Systems of Simultaneous Generalized Vector Quasiequilibrium Problems and their Applications

In this paper, we introduce systems of simultaneous generalized vector equilibrium problems and prove the existence of their solutions. As application of our results, we derive the existence theorems for solutions of systems of vector saddle–point problems. Consequently, we prove the existence of a solution of systems of generalized minimax inequalities. Further application of our results is also given to establish the existence of a solution of a Debreu-type equilibrium problem for vector-valued functions. The first author thanks the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The second and third authors were supported by the National Science Council of the Republic of China. The authors are grateful to the referees for valuable suggestions and comments.     

Influence of oxygen on the guiding properties of V2O5-clad glass waveguide

An optical waveguide clad with V2O5 is proposed as a new type of oxygen sensor in ambient air. The presence of gas changes the light transmission (TE0-polarized mode) through the guide, due to the change in refractive index of the cladding which changes the effective index of the guide. O2 gas concentration is varied from a few (≈10) ppm to several percent (4%). Sensors exhibit the same sensitivity at a slightly elevated temperature. The increase in thickness of the cladding causes a reduction in sensitivity and increase in linearity. It is observed that the sensor exhibits the same performance using the static or incremental mode. This revised version was published online in November 2006 with corrections to the Cover Date.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

A nuclear magnetic relaxation study of the system benzene-methanol

The system benzene-methanol was investigated at 25°C by the nuclear magnetic relaxation method. The total relaxation rates are separated into an intramolecular and an intermolecular part. The rotational and translational mobility of the components were studied. Strong OH...OH association has been confirmed.Work done at Professor Hertz's laboratory in Karlsruhe on a leave from the Quaid-i-Azam University.     

Extraction of $$ {\text{Np}}^{4+} $$ and $$ {\text{NpO}}_{2}^{2+} $$NpO22+ from Nitric Acid Medium Using TODGA in Room Temperature Ionic Liquids

Extraction of Np⁴⁺ and \( {\text{NpO}}_{2}^{2 + } \) was carried out from nitric acid feeds using solutions of N,N,N′,N′-tetra-n-octyldiglycolamide (TODGA) in two imidazolium-based room temperature ionic liquids, viz., 1-butyl-3-methylimidazolium bis(trifluoromethanesulphonyl) imide ([C₄mim][NTf₂]) and 1-octyl-3-methylimidazolium bis(trifluoromethanesulphonyl) imide ([C₈mim][NTf₂]). The extraction equilibrium was attained within 2 h for both the metal ions in both the ionic liquids. While a cation exchange mechanism is proposed for the extraction of \( {\text{NpO}}_{2}^{2 + } , \) an ion-pair mechanism of extraction is proposed for the Np⁴⁺ ion. The nature of the extracted species was determined by carrying out experiments at varying concentrations of TODGA, and species of the type Np(L)₂(NO₃)₄ and NpO₂(L)²⁺ were found to be extracted in 3 mol·dm^?3 HNO₃. The identification of these extracted species was also supported from the variable nitrate and C₄mim⁺ ion concentration experiments.     

Synthesis,characterization and thermal behaviour of adducts

The photoproduct of octacyanomolybdate(IV) and -tungstate(IV) with ethylenediamine and triethylenetetramine give complexes of the type K₃[Mo(O₂)(O)(OH)(C₉H₇ON)]·3C₉H₇ON I, K₂[W(O₂)(O) (C₉H₇ON)₃] II and K₃[Mo(CN)₃(OH)₄(C₉H₇ON)]·2C₉H₇ON·3H₂O III with 8-quinolinol (oxine). The IR spectra of the complex III shows the presence ofv(CN) peaks in the range 2047–2108 cm^?1 and oxine groupv(C-O) in the complex I, II and III in the range of 1100–1150 cm^?1. The lower region of IR spectra shows the M=O stretching while the higher thev(N-H) andv(OH). Thermal studies show the removal of uncoordinated water at 131?C from complex III. The decomposition of complexes I and II start from 150 and 212?C respectively. Oxine and cyano molecules were removed in stages at higher temperatures. The final product of the thermal decomposition was oxide which was of polymeric nature. The kinetic parameters viz. order of reaction ‘n’ and activation energy ‘E’ were determined by different methods.     

Kinetics and mechanism of reaction between mercuric bromoiodide and silver iodide in solid state

Kinetics and the mechanism of the reaction between mercuric bromoidide and silver iodide in solid state were studied by X-ray, chemical analysis, thermal, and electrical conductivity measurements. HgBrI and AgI react in the molar ratio 1:3 to give AgBr and Ag₂HgI₄. The data for the lateral diffusion fit best in the equation X_iⁿ = kt. It has been established that the reaction proceeds via a vapor phase diffusion-controlled mechanism through counterdiffusion of Ag⁺ and Hg²⁺. There also seems to be some evidence for the formation of solid solutions between reactant and product phases.     

THE OXIDATION OF CHOLESTEROL BY HYDROXYL RADICAL

Abstract— The oxidation of chblesterol by hydroxyl radical generated by ⁶⁰Co y-radiolysis of aqueous cholesterol dispersions or of dispersions saturated with N₂O ave in low yields the products 38-hydroxy-cholest-5-en-7-one. the epimeric cholest-5-ene-3β,7-diols, 5,6α-epoxy-5α-cholestan-3β-ol, 5.6β-epoxy-5β-cholestan-3,β-ol, and 5α-cholestane-38,5,6β-triol. Sterol hydroperoxides were not detected except in the radiolysis of dispersions saturated with oxygen.