On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations

We prove the Bianchi permutability (existence of superposition principle) of Bäcklund transformations for asymmetric quad-equations. Such equations and their Bäcklund transformations form 3D consistent systems of a priori different equations. We perform this proof by using 4D consistent systems of quad-equations, the structural insights through biquadratics patterns and the consideration of super-consistent eight-tuples of quad-equations on decorated cubes.     

Classification of hypersurfaces with constant Laguerre eigenvalues in R~n

Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.     

Mechanisms of martensitic transformations in boron nitride and conditions of their development

Abstract

The dependence of the pressure threshold of martensitic transformations on the disordering degree of starting structures is considered for graphite-like BN into diamond-like BN modifications transitions. The effect of loading conditions on transformation mechanisms of rhombohedral BN into zinc blende or wurtzite modifications is analyzed also. Analytical relations obtained allow to explain the experimental data and to predict a behavior of various graphite-like structures under different p, T conditions.     

Kinetic model and mechanism of Y3Al5O12 formation in hydrothermal and thermovaporous synthesis

Abstract

Kinetics and mechanism of fine-crystalline yttrium-aluminum garnet (YAG) formation under hydrothermal and thermovaporous treatment were investigated. It was synthesized from the stoichiomctric mixture of oxides in the temperature range 200-400°C at pressures of water vapor 4.0-26MPa. It was established that in quasiequilibrium with water vapor conditions the synthesis of YAG proceeds with formation of intermediate substance with Y(OH)₃ structure and amorphous aluminous component. The diffusion of this aluminous component into the Y(OH)₃ matrix resulted in the reorganization of oxygen sublattice accompanied with dehydroxylation. The kinetics of YAG formation is described by the equation of solid-phase transformation with the limiting stage of nucleation. Synthesized YAG contains 5-7% of water, which corresponds to a hydrogarnet structure. The study of luminescence properties of YAG doped with Nd³⁺ or Cr³⁺ ions has allowed to determine the positions of hydroxyl groups and oxygen vacancies in the structure.     

关于Bent序列构造的一点注记

本文讨论文献[4]给出的构造bent序列的方法,指出该方法可以通过对级联序列进行下标变换实现,从而大大增加了[4]中给出的由两个已知bent序列构造出的bent序列的个数。     

二阶Dirichlet问题的三维等参元逼近及其数值积分格式

本文研究了求解三维二阶Drichlet问题的四面体等参元逼近格式.基于对等参变换的细致估计,证明了格式的收敛性,并得到了H~1-误差的最优估计.为简化等参元的复杂计算,本文还构造了一种简单的数值积分格式,并证明了其收敛性.     

Computing the Topological Entropy for Piecewise Monotonic Maps on the Interval

A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm.     

Synthesis of 2,6-disubstituted pyrido[2,3-b][1,4]oxazines

A new preparative method for pyrido[2,3-b][1,4]oxazines from 6-substituted 3-nitro-2-pyridones is demonstrated. This method consists of two steps: O-alkylation and reductive cyclization. In the former step, the bulkiness of both starting nitropyridones and C2 reagents is found to be essential for avoiding N-alkylation, which undergoes O-alkylation efficiently. The subsequent reductive cyclization affords pyridoxazines with carbon substituents at both the 2- and the 6-positions that have not been available.     

Matrix analysis for associated consistency in cooperative game theory

Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. The Shapley value as well as the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix M^Sh and the associated transformation matrix M_λ, respectively. We develop a matrix approach for Hamiache’s axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality M^Sh = M^Sh · M_λ. The diagonalization procedure of M_λ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen’s axiomatization of a certain class of linear values. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory.