Decoupling Problem for Systems of Quasi-Linear pde’s

The necessary and sufficient conditions for the decoupling of a quasi-linear system of partial differential equations into k non-interacting subsystems are derived. Several necessary conditions for the decoupling are found and applied to the Benney system.     

Solid-phase extraction on alkyl-bonded silica gels in inorganic analysis.

Solid-phase extraction (SPE) is an effective tool for the preconcentration of trace elements and their separation from various sample constituents. Octadecyl and other alkyl-bonded silica gels are most widely used for these purposes. The fundamentals of the SPE of inorganic ions are reviewed and compared with those of related techniques (liquid-liquid extraction and reversed-phase liquid chromatography). The extraction of ions in the form of chelate compounds, inorganic salts solvated by neutral reagents, and ion-pair compounds is considered. Numerous applications of SPE to the separation and preconcentration of different elements and their species, including on-line combinations with instrumental determination techniques, are described and tabulated.     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

Reduction of operators with almost periodic symbols to operators overC *-Algebras on sections of associated bundles over a torus

A decomposition of any pseudodifferential operator (D) onR ⁿ with almost periodic symbol as 113-1 1 is obtained in the paper, where _A (D) is a pseudodifferential operator over a certainC ^*-algebraA acting on sections of a vector bundle over a torusT ⁿ whose fibre isA. The coincidence of spectra sp (D) = sp _A (D) is proved for all (D) either bounded or elliptic.     

Mild template synthesis of a copper(II)-containing macrocyclic compound with 4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9 in a gelatin-immobilized matrix

The complexing processes in the triple copper(II)–thiocarbohydrazide–propanone system taking place in a copper(II) hexacyanoferrate(II) gelatin-immobilized matrix in contact with aqueous-alkaline solutions (pH12), containing thiocarbohydrazide and propanone, have been studied. Template synthesis leading to a macrocyclic coordination compound with the tetradentate N,N,S,S-donor ligand, (4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9), occurs under these specific conditions when thiocarbohydrazide and propanone are the ligand synthons.     

Soft template synthesis in copper(II)–dithiooxamide–methanal,copper(II)–dithiooxamide–ethanal and copper(II)–dithiooxamide–propanone triple systems in a copper(II)hexacyanoferrate(II) gelatin-immobilized matrix

Novel complexing processes in the Cu^II–dithiooxamide–methanal, Cu^II–dithiooxamide–ethanal and Cu^II–dithiooxamide–propanone triple systems proceeding under specific conditions, to copper(II)hexacyanoferrate(II) gelatin-immobilized matrix systems in contact with aqueous-alkaline (pH 12) solutions containing dithiooxamide and methanal, ethanal or propanone, have been studied. It has been shown that template synthesis leading to the formation of macrocyclic coordination compounds (2,8-dithio-3,7-diaza-5-oxanonandithioamide-1,9)copper(II), (2,8-dithio-3,7-diaza-4,6-dimethyl-5-oxanonandithio-amide-1,9)copper(II) and (4,4,6-trimethyl-2,8-dithio-3,7-diazanonen-6-dithioamide-1,9)copper(II), respectively, takes place under such conditions. Dithiooxamide, methanal, ethanal and propanone act as ligand synthons in these processes.     

Radiation Crosslinking of an Acrylamide–Sodium Acrylate Copolymer in Aqueous Solutions

The effect of concentration of an acrylamide–sodium acrylate copolymer in an aqueous solution on the crosslinking of macromolecules by the action of ionizing radiation was studied. It was shown that the efficiency of radiation crosslinking of the copolymer increased with an increase in the concentration of solution subject to irradiation, which was tentatively explained in terms of the existence of fluctuative entanglement network ensuring the approaching of macroradical sites and, thus, facilitating the combination reactions of macroradicals.     

Synthesis of [1,3]dithiole and spiro[1,3]dithiole thiopyran derivatives of the [1,2]dithiolo[1,4]thiazine ring system

We report the synthesis of some new polysulfur-nitrogen heterocycles by cycloaddition reactions to readily available tricyclic condensed 1,2-dithiole-3-thiones. Thus, treatment of bis[1,2]dithiolopyrrole ketothione 1 with diacyl acetylenes gave the bis-aducts 2a-d. On the other hand, cycloaddition of bis[1,2]dithiolo[1,4]thiazine ketothione 3 with 1 equiv of acyl or diacyl acetylenes gave [1,3]dithiolylidenyl[1,2]dithiolo[1,4]thiazines 4a-f in fair to high yields. Catalysis by scandium triflate was used in the reactions that implied the less reactive dipolarophiles. Treatment of 3 with 2 equiv of DBA gave the bis-aduct 5a, and reaction of 4c with DMAD gave the mixed bis-adduct 5b. Cyclic voltammetry of selected examples showed irreversible processes that were influenced by the electrochemical activity of peripheral groups bonded to the heterocyclic system.     

Fine Structure of Meniscus of a Wetting Liquid

Equilibrium of a capillary meniscus near a wetting film on a solid in a gravitational field is considered. Unlike previous studies, the present study proves that the fine meniscus structure in a gravitational field is a universal feature—it takes place in a wide variety of problems. In the general case, the capillary meniscus is at a certain distance from the wetting film and does not intersect it. The relation for the minimum distance from the arbitrary meniscus to the solid generalizes the Derjaguin formula for a flat slit. An equation that optimally approximates the meniscus with due account of the contribution of the meniscus/film transition region is derived. A refined solution to the problem of a meniscus on a vertical plate is derived within the perturbation theory. Both gravity and nonuniformity of the vertical static film above a capillary–gravitational meniscus do not affect the minimum distance (the influence is less than 0.0001). A general method for solving sophisticated problems of capillary equilibrium in gravitational field is proposed.     

Variation–iteration method for one-dimensional two-electron systems

A quantum chemical study of the two low-lying quartet states of seven model compound I iron–porphyrin complexes with varying axial ligands has been carried out using the INDO method. The varying axial ligands included in this study are five that are models for those in the intact enzymes: imidazole and imidazolate (model peroxidase HRP and CCP), CH₃CONH₂ (Gln175 mutant of CCP), PhO^?1 (catalase), CH₃S^?1 (P450), and two that have been used in biomimetics of these enzymes: Cl^?1 (hemin) and PhS^?1 (model P450s). The purpose of these studies was to determine the role of the axial ligands in determining (i) the relative energies of the two nearly degenerate quartet electronic states of compound I, involved either as an a_1u or a_2u porphyrin π cation radical and (ii) the electron and spin distributions in the a_1u and a_2u radical cations of compound I. For most of the model complexes, including both HRP-I and CAT-I, a moderate effect of the axial ligand on the relative energy of these two states was observed and the a_1u radical cation was found to be the ground state. The energy order of these two radical cations, however, was reversed in the P450-I model complexes, indicating an association of the unique property of the Fe?O bond breaking with an a_2u radical cation. The symmetry-allowed overlap between the Fe?O and 3a_2u orbitals may lower the activation energy for the Fe?O bond cleavage in P450-I. However, the calculated electronic and spin properties, including the unpaired spin and net charge on the oxygen and the Fe?O bond overlap density, important determinants of the reactivity of this complex in the ligand–Fe?O region, are very similar for all complexes and in both cation states. © 1992 John Wiley & Sons, Inc.