The longtime behavior of a nonlinear Reissner-Mindlin plate with exponentially decreasing memory kernels

In this paper we investigate the longtime behavior of the mathematical model of a homogeneous viscoelastic plate based on Reissner-Mindlin deformation shear assumptions. According to the approximation procedure due to Lagnese for the Kirchhoff viscoelastic plate, the resulting motion equations for the vertical displacement and the angle deflection of vertical fibers are derived in the framework of the theory of linear viscoelasticity. Assuming that in general both Lame's functions, λ and μ, depend on time, the coupling terms between the equations of displacement and deflection depend on hereditary contributions. We associate to the model a nonlinear semigroup and show the behavior of the energy when time goes on. In particular, assuming that the kernels λ and μ decay exponentially, and not too weakly with respect to the physical properties considered in the model, then the energy decays uniformly with respect to the initial conditions; i.e., we prove the existence of an absorbing set for the semigroup associated to the model.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Derivation of the Forchheimer Law Via Matched Asymptotic Expansions

Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law.     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.     

Generalized Forchheimer Equation for Two-Phase Flow Based on Hybrid Mixture Theory

In this paper, we derive a Forchheimer-type equation for two-phase flow through an isotropic porous medium using hybrid mixture theory. Hybrid mixture theory consists of classical mixture theory applied to a multiphase system with volume averaged equations. It applies to media in which the characteristic length of each phase is small relative to the extent of the mixture. The derivation of a Forchheimer equation for single phase flow has been obtained elsewhere. These results are extended to include multiphase swelling materials which have nonnegligible interfacial thermodynamic properties.     

A macrocyclic ligand as receptor and Zn(II)-complex receptor for anions in water: binding properties and crystal structures

Binding properties of 24,29-dimethyl-6,7,15,16-tetraoxotetracyclo[19.5.5.0(5,8).0(14,17)]-1,4,9,13,18,21,24,29-octaazaenatriaconta-Δ(5,8),Δ(14,17)-diene ligand L towards Zn(II) and anions, such as the halide series and inorganic oxoanions (phosphate (Pi), sulfate, pyrophosphate (PPi), and others), were investigated in aqueous solution; in addition, the Zn(II)/L system was tested as a metal-ion-based receptor for the halide series. Ligand L is a cryptand receptor incorporating two squaramide functions in an over-structured chain that connects two opposite nitrogen atoms of the Me(2)[12]aneN(4) polyaza macrocyclic base. It binds Zn(II) to form mononuclear species in which the metal ion, coordinated by the Me(2)[12]aneN(4) moiety, lodges inside the three-dimensional cavity. Zn(II)-containing species are able to bind chloride and fluoride at the physiologically important pH value of 7.4; the anion is coordinated to the metal center but the squaramide units play the key role in stabilizing the anion through a hydrogen-bonding network; two crystal structures reported here clearly show this aspect. Free L is able to bind fluoride, chloride, bromide, sulfate, Pi, and PPi in aqueous solution. The halides are bound at acidic pH, whereas the oxoanions are bound in a wide range of pH values ranging from acidic to basic. The cryptand cavity, abundant in hydrogen-bonding sites at all pH values, allows excellent selectivity towards Pi to be achieved mainly at physiological pH 7.4. By joining amine and squaramide moieties and using this preorganized topology, it was possible, with preservation of the solubility of the receptor, to achieve a very wide pH range in which oxoanions can be bound. The good selectivity towards Pi allows its discrimination in a manner not easily obtainable with nonmetallic systems in aqueous environment.     

Gas phase charged aggregates of bis(2-ethylhexyl)sulfosuccinate (AOT) and divalent metal ions: first evidence of AOT solvated aggregates

Assembling and chelating properties of sodium bis(2-ethylhexyl)sulfosuccinate (AOTNa) towards divalent metal ions have been investigated in the gas phase by electrospray ionization mass spectrometry. A variety of positively charged monometallated and mixed metal aggregates are formed. Interestingly, several ions contain solvent (MeOH, H(2)O) molecules and constitute the most abundant AOT cationic aggregates not containing sodium. These species are the first example of solvated AOT-metal ion aggregates in the gas phase. By increasing the surfactant aggregation number, the abundance of solvated species becomes lower than that of unsolvated ones. Decompositions of ionic species have been studied by tandem mass spectrometry, and their stability has been determined through energy resolved mass spectrometry. In contrast with positively charged AOT-alkaline metal ion aggregates, whose decompositions are dominated by the loss of individual surfactant molecules, AOTNa-divalent ion aggregates mainly dissociate through the cleavage of the AOT H(2)C-O bond followed by further intramolecular fragmentations. This finding, that is consistent with an enhanced chelation of divalent ions with AOT(-) head groups, has been taken as an indication that such aggregates are characterized by a reverse micelle-like organization with a ionic core formed by the metal cations interacting with the negatively charged surfactant polar heads, whereas the surfactant alkyl chains point outside.     

