Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Case study: problem formulation and solution for a real-world sports scheduling problem

This case study paper describes a problem faced every year by the Devon Cricket League in England. Every league match requires two officiating umpires. There are various preferences relating to the deployment of umpires that fall short of being definite constraints. The requirement was to produce a computer system that would allocate umpires in a satisfactory manner without the need for human interaction, since the users of the system will be unqualified amateurs. This necessitated the construction of a very complex objective function, using imprecise and ill-defined information. The biggest challenge was thus one of problem formulation; the solution technique was relatively straightforward. The system has been put into successful use and it is expected that its use will continue indefinitely. The work raises ethical issues regarding work done for customers who are inexperienced amateurs.     

Zero-cycles on self-product of modular curves

We use the elements in K-cohomology groups which are constructed by Flach and Mildenhall to obtain a finiteness result for the torsion part of the Chow group of a self-product of a modular curve.     

Three classes of smooth Banach submanifolds in B(E,F)

Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F) RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.     

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.     

Structural study and electrical properties of Zr-doped Nd<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript> pyrochlore compounds

Nd₂Sn₂O₇ pyrochlores with the substitution of Zr⁴⁺ were prepared by conventional ceramic double sintering technique. The single-phase formation was confirmed by X-ray diffraction and neutron diffraction techniques. Relative intensity calculations for X-ray diffraction analysis were performed for oxygen positional parametersx = 0.331 and 0.375, while Rietveld refinements were employed for neutron diffraction data. The neutron diffraction study revealed that there are only two anion sites with 48f and 8b positions. This indicates that the 8a site, i.e. O(3) sublattice, is completely vacant and the structure is a perfect cubic pyrochlore with space group Fd3m (O _h ⁷ ). From the conductivity measurements, it is observed that the electronic conductivity dominates from room temperature up to about 525 K and forT > 525 K, the oxygen ion conduction dominates the charge transport in these compositions. Complex impedance spectroscopy indicates the existence of grain and grain boundary as two separate elements.     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes