Confluence of fuchsian second-order differential equations

Ordinary linear homogeneous second-order differential equations with polynomial coefficients including one in front of the second derivative are studied. Fundamental definitions for these equations: of s-rank of the singularity (different from Poincaré rank), of s-multisymbol of the equation, and of s-homotopic transformations are proposed. The generalization of Fuchs' theorem for confluent Fuchsian equations is proved. The tree structure of types of equations is shown, and the generalized confluence theorem is proved.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 233–247, August, 1995.     

The source of trimuon events in neutrino scattering

A comprehensive study indicates that equally likely sources for trimuon events neutrino scattering are (a) charged heavy lepton production (with decay to three muons) and (b) simultaneous production of a neutral lepton (with decay to two muons) and a heavy quark (with decay to one muon). The sequential decay of a heavy quark to two muons is less likely. An intriguing model yielding simultaneous M⁰ and b quark production is proposed.     

Stability analysis of impulsive control systems

This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system.     

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.     

Characteristics and origin of clusters in submicron WC-Co cermets

The microstructure of the WC phase in submicron WC-Co alloys has been investigated by transmission electron microscopy. The existence of clusters formed by several grains mainly related by Σ =1 and Σ=2 high-coincidence orientation relationships is shown. The features of these grain boundaries are studied using high-resolution electron microscopy. Two cases of Σ =1 orientation are investigated. In one case, the boundary contrast arises from the presence at the interface of a nanometric intermediate layer. In the other case, a grain boundary separating domains with different carbon positions is evidenced. Investigations of the starting WC powder indicate the existence of clusters already in particles and reveal the polygonal shape of WC grains before sintering. Some microstructure characteristics of the clusters suggest that the majority of clusters observed in the sintered material arise from the powder.     

Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Journal of Optimization Theory and Applications - This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to...     

Solid-phase assembly and in situ screening of protein tyrosine phosphatase inhibitors

A highly efficient solid-phase strategy for assembly of small molecule inhibitors against protein tyrosine phosphatase 1B (PTP1B) is described. The method is highlighted by its simplicity and product purity. A 70-member combinatorial library of analogues of a known PTP1B inhibitor has been synthesized, which upon direct in situ screening revealed a potent inhibitor ( Ki = 7.0 microM) against PTP1B.