Implementation of the τ-value

We present a finite noncooperative game in extensive form whose subgame perfect Nash equilibria implement the τ-value.     

New Findings on the Bank–Sauer Approach in Oscillation Theory

In 1988, S. Bank showed that if {z _n } is a sparse sequence in the complex plane, with convergence exponent zero, then there exists a transcendental entire A(z) of order zero such that f″+A(z)f=0 possesses a solution having {z _n } as its zeros. Further, Bank constructed an example of a zero sequence {z _n } violating the sparseness condition, in which case the corresponding coefficient A(z) is of infinite order. In 1997, A. Sauer introduced a condition for the density of the points in the zero sequence {z _n } of finite convergence exponent such that the corresponding coefficient A(z) is of finite order.     

Regular Poles and β-Numbers in the Theory of Holomorphic Semigroups

We introduce the notion of regular (boundary) poles for infinitesimal generators of semigroups of holomorphic self-maps of the unit disc. We characterize such regular poles in terms of β-points (i.e., pre-images of values with positive Carleson–Makarov β-numbers) of the associated semigroup and of the associated Königs intertwining function. We also define a natural duality operation in the cone of infinitesimal generators and show that the regular poles of an infinitesimal generator correspond to the regular null poles of the dual generator. Finally we apply such a construction to study radial multi-slits and give an example of a nonisolated radial slit whose tip does not have not a positive Carleson–Makarov β-number.     

An Existence Theorem for an Analytic First Order PDE in the Framework of Colombeau’s Theory

 Abstract. We study the existence of a holomorphic generalized solution u of the PDE

Perturbation Theory for Dual Cosine Function（Ⅱ）—Time－dependent Perturbation in the Sun－reflexive Case

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Surgery and the Spinorial τ-Invariant

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ _n }, where Λ _n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ _n . Also, below Λ _n the values of τ cannot accumulate from above when varied over all manifolds of dimension n.     

A General Theorem of the Alternative in the Context of Set-Valued Function

1.IntroductionTheclassicalworkOiltheoremsofthealternativeforsingle-valuedfunctionbyG..d..II]andMotzkin[2]wereextendbymanyresearchersinvariousways(suchasJeyakumar['l'],Lily],andTamminen[6]),whereconditionsofconvexityaremoreorlessrelaxed.Met's..rk[:]givesemphasistotheoremsofthealternativeinthesettingofset-valuedfunctionwhereconditionofconvexityissettobecone-convex.Thispaperaimsatprovidinganunifiedextensionoftheabove-mentionedtheorems,andgivesoutageneraltheoremofthealternativeinthecontextofset…     

An axiomatization of the τ-value

The τ-value is characterized by three axioms. It is shown that the τ-value is the unique solution concept which is efficient and has the minimal right property and the restricted proportionality property. The minimal right property is weaker than the additivity property, which plays a role in the axiomatic characterization of the Shapley value: together with individual rationality and efficiency additivity implies the minimal right property. The restricted proportionality property says that for games with minimal right vector zero, the dividend given to the players is proportional to the marginal contribution of the players to the grand coalition.     

On a CR Transversality Problem Through the Approach of the Chern–Moser Theory

In this paper, we give a geometric condition for a CR map, which sends a CR non-umbilical Levi non-degenerate hypersurface in ? ⁿ⁺¹ into the hyperquadric in ? ⁿ⁺² with the same signature, to be CR transversal.     

Perturbation of the Laplacian by the Coulomb potential and a point interaction in L p (ℝ)3

Perturbations of -+/|x| (with >0) by a point interaction centered at zero are defined in L ^p(³). This is done for 3/20 (³{0}), such that the extension is the negative generator of an analytic semigroup on L ^p(³).     

Decay and stability of solutions to the Fokker–Planck–Boltzmann equation in

In this paper, we use the method of constructing the compensating function introduced by Kawashima and the standard energy method to study the global existence of solutions to the Fokker–Planck–Boltzmann equation in the whole space. The time decay and uniform stability of solutions to the global Maxwellian are also obtained.     

Abstract Theory of Pointwise Decay with Applications to Wave and Schrödinger Equations

We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.     

Radioactive Decay and the Structure of e (∞) Quantum Spacetime

Some theoretical arguments and some experimental evidence are given for the hypothesis that the form of the spectra of the Beta radioactive decay, as well as the micro background radiation and related phenomena, can be traced back to the geometrical–topological structure of spacetime itself. It is argued that this structure obeys the same Aufbau principle upon which Plancks black body radiation law is based. The main conclusion here is that the universe is four-dimensional but every point in this space, however small, is again also four-dimensional and that this accounts for the form of classical and quantum behaviour observed.     

Time Decay Rates of the isotropic Non-Newtonian Flows in R^n

This paper is concerned with time decay rates for weak solutions to a class system of isotropicincompressible non-Newtonian fluid motion in R~n.With the use of the spectral decomposition methods ofStokes operator,the optimal decay estimates of weak solutions in L~2 norm are derived under the differentconditions on the initial velocity.Moreover,the error estimates of the difference between non-Newtonian flowand Navier-Stokes flow are also investigated.