查询词典 mathematical

The treatise is the last mathematical work of Xia, as well the first treatise applying the differential and integral calculus after appearance of the DWJ in China.

万象一原》(1862)是夏鸾翔在学习了《代微积拾级》(1859)之后完成的一部著作，这是夏鸾翔的最后一部数学著作，同时也是我国数学家自己写的第一部应用微积分知识的著作。

My performance in the graduate seminars of Differential Calculus and Mathematical and Physical Formulas shows that I have got a good grasp of the fundamentals of mathematics.

我的表现在研究生研讨会的微分学与数学和物理公式表明，我有一个很好的把握其基本的数学。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

Therefore, the differential equation is also described the relationship between the number of objective things of an important mathematical model.

因此，微分方程也是描述客观事物的数量关系的一种重要的数学模型。

The mathematical thought reflected in these researches were, actually, different from modern Game theory, but, still, it showed the possibility of dealing with Game problems with mathematic tools, and meanwhile, the thought of differential game theory in the early time was included in these researches, which in a way inspired the establishment of Game theory.

在这些研究中所包含的数学思想与现代博弈理论的思想基本上是不一样的，但电反应出了用数学工具处理博弈问题的可能性，同时也包含了早期微分博弈的思想，对以后的微分博弈理论的创立有一定的启发作用。

In mathematics, Chinese scholars have achieved important results in fields such as number theory, theorem-proving by computer, differential geometry, topology, complex analysis, probability and mathematical statistics, PDE, functional analysis, numerical analysis and control theory and so on.

在数学方面，据我所知，中国数学家在诸如数论、定理机器证明、微分几何、拓扑学、复分析、概率论与数理统计、偏微分方程、泛函分析、数值分析和控制论等领域里也都取得了具有国际水平的成果。

For this reason, the project creates the mathematical model and numerical method of backcalculation of layer moduli in asphalt pavement based on homotopy method in accordance with the theories of differential topology and optimization. Through selecting the rational objective functions of backcalculation of moduli, a large number of deflection basins of asphalt pavement with FWD are made the backcalculation of moduli to solve effectively the present problems and ensure the reliability of backcalculation of layer moduli in asphalt pavement.

为此，本项目根据微分拓扑和最优化理论，建立了基于同伦方法的沥青路面模量反算的数学模型和计算方法，并通过选取合理的模量反算目标函数，对大量FWD实测的沥青路面弯沉盆进行了模量反算，从而有效地解决了目前存在的问题，保证了沥青路面模量反算的可靠性。

With this approach, a mathematical model of ASVG is developed. The method is simple and can be used to analyze the detailed internal properties of an ASVG. It overcomes the disadvantages of the two methods generally used, one is a method for modeling an ASVG by getting differential equations according to the topology of the ASVG circuit, which is very complicated and it is difficult to get a unified model expression of an ASVG; the other is a method for modeling an ASVG by considering the whole ASVG as a voltage source, which is too simple to analyze the detailed internal properties of ASVG.

该方法既克服了根据ASVG装置拓扑结构列写微分方程组的建模方法过于复杂且不易获得统一模型表达式的缺点，同时又克服了将ASVG装置等效为电压源的建模方法太简单而无法用于分析ASVG装置内部性质的缺点，具有建模简单又能分析ASVG装置的内部性质的优点。

Based on theanalysis of topology structure of parallel mechanisms and using differential topology anddifferential manifolds as mathematical tools, we propose a new classification method. Thismethod classifies singularities of parallel mechanisms into two basic types, i.e. topologysingularity and parameterization singularity. This kind of classification has clear physical andmathematical meaning and fully reveals the characteristic of configuration space of parallelmechanisms.

采用微分拓扑和微分流形等现代数学工具，在对并联机构位形空间的拓扑结构进行分析的基础上，提出了一种新的奇异位形的分类方法，即把奇异位形分为拓扑奇异位形、参数化奇异位形两种类型，这种分类方法充分体现了并联机构位形空间的特点，具有十分明确的物理和数学意义。

After that, a diffusive mathematical model was set up to find the diffusivity of glucose in Ca-Alg MBs by fitting the experimental data.

在选择高扩散系数的前提下，结合动物细胞培养的要求，我们认为适用于动物细胞培养的海藻酸钙胶珠的适宜直径为2 mm左右。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。