Existence and regularity for a chemotaxis model involved in the modeling of multiple sclerosis

We study in this work the global existence of solutions to a system of reaction cross diffusion equations appearing in the modeling of multiple sclerosis, in the one-dimensional case. Weak solutions are obtained for general initial data, and existence, uniqueness, stability and smoothness are proven when initial data are smooth.

     

Inner solvers for interior point methods for large scale nonlinear programming

This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution. In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported. This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project: “Parallel Nonlinear Numerical Optimization PN ² O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ).     

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour

In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor.     

Relating Categorical Semantics for Intuitionistic Linear Logic

There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical models are not sufficient to identify the most appropriate class uniquely. We recommend instead to use the notion of internal language when relating a typed calculus to a class of models. After clarifying the internal languages of the categories of models in the literature we relate these models via reflections and coreflections. Mathematics Subject Classifications (2000) 03G30, 03B15, 18C50, 03B20.     

New conditions for non-stagnation of minimal residual methods

In the solution of large linear systems, a condition guaranteeing that a minimal residual Krylov subspace method makes some progress, i.e., that it does not stagnate, is that the symmetric part of the coefficient matrix be positive definite. This condition results in a well-established worst-case bound for the convergence rate of the iterative method, due to Elman. This bound has been extensively used, e.g., when the linear system comes from discretized partial differential equations, to show that the convergence of GMRES is independent of the underlying mesh size. In this paper we introduce more general non-stagnation conditions, which do not require the symmetric part of the coefficient matrix to be positive definite, and that guarantee, for example, the non-stagnation of restarted GMRES for certain values of the restarting parameter. Work on this paper was supported in part by the U.S. Department of Energy under grant DE-FG02-05ER25672.     

Minimal Blow-Up Solutions to the Mass-Critical Inhomogeneous NLS Equation

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the critical point is a maximum, this solution has minimal mass among the blow-up solutions. As a corollary, we also obtain unstable blow-up solutions of the mass-critical Schrödinger equation on some surfaces. The proof is based on properties of the linearized operator around the ground state, and on a full use of the invariances of the equation with an homogeneous nonlinearity and no potential, via time-dependent modulations.     

Callus Culture of Scorzonera radiata as a New,Highly Productive and Stable Source of Caffeoylquinic Acids

During our ongoing efforts to investigate biotechnological sources of caffeoylquinic acid (CQA) metabolites, we discovered the plant Scorzonera radiata Fisch. (Asteraceae), which is able to produce callus cultures with high yield and extremely high stability. An actively growing callus line, designated as Sr-L1, retained the ability to produce 11 CQAs during long-term cultivation (more than 20 years). A total of 29 polyphenolic compounds were identified in the leaves and Sr-L1 callus culture of S. radiata, including CQAs, lignol derivatives, flavonoids, and dihydrostilbenes. The composition of CQAs in the Sr-L1 culture was identical to that in the S. radiata leaves. Sr-L1 calli did not produce flavonoids and dihydrostilbenes, but produced lignol derivatives, which were absent in leaves. The HPLC-UV-HRMS determination showed the presence of monoacyl derivatives of CQAs such as 5-CQA, 4-CQA, cis-5-CQA, and 5-O-p-coumaroylquinic acid in the Sr-L1 culture. Among diacyl derivatives, 3,4-diCQA, 3,5-diCQA, cis-3,5-diCQA, 4,5-diCQA, 3-O-p-coumaroyl-5-O-CQA, and 3-O-caffeoyl-5-O-p-coumaroylquinic acid were found. The content of 5-CQA reached 7.54 mg/g dry weight and the content of 3,5-diCQA was as high as 18.52 mg/g dry weight. 3,5-diCQA has been reported to be of high nutritional and pharmacological value, as it alleviates inflammatory pain, reverses memory impairment by preventing neuronal apoptosis, and counteracts excessive adipose tissue expansion, serving as an attractive treatment option for obesity. The high content of 3,5-diCQA and the exceptional stability of biosynthesis make callus cultures of S. radiata a promising source for the development of drugs and nutraceuticals.     

