Rate of Convergence of Space Time Approximations for stochastic evolution equations

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.Comment: 33 page

Abelian groups as artinian or noetherian modules above endomorphism rings

The A and B Abellian groups, such that the Hom(A, B) homomorphism group is the Artin module over the ring of the B group endomorphism, are described. Description of the A and B group for which the Hom(A,B) group is the Artin module over the ring of the A group endomorphism is reduced to the case when the A group has no torsion and the B group is either a quasi-cyclic group or a divisible group without torsion. The A and B Abellian groups for which the Hom(A,B) group is the Neter module over the E(A) or E(B) ring are characterized. The research of arbitrary Abellian group with the link Neter ring of endomorphisms is reduced to the research of the group without torsion with the link Neter ring of endomorphisms. The research of the right Neter ring of endomorphisms remained uncompleted. The separable Abele groups without torsion with the link and right Neter rings of endomorphisms are described

On the Green function of linear evolution equations for a region with a boundary

We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.Comment: 9 page

Association of the rs2167270 polymorphism of the leptin gene (LEP) with the intensity of pain in patients with osteoarthritis of the knee

Background: Osteoarthritis (OA) is a significant social problem as it is the most common disease of the joints. OA is a multifactorial disease in which great attention is paid to hereditary factors. Recently, a number of studies have demonstrated the contribution of a number of genes to the subjective assessment of pain in OA, which is the main symptom of this disease. The association of P2X7, TRPV1 and TACR1 genes and some others with pain sensitivity has been shown. One of the risk factors of pain among many others, is the increased weight. Abdominal adipose tissue is a source of release of pro-inflammatory adipokines that cause systemic inflammation associated with damage to many tissues, including subchondral bone, synovial membrane. Leptin is an endogenous hormone from the adipokine family encoded by the obesity gene leptin (LEP) and which is synthesized primarily in adipocytes.Aims: To investigate the possible association of rs2167270 (A19G) polymorphism of the LEP gene with pain intensity in ­patients with knee OA.Materials and methods: The study was conducted among women diagnosed with OA. Using the VAS scale (Visual analog scale), patients with mild knee pain — group 1 (VAS ≤ 40 mm) and patients with moderate or severe pain — group 2 (VAS>40 mm) were selected for pain assessment. Genetic variants of A19G leptin gene polymorphism were studied by polymerase chain reaction followed by restriction fragment length analysis (PCR-RFLP) method.Results: In the group of patients with moderate or severe pain intensity (group 2, n=61), a statistically significant association was shown with a higher body mass index (p=0.006) and an increased frequency of carriers of the 19GG genotype (p=0,051) compared to group 1 (n=36). Carriers of the 19GG genotype statistically significantly had a higher rate of knee pain and an early age of OA debut compared to carriers of the 19AA genotype (p=0,035 and p=0,015, respectively).Conclusions: The findings open up new possibilities for predicting pain symptoms in patients with knee OA by genetic testing of A19G polymorphic variants of the leptin gene

Materials based on BIFEVOX and bismuth or iron simple oxides nanopowders

Received: 22.09.2017; accepted: 17.10.2017; published: 20.10.2017.Compositions of composite materials based on BIFEVOX and nanopowders of bismuth and iron oxides have been obtained. The absence of chemical interaction between the components has been proved, the total electrical conductivity of materials in the average temperature region has been determined. It has been shown that under the selected formation conditions, it has not yet been possible to achieve significant improvement of the functional characteristics of heterogeneous compositions in comparison with individual phases. However positive results on chemical and structural stability give way to further investigations.The work was partially supported by the Scholarship of the President (SP-3376.2016.1) and Russian Foundation for Basic Research (project No 17-53-04098)

Investigation of phase transitions in multiferroics HоFe3-xGax(BO3)4 and TbFe3-xGax(BO3)4 solid solution with huntite structure

RFBR funded the reported study according to the research project № 18-02-00754

Molecular random walks and invariance group of the Bogolyubov equation

Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density is discovered. It results in many exact relations between probability distribution of the path of a test particle and its irreducible correlations with the fluid. As the consequence, significant restrictions do arise on possible shapes of the path distribution. In particular, the hypothetical Gaussian form of its long-range asymptotic proves to be forbidden (even in the Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which possesses power-law long tail (cut off by ballistic flight length).Comment: 23 pages, no figures, LaTeX AMSART, author's translation from Russian of the paper accepted to the TMPh (``Theoretical and mathematical physics''

Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation

In this work we analyze the interaction of isolated solitary structures and ion-acoustic radiation. If the radiation amplitude is small solitary structures persists, but when the amplitude grows energy transfer towards small spatial scales occurs. We show that transfer is particularly fast when a fixed point of a low dimensional model is destroyed.Comment: LaTex + 4 eps file

Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces

Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In this approach, the Maxwell equations are solved exactly on the background of static cosmological Einstein model, parameterized by special cylindrical coordinates and realized as a Riemann space of constant positive curvature. A discrete frequency spectrum for electromagnetic modes depending on the curvature radius of space and three parameters is found, and corresponding basis electromagnetic solutions have been constructed explicitly. In the case of elliptical model a part of the constructed solutions should be rejected by continuity considerations. Similar treatment is given for Maxwell equations in hyperbolic Lobachevsky model, the complete basis of electromagnetic solutions in corresponding cylindrical coordinates has been constructed as well, no quantization of frequencies of electromagnetic modes arises.Comment: 39 page

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi