Large deformations of homogeneous and fiber-reinforced cylinders under the action of centrifugal forces

The problem on large deformations of round cylinders made of homogeneous and fiber-reinforced elastomeric materials under the action of inertia forces caused by rotatory motion is solved. The solution is given in a plane axisymmetric statement, where the deformation parameters of the cylinders depend only on the radial coordinate. Based on the mathematical model presented, the deformation of revolving cylinders made of homogeneous elastomeric materials and reinforced with fibers in the axial, circumferential, and radial directions is investigated. The ultimate rotational speeds for cylinders with different reinforcement schemes and tight and loose fits are found at which their limiting configurations are reached. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 347-366, May-June, 2009.     

Quantum duality in quantum deformations

In accordance with the quantum duality principle, the twisted algebra is equivalent to the quantum group and has two preferred bases: one inherited from the universal enveloping algebra and the other generated by coordinate functions of the dual Lie group . We show howthe transformation can be explicitly obtained for any simple Lie algebra and a factorable chain of extended Jordanian twists. In the algebra , we introduce a natural vector grading , compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying the costructure of the deformed Hopf algebra , considered as a quantum group . The transformation can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian deformations and study it in terms of ; we find new realizations of the parabolic twist. Dedicated to the birthday of my teacher, Yurii Novozhilov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006.     

Amplitude modulation of a low-coherence source, applications to distance and dynamic displacement sensing

The possibilities of the radio-frequency amplitude modulation of a low-coherence source for distance and displacement measurements are discussed. This intensity-based method, used within a Michelson interferometer, is a novel alternative to perform dynamic deformation measurements. The theoretical background is presented, together with the experimental verification of the principle. Besides, the results of the first quasi-dynamic tests are shown and the perspectives of the technique discussed. This method is specially useful for the dynamic monitoring of civil structures, where large measurements bases are needed. Furthermore, the application of the amplitude modulation for distance measurements is demonstrated experimentally.     

Steps in the Classification of Cohen–Macaulay Modules Over Singularities of Type xt + y3

Let k be an algebraically closed field of characteristic 3 and i, j, t some positive integers such that 1 i < j < t, i + j t. Then there exist a finite number of nonisomorphic indecomposable maximal Cohen–Macaulay modules N over k[[x, y]] /(x^t + y³) such that N / y N is a direct sum of copies of k[[x]] /(xⁱ), k[[x]] /(x^j) and we describe them completely.     

On Continuous and Differential Hochschild Cohomology

We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.     

Discrete Structure of Some Schlesinger Systems on the Riemann Sphere

In the present work we investigate the group structure of the Schlesinger transformations for isomonodromic deformations of the Fuchsian differential equations. We perform these transformations as isomorphisms between the moduli spaces of the logarithmic sl(N)-connections with fixed eigenvalues of the residues at singular points. We give a geometrical interpretation of the Schlesinger transformations and perform our calculations using the techniques of the modifications of bundles with connections, or, the Hecke correspondences for the loop group SL(N)C(z).     

Theoretical Modeling of Mechanical Resistance and Stability and Related Characteristics of Polymeric Systems with Branching/Cross-Linking

A theoretical (thermodynamic) method for the estimation of mechanical characteristics of polymeric systems is proposed. This method uses the statistical polymer method for modeling of branched/cross-linked structures. The weak interaction between macromolecules is modeled in the approach of their mutual interpenetration. The proposed method is used for the estimation of mechanical resistance and stability of microporous polymeric materials. An engineer method for the evaluation of mechanical stability and resistance of polymeric materials is derived.     

Study on the generalized prandtl-reuss constitutive equation and the corotational rates of stress tensor

I.IntroductionTilepl'ogl'ess11as.toifcertainextent,beenmadeintheelastic-plasticconstitutivetheoryatII[litedefbrlllations.Coil'paredwitllotherconstitutiverelations,thegeneralizedPrandtlReuss(P-R)equatiollsareextensivelystudiedandwidelyapplied.IndevelopingthegeneralizedP-Requation.itisusuallyassumedthatthedeformationrate(thesymmetricpartorvelocitygradiellt)isdecolllposedintotheelasticpartandplasticpart.TheplasticLIcf\'l.llliltlollrittcobeystilenormalfi(,xvrilleasillthecaseofinfinitcsilllnld…     

Newton法及其各种变形收敛性的统一判定法则

１引言Ｂａｎａｃｈ空间中的算子方程是非常广泛的应用数学课题,而求方程数值解的主要方法是Ｎｅｗｔｏｎ法及其各种变形．自从Ｋａｎｔｏｒｏｖｉｃｈ关于Ｎｅｗｔｏｎ法收敛性的著名定理建立以来,有大量的文献在种种相仿的条件下研究各种变形收敛性的各种判定法则．在此,本文建立了统一的判定法则．首先,把Ｋａｎｔｏｒｏｖｉｃｈ算子类Ｋ（１）（ｘ０,ｙ）扩充为Ｋ（１）（ｘ０,ｙ,Ｃ）,并给出类Ｋ（１）（ｘ０,ｙ,Ｃ）的扩类Ｋｃｅｎｔ（１）（ｘ０,ｙ,Ｃ）和子类Ｋ（２）（ｘ０,ｙ,Ｃ）．对于这些算子类,确定了一个仅依…