Appendix专业外语词典.doc

Appendix:1. Mathematical vocabulary A Abelian group 交换群 Absolute value 绝对值Absolute convergence 绝对收敛Accumulation point 聚点Acute angle 锐角Adjacent angles 邻角 Adjoint matrix 伴随矩阵 Algebra 代数Alternating series 交错级数Amplitude 振幅Analytic function 解析函数 Angular velocity 角速度 Approximation theory 逼近论Arc differential 弧微分Arithmetic root 算术根Associative law 结合律Auxiliary function 辅助函数Average velocity 平均速度 Axiom of choice 选择公理BBall 球 Banach algebra 巴拿赫代数Basic elementary function 基本初等函数Bell shaped curve 钟型曲线 Bernoulli equation 贝努利方程Binomial expansion 二项展开式Bijection 双射Bivariate distributation 二元分布Block matrix 块矩阵; Borel set 波莱尔集Boundary curve 边界曲线 Bounded function有界函数CCalculus 微积分 Cardinal number基数Cartesian coordinates 笛卡尔坐标Cauchy inequality 柯西不等式Centre of a neighborhood 领域的中心Chain rule 链式法则Characteristic curve 特征曲线Chebyshev inequality 切比雪夫不等式Chord theory 弦理论 Choas 混沌Closure 闭包Coefficient matrix 系数矩阵 Cofactor 余子式Clockwise sense 顺针方向Collinear point 共线点 Combinatorial programming 组合规划Commutation law 交换律 Compact set 紧集Complement of event 补事件 Complete space 完备空间Complex integral 复积分 Composite function 复合函数Concave curve 凹曲线 Conditional extreme values 条件极值Conjugate root 共轭根Connected component 连通分支 Consistency theorem 相容性定理Continue function 连续函数 Contractive mapping 压缩映射Converge series 收敛级数 Converse sentence 逆命题Convex analysis 凸分析Corollary 推论Correlation coefficient 相关系数Cosine series 余弦级数Countable set 可数集Cover 覆盖Criterion of convergence 收敛准则Critical point 临界点Curvature 曲率Curve of second class 二次曲线Cyclic subgroup 循环子群Cylindrical surface 柱面DDAlembert formula 达朗贝尔公式 Decomposing subspace 可分解子空间Decreasing series 递减级数 Definite integral 定积分Definition 定义Defined interval 定义区间Dense subset 稠密子集Dependent variable 因变量Derivative 导数Derivative function 导函数Determinant of matrix 矩阵的行列式Differential equation 微分方程Difference of set 差集Dimension number 维数Differential quotient 微商Direct product 直积 Directional derivative 方向导数Discrete distribution 离散分布 Disjoint events 不相交事件Divergent sequence 发散序列Dlliptic cone 椭圆锥面 Domain 定义域Double integral 二重积分Duality principle 对偶原理 EEdge 边Eigendistribution 特征分布Eigenvalue 特征值 Elementary divisor 初等因子Elementary event 初等事件 Elimination 消去法Ellipse 椭圆Empirical formula 经验公式End point 端点Entropy constant 熵常数 Entry 元素 Envelope 包络Equation of linear regression线性回归方程Equidistant 等距Equivalence class等价类 Equivalent matrix 等价矩阵Equivalent infinitesimal 等阶无穷小Error term 误差项Estimation region 置信区间 Euclidean space 欧几里德空间Euler function 欧拉函数 Evolvent 渐近线Even function 偶函数Everywhere dense 处处稠密Exterior point 外点 Expectancy 期望Explicit function 显函数Exponential function 指数函数 Extension theorem 延拓定理Extremum with a condition 条件极值FFactor 因子，商，因素 Factor group 商群Factorial 阶乘Fiber bundle 纤维从Fibonacci method 黄金分割法Field of direction 方向场Finite covering 有限覆盖Finite element method 有限元法First derivation 一阶导数Fully invariant subgroup 完全不变子群Fundamental system of solution 基础解系Fuzzy topology 模糊拓扑GGalois theory 伽罗华理论; Game matrix 对策矩阵Global(absolute) mximum 最大值Graph of a function 函数图形GaussJordan elimination 高斯约当消元法Generalized inverse 广义逆Generating curve 母线 Gradient 梯度Gravitational potential 引力势Greatest lower bound 下确界 Group homomorphism 群同态Group isomorphism 群同构 Group of permutations 置换群HHamilton equation 哈密尔顿方程 Harmonic function 调和函数Hermite matrix 埃尔米特矩阵 Hessian matrix 海塞矩阵Hilbert space 希尔伯特空间 Homeomorphic 同胚Homogeneous linear equation齐次线性方程Horizontal plane 水平面Hybrid partial derivative 混合偏导数Hyperbolic 双曲线Hyperbolic function 双曲函数 Hyperplane 超平面IIdeal 理想 Idempotent 幂等元Identity 单位元 Imaginary part 虚部Implicit difference equation 隐式微分方程Implicit function 隐函数Improper fraction 假分式Impossible event 不可能事件Incompatible event 不相容的事件 Index theory 指标理论Induce mapping 诱导映射 Inertial theorem 惯性定理 Infimum 下确界Infinite point 无穷远点Infinitesimal of higher order 高阶无穷小 Inflection