Altruistic motives,uncertain lifetime and urban public pension replacement rates

This article employs an overlapping generations model with altruistic motives and uncertain lifetime to investigate China's urban public pension system. We examine the effects of the individual account benefit replacement rate, social pool benefit replacement rate, life expectancy and population growth rate on the capital-labour ratio, pension benefits, consumption and utility. We also find the optimal social pool benefit replacement rate. Raising the individual account benefit replacement rate only increases the individual account benefits. Raising the social pool benefit replacement rate increases the social pool benefits and retirement-period consumption, whereas decreases the capital-labour ratio, individual account benefits, working-period consumption and utility. The fall in the population growth rate increases the capital-labour ratio, social pool benefits, individual account benefits, working-period consumption and utility, whereas decreases the retirement-period consumption. The rise in the life expectancy decreases the six variables. The optimal social pool benefit replacement rate falls in case of either risen life expectancy or fallen population growth rate. It further falls under the joint case of risen life expectancy and fallen population growth rate. It will do more good than harm to raise the individual account benefit replacement rate, reduce the social pool benefit replacement rate and strictly implement the population policy.     

Hopf bifurcation for delay differential equation with application to machine tool chatter

In the machining process, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece, hence the relevant measures must be taken to predict and avoid this phenomenon of instability. In this paper, we propose a weakly nonlinear model with square and cubic terms in both structural stiffness and regenerative terms, to represent self-excited vibrations in machining. It is proved that Hopf bifurcation exists when bifurcation parameter equals a critical value, a formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are given by using the normal form method and center manifold theorem. Numerical simulations show excellent agreement with the theoretical results.     

Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay

In this paper, a modified Holling-Tanner predator-prey model with time delay is considered. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.     

Existence of periodic solutions for neutral type cellular neural networks with delays

In this paper, by using the theory of abstract continuation theorem of k contractive operator, we study the existence of periodic solutions for neutral type cellular neural networks with delays.     

Transition metal carbene chemistry 6: Kinetic studies of the reactions of hydroxide ion with (CO)5MoC(XCH2CH2OH)(C6H5) (X = O and S) and (CO)5WC(OCH2CH2OH)(C6H4-Z)

A kinetic study of the reaction of hydroxide ion with (CO)₅MoC(XCH₂CH₂OH)(C₆H₅) (X = O for Mo-OR, and X = S for Mo-SR), and (CO)₅WC(OCH₂CH₂OH)(C₆H₄-Z) (W-OR(Z)) is reported. The results are consistent with a pathway in basic solution that involves rapid deprotonation of the OH group followed by rate-limiting cyclization. The parameter k₁K^OH for the reaction of W-OR(Z) was determined as a function of the phenyl substituents. They were found to correlate well with the Hammett equation. The dependence of the reactivity on the metal atoms in the complexes M-OR (M = Cr, Mo and W) shows that the reactivity decreases slightly down the group of the Periodic Table, while for M-SR the reactivity increases slightly down the group. A plausible explanation of these results is offered based on electronegativity values of the metal atoms. The much higher ρ(k₁K^OH) value for W-OR(Z) over W-SR(Z) arises mainly due to the stabilization of the reactant carbene complex by the stronger π-donor effect of oxygen over sulfur.     

Existence and Uniqueness of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equations with Constant Delays

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form （x（t）＋Bx（t-δ））＂＋Cx＇（t）＋g（x（t-τ））=p（t）.     

Periodic Solutions of Second Order Differential Equations with Discontinuous Nonlinearities

We consider the periodic solutions of