On the use of dense matrix techniques within sparse simplex

In this paper we discuss some instances where dense matrix techniques can be utilized within a sparse simplex linear programming solver. The main emphasis is on the use of the Schur complement matrix as a part of the basis matrix representation. This approach enables to represent the basis matrix as an easily invertible sparse matrix and one or more dense Schur complement matrices. We describe our variant of this method which uses updating of the QR factorization of the Schur complement matrix. We also discuss some implementation issues of the LP software package which is based on this approach.     

Effect of gamma irradiation with or without hot water dip and transportation from Thailand to Canada on nutritional qualities, ripening index and sensorial characteristics of Thai mangoes (Nahng Glahng Wahn variety)

Two lots of mangoes of the Nahng Glahng Wahn variety from Thailand were irradiated at the Thai Irradiation Center (TIC) at 0.49 to 0.77 kGy. Following this, one batch was retained in Thailand while the other was shipped to the Canadian Irradiation Center (CIC) for investigation of the same variables during storage. This way, it was hoped to compare the effects of gamma radiation with hot water dip (HWI) or without (I) before and after transportation on the ripening, vitamin C and vitamin A content and sensory qualities of mangoes. The results indicate that the I and HWI treatments delayed the ripening of the mangoes. The irradiated groups appeared to have a slightly higher content of ascorbic acid on the first day after irradiation than their corresponding controls. The sensory evaluation indicates that the panelists mostly favoured the I and HWI irradiated groups for the overall appearance and texture of whole mangoes and pulp and in taste and palatability of the pulp alone. Transportation stress did not appear to have much of an effect on the ascorbic acid and dehydroascorbic acid levels and the sensorial tests. The mangoes stored and studied in Canada appeared to have a lower vitamin A content.     

Phase transitions and molecular motions in [Cd(H2O)6](BF4)2 studied by DSC, H and F NMR and FT-MIR

Two solid phase transitions of [Cd(H₂O)₆](BF₄)₂ occurring on heating at T_C2=183.3 K and T_C1=325.3 K, with 2 K and 5 K hysteresis, respectively, were detected by differential scanning calorimetry (DSC). High value of entropy changes indicated large orientational disorder of the high temperature and intermediate phase. Nuclear magnetic resonance (¹H NMR and ¹⁹F NMR) relaxation measurements revealed that the phase transitions at T_C1 and T_C2 were associated with a drastic and small change, respectively, of the both spin-lattice relaxation times: T₁(¹H) and T₁(¹⁹F). These relaxation processes were connected with the “tumbling” motions of the [Cd(H₂O)₆]²⁺, reorientational motions of the H₂O ligands, and with the iso- and anisotropic reorientation of the BF₄⁻ anions. The cross-relaxation effect was observed in phase III. The line width and the second moment of the ¹H and ¹⁹F NMR line measurements revealed that the H₂O reorientate in all three phases of the title compound. On heating the onset of the reorientation of 3 H₂O in the [Cd(H₂O)₆]⁺², around the three-fold symmetry axis of these octahedron, causes the isotropic reorientation of the whole cation. The BF₄⁻ reorientate isotropically in the phases I and II, but in the phase III they perform slow reorientation only about three- or two-fold axes. A small distortion in the structure of BF₄⁻ as well as of [Cd(H₂O)₆]²⁺ is postulated. The temperature dependence of the bandwidth of the O-H stretching mode measured by Fourier transform middle infrared spectroscopy (FT-MIR) indicated that the activation energy for the reorientation of the H₂O did not change much at the T_C2 phase transition.     

Phase transitions of [M(H2O)6](MnO4)2 polycrystalline compounds,where M=Mg2+,Ni2+,Zn2+,Cd2+, studied by DSC

Phase transitions of [M(H₂O)₆](MnO₄)₂, where M=Mg, Ni, Zn and Cd, have been studied at 100–400 K by differential scanning calorimetry (DSC). One solid–solid phase transition for the compounds with M=Mg and Ni and two solid–solid phase transitions for these with M=Zn and Cd have been discovered. Additionally, three phase transitions, connected with three-stage melting process of these compounds, were also found. Thermodynamic parameters of the all detected phase transitions were calculated.     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

Characterizations of ɛ-duality gap statements for constrained optimization problems

In this paper we present different regularity conditions that equivalently characterize various ?-duality gap statements (with ? ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ?-subdifferentials. When ? = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.     

An iron carbonyl approach to the influenza neuraminidase inhibitor oseltamivir

A novel synthetic route towards oseltamivir, an influenza neuraminidase inhibitor, has been achieved employing a cationic iron carbonyl complex, providing an alternate pathway with the potential to access diverse analogues.     

Synthesis, characterization and colour determination using CIELAB colour space of stilbene dyes

The synthesis of six new symmetrical disazo direct dyes containing 4,4′-diaminostilbene-2,2′-disulphonic acid as middle component and N-(2-chlorophenyl)-2-hydroxybenzamide, N-(3-chlorophenyl)-2-hydroxybenzamide, N-(4-chlorophenyl)-2-hydroxybenzamide, N-(2-bromophenyl)-2-hydroxybenzamide, N-(3-bromophenyl)-2-hydroxybenzamide, N-(4-bromophenyl)-2-hydroxybenzamide as coupling components is presented. The synthesized dyes were analyzed by thin layer chromatography, electronic spectra and HPLC technique. Their structures were elucidated by FT/IR and 13C-NMR spectroscopy. The CIELAB (1976) colour space was used in all the colour measurements for the six disazo stilbene dyes under the CIE recommended illuminants: D65 (natural day light), A (tungsten light), F2 (fluorescent light) and the standard 10° observer, respectively. The colour differences: ΔEab* and ΔECMC were calculated against one standard. The results reveal a good colouring power of the new azo-stilbene dyes.