Tensor products and relation quantales

A classical tensor product \({A \otimes B}\) of complete lattices A and B, consisting of all down-sets in \({A \times B}\) that are join-closed in either coordinate, is isomorphic to the complete lattice Gal(A,B) of Galois maps from A to B, turning arbitrary joins into meets. We introduce more general kinds of tensor products for closure spaces and for posets. They have the expected universal property for bimorphisms (separately continuous maps or maps preserving restricted joins in the two components) into complete lattices. The appropriate ingredient for quantale constructions is here distributivity at the bottom, a generalization of pseudocomplementedness. We show that the truncated tensor product of a complete lattice B with itself becomes a quantale with the closure of the relation product as multiplication iff B is pseudocomplemented, and that the tensor product has a unit element iff B is atomistic. The pseudocomplemented complete lattices form a semicategory in which the hom-set between two objects is their tensor product. The largest subcategory of that semicategory has as objects the atomic boolean complete lattices, which is equivalent to the category of sets and relations. More general results are obtained for closure spaces and posets.     

Proximal-gradient algorithms for fractional programming

In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-?ojasiewicz property.     

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Bo? R.I., Wanka G., On gap functions for equilibrium problems via Fenchel duality, Pac. J. Optim., 2006, 2(3), 667–678] and [Altangerel L., Bo? R.I., Wanka G., On the construction of gap functions for variational inequalities via conjugate duality, Asia-Pac. J. Oper. Res., 2007, 24(3), 353–371]. By particularizing the perturbation function we rediscover several gap functions from the literature. We also characterize the solutions of various variational inequalities and equilibrium problems by means of the properties of the convex subdifferential. In case no regularity condition is fulfilled, we deliver also necessary and sufficient sequential characterizations for these solutions. Several examples are illustrating the theoretical aspects.     

Mössbauer study of new vanadate glass with large charge-discharge capacity

Charge-discharge capacity and cyclicity of lithium ion battery (LIB) was evaluated in which 15Li₂O·10Fe₂O₃·xSnO₂·5P₂O₅·(70–x)V₂O₅ glass (x?=?0 and 20 in mol%, abbreviated as xLFSPV) was used as a cathode. A local structure of xLFSPV glass before and after charging was investigated by ⁵⁷Fe- and ¹¹⁹Sn-Mössbauer spectroscopies. ⁵⁷Fe-Mössbauer spectrum of xLFSPV glass with ‘x’ of 20 was composed of a doublet with isomer shift (δ) of 0.35_±0.02 mm s^???1 and quadrupole splitting (Δ) of 0.88_±0.03 mm s^???1 due to distorted Fe^IIIO₄ tetrahedra. ¹¹⁹Sn-Mössbauer spectrum of this glass consisted of a doublet with δ of 0.08_±0.01 and Δ of 0.52_±0.01 mms^???1 due to distorted Sn^VIO₆ octahedra. After discharging the battery from 4.5 to 1.0 V, larger δ of 0.40_±0.03 mm s^???1 and Δ of 0.94_±0.04 mm s^???1 were obtained, indicating that both iconicity of Fe-O bonds and local distortion of Fe^IIIO₄ tetrahedra were increased. On the contrary, identical δ of 0.09_±0.01 mm s^???1 and Δ of 0.50_±0.01 mm s^???1 were observed in the ¹¹⁹Sn-Mössbauer spectrum of 20LFSPV glass after the discharge, indicating that chemical environment of Sn^IVO₆ octahedra was not affected after the discharge. Charge-discharge curve of LIB containing 20LFSPV glass as a cathode active material recorded under the current density of 8.3 mA g^???1 (0.011 mA cm^???2) between 1.0 and 4.5 V showed a large initial charge capacity of 431.1 mAh g^???1 and discharge capacity of 382.3 mAh g^???1, respectively. These results indicate that 20LFSPV glass could be a new cathode active material for LIB.     

On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

Redox interactions between structurally different alkylresorcinols and iron(III) in aqueous media: frozen-solution 57Fe Mössbauer spectroscopic studies,redox kinetics and quantum chemical evaluation of the alkylresorcinol reactivities

Iron(III)-containing aqueous solutions of 5-methylresorcinol (5-MR), 5-n-propylresorcinol (5-n-PR) and 4-n-hexylresorcinol (4-n-HR) at pH ~ 3 were studied by means of ⁵⁷Fe transmission Mössbauer spectroscopy. Kinetic considerations were applied to the redox reactions. Density Functional Theory (DFT) calculations were performed for the alkylresorcinol (AR) molecules and their non-alkylated analogue (resorcinol). Mössbauer spectra consisted of quadrupole doublets assigned to high-spin Fe(III) and Fe(II) species. From changes in their relative spectral areas, a gradual reduction of Fe(III) by all the ARs studied was observed. However, significant differences were found for the reduction rates among the ARs. The following series of the reduction rates was established by means of Mössbauer spectroscopy: 4-n-HR ? 5-MR > 5-n-PR, supplemented by rate constants calculated using a kinetic model. DFT calculations resulted in the following series: 4-n-HR ? 5-n-PR > 5-MR ? resorcinol (the latter is not oxidised under the conditions applied). The reversed order of the experimentally observed 5-MR and 5-n-PR oxidation rates may be explained in terms of their different kinetic parameters related to their structure.     

Usefulness of Transgenic Luminescent Bacteria in Direct Bioautographic Investigation of Chamomile Extracts

JPC – Journal of Planar Chromatography – Modern TLC - Direct bioautography performed with luminescence gene-tagged bacteria enables almost real-time detection of antimicrobial compounds...     

Unsteady motion in single-line flow-injection systems

Unsteady motion in single-line flow-injection systems consisting of n tubular elements with valve or hydrodynamic injection is studied theoretically. A formula for the duration of the initial period of unsteady flow is derived. This initial period is much shorter than the mean residence time of the analyte in practical systems. It can therefore be neglected in mathematical modelling of such systems. Experimental data obtained with single-line systems with valve and hydrodynamic injection confirmed the validity of the theoretical equations.     

Separation of Fumonisins by OPLC

JPC – Journal of Planar Chromatography – Modern TLC - Fumonisins were produced by six strains of Fusarium moniliforme and Fusarium proliferatum on inoculated rice culture. For study of...