“双曲抛物偏微分方程奇异摄动问题的差分解法”的一个注记

本文对下述边值问题εＵ＿（ｔｔ）＋Ｕ＿ｔ－Ｕ＿（ｘｘ）＝ｆ（ｘ，ｔ）　　　　　　　０＜Ｘ＜１，０＜ｔ＜ＴＵ（０，ｔ）＝Ｕ（１，ｔ）＝０　　　　　　　　０＜ｔ＜ＴＵ（ｘ，０）＝Ｓ（ｘ），Ｕｔ（ｘ，０）＝Ｗ（ｘ）　０＜ｘ＜１的可解性进行了研究，认为可以放宽文［１］中对函数ｆ、ｓ、ｗ所作的假定，满足一般的可积性条件即可．     

由修正的Navier─Stokes方程产生的动力系统（Ⅰ）

证明了由于１９６８年提出的修正的Ｎａｖｉｅｒ─Ｓｔｏｋｅｓ方程可产生一个作用于一可分的Ｈｉｌｂｅｒｔ空间Ｈ上的单参数半群｛Ｖ＿ｔ｝，算子Ｖ＿ｔ于ｔ＞０连续，于ｔ＞０紧。给出了｛Ｖ＿ｔ｝成为连续半群的充分条件。证明了此半群有非空的紧的不变的可吸引Ｈ中任何有界集的吸引子μ．对于Ｈ中任何有界不变集Ａ（可以是μ），从Ａ上出发的运动的决定模态的个数有限。如果Ａ是Ｈ中的紧不变集（可以是μ），则Ｖ＿ｔ（ｔ≥０）在Ａ上可逆从而容许定义Ｖ＿ｔ＝Ｖ￣（－１）＿ｔ（ｔ＜０）使得｛Ｖ＿ｔ，ｔ∈Ｒ，Ａ｝是一连续群，即在经典意义下的动力系统。证明了Ｈ中任何紧不变集的Ｈａｕｓ─ｄｏｒｆｆ维和分维有限。     

一类H—值扩散过程的大偏差性质

设Ｈ是实可分Ｈｉｌｂｅｒｔ空间，Ｈ＝｛Ｘ（ｔ）；ｔ≥０｝是由下列随机微分言程｛ｄＸ（ｔ）＝σ（Ｘ（ｔ））ｄＷ（ｔ）Ｘ（０）＝０ｔ≥０决定的Ｈ－值扩散过程。λ（．）：「１，＋∞）→」１，＋∞）。本文讨论了Ｃ（「０，１」，Ｈ）上概率测度族｛Ｐ．（Ｘｔ（．）／√ｔλ（ｔ））＾－１；ｔ≥１｝的大偏差性质。在一定的条件下，得到了下界及弱型上界。     

积分C－半群及其谱映射定理

第一节在没有指数有界的假设条件下，讨论了积分Ｃ－半群的一些性质，以及积分Ｃ－半群与Ｃ－半群的关系，推广了［５，定理２］。第二节讨论了积分Ｃ－半群的谱映射定理。主要结果如下：设Ａ为积分Ｃ－半群｛Ｔ（ｔ）｝的生成元，ρｃ（Ａ）≠Φ，则（ｉ）ｔ＞０（ｉｉ）（ａ）反之，若存在ｘ∈Ｘ，ｘ≠０，使得对任何ｔ＞０那么，（Ａ）。（ｂ）若（Ａ），则对任何ｔ＞０，ｔ（Ｔ（ｔ）Ｃ－１）。反之，若对任何ｔ＞０，ｔ（Ｔ（ｔ）Ｃ－１），且存在Ｘ∈Ｘ，Ｘ≠０，使得Ｔ（ｔ）Ｃｘ＝ｔＸ，则，０（Ａ）（ｉｉｉ）｛（ｔ）。     

三瓶分液通用算法

将“三瓶分液问题”推广成“Ｎ等分液体”，即有３个无刻度瓶，容积分别为Ａ＿０，Ａ＿１，Ａ＿２（Ａ＿０＞Ａ＿１＞Ａ＿２），且Ａ＿０大于等于待分液体体积ＮＰ（Ｎ≥２），（Ａ＿１，Ａ＿２）＝１，Ａ＿１＋Ａ＿２＝２Ｐ．并根据数论知识导出了通用分解算法．     

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。     

线性代数方程组的行处理法

线性代数方程组的行处理法杨本立（中国工程物理研究院职工大学）１非奇异线性代数方程组行处理法设ＡＸ＝ｂ是线性方程组ＢＸ＝Ｃ的同解方程组。如果ＡＸ＝ｂ的每一个方程（ａ￣ｉ，ｘ）＝ｂ＿ｉ（ｉ＝１，２，…，ｎ）都有（ａ￣ｉ，ａ￣ｉ）＝１及ｂ＿ｉ≥０，则称ＡＸ...     