point 拐点Inhomogeneous polynomial 非齐次多项式Injection 单射Integer 整数Integrable function可积函数Integration variable 积分变量Integration by parts 分部积分法Integration by substitution 换元积分法Intercept 截矩Interdependent 相互关联Interior 内部Intermediate term 中间项Interpolate 内插 Interval 区间Invariant subspace不变子空间 Inverse dependene 反比Invertible matrix 逆矩阵 Isolated point 孤立点Isometric mapping 等距映射 Isomorphism 同构Iterative process 迭代过程JJacobian matrix 雅克比矩阵 Joint distribution 联合分布KKernel 核 Kitchen drawer principle 抽屉原理LLabile point 不稳定点 Lambda matrix -矩阵Laplacian operator 拉普拉斯算子 Lattice 格Linear algebra 线性代数Linear transformation 线性变换 Linear space 线性空间 Local(relative) maximum 极大值Logarithm function 对数函数 Logic 逻辑Lower semi-continuous 下半连续Lowest common multiple 最小公倍数MMajorization 优化 Manifold 流形Mapping 映射 Markov chain马尔科夫链 Martingale 鞅 Mathematical logic 数理逻辑 Maximum value 极大值Measurable set 可测集Method of least squares 最小二乘法Metric space 度量空间Minimal value 极小值 Minus 减，负号Module 模 Moment 矩Monomial 单项式 Monotone function 单调函数Multinomial expansion 多项式展开Multiobjective optimization 多目标优化Multiple 倍数，多重Multiplication 乘法NNarrow rectangle 窄矩形Negative definite quadratic form负定二次型 Neighbourhood 邻域Nest 套 Nilpotent matrix 幂零矩阵 Norm 范数，模Normal plane 法平面 Numerical Analysis数值分析OObjective function 目标函数Oblique triangle 斜三角形Octant 卦限Odd or even 奇或偶One-sided limits 单侧极限Open disk 开圆盘 Operator algebra 算子代数 Optimization 最优化Ordered set 有序集 Ordinal number序数Orthogonal basis正交基 Over field 扩张域PPair 偶，对 Parabolic 抛物线 Parallel 平行Parallelogram rule 平行四边形法则Paradoxical 悖论 Parameter 参数Parametric equation 参数方程Partial ordered set 偏序集Partition 分割，分拆 Pathological function 病态函数Pedal 垂足 Period function 周期函数Permanency 不变性 Permutation 排列，置换Perpendicular 垂线 Perturbation 扰动Piecewise function 分段函数Poisson distribution 泊松分布 Polynomial 多项式 Postulate 公设 Power series solution 幂级数解Prime number素数Primitive function 原函数 Principle 原理Probability 概率 Problem of fixed point 不动点问题Projection 射影 Proportion 比例Proposition 命题Pure mathematics 基础数学QQuadrant 象限 Quadratic form 二次型Quadric surface二次曲面 Quasi-sphere 拟球Quaternary expression四进制表示 Quotient 商RRadial 径向 Radius of curvature 曲率半径Random process 随机过程 Range 区域，值域Rank 秩 Rational number 有理数Real analysis 实分析 Reciprocal law 互反律，互逆律Rectifiable curve 可求长曲线Recurrence formula 递推公式Rectangular form 矩形Region 区域，范围 Regular curve 正则曲线 Representation 表示Riemann integral黎曼积分 Root 根SSaddle point 鞍点 Sample space 样本空间Scalar 标量，纯量 Selfadjoint matrix 自共轭矩阵 Separable space 可分空间Sequence 序列 Similarity 相似性Sign function 符号函数Slope of the tangent line 切线的斜率 Smooth curve光滑曲线Spectrum 谱Sphere 球面Spline interpolation 样条插值Square 平方，正方形Stable point 稳定点 Stationary point驻点Statistical 统计量Step curve 阶梯曲线Stochastic variable 随机变量 Superlinear 超线性Surface of revolution 旋转曲面Surjection 满射Symmetric transformation 对称变换TTabular 制表，列表 Tangent 正切Tensor product 张量积 Topological space 拓扑空间Torsion 挠率Total differential 全微分 Trace 迹Transposed matrix 转置矩阵Trapezoid with curve edge 曲边梯形 Trigonometric function 三角函数Trivial 平凡的 Typical 典型的UUnbouded 无界的 Uniform convergent 一致收敛Uniform motion 匀速运动Unitary operator酉算子 Universal 范的, 通用的 VVague set 模糊集 Validity 有效性Variable 可变的 Variation 变分Vector 向量Vertical asymptote 铅直渐近线 Vertex 顶点Volume 体积 Volute 螺线WWavelet analysis小波分析Weight number 权数 Wreath product 圈积Xxaxis x轴 YYis axis y轴 Yield function 产出函数 ZZero divisor 零因子Zero element 零元素Zero mearsure set 零测度集Zone 区域2. Writing Paper and ExampleA paper is to be written for solving problems in research and practices, which shows the authors ideas. Often it presents some applications in research and practices. It is an important form of idea and results of communication. Therefore, writing paper is a routine work for people to do research. Generally, they are published in some special journal or international conference.A paper