构式语法:认知语言学的新视角

分析了构式语法产生的历史背景和基本理论,探讨了Goldberg的构式观点和构式语法的特点,并简要概括了其在儿童语言习得和汉语研究方面的贡献。构式语法从一个新的视角对语言本质进行阐释,打破了语言学研究领域的固有模式,使先前未能得到解释的语言现象有了新的突破口,实现了理论创新。     

The existence of pseudo-almost periodic solutions of third-order neutral differential equations with piecewise constant argument

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.     

带逐段常变量微分方程的伪概周期解

利用伪概周期函数唯一分解性质,研究相关差分方程的伪概周期序列解,并以此为工具得出一类带逐段常变量微分方程伪概周期解的存在唯一性.     

Understanding the Small Object Argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an “algebraic” refinement of the small object argument, cast in terms of Grandis and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies.

二阶非线性中立型时滞差分方程的振动性

研究了一类具有多个变滞量的变系数的二阶非线性中立型时滞差分方程的振动性,得到了该类方程振动及其解的一阶差分振动的充分条件,推广了现有文献中的某些结果.     

一类具时滞的Rayleigh型泛函微分方程反周期解的存在性

应用Leray Schauder不动点定理,研究了一类具时滞的Rayleigh型泛函微分方程： x″（t）＋f（x′（t））＋g（x（t-τ（t）））=e（t）的反周期解问题,得到了反周期解存在的新的结果。     

Instability of the standing waves for nonlinear Klein-Gordon equations with damping term

This paper is concerned with the nonlinear Klein-Gordon equations with damping term. In terms of the variational argument, the sharp conditions for blowing up and global existence are derived out by applying the potential well argument and using the concavity method. Further, the instability of the standing waves is shown.     

-loss of derivatives for an evolution type model

This paper is devoted to the study of loss of derivatives for an evolution type model, which allows for non-integer powers of (−Δ). On the one hand, we describe the influence from the orders of principle symbols. On the other hand, we explore the significant impact of ν-related oscillation from the pseudo-differential operators. In the final analysis, to demonstrate the sharpness of our estimates, counter-examples are constructed through the application of Floquet theory and instability arguments.     

Periodic solutions for a kind of Liénard equation with a deviating argument

In this paper, the Liénard equation with a deviating argument

x^″(t)+_f1(t,x(t))x^′(t)+_f2(x(t))(x^′(t))²+g(t,x(t−τ(t)))=p(t)$x^{″}\left(t\right)+f_1(t,x\left(t\right))x^{\prime }\left(t\right)+f_2\left(x\left(t\right)\right){\left(x^{\prime }\left(t\right)\right)}^2+g(t,x(t-\tau \left(t\right)))=p\left(t\right)$

Numerical inversion of a general incomplete elliptic integral

We present a numerical method to invert a general incomplete elliptic integral with respect to its argument and/or amplitude. The method obtains a solution by bisection accelerated by half argument formulas and addition theorems to evaluate the incomplete elliptic integrals and Jacobian elliptic functions required in the process. If faster execution is desirable at the cost of complexity of the algorithm, the sequence of bisection is switched to allow an improvement by using Newton’s method, Halley’s method, or higher-order Schröder methods. In the improvement process, the elliptic integrals and functions are computed by using Maclaurin series expansion and addition theorems based on the values obtained at the end of the bisection. Also, the derivatives of the elliptic integrals and functions are recursively evaluated from their values. By adopting 0.2 as the critical value of the length of the solution interval to shift to the improvement process, we suppress the expected number of bisections to be as low as four on average. The typical number of applications of update formulas in the double precision environment is three for Newton’s method, and two for Halley’s method or higher-order Schröder methods. Whether the improvement process is added or not, our method requires none of the procedures to compute the incomplete elliptic integrals and Jacobian elliptic functions but only those to evaluate the complete elliptic integrals once at the beginning. As a result, it runs fairly quickly in general. For example, when using the improvement process, it is around 2–5 times faster than Newton’s method using Boyd’s starter (Boyd (2012) [25]) in inverting E(φ|m)$E\left(\phi \right|m)$, Legendre’s incomplete elliptic integral of the second kind.