## 统计代写|经济统计代写Economic Statistics代考|ECN329

statistics-lab™ 为您的留学生涯保驾护航 在代写经济统计Economic Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写经济统计Economic Statistics代写方面经验极为丰富，各种代写经济统计Economic Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|经济统计代写Economic Statistics代考|Reengineering the Data Architecture

The opportunities created by the ubiquitous digitization of transactions can only be realized with a new architecture for data collection. The aim is for the statistical system to use all the relevant detail provided by transactions data. There are a number of issues the new data architecture would need to address (see Jarmin 2019). These include issues of privacy, confidentiality, and value of husiness data; cost to husinesses and the statistical agencies of the new architecture; and the technical and engineering issues of building a new architecture.

There are multiple potential modes for businesses providing such data. All have advantages and disadvantages. We expect that the new architecture should support multiple approaches to providing and collecting data. The agencies will need to be flexible.

Direct feed of transaction-level data. The agencies could get transactionlevel data directly from firms and do the calculations necessary to aggregate them. This approach has already been implemented by the Australian Bureau of Statistics for its retail food price index. While the agencies should be receptive to such arrangements, it is unlikely to be practical in the US context because of unwillingness of companies to provide such granular data and the difficulty for the agencies of handling the volume of data that it would entail.

Direct feed of (detailed) aggregate measures of price, quantity, and sales via APIs. Alternatively, and probably more practical in the US context, firms (e.g., retailers) could do the calculations needed to produce detailed but aggregated measures of price, quantity, and sales that could then be transmitted to the statistical agencies. Surveys and enumerations could be replaced by APIs. The agencies – in collaboration with businesses – would have to design a large, but finite, number of APIs that would mesh with would have a substantial fixed cost, but then provide much improved data at low marginal cost.

## 统计代写|经济统计代写Economic Statistics代考|Capabilities and Mandates of the Statistical Agencies

This paper envisions a new architecture for economic statistics that would build consistent measurement of price and quantity from the ground up. Currently, the collection and aggregation of data components is spread across three agencies. Implementing the new architecture we envision undoubtedly will be a challenge. Moving away from a survey-centric form of data collection for retail prices and quantities to computing statistics from detailed transaction-level data requires an approach that would have businesses providing their data in a unified way. The institutional arrangements that fundamentally separate the collection of data on prices and quantities would need to be changed. There have long been calls for reorganizing BEA, BLS, and Census to help normalize source data access, improve efficiencies, and foster innovation. Regardless of whether the agencies are realigned or reorganized, they need to review the current structure given how the production of statis-tics is evolving. Having one agency negotiate access to transaction-level data will be difficult enough. Having multiple agencies doing so unduly burdens both businesses and the taxpayer. Importantly, under the current statistical system structure, no agency has the mandate to collect data on both price and quantities, so implementing the data architecture to measure price and quantity simultaneously is not in scope for any agency. ${ }^{31}$

There are also ditticult questions about the legal and policy structure needed to govern how statistical agencies access private data assets for statistical uses. For instance, a key question is whether companies would seek to charge for access to the type of data described above and, if so, whether the associated fees would be within the budgetary resources of the statistical agencies.

To further test, develop, and implement a solution such as we are proposing here, the statistical agencies must expand their general data science capabilities. Whether transaction level data are transmitted to the agencies or whether retailers provide intermediate calculations, an important point of focus for the statistical agencies will be not only the acquisition but the curation of new types of unstructured data. The ingestion, processing, and curation of these new sources introduces scalability concerns not present in most survey contexts. Also, negotiating access will require the agencies to hire more staff with the skills to initiate and manage business relationships with data providers.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|经济统计代写Economic Statistics代考|ECO380

statistics-lab™ 为您的留学生涯保驾护航 在代写经济统计Economic Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写经济统计Economic Statistics代写方面经验极为丰富，各种代写经济统计Economic Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|经济统计代写Economic Statistics代考|Quality- and Appeal- Adjusted Price Indexes

The promise of digitized data goes beyond the ability to produce internally consistent price and nominal revenue data. The item-level price and quantity data, which are often accompanied by information on item-level attributes, offer the prospect of novel approaches to quality adjustment. Currently, the BLS CPI implements hedonic quality adjustment on a relatively small share of consumer expenditures (about 5 percent). For the remaining items, a matched model approach is used with ad hoc quality adjustments when feasible (e.g., if a new model of an item has more features than a prior matched item, then an attempt is made to adjust the prices to account for the change in features). The sample of products in the CPI consumption basket is rotated every four years and no quality adjustment is made to prices when a new good enters the index due to product rotation.

