Optimization of the Determinant of the Vandermonde Matrix and Related Matrices

The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Gröbner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.     

Synthesis and EPR studies of vanadyl tetrakis(selenodiazole)porphyrazine

Tetrakis(selenodiazole)porphyrazine and its vanadyl (VO²⁺) complex have been prepared and characterized by FT-IR, UV–vis, and MALDI-MS. The magnetic properties of the complex have been investigated by EPR spectroscopy.     

Effect of microfibrillated cellulose and fines on the drainage of kraft pulp suspension and paper strength

Different types of microfibrillated cellulose (MFC) and fines suspensions were produced, characterized, and then added to a papermaking pulp suspension. High and medium molar mass cationic polyelectrolytes were used as fixatives. The drainage behavior of the pulp suspensions with additives were evaluated against the strength properties of hand sheets made thereof. The effects of salt concentration, pH, fixative type, dosage and type of fibrillar material on drainage were examined. All the MFC and fines samples produced had clearly different properties due to their dissimilar production methods, and they also introduced specific responses on the measured drainage and paper strength. Generally, the addition of MFC decreased the drainage rate of pulp suspension and increased the strength of paper. However, it was shown that by optimum selection of materials and process conditions an enhancement of the strength properties could be achieved without simultaneously deteriorating the drainage.     

Pyramidal tours and multiple objectives

In this study, we work on the traveling salesperson problems and bottleneck traveling salesperson problems that have special matrix structures and lead to polynomially solvable cases. We extend the problems to multiple objectives and investigate the properties of the nondominated points. We develop a pseudo-polynomial time algorithm to find a nondominated point for any number of objectives. Finally, we propose an approach to generate all nondominated points for the biobjective case.     

Synthesis and Spectroscopic Characterization of Group 6 Pentacarbonyl(4-substituted pyridine)metal(0) Complexes

Carbonyl-metal (M:Cr, Mo, W) derivatives of 4-substituted pyridines [4-methylpyridine (4-mp), 4-tert-butylpyridine (4-tbp) and 4-dimethylaminopyridine (4-dmap)] where the metal center is bonded to the nitrogen atom of the substituted pyridine ring are described. The organometallic complexes, M(CO)₅L, were synthesized by either the direct reaction of the metal hexacarbonyls or by the thermal substitution of M(CO)₅(THF) with the pyridine ligands; 4-methylpyridine (1), 4-tert-butylpyridine (2), 4-dimethylaminopyridine (3). The reported complexes were purified by column chromatography and recrystallization. The complexes were all characterized in solution by elemental analysis, MS, ir , ¹H-nmr and ¹³C-nmr spectroscopies.     

Oxidative polymerization of acrylamide in the presence of thioglycolic acid

Chemical polymerization of acrylamide at room temperature was examined by using thioglycolic acid-cerium (IV) sulfate and thioglycolic acid-KMnO₄ redox systems in acid aqueous medium. Water soluble polyacrylamides containing thioglycolic acid end groups were synthesized. The effects of the molar ratio of acrylamide to Ce(IV) n _AAm /n _Ce(IV) , the polymerization time, the temperature, the monomer concentration, the molar ratio of cerium (IV) sulfate to thioglycolic acid and the concentration of sulfuric acid on the yield and molecular weight of polymer were investigated. Lower molar ratios of acrylamide/Ce(IV) at constant monomer concentration resulted in an increase in the yield but a decrease in molecular weight of polymer. The increase of reaction temperature from 20 to 70°C resulted in a decrease in the yield but generally resulted in a constant value for the molecular weight of polymer. With increasing polymerization time, the yield and molecular weight of polymer did not change substantially. Ce(IV) and Mn(VII) ions are reduced to Ce(III) and Mn(II) ions respectively in the polymerization reaction. The existence of Ce(III) ion bound to polymer was investigated by UV-visible spectrophotometry and fluoresce measurements. The amount of Mn(II) incorporated into the polymer was determined using graphite furnace atomic absorption spectrometry. The mechanism of this phenomenon is discussed.     

The orthorhombic polymorph of diammonium trichromate(VI) decaoxide, <Emphasis Type="Italic">α</Emphasis>–(NH<Subscript>4</Subscript>)<Subscript>2</Subscript>Cr<Subscript>3</Subscript>O<Subscript>10</Subscript>

Synthesis and crystal structure of a trichromium(VI) decaoxide compound, α–(NH₄)₂Cr₃O₁₀, is reported. The crystal structure has been determined from three dimensional X-ray data collected at low temperature, 173 K. The structure is isomorphous with its Rb and Cs trichromate analogues, orthorhombic, space group Pbca, with a = 11.2558(3), b = 9.3193(3), c = 18.9819(5) ? and Z = 8. The title compound is composed of discrete [Cr₃O₁₀]^2– chains held together by the counter ion charge and a hydrogen bonding network. The different conformations adopted by trichromate anion within its ammonium, alkali and organic salts are discussed.     

On γ-semi-open sets

Summary We introduce the concepts of γ-semi-open set, γ_s-set, γ^s-set, generalized γ_s-set, generalized γ^s-set, semi-T₁^γspace and semi-R₀^γspace by using γ-open-sets.     

Component testing of repairable systems in multistage missions

We consider the component testing problem of a device that is designed to perform a mission consisting of a sequence of stages. Once a stage is over, the device is overhauled to replace all failed components before the next stage starts to improve mission reliability. The components fail exponentially where the failure rate depends on the stage of the mission. The reliability structure of the device involves a series connection of redundant subsystems. The optimal component testing problem is formulated as a semi-infinite linear programme. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.     

Boundary-layer flow about a vertical spinning cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar boundary-layer flow in the presence of a transverse magnetic field over a down-pointing and spinning cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic and spin parameters and the Prandtl number. The spin of the cone compresses the velocity profiles towards the surface by inducing an upward flow and decreases the surface temperature. The magnetic field suppresses the velocity profiles and increases the surface temperature. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.