Posted on Categories:LU分解代写, Numerical analysis, 多项式插值方法代写, 数值分析, 数值积分代写, 数学代写, 最小二乘法代写

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## 数学代写数值分析代写Numerical analysis代考|Machine representation

So far, we have described a floating point representation in the abstract. Here are a few more details about how this representation is implemented on a computer. Again, in this section we will discuss the double precision format; the other formats are very similar.

Each double precision floating point number is assigned an 8-byte word, or 64 bits, to store its three parts. Each such word has the form
$$s e_1 e_2 \ldots e_{11} b_1 b_2 \ldots b_{52}$$
where the sign is stored, followed by 11 bits representing the exponent and the 52 bits following the decimal point, representing the mantissa. The sign bit $s$ is 0 for a positive number and 1 for a negative number. The 11 bits representing the exponent come from the positive binary integer resulting from adding $2^{10}-1=1023$ to the exponent, at least for exponents between -1022 and 1023 . This covers values of $e_1 \ldots e_{11}$ from 1 to 2046 , leaving 0 and 2047 for special purposes, which we will return to later.

The number 1023 is called the exponent bias of the double precision format. It is used to convert both positive and negative exponents to positive binary numbers for storage in the exponent bits. For single and long-double precision, the exponent bias values are 127 and 16383 , respectively.

MATLAB’s format hex consists simply of expressing the 64 bits of the machine number $(0.10)$ as 16 successive hexadecimal, or base 16 , numbers. Thus, the first 3 hex numerals represent the sign and exponent combined, while the last 13 contain the mantissa.

## 数学代写|数值分析代写Numerical analysis代考|Addition of floating point numbers

Machine addition consists of lining up the decimal points of the two numbers to be added, adding them, and then storing the result again as a floating point number. The addition itself can be done in higher precision (with more than 52 bits) since it takes place in a register dedicated just to that purpose. Following the addition, the result must be rounded back to 52 bits beyond the binary point for storage as a machine number.
For example, adding 1 to $2^{-53}$ would appear as follows:
\begin{aligned} & 1.00 \ldots 0 \times 2^0+1.00 \ldots 0 \times 2^{-53} \ = & 1.0000000000000000000000000000000000000000000000000000 \times 2^0 \ • & 0.0000000000000000000000000000000000000000000000000000 \times 2^0 \ = & 1.00000000000000000000000000000000000000000000000000001 \times 2^0 \end{aligned}
This is saved as $1 . \times 2^0=1$, according to the rounding rule. Therefore, $1+2^{-53}$ is equal to 1 in double precision IEEE arithmetic. Note that $2^{-53}$ is the largest floating point number with this property; anything larger added to 1 would result in a sum greater than 1 under computer arithmetic.

The fact that $\epsilon_{\text {mach }}=2^{-52}$ does not mean that numbers smaller than $\epsilon_{\text {mach }}$ are negligible in the IEEE model. As long as they are representable in the model, computations with numbers of this size are just as accurate, assuming that they are not added or subtracted to numbers of unit size.

## 数学代写数值分析代写Numerical analysis代考|Machine representation

$$s e_1 e_2 \ldots e_{11} b_1 b_2 \ldots b_{52}$$

MATLAB 的 format hex 只是表示机器号的 64 位 $(0.10)$ 作为 16 个连续的十六进制数或以 16 为基数的数字。 因此，前 3 个十六进制数字代表符号和指数的组合，而后 13 个包含尾数。

## 数学代写|数值分析代写Numerical analysis代考|Addition of floating point numbers

$\$ \|begin { aligned } \& 1.00 \backslash Idots 0 \backslash times 2 \wedge 0+1.00 \backslash Idots 0 \backslash times 2 \wedge{-53} \backslash=\& 1.0000000000000000000000000000000000000000000000000000000 |times 2 \wedge 0 1 • \& 0.0000000000000000000000000000000000000000000000000000000 \backslash times 2 \wedge 0 \backslash =\& 1.000000000000000000000000000000000000000000000000000000001 \backslash times保存为 \

## 数学代写|密码学理论代考|代数闭合

$F$的代数封闭是$F$的代数扩展，是代数封闭的。每个场$F$（基本上）都有一个唯一的代数闭合，我们把它表示为$bar{F}$；它是$F$的最大代数扩展。例如，如果$F=mathbb{R}$，那么$overline{mathbb{R}}=/mathbb{C}$。

## 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。

Posted on Categories:Operations Research, 数学代写, 运筹学

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## 数学代写|运筹学代写Operations Research代考|Crop Insurance in India: Earlier Attempts and Schemes

In India, the agricultural sector occupies a vital position in the overall economy of the country. Consequently, growth of Indian economy is inextricably connected to Indian agricultural growth and vice versa. Therefore, policy makers in India have also been concerned about the risk and uncertainty involved in agriculture.

For the economic stability of the country, various crop insurance schemes have been implemented in India since independence. In 1947, in the Central Legislature, Rajendra Prasad, Minister of Food and Agriculture, gave an assurance that the government would examine the feasibility of introducing crop and cattle insurance in the country. To pursue this matter, one special officer studied this issue and formulated experimental schemes of crop and cattle insurance for operation in selected areas. He proposed two pilot schemes which were not accepted by any of the states. Later, Government of Punjab submitted a proposal to introduce crop insurance as a part of the Third Five-Year Plan of the state and requested the government of India for financial assistance. Since, under the Constitution, the central legislature alone is competent to enact necessary legislation for the purpose, the government of India decided in October 1965 to have a Crop Insurance Bill and a Model Scheme of Crop Insurance formulated so that the states, if needed, can introduce crop insurance in their areas.

