On the determination of loads upon the ground support in underground mine workings

The piecewise-homogeneous model and the three-dimensional linearized theory of stability for small subcritical strains are used to study the surface instability of a regularly layered rock mass under biaxial loading. A plane problem is formulated. Basic characteristic equations are derived. A specific problem is solved as an example to demonstrate the selection of loads and the interaction of support elements with the wall rock __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 38–46, November 2005.     

Interaction of boundaries of opening and rigid inclusion under unsteady convective heat exchange on external surfaces of cylindrical shell

The stressed state of a thin cylindrical shallow shell containing a circular opening and a circular undeformable inclusion is investigated using a thermoelasticity equation in complex forces. The boundaries of the opening and inclusion are thermally insulated. The unsteady convective heat exchange between the environment and the shell surfaces is described by Newton's law. Numerical studies of thermal stresses are carried out for various times and reduced distances between the boundaries of the opening and inclusion. Simferopol University. Donetsk University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 61–66, April, 1999.     

Observables in 3d gravity and geodesic algebras

The algebra of quantum geodesics obtained by quantizing the coordinates of the Teichmller spaces is the quantumso _q(m) algebra by Nelson and Regge. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Poisson Algebras of Block-Upper-Triangular Bilinear Forms and Braid Group Action

In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on ${\mathbb{C}^{N}}$ C N with the property that for any ${n, m \in \mathbb{N}}$ n , m ∈ N such that n m = N, the restriction of the Poisson algebra to the space of bilinear forms with a block-upper-triangular matrix composed from blocks of size ${m \times m}$ m × m is Poisson. We classify all central elements and characterise the Lie algebroid structure compatible with the Poisson algebra. We integrate this algebroid obtaining the corresponding groupoid of morphisms of block-upper-triangular bilinear forms. The groupoid elements automatically preserve the Poisson algebra. We then obtain the braid group action on the Poisson algebra as elementary generators within the groupoid. We discuss the affinisation and quantisation of this Poisson algebra, showing that in the case m = 1 the quantum affine algebra is the twisted q-Yangian for ${\mathfrak{o}_{n}}$ o n and for m = 2 is the twisted q-Yangian for ${(\mathfrak{sp}_{2n})}$ ( sp 2 n ) . We describe the quantum braid group action in these two examples and conjecture the form of this action for any m > 2. Finally, we give an R-matrix interpretation of our results and discuss the relation with Poisson–Lie groups.     

Matrix FEM equation describing the large-strain deformation of an incompressible material

A tensor–matrix FEM equation describing large-strain deformation is derived. The equation is simplified and modified to describe the deformation of incompressible materials. The results of test analysis are presented     

Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions

The refined Timoshenko-type theory that takes into account the transverse shear strains is used to find an analytic solution for the stress state of transversely isotropic shallow spherical shell with two circular rigid inclusions. The case of a shell with closely spaced rigid inclusions of unequal radii under internal pressure is analyzed numerically. The stresses in the shell increase considerably with decrease in the distance between the inclusions and increase in the transverse shear parameter     

Heat transfer characteristics for disk fans

Multiple-disk fans belong to the class of friction machines; they can be designed in two variants: centrifugal disk fans and diametrical disk fans. Flow patterns in these two types of machines are different, and they possess different heat transfer characteristics. The paper presents results of experimental study for a centrifugal disk fan under atmospheric pressure with air taken as working gas. The radial temperature distribution for a disk was obtained at different rotation speed of the rotor and different heating of the disks. Heat transfer characteristics of a centrifugal disk fan and a diametrical disk fan were compared. The research results demonstrate a higher heat transfer efficiency for centrifugal design versus diametrical disk design.     

Boltzmann spectral distribution or “infrared catastrophe” in the resonance radiation of a gas

The purely thermal infrared emission spectra of a resonance medium (sodium vapor) are investigated experimentally. It is shown that the emission intensity in the 2–3 μm range at temperatures of 600–1200 K is several orders of magnitude higher than the intensity obtained from the standard theory of resonance radiation transfer. This phenomenon can be conventionally termed an “infrared catastrophe.” The form of the recorded spectra and the absolute intensity of the emission in both the infrared and visible regions of the spectrum are in agreement with the theory developed by Yu. L. Zemtsov and A. M. Starostin, Zh. éksp. Teor. Fiz. 103, 345 (1993) [JETP 76, 186 (1993)], in which the Boltzmann spectral distribution of the population of the resonance level is proportional to exp(−ħω/T). Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 807–811 (10 June 1997)     

R-Matrix Quantization of the Elliptic Ruijsenaars–Schneider Model

It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed by two dynamical r and ?r-matrices satisfying a closed system of equations. The corresponding quantum R and ?R-matrices are found as solutions to quantum analogs of these equations. We present the quantum L-operator algebra and show that the system of equations on R and ?R arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder elliptic R ^F -matrix with ?R playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic R matrix is established. As a byproduct of our construction, we find a new N-parameter elliptic solution to the classical Yang-Baxter equation. Received: 17 March 1997 / Accepted: 8 July 1997     

Stress state of a transversely isotropic spherical shell with a rigid circular inclusion

Analytical expressions are derived for the stresses near a rigid circular inclusion in a transversely isotropic shallow spherical shell under uniform pressure. The form of solution depends on the range of the transverse shear compliance parameter. The influence of the relative radius of a rigid inclusion and transverse shear compliance on stress concentration is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 67–73, December 2005.