The heat equation for three-layer plates with a moving filler

The three-dimensional nonstationary problem of coupled heat exchange during the flow of an incompressible fluid (a heating or cooling agent) between walls of finite thickness is reduced by operator methods to a system of two-dimensional nonstationary equations of heat conduction: an effective method of solving this system is proposed.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 1–3.     

Environmental dispersion in a three-layer wetland flow with free-surface

To further address the characteristic of contaminant transport in wetlands of a multi-layer structure, environmental dispersion of a pulsed contaminant emission into a steady flow is analytically explored in this paper for the typical case of a respectively vegetated or packed three-layer wetland dominated with free-water-surface-effect. The hierarchical structure for the critical length and duration of the contaminant cloud is illustrated for the dispersion of typical contaminant constituents.     

Stress concentration in a three-layer plate with two cylindrical cavities

The stressed state of a thick three-layer plate with two circular holes is studied. Resolving functions are expressed in terms of Kolosov-Muskhelishvili integral potentials and modified Bessel functions. The problem is reduced to solving an infinite set of linear algebraic equations.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 25–28, 1987.     

Permanent rotations of a body with a viscous filler suspended on a rod

Problems of the existence, stability, and branching of the permanent rotations of a heavy, dynamically symmetrical rigid body suspended on a rod and which has an axisymmetric ellipsoidal cavity filled with a fluid are discussed. The phenomenological model of the friction of the fluid against the cavity wall proposed by Samsonov is used. All the trivial permanent rotations of the system and the non-trivial rotations that branch off from the trivial ones are found. Their stability and branching are investigated using a modified Routh's theory. The results obtained are presented in the form of an atlas of bifurcation diagrams.     

Thermal expansion of a composite with a hybrid granular-fibrous filler

Conclusion The thermal deformation of LDPE with a granular-fibrous filler was studied experimentally within a broad temperature range. We analyzed the effect of fillers on characteristics of relaxational transitions in LDPE as determined from dilatometric tests. A method was proposed for calculating the effective CLE of a composite with allowance for aggregation of a powdered filler and the statistical distributions of the length and orientation of the anisotropic fibers. The method was substantiated experimentally. Results were also presented of a theoretical analysis of the effect of the parameters of the fiber distributions f(l.) and (, ) and the relative volume contents of granular and fibrous fillers on _ij for the composite. It was established that aggregation of the granular filler may produce a hybrid effect consisting of maximum suppression of thermal expansion of the binder by the combination filler relative to a two-component composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 237–246, March–April, 1989.     

Modules over rings with a power basis

A homological category is constructed and also a functor into it from the category of finitely generated modules over a ring with a power basis such that from an object that corresponds to a module the latter is uniquely determined to within free direct summands, and from a morphism corresponding to a module homomorphism this homomorphism can be uniquely reconstructed to within norms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 259–281, 1977.     

On polynomial rings over a ring with a selfduality

We prove that a ringR has a self duality induced by a leftR-moduleM if and only if its polynomial ringR[x] has a graded self duality induced by a graded leftR[x]-moduleM[x ⁻¹]. Supported by the Natural Science Foundation of Fujian Province (1994–1997)     

A note on rings with involution

LetR be a ring with involution_* and π a right ideal ofR. It is shown that if every symmetric elements∈p satisfiess ⁿ=0 wheren is a fixed positive integer then ?^*?(L(R), the lower nil radical ofR.