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# 计算机代写|数据库代考Database代考|CS4250 First Normal Form

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## 计算机代写|数据库代考Database代考|First Normal Form

We begin with a definition of the first normal form:
A relation is in the first normal form (1NF) iff all its attributes are atomic (i.e., each attribute is defined on a single domain), and each record in the relation is characterized by a unique primary key value.

In defining atomic attributes, Codd was deliberate about eliminating repeating groups $-$ the scenario where a column (attribute) could store an array or list of possible values; this was prevalent in CODASYL and COBOL. Atomicity means each attribute is defined on a single domain and stores a single value for any tuple in the relation. Moreover, implicit in this definition is the enforcement of the entity integrity constraint (Section 4.1). As such, tuples that have null values in their primary key will not be allowed to exist; neither will there be tuples with duplicate primary key values in the relation. [These are problems that persisted and perhaps still do outside of the context of $1 \mathrm{NF}$ ].

By this definition, all relations are in 1NF. This is by no means coincidental, but by design: We define a relation to consist of atomic attributes, and subject to the entity integrity constraint and the referential integrity constraint. However, as you will soon see, having relations in 1NF only is often not good enough.

Example $4.4$ provides an example of a relation that is in $1 \mathrm{NF}$ but is poorly designed. It may surprise you to learn that this problem was once very widespread in accounting software systems. As an exercise, try proposing a more efficient design for the relation described in the example.

## 计算机代写|数据库代考Database代考|Second Normal Form

The second normal form draws in the concept of functional dependence to shape an elevated benchmark beyond mere 1NF requirement. Here is the definition:
A relation is in the second normal form (2NF) iff it is in $1 \mathrm{NF}$ and every non-key attribute is fully functionally dependent on the primary key.
By non-key attribute, we mean that the attribute is not part of the primary key. Relation R0 (of the previous section), though in 1NF, is not in 2NF, due to FD1 and FD2. Using Heath’s theorem, we may decompose relation $\mathbf{R 0}$ as follows (note that the abbreviation PK is used to denote the primary key):
R1 {Suppl#, SupplName, Location, SupplStatus} PK[Suppl#]
R2 {Item#, ItemName} PK[Item#]
$\mathbf{R 3}{$ Suppl#, Item#, Quantity} PK[Suppl#, Item#]

We then check to ensure that the resulting relations are in $2 \mathrm{NF}$. Relation $\mathbf{R} 1$ has a single attribute as its primary key, and so does $\mathbf{R 2}$; there is therefore no possibility of either relation being in violation of $2 \mathrm{NF}$. As for relation $\mathbf{R 3}$, there is only one non-key attribute and it is dependent on the primary key. We may therefore conclude with confidence that all three relations ( $\mathbf{R} 1, \mathbf{R} 2$, and $\mathbf{R 3})$ are in $2 \mathrm{NF}$.

So, based on the definition of 2NF, and on the authority of Heath’s theorem, we would replace R0 with R1, R2, and $\mathbf{R 3}$. Please note the consequences of our treatment of $\mathbf{R 0}$ so far:

1. The problems with relations in $1 \mathrm{NF}$ only have been addressed.
2. By decomposing, we have introduced foreign keys in relation $\mathbf{R 3}$.
3. JOINing is the opposite of PROJecting. We can rebuild relation $\mathbf{R 0}$ by simply JOINing $\mathbf{R 3}$ with $\mathbf{R} \mathbf{1}$ and $\mathbf{R} 3$ with $\mathbf{R 2}$, on the respective foreign keys.
4. From the definition of 2NF, two observations should be obvious: Firstly, if you have a relation with a single attribute as the primary key, it is automatically in $2 \mathrm{NF}$. Secondly, if you have a relation with $n$ attributes and $n$-1 of them form the primary key, the relation may very well be in 2NF, but you must first verify this.

## 计算机代写|数据库代考Database代考|Second Normal Form

R1 {Suppl#, SupplName, Location, SupplStatus} PK[Suppl#]
R2 {Item#, ItemName} PK[Item#]
$\mathbf{R 3}{$ Suppl#, Item#, Quantity} PK[Suppl#, Item#]

1. 关系中的问题1NF只得到解决。
2. 通过分解，我们在关系中引入了外键R3.
3. JOINing 与 PROJecting 相反。我们可以重建关系R0通过简单地加入R3和R1和R3和R2, 在各自的外键上。
4. 根据 2NF 的定义，两个观察结果应该是显而易见的：首先，如果你有一个以单个属性作为主键的关系，它会自动在2NF. 其次，如果你有关系n属性和n其中-1构成主键，关系很可能是2NF，但你必须先验证这一点。

## 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。