Implicit Euler scheme for an abstract evolution inequality

For a triple {V, H, V*} of Hilbert spaces, we consider an evolution inclusion of the form u′(t)+A(t)u(t)+δφ{symbol}(t, u(t)) ∋f(t), u(0) = u0, t ∈ (0, T ], where A(t) and φ{symbol}(t, ·), t ∈ [0, T], are a family of nonlinear operators from V to V * and a family of convex lower semicontinuous functionals with common effective domain D(φ{symbol}) ⊂ V. We indicate conditions on the data under which there exists a unique solution of the problem in the space H1(0, T; V)∩W∞ 1 (0, T;H) and the implicit Euler method has first-order accuracy in the energy norm. © 2011 Pleiades Publishing, Ltd

Exact penalty operators and regularization of parabolic variational inequalities with an obstacle inside a domain

A class of parabolic variational inequalities with zero obstacle inside the domain is considered. For this class, exact penalty operators are defined, which are then used to construct and study regularization methods. The following estimates are obtained for the closeness of the original and regularized problem: u - ε1 ≤uε + ε1 and ∥u-uε ∥ L2(0,T;V0) = O(ε3/4). © 2008 MAIK Nauka

Accuracy of discrete schemes for a class of abstract evolution inequalities

For a triple of Hilbert spaces {V, H, V*}, we study a discrete and a semidiscrete scheme for an evolution inclusion of the form u′(t) + A(t)u(t) + ∂φ{symbol}(t, u(t)) ∋ f(t), u(0) = u 0, t ∈ (0, T], where the pair {A(t), φ{symbol}(t, ·)} consists of a family of nonlinear operators from V into V* and a family of proper convex lower semicontinuous functionals with common effective domain D(φ{symbol}) ⊂ V. The discrete scheme is a combination of the Galerkin method with perturbations and the implicit Euler method. Under conditions on the data providing the existence and uniqueness of the solution of the problem in the space H1(0, T; V) ∩ W∞ 1(0, T;H), we obtain an abstract estimate for the method error in the energy norm of first-order accuracy with respect to the time increment. By way of application, we consider a problem with an obstacle inside the domain, for which we obtain an optimal estimate of the accuracy of two implicit schemes (standard and new) on the basis of the finite element method. © 2013 Pleiades Publishing, Ltd

Stability of the coincidence set of a solution to a parabolic variational inequality with an obstacle

In this paper we propose a new technique for the stability analysis of the coincidence set of a solution to a parabolic variational inequality with an obstacle inside the domain. It is based on the reformulation of the initial inequality in the form of a parabolic initial boundary value problem with an exact penalty operator. © 2010 Allerton Press, Inc

Role of Nitric Oxide Produced by Lactobacilli in Relaxation of Intestinal Smooth Muscles

© 2016, Springer Science+Business Media New York.Application of NO-producing lactobacilli to a rat jejunum segment induced muscle relaxation that was potentiated after activation of bacterial NO production with NO synthase substrate L-arginine. Similar changes in the intestinal contractile activity were observed in response to exogenous NO formed by sodium nitroprusside. These results indicated the involvement of NO synthesized by probiotic lactobacilli in the regulation of the intestinal motor function

Role of Nitric Oxide Produced by Lactobacilli in Relaxation of Intestinal Smooth Muscles

© 2016 Springer Science+Business Media New York Application of NO-producing lactobacilli to a rat jejunum segment induced muscle relaxation that was potentiated after activation of bacterial NO production with NO synthase substrate L-arginine. Similar changes in the intestinal contractile activity were observed in response to exogenous NO formed by sodium nitroprusside. These results indicated the involvement of NO synthesized by probiotic lactobacilli in the regulation of the intestinal motor function

On creating mass/matter by extra dimensions in the Einstein-Gauss-Bonnet gravity

Kaluza-Klein (KK) black hole solutions in the Einstein-Gauss-Bonnet (EGB) gravity in $D$ dimensions obtained in the current series of the works by Maeda, Dadhich and Molina are examined. Interpreting their solutions, the authors claim that the mass/matter is created by the extra dimensions. To support this claim, one needs to show that such objects have classically defined masses. We calculate the mass and mass flux for 3D KK black holes in 6D EGB gravity whose properties are sufficiently physically interesting. Superpotentials for arbitrary types of perturbations on arbitrary curved backgrounds, recently obtained by the author, are used, and acceptable mass and mass flux are obtained. A possibility of considering the KK created matter as dark matter in the Universe is discussed.Comment: 15 pages, no figures, minor changes related to the Journal publication with adding two references in footnote

Role of Nitric Oxide Produced by Lactobacilli in Relaxation of Intestinal Smooth Muscles

© 2016, Springer Science+Business Media New York.Application of NO-producing lactobacilli to a rat jejunum segment induced muscle relaxation that was potentiated after activation of bacterial NO production with NO synthase substrate L-arginine. Similar changes in the intestinal contractile activity were observed in response to exogenous NO formed by sodium nitroprusside. These results indicated the involvement of NO synthesized by probiotic lactobacilli in the regulation of the intestinal motor function

Observational Manifestations of the First Protogalaxies in the 21 cm Line

The absorption properties of the first low-mass protogalaxies (mini-halos) forming at high redshifts in the 21-cm line of atomic hydrogen are considered. The absorption properties of these protogalaxies are shown to depend strongly on both their mass and evolutionary status. The optical depths in the line reach $\sim$0.1-0.2 for small impact parameters of the line of sight. When a protogalaxy being compressed, the influence of gas accretion can be seen manifested in a non-monotonic frequency dependence of the optical depth. The absorption characteristics in the 21-cm line are determined by the thermal and dynamical evolution of the gas in protogalaxies. Since the theoretical line width in the observer's reference frame is 1-6 kHz and the expected separation between lines 8.4 kHz, the lines from low mass protogalaxies can be resolved using ongoing and future low frequency interferometers.Comment: 12 pages, 5 figure

The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine

We study the propagator of a non-relativistic, non-interacting particle in any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and $V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from the past side of $V_-$ to t the future side of $V_+$ and the other from the past side of $V_+$ to the future side of $V_-$. We express the propagator explicitly in terms of those for ordinary, flat spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any non-relativistic time-machine spacetime; it is the non-relativistic version of a theorem by Friedman, Papastamatiou and Simon, which says that for a free scalar field, quantum mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product