The digitized data offer the possibility of accounting for the enormous product turnover observed in item-level transactions data. For the Nielsen scanner data, the quarterly rates of product entry and exit are $9.62$ percent and $9.57$ percent, respectively. By product entry and exit, we mean the entry and exit of UPCs from the data. Some of the product turnover at the UPC code level in the scanner data involves minor changes in packaging and marketing, but others represent important changes in product quality.
We consider two approaches for capturing the variation in quality in price indexes using transactions data. The first approach is based on consumer demand theory and has been developed by Redding and Weinstein (2018, 2020) who build on the earlier work by Feenstra (1994). The second approach uses hedonic methods, following the insights of Pakes $(2003,2005)$ and Erickson and Pakes (2011). While these hedonic approaches are already partly in use by BLS and BEA, the item-level transactions data offer the potential for implementing these approaches with continuously updated weights and with methods to avoid selection bias arising from product entry and exit and – equally importantly – at scale. Bajari et al. (2021) is an initial attempt to implement hedonics at scale using a rich set of product attributes. We draw out the many different issues that must be confronted for practical implementation of these modern methods by the statistical agencies. Since both methods are part of active research agendas, we emphasize that our discussion and analysis is exploratory rather than yielding ultimate guidance for implementation.

## 统计代写|经济统计代写Economic Statistics代考|The Demand Residual

The large declines in the UPI, even for product categories such as soft drinks that are not obvious hotbeds of technological innovation, raise the question of whether the implied estimates are reasonable, and if so, how best to interpret them.

Redding and Weinstein (2018) take a strong view in formulating the UPI: they treat all of the measured residual demand variation not accounted for by changing prices as reflecting changes in product appeal or quality. The UPI exactly rationalizes observed prices and expenditure shares by treating the entire error in an estimated demand system as reflecting such changes. In contrast, other approaches such as hedonics or the Feenstra (1994) approach, leave an estimated residual out of the price index calculation. Although hedonic approaches can in principle capture much of the variation from changing product quality and appeal, the $R^2$ in period-by-period hedonic regressions is typically substantially less than one. Conceptually, therefore, although both the UPI and hedonics capture time-varying quality and appeal valuations from both product turnover and continuing products, the UPI is arguably more general because it comprehensively captures the error term from the underlying demand system in the price index.

The debate over whether it is appropriate to treat the entire error term from an estimated consumer demand system as reflecting changes in product quality and appeal that affect the cost of living is very much in its infancy, however. The measured error term from the estimated demand system may reflect measurement or specification error from several sources. Specification error may reflect not only functional form but also a misspecified degree of nesting or level of aggregation. Presumably, those errors would ideally be excluded from the construction of a price index.

Another possible source of specification error relates to permitting richer adjustment dynamics in consumer demand behavior. Diffusion of product availability, diffusion of information about products, habit formation, and learning dynamics will show up in the error term from estimation of specifications of static CES demand models. A related but distinct possibility is that the underlying model of price and quantity determination should reflect dynamic decisions of the producing firms (through endogenous investments in intangible capital like customer base as well as related marketing, promotion, and distribution activity by firms). It is important to remember that the approaches being used to estimate the elasticity of substitution are jointly estimating the demand and supply system, so misspecification of either the demand or supply equations can yield specification error.

## 统计代写|经济统计代写Economic Statistics代考|The Demand Residual

UPI 的大幅下降，即使是软饮料等不是技术创新的明显温床的产品类别，也引发了隐含估计是否合理的问题，如果是，如何最好地解释它们。

Redding 和 Weinstein（2018 年）在制定 UPI 时持强烈观点：他们将所有测量的剩余需求变化视为反映了产品吸引力或质量的变化，而不是通过价格变化来解释。UPI 通过将估计需求系统中的整个误差视为反映此类变化，从而准确地使观察到的价格和支出份额合理化。相比之下，其他方法，如享乐主义或 Feenstra (1994) 方法，将估计残差排除在价格指数计算之外。尽管享乐方法原则上可以捕捉到产品质量和吸引力变化带来的大部分变化，但R2在逐周期特征回归中，通常远小于 1。因此，从概念上讲，尽管 UPI 和享乐主义都从产品周转率和持续产品中捕捉到随时间变化的质量和吸引力估值，但 UPI 可以说更普遍，因为它从价格指数的潜在需求系统中全面捕捉了误差项。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|经济统计代写Economic Statistics代考|ECON227

statistics-lab™ 为您的留学生涯保驾护航 在代写经济统计Economic Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写经济统计Economic Statistics代写方面经验极为丰富，各种代写经济统计Economic Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|经济统计代写Economic Statistics代考|Existing Architecture

Table $1.1$ summarizes the source data and statistics produced to measure real and nominal consumer spending. ${ }^3 \mathrm{~A}$ notable feature of the current architecture is that data collection for total retail sales (Census) and for prices (BLS) are completely independent. The consumer price index program collects prices based on (1) expenditure shares from the Consumer Expenditure Survey (BLS manages the survey and Census collects the data), (2) outlets selected based on the Telephone Point of Purchase Survey, and (3) a relatively small sample of goods at these outlets that are chosen probabilistically (via the Commodities and Services Survey). The Census Bureau collects sales data from retailers in its monthly and annual surveys. The monthly survey is voluntary and has suffered from declining response rates. In addition, the composition of the companies responding to the monthly survey can change over time, which complicates producing a consistent time series. Store-level sales data are only collected once every five years as part of the Economic Census.

