Isolated periodic wave trains in a generalized Burgers-Huxley equation

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with a degenerate equilibrium arising after the traveling transformation are investigated. By finding certain positive definite Lyapunov functions in the neighborhood of the degenerate singular points and the Hopf bifurcation points, the number of possible limit cycles in the corresponding planar systems is determined. The existence of isolated periodic wave trains in the equation is established, which is universal for any positive integer n in this model. Within the process, one interesting example is obtained, namely a series of limit cycles bifurcating from a semi-hyperbolic singular point with one zero eigenvalue and one non-zero eigenvalue for its Jacobi matrix

Externalities and compensation: Primeval games and solutions

The classical literature [Pigou, A.C., 1920. The Economics of Welfare. Macmillan, London; Coase, R.H., 1960. The problem of social cost. Journal of Law and Economics 3, 1-44; Arrow, K., 1970. The organization of economic activity: issues pertinent to the choice of market versus non-market allocation. In: Haveman, R.H., Margolis, J. (Eds.), Public Expenditures and Policy Analysis. Markham, Chicago, pp. 59-73] and the relatively recent studies [cf. Varian, H.R., 1994. A solution to the problem of externalities when agents are well-informed. American Economic Review 84, 1278-1293] associate the externality problem with efficiency. This paper focuses explicitly on the compensation problem in the context of externalities. To capture the features of inter-individual externalities, this paper constructs a new game-theoretic framework: primeval games. These games are used to design normative compensation rules for the underlying compensation problems: the marginalistic rule, the concession rule, and the primeval rule. Characterizations of the marginalistic rule and the concession rule are provided and specific properties of the primeval rule are studied. (C) 2007 Elsevier B.V. All rights reserved

On mixed variational relation problems

AbstractIn this paper we exploit the method of variational relations to establish existence of solutions to a general inclusion problem. The result is applied to variational relation problems in which several relations are simultaneously considered. Particular cases of variational inclusion and intersection of set-valued maps are also discussed

Theoretical Aspects of Charge Ordering in Molecular Conductors

Theoretical studies on charge ordering phenomena in quarter-filled molecular (organic) conductors are reviewed. Extended Hubbard models including not only the on-site but also the inter-site Coulomb repulsion are constructed in a straightforward way from the crystal structures, which serve for individual study on each material as well as for their systematic understandings. In general the inter-site Coulomb interaction stabilizes Wigner crystal-type charge ordered states, where the charge localizes in an arranged manner avoiding each other, and can drive the system insulating. The variety in the lattice structures, represented by anisotropic networks in not only the electron hopping but also in the inter-site Coulomb repulsion, brings about diverse problems in low-dimensional strongly correlated systems. Competitions and/or co-existences between the charge ordered state and other states are discussed, such as metal, superconductor, and the dimer-type Mott insulating state which is another typical insulating state in molecular conductors. Interplay with magnetism, e.g., antiferromagnetic state and spin gapped state for example due to the spin-Peierls transition, is considered as well. Distinct situations are pointed out: influences of the coupling to the lattice degree of freedom and effects of geometrical frustration which exists in many molecular crystals. Some related topics, such as charge order in transition metal oxides and its role in new molecular conductors, are briefly remarked.Comment: 21 pages, 19 figures, to be published in J. Phys. Soc. Jpn. special issue on "Organic Conductors"; figs. 4 and 11 replaced with smaller sized fil