5.Quarter LCU based integer motion estimation algorithm for HEVC

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数学专业英语词汇（U）

数学专业英语词汇(U)u statistic u统计量ulm factor 乌姆因子ultra filter base 超滤子基ultra ideal 超理想ultra power 超幂ultrabarrelled space 超桶型空间ultrabornological space 超有界型空间ultrafilter 超滤子ultrafilter space 超滤子空间ultrahyperbolic equation 超双曲型方程ultrametric space 超度量空间ultraproduct 超积ultraspherical polynomials 特种球多项式umbilical point 脐点unary operation 一元运算unary relation 一元关系unbiased confidence estimation 无偏置信估计unbiased estimate 无偏估计unbiased estimating equation 无偏估计方程unbiased estimator 无偏估计量unbiased sample 无偏样本unbiased test 无偏检验unbiasedness 无偏性unbounded function 无界函数unbounded interval 无界区间unbounded operator 无界算子unbounded quantifier 无界量词unbounded sequence 无界序列unbounded set 无界集unboundedness 无界性uncertainty 不定uncertainty principle 测不准原理unconditional convergence 无条件收敛unconditional inequality 无条件不等式unconditional jump 无条件跳跃unconditionally convergent 无条件收敛的unconditionally convergent series 无条件收敛级数unconnected graph 不连通图unconnected space 不连通空间unconnectedness 不连通性uncorrelated 不相关的uncorrelated random variables 不相关随机变量uncountability 不可数性uncountable 不可数的uncountable ordinal 不可数序数undecidability 不可判定性undecidability theorem 不可判定性定理undecidable theory 不可判定理论underdeterminate system 欠定组underdeterminate system of partial differential equations 欠定偏微分方程组underlying graph 底图underlying group 基础群underlying topological space 基础拓扑空间underlying topology 基础拓扑undetermined 未定的undetermined coefficient 末定系数undetermined number 未定数undirected edge 无向棱undirected graph 无向图undisturbed differential equation 无扰动微分方程unduloid 波状体unequal 不等的ungula of the cone 锥的蹄状体ungula of the cylinder 柱的蹄状体ungula of the prism 棱柱的蹄状体uniaxial 单轴的unicity 唯一性uniconvergence space 单收敛空间unicursal 单行的unicursal curve 有理曲线unicursal graph 单行图unicursal involution 单行对合unicursal surface 单行曲面unidirectional 单方面的unified field theory 统一场论uniform 匀的uniform approximation 一致逼近uniform boundedness principle 一致有界原理uniform continuity 一致连续性uniform convergence 一致收敛uniform cover 一致覆盖uniform distribution 均匀分布uniform equicontinuity 一致同等连续性uniform invariant 一致不变量uniform isomorphism 一致同胚uniform limit 一致极限uniform scale 等分标尺uniform space 一致空间uniform stability 一致稳定性uniform structure 一致结构uniform topology 一致拓扑uniformity 一致结构uniformity generated by a pseudometric 伪度量一致性uniformizable 可一致化的uniformizable point 单值化点uniformizable space 单值化空间uniformization 单值化uniformization principle 一般单值化定理uniformization theorem 单值化定理uniformization theory 单值化理论uniformizing covering surface 单值化覆盖面uniformizing function 单值化函数uniformly bounded 一致有界的uniformly bounded sequence of functions 一致有界函数序列uniformly bounded series 一致有界级数uniformly bounded set 一致有界集uniformly continuous 一致连续的uniformly continuous map 一致连续映射uniformly convergent 一致收敛的uniformly convergent sequence of functions 一致收敛函数序列uniformly convex 一致凸的uniformly convex space 一致凸空间uniformly distributed random variable 均匀分布随机变量uniformly elliptic operator 一致椭圆算子uniformly equicontinuous 一致同等连续的uniformly equivalent metric 一致等价度量uniformly equivalent space 一致等价空间uniformly integrable 一致可积的uniformly locally compact space 一致局部紧空间uniformly most powerful test 一致最大功效检定uniformly open map 一致开映射uniformly strongly elliptic operator 一致强椭圆算子uniformly summable family of functions 一致可积函数族unilateral 单侧的unilateral surface 单侧曲面unimodal 单峰的unimodal distribution 单峰分布unimodular group 幺模群unimodular map 幺模映射unimodular matrix 幺模阵unimodular number 单模数unimodularly bounded function 幺模有界函数union 并集union of sets 集的并unipotent element 幂幺元unipotent group 幂单群unipotent matrix 幂单矩阵unique existence 唯一存在性unique factorization domain 唯一析因整环unique factorization theorem 唯一析因定理unique solution 唯一解uniquely defined 唯一定义的uniqueness 唯一性uniqueness condition 唯一性条件uniqueness theorem 唯一性定理unirational variety 单有理簇uniserial algebra 单列代数unit ball 单位球unit character 单位特贞unit circle 单位圆unit disk 单位园板unit divisor 单位因子unit dyad 单位并向量unit filter 单位滤子unit function 单位函数unit group 单位群unit ideal 单位理想unit idele 单位伊代尔unit interval 单位区间unit line 单位线unit lower triangular matrix 单位下三角阵unit matrix 单位矩阵unit of angle 角的单位unit of area 面积单位unit of volume 体积单位unit operator 恒等算子unit point 单位点unit representation 恒等表示unit simplex 单位单形unit sphere 单位球unit square 单位平方形unit tangent 单位切向量unit tensor 单位张量unit theorem 单元定理unit transformation 恒等变换unit vector 单位向量unitarily equivalent operator 酉等价算子unitarily equivalent representation 酉等价表示unitarity 酉性unitary 单式的unitary algebra 单式代数unitary bundle 酉丛unitary connection 酉朕络unitary geometry 酉几何unitary group 酉群unitary homomorphism 单式同态unitary invariant 酉不变量unitary matrix 酉矩阵unitary modular group 特殊酉群unitary operator 酉算子unitary r module 单式r模unitary representation 酉表示unitary similar matrix 酉相似矩阵unitary space 酉空间unitary transfer 酉朕络unitary transformation 酉变换unity 单位元素unity element 单位元素unity group 单位群univalent 单叶的univalent function 单叶函数univariable series 单变量级数universal affirmative proposition 全称肯定命题universal bundle 通用丛universal class 全类universal coefficient formula 万有系数公式universal coefficient theorem 万有系数定理universal covering 通用覆盖universal covering group 通用覆盖群universal covering manifold 通用覆盖廖universal covering space 万有覆盖空间universal covering surface 万有覆盖面universal curve 万有曲线universal domain 万有域universal enveloping algebra 通用包络代数universal function 通用函数universal map 通用映射universal negative proposition 全称否定命题universal proposition 一般命题universal quantifier 全称量词universal relation 通用关系universal set 通用集合universal subgroup 通用子群universal validity 一般有效性universal variety 普遍簇universally japanese ring 伪几何环universally maximal left ideal 普遍极大左理想universally maximal twosided ideal 普遍极大双侧理想universally minimal right ideal 普遍极小右理想universally valid formula 普遍有效公式unknown 末知的unknown number 未知数unlimited 无限的unlimited covering manifold 无限覆盖廖unlimitedness 无穷unmixed ideal 纯理想unordered pair 无序对unparted hyperboloid 单叶双曲面unramified covering 非分歧覆盖unramified covering surface 非分歧覆盖面unramified extension 非分歧扩张unramified manifold 非分歧廖unramified prime ideal 非分歧素理想unramified ring 非分歧环unsolvability 不可解性unsolvable 不可解的unsolvable equation 不可解方程unstability 不稳定性unstable 不稳定的unstable solution 不稳定解unweighted mean 未加权平均数upper bound 上界upper central series 上中心列upper class 上类upper control limit 上控制限upper derivative 上导数upper envelope 上包络upper half plane 上半平面upper limit 上极限upper limit of integration 积分的上限upper pure value 上纯值upper quartile 上四分位数upper semi continuous decomposition 上半连续分解upper semicontinuity 上半连续性upper semicontinuous 上半连续的upper semilattice 上半格upper triangular matrix 上三角形矩阵upper value of game 对策上方值upper variation 正变差useful direction 有效方向utility 效用utility function 效用函数utility theory 效用理论。

数据结构专业英语词汇汇总

数据结构专业英语词汇汇总
- Data structure: 数据结构
- Array: 数组
- Linked list: 链表
- Stack: 栈
- Queue: 队列
- Binary tree: 二叉树
- AVL tree: AVL树 (一种自平衡二叉查找树)
- Red-black tree: 红黑树 (一种自平衡二叉查找树)
- Hash table: 哈希表
- Graph: 图
- Vertex: 顶点
- Edge: 边
- Adjacency list: 邻接表 (一种表示图的数据结构)
- Adjacency matrix: 邻接矩阵 (一种表示图的数据结构) - Heap: 堆
- Binary heap: 二叉堆 (一种特殊的堆数据结构)
- Priority queue: 优先队列 (用堆实现的一种队列)
- Trie: 字典树 (一种用于快速检索的树形数据结构)
- Big O notation: 大O符号 (一种表示算法时间复杂度的记号) - Sorting algorithm: 排序算法
- Searching algorithm: 算法
- Abstract data type (ADT): 抽象数据类型
- Hashing: 哈希函数的计算过程
- Collision: 哈希冲突 (发生在两个不同的键值被映射到相同的哈希桶时)。

