Study on the Relation of Definite Integral and Indefinite Integral

Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral of f(x), where x is a self-variable, s is a parameter,~f(x) is a function defined in(-∞, +∞), which comes from f(x) by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.

定积分integral from n =0 to π/2(cosθ/(sinθ+cosθ))dθ的解法

定积分I=integral from n =0 to π/2(cosθ/(sinθ+cosθ))dθ有多种解法,除一般解法外,还有若干简单、灵巧的解法。以此为例,强调"一题多解"对学习数学的意义和作用。

一类广义积分integral from n=(-∞) to (+∞)(((sin^nx)/x^r)dx)的计算

在不涉及Hadamard主值积分的情况下,利用推广的留数定理,给出了广义积分integral from n=(-∞) to (+∞)(((sin^nx)/x^r)dx)的一种求值方法.

关于定积分integral from n=0 to 2π (1/(a^2sin^2u+b^2cos^2u)~n)du(n∈N,a,b∈R^+)的计算

提供一类含有三角函数的定积分的计算方法及计算公式。

关于定积分integralfromn=0toa(e^(-x^2)dx)的几种解法

本文在高等数学、数值分析的研究过程中,总结了定积分的几种解法,如重积分法、无穷级数法、数值解法。

典型无穷积分integral from n=0 to +∞(e^(-ax)dx)在解高等代数问题上的应用

高等代数中综合性问题比较复杂,解题过程中用到的知识又多,学生解题普遍感到困难.在此应用数学分析中一个典型无穷积分+∫∞0e-axdx=1a来解决高等代数的一些综合问题.

Generalized Fourth-Order Decompositions of Imaginary Time Path Integral:Implications of the Harmonic Oscillator

The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.

Thermodynamic Parameters of Central Spin Coupled to an Antiferromagnetic Bath: Path Integral Formalism

A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites n when β → 0.

关于integral from n=0 to 1 ((lnx)~2/(1+x^2))dx的计算

通过构造两个辅助函数f(t)及 φ(x) ,并分别将其展开为马克劳林级数及富里哀级数 ,在这两个级数各自收敛域内 ,当自变量t及x分别取某特定值时 ,得到同一级数 。

integral from n=0 to (π/2)sin^n xdx与瓦里斯公式的一个应用

对与定积分integral from n=0 to (π/2)sin^n xdx有关的一些积分进行了讨论,介绍瓦里斯公式及其证明,给出了瓦里斯公式在级数研究中的应用问题。

Integrated gravity and magnetic study on patterns of petroleum basin occurrence in the China seas and adjacent areas

The China seas and adjacent areas contain numerous petroleum basins.One of the main challenges for future oil and gas exploration is to identify the inherent patterns of petroleum basin distribution.The formation and evolution of petroleum basins along with the migration and accumulation of oil and gas are often closely related to the tectonic environment.The gravity and magnetic fields with high lateral resolution and wide coverage provide important data for regional tectonic research.Based on the gravity data in the Global Satellite Gravity Anomaly Database(V31.1)and magnetic data from the Earth Magnetic Anomaly Grid(2-arc-minute resolution)(V2),this study uses integrated gravity and magnetic field technique to obtain integrated gravity and magnetic field result for the China seas and adjacent areas,and then adopts the normalized vertical derivative of the total horizontal derivative technique to conduct partition.Finally,it identifies the relationship between the partition characteristics and tectonics as well as the patterns of petroleum basin occurrence.The research shows that the partition of gravity and magnetic field integrated result has a good correlation with the Neo-Cathaysian tectonic system and tectonic units.The petroleum basins are characterized according to three blocks arranged from north to south and four zones arranged from east to west.The north-south block structure causes the uneven distribution of oil and gas resources in the mainland area and the differences in the hydrocarbon-bearing strata.Petroleum basins are more abundant in the north than in the south.The ages of the main oil-and gas-bearing strata are“Paleozoic–Mesozoic,Paleozoic–Mesozoic–Cenozoic,and Paleozoic–Mesozoic”,in order from north to south.The difference in the overall type of oil and gas resources in all basins is controlled by the east–west zonation.From east to west,the oil and gas resource type exhibits a wave-like pattern of“oil and gas,gas,oil and gas,gas”.The vertical distribution is characterized by an upper oil(Mesozoic–Cenozoic)and lower gas(Mesozoic–Paleozoic)structure.Within the study area,the Paleozoic marine strata should be the main strata of future natural gas exploration.

Integrated QoE Assessment Mechanism in Wireless Ubiquitous Networks

To assess Quality of Experience (QoE) for multimedia services in wireless ubiquitous networks, integrated QoE assessment mechanism is proposed. Firstly, hierarchical QoE definition considering device capacity and environment factor is introduced, and then corresponding QoE measurement architecture is described. Secondly, quantitative mapping scheme among the defined sets is introduced. Simulation for Video on Demand (VoD) and video telephone service in Universal Mobile Telecommunications System (UMTS) urban scenario shows experience and network condition can be well measured. Useful suggestions are still given for operators to keep user experience at an acceptable level.

An Explicit-Implicit Mixed Staggered Asynchronous Step Integration Algorithm in Structural Dynamics

Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the structural dynamics in multi-scale both the space domain and time domain.The discrete FEA model is partitioned into explicit and implicit parts using the nodal partition method.Multiple boundary node method is adopted to handle the interface coupled problem.In coupled region,the implicit Newmark coupled with an explicit predictor corrector Newmark whose predictive wave propagates into the implicit mesh.During the explicit subcycling process,the variables of boundary nodes are solved directly by dynamics equilibrium equation.The dissipation energy is dynamically determined in accordance with the energy balance checking.A cantilever beam and a building two numerical examples are proposed to verify that the method can greatly reduce the computing time while maintaining a high accuracy.

CAS-Based Approach for Automatic Data Integration

Research of automatic integration of structured and semi-structured data has not resulted in success over the past fifty years. No theory of data integration exists. It is unknown what the theoretical necessary requirements are, to fully support automatic data integration from autonomous heterogeneous data sources. Therefore, it is not possible to objectively evaluate if and how much new algorithms, techniques, and specifically Data Definition Languages, move towards meeting such theoretical requirements. To overcome the serious reverse salient the field and industry are in, it will be helpful if a data integration theory would be developed. This article proposes a new look at data integration by using complex adaptive systems principles to analyze current shortcomings and propose a direction that may lead to a data integration theory.

面向区域自治的配电网动态区域划分方法

具有间隙性及波动性特征的大量分布式光伏接入配电网,为配电网的源荷功率平衡及节点电压调节等带来了新的技术挑战。为充分利用配电网中多类型调节资源的调节能力,提高新能源高比例接入下配电网的自治能力,提出了一种面向区域自治的配电网动态区域划分方法。首先,结合分布式光伏和负荷预测数据,衡量配电网中多类型可调资源的调节能力,建立考虑模块度、电压调节能力和功率持续调节能力的综合指标体系。其次,采用遗传算法求解各区域最优综合指标,结合运行状态及调控需求设计分区结构更新触发机制,更新分区结果。最后,结合实际配电网典型日运行数据的仿真算例及对比分析验证了所提区域动态划分方法在提高区域电压调节能力和功率持续调节能力方面的优势,并分析了不同指标权重,不同触发阈值以及不同时间尺度对分区结果的影响。

探究微积分——让知识成为智慧

沿着历史脉络,准确把握微积分概念,领悟微积分蕴含的丰富智慧.数学智慧可以充实读者的精神世界,促进学生的心智成长,对他们的思维方式和世界观产生积极影响.在培养逻辑思维能力的同时,重视直觉思维能力,促进创新能力的培养.

定积分在两点展开的渐近公式

对于具有m+n阶连续导数的被积函数的定积分,通过多次分部积分给出了在积分上限和积分下限两点处同时展开的定积分的渐近展开式,其余项类似于Taylor公式的积分型余项,这种展开式可看作是Taylor公式的一种推广.被积函数在积分上下限处的值有不同情形,展开式也会随之变化而具有多种形式.通过分析与举例也发现这种展开式的近似计算优于Taylor公式的近似计算,而且在某些积分不等式的证明中也体现了其快捷方便的优点.

云存储环境下基于模格算法的数据存储完整度检测

在云存储环境下进行数据保存后,需要依托于数据持有性证明检测数据存储完整度,每次验证的计算较为庞大,导致完整度检测的时间较长.对此,提出存储环境下基于模格算法的数据存储完整度检测方法 .基于热点循迹的数据分块技术,得到待检测的存储数据子块.根据数据块数量搭建包含众多叶子节点的多分支路径树,并通过哈希值匹配实现验证数据块动态更新.考虑数据存储完整度检测的3种参与实体,建立包含6种算法的验证机制,指导完整度检测的具体流程.最后,利用模格算法实现数据存储完整度检测.实验结果表明:在数据量为1 024 MB时,采用所提方法进行数据存储完整度检测的时间开销仅为3.5 s,满足了云存储数据检测要求.

基于MBD的电子装备研发数字化集成协同环境构建

电子装备的研发是一项复杂且系统化的工程,而现有研发模式下存在多专业协同不足、产品研发周期长、技术状态变更频繁、研发成本高等问题,已无法满足市场需求。针对上述问题,以产品研发流程再造和优化为基础,开展数字化集成协同研发环境构建,系统性探索产品多专业协同、多领域共享的研发管控模式。通过基于模型定义(Model-based Definition,MBD)技术,规范了装备研制过程,实现了电子装备基于xBOM的数字化定义和数字量的传递,以及设计工艺一体化数据管理,从而提高了研发效率,缩短产品研制周期10%以上,设计重用率超过30%,降低了研发成本,提高了装备的性能和可靠性。

关于定积分原函数的一点注记

首先说明当换元积分法中的变量变换不满足换元定理的条件时,由f(x)积分后得到的F(x)只是f(x)在局部区间上的原函数,然后通过两个例子说明如何求f(x)在整体区间[a,b]上的原函数.