Catalysis of the beta-elimination of HF from isomeric 2-fluoroethylpyridines and 1-methyl-2-fluoroethylpyridinium salts. Proton-activating factors and methyl-activating factors as a mechanistic test to distinguish between concerted E2 and E1cb irreversible mechanisms

Second-order rate constants, k(OH)(N), M(-)(1) s(-)(1), for the beta-elimination reactions of HF with 2-(2-fluoroethyl)pyridine (2), 3-(2-fluoroethyl)pyridine (3), and 4-(2-fluoroethyl)pyridine (4) in OH(-)/H(2)O, at 50 degrees C and mu = 1 M KCl, are = 0.646 x 10(-)(4) M(-)(1) s(-)(1), = 2.97 x 10(-)(6) M(-)(1) s(-)(1), and = 5.28 x 10(-)(4) M(-)(1) s(-)(1), respectively. When compared with the second-order rate constants for the same processes with the nitrogen-methylated substrates 1-methyl-2-(2-fluoroethyl)pyridinium iodide (5), 1-methyl-3-(2-fluoroethyl)pyridinium iodide (6), and 1-methyl-4-(2-fluoroethyl)pyridinium iodide (7), the methyl-activating factor (MethylAF) can be calculated from the ratio k(OH)(NCH)3/, and a value of 8.7 x 10(5) is obtained with substrates 5/2, a value of 1.6 x 10(3) with 6/3, and a value of 2.1 x 10(4) with 7/4. The high values of MethylAF are in agreement with an irreversible E1cb mechanism (A(N)D(E) + D(N)) for substrates 5 and 7 and with the high stability of the intermediate carbanion related to its enamine-type structure. In acetohydroxamate/acetohydroxamic acid buffers (pH 8.45-9.42) and acetate/acetic acid buffers (pH 4.13-5.13), the beta-elimination reactions of HF, with substrates 2 and 4, occur at NH(+), the substrates protonated at the nitrogen atom of the pyridine ring, even when the [NH(+)] is much lower than the [N], the unprotonated substrate, due to the high proton-activating factor (PAF) value observed: 3.6 x 10(5) for 2 and 6.5 x 10(4) for 4 with acetohydroxamate base. These high PAF values are indicative of an irreversible E1cb mechanism rather than a concerted E2 (A(N)D(E)D(N)) mechanism. Finally, the rate constant for carbanion formation from NH(+) with 2 is k(B)(NH)+ = 0.35 M(-)(1) s(-)(1), which is lower than when chlorine is the leaving group ( = 1.05 M(-)(1) s(-)(1); Alunni, S.; Busti, A. J. Chem. Soc., Perkin Trans. 2 2001, 778). This is direct experimental evidence that some lengthening of the carbon-leaving group bond can occur in the intermediate carbanion. This is a point of interest for interpreting a heavy-atom isotope effect.     

Electrochemical determination of minoxidil in different pharmaceutical formulations by flow injection analysis.

The electrochemical behavior and amperometric-FIA quantification of minoxidil at a glassy carbon electrode is described. The procedure is based on electrochemical oxidation at 0.800 V (vs. Ag/AgCl/NaCl(3 M) in a phosphate buffer solution. Minoxidil was determined over the range 1 x 10(-7) - 1 x 10(-4) M. Different analytical parameters and electrode stability were analyzed to obtain the best electrode performance. The optimal conditions were: working potentials, 0.800 V; flow rate, 0.74 mL min(-1); and solution pH 7.0. This system allowed a sampling rate of 120 samples per hour without any pretreatment. The proposed method was used for minoxidil quantification in pharmaceutical preparations with satisfactory results. The accuracy of FIA-amperometric method was established by a comparison with the conventional UV determination technique using a paired t-test indicating the absence of systematic errors.