Integration of nominal sales and prices by BEA is done at a high level of aggregation that is complicated by the availability of product class detail for nominal sales that is only available every five years from the Economic Census. In the intervening periods, BEA interpolates and extrapolates based on the higher frequency annual, quarterly, and monthly surveys of nominal sales by the Census Bureau. These higher frequency surveys are typically at the firm rather than establishment level. Moreover, they classify firms by major kinds of business. For example, sales from the Census Monthly Retail Trade Survey (MRTS) reflect sales from “Grocery Stores” or “Food and Beverage Stores.” Such stores (really firms) sell many items beyond food and beverages, complicating the integration of the price indexes that are available at a finer product-class detail.

This complex decentralized system implies that there is limited granularity in terms of industry or geography in key indicators such as real GDP. BEA’s GDP by industry provides series for about 100 industries, with some 4-digit (NAICS) detail in sectors like manufacturing, but more commonly 3-digit and 2-digit NAICS detail. The BEA recently released county-level GDP on a special release basis, a major accomplishment. However, this achievement required BEA to integrate disparate databases at a high level of aggregation with substantial interpolation and extrapolation. Digitized transactions data offer an alternative, building up from micro data in an internally consistent manner.

## 统计代写|经济统计代写Economic Statistics代考|Using Item- Level Transactions Data

In the results presented here, we focus on two sources of transactions data summarized to the item level. One source is Nielsen retail scanner data, which provide item-level data on expenditures and quantities at the UPC code level for over 35,000 stores, covering mostly grocery stores and some mass merchandisers. ${ }^4$ Any change in product attributes yields a new UPC code so there are no changes in product attributes within the item-level data we use. The Nielsen data cover millions of products in more than 100 detailed product groups (e.g., carbonated beverages) and more than 1,000 modules within these product groups (e.g., soft drinks is a module in carbonated beverages). While the Nielsen scanner item-level data are available weekly at the store level, our analysis aggregates the item-level data to the quarterly, national level.5 Since the weeks may split between months, we use to monthly data. The NRF calendar places complete weeks into months and controls for changes in the timing of holidays and the number of weekends per month, and we use the months to create the quarterly data used in this paper. For more than 650,000 products in a typical quarter, we measure nominal sales, total quantities, and unit prices at the item level. We use the Nielsen scanner data from 2006:1 to 2015:4. The NPD Group (NPD) ${ }^6$ data cover more than 65,000 general merchandise stores, including online retailers, and include products that are not included in the Nielson scanner data. We currently restrict ourselves to the analysis of one detailed product module: memory cards. ${ }^7$ The NPD raw data are at the item-by-store-bymonth level; NPD produces the monthly data by aggregating weekly data using the NRF calendar, as we do ourselves with the Nielsen data. Again, for our analysis we aggregate the data to the quarterly, national item level. For example, the item-level data for memory cards tracks more than 12,000 item-by-quarter observations for the 2014:1 to $2016: 4$ sample period. As with the Nielsen data, we measure nominal sales, total quantities, and unit prices at the item-level by quarter.

## 统计代写|经济统计代写Economic Statistics代考|Existing Architecture

BEA 对名义销售额和价格的整合是在高水平的聚合中完成的，由于名义销售额的产品类别详细信息的可用性而复杂化，而名义销售额的产品类别详细信息仅在经济普查中每五年提供一次。在中间期间，BEA 根据人口普查局对名义销售额的较高频率的年度、季度和月度调查进行内插和外推。这些较高频率的调查通常是在公司而不是机构层面进行的。此外，他们按主要业务类型对公司进行分类。例如，人口普查每月零售贸易调查 (MRTS) 的销售额反映了“杂货店”或“食品和饮料店”的销售额。此类商店（实际上是公司）销售食品和饮料以外的许多商品，从而使价格指数的整合变得复杂，这些价格指数可以在更精细的产品级细节中获得。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|概率论代写Probability theory代考|MATHS7103

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|概率论代写Probability theory代考|Set, Operation, and Function

Set. In general, a set is a collection of objects equipped with an equality relation. To define a set is to specify how to construct an element of the set, and how to prove that two elements are equal. A set is also called a family.