耶茨算法析因设计

耶茨算法析因设计耶茨（Yates）算法，又称为焦炭算法或随机重排算法，是一种用于随机打乱或重排一个数组的算法。

它的设计思想是通过迭代遍历数组，每次取出一个元素与剩余未遍历的元素中的随机一个元素进行交换，从而构成一个随机排列的数组。

这样可以确保每个元素随机的概率是相等的。

耶茨算法的设计思想比较简单，但实现起来需要注意一些细节。

下面将详细解析耶茨算法的步骤和实现。

步骤一：遍历整个数组，从最后一个元素开始（i=n-1），依次向前遍历到第一个元素（i=1）。

步骤二：针对每个元素，生成一个随机的索引值r，取值范围是[0,i]，包括i。

步骤三：将当前元素与索引值r对应的元素进行交换。

步骤四：重复步骤二和步骤三，直到遍历完整个数组。

步骤五：返回打乱后的数组。

实现耶茨算法的关键是生成一个随机整数。

一种常用的实现方式是使用伪随机数生成器（PRNG），例如使用随机数种子和取余操作来生成一个随机的索引。

另外，需要注意的是，耶茨算法中使用的随机索引是包括当前遍历的元素的，这样可以保证每个元素随机被交换的概率是相等的。

以下是用Python实现耶茨算法的代码示例：```pythonimport randomdef yates_shuffle(arr):n = len(arr)for i in range(n-1, 0, -1):#生成随机索引r = random.randint(0, i)#交换当前元素和随机索引对应的元素arr[i], arr[r] = arr[r], arr[i]return arr```以上的代码实现了一个通用的耶茨算法打乱数组的函数，可以接受一个任意长度的数组作为输入，并返回打乱后的数组。

可以将该函数作为一个工具函数，用于在需要的时候对数组进行打乱操作。

耶茨算法是一种简单且高效的随机打乱数组的算法。

由于遍历整个数组并交换元素的操作，它的时间复杂度为O(n)，其中n是数组的长度。

通过使用耶茨算法，我们可以在保证每个元素随机的概率相等的情况下，快速地生成一个随机排列的数组。

ABAQUS Theory Manual

ABAQUS Theory ManualIntroductionThe ABAQUS software, developed by Dassault Systèmes, provides powerful capabilities for finite element analysis (FEA) and allows engineers and researchers to simulate and analyze the behavior of structures and materials under various loadings and boundary conditions. This theory manual aims to provide a comprehensive overview of the underlying principles and theories that form the foundation of ABAQUS.1. Finite Element MethodThe finite element method (FEM) is the basis of ABAQUS. This section will introduce the fundamental concepts and principles of FEM, including discretization, interpolation, element types, and numerical integration techniques. Understanding these concepts is essential for users to accurately model and analyze their structures using ABAQUS.2. Constitutive ModelsMaterial behavior is a crucial aspect of structural analysis. This section will cover the various constitutive models available in ABAQUS, including linear elasticity, nonlinear elasticity, plasticity, and viscoelasticity. Each model will be explained in detail, along with their mathematical formulations and implementation in ABAQUS. By understanding these models, users can accurately simulate the response of different materials under various loading conditions.3. Boundary Conditions and LoadingBoundary conditions and loading are essential components of structural analysis. This section will discuss the different types of boundary conditions and loading options available in ABAQUS. Topics such as fixed displacements, applied loads, temperature effects, and contact conditions will be covered. Users will learn how to appropriately define these conditions to accurately represent their structures in ABAQUS.4. MeshingMeshing is the process of dividing the model into small, interconnected elements to numerically solve the equations of motion. This section will explain the different meshing techniques available in ABAQUS, including structured and unstructured meshes. It will also discuss mesh refinement strategies and element quality considerations, which are crucial for obtaining accurate results. Users will learn how to create and refine meshes in ABAQUS to ensure reliable simulations.5. Solution TechniquesThis section will cover the various solution techniques available in ABAQUS. It will discuss the iterative solvers, direct solvers, and solution algorithms used to solve the system of equations obtained from the finite element model. The advantages and limitations of each technique will be explained, along with best practices for achieving efficient and accurate solutions in ABAQUS.6. Post-Processing and VisualizationPost-processing and visualization are vital for interpreting and analyzing simulation results. This section will introduce the different post-processing and visualization tools provided by ABAQUS. Topics such as result extraction, contour plots, animations, and xy plotting will be covered. Users will learn how to effectively visualize and interpret their simulation results using ABAQUS.7. Advanced TopicsThis final section will cover advanced topics in ABAQUS, including dynamic analysis, buckling analysis, thermal analysis, and coupled field analysis. Each topic will be explained in detail, along with relevant theory, modeling considerations, and solution techniques. Users will gain a deeper understanding of these advanced capabilities and learn how to apply them to their own projects.ConclusionThis ABAQUS Theory Manual provides a comprehensive overview of the underlying theories and principles behind ABAQUS. By understanding these theories, users can effectively model and analyze structures and materials using ABAQUS software. The manual covers a range of topics, from the basics of finite element method to advanced analysis techniques. With this knowledge, users can confidently utilize ABAQUS for their engineering and research projects.。

人工智能基础(习题卷9)

人工智能基础(习题卷9)第1部分：单项选择题，共53题，每题只有一个正确答案,多选或少选均不得分。

1.[单选题]由心理学途径产生，认为人工智能起源于数理逻辑的研究学派是（）A)连接主义学派B)行为主义学派C)符号主义学派答案:C解析:2.[单选题]一条规则形如：，其中“←"右边的部分称为(___)A)规则长度B)规则头C)布尔表达式D)规则体答案:D解析:3.[单选题]下列对人工智能芯片的表述，不正确的是（）。

A)一种专门用于处理人工智能应用中大量计算任务的芯片B)能够更好地适应人工智能中大量矩阵运算C)目前处于成熟高速发展阶段D)相对于传统的CPU处理器，智能芯片具有很好的并行计算性能答案:C解析:4.[单选题]以下图像分割方法中，不属于基于图像灰度分布的阈值方法的是( )。

A)类间最大距离法B)最大类间、内方差比法C)p-参数法D)区域生长法答案:B解析:5.[单选题]下列关于不精确推理过程的叙述错误的是（）。

A)不精确推理过程是从不确定的事实出发B)不精确推理过程最终能够推出确定的结论C)不精确推理过程是运用不确定的知识D)不精确推理过程最终推出不确定性的结论答案:B解析:6.[单选题]假定你现在训练了一个线性SVM并推断出这个模型出现了欠拟合现象，在下一次训练时，应该采取的措施是（）0A)增加数据点D)减少特征答案:C解析:欠拟合是指模型拟合程度不高，数据距离拟合曲线较远，或指模型没有很好地捕捉到数据特征，不能够很好地拟合数据。

可通过增加特征解决。

7.[单选题]以下哪一个概念是用来计算复合函数的导数？A)微积分中的链式结构B)硬双曲正切函数C)softplus函数D)劲向基函数答案:A解析:8.[单选题]相互关联的数据资产标准，应确保()。

数据资产标准存在冲突或衔接中断时，后序环节应遵循和适应前序环节的要求，变更相应数据资产标准。

A)连接B)配合C)衔接和匹配D)连接和配合答案:C解析:9.[单选题]固体半导体摄像机所使用的固体摄像元件为( )。

微积分介值定理的英文

微积分介值定理的英文The Intermediate Value Theorem in CalculusCalculus, a branch of mathematics that has revolutionized the way we understand the world around us, is a vast and intricate subject that encompasses numerous theorems and principles. One such fundamental theorem is the Intermediate Value Theorem, which plays a crucial role in understanding the behavior of continuous functions.The Intermediate Value Theorem, also known as the Bolzano Theorem, states that if a continuous function takes on two different values, then it must also take on all values in between those two values. In other words, if a function is continuous on a closed interval and takes on two different values at the endpoints of that interval, then it must also take on every value in between those two endpoint values.To understand this theorem more clearly, let's consider a simple example. Imagine a function f(x) that represents the height of a mountain as a function of the distance x from the base. If the function f(x) is continuous and the mountain has a peak, then theIntermediate Value Theorem tells us that the function must take on every height value between the base and the peak.Mathematically, the Intermediate Value Theorem can be stated as follows: Let f(x) be a continuous function on a closed interval [a, b]. If f(a) and f(b) have opposite signs, then there exists a point c in the interval (a, b) such that f(c) = 0.The proof of the Intermediate Value Theorem is based on the properties of continuous functions and the completeness of the real number system. The key idea is that if a function changes sign on a closed interval, then it must pass through the value zero somewhere in that interval.One important application of the Intermediate Value Theorem is in the context of finding roots of equations. If a continuous function f(x) changes sign on a closed interval [a, b], then the Intermediate Value Theorem guarantees that there is at least one root (a value of x where f(x) = 0) within that interval. This is a powerful tool in numerical analysis and the study of nonlinear equations.Another application of the Intermediate Value Theorem is in the study of optimization problems. When maximizing or minimizing a continuous function on a closed interval, the Intermediate Value Theorem can be used to establish the existence of a maximum orminimum value within that interval.The Intermediate Value Theorem is also closely related to the concept of connectedness in topology. If a function is continuous on a closed interval, then the image of that interval under the function is a connected set. This means that the function "connects" the values at the endpoints of the interval, without any "gaps" in between.In addition to its theoretical importance, the Intermediate Value Theorem has practical applications in various fields, such as economics, biology, and physics. For example, in economics, the theorem can be used to show the existence of equilibrium prices in a market, where supply and demand curves intersect.In conclusion, the Intermediate Value Theorem is a fundamental result in calculus that has far-reaching implications in both theory and practice. Its ability to guarantee the existence of values between two extremes has made it an indispensable tool in the study of continuous functions and the analysis of complex systems. Understanding and applying this theorem is a crucial step in mastering the powerful concepts of calculus.。

