Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate

We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent and inconsistent systems. In this paper, we establish a formula for measuring the distance from the nominal system to the set of ill-posed systems. To this aim, we use the Fenchel-Legendre conjugation theory and prove a refinement of the formula in Ref. 1 for the distance from any point to the boundary of a convex set.This research has been partially supported by grants BFM2002–04114-C02 (01–02) from MEC (Spain) and FEDER (EU) and by grants GV04B-648 and GRUPOS04/79 from Generalitat Valenciana (Spain).     

New 1,2,4- and 1,3,4-oxadiazole materials: synthesis, and mesomorphic and luminescence properties

The synthesis and liquid crystalline properties of new series of 1,2,4- and 1,3,4-oxadiazole derivatives (2a-f and 5a-f respectively) are reported. These compounds contain only one terminal flexible alkoxy chain, the other terminal substituent is a protecting benzyl group. All compounds of series 2 exhibit an enantiotropic nematic phase. The homologue with the longest chain (2f) displays an enantiotropic dimorphism smectic A- nematic. None of the compounds of series 5 shows mesomorphism and only crystal-isotropic transitions were observed. The liquid crystalline properties were investigated by differential scanning calorimetry, polarizing optical microscopy and X-ray measurements. Luminescence properties, in chloroform solution, of 2f and the series 5 compounds were evaluated. Good photoluminescence quantum yields for compounds of series 5 were observed. Compound 2f, incorporating the 1,2,4-oxadiazole ring shows a very strong reduction in emissive properties.     

On the validity of the Fokker-Planck equation for the Heisenberg magnet

We assume an explicit stochastic dynamics for the microscopic variables in the Heisenberg magnet based on experimental data. We obtain additional terms to the Fokker-Planck Equation and also explicit expressions for the numerical coefficients in the Master Equation, near T_c.     

Quantitative plasma determination of a novel antiretroviral derivative of zidovudine by solid-phase extraction and high-performance liquid chromatography

A solid-phase extraction methodology, followed by high-performance liquid chromatography (HPLC) quantification with UV absorbance detection (λ=267 nm), was developed in order to study the stability of 3′-azido-3′-deoxy-5′-O-isonicotinoylthymidine (AZT-Iso), a novel derivative of the antiretroviral AZT, in different matrixes. The half-lives (t _1/2) for AZT-Iso were 1.19, 1.13 and 0.30 h for human, rat and rabbit plasma, respectively, and 14.91 and 25.49 h for potassium phosphate buffer (pH 7.4) and human serum albumin solution, respectively. The HPLC method proved to be selective, sensitive and accurate. Good recovery, linearity and precision were achieved using p-fluorophenol as an internal standard. The validity of this method was tested using synthetic mixtures of the intact drug with its decomposition products. In conclusion, the method presented is applicable to in vivo pharmacokinetics studies of AZT-Iso in rats.     

Sensory hybrid host materials for the selective chromo-fluorogenic detection of biogenic amines

Pyrylium-containing mesoporous materials have been used for the chromo-fluorogenic sensing of biogenic amines in an aqueous environment.     

Comparison Between Different Syntesis Methods of PMMA/HA Using Ultrasonic Radiation

Summary: The use of PMMA as dental and osseous cement and also in the fabrication of intraocular lenses has been widely reported. The combination of its excellent properties with those of hydroxyapatite (HA) to form a composite material, can result in very interesting properties as a biomaterial. The key is to obtain a good filler dispersion and interface bonding. Ultrasonic radiation seems to be a very versatile method for the synthesis of these materials, since the use of conventional initiators can be avoided, the filler dispersion improved and the interface interaction can be promoted. In the present work PMMA/HA composite materials were prepared by three different synthesis routes using ultrasonic radiation, in order to study the effect of the synthesis method on the final microstructure. Method I : in situ synthesis of PMMA and HA, under ultrasonic radiation by emulsion polymerization of MMA and HA precursors. Method II : in situ synthesis of HA, (from its precursors) by high frequency ultrasound in commercial PMMA solution Method III : in situ polymerization of MMA under high frequency ultrasonic radiation and adding HA to the solution and Method IV Mixing of hydroxyapatite nanocrystals, in different proportions, in a solution of commercial PMMA, by different periods from 10 min to 7 h, under low frequency (conventional) ultrasonic radiation, to compare the effect of high frequency and conventional ultrasound radiation. The different materials were characterized by FTIR, SEM, TEM, DRX, ¹H NMR and TGA. The results showed that, all the composites prepared by in situ synthesis showed an interaction between HA and PMMA, manifested by a bonding of the phosphate groups with the polar groups of the polymer matrix observed by FTIR. On the other hand, when the synthesis was carried out simultaneously adding HA and PMMA precursors a inhibition of the polymerization reaction of MMA was observed.     

A one side superlinear Ambrosetti-Prodi problem for the Dirichlet p-laplacian

We study the solvability of the quasilinear elliptic problem of parameter s

     

Operational Calculus Approach to Nonlocal Cauchy Problems

Let Φ be a linear functional of the space ${\mathcal{C} =\mathcal{C}(\Delta)}$ of continuous functions on an interval Δ. The nonlocal boundary problem for an arbitrary linear differential equation $$ P\left(\frac{d}{d t}\right)y = F(t) $$ with constant coefficients and boundary value conditions of the form $$ \Phi\{\,y^{(k)}\} =\alpha_k,\,\,\,k = 0,\,1,\,2,\, \ldots,\,{\rm deg} P-1 $$ is said to be a nonlocal Cauchy boundary value problem. For solution of such problems an operational calculus of Mikusiński’s type, based on the convolution $$ (f*g)(t) = \Phi_\tau\, \left\{{\int\limits_\tau^t} f(t+\tau - \sigma)\,g(\sigma)\, d \sigma\, \right\}, $$ is developed. In the frames of this operational calculus the classical Heaviside algorithm is extended to nonlocal Cauchy problems. The obtaining of periodic, antiperiodic and mean-periodic solutions of linear ordinary differential equations with constant coefficients both in the non-resonance and in the resonance cases reduces to such problems. Here only the non-resonance case is considered. Extensions of the Duhamel principle are proposed.