### 数学代写|概率论代写Probability theory代考|STAT4528

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|Recognizing Nonconstructive Theorems

Consider the simple theorem “if $a$ is a real number, then $a \leq 0$ or $0<a$,” which may be called the principle of excluded middle for real numbers. We can see that this theorem implies the principle of infinite search by the following argument. Let $(x){i=1,2, \ldots}$, be any given sequence of 0 -or-1 integers. Define the real number $a=\sum{i=1}^{\infty} x_i 2^{-i}$. If $a \leq 0$, then all members of the given sequence are equal to 0 ; if $0<a$, then some member is equal to 1 . Thus the theorem implies the principle of infinite search, and therefore cannot have a constructive proof.

Consequently, any theorem that implies this limited principle of excluded middle cannot have a constructive proof. This observation provides a quick test to recognize certain theorems as nonconstructive. Then it raises the interesting task of examining the theorem for constructivization of a part or the whole, or the task of finding a constructive substitute of the theorem that will serve all future purposes in its stead.

For the aforementioned principle of excluded middle of real numbers, an adequate constructive substitute is the theorem “if $a$ is a real number, then, for arbitrarily small $\varepsilon>0$, we have $a<\varepsilon$ or $0<a$.” Heuristically, this is a recognition that a general real number $a$ can be computed with arbitrarily small, but nonzero, error.

## 数学代写|概率论代写Probability theory代考|Notations and Conventions

If $x, y$ are mathematical objects, we write $x \equiv y$ to mean ” $x$ is defined as $y$,” ” $x$, which is defined as $y, ” ~ ” x$, which has been defined earlier as $y$,” or any other grammatical variation depending on the context.

Unless otherwise indicated, $N, Q$, and $R$ will denote the set of integers, the set of rational numbers in the decimal or binary system, and the set of real numbers, respectively. We will also write ${1,2, \ldots}$ for the set of positive integers. The set $R$ is equipped with the Euclidean metric $d \equiv d_{\text {ecld }}$. Suppose $a, b, a_i \in R$ for $i=m, m+1, \ldots$ for some $m \in N$. We will write $\lim {i \rightarrow \infty} a_i$ for the limit of the sequence $a_m, a{m+1}, \ldots$ if it exists, without explicitly referring to $m$. We will write $a \vee b, a \wedge b, a_{+}$, and $a_{-}$for $\max (a, b), \min (a, b), a \vee 0$, and $a \wedge 0$, respectively. The sum $\sum_{i=m}^n a_i \equiv a_m+\cdots+a_n$ is understood to be 0 if $n{n \rightarrow \infty} \sum{i=m}^n a_i$. In other words, unless otherwise specified, convergence of a series of real numbers means absolute convergence. Regarding real numbers, we quote Lemma $2.18$ from [Bishop and Bridges 1985] which will be used, extensively and without further comments, in the present book. Limited proof by contradiction of an inequality of real numbers. Let $x, y$ be real numbers such that the assumption $x>y$ implies a contradiction. Then $x \leq y$. This lemma remains valid if the relations $>$ and $\leq$ are replaced by $<$ and $\geq$, respectively.

We note, however, that if the relations $>$ and $\leq$ are replaced by $\geq$ and $<$ respectively, then the lemma would not have a constructive proof. Roughly speaking, the reason is that a constructive proof of $x0$ such that $y-x>\varepsilon$, which is more than a proof of $x \leq y$; the latter requires only a proof that $x>y$ is impossible and does not require the calculation of anything. The reader should ponder on the subtle but important difference.

## 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。