Approximate iterations in Bregman-function-based proximal algorithms

This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. The problem being solved is modeled as a general maximal monotone operator, and need not reduce to minimization of a function. The accuracy conditions on the iterates resemble those required for the classical “linear” proximal point algorithm, but are slightly stronger; they should be easier to verify or enforce in practice than conditions given in earlier analyses of approximate generalized proximal methods. Subjects to these practically enforceable accuracy restrictions, convergence is obtained under the same conditions currently established for exact Bregman-function-based proximal methods.     

Strong Convergence Theorems for Perturbed Maximal Monotone Operators in Banach Spaces

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On the complexity of monotone dualization and generating minimal hypergraph transversals

In 1994 Fredman and Khachiyan established the remarkable result that the duality of a pair of monotone Boolean functions, in disjunctive normal forms, can be tested in quasi-polynomial time, thus putting the problem, most likely, somewhere between polynomiality and coNP-completeness. We strengthen this result by showing that the duality testing problem can in fact be solved in polylogarithmic time using a quasi-polynomial number of processors (in the PRAM model). While our decomposition technique can be thought of as a generalization of that of Fredman and Khachiyan, it yields stronger bounds on the sequential complexity of the problem in the case when the sizes of f and g are significantly different, and also allows for generating all minimal transversals of a given hypergraph using only polynomial space.     

Quasi-steady state in the Michaelis–Menten system

We discuss the differential equations derived from the Michaelis–Menten model of an enzyme-catalyzed reaction, with no a priori conditions on parameters or initial concentrations. Using an elementary approach, we derive and investigate inequalities and conditions for the validity of the quasi-stationary approximation, confirming results by Segel and Slemrod, and determine new estimates for the pre-steady state period.     

一阶混合型脉冲积分-微分方程周期边值问题极解研究

通过得到的一个比较结果，并利用单调迭加技巧，给出了一阶混合型脉冲积分-微分方程周期边值问题最大以及最小解的存在性证明。     

Advanced differential equations with nonlinear boundary conditions

We investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions. Sufficient conditions when the problem has extremal solutions or a unique solution are formulated. Linear advanced differential inequalities are also discussed.     

On a characterization of monotone likelihood ratio experiments

Summary Pfanzagl (1962,Zeit. Wahrscheinlichkeitsth.,1, 109–115) showed that a dominated family of probability measures has monotone likelihood ratios with respect to some real valued statistic if there exists a set of tests which has certain nice properties. A similar characterization was given by Dettweiler (1978,Metrika,25, 247–254), who did not assume domination. However, Pfanzagl's result is not a special case of the one proved by Dettweiler. We present a theorem which comprises the results of both authors. Our proof shows that not all conditions introduced by them are needed. Furthermore, we investigate the question concerning the generality we get if we do not assume domination.     

Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem