Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate     

Monoesterification of styrene–maleic anhydride copolymers with alcohols in ethyl benzene: Catalysis and kinetics

A kinetic investigation on the monoesterification reaction of the maleic anhydride residue (MA) in styrene-maleic anhydride copolymers with aliphatic alcohols was carried out in ethyl benzene solution. By comparison to classic catalysts such as tributylamine (TBA) and pyridine, 4-dimethylaminopyridine (4DMAP) is by far the most effective catalyst for this reaction. While both general base and nucleophilic mechanisms contribute to the reaction catalyzed by TBA or pyridine, a nucleophilic mechanism prevails with 4DMAP. This reaction is reversible, and its chemical equilibrium constant decreases significantly with increasing temperature. Both kinetic and thermodynamic results showed that in the presence of 4DMAP, the forward and reverse reactions are second and first order, respectively. The existence of side reactions, reactivity of two styrene-maleic anhydride copolymers of different MA contents as well as two aliphatic alcohols of different lengths are also addressed. © 1993 John Wiley & Sons, Inc.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

多重积分Nash平衡点的Lipschitz估计

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．     

Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches

The conjecture according to which the mean energy of an equilibrium system in quantum theory exceeds the mean energy of the corresponding classical system is considered. It is rigorously proved that the conjecture holds for the potential well. The estimates for the mean energy of the potential well at high and low temperatures are of special interest.     

随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

Reductions of interval noncooperative games

Noncooperative games of a finite number of persons with interval-valued payoff functions are considered. The concept of an equilibrium situation is introduced. A reduction of such games to deterministic noncooperative games is proposed. Properties of the reduced games are discussed. Interval antagonistic and bimatrix games are examined, and illustrative examples are considered.     

Trovacenchemie. 13 [1] Weg und Irrweg zu Di([5]trovacenyl)keton

Trovacene Chemistry. 13 [1] On Being Lead and Mislead in the Synthesis of Di([5]trovacenyl)ketone Di([5]trovacenyl)ketone ( 3¨ ) has been prepared from lithio‐[5]trovacene and dimethylcarbamoyl chloride and studied by X‐ray diffraction, cyclic voltammetry, magnetic susceptometry and EPR spectroscopy. Slight variation of the synthetic protocol affords an unusual trinuclear complex 5 ? that is also fully characterized. Spin‐spin exchange interaction is smaller in 3¨ than in 1,1‐di([5]trovacenylethene ( 2¨ ), which differs from 3¨ by a replacement of O for CH₂. The novel trinuclear complex 5 ? , however, displays exchange coupling very similar to that observed in 1‐methoxy‐2,5,6‐tri([5]trovacenyl)benzene ( 7 ? ). In both cases, an unsymmetrical triangular arrangement of S = 1/2 centers is encountered. These findings are discussed in terms of the nature of the respective spacers.     

Mechanistic Insights into the Reversible Formation of Iodosylarene–Iron Porphyrin Complexes in the Reactions of Oxoiron(IV) Porphyrin π‐Cation Radicals and Iodoarenes: Equilibrium,Epoxidizing Intermediate,and Oxygen Exchange

We have shown previously that iodosylbenzene–iron(III ) porphyrin intermediates ( 2 ) are generated in the reactions of oxoiron(IV ) porphyrin π‐cation radicals ( 1 ) and iodobenzene (PhI), that 1 and 2 are at equilibrium in the presence of PhI, and that the epoxidation of olefins by 2 affords high yields of epoxide products. In the present work, we report detailed mechanistic studies on the nature of the equilibrium between 1 and 2 in the presence of iodoarenes (ArI), the determination of reactive species responsible for olefin epoxidation when two intermediates (i.e., 1 and 2 ) are present in a reaction solution, and the fast oxygen exchange between 1 and H₂¹⁸O in the presence of ArI. In the first part, we have provided strong evidence that 1 and 2 are indeed at equilibrium and that the equilibrium is controlled by factors such as the electronic nature of iron porphyrins, the electron richness of ArI, and the concentration of ArI. Secondly, we have demonstrated that 1 is the sole active oxidant in olefin epoxidation when 1 and 2 are present concurrently in a reaction solution. Finally, we have shown that the presence of ArI in a reaction solution containing 1 and H₂¹⁸O facilitates the oxygen exchange between the oxo group of 1 and H₂¹⁸O and that the oxygen exchange is markedly influenced by factors such as ArI incubation time, the amounts of ArI and H₂¹⁸O used, and the electronic nature of ArI. The latter results are rationalized by the formation of an undetectable amount of 2 from the reaction of 1 and ArI through equilibrium that leads to a fast oxygen exchange between 2 and H₂¹⁸O.