often is composed of five parts, such as, title, authors names, abstract, American classification number, concrete contents, reference. First, title gives the research problem. Second, the authors names will be given in turns. Third, abstract, from its meaning, the problem is described and the main research results are given. American classification number shows the research range of this paper, by it, we can find the paper easily. The following part is the core of paper. It often includes three sections. Authors will illustrate the background of problems that be given in this paper. Then authors will give the idea, results and proofs of results. Finally, applications in research and practices are given. After the main content of the paper, reference is given. In reference, authors will list related materials used in this paper so that readers are convenient to learn it. In addition, at the end, author will give his e-mail address. English Paper ExampleBull. London Math. Soc. 36(2004)53-58 2004 London Mathematical SocietyGAPS BETWEEN CLASSES OF MATRIX MONOTONEFUNCTIONSFRANK HANSEN, GUOXIN JI AND TOMIYAMAABSTRACTThe class of matrix monotone function of order n, defined on an interval I, is considered in this paper. Explicit examples are given to prove that if I is different from the whole real line, then is a proper subset of for each nature number n. The subhomogeneous C*-algebra are then characterized in term of matrix monotone functions. 1IntroductionAlmost seventy years have passed since Lowner8 proposed the notation of operator monotone function .A real, continuous function defined on a nontrivial interval is said to be matrix monotone of order n if for any pair of self-adjoint matrix x and y with eigenvalues in . We denote by the set of such functions. 2. The gaps between and For a positive integer n, let be the polynomial defined by .(2).Following the notations in 3, we consider the matrix-valued function associated with and given by . The following lemma is an application of standard argument taken from the theory of moment problems for Hankel matrices.Lemma 1. The matrix is a positive definite.Proof : We set , and we calculate that . Hence we can write as ,and we therefore obtain .Consequently, .Now we take a vector , and calculate .It follows that the matrix is positive semidefinite. Moreover, if , we see that , almost everywhere in -1,1. Since the left-hand side is a polynomial, it is identity zero on the interval -1,1. All entries of the vector c are therefore zero, and the matrix is positive definite.3. Characterization of -algebras in terms of matrix monotone functions.Reference1. J. bendat and S. Sherman, Monotone and convex operator functions, Trans. Amer. Math. Soc. 79(1955) 58-71.2. O. Dobsch, Matrix funktionen beschrankter Schwankung, Math. Z. 43 (1973)353-388.3. W. Donoghue, Monotone matrix functions and analytic continuation (Springer, 1974).4. K. Lowner, Uber monotone Matrixfunktionen, Math. Z. 38 (1934)177-216.Frank Hansen Guoxing ji Institute of Economics College of Mathematics University of Copenhagen and informationStudiestrance 6 Shannxi Normal UniversityDK-1455, Copenhagen K Xi,an 710062Denmark P.R.China frank.hansenecon.ku.dk Jun Tomiyama Department of mathematics and Physics Japan Women,s University Mejirodai Bunkyo-ku Japan jtomiyamafc.jwuac.jp英语数学论文的组成及写作要求1 Titile（标题）简短明了又能概括全篇中心内容标题要求：标题一般是一个名词短语或者加上介词on;标题通常不写成句子或不定式短语，也不出现从句。标题常用名词或动名词代替动词2 About author(s)(作者信息)3 Abstract（摘要）关于论文内容简短而又精炼的表述摘要要求：文句精炼、论点具体、语句规范、相对完整；4 Keywords（关键词）从论文的正文及摘要中选取的，在表达论文的内容、主题等方面具有实际意义并起着关键作用的词汇关键词要求：采用规范的数学词汇，部分具有检索意义的动词和形容词；一般选用3-8个关键词5 Introduction（引言）解释论文的主题、目的和总纲引言要求：言简意赅、突出重点、开门见山、实事求是 包括：研究依据、目的、背景、理论依据、研究方法；6 Proof（论证）是论文的主体；论证部分要求：论点明确、论据充分、参考文献引用充分且必要。