跨共振点的周期扰动Duffing方程周期解的存在性

讨论Ｄｕｆｆｉｎｇ方程ｄ＾２ｘ／ｄｔ＾２＋ｇ（ｘ）＝ｐ（ｔ），此处ｇ（０）＝０，ｇ∈Ｃ（Ｒ），ｐ∈Ｃ（Ｒ），ｐ（ｔ）＝ｐ（ｔ＋２π），存在常数Ｋ＞０，｜ｇ＇（ｘ）｜＜Ｋ对ｘ∈Ｒ，及存在Ａ０＞０，Ｍ０＞０，ｘ＾－１ｇ（ｘ）＞Ａ０当｜ｘ｜＞Ｍ０下，给出了此类方程２π周期解存在的某些充分条件，扩展了已有的结果。     

二元函数的微积分基本定理

从二元函数的面导数出发定义原函数和不定积分，研究了它们的性质．证明了：（１）若ｆ（ｘ，ｆｙ）有原函数，则有一族原函数且任意两个原函数相差ｋ（ｘ，ｙ）＝Ｃ（Ｘ）＋Ｄ（ｙ）＋Ｅ，其中Ｃ（ｘ），Ｄ（ｙ）为一元函数，Ｅ为常数；（２）若ｆ（ｘ，ｙ）在闭区间［Ａ，Ｂ］Ｒ２上连续，Ｚ＝（ｘ，ｙ）∈［Ａ，Ｂ］，则Φ（ｘ，ｙ）＝ｆ（ｓ，ｔ）ｄｓｄｔ在（ｘ，ｙ）可导且Φ’ｘｙ＝ｆ（ｘ，ｙ）；（３）若ｆ（ｘ，ｙ）在［Ａ，Ｂ］上连续，Ｆ（ｘ，ｙ）为其一个原函数，则ｆ（ｘ，ｙ）ｄｘｄｙ＝Ｆ（［Ａ，Ｂ］）．     

欧拉方程的算子算法

在算子Ｂ＝ｘ．ｄ／ｄｘ作用下,欧拉方程ｘｎｄｎｙ／ｄｘｎ＋Ｐ１ｘ＾ｎ－１ｄｎ－１／ｄｘ＾ｎ－１＋．．．＋Ｐｎ－１ｘｄｙ／ｄｘ＋Ｐｎｙ＝ｆ（ｘ）,其中Ｐ１,Ｐ２,．．．,Ｐｎ为常数）,可化为：（Ａ＾ｎＢ＋Ｐ１Ａ＾ｎ－１Ｂ＋．．．＋Ａ＾０Ｂ）ｙ＝ｆ（ｘ）。并简记为Ｌ（Ｂ）ｙ＝ｆ（ｘ）,把Ｂ待定系数ｋ,则Ｌ（Ｂ）＝０即为欧拉方程的特征方程,从而可求出齐次方程的通解ｙＨ,再根据Ｌ（Ｂ）的逆算子性质求欧拉方程的特解ｙｐ＝１／Ｌ（Ｂ）ｆ（ｘ）,便求得欧拉方程的通解：ｙ＝ｙＨ＋ｙｐ。     

LaSalle矩阵不等式的加强

设Ａ是ｎｘｎ 非奇异矩阵,Ｂ是ｎｘｎ 对称矩阵,且Ｇ＝ － （ＡＴＢ＋ ＢＡ） 正定,那么对任意ｘ,ｙ ∈Ｒｎ,且ｘ ≠０,有（Ｂｘ ＋ ｙ）ＴＧ－ １（Ｂｘ ＋ ｙ） ≥〔ｘＴ（ＡＴ）－ １（Ｂｘ ＋ ｙ）〕２ｘＴ（ＡＴ）－ １ＧＡ－ １ｘ ≥－ ２ｙＴＡＴｘ     

一类阿贝尔方程极限环的几个判定准则

当ｎ次微分系统ｘ′＝λｘ－ｙ＋Ｐｎ（ｘ,ｙ）,ｙ′＝ｘ＋λｙ＋Ｑｎ（ｘ,ｙ）（ｎ≥２）化为Ａｂｅｌ方程ｄｚ／ｄθ＝Ａ（θ）ｚ３＋Ｂ（θ）ｚ２＋Ｃ（θ）ｚ后,利用λＡ（θ）的符号给出了判定Ａｂｅｌ方程极限环的几个准则：（１）当λＡ（θ）≥０且ｎ为偶数时方程无极限环;（２）若λＡ（θ）≤０时,则方程存在唯一极限环;（３）若λＡ（θ）≥０且ｎ为奇数,则方程最多只有两个极限环．     

