## 统计代写|抽样理论作业代写sampling theory代考|MATH525

2022年9月29日

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## 统计代写|抽样理论作业代写sampling theory代考|Constitution Heterogeneity

We shall call the Constitution Heterogeneity of a lot to sample $\left(\mathrm{CH}_L\right)$ the kind of heterogeneity we are confronted with when we consider the fundamental properties of the fragments present in that lot and looking at them one by one.

By definition, the zero of Constitution Heterogeneity would be a lot made of strictly identical fragments in composition, shape, size, density, and so on. Then the Constitution Heterogeneity relative to the fragments of a given lot under a given state of comminution is an intrinsic property of the lot and cannot vary, unless we proceed with a comminution. We also say it is a primary structural property of the lot. Mixing and homogenizing have no influence on Constitution Heterogeneity.

A sample $S$ selected from a lot $L$ is affected by an error specifically related to the Constitution Heterogeneity $\mathrm{CH}_{\mathrm{L}}$ of the same lot. This error is defined as the Fundamental Sampling Error (FSE). For a given sample of weight $M_S$, we see that FSE is an incompressible minimum depending on factors such as mineral composition, liberation, shape, and fragment size distribution which are intrinsic properties of a given lot. The Fundamental Sampling Error FSE is the only error that is never zero and its importance may be secondary for major constituents; however, it often becomes primary for minor constituents and indeed overwhelming for trace constituents in high purity materials, low level precious metals, or in the environment, food, pharmaceutical products, and so on.

The notion of Constitution Heterogeneity shows differences between individual fragments. Now we may consider a lot as a set of groups of fragments, each group being made of a given number of neighboring fragments. By definition, we say that a lot has a homogeneous distribution when all groups or subsets of fragments we may select from the lot have the same average composition. If this is not the case, then the lot has a heterogeneous distribution.

For each critical constituent, the respective Distribution Heterogeneity $\left(\mathrm{DH}_L\right)$ depends on three factors:

• the Constitution Heterogeneity $\mathrm{CH}_L$
• the spatial distribution of the constituents (i.e., how they are segregated)
• the shape of the lot.
The shape of the lot is an important factor because its Distribution Heterogeneity is greatly affected by the omnipresent gravitational forces affecting our environment that create segregation. These gravitational forces introduce a strong anisotropy in the Distribution Heterogeneity of a lot, generating hybrids between tridimensional distribution Homogeneity and the tridimensional Distribution Heterogeneity, namely, the twodimensional distribution homogeneity, the one-dimensional homogeneity, and the revolution distribution homogeneity. The concept of Distribution Heterogeneity is complex which makes it necessary to consider several categories of lots.

## 统计代写|抽样理论作业代写sampling theory代考|Number of Dimensions Characterizing a Lot

From a theoretical standpoint a lot always has three dimensions, however, in practice, one or even two of these dimensions can often be regarded to be of secondary importance. When the dimensions are fewer, the easier the solution of the sampling problem associated with the lot; in fact, we found out that only sampling problems generated by zero-, one-, and two-dimensional lots were economically solvable. We can encounter the following:

• three-dimensional lots: the content of a ship, truck, railroad car, bag, jar, and so on, as long as one of these three-dimensional objects is considered as the whole lot. It can also be a compact solid such as a block inside a mineral deposit.
• Two-dimensional lots: A three-dimensional object in which the thickness becomes negligible because it is very small when compared to the two other dimensions (e. g., the seam of a coal deposit, a 2-meter slice of a mineral deposit, a copper cathode, etc.).
• One-dimensional lots: continuous and elongated piles, material travelling on a conveyor belt, flowing streams, and so on, or series of trucks, railroad cars, bags, jars, and so on, as long as these objects are considered as a set of nonrandom, discontinuous units making up the lot, the order of which is highly relevant.
• Zero-dimensional lots: the content of a series of trucks, railroad cars, bags, jars, and so on, as long as these objects are considered as a set of random, discontinuous units making up the lot. A zero-dimensional lot can be regarded as a suitable convention to describe a set of unarranged units. It can also be a one-dimensional lot for which the chronological order of the various units has been lost.

Perhaps, there is a subtlety worth mentioning; the number of dimensions regarding a lot to sample may have nothing to do with the way it looks, but everything to do with the way we decide how to sample it. This will be a huge issue well addressed in Part seven of this book.

# 抽样理论代考

## 统计代写|抽样理论作业代写sampling theory代考|体质异质性

.

• 成分异质性$\mathrm{CH}_L$
• 成分的空间分布(即它们是如何分离的)
• 块的形状。土地的形状是一个重要的因素，因为它的分布异质性很大程度上受到无处不在的引力的影响，影响我们的环境，产生隔离。这些引力在大量的分布异质性中引入了很强的各向异性，产生了三维分布异质性和三维分布异质性之间的杂交，即二维分布异质性、一维分布异质性和旋转分布异质性。分布异质性的概念是复杂的，这使得有必要考虑若干类别的地段。

## 统计代写|抽样理论作业代写采样理论代考|表征大量的维度数

. 从理论的角度来看，很多总是有三个方面，然而，在实践中，这些方面中的一个甚至两个往往被认为是次要的。当尺寸越小，与批次相关的抽样问题越容易解决;事实上，我们发现只有由零、一和二维批次产生的抽样问题是经济可解决的。我们可能会遇到以下情况:

• 三维地段:一艘船、卡车、火车车厢、袋子、罐子等的内容，只要这些三维物体中的一个被认为是整个地段。它也可以是致密的固体，如矿床中的块体。二维地段:一种三维物体，它的厚度可以忽略不计，因为它与其他两个维度(例如，煤层，2米的矿床切片，铜阴极等)相比非常小。一维地段:连续的和拉长的桩，输送带上的材料，流动的小溪，等等，或者一系列的卡车，火车车厢，袋子，罐子，等等，只要这些物体被认为是组成地段的一组非随机的，不连续的单元，它们的顺序是高度相关的。
• 零维批次:一系列卡车、火车车厢、袋子、罐子等的内容，只要这些对象被认为是一组随机的、不连续的单位组成的批次。零维群可以被认为是描述一组未排列单元的合适约定。它也可以是一个一维的地块，其中各个单元的时间顺序已经丢失。

## 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。