A Faster Deterministic Maximum Flow Algorithm

Cheriyan and Hagerup developed a randomized algorithm to compute the maximum flow in a graph with n nodes and m edges in O(mn + n² log²n) expected time. The randomization is used to efficiently play a certain combinatorial game that arises during the computation. We give a version of their algorithm where a general version of their game arises. Then we give a strategy for the game that yields a deterministic algorithm for computing the maximum flow in a directed graph with n nodes and m edges that runs in time O(mn(log_{m/n log n}n)). Our algorithm gives an O(mn) deterministic algorithm for all m/n = Ω(n^ε) for any positive constant ε, and is currently the fastest deterministic algorithm for computing maximum flow as long as m/n = ω(log n).     

The elastoplastic stressed state of a half-plane under local nonstationary heating

We solve the thermoplastic problem for a semi-infinite plate under local nonstationary heating by heat sources. The physical equations are taken to be the relations of the nonisothermic theory of plastic flow associated with the Mises fluidity condition. The solution of the problem is constructed by the method of integral equations and the self-correcting method of sequential loading, where time is taken as the loading parameter. We carry out numerical computations of the stresses in the case of heating a plate with heat output by normal-circular heat sources. We study the problem of optimization of heating regimes in order to introduce favorable residual compressive stresses (from the point of view of hardness) in a given region of a half-plane. Two figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 29–34.     

Solution of a problem in the optimal estimation of the states of linear dynamical systems

A problem in the optimal estimation of a linear dynamical system is solved under the condition that the effects on the system of noise and observation error belong to a prescribed parallelepiped region.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 110–114, 1989.     

Synthesis and some reactions of indolo[2,1-c]-1,4-oxazinium perchlorates

Summary The reaction of acyl perchlorates with 1 phenacylskatole affords the previously unknown 1-R-lamethyl-3phenylindolo[2,1-c1-1,4oxazinium salts, which undergo recyclization by the action of ammonia to the corresponding indolo[2,1-alpyrazines. It is found that the salts (R = CHj, CZHS) also form dimers of their anhydro bases. The perchlorate (R = Ph) is converted to indolo[2,141-1, 2, S-triazepine by the action of hydrazine.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1041-1047, August, 1994.     

Identification of nonlinear elliptic equations

An optimization theoretic approach and algorithm for the estimation of state-dependent coefficients in nonlinear elliptic equation is presented. It is based on a splitting method combined with convex analysis techniques. Convergence of the algorithm is established and numerical examples are included.The research of K. Kunisch was supported in part by a grant from the Bundesministerium für Wissenschaft und Forschung, Austria.