退位减法数学专业词汇英语词典

退位减法数学专业词汇英语词典Mathematics is a universal language that transcends cultural and linguistic boundaries. It is a language of logic, precision, and abstract reasoning that has shaped the course of human civilization. One of the fundamental concepts in mathematics is the operation of subtraction, which is often referred to as "taking away" or "removal." In the realm of advanced mathematics, subtraction takes on a more specialized term known as "retrograde operation" or "retrograde subtraction." This concept is particularly relevant in the study of number theory, where it forms the basis of various computational techniques and algorithms.Retrograde subtraction, also commonly referred to as "reverse subtraction" or "descending subtraction," is a method of subtracting a larger number from a smaller number. Unlike traditional subtraction, where the smaller number is subtracted from the larger number, retrograde subtraction involves subtracting the larger number from the smaller number. This operation is particularly useful in modular arithmetic, where numbers are considered within a specific range or modulus. By employing retrograde subtraction, mathematicians can work with negative numbers and effectively "wrap around" the modulus, ensuring that the result remains withinthe desired range.One of the key applications of retrograde subtraction is in the computation of modular inverses, which are essential in cryptography and other areas of mathematics. The modular inverse of a number is a value that, when multiplied by the original number and then taken modulo a specific value, results in a value of 1. Retrograde subtraction plays a crucial role in the extended Euclidean algorithm, which is commonly used to calculate modular inverses efficiently.Furthermore, retrograde subtraction finds applications in the study of congruences and number theory problems involving residues. It allows mathematicians to work with numbers in a more flexible manner, enabling them to navigate the intricate relationships between numbers within a specific modular system. This concept also has implications in the field of coding theory, where retrograde subtraction is used in the construction and analysis of error-correcting codes.Beyond its practical applications, retrograde subtraction also holds theoretical significance in the realm of abstract algebra and group theory. It is closely related to the concept of group inverses, where the inverse of an element in a group is defined as the element that, when combined with the original element through the groupoperation, results in the identity element. This connection highlights the deep algebraic underpinnings of retrograde subtraction and its role in the broader study of mathematical structures.In conclusion, retrograde subtraction, or "descending subtraction," is a specialized mathematical term that refers to the operation of subtracting a larger number from a smaller number. It is a fundamental concept in number theory, cryptography, coding theory, and abstract algebra, enabling mathematicians to work with numbers in a more flexible and efficient manner. The study of retrograde subtraction not only enhances our understanding of computational techniques but also sheds light on the intricate relationships between numbers and the underlying algebraic structures that govern them.。

quaruts 时序约束

quaruts 时序约束English Answer:Quarts Timing Constraints.Quartus Prime timing constraints drive the Quartus Prime timing analyzer engine to achieve fast and accurate timing analysis results. Timing constraints specify the timing relationships and requirements between different parts of the design. These constraints can be applied to clocks, registers, I/O ports, and other design components.Quartus Prime supports two main types of timing constraints:Static timing constraints (STCs) specify absolute timing relationships between two points in the design. For example, you can use STCs to specify the maximum or minimum time between a clock edge and a register setup time.Dynamic timing constraints (DTCs) specify timing relationships between two points in the design that may change over time. For example, you can use DTCs to specify the maximum or minimum time between a clock edge and a register setup time when the clock frequency is changing.Quartus Prime Timing Constraints Syntax.The syntax for timing constraints in Quartus Prime isas follows:<constraint_type> <constraint_name> <constraint_value>。

算法面试英文词汇

算法面试英文词汇以下是一些算法面试中可能会遇到的英文词汇：1. 算法分析：Algorithm Analysis2. 时间复杂度：Time Complexity3. 空间复杂度：Space Complexity4. 递归：Recursion5. 动态规划：Dynamic Programming6. 分治法：Divide and Conquer7. 贪心算法：Greedy Algorithm8. 回溯法：Backtracking9. 插入排序：Insertion Sort10. 快速排序：Quick Sort11. 归并排序：Merge Sort12. 堆排序：Heap Sort13. 二分查找：Binary Search14. 深度优先搜索：Depth-First Search (DFS)15. 广度优先搜索：Breadth-First Search (BFS)16. 优先队列：Priority Queue17. 并查集：Disjoint Set18. 线段树：Segment Tree19. 平衡二叉树：Balanced Binary Tree20. 红黑树：Red-Black Tree21. AVL树：AVL Tree22. 图论：Graph Theory23. 最小生成树：Minimum Spanning Tree (MST)24. 最短路径：Shortest Path25. Dijkstra算法：Dijkstra's Algorithm26. Bellman-Ford算法：Bellman-Ford Algorithm27. Floyd-Warshall算法：Floyd-Warshall Algorithm28. 拓扑排序：Topological Sort29. 网络流：Flow in Networks30. 最少生成树：Minimum Cost Spanning Tree (MCTS)31. 二分图匹配：Bipartite Matching32. 并查集操作：Union, Find, Union-by-Rank, Path Compression33. 二叉堆操作：Insert, Delete, Decrease Key, Increase Key, Merge34. 数据结构操作：Insert, Delete, Search, Get Size, Is Empty, Clear35. 链表操作：Create, Delete, Insert Before, Insert After, Print, Find, Merge36. 数组操作：Sort, Reverse, Find Max/Min, Find Index of Max/Min, Rotate, Transpose37. 树操作：Create Root, Insert Node, Delete Node, Find Node, Find Parent of Node, Print Tree38. 图操作：Create Graph, Add Edge, Delete Edge, Find Nodes Connected by Edge, BFS/DFS from Source Node39. 图论问题常见术语：Vertex Cover, Independent Set, Connected Component, Shortest Path, Bipartite Checking, Max Flow/Min Cut 40. 其他常见术语：Big O notation, Amortized analysis, Randomized algorithm, NP-hard problem41. 其他常用算法术语：Divide and Conquer approach, Greedy approach, Dynamic Programming approach42. 动态规划的边界情况处理：Base case/Recursion case。

微分几何中的英文单词和短语

Chapter 3 Intrinsic Geometry of Surfaces
共变导数
covariant derivative
高斯方程
Gauss equation
曲面局部理论的 fundamental theorem of local theory
基本定理
of surface
高斯-博内定理 Gauss-Bonnet theorem
超曲面空间旋轮线高斯曲率伸展曲面方向导数黑塞矩阵椭圆点
hyper surface space cycloid Gauss curvature elongated surface directional derivative Hessian matrix elliptic point
第三章曲面的内蕴几何
第四章常曲率空间
Chapter 4 Spaces of Constant Curvature
双曲空间截空间弧长的变差最短路径旋转群四元数空间双二面体群等度量变换等距表示
hyperbolic space truncated space variation of arc length shortest path rotation group quaternion space double dihedral group isometric transformation isometric representation
正方环面黎曼流形切线空间
square torus Riemannian manifold tangent space
第五章黎曼流形
Chapter 5 Riemannian Manifold
凯莱映射链规则复流形可数性公理曲率张量共变张量对偶基爱因斯坦空间爱因斯坦张量克莱因瓶拉普拉斯算子李导数测度张量距离张量射影平面旋转矩阵

利特伍德理查德森规则英文

利特伍德理查德森规则英文English:The Littwood-Richardson rule is a combinatorial algorithm for calculating the Littlewood-Richardson coefficients, which arise in representation theory and algebraic geometry. These coefficients are a fundamental and important part of algebraic combinatorics and have applications in various fields such as quantum physics, quantum computation, and computer science. The rule provides a method for decomposing the tensor product of irreducible representations of a symmetric group into a direct sum of irreducible representations. It is an essential tool for understanding the structure of tensor products and has important implications in the study of symmetric functions and Schur functions.中文翻译:利特伍德理查德森规则是一种组合算法，用于计算利特伍德理查德森系数，这些系数出现在表示论和代数几何中。

