Singular and degenerate anisotropic parabolic equations with a nonlinear source

The Dirichlet problem in arbitrary domain for degenerate and singular anisotropic parabolic equations with a nonlinear source term is considered. We state conditions that guarantee the existence and uniqueness of a global weak solution to the problem. A similar result is proved for the parabolic p-Laplace equation.     

Study on low-energy positron polarimetry

A polarised positron source has been proposed for the design of the international linear collider (ILC). In order to optimise the positron beam, a measurement of its degree of polarisation close to the positron creation point is desired. In this contribution, methods for determining the positron polarisation at low energies are reviewed. A newly developed polarisation extension to GEANT4 will provide the basis for further polarimeter investigations.      

Coincidence of Least Uniform Deviations of Functions from Polynomials and Rational Fractions

For a given nonincreasing vanishing sequence {a _n } _{n = 0} of nonnegative real numbers, we find necessary and sufficient conditions for a sequence {n _k } _{k = 0} to have the property that for this sequence there exists a function f continuous on the interval [0,1] and satisfying the condition that , k = 0,1,2,..., where E _n (f) and R _n,m (f) are the best uniform approximations to the function f by polynomials whose degree does not exceed n and by rational functions of the form r _n,m (x) = p _n (x)/q _m (x), respectively.     

Inverse diagnostic problems associated with image processing

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 9–20.     

Deformation of a Three-Layer Rod with a Compressible Core in a Neutron Flow*

International Applied Mechanics - We studied the deformation of a three-layer elastoplastic rod with a compressible core in a neutron flow. To describe the kinematics of the sandwich asymmetric...     

Effect of Vavilov–Cherenkov radiation cone transformation upon entry of a relativistic electron into a substance layer

Transformation of the Vavilov–Cherenkov radiation cone under grazing interaction of a relativistic electron with a layer of substance is theoretically studied. It is shown that this effect can occur when the electron enters the substance layer.     

Solvability of a nonstationary problem of a rigid body motion in the flow of a viscous incompressible fluid in a pipe of arbitrary cross-section

The existence of a generalized weak solution is proved for the nonstationary problem of motion of a rigid body in the flow of a viscous incompressible fluid filling a cylindrical pipe of arbitrary cross-section. The fluid flow conforms to the Navier–Stokes equations and tends to the Poiseuille flow at infinity. The body moves in accordance with the laws of classical mechanics under the influence of the surrounding fluid and the gravity force directed along the cylinder. Collisions of the body with the boundary of the flow domain are not admitted and, by this reason, the problem is considered until the body approaches the boundary.