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.     

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.     

Ekeland’s principle for vector equilibrium problems

In this paper, the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vector-valued function is considered, and some of its properties are presented. Via the vector Ekeland’s principle, existence results for vector equilibria are proved in both compact and noncompact domains.     

病毒感染群体动力学模型分析

本文构建并讨论了一类病毒感染的群体动力学模型,得到了模型存在轨道稳定周 期解的充分条件,较好地解释了在病毒持续感染者体内观察到的病毒载量波动现象.     

Dynamic Model of R&D,Spillovers, and Efficiency of Bertrand and Cournot Equilibria

Using an infinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes, and spillovers are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.     

Symmetries of flat rank two distributions and sub-Riemannian structures

Flat sub-Riemannian structures are local approximations -- nilpotentizations -- of sub-Riemannian structures at regular points. Lie algebras of symmetries of flat maximal growth distributions and sub-Riemannian structures of rank two are computed in dimensions 3, 4, and 5.

     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

The effect of construction material, contents and room geometry on the sound field in dwellings at low frequencies

An experimentally validated finite element method is used to model the sound level in rooms at low frequencies. It is demonstrated that the dimensions of rectangular rooms strongly influence the sound pressure level difference. Additional factors were investigated which are not normally considered in the frequency range where diffuse sound field conditions can be assumed. Three effects were investigated: room damping due to wall vibrations, furniture, the effect of small deviations from simple rectangular shapes. It is confirmed by field measurements that the vibrations of masonry walls and floors introduce less damping than surfaces of lightweight construction. Assigning to the FE model a damping equivalent to a surface absorption of 0.02 reproduces the effect of walls of heavyweight construction. Damping equivalent to a surface absorption of 0.15 reproduces the effects of plastered timber-frame walls, floors and ceilings. The work was briefly extended to a room pair built with heavyweight and lightweight material of construction. The modification of the shape of the room frequency response highlights well the effect of material of construction. In-situ and laboratory measurements show that furniture has little effect on steady-state room response below 100 Hz. Modelling a wall recess smaller than 0.5 m improved the agreement between prediction and measurements but the assumption of a simple rectangular room remains appropriate.     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.