这些系数是代数组合学的基本和重要部分，并在量子物理学、量子计算和计算机科学等各个领域得到应用。

人工智能基础_青岛大学中国大学mooc课后章节答案期末考试题库2023年

人工智能基础_青岛大学中国大学mooc课后章节答案期末考试题库2023年1.AlphoGo在落子选择时用的搜索技术是答案:蒙特卡洛树搜索2.下面关于搜索过程描述错误的是答案:对CLOSED表上的节点进行排序的准则，以便选出一个“最好”的节点作为扩展使用3.以下关于与或树说法错误的是答案:或树中各子节点间用弧链接4.以下关于博弈理论说法错误的是答案:博弈双方均力图选取对自己最为不利的方案5.以下关于说法错误的是答案:剪枝就是在搜索深度不变的情况下，利用已有的搜索信息增加生成的节点数6.关于鲁滨逊归结原理叙述错误的是答案:若子句集S不包含空子句，则称子句集S是可满足的7.下面关于概率分配函数说法错误的是答案:样本空间的概率分配函数值为08.以下关于模糊集合的运算说法错误的是答案:A交B的隶属度等于对应元素隶属度的大者9.以下不是常用的模糊推理模式的是答案:模糊因果推理10.以下哪一项不属于专家系统知识库的建立环节答案:知识排序11.下列属于人工智能的知识表示方法的有答案:状态空间表示法逻辑表示法本体表示法产生式表示法12.状态空间表示法用（）和（）来表示问题算符状态13.以下情况首选广度优先搜索的有答案:问题的解出现在相对较浅的水平分支因子不是太大没有一条路径是特别深的14.下面关于爬山法叙述正确的是答案:随机选择一个登山的起点每次拿相邻点与当前点进行比对，取两者中较优者，作为爬坡的下一步选择最大点作为本次爬山的顶点，即为该算法获得的最优解重复直至该点的邻近点中不再有比其大的点15.爬山法中可能遇到的问题有山篱问题高原问题山脊问题16.下面关于最佳优先搜索叙述正确的是答案:open表中节点按照节点接近目标状态的启发式估值实现需要open表和closed表不保留重复状态是一种智能搜索算法17.动态规划算法的特点包括答案:使用最优化原理无后效性有重叠子问题18.搜索算法的评价指标包括答案:完备性最优性单调性可接受性19.关于知识表示叙述正确的有答案:知识表示就是把知识形式化或者模型化好的知识表示形式应便于理解知识表示是一种计算机可以接受的数据结构知识表示具有一定的针对性和局限性20.常用的连接词有答案:蕴含析取否定合取21.推理过程中常用的等价性包括答案:德摩根律结合律分配律交换律22.一个良好的规则库应该具有以下哪些特性答案:知识一致表达灵活知识完整组织合理23.模糊集可用的描述方式有答案:图示表示法扎德表示法函数表示法向量表示法24.专家系统中的知识包括答案:知识库级知识数据级知识控制级知识25.专家系统包括答案:推理机综合数据库知识库26.以下哪些情况适合开发为专家系统答案:问题需要使用启发式知识、经验规则才能得到答案问题有一定的实用价值问题可以通过符号操作和符号结构进行求解问题相对较为复杂27.模仿还原就是一个从当前混乱状态寻找路径到达期望即目标状态的过程答案:正确28.如果所求序列可以使得总代价最低，则问题称为最优搜索问题。

大连理工大学智慧树知到“选修课”《专业英语(计算机英语)》网课测试题答案3

大连理工大学智慧树知到“选修课”《专业英语（计算机英语）》网课测试题答案（图片大小可自由调整）第1卷一.综合考核(共15题)1.CD is designed to read the disks and translate the data into a it can process.()A.正确B.错误2.However what really triggered the tremendous growth of computers and its significant impact on our lives is the invention of the microprocessor.()A.正确B.错误3.An audio wave is a two-dimensional acoustic wave.()A.正确B.错误4.Click the backward Undo arrow to cancel the first action you performed.()A.正确B.错误5.Most networks-even those with just two computers also contain a hub or switch to act as a connection point between the computers.()A.正确B.错误6.The keyboard is classified as a of output.()A.正确B.错误7._____ is an operating system similar to Unix.A.Windows NTB.MS-DOSC.OS/2D.Linux8.A computer can be broken down into three distinct categories, namely output, and CPU.()A.正确B.错误9.It wasn't until the 1980's that people began buying computer for personal use.()A.正确B.错误10.The fourth generation computers can be characterized by both the jump to monolithic integrated circuits and the invention of _____.A.microprocessorB.transistorC.chipD.circuit11.A(n) _____ mouse emits and senses light to detect movement.A.cordlessB.opticalC.cameraD.microphone12.Each web page has a unique address, called a URL that identifies its location on the network.()A.正确B.错误13.A computer must include three of following. Which one is not necessary?A. systemB.output systemC.processing systemworking system14.A network interface on each computer, usually called a network interface card(NIC) or adapter.()A.正确B.错误15.Microsoft Office 2000 includes Word, _____, Outlook and FrontPage.A.ExcelB.Power PointC.AccessD.All of the above第2卷一.综合考核(共15题)1.Database management system(DBMS) programs are designed to work with data that is logically structured or arranged in a particular way, known as _____.A.data modelB.databaseC.inationD.data2.A _____ is a collection of relation fields.A.fieldB.recordC.characterD.file3.Which one is an image-editing tool?A.PhotoshopB.WordC.Extreme 3DD.Premiere4.To access the Web, users require a _____, which is the software program used to access the World Wide Web.A.Plug-insB.HelperC.Add-onsD.Web browser5.Telnet enables users to cute terminal sessions with local hosts.()A.正确B.错误6._____ provides reliable, full-duplex connections and reliable service by ensuring that data is resubmitted when transmission results in an error.A.TCPB.ARPC.UDPD.IP7.Click the open folder button to open an existing workbook.() A.正确B.错误8.Which of the following is not a format for a graphical image file?A.BMP fileB.GIF fileC.JPG fileD.AVI file9.TCP/IP application layer protocols include the following except _____.A.HTTPB.FTPC.UDPD.Telnet10.C is an object-oriented programming language.()A.正确B.错误11.Transistors were a tremendous breakthrough in advancing the computer.()A.正确B.错误12.A VPN offers the security and full data access of a private WAN, but because it runs over the Internet, it is more affordable and complex.()A.正确B.错误13.ERP is _____.A.Enterprise resource planning softwareB.Enterprise Application IntegrationC.Electronic Application IntegrationD.None of the above.e the spell checker to correct spelling errors on the worksheet.()A.正确B.错误15.FTP performs basic interactive file transfers between hosts.()A.正确B.错误第1卷参考答案一.综合考核1.参考答案：B2.参考答案：A3.参考答案：B4.参考答案：B5.参考答案：A6.参考答案：B7.参考答案：D8.参考答案：A9.参考答案：B10.参考答案：A11.参考答案：B12.参考答案：A13.参考答案：D14.参考答案：A15.参考答案：D第2卷参考答案一.综合考核1.参考答案：A2.参考答案：D3.参考答案：A4.参考答案：D5.参考答案：B6.参考答案：A7.参考答案：A8.参考答案：D9.参考答案：C10.参考答案：B11.参考答案：A12.参考答案：A13.参考答案：A14.参考答案：A15.参考答案：A。