After getting the state governments’ view over the Draft Bill and the Model Scheme, the government of India referred the same to an expert committee for its full examination with respect to its economic, administrative, financial and actuarial implications. In accordance, a committee headed by the late Dharam Narain was set up to examine the pros and cons of the scheme. After a thorough scrutiny, the Dharam Narain Committee recommended against the introduction of the crop insurance scheme in the country.

## 数学代写|运筹学代写Operations Research代考|Mathematical Techniques for Crop Insurance

Crop insurance scheme and its mathematical models are extensively studied and analyzed by the academicians/policy makers. Studies over crop insurance schemes are focused on various issues particularly related to the failure of the performance of the crop insurance programs as required. The major reason for its failure is moral hazard, adverse selection, and systemic risks [4-9]. In this section, some mathematical model of crop insurance schemes, applied in all over the world, are considered and discussed in brief.

The significant role of crop insurance products has to indemnify adversely affected risk-averse individuals. The perspective of insurance is the distribution of the risk over a large number of individuals. For the success of the insurance program, it is required that the insurer should have adequate information about the nature of the risks being insured. It has been proven to be extremely difficult for farm-level yield insurance. To provide a sustainable insurance, an insurer should be able to properly classify risk. Farmers, who are favorably classified, will opt for the insurance. This phenomenon, known as adverse selection, initiates a cycle of losses [9, 10]. Moral hazard occurs when producers, after purchasing insurance, alter their production practices in a manner that increases their chances of collecting an indemnity [11]. Systemic risk is considered as the possibility by which an event can trigger a collapse in the agricultural industry.

## 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。

Posted on Categories:Number Theory, 数学代写, 数论

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## 数学代写|数论代写Number Theory代考|Random variables

Let $\mathbf{D}=(\mathcal{U}, \mathrm{P})$ be a probability distribution.
It is sometimes convenient to associate a real number, or other mathematical object, with each outcome $u \in \mathcal{U}$. Such an association is called a random variable; more formally, a random variable $X$ is a function from $\mathcal{U}$ into a set $\mathcal{X}$. If $\mathcal{X}$ is a subset of the real numbers, then $X$ is called a real random variable. When we speak of the image of $X$, we simply mean its image in the usual function-theoretic sense, that is, the set $X(\mathcal{U})={X(u): u \in \mathcal{U}}$.

One may define any number of random variables on a given probability distribution. If $X: \mathcal{U} \rightarrow \mathcal{X}$ is a random variable, and $f: \mathcal{X} \rightarrow \mathcal{Y}$ is a function, then $f(X):=f \circ X$ is also a random variable.

Example 6.13. Suppose we flip $n$ fair coins. Then we may define a random variable $X$ that maps each outcome to a bit string of length $n$, where a “head” is encoded as a 1-bit, and a “tail” is encoded as a 0-bit. We may define another random variable $Y$ that is the number of “heads.” The variable $Y$ is a real random variable.

## 数学代写|数论代写Number Theory代考|Expectation and variance

Let $\mathbf{D}=(\mathcal{U}, \mathrm{P})$ be a probability distribution. If $X$ is a real random variable, then its expected value is
$$\mathrm{E}[X]:=\sum_{u \in \mathcal{U}} X(u) \cdot \mathrm{P}[u] .$$
If $\mathcal{X}$ is the image of $X$, we have
$$\mathrm{E}[X]=\sum_{x \in \mathcal{X}} \sum_{u \in X^{-1}({x})} x \mathrm{P}[u]=\sum_{x \in \mathcal{X}} x \cdot \mathrm{P}[X=x] .$$
From (6.13), it is clear that $\mathrm{E}[X]$ depends only on the distribution of $X$ (and not on any other properties of the underlying distribution D). More generally, by a similar calculation, one sees that if $X$ is any random variable with image $\mathcal{X}$, and $f$ is a real-valued function on $\mathcal{X}$, then
$$\mathrm{E}[f(X)]=\sum_{x \in \mathcal{X}} f(x) \mathrm{P}[X=x] .$$
We make a few trivial observations about expectation, which the reader may easily verify. First, if $X$ is equal to a constant $c$ (i.e., $X(u)=c$ for all $u \in \mathcal{U})$, then $\mathrm{E}[X]=\mathrm{E}[c]=c$. Second, if $X$ takes only non-negative values (i.e., $X(u) \geq 0$ all $u \in \mathcal{U}$ ), then $\mathrm{E}[X] \geq 0$. Similarly, if $X$ takes only positive values, then $\mathrm{E}[X]>0$.

## 数学代写|数论代写Number Theory代考|Random variables

$$\text { 让 } \mathbf{D}=(\mathcal{U}, \mathrm{P}) \text { 是一个概率分布。 }$$

## 数学代写|数论代写Number Theory代考|Expectation and variance

$$\mathrm{E}[X]:=\sum_{u \in \mathcal{U}} X(u) \cdot \mathrm{P}[u] .$$

$$\mathrm{E}[X]=\sum_{x \in \mathcal{X}} \sum_{u \in X^{-1}(x)} x \mathrm{P}[u]=\sum_{x \in \mathcal{X}} x \cdot \mathrm{P}[X=x] .$$

$$\mathrm{E}[f(X)]=\sum_{x \in \mathcal{X}} f(x) \mathrm{P}[X=x] .$$

## 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。
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