Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

剖析博彩弹子机的赢钱原理

介绍了博彩弹子机 ,运用数学建模法剖析了它的赢钱原理 ,强调了一般博彩业主永远是赢家的道理     

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.     

Determination of the arc-root position in a DC plasma torch

The behavior of an arc operated in the nontransferred mode with a conical-shaped cathode and a nozzle-shaped anode is studied by applying general tyro-dimensional conservation equations and auxiliary relations for the simulation of arc channel flows. The position of the arc-root attachment at the anode surface is determined by using Steenbeck's minimum principle, which postulates a minimum arc voltage for a given current and certain given boundary conditions. The overall effects of the anode-arc root on the plasma flow are, studied by comparing the results with those of the transferred mode of operation. Specific arc-channel diameters are chosen in the simulation in order to verify flit, numerical model through comparisons with experimental results. The results show that Steenbeck's minimum principle is useful for determining the position of the arc-root attachment at the anode surface. Application of this method for control of the arc-anode attachment may be valuable in the design and operation of plasma spray torches to avoid jet instabilities.     

A new insight into the understanding of the collapsed form of poly(N-isopropylacrylamide) molecules

Possible collapsed forms of poly(N-isopropylacrylamide) molecules are reviewed on the basis of first principle calculations. Various configurations and associated conformations are detailed. The calculated optimized structures exhibit different possibilities of creating networks of intra-molecular bonds of the hydrogen type. We show that the most remarkable one is able to form a local, self-saturated and well ordered helix. We also indicate in which direction the synthesis of the molecule should be oriented to improve its global behavior in term of hydrophobic/hydrophilic behavior.     

Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

Chemical reactivity of hypervalent silicon compounds: The local hard and soft acids and bases principle viewpoint

The silicon atom may increase its coordination number to values greater than four, to form pentacoordinated compounds. It has been observed experimentally that, in general, pentacoordinated compounds show greater reactivity than tetracoordinated compounds. In this work, density functional theory is used to calculate the global softness and the condensed softness of the silicon atom for SiH _n F_4−n and SiH _n F _5−n ¹⁻ . The values obtained show that the global and condensed softness are greater in the pentacoordinated compounds than in the tetracoordinated compounds, a result that explains the enhanced reactivity. If the results are analysed through a local version of the hard and soft acids and bases principle, it is possible to suggest that in nucleophilic substitution reactions, soft nucleophiles preferably react with SiH _n F _5−n ¹⁻ , and hard nucleophiles with SiH _n F_4−n .     

Normality of the maximum principle for nonconvex constrained Bolza problems

We consider a Bolza optimal control problem with state constraints. It is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle. In general, the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about optimal controls. In the recent literature some sufficient conditions were proposed to guarantee that at least one maximum principle is nondegenerate, cf. [A.V. Arutyanov, S.M. Aseev, Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints, SIAM J. Control Optim. 35 (1997) 930–952; F. Rampazzo, R.B. Vinter, A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control, IMA 16 (4) (1999) 335–351; F. Rampazzo, R.B. Vinter, Degenerate optimal control problems with state constraints, SIAM J. Control Optim. 39 (4) (2000) 989–1007]. Our aim is to show that actually conditions of a similar nature guarantee normality of every nondegenerate maximum principle. In particular we allow the initial condition to be fixed and the state constraints to be nonsmooth. To prove normality we use J. Yorke type linearization of control systems and show the existence of a solution to a linearized control system satisfying new state constraints defined, in turn, by linearization of the original set of constraints along an extremal trajectory.