Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

     

Luminescence kinetic and association equilibria of lanthanide ions in aqueous solutions. II. Determination of the formation constant of Tb acetato complex by means of luminescence lifetime measurement

The association constant K of mono-acetato complex of Tb³⁺ has been determined at normal p and T conditions by measurement of its luminescence lifetime in aqueous solution containing increasing concentrations of acetate. Two experimental arrangements used for the measurement are described.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

Trennung von Spurenelementaktivitäten aus Neutronenbestrahltem Selen mit Hilfe der Gegenstrom-Ionenwanderung

For the determination of trace elements in neutron irradiated, selenium by gamma-ray spectrometry the separation of the matrix activity is often necessary. In model experiments the decontamination of cation and anion impurities from the matrix solution was investigated by the counter current ion migration. After a processing of 3 hrs the trace activities of Co, Cr, Ga, Na and Zn were decontaminated from Se with a factor of >10³. For the trace elements As and Te representing the anionic constituents, a decontamination factor of 3·10² was obtained.     

Association of hydrofluoric acid in NaCl aqueous media under hydrothermal conditions

The apparent association constant of hydrofluoric acid Q _HF ^' in 1m NaCl aqueous media has been determined potentiometrically at pressures up to 1 kbar and temperatures up to 250°C. A concentration cell employing hydrogen electrodes was used. The association of HF increases with increasing temperature but decreases with increasing pressure.     

On the Sturm-Liouville operator

We consider the homogeneous Sturm-Liouville differential equation, prove the existence of two linearly independent solutions that form a fundamental system, and obtain some of their properties.     

Organotin(IV) Carboxylates of Substituted α‐Cinnamic Acid,RnSn(OCOC(R2)=CHR1)4 – n: Synthesis,Spectroscopic Characterization and Biological Evaluation

Di‐ and triorganotin(IV) carboxylates, R_nSn(OCOC(R²)=CHR¹)_4–n (n = 2 and 3; R = Me, Et, n‐Bu, Ph; R¹ = 3‐CH₃O‐4‐OHC₆H₃, R² = C₆H₅) were prepared by reacting the corresponding organotin(IV) chloride with the silver salt of the (E)‐3‐(4‐hydroxy‐3‐methoxyphenyl)‐2‐phenylpropenoic acid. The title compounds were investigated and characterized by elemental analysis, infrared (FT‐IR), multinuclear (¹H, ¹³C, ¹¹⁹Sn) NMR, and mass spectrometry, and possible structures were proposed. The complexes and ligand acid ( HL ) have been evaluated in vitro against various bacteria and fungi. The results noticed during the biocidal activity screenings proved their in vitro biological potential. They were also tested for cytotoxicity.     

Experimental comparison of performance and emission characteristics of 4-stroke CI engine operated with Roselle and Jatropha biodiesel blends

The environmental degradation, combined with the continuous depletion of the world's fossil fuel reserves, has forced the search for alternative fuels. This study was performed to investigate the performance of novel biodiesels in the CI engine. The experiments were performed at three different compressions ratios (16:1, 17:1, 18:1) and four loading conditions (25%, 50%, 75%, 100%). Different types of fuels such as jatropha biodiesel (JB), roselle biodiesel (RB), and ternary biodiesel (TB) were prepared and analyzed. The thermal performance of different fuels was analyzed in terms of brake thermal efficiency (BTE), brake specific fuel consumption (BSFC), and exhaust gas temperature (EGT). The emission characteristics such as CO₂ emission, NO_x emission, and smoke emission were analyzed for all types of fuels. The results of these fuels in the engine were compared with mineral diesel (MD). The BTE was increased with increasing compression ratios and loads for all types of fuels. The BSFC was increased with increasing compression ratios but decreased with increasing loads. The increase in emission of NO_x was observed at higher compression ratios and loads. However, the CO₂ emission was decreased at higher loads and lower compression ratio. The performance curves achieved with a 20% jatropha biodiesel blend showed results that were approximate to those obtained with pure MD. The comparative analysis between different fuels showed that JB exhibit higher thermal performance as compared to other biodiesels. Therefore, JB can be a better alternative to conventional fuel.