A member $\omega$ in the collection $\Omega$ is called an element of the latter, or, in symbols, $\omega \in \Omega$

The usual set-theoretic notations are used. Let two subsets $A$ and $B$ of a set $\Omega$ be given. We will write $A \cup B$ for the union, and $A \cap B$ or $A B$ for the intersection. We write $A \subset B$ if each member $\omega$ of $A$ is a member of $B$. We write $A \supset B$ for $B \subset A$. The set-theoretic complement of a subset $A$ of the set $\Omega$ is defined as the set ${\omega \in \Omega: \omega \in A$ implies a contradiction $}$. We write $\omega \notin A$ if $\omega \in A$ implies a contradiction.

Nonempty set. A set $\Omega$ is said to be nonempty if we can construct some element $\omega \in \Omega$.

Empty set. A set $\Omega$ is said to be empty if it is impossible to construct an element $\omega \in \Omega$. We will let $\phi$ denote an empty set.

Operation. Suppose $A, B$ are sets. A finite, step-by-step, method $X$ that produces an element $X(x) \in B$ given any $x \in A$ is called an operation from $A$ to $B$. The element $X(x)$ need not be unique. Two different applications of the operation $X$ with the same input element $x$ can produce different outputs. An example of an operation is [. $]_1$, which assigns to each $a \in R$ an integer $[a]_1 \in$ $(a, a+2)$. This operation is a substitute of the classical operation [-] and will be used frequently in the present work.

Function. Suppose $\Omega, \Omega^{\prime}$ are sets. Suppose $X$ is an operation that, for each $\omega$ in some nonempty subset $A$ of $\Omega$, constructs a unique member $X(\omega)$ in $\Omega^{\prime}$. Then the operation $X$ is called a function from $\Omega$ to $\Omega^{\prime}$, or simply a function on $\Omega$. The subset $A$ is called the domain of $X$. We then write $X: \Omega \rightarrow \Omega^{\prime}$, and write domain $(X)$ for the set $A$. Thus a function $X$ is an operation that has the additional property that if $\omega_1=\omega_2$ in $\operatorname{domain}(X)$, then $X\left(\omega_1\right)=X\left(\omega_2\right)$ in $\Omega^{\prime}$. To specify a function $X$, we need to specify its domain as well as the operation that produces the image $X(\omega)$ from each given member $\omega$ of $\operatorname{domain}(X)$.
Two functions $X, Y$ are considered equal, $X=Y$ in symbols, if
$\operatorname{domain}(X)=\operatorname{domain}(Y)$,
and if $X(\omega)=Y(\omega)$ for each $\omega \in \operatorname{domain}(X)$. When emphasis is needed, this equality will be referred to as the set-theoretic equality, in contradistinction to almost everywhere equality, to be defined later.

## 数学代写|概率论代写Probability theory代考|Metric Space

The definitions and notations related to metric spaces in [Bishop and Bridges 1985], with few exceptions, are familiar to readers of classical texts. A summary of these definitions and notations follows.

Metric complement. Let $(S, d)$ be a metric space. If $J$ is a subset of $S$, its metric complement is the set ${x \in S: d(x, y)>0$ for all $y \in J}$. Unless otherwise specified, $J_c$ will denote the metric complement of $J$.

Condition valid for all but countably many points in metric space. A condition is said to hold for all but countably many members of $S$ if it holds for each member in the metric complement $J_c$ of some countable subset $J$ of $S$.

Inequality in a metric space. We will say that two elements $x, y \in S$ are unequal, and write $x \neq y$, if $d(x, y)>0$.

Metrically discrete subset of a metric space. We will call a subset $A$ of $S$ metrically discrete if, for each $x, y \in A$ we have $x=y$ or $d(x, y)>0$. Classically, each subset $A$ of $S$ is metrically discrete.

Limit of a sequence of functions with values in a metric space. Let $\left(f_n\right){n=1,2, \ldots .}$ be a sequence of functions from a set $\Omega$ to $S$ such that the set $$D \equiv\left{\omega \in \bigcap{i=1}^{\infty} \operatorname{domain}\left(f_i\right): \lim {i \rightarrow \infty} f_i(\omega) \text { exists in } S\right}$$ is nonempty. Then $\lim {i \rightarrow \infty} f_i$ is defined as the function with domain $\left(\lim {i \rightarrow \infty} f_i\right) \equiv D$ and with value $$\left(\lim {i \rightarrow \infty} f_i\right)(\omega) \equiv \lim {i \rightarrow \infty} f_i(\omega)$$ for each $\omega \in D$. We emphasize that $\lim {i \rightarrow \infty} f_i$ is well defined only if it can be shown that $D$ is nonempty.

## 数学代写|概率论代写Probability theory代考|Set, Operation, and Function

. Inotherwords, unlessotherwisespecified, convergenceofaseriesofrealnumbersmeansabsolute $2.18$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。