Studies on dissociation energies of diatomic molecules using vibrational spectroscopic constants

New analytical expression and numerical approach are suggested to calculate dissociation energies De of diatomic molecular states using an extreme value method (EVM). Studies on some electronic states of OH, BH, N2, Br2, ClF and CO molecules show that the accuracy of the EVM dissociation energies depends on the number of correct vibrational constants used in the calculations. The convergence qualities of De are suggested to be an alternative physical criterion to measure the qualities of the various sets of vibrational constants from different literature for the same diatomic state.     

Detecting Incompressibility of Boundary in 3-Manifolds

A construction is presented which can be utilized to prove incompressibility of boundary in a 3-manifold W. One constructs a new 3-manifold DW by doubling W along a subsurface in its boundary. If DW is hyperbolic, and if W has compressible boundary, then DW must have a longitude of 'length' less than 4. This can be applied to show that an arc that is a candidate for an unknotting tunnel in a 3-manifold cannot be an unknotting tunnel. It can also be used to show that a 'tubed surface' is incompressible. For knot and link complements in S ³, and an unknotting tunnel, DW is almost always hyperbolic. Empirically, this construction appears to provide a surprisingly effective procedure for demonstrating that specific arcs are not unknotting tunnels.     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…     

The blow-up rates for systems of heat equations with nonlinear boundary conditions

This paper deals with the blow-up rate estimates of positive solutions for systems of heat equations with nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained.     

SOME NEW RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF MIXED TYPE INTEGRODIFFERENTIAL EQUATION

In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u" = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.     

Consistent values and the core in continuum market games with two types of players

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility.? In this paper, the consistent value will be characterized for market games with a continuum of players of two types. We will show that for such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between the two concepts. Received: October 1998 RID="*" ID="*"  This thesis was completed under the supervision of Professor Sergiu Hart, The Center for Rationality and Interactive Decision Theory, Department of Mathematics, Department of Economics, The Hebrew University of Jerusalem. I would like to thank Professor Hart for introducing me to this area of research, for his help and guidance, and, especially, for all his patience.? I would also like to thank Michael Borns for improving the style, and an anonymous referee for helpful comments.     

Shapley value for constant-sum games

It is proved that Youngs [4] axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games with nonzero worth of grand coalition and on the entire class of constant-sum games as well.The research was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047-008-010.I am thankful to Theo Driessen, Natalia Naumova and Elena Yanovskaya for interesting discussions and comments. The useful remarks of two anonymous referees are also appreciated.     

On Vector Quasi-Equilibrium Problems with Set-Valued Maps

In this paper, we introduce a new class of vector quasi-equilibrium problems with set-valued maps. Almost all the vector equilibrium models of the Blum-Oettli type in the literature are special cases of our new class of equilibrium problems under consideration. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the -diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for such vector equilibrium problems.     

A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries

We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.