Compact right multipliers on a Banach algebra related to locally compact semigroups

For a locally compact semigroup \({\mathcal{S}}\), let \(L_{0}^{\infty}({\mathcal{S}},M_{a}({\mathcal{S}}))\) be the Banach space of all μ-measurable (\(\mu\in M_{a}({\mathcal{S}})\)) functions vanishing at infinity, where \(M_{a}({\mathcal{S}})\) denotes the algebra of all measures in the measure algebra \(M({\mathcal{S}})\) of \({\mathcal{S}}\) with continuous translations. Here, we study right compact multipliers on the Banach algebra \(L_{0}^{\infty}({\mathcal{S}},M_{a}({\mathcal{S}}))^{*}\) equipped with an Arens product.     

Cross-linking mechanisms of arginine and lysine with α,β-dicarbonyl compounds in aqueous solution

Cross-linking in proteins by α,β-dicarbonyl compounds is one of the most damaging consequences of reactive carbonyl species in vivo and in foodstuffs. In this article we investigate computationally the cross-linking of glyoxal and methylglyoxal with lysine and arginine residues using density functional theory and the wB97XD dispersion-corrected functional. Five pathways, A-E, have been characterized. In pathways A and B, the reaction proceeds via formation of the Schiff base, aldimine, followed by addition of arginine. In contrast, in pathways C-E, direct addition of arginine to the dicarbonyl compounds occurs first, leading to a dihydroxyimidazolidine intermediate, which then reacts with lysine after dehydration and proton transfer reactions. The results reveal that pathways A, C, and E are competitive whereas reactions via pathways B and D are much less favorable. Inclusion of up to five explicit water molecules in the proton transfer and dehydration steps is found to lower the energy barriers in the feasible pathways by about 5-20 kcal/mol. Comparison of the mechanisms of methylglyoxal-derived imidazolium cross-linking (MODIC) and glyoxal-derived imidazolium cross-linking (GODIC) shows that the activation barriers are lower for GODIC than MODIC, in agreement with experimental observations.     

Novel Supramolecular Hydrogels as Artificial Vitreous Substitutes

The possibility of employing self-healing gels as potential artificial vitreous substitutes is being explored. Advancement of traditional synthetic hydrogels as vitreous substitutes is hindered by their fragmentation upon injection into the vitreous cavity leading ultimately to inflammation. Preliminary work involved developing first generation self-healing gels, using amphiphilic tri-block copolymers of poly(propylene glycol)-block-poly(ethylene glycol)-block-poly(propylene glycol) (PPG-PEG-PPG) as the building block. Eight linear self-healing gels are synthesized by tethering an ureidopyrimidinone system to synthetically modified PPG-PEG-PPG via the formation of a bis-urea as a linker. The reversible nature of the hydrogen bonds permits alteration of their physical properties by changing the environment, yet retaining desirable characteristics. Despite low solubility in water, these polymers demonstrated associating behaviour under the investigated conditions, which is encouraging. Future generations of self-healing gels should involve the selection of a more hydrophilic core and/or star-like polymers to facilitate gel formation and strengthen the network.     

Weakly almost periodic functionals on certain Banach algebras

For a Lau algebra A, we study the Banach space WAP(A) of all weakly almost periodic functionals on A to obtain some equivalent conditions for the existence of topological left invariant means on a topological left introverted subspace X of A contained in WAP(A). Finally, we consider relations between the existence of a topological left invariant mean on X and a common fixed point property.     

Carbonate adsorption on goethite in competition with phosphate

Competitive interaction of carbonate and phosphate on goethite has been studied quantitatively. Both anions are omnipresent in soils, sediments, and other natural systems. The PO4-CO3 interaction has been studied in binary goethite systems containing 0-0.5 M (bi)carbonate, showing the change in the phosphate concentration as a function of pH, goethite concentration, and carbonate loading. In addition, single ion systems have been used to study carbonate adsorption as a function of pH and initial (H)CO3 concentration. The experimental data have been described with the charge distribution (CD) model. The charge distributions of the inner-sphere surface complexes of phosphate and carbonate have been calculated separately using the equilibrium geometries of the surface complexes, which have been optimized with molecular orbital calculations applying density functional theory (MO/DFT). In the CD modeling, we rely for phosphate on recent parameters from the literature. For carbonate, the surface speciation and affinity constants have been found by modeling the competitive effect of CO3 on the phosphate concentration in CO3-PO4 systems. The CO3 constants obtained can also predict the carbonate adsorption in the absence of phosphate very well. A combination of inner- and outer-sphere CO3 complexation is found. The carbonate adsorption is dominated by a bidentate inner-sphere complex, (FeO)2CO. This binuclear bidentate complex can be present in two different geometries that may have a different IR behavior. At a high PO(4) and CO3 loading and a high Na+ concentration, the inner-sphere carbonate complex interacts with a Na+ ion, probably in an outer-sphere fashion. The Na+ binding constant obtained is representative of Na-carbonate complexation in solution. Outer-sphere complex formation is found to be unimportant. The binding constant is comparable with the outer-sphere complexation constants of, e.g., SO(2-)4 and SeO(2-)4.     

Relativistic Oscillators in a Noncommutative Space and in a Magnetic Field

In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete withthat of the noncommutative space and that is able to vanish the effect of the noncommutative space.     

Electrochemical determinations of 6-mercaptopurine on the surface of a carbon nanotube-paste electrode modified with a cobalt salophen complex

A mixture of multi-walled carbon nanotube/graphite paste electrode modified with a salophen complex of cobalt was prepared and was applied for the study of the electrochemical behavior of 6-mercaptopurine (MP) using cyclic and differential pulse voltammetry (DPV). An excellent electrocatalytic activity toward the oxidation of MP was achieved, which led to a considerable lowering in the anodic overpotential and remarkable increase in the response sensitivity in comparison with unmodified electrode. Utilizing DPV method, a linear dynamic range of 1–100 μM with detection limit of 0.1 μM was obtained in phosphate buffer of pH 3.0. The electrochemical detection system was very stable, and the reproducibility of the electrode response, based on the six measurements during 1 month, was less than 3.0% for the slope of the calibration curves of MP. The electrochemical method as a simple, sensitive, and selective method was developed for the determination of MP in pharmaceutical dosage form and human plasma without any treatments.     

Bochner algebras and their compact multipliers

Let \mathfrakA\mathfrak{A} be a normed algebra with identity, Ω be a locally compact Hausdorf space and λ be a positive Radon measure on Ω with supp(λ) = Ω. In this paper, we establish a necessary and sufficient condition for L ¹(Ω, \mathfrakA\mathfrak{A}) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left multipliers on L ¹(Ω, \mathfrakA\mathfrak{A}).     

An improved heuristic for the far from most strings problem

The Far From Most Strings Problem (FFMSP) asks for a string that is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are far if their Hamming distance is greater than or equal to a given threshold. FFMSP belongs to the class of sequence consensus problems which have applications in molecular biology, amongst others. FFMSP is NP-hard. It does not admit a constant-ratio approximation either, unless P=NP. In the last few years, heuristic and metaheuristic algorithms have been proposed for the problem, which use local search and require a heuristic, also called an evaluation function, to evaluate candidate solutions during local search. The heuristic function used, for this purpose, in these algorithms is the problem’s objective function. However, since many candidate solutions can be of the same objective value, the resulting search landscape includes many points which correspond to local maxima. In this paper, we devise a new heuristic function to evaluate candidate solutions. We then incorporate the proposed heuristic function within a Greedy Randomized Adaptive Search Procedure (GRASP), a metaheuristic originally proposed for the problem by Festa. The resulting algorithm outperforms state-of-the-art with respect to solution quality, in some cases by orders of magnitude, on both random and real data in our experiments. The results indicate that the number of local optima is considerably reduced using the proposed heuristic.