Independent joins of tolerance factorable varieties

Let Lat denote the variety of lattices. In 1982, the second author proved that Lat is strongly tolerance factorable, that is, the members of Lat have quotients in Lat modulo tolerances, although Lat has proper tolerances. We did not know any other nontrivial example of a strongly tolerance factorable variety. Now we prove that this property is preserved by forming independent joins (also called products) of varieties. This enables us to present infinitely many strongly tolerance factorable varieties with proper tolerances. Extending a recent result of G. Czédli and G. Grätzer, we show that if ${\mathcal{V}}$ is a strongly tolerance factorable variety, then the tolerances of ${\mathcal{V}}$ are exactly the homomorphic images of congruences of algebras in ${\mathcal{V}}$ . Our observation that (strong) tolerance factorability is not necessarily preserved when passing from a variety to an equivalent one leads to an open problem.     

Four-Mode Coupling in Fiber Bragg Grating Sensors Using Full Fields of the Fundamental Modes

Abstract

The four-mode coupling in shear-strain-loaded fiber Bragg grating sensors has been demonstrated to have influence on the measured spectra and, thus, on the application of embedded fiber Bragg gratings for strain field measurements. In a recent work, these coupling coefficients were derived using a set of assumptions on the properties of the fiber's modes. However, the validity of these approximations was not explicitly tested. Here, the required coupling coefficients are computed, making use of the full-field components. It is demonstrated that additional terms will appear; however, they are negligible in practical fibers, and thus, the made approximations are valid.     

Synthesis and characterization of nanostructured aluminum borate by sol–gel method

Nanostructured aluminum borate was synthesized using sol?Cgel technique. X-ray diffraction study revealed that the synthesized aluminum borate was single crystal. These nanorods have very uniform diameter. High-resolution transmission electron microscope images indicate that aluminum borate is well crystallized. The alternating current (AC) conductivity of the aluminum borate was studied as a function of temperature and frequency. The AC conductivity mechanism of the aluminum borate was found to be proportional to ??^s. The exponent s is almost independent with temperature. This suggests that AC conductivity mechanism of the aluminum borate can be interpreted by localized hopping model.     

Spectrophotometric and spectrodensitometric determination of Clopidogrel Bisulfate with kinetic study of its alkaline degradation

Four sensitive, selective and precise stability-indicating methods for the determination of Clopidogrel Bisulfate (CLP) in presence of its alkaline degradate and in pharmaceutical formulations were developed and validated. Method A is a second derivative (D²) spectrophotometric one, which allows the determination of CLP in presence of its alkaline degradate at 219.6, 270.6, 274.2 and 278.4 nm (corresponding to zero-crossing of the degradate) over a concentration range of 4-37 μg mL⁻¹ with mean percentage recoveries 99.81 ± 0.893, 99.72 ± 0.668, 99.88 ± 0.526 and 100.46 ± 0.646, respectively. CLP can be determined in the presence of up to 65% of its degradate. D² method was used to study the kinetic of CLP alkaline degradation that was found to follow a first-order reaction. The t_1/2 was 6.42 h while K (reaction rate constant) was 0.1080 mol/h. Method B is the first derivative of the ratio spectra (DD¹) spectrophotometric method, by measuring the peak amplitude at 217.6 and 229.4 nm using acetonitrile and CLP can be determined in the presence of up to 70% of its degradate. The linearity range was 5-38 μg mL⁻¹ with mean percentage recoveries 99.88 ± 0.909 and 99.70 ± 0.952, respectively. Method C based on the determination of CLP by the bivariate calibration depending on simple mathematic algorithm which provides simplicity and rapidity. The method depends on quantitative evaluation of the absorbance at 210 and 225 nm over a concentration range 5-38 μg mL⁻¹ with mean percentage recovery 99.27 ± 1.115. CLP can be determined in the presence of up to 70% of its degradate. Method D is a TLC-densitometric one, where CLP was separated from its degradate on silica gel plates using hexane:methanol:ethyl acetate (8.7:1:0.3, v/v/v) as a developing system. This method depends on quantitative densitometric evaluation of thin layer chromatogram of CLP at 248 nm over a concentration range of 0.6-3 μg/band with mean percentage recovery 99.97 ± 1.161. CLP can be determined in the presence of up to 90% of its alkaline degradate. The selectivity of the proposed methods was checked using laboratory prepared mixtures. The proposed methods have been successfully applied to the analysis of CLP in pharmaceutical dosage forms without interference from other dosage form additives and the results were statistically compared with the official method.     

Diverse features of magnetization curves of uniaxial crystals:A simulation study

We present a simulation of the magnetization curves, energy, probability, and torque landscapes of uniaxial systems with up to five anisotropy constants. The total energy used in the simulation is the sum of the anisotropy and Zeeman energies. The exchange interaction is not considered in the present work in which we treat single-domain-particle systems within a classical mechanics-based model. Diverse features of the calculated magnetization curves are highlighted for the studied systems. These diverse features are strongly dependent on the sign and magnitude of the simulation parameters.The model is versatile enough to handle both hypothetical and real material systems, e.g. HoFe_(11)Ti and Y_2Co_(17).     

Optimization of the input surface of a thick-lens spatial-integrator array for maximum flux transfer efficiency

The radius of curvature of the input surface of a thick lens spatial integrator array is a free parameter that can be customized for a maximum flux transfer efficiency. With this procedure each element is different but the spatial integration feature remains for the whole array. The calculation is based on a real ray-tracing evaluation that also takes into account the transmissivity of the diopters. The flux transfer on the synthetic image is doubled when the input surfaces are propoerly optimized.     

Ideals and the binary discriminator in universal algebra

We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties. Received April 3, 1997; accepted in final form July 28, 1998.     

Spectroscopic studies of molecular interactions involving 2,6-diethylaniline and N-ethylaniline donors and iodine as an electron acceptor in different solvents

The charge-transfer complexes of 2,6-diethylaniline (DEA) and N-ethylaniline (NEA) with iodine, as a typical sigma-acceptor were studied spectrophotometrically in chloroform, dichloromethane and carbontetrachloride solutions. Spectral data, formation constants and effect of solvent have been determined. Spectral characteristics and formation constants are discussed in the terms of donor molecular structure and solvent polarity. The stoichiometry of the complexes was established to be 1:1. For this purpose, optical data were subjected to the form of the Rose-Drago equation for 1:1 equilibria. The formation constant (KAD) and molar absorptivities (epsilonlambda) of complexes were determined by least square method. Electronic absorption spectra of the anilines were measured in different solvents. Spectral data were reported and band maxima were assigned to the appropriate molecular orbital transitions. Quantum chemical calculations were performed with the aid of the Gaussian 98 set of programs. The structure were fully optimized at MP2 level using 6-31+G** basis set. The computations show that DEA is not planner with the amino group having a somewhat sp3 hybridization-like character.