qt牛顿插值算法

qt牛顿插值算法Qt牛顿插值算法牛顿插值算法是一种常用的数值插值方法，用于构造一条通过给定数据点的多项式曲线。

它由英国数学家艾萨克·牛顿于17世纪提出，并被广泛应用于科学计算和工程领域。

牛顿插值算法的基本思想是根据给定的数据点，构造一个逐步逼近的多项式函数。

这个多项式函数通过给定数据点的横坐标和纵坐标来确定，可以用于在给定数据点之外的位置进行插值计算。

具体来说，牛顿插值算法通过构造一个拉格朗日插值多项式的等价形式，使用差商的概念来递归地计算多项式的系数。

差商表示了给定数据点之间的差异和变化率，它是通过逐步逼近的方式来构造多项式的关键。

在Qt中，实现牛顿插值算法的步骤如下：1. 准备数据点：首先，需要准备一组给定的数据点，包括横坐标和纵坐标。

这些数据点可以来自于实际测量或者是由其他方法计算得到的。

2. 计算差商：根据给定的数据点，使用差商的概念来递归地计算多项式的系数。

差商的计算可以使用递归的方式，从而减少计算量。

3. 构造多项式：通过差商的计算结果，构造牛顿插值多项式。

多项式的形式可以表示为f(x) = a0 + a1(x-x0) + a2(x-x0)(x-x1) + ...，其中a0、a1、a2等系数是通过差商计算得到的。

4. 插值计算：通过构造的多项式，可以进行插值计算。

给定任意一个横坐标x，通过多项式计算可以得到对应的纵坐标y，实现了对给定数据点之外位置的插值计算。

牛顿插值算法的优点是计算简单、效率高，且在插值计算过程中不需要重新计算整个多项式。

它的缺点是在插值区间的两端，多项式的误差较大，需要增加插值点的密度来提高插值精度。

总结一下，牛顿插值算法是一种常用的数值插值方法，通过逐步逼近的方式构造多项式函数，实现对给定数据点之外位置的插值计算。

在Qt中，可以使用差商的概念来递归地计算多项式的系数，并通过构造的多项式进行插值计算。

牛顿插值算法简单高效，但在插值区间的两端误差较大，需要增加插值点的密度来提高插值精度。

intriguing properties of neural networks 精读

intriguing properties of neural networks 精读Intriguing Properties of Neural NetworksIntroduction:Neural networks are a type of machine learning model inspired by the human brain's functioning. They are composed of interconnected nodes known as neurons that work together to process and analyze complex data. Neural networks have gained immense popularity due to their ability to learn, adapt, and make accurate predictions. In this article, we will delve into some of the intriguing properties of neural networks and explore how they contribute to their success in various fields.1. Non-linearity:One of the key properties of neural networks is their ability to model nonlinear relationships in data. Traditional linear models assume a linear relationship between input variables and the output. However, neural networks introduce non-linear activation functions that allow them to capture complex patterns and correlations. This property enables neural networks to excel in tasks such as image recognition, natural language processing, and voice recognition.2. Parallel Processing:Neural networks possess the remarkable ability to perform parallel processing. Unlike traditional algorithms that follow a sequential execution path, neural networks operate by simultaneously processing multiple inputs in parallel. This parallel architecture allows for faster and efficientcomputations, making neural networks suitable for handling large-scale datasets and real-time applications.3. Distributed Representation:Neural networks utilize distributed representation to process and store information. In traditional computing systems, data is stored in a centralized manner. However, neural networks distribute information across interconnected neurons, enabling efficient storage, retrieval, and association of knowledge. This distributed representation enhances their ability to learn complex patterns and generalize from limited training examples.4. Adaptability:Neural networks exhibit a high degree of adaptability, enabling them to adjust their internal parameters and optimize their performance based on changing input. Through a process called backpropagation, neural networks continuously learn from the errors they make during training. This iterative learning process allows them to adapt to new data and improve their accuracy over time. The adaptability of neural networks makes them robust to noise, varying input patterns, and changing environments.5. Feature Extraction:Neural networks are adept at automatically extracting relevant features from raw data. In traditional machine learning approaches, feature engineering is often a time-consuming and manual process. However, neural networks can learn to identify important features directly from the input data. This property eliminates the need for human intervention and enables neuralnetworks to handle complex, high-dimensional data without prior knowledge or domain expertise.6. Capacity for Representation:Neural networks possess an impressive capacity for representation, making them capable of modeling intricate relationships in data. Deep neural networks, in particular, with multiple layers, can learn hierarchies of features, capturing both low-level and high-level representations. This property allows neural networks to excel in tasks such as image recognition, where they can learn to detect complex shapes, textures, and objects.Conclusion:The intriguing properties of neural networks, such as non-linearity, parallel processing, distributed representation, adaptability, feature extraction, and capacity for representation, contribute to their exceptional performance in various domains. These properties enable neural networks to tackle complex problems, make accurate predictions, and learn from diverse datasets. As researchers continue to explore and enhance the capabilities of neural networks, we can expect these models to revolutionize fields such as healthcare, finance, and autonomous systems.。

A type-A-choking-oriented unified model for fast fluidization dynamics

A type-A-choking-oriented uni ﬁed model for fast ﬂuidization dynamicsMing-Chuan Zhang ⁎,Chu ZhangSchool of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,Chinaa b s t r a c ta r t i c l e i n f o Article history:Received 9October 2012Received in revised form 24January 2013Accepted 26January 2013Available online 13March 2013Keywords:Fast ﬂuidizationSeparate-phase model Type A choking Solids holdupHigh-density fast-bedStarting from analysis to Yang's formula for type A choking,a uni ﬁed and self-consistent model for fast ﬂu-idization dynamics,named the separate-phase-coexistence model,was proposed in this paper.The basic assumptions used in the model are that all the gas from outside enters the solid-saturated upward dilute phase,to which the Yang's formula is still applied,yet revised with an effective velocity factor F (β);while the clusters fall down freely at a velocity consistent with their voidage.The impact of falling clusters on the upward dilute phase was considered with the equivalent wall friction,from which the method to predict the apparent solids holdup of upper dilute region was obtained.The force balance for falling clusters was also an-alyzed,from which the cluster voidage was determined.When the cluster viodage reaches its minimum value,a small part of outside gas will invade the cluster,resulting in the so-called “secondary ﬂuidization of clusters ”.It well predicted that the solids holdups of upper dilute region and bottom dense region did not change obviously with further increase of the solid circulation rate,the most impressive feature of high-density fast beds.Further-more,by analogy to bubbling beds,the phenomena of clusters in risers of fast beds were analyzed in a meso-scale mechanism,from which the effective velocity factors of dilute phase F (β)were theoretically determined.And the solid-wall friction factors in Yang's formula and the Harris's correlation for cluster size were also reconstructed based on the experimental data available in the literatures.Without any model parameters adjusted,the uni ﬁed model predicted successfully the type C choking,the solids holdups for both upper dilute region and bottom dense region,and the transitions to high-density fast bed and dense suspension up-ﬂow.The predictions were compared with several hundreds of experimental data available in the literatures,which veri ﬁed well the model's uni ﬁcation and acceptable accuracy.©2013Elsevier B.V.All rights reserved.1.IntroductionFast ﬂuidization or circulating ﬂuidized bed (CFB)has attracted people more and more attention in chemical,metallurgy,energy en-gineering and other applied ﬁelds as an ef ﬁcient gas-solid contacting technology [1–3].With certain rate of particle circulation,fast ﬂuid-ization provides the possibility that small particles could be operat-ed under quite high gas velocity due to agglomeration of particles in the CFB riser.Under this condition,the fast ﬂuidized bed is charac-terized by a non-uniform axial distribution of particle concentration,where the solids holdup is small in the top,and large in the bottom.The basic requirements to form a fast ﬂuidized bed are generally de-scribed as [4]:i)the circulating solid ﬂux G s is greater than the min-imum value of that G sm ;and ii)for a given solid ﬂux G s >G sm ,the super ﬁcial gas velocity u f is kept within the range of velocities for type A choking and type C choking,i.e.u ch,C b u f b u ch,A .A large number of studies have been done to ﬁnd how these char-acteristic parameters change with properties of the gas and the solid,the system geometry,and operating conditions.Empirical correla-tions were usually given in the form of non-dimensional criteria.For example,correlations for different types of choking were given by Yang [5,6],Yous ﬁand Gau [7],and other researchers [8–10].There were also quite a lot empirical correlations of solids holdups for both the upper dilute region and the bottom dense region [11–15].However,most of these studies were carried out separately;there were little physical relations among them.In some cases,incompatible results would be predicted from these empirical correlations,for in-stance u ch,A b u ch,C .On the other hand,the recently recognized “high density fast ﬂuidization (HDFF)”[16]and “dense suspension up-ﬂow (DSU)”[17]have shown some different two-phase-ﬂow behaviors.How these ﬂow regimes relate with the traditional one are also not clear.The present work tried to establish a self-consistent model for fast ﬂuidization dynamics,in which all the characteristic parameters mentioned above can be easily deduced from a same origin;and the uni ﬁed model can be applied for both traditional fast ﬂuidized bed and high density fast ﬂuidized bed.2.Theoretical considerations 2.1.Start point of the modelConcepts of choking in vertical upward co-current gas –solid systems have been used for a long time to describe some critical conditions,atPowder Technology 241(2013)126–141⁎Corresponding author.E-mail address:mczhang@ (M.-C.Zhang).0032-5910/$–see front matter ©2013Elsevier B.V.All rights reserved./10.1016/j.powtec.2013.01.070Contents lists available at SciVerse ScienceDirectPowder Technologyj o u r na l h o me p a g e :ww w.e l s e v i e r.c o m /l o c a t e /p o w t e cwhich the two-phase ﬂow system cannot run properly or ef ﬁciently.For systems with different application purposes,the de ﬁnitions may also be different.In a pneumatic conveying system,the choking is usually de-ﬁned as the onset of particle precipitation downward,which makes the transportation less ef ﬁcient.However,it doesn't breach the system operation as a whole.On the opposite,in a CFB riser the choking is usu-ally de ﬁned as a critical condition,at which a small decrease of operat-ing gas velocity or increase of circulating solid ﬂux will cause signi ﬁcant increase of bed pressure drop,leading to collapse,to some extents,of the whole system.Differences of the two types of choking did not get enough attention until Bi and Grace [18],where the former was de ﬁned as the accumulative choking or type A choking,and the latter as the classical choking or type C choking.Predictions to type A choking and type C choking are obviously im-portant for fast ﬂuidization,since they will determine the allowable ranges for gas velocity or solid circulation ﬂux.There were quite a lot of formulas developed in the past to correlate the gas velocities and the solid ﬂuxes at the two types of choking.However,only one of them can be chosen as the start point of the uni ﬁed model,while the other should be deducted from the chosen one.Considering the re-search history for pneumatic conveying system is much longer than that for fast ﬂuidized bed,and the two-phase ﬂow structure in the for-mer is much simpler than that in the latter,it is believed that the theo-retical and experimental bases for type A choking are more reliable and universal.Among the numerous formulas existed in the literatures for type A choking,the form of Yang's formula [5,6]looks the best,since deriva-tion of the formula involves only two theoretical deductions.The ﬁrst one is that the terminal velocity of particles for a uniform suspension of voidage εin a riser of diameter D t can be calculated from Eq.(1).u 0t ¼u t ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1þf p u 2pt!Âε4:7v u u t ð1ÞWhere,u p =G s /[ρs (1−ε)]is the particle velocity,while f p stands for the solid-wall friction factor.This is a theoretically logical formula,and detailed derivation and discussion on that can be found in Yang's series work from 1973to1975[5,19,20].The second deduction is when type A choking happens,the slip velocity between gas and solid,i.e.the terminal velocity of a particlesuspension in a ﬁnite diameter riser u t',is just equal to the terminal velocity of a single particle in the in ﬁnity u t [5,6].u 0t ¼u tð2ÞThis deduction was actually used in the derivation of Yang's pre-dictive equation [5,6](Eq.(3)),but was not clearly declared and explained in his work.2D t g ε−4:7ch −1 u ch −u t ðÞ2¼f p ð3ÞThe followings are the present authors'try to explain “what does the deduction really mean?”It can be seen from Eq.(1),the ﬁrst item withsquare root sign ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1þf pu 2p2gD tr represents the in ﬂuence of wall friction onu t',since it will always be unity in an in ﬁnitely wide riser.When D t gets smaller,the wall friction gets greater,then u t'gets greater.The second item with square root sign ﬃﬃﬃﬃﬃﬃﬃﬃε4:7p represents the in ﬂuence of bed voidage,i.e.the in ﬂuence of surrounding particles.When the particleconcentration (1−ε)gets greater,εgets smaller,then u t 'gets smaller.The reason is that the surrounding particles will cause both increase ofreal gas velocity ﬃﬃﬃﬃﬃε2pand more ﬂexuous ﬂow-pass of gas around theparticle,then increase of the drag force coef ﬁcient ﬃﬃﬃﬃﬃﬃﬃﬃε2:7p[21].There-fore,the amendment of u t 'is on the basis of super ﬁcial gas velocity.If we resolve the increased ﬂuid drag on one particle in a uniform suspension into the basal ﬂuid drag on a single particle F f and the sur-plus F s due to the surrounding particles,the overall force balance for the suspension,or a single particle in a long time duration,can be expressed asF f þF s ¼G þW ð4Þwhere,G stands for the gravity of particle or particle suspension,whileW for the wall friction.Comparing the values of F s and W ,two different situations can be distinguished.For a relatively dilute suspension,the drag force caused by the surrounding particles is relatively small,resulting in F s b W ,and then F f >G .The ﬂuid drag given by the gas solely F f is greater than the gravity of the particle,which means that besides supporting the particle there will be something rest to balance the wall friction,simply shown as F f −G =W −F s .This will be a relatively simple dy-namic system centered on each single particles;the relatively indepen-dent movement of these particles will lead to a uniformly dispersed gas-solid two phase ﬂow,i.e.the custom dilute suspension transporta-tion.On the opposite,if we have F s >W and F f b G ,the ﬂuid drag given by the gas F f will no longer be able to support the particle gravity solely,but needs something else from the surrounding particles,simply shown as F f +(F s −W )=G .Then the force balance for any particle will depend more on the others,making the dynamic system more complex and easier to lose its uniformity.For instance,an occasionally local condensation of particles will result in less gas ﬂowing through them and decrease of F f ,which will make these particles to move close further to increase F s as the overall force balance needs.This may probably be the physical reason of cluster formation for the case of F s >W .Therefore,what can be used to separate the two different types of ﬂows mentioned above is just the criteria of F s =W or F f =G ,i.e.u t'=u t from their de ﬁnitions.It means that the in ﬂuence of ﬁnite riser diameter D t on u t'is just compensated by the in ﬂuence of bed voidage εat the type A choking.At this unique condition,the moving particle looks as if there is neither wall nor surrounding particles.The authors suggest that this is the real meaning of the deduction,and then can be seen as the physical essence of type A choking.Just because of its sound physical meaning,the relationship given by Eq.(3)for the super ﬁcial gas velocity and the bed voidage under solid-saturated conditions (type A choking)can be considered as “inherent ”,then the equation as “constitutive equation ”.However,it should also be pointed out here,the functional relation of u ch and εch is the most important in Eq.(3),but not the value of f p at this moment.Actually,the solid friction factor f p =0.01was taken originally by Yang in 1975[5],and changed later to the present form in 1983[6]f p ¼6:81Â105ρgρs2:2:ð5ÞThe rationality or accuracy of above mentioned values for f p will bediscussed in detail and re-correlation of f p with more experimental data will be made later in Section 3.3.For the time being,the solid fric-tion factor used in the calculations before Section 3.3was f p =0.01,the value given in 1975[5],since it was better than the other according to the accuracy evaluation of Xu et al.[10].2.2.Physical description of the modelAs we discussed above,Eq.(3)shows the relationship of super ﬁcial gas velocity u ch and bed voidage εch under solid-saturated conditions,127M.-C.Zhang,C.Zhang /Powder Technology 241(2013)126–141i.e.type A choking.For a given ﬂuidizing system,when u ch increases,εch will decrease;then the particle concentration (or solids hold-up)(1−εch )increases,and the saturation carrying capacity of gas G s ⁎will increase even faster.G Ãs ¼ρs u ch −u t ðÞ1−εchεchð6ÞThe equation derived here is a little bit different from what was used in Yang's articles [5,6]by 1/εch ,since the modi ﬁcation of ﬃﬃﬃﬃﬃﬃﬃﬃε4:7p includes also the in ﬂuence of the gas velocity ﬃﬃﬃﬃﬃε2p ,then the real par-ticle velocity is (u ch −u t )/εch .As an example,Fig.1shows the cal-culated results of (1−εch )and G s ⁎varied with u ch for a FCC-air ﬂuidizing system.It can be seen from the ﬁgure that the saturation carrying capacity G s ⁎varies with the super ﬁcial gas velocity u ch in an exponential form with power >1.Just because of this special relationship between G s ⁎and u ch ,one can imagine when the circulating solid ﬂux is greater than G s ⁎at a given gas velocity,the system will not completely collapse but run in a more complicated separate-phase-coexistence mode.Some par-ticles will segregate from the gas stream and get agglomerated to form a free-falling dense phase (clusters),which occupies a part of the riser cross-sectional area,but without outer gas getting in;while in the rest of the riser,more concentrated gas with higher ve-locity could carry even more particles upward in the form of dilute phase.Without outer gas getting in clusters is a logical deduction from two-way stability analysis,and is coincident with Mueller and Reh's investigation [22],i.e.“the acceleration of particle inside the strand (cluster)is equal to the acceleration of free fall,which implies that no drag force acts on the particle within the strand ”[21].Let βbe the cross-sectional area fraction occupied by the falling dense phase or clusters,which is also the volume fraction of randomlydistributed clusters;m s−as the corresponding solid ﬂux downward,and m s +as the solid ﬂux upward in solid-saturated dilute phase.Both m s+and m s −are de ﬁned on the basis of the total cross-sectional area,but not their own occupied.Then,the solid ﬂux circulating into the riser G s can be expressed as G s ¼m þs −m −s :ð7ÞThe sketch map for m s +and m s −varied with βat a constant gas velocity is shown in Fig.2.It can be seen from the ﬁgure,if we haved m þs d βj β¼0>d m −sd βj β¼0;ð8Þthe separate-phase-coexistence mode can really transport more par-ticles upward in the riser than the saturation carrying capacity ofgas at type A choking,i.e.G s =m s +−m s −>G s ⁎.This will be trueuntil a critical point β=βch is reached,where d m þs d βj β¼βch ¼d m −sd βj β¼βch;ð9Þand the transportable solid ﬂux at the given gas velocity takes its max-imum value G s,max .Beyond this point the separate-phase-coexistence mode has no more ability to balance the excess solid ﬂux,leading to the system being totally “collapsed ”,i.e.the type C choking.The analysis above indicates also that the critical requirement for separate-phase-coexistence mode is d m þs d βj β¼0¼d m −sd βj β¼0:ð10ÞThis criterion can be used for determination of G sm ,which will bediscussed later elsewhere.As a sum,the key points af ﬁrmed or the basic assumptions to be used in the uni ﬁed model are as follows:i)the relationship between bed voidage εch and gas velocity u ch given by Yang's formula for type A chok-ing can be seen as “inherent ”or “constitutive ”for solid-saturated dilute phase,which provides the theoretical basis of the model;ii)with neces-sary amendment,this relationship can also be applied for the solid-saturated upward dilute phase when coexisted separate-phases appear;and iii)in the separate-phase-coexistence mode,all the gas from outside enters the solid-saturated upward dilute phase,while the clusters fall down freely at a velocity consistent with their voidage (ex-cept for HDFF or DSU).3.Mathematical model kernels3.1.Model kernels3.1.1.Dilute phase modelAs discussed above,at type A choking,the very beginning of the separate-phase-coexistence mode (β=0),the gas –solid slip velocity can take the value of terminal velocity of a single particle u t .When separate phases visibly appear,due to the impact of falling clusters,it is expected that the saturation carrying capacity per unit gas in the dilute phase will be less than that for β=0.It means that the gas –solid slip velocity in this case has increased.However,this im-pact can also be expressed by decrease of the effective gas velocity in dilute phase,while keeping the slip velocity unchanged.This can123456G *s (k g /m 2s )u ch (m/s)1-c hεFig.1.Saturated carryings G s ⁎and solid concentration (1−εch )at different gas velocity u ch (FCC –air system,ρs =1620kg/m 3,d p =100μm,D t =0.1m).G s ,m sG *schββFig.2.Sketch map for m s +and m s −varied with βat constant gas velocity.128M.-C.Zhang,C.Zhang /Powder Technology 241(2013)126–141be easily done by using an effective velocity factor of dilute phase F (β)b 1in the calculation.Thus,the upward solid ﬂux based on unit dilute phase area can be expressed as G þs ¼ρsu f F βðÞ−u t !1−εch εch ;ð11Þand the relationship between the calculation velocityu Ãch¼u f F βðÞ1−βand the solid-saturated dilute phase viodage εch still ﬁts the revised Yang's formula,as we discussed above.Therefore,the super ﬁcial up-ward solid ﬂux de ﬁned on the basis of the total cross-sectional area of the riser will be m þs ¼ρs u f F βðÞ−u t 1−βðÞ½1−εchεch:ð12ÞFrom the analysis above,the function F (β)chosen should meet the requirements of F βðÞj β¼0¼1;andd F βðÞd βjβ¼0¼0:ð13ÞThe simplest form of that is F βðÞ¼1−c βn:ð14ÞAs βincreases,the impact of falling clusters gets greater andgreater.The upward solids ﬂux of dilute phase m s+will reach its max-imum,then decrease gradually until slugging occurs at β=1.Sincethe solid ﬂux m s+at slugging is still ﬁnite but not zero,it can be roughly estimated that m s +|β=1=G s ⁎,i.e.the saturation carryingcapacity of gas at type A choking G s ⁎(see Fig.2).From that,we haveρs u f F 1ðÞ½ 1−εslεsl ¼ρs u f −u t ½ 1−εch ;A εch ;Að15Þwhere F (1)is the value of F (β)at β=1;εsl and εch,A are the bedvoidages for slugging (β=1)and type A choking (β=0),respec-tively.Therefore,F 1ðÞ¼1−u t f1−εch ;A εch ;A εslsl:ð16ÞSuppose the solid span equals to the gas span when slugging occurs,and the voidage equals εmf in the solid span,then we have the average asεsl ¼1−1−εmf ðÞ=2:ð17ÞFinally,the effective velocity factor of dilute phase F (β)can be calcu-lated asF βðÞ¼1−1−F 1ðÞ½ βn:ð18Þ3.1.2.Dense phase modelThe sub-model for dense-phase or falling clusters is relatively simple in form,i.e.m −s ¼ρs βu cl 1−εcl ðÞ:ð19ÞAs we mentioned above,the falling velocity of clusters u cl should be in consistence with their voidage εcl to keep the outside gas ﬂow within the cluster being zero.Therefore,the modi ﬁed Richardson –Zaki'sequation [23]must be satis ﬁed for the force balance of gas-particles in-side of clusters,i.e.u cl ¼u tεcl1m¼u t εm cl :ð20ÞHere,m ¼lg u mfu t=lg εmf ;ð21Þand εmf =0.45was used in the following calculations.However,to determine both εcl and u cl ,a supplementary condi-tion is needed.This will be discussed later in Section 5.1,i.e.the weight of clusters should be balanced by the inter-phase drag,which can be solved with other parameters together through itera-tions.Nevertheless,for the initial value of εcl with iteration or a sim-pli ﬁed calculation (no iteration)a rough estimation is still needed.According to the experimental data collected by Harris and Davidson [24],the solid concentration in clusters can be seen approximately twice of that in the dilute phase.Then,we have εcl ;0¼1−21−εch ðÞ¼2εch −1:ð22Þ3.1.3.Empirical estimation of model parameter nAccording to the derivations above,the model equations can be used in following procedures.i)The type A choking velocity u ch,A is calculated for a given solids ﬂux G s (>G sm ).ii)Decrease super ﬁcialgas velocity to make u f b u ch,A ;then,m s+and m s −are calculated by using different βuntil G s =m s +−m s −is satis ﬁed;the voidage of upward dilute phase εch at the operating velocity u f is then deter-mined.iii)Repeat the steps above until type C choking occur;the type C choking velocity u ch,C is ﬁnally ing a different model parameter n ,the variations of dilute phase voidage εch with operating gas velocity u f for a FCC –air system (D t =0.1m,the typ-ical diameter of laboratory scale risers)are shown in Fig.3.It can be seen from the ﬁgure,when the operating gas velocity u f is close to u ch,C ,a small reduction of gas velocity will cause a great increase of bed concentration (1−ε).That is the characteristic feature of type C choking.It can also be seen from the ﬁgure,as n gets greater,the type C chok-ing velocity calculated gets smaller.Then,the empirical correlation0.920.930.940.950.960.970.980.991.00u f (m/s)u ch,CεFig.3.Variations of dilute phase voidage εch with gas velocity u f calculated from different n for a FCC –air system (D t =0.1m,ρs =1620kg/m 3,d p =100μm,G s =100kg/(m 2s)).129M.-C.Zhang,C.Zhang /Powder Technology 241(2013)126–141given by Yous ﬁand Gau [7](Eq.(23)),which was veri ﬁed to be the best for type C choking [10],can be used to estimate the proper value of n .u ch ;C ﬃﬃﬃﬃﬃﬃﬃﬃgd pq ¼32Re −0:06tG s g u ch ;C!0:28ð23ÞFrom this kind of “calibration ”,the model parameter n =4.5can be chosen for a simpli ﬁed version of the model without iteration.More fundamental determination of the model parameter n will be given in detail in Section 3.2later.Fig.4shows the comparison be-tween the model predictions with n =4.5and those given by Eq.(23),for both FCC –air and sand –air systems with different parti-cle sizes (50,100,150and 200μm)and solid ﬂuxes (50,100and 200kg/(m 2s)).The result looks quite satisfactory.3.2.Mechanistic determination of F(β)and nThe wake effect was used quite often in the literature to explain how the cluster was formed in a CFB riser.For example,Basu et al.stated in their Book [25],“For a given velocity,the feed rate may be increased to a level where the solid concentration will be so high that one particle will enter the wake of the other.When that hap-pens,the ﬂuid drag on the ﬁrst particle will decrease,and it will fall under gravity to drop on the trailing particle.The effective surface area of the pair just formed is low,and so the ﬂuid drag will be lower than their combined weight,making the pair fall further to collide with other particles.Thus an increasing number of particles combine together to form particle agglomerates known as clusters.These clusters are,however,not permanent.They are continuously torn apart by the up-ﬂowing gas.Thus,the formation of clusters and their disintegration continue.”Though most of these words were actually from analytical consequence only,the description was quite reasonable.Recently,He et al.carried out an excellent PIV measurement for particle movement in a CFB riser [26]showing clearly the details of this phenomenon as in Fig.5(a)and (b).They described in their arti-cle,“it can be easily seen that a cluster is followed by a wake,in which particles move downward quickly ”,and “when a cluster is passing by,the particles are dragged down at a higher velocity ”.Be-sides a very clear veri ﬁcation of the wake effect,the measurement showed that those particles moved towards the cluster at velocitiesof the same order for up-ﬂowing ones,which will result in a notable deposition on the back side of the cluster.And due to the size limitation for a stable cluster,there must be the same quantities of particles pouring out the cluster from its nose.The continuous deposition and pour out of those particles will cause the downward displacement of particles inside the cluster,too.The particles moving towards the clus-ter in the wake,the inside displacement,and the front pour out can then be viewed as an integrated penetration of these particles through the cluster.From this point of view,the phenomenon can be analogous to what happens around a rising bubble in a bubbling bed as shown in Fig.1(c)[27].It can be seen that except the directions are opposite-down,the ﬂow patterns of the two are quite similar.Furthermore,through phase reversal the following correspondences could be easily af-ﬁrmed.(1)A falling cluster with concentrated particles vs.a rising bubble with null or few particles;(2)the upward dilute ﬂow around the cluster vs.the downward dense particle ﬂow around the bubble;(3)the downward penetrating particle ﬂow through the cluster vs.the upward penetrating gas ﬂow through the bubble.The scenarios in CFB risers described above are quite in consistent with the results from detailed numerical simulations by combining the two-ﬂuid model with the EMMS approach [21],i.e.“the particles tend to enter into clusters instead of suspending in dilute broth (phase),whereas the gas tends to pass around,instead of penetrating through,the dense cluster phase.”[21]Then,some results obtained for bubbling beds may also be used to estimate the in ﬂuence of fall-ing clusters on the upward dilute phase,as explained below.Suppose that a spherical cluster of voidage εcl falls down in a di-lute suspension with a constant pressure gradient d p /dz =−J ,i.e.the pressure drop per unit riser height which can be calculated in the way described in Section 4.1below.If we put the cluster in a sur-rounding bed with the same voidage εcl ,the through ﬂow penetrat-ing the cluster u fu under the pressure gradient −J would be the same as that in the surroundings.On the other hand,the cluster is also penetrated by a particle ﬂow from the opposite direction,which results in a downward displacement of particles at u sd inside the cluster,as we discussed above.To keep the gas ﬂow inside the cluster being null,which is a primer assumption for the model estab-lishment,there must be u sd =u fu .Just because the null ﬂows inside of cluster,the pressures everywhere inside are constant.Therefore,the isobars above and below the cluster will get condensed,which will then suck more gas ﬂowing through the cluster.Though the cluster is full of particles,it functions as an empty bubble.According to the well-known Davidson's model for a single bubble immerged in an incipiently ﬂuidized bed [27],the total volume ﬂow-rate through the cluster is q ¼3u pen πR 2clð24Þwhere R cl stands for the radius of the cluster,and u pen stands for the super ﬁcial percolation velocity in a packed bed of voidage εcl under the pressure gradient −J .It can be easily calculated by the Ergun's equation or the extended Ergun's equations [21,28],i.e.Ergun's for εb 0.8and Wen's for ε≥0.8.Then the interstitial gas velocity through the cluster,which will be counteracted ﬁnally by the down-ward displacement of particles inside,can be written asu sd ¼u fu ¼3u pen =εcl :ð25ÞIn bubbling ﬂuidized beds [27],rising bubbles can be classi ﬁed as the fast bubble or the slow bubble,according to the ratio of the bub-ble rising velocity u br to the interstitial gas velocity far away from the bubble u f,∞.For a fast bubble [27],i.e.u br >u f,∞,the gas leaves at the top of the bubble will be sucked in again from the bottom;the1.01.52.02.53.03.54.0u c h ,C (m /s ,t h i s m o d e l )u ch,C (m/s,Yousfi & Gau)parison of model predictions for type C choking (n =4.5,D t =0.1m)and those from Yous ﬁand Gau [7].130M.-C.Zhang,C.Zhang /Powder Technology 241(2013)126–141。

