Search

The influence of roller strengthening on endurance limit under bending of the 25 mm and 50 mm diameter shafts made of steel 20 and 25 mm diameter shafts made of steel 40X with a pressurized hub has been examined. Its been stated that the endurance limit of roller strengthened shafts with a pressurized hub depends not only on a value of compressive residual stresses in their dangerous section but on the character of its distribution. The valuation of a surface hardening influence on the endurance limit of shafts by the surface residual stresses criterion and the average integral residual stresses criterion has been shown that the average integral residual stresses criterion calculated through the parts dangerous section surface layer thickness equal the critical depth of the non-propagating fatigue crack can be recommended for the hardened shafts with a pressurized hub endurance limit increase prediction. Its been shown that on a diameter of a shaft with a pressurized hub raising it is necessary to increase a thickness of a hardened surface layer with compressive residual stresses.

The article describes the evolution of the classical group analysis of ordinary differential equations. The article deals with the regular algorithms of searching for the higher symmetries. The factorization theorem is discussed. The authors analyze the first integrals. An example of the Lienard equation describes a method of alternative symmetries.

For a T × n matrix A = ‖ aij‖ in GF(2) we define a hypergraph GA with n vertices and T hyperedges et = {j: atj = 1}, t = 1,…, T. Denote at = (atn),t= 1,…, T. A set of row numbers {t1,…,tm} is called a critical set if the sum of vectors at1 + … + at m is the zero vector. In terms of hypergraph GA a critical set can be interpreted as a hypercycle. We can naturally definite the concept of independence for critical sets. Let s(A) be the maximal number of independent critical sets in A. The rank r(A) of the matrix A and s(A) are connected by the equality r(A) + s(A) = T. The total number of critical sets S(A) is equalt 2s(A) −1. Consider the folowing system of T random equations in GF(2): where i1(t.…,i(t), i = 1,…,T are indepndent identically distributed random variables which take values 1,…., n with equal probabilities. Denote Ar, n, T the matrix of this system. We prove that the number S(Ar,n,T) of critical sets in Ar, n, T or hypercycles in GAr,n,T has a threshold property. Let n, T→∞ and T/n→ α. Then for any fixed integer r ⩾ 3 there exists a constant α, such that MS(Ar,n,T)→0 if α α αr. © 1994 John Wiley & Sons, Inc.

1. Basic Ideas Regular and singular perturbations Asymptotic approximations Asymptotic and convergent series Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems 2. Singularly perturbed ordinary differential equations Initial value problem The critical case Boundary value problems Spike-type solutions and other contrast (dissipative) structures 3. Singularly perturbed partial differential equations The method of Vishik-Lyusternik Corner boundary functions The smoothing procedure Systems of equations in critical cases Periodic solutions Hyperbolic systems 4. Applied problems Mathematical model of combustion process in the case of autocatalytic reaction Heat conduction in thin Bodies Application of the boundary function method in the theory of semiconductor devices Relaxation waves in the FitzHugh-Nagumo system On some other applied problems Index.