Effects of the net charge on abundance and stability of supramolecular surfactant aggregates in gas phase

Self-assembling of amphiphilic molecules under electrospray ionization (ESI) conditions is characterized by quite unexpected phenomenology. The noticeable differences with respect to the condensed phase are attributable to the absence of the surfactant-solvent interactions, the presence of net charge in the aggregates, and the strong deviation from equilibrium conditions. Aiming to investigate the effects of the net charge on abundance and stability of supramolecular surfactant aggregates, positively and negatively charged aggregates of sodium bis(2-ethylhexyl)sulfosuccinate (AOT) and sodium methane sulfonate (MetS), butane sulfonate (ButS) and octane sulfonate (OctS) have been studied by ESI mass spectrometry, energy resolved mass spectrometry and density functional theory calculations. The negatively charged aggregates are found to be less stable than their positive counterparts. The results are consistent with a self-assembling pattern dominated by electrostatic interactions involving the counterions and head groups of the investigated amphiphilic compounds while the alkyl chains point outwards, protecting the aggregates from unlimited growth processes.     

Simultaneous detection and quantification of parecoxib and valdecoxib in canine plasma by HPLC with spectrofluorimetric detection: development and validation of a new methodology

Parecoxib is the injectable prodrug of valdecoxib, a cicloxygenase-2 selective drug, currently used in human medicine. Recent studies have suggested both its excellent clinical effectiveness and wide safety profile. The aim of the present study was to develop and validate a new high-performance liquid chromatography (HPLC) with spectrofluorimetric detection method to quantify parecoxib and valdecoxib in canine plasma. Several parameters both in the extraction and the detection method were evaluated. The applicability of the method was determined by administering parecoxib to one dog: the protocol provided the expected pharmacokinetic results. The final mobile phase was acetonitrile: AcONH₄ (10 mM; pH 5.0) 55:45, v/v, with a flow rate of 0.4 mL min⁻¹, and excitation and emission wavelengths of 265 and 375 nm, respectively. The analytical column was a reverse-phase C18 ODS2 3-μm particle size. Protein precipitation in acidic medium followed by two successive liquid–liquid steps was carried out. The best extraction solvent was cyclohexane:Et₂O (3:2, v/v) that gave recoveries ranging from 81.1% to 89.1% and from 94.8% to 103.6% for parecoxib and valdecoxib, respectively. The limits of quantification were 25 and 10 ng mL⁻¹ for parecoxib and valdecoxib, respectively. The chromatographic runs were specific with no interfering peaks at the retention times of the analytes, as confirmed by HPLC–mass spectrometry experiments. The other validation parameters were in agreement with the European Medicines Evaluation Agency and International Conference on Harmonisation guidelines. In conclusion, this method (extraction, separation and applied techniques) is simple and effective. This is the first time that use of a HPLC with spectrofluorimetric detection technique to simultaneously detect parecoxib and valdecoxib in plasma has been reported. This technique may have applications for pharmacokinetic studies.     

Efficient organic monoliths prepared by γ-radiation induced polymerization in the evaluation of histone deacetylase inhibitors by capillary(nano)-high performance liquid chromatography and ion trap mass spectrometry

New monolithic HPLC columns were prepared by γ-radiation-triggered polymerization of hexyl methacrylate and ethylene glycol dimethacrylate monomers in the presence of porogenic solvents. Polymerization was carried out directly within capillary (250-200 μm I.D.) and nano (100-75 μm I.D.) fused-silica tubes yielding highly efficient columns for cap(nano)-LC applications. The columns were applied in the complete separation of core (H2A, H2B, H3, and H4) and linker (H1) histones under gradient elution with UV and/or electrospray ionization (ESI) ion trap mass spectrometry (MS) detections. Large selectivity towards H1, H2A-1, H2A-2, H2B, H3-1, H3-2 and H4 histones and complete separation were obtained within 8 min time windows, using fast gradients and very high linear flow velocities, up to 11 mm/s for high throughput applications. The method developed was the basis of a simple and efficient protocol for the evaluation of post-translational modifications (PTMs) of histones from NCI-H460 human non-small-cell lung cancer (NSCLC) and HCT-116 human colorectal carcinoma cells. The study was extended to monitoring the level of histone acetylation after inhibition of Histone DeACetylase (HDAC) enzymes with suberoylanilide hydroxamic acid (SAHA), the first HDAC inhibitor approved by the FDA for cancer therapy. Attractive features of our cap(nano)-LC/MS approach are the short analysis time, the minute amount of sample required to complete the whole procedure and the stability of the polymethacrylate-based columns. A lab-made software package ClustMass was ad hoc developed and used to elaborate deconvoluted mass spectral data (aligning, averaging, clustering) and calculate the potency of HDAC inhibitors, expressed through a Relative half maximal Inhibitory Concentration parameter, namely R_IC(50) and an averaged acetylation degree.