q开头关于数学的英语单词

q开头关于数学的英语单词1. Quadratic equation（二次方程）2. Quantity（数量）3. Quadrilateral（四边形）4. Quotient（商）5. Quaternion（四元数）6. Quadrant（象限）7. Quartile（四分位数）8. Quinary（五进制的）9. Qubit（量子位）10. Quotient rule（商法则）11. Quasigroup（拟群）12. Quotient group（商群）13. Quick sort（快速排序）14. Quotient space（商空间）15. Quadrature（积分）16. Quincunx（六点定则）17. Quiver（箭头图）18. Quasi-isomorphism（拟同构）19. Quotient ring（商环）20. Quasilinear（拟线性的）21. Quadratic form（二次型）22. Quaternionic analysis（四元数分析）23. Quotient set（商集）24. Quotient topology（商拓扑）25. Quotient space（商空间）26. Quotient field（商域）27. Quotient module（商模）28. Quotient map（商映射）29. Quaternion group（四元数群）30. Quasicrystal（准晶体）31. Quasi-concave（拟凹）32. Quasi-linearization（拟线性化）33. Quasi-periodic（拟周期的）34. Quasipolynomial（拟多项式）35. Quasi-stationary（拟静态的）36. Quasisymmetric（拟对称的）37. Quasitopological（拟拓扑的）38. Quadratic mean（均方根）39. Quotient function（商函数）40. Quasiconformal（拟保形的）41. Quasigroupoid（拟群oid）42. Quasiregular（拟正则的）43. Quotient property（商性质）44. Quotient sequence（商序列）45. Quasidifferential（拟微分的）46. Quasiconvex（拟凸的）47. Quotient space（商空间）48. Quasilinear partial differential equation（拟线性偏微分方程）49. Quasivariety（拟变种）50. Quasi-Newton method（拟牛顿法）51. Quadrature formula（求积公式）52. Quotient matrix（商矩阵）53. Quaternary numeral system（四进制数制）54. Quasipolynomial time（拟多项式时间）55. Quasi-homomorphism（拟同态）56. Quasi-isometry（拟等距）57. Quadrature method（求积方法）58. Quasilinearization method（拟线性化方法）59. Quasiperiodic function（拟周期函数）60. Quasirandom number（拟随机数）61. Quasiconvex optimization（拟凸优化）62. Quasiconformal mapping（拟保形映射）63. Quasitopological space（拟拓扑空间）64. Quasiregular mapping（拟正则映射）65. Quasilinear diffusion equation（拟线性扩散方程）66. Quasilinearity principle（拟线性原理）67. Quadratic programming（二次规划）68. Quasiparticle（拟粒子）69. Quasiprime（拟素数）70. Quaternionic algebra（四元数代数）71. Quadrature rule（求积规则）72. Quasigeodesic（拟测地线）73. Quasiconvex function（拟凸函数）74. Quasitriangular algebra（拟三角代数）75. Quadratic residue（二次剩余）76. Quasipolynomial algorithm（拟多项式算法）77. Quasigroup identity（拟群恒等式）78. Quasigeostrophic model（拟地转模型）79. Quasilinear elliptic equation（拟线性椭圆方程）80. Quasistatic process（拟静态过程）81. Quadratic formula（二次公式）82. Quasiperiodicity theorem（拟周期定理）83. Quasimetric space（拟度量空间）84. Quadrilateral mesh（四边形网格）85. Quasilinear parabolic equation（拟线性抛物方程）86. Quasilinear elliptic operator（拟线性椭圆算子）87. Quadrature points（求积点）88. Quadrature weights（求积权重）89. Quasiperiodic tiling（拟周期镶嵌）90. Quasiconformal deformation（拟保形变形）91. Quasilinear hyperbolic equation（拟线性双曲方程）92. Quadratic reciprocity（二次互反律）93. Quasiconvex analysis（拟凸分析）94. Quasilinear second-order PDE（拟线性二阶偏微分方程）95. Quasilinear parabolic PDE（拟线性抛物型偏微分方程）96. Quadrature-based moment method（基于求积的矩方法）97. Quasilinear transport equation（拟线性输运方程）98. Quasi-stationary distribution（拟稳态分布）99. Quasilinear wave equation（拟线性波动方程）100. Quadratic sieve（二次筛法）。

cubic ft的数值 -回复

cubic ft的数值-回复Cubic Feet: Measurement and ApplicationsIntroduction:Cubic feet (ft³) is a unit of measurement commonly used to describe the volume of three-dimensional objects or spaces. It is derived from the standard unit of length, the foot, and is often used in various fields such as architecture, engineering, construction, and even everyday household tasks. In this article, we will delve into the concept of cubic feet, understand its importance, and explore its applications in different areas.Understanding Cubic Feet:To comprehend cubic feet, it is essential to comprehend the concept of volume. Volume refers to the amount ofthree-dimensional space an object occupies. In simpler terms, it is the capacity or size of an object or space. The cubic foot, often written as ft³, is the measure of volume equal to a cube that is one foot on each side.Calculating Cubic Feet:To calculate the volume in cubic feet, you need to measure the length, width, and height dimensions of an object or space. Once you have these measurements, multiply them together. For example, if you have a rectangular box measuring 2 feet in length, 3 feet in width, and 4 feet in height, you would multiply these dimensions to find the volume in cubic feet: 2 ft x 3 ft x 4 ft = 24 ft ³. This means that the box has a volume of 24 cubic feet.It is important to note that if the measurements are in different units, such as inches or meters, they need to be converted to feet before calculating the volume in cubic feet.Applications of Cubic Feet:1. Architecture and Construction: Architects and construction professionals often utilize cubic feet to determine the required amount of materials, such as concrete, flooring, or paint, for a project. They calculate the volume of the space, including rooms, hallways, or buildings, in cubic feet to estimate the necessary quantities accurately.2. Shipping and Storage: When it comes to shipping and storage, understanding the volume in cubic feet is crucial. Logistic companies and warehouses utilize this measurement to determine the space required for storing goods or shipping containers. It helps in efficiently utilizing the available space and estimating transportation costs.3. HVAC Systems: Heating, ventilation, and air conditioning (HVAC) professionals use cubic feet to determine the capacity and requirements of HVAC systems. By calculating the cubic feet of a room or building, they can appropriately size the HVAC equipment for effective climate control.4. Swimming Pool Design: In the realm of swimming pool design and construction, cubic feet play a vital role in calculating the water volume. Knowing the volume is crucial for chemical treatment, energy efficiency, and overall functionality of the pool.5. Agriculture and Gardening: Farmers and gardeners often refer to cubic feet when measuring the capacity of raised beds, greenhouses, or even the amount of soil required for planting.Understanding the volume helps in planning and managing crops efficiently.Conclusion:Cubic feet is a versatile and essential measurement unit used in various fields. Whether it is for construction, shipping, HVAC design, or even gardening, understanding the concept of cubic feet enables accurate calculations of volume. By knowing the volume in cubic feet, professionals can better plan, estimate, and execute their projects, leading to increased efficiency andcost-effectiveness.。

费登奎斯抖动方法

费登奎斯抖动方法
费登奎斯抖动方法（Feynman-Kac path integration method）是一种数值计算方法，用于求解偏微分方程。

该方法利用费登奎斯公式（Feynman-Kac formula），通过将偏微分方程转化为积分方程的形式，从而以抽样路径（path sampling）的方式近似求解原方程。

费登奎斯公式是基于物理学家理查德·费曼（Richard Feynman）和数学家马克·卡茨（Mark Kac）的工作，将量子力学中的路径积分理论应用到概率论和偏微分方程的求解中。

费登奎斯公式给出了一个连续时间随机过程的解，它将该随机过程与一个偏微分方程联系起来。

费登奎斯抖动方法的基本思想是将偏微分方程的解表示为积分形式，其中被积函数是一个伴随方程（adjoint equation）的解和一个权重函数的乘积。

然后，通过对路径抽样并计算路径的贡献，以蒙特卡洛方法的形式逼近积分，从而求解偏微分方程。

费登奎斯抖动方法的优点包括可以处理高维问题和非线性问题，同时还可以处理带约束的问题。

然而，该方法的缺点是计算量较大和收敛速度较慢。

总而言之，费登奎斯抖动方法是一种用于数值求解偏微分方程的方法，它利用费登奎斯公式将偏微分方程转化为积分方程，并通过对路径抽样以蒙特卡洛方法逼
近积分来求解方程。

多物理场耦合英语

多物理场耦合英语英文回答：Multiphysics coupling is a technique used to solve problems that involve the interaction of multiple physical phenomena. These phenomena can include fluid flow, heat transfer, solid mechanics, electromagnetics, and chemical reactions. Multiphysics coupling is important because it allows engineers to capture the complex interactions between different physical phenomena and to design systems that are more efficient and reliable.There are a number of different methods that can be used to solve multiphysics problems. One common method is the finite element method (FEM). FEM is a numerical technique that divides a problem domain into a number of small elements. The governing equations for each element are then solved using a numerical method. The solutions for the individual elements are then combined to obtain a solution for the entire problem domain.Another common method for solving multiphysics problems is the boundary element method (BEM). BEM is a numerical technique that solves the governing equations for a problem on the boundary of the problem domain. BEM is often more efficient than FEM for problems that involve large problem domains.Multiphysics coupling is a powerful tool that can be used to solve a wide range of problems. However, it is important to note that multiphysics coupling can be computationally expensive. Therefore, it is important to carefully consider the trade-offs between accuracy and computational cost when using multiphysics coupling.中文回答：多物理场耦合是一种用于解决涉及多种物理现象相互作用问题的技术。

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