Weak sharp solutions for generalized variational inequalities

We consider weak sharp solutions for the generalized variational inequality problem, in which the underlying mapping is set-valued, and not necessarily monotone. We extend the concept of weak sharpness to this more general framework, and establish some of its characterizations. We establish connections between weak sharpness and (1) gap functions for variational inequalities, and (2) global error bound. When the solution set is weak sharp, we prove finite convergence of the sequence generated by an arbitrary algorithm, for the monotone set-valued case, as well as for the case in which the underlying set-valued map is either Lipschitz continuous in the set-valued sense, for infinite dimensional spaces, or inner-semicontinuous when the space is finite dimensional.     

On some λ difference sequence spaces of fractional order

In the present paper, the difference sequence spaces $c{s}_0^{\lambda }\left(\Delta \right),c{s}^{\lambda }\left(\Delta \right)$ and bs^λ(Δ) of nonabsolute type are generalized by introducing a generalized Λ difference operator $\Lambda \left({\Delta }^{\left(\stackrel{?}{\alpha }\right)}\right)$. Also, their Schauder basis are calculated and α-, β- and γ-duals of these spaces are investigated. Finally, some matrix transformations between these spaces and the basic sequence spaces ?_p, c and c₀ are characterized, where 1 ≤ p ≤ ∞.     

Competitive 7Li NMR Study on the Mn2+, Zn2+ and Cd2+ Complexes of Two New Branched Hexadentate (N6) Amines Containing the Pyridine Moiety in Nitromethane and Acetonitrile Solutions

Lithium-7 NMR spectroscopy was used to investigate the stoichiometry and stability of a Li⁺ complex with two new branched amines, 4,7-bis(2-pyridylmethyl)-4,7-diazadecane-1,10-diamine (L¹) and 4,8-bis(2-pyridylmethyl)-4,8-diazaundecane-1,11-diamine (L²), in acetonitrile and nitromethane. A competitive ⁷Li NMR method was also employed to probe the complexation of Mn²⁺, Zn²⁺ and Cd²⁺ ions with L¹ and L² in the same solvent systems. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data with an equation that relates the observed chemical shifts to the formation constant. In both solvents, the stability of the resulting 1:1 complexes was found to vary in the order Cd²⁺ > Zn²⁺ > Mn²⁺ > Li⁺.     

Potentiometric and Theoretical Studies of (2Z, 3Z)-2H-benzo[b][1,4]thiazine-2,3(4H)-dionedioxime with Some Divalent Transition Metal Ions

The protonation equilibria of (2Z, 3Z)-2H-benzo[b][1,4]thiazine-2,3(4H)-dionedioxime (BTDH₂) together with the equilibria of its bis- binary complexes of Co(II), Ni(II), Cu(II) and Zn(II) were investigated potentiometrically. The investigation was carried out at 25 ± 0.1 °C, in aqueous solution, with a constant ionic strength of 0.100 mol·dm^?3 NaCl. The protonation constants of the ligand together with the stability constants of a variety of complexes were determined potentiometrically in 10 % ethanol–water mixed solution using the SUPERQUAD computer program. Theoretical calculations were set up to assist in understanding the protonation sequence in the ligand molecule via the semi-empirical molecule orbital method of parameterized model number 3. Results are discussed in connection to the basicity of the donor atoms and structural arrangement of the ligand. Although BTDH₂ has two dissociable protons, four protonation constants can be measured under the experimental conditions presented. These four protonation constants (as log₁₀ βs) are 10.245, 19.397, 22.414 and 25.176.     

Conversion of Industrial Paper Sludge to Ethanol: Fractionation of Sludge and Its Impact

Paper sludge is an attractive biomass source for the conversion to ethanol due to its low cost and the lack of severe pretreatment required. Four sludges from pulp and paper operations including both virgin kraft (VK) and recycled and deinking (RD) paper mills were analyzed. A fractionation process using a laboratory screen was utilized to produce a fiber-rich stream for enzymatic hydrolysis. This process removed 82–98 % of the ash with fiber yields from 39 to 69 %. Even though sludges in both non-fractionated and fractionated scenarios were pH-adjusted, total sugar conversion was still improved by 12–27 % by fractionation with 4.5 times less acid required for pH adjustment. Fermentation of the fractionated sludges showed very high ethanol yields. Acid insoluble clay adsorbs 3–5 mg enzyme per gram of clay depending on enzyme dosage. Acid soluble CaCO₃ adsorbs about half of the enzyme compared to clay. Fractionation efficiency was also evaluated by testing different size mesh screen openings (100 to 500 mesh). The 400-mesh screen presented the best fiber yield, ash removal and ash fractionation ratio for both VK and RD sludges. The ash-rich streams have a lower C/N ratio than the original sludge which improves its suitability as soil amendment.     

