模糊集的基数与连续统假设

本文在模糊映射的基础上给出了模糊集基数的定义，它把普通集的基数作为特款；不但得到有关基数的大部分结论，而且有其自身的特殊性质；特别，对于连续统假设这一世界难题可能有新的启示．     

广义Riemann猜想下的奇数Goldbach问题（Ⅱ）

本文证明了在广义Ｒｉｅｍａｎｎ猜想下每一个奇数Ｎ≥ｅｘＰ（９４）都可以表示成为三个素数之和．     

Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler–Poincaré (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then state the EP Averaging Result—that GLM equations arise from GLM Hamilton’s principles in the EP framework. Next, we derive a new set of approximate small-amplitude GLM equations (gℓm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the gℓm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The gℓm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction (WMFI). The gℓm EP motion equations for compressible and incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or gℓm) fluid theory with a Taylor hypothesis closure (THC). Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha closure equations. We use the EP Averaging Result to bridge between the GLM equations and the Euler-alpha closure equations. Hence, combining the small-amplitude approximation with THC yields in new turbulence closure equations for compressible fluids in the EP variational framework.     

D-、L-和DL-缬氨酸晶体低温旋光性研究

由于电弱力宇称不守恒,氨基酸对映体分子间存在宇称破缺能差，通过Z0粒子的介导，在某临界温度下，氨基酸分子会发生类似于BCS(Bardeen-Cooper-Schrieffer)超导的玻色凝聚,引起二级相变,理论推测相变温度约在250 K.本文通过原位测量在240～290 K下， D型、L型和DL型缬氨酸晶体的旋光角随温度的变化，发现D型和DL型缬氨酸晶体在270 K有旋光角跃变， L型缬氨酸晶体的旋光角基本不变，为Salam预言的二级相变提供了直接证据.     

Stepwise test procedures and approximate chi-square analysis

Let an overall null hypothesisH be factored in a certain stepwise manner intok subhypotheses as . Suppose the test statisticw forH be correspondingly expressed asw=w ₁ w₂…w_k wherew _i is the test statistic forH _i. We consider the case where the Box method [2] is applicable for the distributions ofw andw _i's. Ifw _i's are independent underH, we obtain a stepwise test procedure forH on the basis of an approximate chi-square analysis. To demonstrate the procedure of this sort, the testing hypotheses of equality of several convariance matrices and of the multiple independence are discussed. Finally the related asymptotic distributions are shortly noted.     

Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second‐order time evolution

Fully implicit schemes with second‐order time evolutions have been applied to simulate nonlinear diffusion problems precisely for a long time, but there is seldom theoretical study for either their convergence properties or efficient iterations. Here, a second‐order time evolution fully implicit scheme for two‐dimensional nonlinear divergence diffusion problem is analyzed. The unique existence of its solution is given. Two new methods are provided to prove its convergence, including entire inductive hypothesis reasoning and a two‐step reasoning process. Rigorous analysis shows the scheme is stable; its solution has second‐order convergence in both space and time to the exact solution of the problem. The convergence is applied to analyze a Newton iteration accelerating the computation and show its quadratic convergent speed and second‐order accuracy. The reasoning techniques also adapt to first‐order time accuracy schemes, and can be extended to analyze a wide class of nonlinear schemes for nonlinear problems. Numerical tests highlight the theoretical results and demonstrate the high performance of the algorithms. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 121–140, 2016     

Possible steps to the emergence of life: the [GADV]-protein world hypothesis

Based on the fact that RNA has not only a genetic function but also a catalytic function, the RNA world theory on the origin of life was first proposed about 20 years ago. The theory assumes that RNA was amplified by self-replication to increase RNA diversity on the primitive earth. Since then, the theory has been widely accepted as the most likely explanation for the emergence of life. In contrast, we reached another hypothesis, the [GADV]-protein world hypothesis, which is based on pseudo-replication of [GADV]-proteins. We reached this hypothesis during studies on the origins of genes and the genetic code, where [G], [A], [D], and [V] refer to Gly, Ala, Asp, and Val, respectively. In this review, possible steps to the emergence of life are discussed from the standpoint of the [GADV]-protein world hypothesis, comparing it in parallel with the RNA world theory. It is also shown that [GADV]-peptides, which were produced by repeated dry-heating cycles and by solid phase peptide synthesis, have catalytic activities, hydrolyzing peptide bonds in a natural protein, bovine serum albumin. These experimental results support the [GADV]-protein world hypothesis for the origin of life.     

Growth of the Lerch zeta-function

It is believed that the Lindelöf hypothesis is also true for the Lerch zeta-function. Here we present results supporting this conjecture. We first consider the growth of the Lerch zeta-function assuming the generalized Lindelöf hypothesis for Dirichlet L-functions. We next prove that Huxleys exponent 32/205 in the Lindelöf hypothesis for the Riemann zeta-function holds also for the Lerch zeta-function.__________Partially supported by a grant from the Lithuanian State Science and Studies Foundation.Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 45–56, January–March, 2005.     

Application of current algebra and partial conservation of axialvector current to kaon-proton interactions

A soft-pion study using current algebra and the partially conserved axial vector current (PCAC) hypothesis is made of the kaon-proton interaction processKp →Kp2π ⁰. Considering both pions to be soft, the differential rate for the process is normalized to the differential rate of the corresponding process without the pions. Theoretical predictions for the ratio of cross-sections at various kaon momenta are compared with experimental results.     

Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases

We analyse an exponential family of distributions which generalises the exponential distribution for censored failure time data, analogous to the way in which the class of generalised linear models generalises the normal distribution. The parameter of the distribution depends on a linear combination of covariates via a possibly nonlinear link function, and we allow another level of heterogeneity: the data may contain "immune" individuals who are not subject to failure. Thus the data is modelled by a mixture of a distribution from the exponential family and a "mass at infinity" representing individuals who never fail. Our results include large sample distributions for parameter estimators and for hypothesis test statistics obtained by maximising the likelihood of a sample. The asymptotic distribution of the likelihood ratio test statistic for the hypothesis that there are no immunes present in the population is shown to be "non-standard"; it is a 50-50 mixture of a chi-squared distribution on 1 degree of freedom and a point mass at 0. Our analysis clearly shows how "negligibility" of individual covariate values and "sufficient followup" conditions are required for the asymptotic properties.