Lifetime measurement of the ((11/2)−) isomer in 125Cs

A new rotational band has been observed in ¹⁶⁷Lu by ¹⁵²Sm (¹⁹F,4n)reaction at the HI-13 tandem accelerator of CIAE in Beijing. The high spin transition energies of the new band are almost identical to the triaxial superdeformed bands recently discovered in ¹⁶³Lu and ¹⁶⁵Lu. This new band is predicted as a triaxial superdeformed band by total routhian surface calculations. Received: 6 October 1997     

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

Cone complementarity problems with finite solution sets

We introduce the notion of a complementary cone and a nondegenerate linear transformation and characterize the finiteness of the solution set of a linear complementarity problem over a closed convex cone in a finite dimensional real inner product space. In addition to the above, other geometrical properties of complementary cones have been explored.     

Recoil distance half-life measurements of the excited states in 145Sm

A recoil distance method was used to measure half-lives of the excited states of ₁₄₅Sm. The reaction used was ₁₃₉La(₁₀B, 4n)₁₄₅Sm. A plunger system was used. Half-lives were determined for two excited states for the first time. The yrast 27/2₊ state was found to have a half-life of 1.1 ± 0.2 ns corresponding to the retardation of 3.1 × 10₋₄ comparing with the single particle estimate of M1. The excitation energy of this state was well reproduced by the shell model calculation having a mixed configuration of [π{h^11/2(g^7/2)₋₂ (d^5/2)₋₁}¹⁰⁻, νf^7/2] + [π{h^11/2(g^7/2)₋₁}⁹⁻,νh^9/2]. Another retarded E1 transition was also found in a decay of a 21/2₊ state. Its retardation was 1.6 × 10₋₄ comparing with the single particle value. Received: 9 September 1997 / Revised version: 12 June 1998     

Theoretical study of anion carriers based on trifluoroacetophenone

Model calculations on anion carrier ligands related to trifluoroacetophenone were carried out using the semiempirical AM 1 method in order to investigate the factors involved in such anion-ligand complexation. The reaction of halogen derivatives of acetophenone with various nucleophiles such as water, carbonic acid, and bicarbonate anion was studied. By this means, the effect of various structural changes, such as variation of the ring substituents and variation of the degree and type of halogen atom substitution, could be determined. It is shown that in terms of relative stability, fluorine derivatives are preferable to chlorine derivatives for the binding of water and carbonic acid. Monosubstitution of a methoxy group in the ortho position of the trifluoroacetophenone ring also brought about stability in the case of the hydration reaction. An electron-withdrawing ester group in the para position on the trifluoroacetophenone ring brings about stabilization also.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.