Relation between fracture and deformation in oriented polymers

The development of submicroscopic cracking under load has been studied (by a small-angle X-ray scattering technique) in such oriented polymers as Kapron (Nylon 6), polypropylene, etc. The increase in crack density (N_cr) is compared with the variation of the tensile strain (). The observed correlation between and N_cr indicates that the processes of fracture and deformation of oriented polymers are closely connected. The presence of a similar correlation in loading-relaxation-repeat loading experiments establishes fracture as the primary process.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 43–47, January–February, 1970.     

Relation between the temperature and deformation dependences of the modulus of elasticity

An analysis of the temperature and deformation dependences of the modulus of elasticity and the rate of stress relaxation has revealed the existence of a strain-temperature analogy. It is suggested that the physical significance of this analogy is associated with the change of volume. The experimental expression of the temperature and deformation dependences of the modulus in terms of change of volume leads to coincidence of the curves in the region above T_g, which confirms the correctness of the conclusion that the temperature-strain equivalence may be associated with the volume changes in that region.     

Relation between the elastic deformation of oriented specimens of crystalline polymers and the "large-period" deformation

Illustrative calculations for a specific model of the supermolecular organization of an oriented crystalline polymer are presented as an explanation of the fact that the "large-period" deformation may exceed the macrodeformation of the specimen.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 579–583, July–August, 1973.     

Relation between local strains theory and deformation theory in the problem of stability of inelastic shells

In accordance with the theory of local plastic strains and the deformation theory of plasticity the coefficients of the compliance matrices are determined for the problem of stability of inelastic shells in the uniaxial precritical stress state. A comparison of the compliance matrices shows that for integration over a complete sphere the results obtained using the local strains theory and deformation theory are very close.Mekhanika Polimerov, Vol. 1, No. 6, pp. 54–60, 1965     

Relation between metric spaces and Finsler spaces

In a connected Finsler space Fn=(M,F) every ordered pair of points p,q∈M determines a distance ?F(p,q) as the infimum of the arc length of curves joining p to q. (M,?F) is a metric space if Fn is absolutely homogeneous, and it is quasi-metric space (i.e. the symmetry: ?F(p,q)=?F(q,p) fails) if Fn is positively homogeneous only. It is known the Busemann-Mayer relation , for any differentiable curve p(t) in an Fn. This establishes a 1:1 relation between Finsler spaces Fn=(M,F) and (quasi-) metric spaces (M,?F).We show that a distance function ?(p,q) (with the differentiability property of ?F) needs not to be a ?F. This means that the family {(M,?)} is wider than {(M,?F)}. We give a necessary and sufficient condition in two versions for a ? to be a ?F, i.e. for a (quasi-) metric space (M,?) to be equivalent (with respect to the distance) to a Finsler space (M,F).     

容量和Hausdorff测度的关系

Let X be a locally compact seperable metric space of diameter △≤∞. Demote by r_PQ the distance between two arbitrary points P∈X and Q∈X. Let h(r) be a possitive non-increasing positive function in the interval (0,△) with.     

Relation between decomposition of comodules and coalgebras

LetM be aC-comodule. It is clear thatM andC can both be decomposed into a direct sum of the indecomposable subcoalgebras ofC and subcomodules ofM. The relation between the two decompositions is given.     

图的支配划分与最小团的关系

本文用色函数讨论了图Ｇ的团图Ｋ（Ｇ）为奇圈时ｃ（Ｇ）≤ｄ（Ｇ）成立的一个充分条件和Ｋ（Ｇ）为简单连通图时ｃ（Ｇ）≤ｄ（Ｇ）成立的一个充分条件．     

On isomorphisms between deformation rings and Hecke rings

Inventiones mathematicae -     

Relation between branches of chord and distance densities

Institute of Mathematics and Information, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys) Vol. 31, No. 4, pp. 594–597, October–December, 1991.     

A Relation between Multiprocessor Scheduling and Linear Programming

The general non preemptive multiprocessor scheduling problem (NPMS) is NP-Complete, while in many specific cases, the same problem is Time-polynomial. A first connection between PMS and linear programming was established by Yannanakis, Sauer and Stone, who associated to any PMS instance some specific linear program. The main result inside this paper consists in a characterization of the partially ordered structures which allow the optimal values of any associated PMS instance to be equal to the optimal values of the corresponding linear programs.     

Relation between PVM schemes and simple Riemann solvers

Approximate Riemann solvers (ARS) and polynomial viscosity matrix (PVM) methods constitute two general frameworks to derive numerical schemes for hyperbolic systems of Partial Differential Equations (PDE's). In this work, the relation between these two frameworks is analyzed: we show that every PVM method can be interpreted in terms of an approximate Riemann solver provided that it is based on a polynomial that interpolates the absolute value function at some points. Furthermore, the converse is true provided that the ARS satisfies a technical property to be specified. Besides its theoretical interest, this relation provides a useful tool to investigate the properties of some well‐known numerical methods that are particular cases of PVM methods, as the analysis of some properties is easier for ARS methods. We illustrate this usefulness by analyzing the positivity‐preservation property of some well‐known numerical methods for the shallow water system. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1315–1341, 2014     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

关于矩阵和与矩阵积的特征值的关系

本文给出了两个矩阵积的迹与其特征值之间的若干等价关系,并推广到两个矩阵和的情形.     

Relation between o-equivalence and EA-equivalence for Niho bent functions

Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence.     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

二次曲线局部与整体的关系

用射影几何知识讨论欧氏平面上二次曲线局部与整体的关系,讨论如何通过二次曲线的一些已知点与切线判断它的类型,作出它的对称轴,渐近线,焦点与准线.