Determination of Temperature due to Slip between the Wheel and the Rail Taking into Account Convective Cooling of Free Surfaces

A computational algorithm for determining temperature due to slip between the train wheel and the rail is proposed. The algorithm uses Ling's solution of the mixed twodimensional quasisteady'state thermalconductivity problem for a half'space heated locally by a fast moving distributed heat flow. This solution is calculated using the method of piecewise linear approximation by finite functions. An analytical solution of the problem is obtained for the particular case of uniform distribution of the frictional heat flow rate. The effect of different forms of heat flow rate distribution and the Biot number on the rail temperature field is studied.     

Potentiometric determination of maleic anhydride in the presence of cis-3,6-endomethylene-1,2,3,6-tetrahydrophthalic (endic) anhydride

A procedure is developed for the determination of maleic anhydride in the presence of endic anhydride by potentiometric titration in aqueous-organic solutions. It is found that separate titration of a hydrolyzed mixture of anhydrides is most efficient in the system acetonitrile-water (3 : 2).     

An Approach to Determining the Variation of a Functional with Singularities

Computational Mathematics and Mathematical Physics - A new method is proposed for computing the first variation of a functional in the case when the considered domain or its boundary contains...     

Stress-induced martensitic transformations in [001] crystals of titanium nickelide and its relation to mechanical twinning in the <Emphasis Type="Italic">В</Emphasis>2-phase

Methods of transmission electron microscopy were used to investigate the mechanisms of plastic deformation of TiNi(Fe, Mo) [001] crystals on compression in the interval of stress-induced martensitic transformations. It has been revealed that the formation of {113} and {114} twins of the В2-phase by the В19′→В2 reverse martensitic transformation over another path is, alongside with mechanical (100) twinning of В19′ martensite, an important deformation mechanism in this interval.     

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton’s method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton’s method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.     

Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy

The nonuniform covering method is applied to multicriteria optimization problems. The ?-Pareto set is defined, and its properties are examined. An algorithm for constructing an ?-Pareto set with guaranteed accuracy ? is described. The efficiency of implementing this approach is discussed, and numerical results are presented.