The matrix equation AXB+CYD=E

A necessary and sufficient condition for the matrix equation $\text{AXB}\text{+}\text{CYD}\text{=}\text{E}$ to be consistent is established, and if it is, a representation of the general solution is given, thus generalizing earlier results concerning the equation $\text{AX}\text{+}\text{YB}\text{=}\text{C}$.     

Potentiometric transducer based biomimetic sensors for priority envirotoxic markers--an overview

Most of the potentiometric sensing electrodes offer detection limits of the order of approximately 1 micromol L(-1) rarely stretching down to 0.1 micromol L(-1). Recent advances have made it possible to bring these levels down to 0.01-10 nmol L(-1) for some inorganic ions. Most of these electrodes (barring a few) have come up to expectations in terms of selectivity in spite of significant strides made in the design and synthesis of novel chemical receptors. Imprinted polymers or plastic antibodies which rely on lock and key mechanism can, in principle, selectively rebind and sense a particular analyte in a host of other analogous species of similar size, shape and geometry. Thus, the integration of imprinted polymers with potentiometric transducers has immense potentialities in the fabrication of commercial sensing devices. This review gives an overview of research efforts made so far in this direction, critically discusses the virtues and vices and presents the futuristic scenario on imprinted polymer based potentiometric sensors.     

Slowness surfaces, ray velocity surfaces and phonon focussing in highT c superconductor crystals

This paper reports the results of the study of anisotropy in elastic wave propagation in single crystal superconducting BSCCO. The inverse and group velocities of elastic waves propagating in different directions have been computed and the corresponding slowness and ray velocity surfaces plotted, taking elastic constant data from literature. In addition, the phenomenon of phonon focussing has been investigated in this material by computing the phonon enhancement factor along different directions in spherical polar coordinates. The abnormally high values in phonon enhancement factor exhibited in certain directions for the phonon modes are interpreted as due to caustics occurring in the geometrical acoustics approximation adopted in the computational analysis. The results in LSCO and YBCO are found to be similar to those in BSCCO.     

Anodic Synthesis of New Benzofuran Derivatives Using Active Methylene Group at Platinum Electrode

A facile and Eco-compatible synthesis of benzofuran derivatives (4a–4h) has been carried out at platinum electrode by electrochemical oxidation of catechol in the presence of active methylene groups. Electro- organic synthesis has been performed in an undivided cell at ambient conditions. The products of electrolysis have been purified and characterized by FTIR, ¹H NMR and ¹³C NMR and mechanism was deduced by voltammetric studies.     

LC and Non-Aqueous CE Determination of Phenothiazines in Autopsy Samples

Comparative determinations of various phenothiazine derivatives in blood and urine samples were carried out using HPLC in reversed-phase mode and non-aqueous capillary electrophoresis (NACE). The examined samples of biological fluids originated from six forensic cases concerning poisonings with drugs, including the following commonly used phenothiazines: chlorpromazine, levomepromazine, promazine, and perazine. The quantification limits for both methods were similar and ranged from 0.02 to 0.35 µg mL^?1. The correlation coefficient (r²) between the results obtained by two methods was 0.9869.     

Solid phase extraction vis-à-vis coprecipitation preconcentration of cadmium and lead from soils onto 5,7-dibromoquinoline-8-ol embedded benzophenone and determination by FAAS

This article compares the solid phase extraction (SPE) and coprecipitative preconcentration of cadmium and lead from dilute aqueous solutions as a function of pH and weight of chelating agent. SPE enriches cadmium and lead over a wider pH range (6.0-8.0) and requires lower weight of DBQ chelate embedded benzophenone. Among the quinoline-8-ol and its dihaloderivatives, DBQ embedded benzophenone allows quantitative enrichment over a wide pH range (6.0-8.0) for both cadmium and lead unlike DCQ (∼6.5 for Cd and 6.5-7.0 for Pb), DBQ was preferred. The calibration plots were rectilinear over the concentration range of 0.1-50 and 2.5-200 μg l⁻¹ of cadmium and lead with detection limits of 0.1 and 2.0 μg l⁻¹, respectively, which are 400 times lower than the direct FAAS method. The precision of the developed procedure is good as it provides relative standard deviation values of 2.20 and 2.45% during five replicate determinations of 2 and 25 μg l⁻¹ of cadmium and lead, respectively. The accuracy of the developed procedure was tested by analyzing certified reference materials (CRM's) of soil and marine sediment samples supplied by IAEA, Italy and NRC, Canada, respectively. Furthermore, the developed procedure has been successfully used for the speciative determination of cadmium and lead in soil samples collected from the vicinity of industries in India.     

Latin bitrades,dissections of equilateral triangles,and abelian groups

Let T=(T^*, T^?) be a spherical latin bitrade. With each a=(a₁, a₂, a₃)∈T^* associate a set of linear equations Eq(T, a) of the form b₁+b₂=b₃, where b=(b₁, b₂, b₃) runs through T^*\{a}. Assume a₁=0=a₂ and a₃=1. Then Eq(T,a) has in rational numbers a unique solution $b_{i}=\bar{b}_{i}Let T=(T^*, T^?) be a spherical latin bitrade. With each a=(a₁, a₂, a₃)∈T^* associate a set of linear equations Eq(T, a) of the form b₁+b₂=b₃, where b=(b₁, b₂, b₃) runs through T^*\{a}. Assume a₁=0=a₂ and a₃=1. Then Eq(T,a) has in rational numbers a unique solution $b_{i}=\bar{b}_{i}$. Suppose that $\bar{b}_{i}\not= \bar{c}_{i}$ for all b, c∈T^* such that $\bar{b}_{i}\not= \bar{c}_{i}$ and i∈{1, 2, 3}. We prove that then T^? can be interpreted as a dissection of an equilateral triangle. We also consider group modifications of latin bitrades and show that the methods for generating the dissections can be used for a proof that T^* can be embedded into the operational table of a finite abelian group, for every spherical latin bitrade T. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 1–24, 2010     

Metal Schiff-Base Complex Catalyzed Oxidation of p-Xylene and Methyl 4-Methylbenzoate to Carboxylic Acids

Oxidation of p-xylene and methyl 4-methylbenzoate were catalyzed by transition metal Schiff-base complexes having the general formula LMCl_1–2 (where M = manganese or ruthenium and L = salen, salicylaldehydeethylenediimine, saloph, salicylaldehyde-o-phenylenediimine and EDTA, ethylenediaminetetraacetate) at 150°C and 500 psig air and gave p-toluic acid (> 85 %) and monomethyl terephthalate (> 70%) as the major oxidation products, respectively.