On (p, q) − equations with concave terms

We consider a (p, q)− equation (1 < q < p, p ≥ 2) with a parametric concave term and a (p − 1)− linear perturbation. We show that the problem have five nontrivial smooth solutions: four of constant sign and the fifth nodal. When q = 2 (i.e., (p, 2) equation) we show that the problem has six nontrivial smooth solutions, but we do not specify the sign of the sixth solution. Our approach uses variational methods, together with truncation and comparison techniques and Morse theory.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Técnica de parametrização geométrica para o fluxo de carga continuado baseado nas variáveis tensão nodal e fator de carregamento

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

High-temperature superconductivity in the two-dimensional t-J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t-J model with the hopping electron amplitudes t (and t') between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the method's results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed 'grand-canonical Gutzwiller approximation' (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a d(x2-y2) wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the

Comparison Of The Solution Of Histidine-tryptophan-alfacetoglutarate With Histidine-tryptophan-glutamate As Cardioplegic Agents In Isolated Rat Hearts: An Immunohistochemical Study.

Cardiac arrest during heart surgery is a common procedure and allows the surgeon to perform surgical procedures in an environment free of blood and movement. Using a model of isolated rat heart, the authors compare a new cardioplegic solution containing histidine-tryptophan-glutamate (group 2) with the histidine-tryptophan-alphacetoglutarate (group 1) routinely used by some cardiac surgeons. To assess caspase, IL-8 and KI-67 in isolated rat hearts using immunohistochemistry. 20 Wistar male rats were anesthetized and heparinized. The chest was opened, cardioctomy was performed and 40 ml/kg of the appropriate cardioplegic solution was infused. The hearts were kept for 2 hours at 4ºC in the same solution, and thereafter, placed in the Langendorff apparatus for 30 minutes with Ringer-Locke solution. Immunohistochemistry analysis of caspase, IL-8, and KI-67 were performed. The concentration of caspase was lower in group 2 and Ki-67 was higher in group 2, both P<0.05. There was no statistical difference between the values of IL-8 between the groups. Histidine-tryptophan-glutamate solution was better than histidine-tryptophan-alphacetoglutarate solution because it reduced caspase (apoptosis), increased KI-67 (cell proliferation), and showed no difference in IL-8 levels compared to group 1. This suggests that the histidine-tryptophan-glutamate solution was more efficient than the histidine-tryptophan-alphacetoglutarate for the preservation of hearts of rat cardiomyocytes.

Remediation Of 17-α-ethinylestradiol Aqueous Solution By Photocatalysis And Electrochemically-assisted Photocatalysis Using Tio2 And Tio2/wo3 Electrodes Irradiated By A Solar Simulator.

TiO2 and TiO2/WO3 electrodes, irradiated by a solar simulator in configurations for heterogeneous photocatalysis (HP) and electrochemically-assisted HP (EHP), were used to remediate aqueous solutions containing 10 mg L(-1) (34 μmol L(-1)) of 17-α-ethinylestradiol (EE2), active component of most oral contraceptives. The photocatalysts consisted of 4.5 μm thick porous films of TiO2 and TiO2/WO3 (molar ratio W/Ti of 12%) deposited on transparent electrodes from aqueous suspensions of TiO2 particles and WO3 precursors, followed by thermal treatment at 450 (°)C. First, an energy diagram was organized with photoelectrochemical and UV-Vis absorption spectroscopy data and revealed that EE2 could be directly oxidized by the photogenerated holes at the semiconductor surfaces, considering the relative HOMO level for EE2 and the semiconductor valence band edges. Also, for the irradiated hybrid photocatalyst, electrons in TiO2 should be transferred to WO3 conduction band, while holes move toward TiO2 valence band, improving charge separation. The remediated EE2 solutions were analyzed by fluorescence, HPLC and total organic carbon measurements. As expected from the energy diagram, both photocatalysts promoted the EE2 oxidation in HP configuration; after 4 h, the EE2 concentration decayed to 6.2 mg L(-1) (35% of EE2 removal) with irradiated TiO2 while TiO2/WO3 electrode resulted in 45% EE2 removal. A higher performance was achieved in EHP systems, when a Pt wire was introduced as a counter-electrode and the photoelectrodes were biased at +0.7 V; then, the EE2 removal corresponded to 48 and 54% for the TiO2 and TiO2/WO3, respectively. The hybrid TiO2/WO3, when compared to TiO2 electrode, exhibited enhanced sunlight harvesting and improved separation of photogenerated charge carriers, resulting in higher performance for removing this contaminant of emerging concern from aqueous solution.

Human Mitochondrial Hsp70 (mortalin): Shedding Light On Atpase Activity, Interaction With Adenosine Nucleotides, Solution Structure And Domain Organization.

The human mitochondrial Hsp70, also called mortalin, is of considerable importance for mitochondria biogenesis and the correct functioning of the cell machinery. In the mitochondrial matrix, mortalin acts in the importing and folding process of nucleus-encoded proteins. The in vivo deregulation of mortalin expression and/or function has been correlated with age-related diseases and certain cancers due to its interaction with the p53 protein. In spite of its critical biological roles, structural and functional studies on mortalin are limited by its insoluble recombinant production. This study provides the first report of the production of folded and soluble recombinant mortalin when co-expressed with the human Hsp70-escort protein 1, but it is still likely prone to self-association. The monomeric fraction of mortalin presented a slightly elongated shape and basal ATPase activity that is higher than that of its cytoplasmic counterpart Hsp70-1A, suggesting that it was obtained in the functional state. Through small angle X-ray scattering, we assessed the low-resolution structural model of monomeric mortalin that is characterized by an elongated shape. This model adequately accommodated high resolution structures of Hsp70 domains indicating its quality. We also observed that mortalin interacts with adenosine nucleotides with high affinity. Thermally induced unfolding experiments indicated that mortalin is formed by at least two domains and that the transition is sensitive to the presence of adenosine nucleotides and that this process is dependent on the presence of Mg2+ ions. Interestingly, the thermal-induced unfolding assays of mortalin suggested the presence of an aggregation/association event, which was not observed for human Hsp70-1A, and this finding may explain its natural tendency for in vivo aggregation. Our study may contribute to the structural understanding of mortalin as well as to contribute for its recombinant production for antitumor compound screenings.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Enhanced response of the fricke solution doped with hematoporphyrin under X-rays irradiation

The vials filled with Fricke solutions were doped with increasing concentrations of Photogem®, used in photodynamic therapy. These vials were then irradiated with low-energy X-rays with doses ranging from 5 to 20 Gy. The conventional Fricke solution was also irradiated with the same doses. The concentration of ferric ions for the Fricke and doped-Fricke irradiated solutions were measured in a spectrophotometer at 220 to 340 nm. The results showed that there was an enhancement in the response of the doped-Fricke solution, which was proportional to the concentration of the photosensitizer. The use of such procedure for studying the radiosensitizing property of photosensitizers based on the production of free radicals is also discussed.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

Determination of the molecular weight of proteins in solution from a single small-angle X-ray scattering measurement on a relative scale

This paper describes a new and simple method to determine the molecular weight of proteins in dilute solution, with an error smaller than similar to 10%, by using the experimental data of a single small-angle X-ray scattering (SAXS) curve measured on a relative scale. This procedure does not require the measurement of SAXS intensity on an absolute scale and does not involve a comparison with another SAXS curve determined from a known standard protein. The proposed procedure can be applied to monodisperse systems of proteins in dilute solution, either in monomeric or multimeric state, and it has been successfully tested on SAXS data experimentally determined for proteins with known molecular weights. It is shown here that the molecular weights determined by this procedure deviate from the known values by less than 10% in each case and the average error for the test set of 21 proteins was 5.3%. Importantly, this method allows for an unambiguous determination of the multimeric state of proteins with known molecular weights.

Solution structure of the human signaling protein RACK1

Background: The adaptor protein RACK1 (receptor of activated kinase 1) was originally identified as an anchoring protein for protein kinase C. RACK1 is a 36 kDa protein, and is composed of seven WD repeats which mediate its protein-protein interactions. RACK1 is ubiquitously expressed and has been implicated in diverse cellular processes involving: protein translation regulation, neuropathological processes, cellular stress, and tissue development. Results: In this study we performed a biophysical analysis of human RACK1 with the aim of obtaining low resolution structural information. Small angle X-ray scattering (SAXS) experiments demonstrated that human RACK1 is globular and monomeric in solution and its low resolution structure is strikingly similar to that of an homology model previously calculated by us and to the crystallographic structure of RACK1 isoform A from Arabidopsis thaliana. Both sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation techniques showed that RACK1 is predominantly a monomer of around 37 kDa in solution, but also presents small amounts of oligomeric species. Moreover, hydrodynamic data suggested that RACK1 has a slightly asymmetric shape. The interaction of RACK1 and Ki1/57 was tested by sedimentation equilibrium. The results suggested that the association between RACK1 and Ki-1/57(122-413) follows a stoichiometry of 1:1. The binding constant (KB) observed for RACK1-Ki-1/57(122-413) interaction was of around (1.5 +/- 0.2) x 10(6) M(-1) and resulted in a dissociation constant (KD) of (0.7 +/- 0.1) x 10(-6) M. Moreover, the fluorescence data also suggests that the interaction may occur in a cooperative fashion. Conclusion: Our SAXS and analytical ultracentrifugation experiments indicated that RACK1 is predominantly a monomer in solution. RACK1 and Ki-1/57(122-413) interact strongly under the tested conditions.