Generalized Lob’s Theorem.Strong Reflection Principles and Large Cardinal Axioms

In this article, a possible generalization of the Lob’s theorem is considered. Main result is: let κ be an inaccessible cardinal,

Convergence of Impact Measures and Impact Bundles

Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.

Riemann Hypothesis and Value Distribution Theory

Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.

The Degenerated Second Main Theorem and Schmidt's Subspace Theorem

In this paper, we establish a Second Main Theorem for an algebraically degenerate holomorphic curve f : C → Pn(C) intersecting hypersurfaces in general position. The related Diophantine problems are also considered.

A Second Main Theorem of Nevanlinna Theory for Closed Subschemes in Subgeneral Position

In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an application of his second main theorem,he obtain a Brody hyperbolicity result for the complement of nef effective divisors.He also give the corresponding Schmidt’s subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.

Cartan's Second Main Theorem and Mason's Theorem for Jackson Difference Operator

Let f:C→P^(n)be a holomorphic curve of order zero.The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves.In addition,a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial.Furthermore,they extend the Mason’s theorem for m+1 polynomials.Some examples are constructed to show that their results are accurate.

直接边界元法时域全非线性兴波计算(英文)

文章在时域中采用直接边界元的方法计算模拟了以稳定航速运动的近水面潜体全非线性兴波现象。从格林定理出发,在边界面上布置Rankine源和偶极子,采用时间步进的方法计算模拟潜体近自由面运动的兴波现象。每个时步自由面上的势和节点位置采用全非线性拉格朗日自由面边界条件求解,重新生成自由面网格准备下一个时步计算的初始条件。文中给出了数值计算的结果并与试验和线性计算的结果相比,证实了该方法是可靠的,并可以利用该方法建立数值波浪水池。

双曲正切跟踪微分器设计及相平面分析

针对离散跟踪微分器(Han-TD)加速度函数结构复杂、参数整定繁琐的不足,提出了双曲正切函数改进微分器的加速度函数。双曲正切函数是一种光滑连续非线性函数,该函数在坐标零点附近呈线性特性,所以消除震颤效果显著。通过使用李雅普诺夫第二定理从理论证明了改进跟踪微分器的全局收敛的稳定特性。使用相平面法寻找微分器奇点的稳定结点,进一步指导参数的整定。通过MATLAB仿真,比较双曲正切跟踪微分器(Tanh-TD)与Han-TD的跟踪微分性能和滤波特性。仿真结果表明,双曲正切跟踪微分器对输入信号的跟踪可以实现快速无超调,滤波性能更优,且提取的微分信号较为理想,具有工程实用价值。

基于第二类四边形面积坐标的弹性力学纯弯解及MacNeal局限定理的破解

为了提高有限元的性能,弹性力学的解析解(齐次方程的通解)常常可用作有限元的试探函数。然而单元自由度数与完备的直角坐标解析解个数并不匹配,不完备的试函数会导致单元有方向依赖性。利用新型局部自然坐标——第二类四边形面积坐标QACM-II(S,T),给出了平面问题对应任意方向纯弯曲状态的应力函数解析解,即S3和T3的线性组合,并推导出了这两组应力函数对应的应力、应变和位移解析解。之后,利用QACM-II表示的解析解构造了非对称的平面4节点8自由度单元USQ4,该单元可以同时通过常应力/应变分片检验和纯弯测试,从而破解了MacNeal局限定理对平面低阶单元的限制。

一类二阶时滞微分方程三点边值迭代解的存在性

利用上下解方法和Mawhin连续性定理研究了一类二阶时滞微分方程三点边值问题.得到了这类边值问题解存在的充分条件,并建立了收敛到该解的单调迭代序列,推广和改进了一些已有文献的结果.

微动并联机构柔性平板移动副求解

柔性关节的柔度是影响微动机器人机构整体机械性能的关键因素。基于一种二维平动并联微定位机构,应用卡氏第二定理建立了适于柔性平板移动副柔度的计算公式,分析了各柔度系数在其运动平面内随结构参数的变化规律,利用有限元验证了理论计算公式的正确性,并将其计算结果与传统计算方法所得结果进行了比较。该方法考虑了剪切变形的影响,理论计算精度得到了明显提高,为今后高精密微动机构的设计和精度分析提供了理论基础。

具有变号位势的二阶Hamilton系统周期解的存在性定理

Hamilton系统是动力系统的特例,Hamilton系统的研究对气体力学、流体力学、相对论力学和核物理等学科起着重要作用.研究具有变号位势的非自治二阶Hamilton系统ü(t)+b(t)▽(u(t))=0,a.e.t∈[0,T]在满足边界条件u(0)-u(T)=u(0)-u(T)=0下周期解的存在性,其中,T>0,b∈C(0,T;R)满足b■0,∫T0b(t)dt=0并且V∈C1(RN,R).利用Rabinowitz的广义山路引理,证明了系统至少存在一个非平凡的解,推广了一些文献的结论.

非线性二阶四点边值问题正解的存在性

运用格林函数性质和锥不动点定理研究了非线性微分方程u″+a(t)f(t,u(t))=0四点边值问题正解的存在性.

弹性圆杆扭转的二阶效应

本文基于拖带坐标方法和S-R分解定理分析了弹性圆杆扭转的二阶效应.应用渐近方法,证明了弹性圆杆扭转伸长效应的存在,并导出轴向力、扭矩的表达式.

从圆环到紧黎曼曲面上全纯映射的第二基本定理

通过定义一个在圆环A(r)={z∈C:1/r<|z|<r}上的次调和函数的一个特殊的流,全纯映射的特征函数和Green-Jensen公式,进而得到了圆环到紧黎曼曲面上全纯映射的第二基本定理。

一类二阶时滞微分方程周期解的存在性

利用马文重合度拓展定理以及不等式放缩技巧,探讨一类二阶时滞微分方程x″(t)+f(x(t))x'(t)+g(x(t-ω))+h(x(t))=e(t)周期解的存在性,得到一个周期解存在性结果。当方程为变时滞时,通过引理中的第一个不等式消除变时滞在函数内的影响,使得本方法对于变时滞量方程同样适用。

二阶微分方程组正周期解的存在性

考虑二阶微分方程组{x″+H(t)x'+A(t)x=F(t,x),0<t<T,x(0)=x(T),x'(0)=x'(T{),正周期解的存在性。利用Krasnoselskii不动点定理以及所对应的格林函数正性,证明上述二阶微分方程组新的正周期解的存在定理,将所得结论进行推广,得到上述二阶微分方程组多个正周期解的存在定理。将结论应用在经典实例上,验证了所得结果的正确性。

多导体系统中的几个证明

本文论证了多导体系统的电势与电荷之间的关系。

Banach空间二阶常微分方程边值问题解的存在性

应用凝聚映射的Leray-Shauder不动点定理,研究了Banach空间中二阶常微分方程两点边值问题解的存在性.

Delta并联机器人静刚度理论分析与仿真

为研究静平衡状态下Delta并联机器人对外部载荷的响应情况,将相对刚度大的构件视为刚体以简化建模难度,同时将驱动臂和从动杆理想化为线弹性杆件,采用卡氏第二定理对其进行了静刚度理论分析与建模。利用该模型模拟实际情况下动平台所受到的负载情况,进而在不同位姿下探究了动平台位移和转角弹性变形量在可达工作空间内指定区域中的分布规律和特点。最后利用ISIGHT进行联合仿真,从而相互验证理论建模和仿真的正确性。