两类特殊单峰映射

文章首先研究了ｆ（ｃ）＝１的单峰映射，得到如下结论（１）ｐｐ（ｆ）＝Ｚ＋（２）ｋ（ｆ）＝ＲＬ∞（３）｛Ａ：Ａ∈ｆ，Ａ不以ＲＬ∞为结尾｝｛Ｉ（ｘ）：ｘ∈Ｉ｝，（４）ｆ（ｃ）＝１，且ｆ严格上凸时，｛Ａ：Ａ∈ｆ，Ａ不以ＲＬ∞结尾｝＝｛Ｉ（ｘ）：ｘ∈Ｉ，ｘ≠１｝，其次，研究了ｆ（ｃ）≤ｃ的单峰映射，得到（５）ｐｐ（ｆ）＝｛１｝（６）若Ｆ（ｆ）＝｛０｝，则对ｘ∈Ｉ，ｌｉｍｎ→∞ｆｎ（ｘ）＝０，（７）若Ｆ（ｆ）＝｛０，ｙ｝，则ｙ为渐近周期点。（８）｛Ｉ（ｘ）：ｘ∈Ｉ｝｛Ｌ∞，Ｃ，ＲＬ∞｝     

偶图的周长

设Ｇ（Ａ，Ａ２；Ｅ）为２连通偶图，（Ａ１，Ａ２）为顶点二分划，Ｄ（ｘ）＝｛ｙ｜ｙ∈Ｖ（Ｇ）＼｛ｘ｝，ｄ（ｘ，ｙ）＝２｝，ｄ＾＊ｄ（ｘ）表示Ｄ（ｘ）∪｛ｘ｝中所有的度排成的非减度序列（ｄ＾＊１，ｄ＾＊２，…，ｄ＾＊ｊ，…，ｄ＾＊｜Ｄ（ｘ）｜＋１）中当下标ｊ＝ｄ（ｘ）时的度而当｜Ｄ（ｘ）｜＋１＜ｄ（ｘ）时ｄ＾＊ｄ（ｘ）＝ｄ＾＊｜Ｄ（ｘ）｜＋１。δ０＝ｍｉｎ｛ｄ（ｘ）｜ｘ∈Ｖ（Ｇ）｝，δｉ＝ｍｉｎ｛ｄ＾     

一类非线性系统解的渐近稳定性的判据

考虑 Ｓ Ｉ Ｓ Ｏ 非线性系统ｘ·＝ ｆ（ ｘ） ＋ ｇ（ ｘ） ｕ ，ｙ ＝ ｈ（ ｘ） ，仅在假定ｄｉｍ △（ ｘ０） ＝ ｎ ，△（ ｘ） ＝ ｓｐａｎ｛ｄｈ ，ｄ Ｌｆｈ ，…，ｄ Ｌ Ｎ－１ｆ ｈ｝（ ｘ） 之下，给出 ｘ０ 点附近的局部状态观测器设计，并讨论其综合问题     

以广义Logistic方程为基础的两种群互惠共存数学模型

以广义Ｌｏｇｉｓｔｉｃ方程ｄｘ／ｄｔ＝μｘｘｍ－ｘ／ｘｍ＋（ｋ－１）ｘ（μ,ｋ,ｘｍ为常系数）为基础,推广了Ｍａｙ－两种群互惠模型ｄｘ／ｄｔ＝μ１ｘ「１－ｘ／ｘｍ＋α２ｙ」 ｄｙ／ｄｔ＝μ２ｙ「１－ｘ／ｙｍ＋α１ｘ」用方程ｄｘ／ｄｔ＝μ１ｘｘｍ＋α２ｙ－ｘ／ｘｍ＋α２ｙ＋（ｋ１－１）ｘ ｄｙ／ｄｔ＝μ２ｙ／ｙｍ＋α１ｘ－ｙ／ｙｍ＋α１ｘ＋（ｋ２－１）ｙ描述两种群互惠共存,当ｋ１＝ｋ２＝１时,该方程     

