1,207 research outputs found
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 -regularity for stochastic evolution equations
We prove maximal -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 is a sectorial
operator with a bounded -calculus of angle less than on
a space . The driving process is a cylindrical
Brownian motion in an abstract Hilbert space . For and
and initial conditions 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 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 . 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
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