Optimal Error Estimate of the Penalty Finite Element Method for the Micropolar Fluid Equations

We present an optimal error estimate of the numerical velocity, pressure, and angular velocity for the fully discrete penalty finite element method of the micropolar equations when the parameters ?, Δ t, and h are sufficiently small. In order to obtain this estimate, we present the time discretization of the penalty micropolar equation that is based on the backward Euler scheme; the spatial discretization of the time discretized penalty micropolar equation is based on a finite elements space pair (X _h , M _h ) that satisfies some approximations properties.     

Extensions of the Fill–Fishkind formula and the infimum – parallel sum relation

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015;467), authors gave a generalization of a formula by Fill and Fishkind, regarding the Moore–Penrose inverse of the sum of two matrices, in the setting of arbitrary Hilbert spaces. We consider this formula under some weaker assumptions and derive certain conclusions generalizing the mentioned result. We also extend a formula connecting the infimum of two orthogonal projections and their parallel sum to a formula connecting the star-infimum and the parallel sum of operators which need not be positive, using the concept of parallel sum that was introduced in (Antezana J, Corach G, Stojanoff D. Bilateral shorted operators and parallel sums. Linear Algebra Appl. 2006;414).     

Free energy and entropy production in planar Couette flow far from equilibrium

The macroscopic thermodynamic stability of a system of 108 diatomic molecules undergoing planar Couette flow far from equilibrium is reported. The system is perturbed from the steady state using a nondissipative variable colour field which induces a polarization in the system. It is found that the steady state for the system corresponds to an extremum in the generalized free energy and entropy production. However, while the free energy is always a minimum, the entropy production may be either a minimum or a maximum depending upon the direction of the colour field. These results, for a molecular system, are fundamentally different from those for an equivalent atomic system.     

The <Emphasis Type="Italic">D</Emphasis><Superscript>(−)</Superscript>-Center Energy Spectrum in the Quantum Narrowing in the Presence of a Longitudinal Magnetic Field

The dispersion equation for an electron localized at the D⁰-center in the quantum narrowing in the presence of a magnetic field longitudinal with respect to the axis of constriction is analytically derived within the model of zero-radius potential. It is found that a special feature of the electron spectrum in the quantum narrowing manifests itself in the dependence of the D(−)-state binding energy on the effective constriction length. The evolution of the D(−)-state binding energy with changes in the longitudinal magnetic-field strength is investigated and compared with the case of D(−)-states in quantum wires. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 23–27, June, 2005.     

URB754 has no effect on the hydrolysis or signaling capacity of 2-AG in the rat brain

Previous studies indicate that in brain tissue the endocannabinoid 2-AG is inactivated by monoglyceride lipase (MGL)-catalyzed hydrolysis, and a recent report has indicated that MGL activity could be specifically inhibited by URB754 . In the present study, URB754 failed to inhibit 2-AG hydrolysis in rat brain preparations. In addition, brain cryosections were employed to assess whether URB754 could facilitate the detection of 2-AG-stimulated G protein activity. Nevertheless, whereas pretreatment with PMSF readily allowed detection of 2-AG-stimulated G protein activity, URB754 was ineffective. In contrast to previous claims, brain FAAH activity was also resistant to URB754. Thus, in our hands URB754 was not able to block the endocannabinoid-hydrolyzing enzymes and cannot serve as a lead structure for future development of MGL-specific inhibitors.     

Single-Chain Fv Antibody Fragments Retain Binding Properties of the Monoclonal Antibody Raised Against Peptide P1 of the Human Prion Protein

Prion diseases are incurable neurodegenerative diseases that affect both humans and animals. The infectious agent is a pathogenic form of the prion protein that accumulates in brain as amyloids. Currently, there is neither cure nor reliable preclinical diagnostics on the market available. The growing number of reports shows that passive immunisation is one of the most promising strategies for prion disease therapy, where antibodies against prions may prevent and even cure the infection. Since antibodies are large molecules and, thus, might not be suitable for the therapy, different antibody fragments are a good alternative. Therefore, we have designed and prepared single-chain antibody fragments (scFvs) derived from the PrP^Sc-specific murine monoclonal antibody V5B2. Using a new expression vector pMD204, we produced scFvs in two opposing chain orientations in the periplasm of Escherichia coli. Both recombinant antibody fragments retained the specificity of the parent antibody and one of these exhibited binding properties comparable to the corresponding murine Fab fragments with the affinity in nM range. Our monovalent antibody fragments are of special interest in view of possible therapeutic reagents for prion diseases as well as for development of a new generation of diagnostics.     

Synthesis,characterization, thermal properties and biological activity of diazine-ring containing hydrazones and their metal complexes

Journal of Thermal Analysis and Calorimetry - New coordination compounds have been synthesized by reacting Zn(II) and Co(II) nitrate or acetate in the presence of triethylamine with Schiff-base...