for three months. Indicators of standing balance related to static balance, dynamic balance and postural response were measured before and after the intervention. As an effect of the intervention on static balance, the sway of center of pressure (COP) in the static stance significantly increased. In the dynamic balance, significant improvements were observed in one leg standing time, the 10-m gait time, functional reach. Additionally, the maximal movable length of COP which subjects can move voluntarily to right and left significantly increased. In the postural response, the integrated electromyography (IEMG) induced by postural response for sudden postural perturbation significantly decreased in the lower leg muscles. Since less muscular activities were sufficient to maintain posture, it was suggested that postural response was elicited more efficiently following the intervention. This study suggested that the comprehensive exercise program, which has been widely introduced as community-based interventions for the prevention of falling, have extensive effects on the control of standing balance covering static balance, dynamic balance and postural response in the elderly persons.     

Common-path achromatic interferometer-coronagraph: nulling of polychromatic light

A three-dimensional common-path interferometer is proposed, which can achromatically null out an on-axis source while it maintains the detectability of an off-axis source. A geometric phase in the three-dimensional interferometer introduces an achromatic pi-phase shift to the light from the on-axis source, such that destructive interference nulls out the axial light at one of the ports of the interferometer. Light from the off-axis source, which is exempt from the pi-phase shift, comes out from both ports with equal intensity. The common-path scheme makes the system highly immune to environmental disturbances.     

Immobilization of microbial cells by radiation-induced polymerization of glass-forming monomers and immobilization ofStreptomyces phaeochromogenes cells by polymerization of various hydrophobic monomers

The immobilization ofStreptomyces phaeochromogenes cells was studied by the radiation-induced polymerization of various hydrophobic glass-forming monomers at low temperatures. The glucose isomerase activity of cells immobilized in hydrophobic polymers showed no decrease in activity with repeated use (batch enzyme reaction). Activity increased with increasing monomer concentration in contrast to results with the immobilized enzyme. The hydrophobic polymer composite was microspheric in form. The particle diameter of the composite increased with the increasing monomer concentration.K _m values of the immobilized cells were close to that of intact cells. It was deduced that the cells were trapped on the surface part of the hydrophobic polymer ready to react with the substrate, and not within the matrix where diffusion would play an important role in reaction rates.     

Determination of sulphide ion at trace levels by ethylation and gas chromatography

Summary A method is described for the determination of sulphide ion in aqueous samples by gas chromatography. Sulphide is ethylated with diethyl sulphate and the resulting diethyl sulphide is extracted with chloroform and determined with a gas chromatograph equipped with a flame ionization or a flame photometric detector. In the case of a flame photometric detector, the detection limit for sulphide ion is 0.05 g/ml. Other anions commonly found with sulphide ion do not interfere. Sulphide ion in spring waters was analysed by this new method and for comparison also by colorimetry (methylene blue). The results revealed the reliability of the new method.

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Bestimmung von Sulfidspuren durch Ethylierung und Gas-Chromatographie

Zusammenfassung Sulfid wird mit Diethylsulfat ethyliert, das gebildete Diethylsulfid mit Chloroform extrahiert und gaschromatographisch mit Hilfe eines Flammenionisationsoder eines flammenphotometrischen Detektors bestimmt. Die Nachweisgrenze beträgt 0,05 g S/ml für den FPD. Anionen, die üblicherweise mit Sulfid zusammen vorkommen, stören nicht. Das Verfahren wurde, im Vergleich mit der colorimetrischen Methylenblaumethode, auf Quellwasser angewendet. Es wurde gute Übereinstimmung der Ergebnisse erzielt.