Kinetic studies on acid- and base-catalyzed aquation of bis-alaninatochromium(III) and on oxidation of tris- and bis-Aa–chromium(III) complexes (Aa = Gly,Ala, Asn) by H2O2

Two aqua derivatives of [Cr(Ala)₃] were characterized in solution. Acid-catalyzed aquation of cis-[Cr(Ala)₂(H₂O)₂]⁺ leads to inert [Cr(Ala)(H₂O)₄]²⁺, whereas base hydrolysis of cis-Cr(Ala)₂(OH)₂]^? causes dissociation of both the Ala ligands and formation of chromates(III). Kinetics of these processes have been studied spectrophotometrically in both 0.1–1.0 M HClO₄ and 0.2–0.9 M NaOH under first-order conditions. A linear dependence of the k _obs,H on [H⁺] and a small dependence of the (k _obs)_OH on [OH^?] were established. In the proposed mechanism, the rate determining step is Cr–N bond breaking in the reactive form of the substrate, i.e., in the protonated aqua- or dihydroxo complex. The effect of pH on the complex reactivity is discussed. The kinetic results are compared with those determined previously for analogous glycine and asparagine complexes. Additionally, oxidation of tris- and bis-Aa–chromium(III) complexes, where Aa = Gly, Ala or Asn, by hydrogen peroxide in alkaline medium was studied. Two reaction products were detected: thermodynamically stable CrO₄ ^2? and [Cr(O₂)₄]^3? that under a large excess of hydrogen peroxide is metastable. The rate-limiting stage of this process is an inner sphere two-electron transfer within the peroxido intermediate.     

Nuclear magnetic resonance study of the stoichiometry and stability of several HgX<Subscript>2</Subscript>–acetylemethylentriparatolylphosphorane complexes in various acetone–dimethylformamide mixtures

The reaction of phosphorus ylide, acetylmethylenetriparatolylphosphorane (L) with HgX₂ (X = Cl, Br, I and NO₃) in equimolar ratios using acetone and dimethylformamide as solvents leads to binuclear products. ³¹P NMR spectroscopy was used to investigate the stoichiometry and stability of a HgX₂ complex with CH₃COCHP(p-tolyl)₃ (L) in binary acetone–dimethylformamide mixtures of varying composition. In all cases studied, the variation of ³¹P NMR chemical shift with the [HgX₂]/[L] mole ratio indicated the formation of 1:1 complexes. The formation constants of the resulting complexes were evaluated from computer fitting of the mole ratio data to an equation that relates the observed chemical shifts to the formation constant. In all mercuric salts used, the stabilities of the resulting 1:1 complexes varied in the order Hg(NO₃)₂ > HgCl₂ > HgBr₂ > HgI₂. It was found that, in the case of all complexes, an increase in the percentage of dimethylformamide in the solvent mixtures significantly decreases the stability of the complexes.     

On the respective terms of the derived and the polycentral series of a free lie algabra and an ideal

Let F be a free Lie algebra of rank> 1 and S be an ideal of F. Denote by F_m and F_{n l},…,n_k the terms of the lower central and the polycentral series of F. The aim of this paper is to provide a sufficient condition for the quotient algebra F_{n l},…,n_k/S_{n l},…,n_k to be infinitely generated. The case F_m/S_m was studied in [6] for free groups and in [ 2 ] for free Lie algebras. In this paper the following main theorem is proved : If F = F2 = S, k > 1 and n_i > 1 for i=l,…, k, then F_{n l}…,n_k/S_{n l} is infinitely generated.     

ESR spectroscopic investigation of gamma-irradiated lithium trifluoromethanesulfonate

ABSTRACT

The effect of gamma radiation on lithium trifluoromethanesulfonate (LiTf) was investigated in detail using electron spin resonance (ESR) spectroscopy. The experimental spectra consisted of complex overlapped signals. Simulations of both the 1st- and 10th-day ESR spectra gave valuable information about the spectroscopic and structural features of radiation-induced radicals. More information about the qualitative and quantitative features of the radicals were gathered from the microwave power, storage time and dosimetric feature findings. In the light of the information obtained, four radicals were accepted to be produced after irradiation of LiTf.