一类混合单调算子的不动点定理

运用锥理论与迭代方法,讨论了在较弱条件下一类混合单调算子的不动点的存在唯一性,所得结果是某些已有结果的本质改进和推广.     

Stereoisomeric Tris-BINOL-Menthol Bulky Monophosphites: Synthesis,Characterisation and Application in Rhodium-Catalysed Hydroformylation

Four stereoisomeric monoether derivatives, based on axially chiral (R)- or (S)-BINOL bearing a chiral (+)- or (−)-neomenthyloxy group were synthesised and fully characterised by NMR spectroscopy and X-ray crystallography. The respective tris-monophosphites were thereof prepared and fully characterised. The coordination ability of the new bulky phosphites with Rh(CO)₂(acac), was attested by ³¹P NMR, which presented a doublet in the range of δ = 120 ppm, with a ¹J(¹⁰³Rh-³¹P) coupling constant of 290 Hz. The new tris-binaphthyl phosphite ligands were further characterised by DFT computational methods, which allowed us to calculate an electronic (CEP) parameter of 2083.2 cm⁻¹ and an extremely large cone angle of 345°, decreasing to 265° upon coordination with a metal atom. Furthermore, the monophosphites were applied as ligands in rhodium-catalysed hydroformylation of styrene, leading to complete conversions in 4 h, 100% chemoselectivity for aldehydes and up to 98% iso-regioselectivity. The Rh(I)/phosphite catalytic system was also highly active and selective in the hydroformylation of disubstituted olefins, including (E)-prop-1-en-1-ylbenzene and prop-1-en-2-ylbenzene.     

Quantum-classical correspondence for motion on a plane with deficit angle

A particle constrained to move on a cone and bound to its tip by harmonic oscillator and Coulomb-Kepler potentials is considered both in the classical as well as in the quantum formulations. The SU(2) coherent states are formally derived for the former model and used for showing some relations between closed classical orbits and quantum probability densities. Similar relations are shown for the Coulomb-Kepler problem. In both cases a perfect localization of the densities on the classical solutions is obtained even for low values of quantum numbers.     

Path-following interior point algorithms for the Cartesian <Emphasis Type="Italic">P</Emphasis><Subscript>*</Subscript>(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)     

Berezin Symbols and Schatten--von Neumann Classes

In terms of Berezin symbols, we give several criteria for operators to belong to the Schatten--von Neumann classes . In particular, for functions of model operators, we give a complete answer to a question posed by Nordgren and Rosenthal.     

A NEW FIXED POINT THEOREM FOR CONE MAPS AND ITS APPLICATIONS

1IntroductionLetEbearealBanachspace.AnonemptyconvexclosedsetPCEiscalledaconeinEifitsatisfiesthefollowingtwoconditionsf(i)xEP,A20impliesAxEP,(n)xEP,--xEPimpliesx=0.AconePiscalledsolidifitcontainsinteriorpoints,i.e.,P/gi.TheconePinEdefinesapartialorderingx5…     

Positive solutions for three-point boundary value problems with dependence on the first order derivative

A new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three-point boundary value problem

     

Semistrictly quasiconvex mappings and non-convex vector optimization

This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with P ^m being the underlying ordering cone, called semistrictly ( ^m\ –int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit ( ^m\ –int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.Acknowldegements.The author wishes to thank both referees for their careful reading of the paper, their comments, remarks, helped to improve the presentation of some results. One of the referee provided the references [5, 6] and indirectly [20].     

Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems

We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workload-intensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have long-term average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and non-negligible switching times between service modes are addressed. The analysis is extended to cover feed-forward networks of such processing systems/nodes. The approach taken unifies and generalizes prior studies, by developing a general trace-based modeling framework (sample-path approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is typically used in previous approaches. Probability can be superposed later to address finer performance questions (e.g., delay). The throughput maximization problem is seen to be primarily of structural nature. The developed methodology appears to have broader applicability to other queueing systems.     

Additive stable solutions on perfect cones of cooperative games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described. Received: December 2001/Revised: July 2002 RID="*" ID="*"  This note contains the new results, which were presented by the first author in an invited lecture at the XIV Italian Meeting on Game Theory and Applications in Ischia, July 2001. The lecture was dedicated to Irinel Dragan on the occasion of his seventieth birthday.