包括：预备知识、引理、主要结果及其证明7 Acknowledgement（致谢）感谢对论文的指导及给出重要帮助的师友。8 References（参考文献）反映作者严肃的科学态度及科学研究的广泛根据。3. Translation Exercises1. Complex analysis arose from a dilemma that confronted Italian mathematicians during the Renaissance. For coping with certain problems in algebra, they needed to make use of the square root of -1, Yet it went against the grain to admit into the family of numbers this “imaginary” unit, which has no value mathematicians overcame their prejudice against imaginary numbers and built up a distinct body of mathematics around them. They learned that the square root of -1 could be combined with real numbers and that the result, complex numbers, obeyed the laws of ordinary algebra and arithmetic. Today complex analysis is one of the universal tools in both pure mathematics and applications to science and engineering. It is the key problems in aeronautics, liquid flow, the design of electronic circuits, and many other fields. 2. Euclid himself was uneasy about one of the pillars of his geometry, the familiar postulate lines. After trying without success to prove this supposedly self-evident truth, later mathematicians finally began to wonder what would happen if their discarded if in favor of other assumptions. The result of their experiments was non-Euclidean kind but no less stimulated mathematicians to use their imagination much more freely. As a consequence, geometry today is concerned with Euclidean geometry may seem peculiar at first glance, it ma actually turn out to be the best way to describe the cosmos.3. When a mathematician comes upon an exciting new idea, he usually tries to generalize it as far as possible. The familiar Pythagorean Theorem, which applies to right triangles in plane geometry, for example, has been extended to spaces of many dimensions, even infinitely many dimensions. As so often happens with such mathematical flights of fancy, this generalization turns out to be useful in many branches of physics and engineering. Recent investigations are carrying the generalization still further, to infinite-dimensional curved spaces“glued together”in complicated ways.4. A great many of the mathematical ideas that apply directly to physics and engineering are collected in the concept of vector spaces. This branch of mathematics has applications in such practical problems as calculating the vibrations of bridges and airplane wings. Logical extensions to spaces of infinitely many dimensions are widely used in modern theoretical physics as well as in many branches of mathematics itself.5. The mathematical theory of analytic functions has come to play an essential role in the theory of elementary particles in collision. Experiments produce probability curves describing the chance that one thing or another will happen when two or more particles collide, for example, a certain new particle will be produced and will emerge from the target, heading in a particular direction with a particular energy. The theoretical physicist seeks laws that correspond to these empirical curves. Subtle mathematical analysis of the theoretical curves probes into such fundamental physical questions as the role of causality in the subatomic world. “Do these concepts provide a framework within which an essentially complete and unique description of the structure and collisions of elementary particles is to be constructed?” the author asks. 6. Laplace, a famous contributor to this branch of mathematics, once wrote that “the most important questions of life are, for the most part, really only problems of probability.” At one time mathematicians had serious misgivings about probability theory; the logical foundations seemed flimsy. But after they learned how to resolve some confusing paradoxes, pr