The nonlinear boundary value problem for a class of integro-differential system

In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.     

非整数年龄假设中的二次多项式死亡力研究

由于生命表只提供了整数年龄点上的生存函数值和死亡率值,所以在人口统计和寿险精算中计算非整数年龄处的生存函数值时,需要进行非整数年龄假设。传统的非整数年龄假设有死亡力函数和密度函数在整数年龄处有较大跳跃的缺点,而针对它们连续性的改进甚少,且没有针对死亡力函数二次多项式形式的研究。本文提出了死亡力的二次多项式形式,通过积分约束下的分段抛物插值方法给出了二次多项式死亡力形式对应的非整数年龄假设,并与前人已经提出的各种假设进行了比较,结果表明二次死亡力假设可以更精确地描述生存模型,从而使人口统计和保费、年金的计算更加精确。     

The second order approximation theory of three dimensional elastic plates and its boundary conditions without using kirchhoff-love assumptions

The first order approximation theory of three dimensional elastic plates and its boundary conditions presented in the previous paper^[1] establishes six differential equations for the solutions of six undetermined functions u_o, u_a, A_(o) and S_(2)a defined in the x, y plane. They can be divided into two groups, each constitutes three equations to calculate u_o, S_(2)a and u_a, A_(o) respectively. Their boundary conditions as well as these equations are derived from the stationary conditions of variations of a functional for this problem based on the generalized variational principle. The solutions given by this theory are close to those given by the classical theory of thin plates as the ratio of thickness h to width a is small. For large ratio, say h/a=0.3 a considerable difference arises between the two theories. It has not been made clear that in what range of the ratio such difference is reasonable to give more precise solutions. In order, to solve this problem, we must study the second order approximation theory. In this paper following the previous one, we shall establish the second order approximation theory by applying the, stationary condition of variations of a functional for this problem based on the generalized variational principle, to derive nine differential equations and the relate boundary conditions, which are used to calculate nine undetermined functions u_o u_a, A_(o), A₍₁₎, S_(2)a and S_(3)a. And the range of the validity of the first order approximation theory can be found out by comparing the second order theory with the first order theory and the classical theory. It should be pointed out here that the equations of, the second order theory can also be divided into two groups to be solved separately, and the procedure of solution is not too complicate to perform as well. Here, we will use the same notations adopted in the previous paper, and not repeat their definitions.     

On uniqueness properties of solutions of the k-generalized KdV equations

In this paper we study uniqueness properties of solutions of the so-called k-generalized Korteweg-de Vries equations. Our goal is to obtain sufficient conditions on the behavior of the difference u₁−u₂ of two solutions u₁,u₂ of (1.1) at two different times t₀=0 and t₁=1 which guarantee that u₁≡u₂.     

Variable stepsize schemes for effective order methods and enhanced order composition methods

The interest in the concept of effective order has been revived by its rediscovery in applications to symplectic problems. In this paper we revert to the original application, the construction of explicit Runge–Kutta methods. Changing stepsize is a characteristic difficulty with effective order methods and we propose a way of overcoming this difficulty. We also consider the possible cancellation of local truncation errors of two methods over two successive steps. Using the algebraic approach for deriving these results gives us further insight into these methods and compositions of methods. A particular sixth stage Runge–Kutta pair is derived in the paper and is shown to be competitive.     

On the existence in a problem of the calculus of variations without convexity assumptions

Summary We obtain new sufficient conditions for the existence in a problem of the calculus of variations without convexity assumptions.     

Comparative study of the thermodynamics and extrathermodynamics on the conformational transformation and adsorption of bovine serum albumin

The adsorption and conformation transformation of bovine serum albumin (BSA) on a reversed-phase octadecylsilyl group based on silica reversed-phase chromatographic column were studied in the temperature of 12–50°C. The thermodynamic and extrathermodynamic data were determined and compared to each other. The results showed that when temperature was below 20°C, BSA existed only in its native conformation state A; whereas when temperature was over 20°C, parts of the conformation state A changed to state B. In transformation process, endothermal and nonspontaneous reaction occurred and the entropy change was favorable for the transformation; while in adsorption process, the reaction was exothermal and spontaneous and driven simultaneously by enthalpy and entropy change. The compensation temperature in the conformation transformation of BSA was significantly less than that in the adsorption of the two conformation states. This phenomenon demonstrated the big difference during the two processes.     

Quiescent cells: A natural way to resist chemotherapy

Most chemotherapeutic treatments use drugs that target proliferating cancer cells. Therefore, they do not affect quiescent cells which are naturally resistant. Surviving cancer cells can reactivate their cell cycles in the intervals between doses, becoming proliferative again and thus restarting tumor growth. In this work, we present a mathematical model to study the impact of quiescent cells on chemotherapy effectiveness. Our simulations show that, although tumor growth is delayed after the beginning of each dose, the resistance of quiescent cells is enough to reactivate it due to accelerated repopulation, eventually causing therapy failure even in the absence of acquired resistance.     

Goodness-of-fit tests based on Rao''s divergence under sparseness assumptions

In many practical situations the classical (fixed-cells) assumptions to test goodness-of-fit are inappropriate, and we consider an alternative set of assumptions, which we call sparseness assumptions. It is proved that, under general conditions, the proposed family of statistics based on Rao's divergence is asymptotically normal when the sample size n and the number of cells M_n tend to infinity so that n/M_n→ν>0. This result is extended to contiguous alternatives, and subsequently it is possible to find the asymptotically most efficient member of the family.