ultrafilter

简明释义

英[ˌʌltrəˈfɪltə]美[ˌʌltrəˈfɪltər]

vt. 以超滤器过滤

n. [化工] 超滤器

英英释义

单词用法

同义词

反义词

例句

1.The experimental results showed that it is feasible to separate protein from rapeseed meal by using the hollow fiber ultrafilter.

试验结果表明利用中空纤维超滤膜分离菜籽饼粕中蛋白质的方法是可行的。

2.The extract was decolored and desalted by using anion and cation exchange resin. The desalted liquid was filtered with an ultrafilter membrane.

用阴阳离子交换柱去除杂质，同时起到一定的脱色作用，进而运用超滤进行澄清。

3.Flush cleaning solution from the ultrafilter with D. I. water and return paint to the unit.

用去离子水冲洗超滤器中的清洗液后，使漆液再返回超滤装置重。

4.With ultrafilter medium it can attain the goal of clarification and desterilization.

使用超滤过滤介质可达到澄清、除菌的目的。

5.This paper introduced the typical equipment and their running process and their optimizing of low energy consumption ultrafilter membrane.

本文介绍了半死端超滤膜技术的典型设备和运行工艺及其优化。

6.The types and functions of ultrafilter for cathodic electrodeposition (CED) painting and the functions of charged membrane ultrafilter for CED have been described.

介绍了超滤器在阴极电泳涂装中的作用、阴极电泳用超滤器的类型、荷电膜超滤器在阴极电泳涂装线中的应用。

7.In the food industry, an ultrafilter is essential for separating proteins from whey.

在食品工业中，超滤器对于从乳清中分离蛋白质是必不可少的。

8.The ultrafilter membrane is designed to allow only certain sizes of particles to pass through.

超滤器膜的设计只允许特定尺寸的颗粒通过。

9.The laboratory utilized an ultrafilter to purify the water used in experiments.

实验室使用了一个超滤器来净化实验中使用的水。

10.An ultrafilter can remove bacteria and viruses from water, making it safe for consumption.

超滤器可以去除水中的细菌和病毒，使其适合饮用。

11.Many home water purification systems include an ultrafilter to ensure safe drinking water.

许多家庭水净化系统都包含一个超滤器以确保饮用水安全。

作文

In the realm of mathematics and logic, the concept of an ultrafilter plays a crucial role in the study of set theory and topology. An ultrafilter is a special kind of filter that has unique properties, making it a powerful tool in various mathematical applications. To understand what an ultrafilter is, we first need to grasp the basic idea of a filter. In simple terms, a filter is a collection of subsets of a given set that satisfies certain properties. It is used to formalize the notion of 'largeness' or 'generality' in mathematics.An ultrafilter is a filter that is maximal, meaning that it cannot be extended any further without losing its properties. This maximality gives the ultrafilter its distinctive characteristics. For instance, for any subset of the original set, either that subset or its complement must belong to the ultrafilter, but not both. This property allows mathematicians to make strong conclusions about the behavior of functions and sequences defined on the set.One of the most significant applications of ultrafilters is in the field of topology. In topology, we often deal with convergent sequences and limits. The use of ultrafilters helps in defining convergence in a more generalized way. Instead of just looking at individual sequences, we can consider entire collections of sequences using ultrafilters. This leads to the development of the concept of limit points and cluster points, which are essential in understanding the structure of topological spaces.Moreover, ultrafilters are also instrumental in model theory, a branch of mathematical logic that deals with the relationship between formal languages and their interpretations or models. In this context, ultrafilters help in constructing models that satisfy certain properties, allowing mathematicians to explore the consistency and completeness of various logical systems.The existence of ultrafilters is guaranteed by the Axiom of Choice, a fundamental principle in set theory. While the Axiom of Choice is somewhat controversial due to its non-constructive nature, it is widely accepted in modern mathematics. The existence of ultrafilters can lead to some counterintuitive results, such as the existence of non-principal ultrafilters, which do not concentrate on any particular point but rather spread out over the entire space.In conclusion, the concept of an ultrafilter is a fascinating and powerful idea in mathematics. Its properties allow for a deeper understanding of convergence, topology, and model theory. As we continue to explore the vast landscape of mathematics, the role of ultrafilters will undoubtedly remain significant, providing insights and tools that help us uncover the underlying structures of mathematical truths. Whether in pure mathematics or applied fields, the influence of ultrafilters is profound and far-reaching, illustrating the beauty and complexity of mathematical thought.

在数学和逻辑的领域中，ultrafilter（超滤子）的概念在集合论和拓扑学的研究中起着至关重要的作用。ultrafilter是一种特殊类型的滤子，具有独特的属性，使其成为各种数学应用中的强大工具。要理解ultrafilter是什么，我们首先需要掌握滤子的基本概念。简单来说，滤子是给定集合的子集的一个集合，满足某些属性。它用于形式化数学中的“巨大”或“普遍性”的概念。ultrafilter是一个极大滤子，这意味着它不能进一步扩展而不失去其属性。这种极大性赋予了ultrafilter其独特的特征。例如，对于原始集合的任何子集，要么该子集要么其补集必须属于ultrafilter，但两者不能同时存在。这一属性使得数学家能够对定义在该集合上的函数和序列的行为做出强有力的结论。ultrafilters最重要的应用之一是在拓扑学领域。在拓扑学中，我们常常处理收敛序列和极限。使用ultrafilters帮助以更广泛的方式定义收敛。我们不仅仅关注单个序列，而是可以考虑整个序列集合，利用ultrafilters。这导致了极限点和聚点的概念的发展，这对于理解拓扑空间的结构至关重要。此外，ultrafilters在模型理论中也发挥着重要作用，模型理论是数学逻辑的一个分支，研究形式语言及其解释或模型之间的关系。在这种背景下，ultrafilters有助于构建满足某些属性的模型，使数学家能够探索各种逻辑系统的一致性和完备性。ultrafilters的存在由选择公理保证，这是集合论中的一个基本原则。虽然选择公理由于其非构造性的性质而略显争议，但在现代数学中被广泛接受。ultrafilters的存在可能导致一些反直觉的结果，例如存在非主滤子ultrafilters，这些滤子并不集中于任何特定点，而是遍布整个空间。总之，ultrafilter的概念是数学中一个迷人而强大的思想。其属性使我们能够更深入地理解收敛、拓扑学和模型理论。随着我们继续探索数学的广阔领域，ultrafilters的角色无疑将保持重要性，提供帮助我们揭示数学真理基础结构的见解和工具。无论是在纯数学还是应用领域，ultrafilters的影响都是深远的，展示了数学思想的美丽和复杂性。