两分子饱和反应系统的极限环的存在性与唯一性

陈兰荪等在第二届中国生物数学学术会议上提出了生物动力学系统中研究的１１个问题。作者所研究的是第１１个问题，生物化学中两分子饱和反应。其数学模型为ｘ＝Ｊ＿１（１＋ｘ＋ｙ＋Ａｘ￣２）－ｘ（１＋ｘ＋ｙ＋Ａｘ￣２）－Ｂｘｙ；ｙ＝Ｊ＿２（１＋ｘ＋ｙ＋Ａｘ￣２）－Ｂｘｙ．其中：Ｊ＿１、Ｊ＿２、Ａ、Ｂ为非负常数，当Ｊ＿１－３Ｊ＿２＜－［１＋Ｂｘ＋（Ｂ＋１）ｙ］／（１＋Ａｘ）时，该模型在第一象限内至少存在一个极限环；当Ｊ＿１＜Ｊ．ｘ＜ｙ，Ｂ＞ｌ且ｘ＞ａ时，该模型在第一象限内存在唯一的极限环。其中ａ＜０为方程ｐ（ｘ＝）＝０的最大负实根．     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Characterization of Ordovician carbonate reservoirs, southeastern Saskatchewan, Canada

The discovery of the prolific Ordovician Red River reservoirs in 1995 in southeastern Saskatchewan was the catalyst for extensive exploration activity which resulted in the discovery of more than 15 new Red River pools. The best yields of Red River production to date have been from dolomite reservoirs. Understanding the processes of dolomitization is, therefore, crucial for the prediction of the connectivity, spatial distribution and heterogeneity of dolomite reservoirs.The Red River reservoirs in the Midale area consist of 3～4 thin dolomitized zones, with a total thickness of about 20 m, which occur at the top of the Yeoman Formation. Two types of replacement dolomite were recognized in the Red River reservoir: dolomitized burrow infills and dolomitized host matrix. The spatial distribution of dolomite suggests that burrowing organisms played an important role in facilitating the fluid flow in the backfilled sediments. This resulted in penecontemporaneous dolomitization of burrow infills by normal seawater. The dolomite in the host matrix is interpreted as having occurred at shallow burial by evaporitic seawater during precipitation of Lake Almar anhydrite that immediately overlies the Yeoman Formation. However, the low δ18O values of dolomited burrow infills (-5.9‰～ -7.8‰, PDB) and matrix dolomites (-6.6‰～ -8.1‰, avg. -7.4‰ PDB) compared to the estimated values for the late Ordovician marine dolomite could be attributed to modification and alteration of dolomite at higher temperatures during deeper burial, which could also be responsible for its 87Sr/86Sr ratios (0.7084～0.7088) that are higher than suggested for the late Ordovician seawaters (0.7078～0.7080). The trace amounts of saddle dolomite cement in the Red River carbonates are probably related to "cannibalization" of earlier replacement dolomite during the chemical compaction.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

A computer generator for randomly layered structures

AcomputergeneratorforrandomlylayeredstructuresYUJia shun1,2,HEZhen hua2(1.TheInstituteofGeologicalandNuclearSciences,NewZealand;2.StateKeyLaboratoryofOilandGasReservoirGeologyandExploitation,ChengduUniversityofTechnology,China)Abstract:Analgorithmisintrod…     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

海南岛地体及其毗邻陆缘晚中生代—新生代古地磁研究和构造演化

本文叙述了对海南岛及其毗邻大陆边缘白垩纪到第四纪地层岩石进行古地磁研究的全部工作过程。通过分析岩石中剩余磁矢量的磁偏角及磁倾角的变化,提出海南岛白垩纪以来经历的构造演化模式如下:早期伴随顺时针旋转而向南迁移,后期伴随逆时针转动并向北运移。联系该地区及邻区的地质、地球物理资料,对海南岛上述的构造地体运动提出以下认识:北部湾内早期有一拉张作用,主要是该作用使湾内地壳显著伸长减薄,形成北部湾盆地。从而导致了海南岛的早期构造运动,而海南岛后期的构造运动则主要是受南海海底扩张的影响。海南地体运动规律的阐明对于了解北部湾油气盆地的形成演化有重要的理论和实际意义。     

《Chinese Science Bulletin》SUBJECT INDEX TO VOLUME 59(2014)

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Achieving Unusual States of Matter Under High Pressure

The elongation method,originally proposed by Imamura was further developed for many years in our group.As a method towards O(N)with high efficiency and high accuracy for any dimensional systems.This treatment designed for one-dimensional(ID)polymers is now available for three-dimensional(3D)systems,but geometry optimization is now possible only for 1D-systems.As an approach toward post-Hartree-Fock,it was also extended to     

Exciton Seebeck in Molecular Systems

Various applications relevant to the exciton dynamics,such as the organic solar cell,the large-area organic light-emitting diodes and the thermoelectricity,are operating under temperature gradient.The potential abnormal behavior of the exicton dynamics driven by the temperature difference may affect the efficiency and performance of the corresponding devices.In the above situations,the exciton dynamics under temperature difference is mixed with