关于图B（m,n）的优美性

证明了：当ｍ≡１或２（ｍｏｄ４）时，Ｂ（ｍ，ｎ）＝Ｃ＿ｍ∪Ｐ＿ｎ是优美图，其中Ｃ＿ｍ＝Ａ＿１Ａ＿２…Ａ＿ｍＡ＿１，Ｐ＿ｎ＝Ａ＿１Ｂ＿１Ｂ＿２…Ｂ＿ｎ（ｍ≥３，ｎ＞０）。     

一类含零导数的算子方程分歧解的存在性

该文用同伦法和拓朴度证明一类含零导数的算子方程μＡｘ＋Ｎ（μ，ｘ）＝０，在（μ，ｘ）＝（０，０）附近分歧解的存在性，其中ｘ∈Ｘ，μ∈（０，μ０）。Ｘ和Ｙ是Ｂａｎａｃｈ空间。Ａ：Ｘ→Ｙ是零指标Ｆｒｅｄｈｏｌｍ有界线性算子。对固定的μ∈（０，μ０），Ｎ：Ｘ→Ｙ是非线性全连续算子，且满足Ｎ（μ，０）＝０，对一切μ∈Ｒ。当ｘ→０时，Ｎ（μ，ｘ）＝ｏ（ｘ）。当ｘ→＋∞时，Ｎ（μ，ｘ）／ｘ→＋∞。对充分小ｒ＞０，当ｘ≥ｒ时，Ｎ（μ，ｘ）≥μαｘ１＋δ，其中α＜１，δ＞０，μ∈（０，μ０）。ｋｅｒＡ是ｎ维空间。在上述条件下，证明了在（０，０）点附近存在非平凡解ｘ（μ），且μ→０＋时，ｘ（μ）→０。     

Banach空间中常微分方程Cauchy问题的近似解与解的关系

讨论Ｂａｎａｃｈ空间中常微分方程Ｃａｕｃｈｙ问题的近似解与解的关系，得到一个Ｃａｕｃｈｙ问题的近似解与解的关系的定理：定理设ｆ＿ｎ∈Ｃ［Ｒ＿０，Ｅ］（ｎ≥１），ｆ∈Ｃ［Ｒ＿０，Ｅ］，序列｛ｆ＿ｎ｝在Ｒ＿０上一致收敛于ｆ；又设０＜α≤ａ，ｘ＿ｎ∈Ｃ￣１［［ｔ＿０，ｔ＿０＋α］，Ｂ（ｘ＿０，ｂ）］，且满足Ｃａｕｃｈｙ问题ｘ＇＿ｎ（ｔ）＝ｆ＿ｎ（ｔ，ｘ＿ｎ（ｔ））ｘ＿ｎ（ｔ＿０）＝ｚ＿ｎ其中ｔ∈［ｔ＿０，ｔ＿０，ｔ＿０＋α］，ｎ＝１，２，…，ｚ＿ｎ∈Ｅ，ｚ＿ｎ→ｘ＿０（ｎ→∞），如果ｘ＿ｎ（ｔ）在［ｔ＿０，ｔ＿０＋α］上一致收敛于ｘ（ｔ），则ｘ∈Ｃ￣１［［ｔ＿０，ｔ＿０＋α］，Ｂ（ｘ＿０，ｂ）］，且对ｔ∈［ｔ＿０，ｔ＿０＋α］，有ｘ＇（ｔ）＝ｆ（ｔ，ｘ＿ｎ（ｔ））ｘ（ｔ＿０）＝ｘ＿０     

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.     

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.     

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.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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Brief Introduction to “Journal of Jilin University( Science Edition) ”

<正>"Journal of Jilin University(Science Edition)"is a comprehensive academic journal in the fields of science sponsored by Jilin University and administrated by the Ministry of Education of the Peoples Republic of China.The journal started publication in 1955.The original name at starting publication was"Journal of Natural Science of Northeast People University",which was changed into"Acta Scientiarum Naturalium Universitatis Jilinensis"in 1958 owing to the name change of the university.The present journal name has