injective

简明释义

英[ɪnˈdʒektɪv]美[ɪnˈdʒektɪv]

adj. [数] 内射的；[数] 单射的

英英释义

单词用法

同义词

反义词

例句

1.Objective to expel the artificial technique factor, study the main factors that affect the effect of injective augmentation mammaplasty.

目的：排除人为技术因素，探讨影响注射式隆乳外形效果的主要因素。

2.The influence of the four-node structure destroying the injective preservation under reductions is studied.

我们对四点结构在破坏单射的归约保持性方面的作用进行了分析。

3.In nonmonotonic logic, injective preferential models play an important role.

单射占优模型在非单调逻辑中具有重要的地位。

4.Objective: To evaluate the efficacy of injective therapy for non parasitic hepatic cyst.

目的：评价非寄生虫性肝囊肿B超引导经皮穿刺注射治疗的临床效果。

5.Injective emulsion can relieve pain and improve life quality of patients with lung cancer in advanced stage.

结论康莱特注射乳剂，能缓解疼痛症状，改善晚期癌症患者的生活质量。

6.Prepositive polymer slug displacement can decrease the effect by the formation heterogeneity, prevent the gas breakthrough and improve the displacement sweep efficiency of the injective gas.

对于地层非均质性的影响，通过注入聚合物段塞调驱，能起到防止气窜，增加注入气驱扫效率。

7.Objective: to observe the effect of injective triamcinolone acetonide for the treatment of keloid.

目的：观察曲安奈德注射液瘢痕内注射治疗瘢痕疙瘩的疗效。

8.These results reveal that KLM valuation structure provides a sufficient and canonical approach to establish representation theorems for any injective inference relations in finite framework.

这些结果说明，KLM赋值结构为证明有限语言下单可表示类后承的表示定理提供了一种充分的通用性方法。

9.This topic is about the design and manufacture of the Nokia 7610 covers precise injective mould.

本课题是诺基亚7610外壳精密注塑模的设计与制造。

10.Prepositive polymer slug displacement can decrease the effect by the formation heterogeneity, prevent the gas breakthrough and improve the displacement sweep efficiency of the injective gas.

对于地层非均质性的影响，通过注入聚合物段塞调驱，能起到防止气窜，增加注入气驱扫效率。

11.An injective function is essential in defining a one-to-one correspondence between two sets.

在定义两个集合之间的一一对应关系时，单射函数是必不可少的。

12.The proof shows that the transformation is injective, ensuring no two elements map to the same element.

证明表明该变换是单射，确保没有两个元素映射到同一个元素。

13.In mathematics, a function is called injective if it maps distinct inputs to distinct outputs.

在数学中，如果一个函数将不同的输入映射到不同的输出，则该函数称为单射。

14.In computer science, an injective mapping can help ensure data integrity when transferring information.

在计算机科学中，单射映射可以帮助确保在传输信息时的数据完整性。

15.If a function is injective, it guarantees that every output is produced by at most one input.

如果一个函数是单射，它保证每个输出最多由一个输入产生。

作文

In the realm of mathematics, particularly in the study of functions, the term injective refers to a specific property of a function that is crucial for understanding its behavior. A function is considered injective (或称为一一映射) if it assigns distinct outputs to distinct inputs. This means that for every pair of different elements in the domain of the function, their images under the function are also different. In simpler terms, no two different inputs can produce the same output. This concept is fundamental in various areas of mathematics, including algebra and calculus, and is essential for establishing relationships between sets.To illustrate this concept, let us consider a simple example: the function f(x) = 2x. For any two different values of x, say x1 and x2, if x1 is not equal to x2, then f(x1) will not equal f(x2). This clearly shows that the function is injective. The significance of injective functions lies in their ability to maintain uniqueness; they preserve the distinctiveness of elements in their mappings.Understanding injective functions is not just an academic exercise; it has practical implications as well. For instance, in computer science, algorithms often rely on the properties of functions to ensure data integrity and uniqueness. When designing databases, ensuring that certain fields are injective can prevent data duplication and maintain the accuracy of the information stored.Moreover, the concept of injective functions extends beyond basic mathematical functions. In advanced topics such as topology and abstract algebra, the idea of injectivity plays a critical role in defining isomorphisms and homeomorphisms, which are foundational concepts in these fields. An isomorphism, for instance, is a mapping between two structures that preserves their operations and relations, and it requires that the function involved be injective.In real-world applications, the principle of injective mapping can be seen in various scenarios. For example, consider a scenario in a school where each student is assigned a unique identification number. The mapping from students to their identification numbers is injective because no two students can share the same ID. This ensures that each student's record is distinct and easily retrievable, showcasing the importance of maintaining uniqueness in data representation.Furthermore, in the field of cryptography, injective functions are vital for creating secure encryption methods. When encrypting data, it is essential that the encryption function is injective so that each piece of plaintext translates to a unique piece of ciphertext. This prevents ambiguity and ensures that the original data can be accurately recovered during decryption.In conclusion, the concept of injective functions is a fundamental aspect of mathematics that permeates various disciplines, including computer science, cryptography, and data management. By ensuring that distinct inputs yield distinct outputs, injective functions help maintain the integrity and uniqueness of data, making them indispensable in both theoretical and practical applications. As we continue to explore the depths of mathematics and its applications, understanding the significance of injective functions will undoubtedly enhance our comprehension and enable us to tackle more complex problems with confidence.

在数学领域，特别是在函数研究中，术语injective指的是一个函数的特定属性，这对理解其行为至关重要。如果一个函数被认为是injective（或称为一一映射），则它对不同的输入分配不同的输出。这意味着对于函数定义域中的每一对不同元素，它们在函数下的映像也是不同的。简单来说，两个不同的输入不能产生相同的输出。这个概念在代数和微积分等多个数学领域中是基础性的，并且对于建立集合之间的关系至关重要。为了说明这个概念，我们考虑一个简单的例子：函数f(x) = 2x。对于任何两个不同的x值，比如x1和x2，如果x1不等于x2，那么f(x1)将不等于f(x2)。这清楚地表明该函数是injective的。injective函数的重要性在于它们保持唯一性；它们在映射中保留元素的独特性。理解injective函数不仅仅是学术上的练习；它也具有实际意义。例如，在计算机科学中，算法通常依赖于函数的属性来确保数据的完整性和唯一性。在设计数据库时，确保某些字段是injective可以防止数据重复并维护存储信息的准确性。此外，injective函数的概念超越了基本数学函数。在拓扑学和抽象代数等高级主题中，单射性概念在定义同构和同胚等基础概念中起着关键作用。例如，同构是两个结构之间的映射，它保持它们的运算和关系，而这需要所涉及的函数是injective的。在现实世界的应用中，injective映射的原理可以在各种场景中看到。例如，考虑一个学校的场景，每个学生被分配一个唯一的身份证号码。学生与其身份证号码之间的映射是injective的，因为没有两个学生可以共享同一个ID。这确保了每个学生的记录是独特的，易于检索，展示了在数据表示中保持唯一性的重要性。此外，在密码学领域，injective函数对于创建安全加密方法至关重要。在加密数据时，加密函数必须是injective的，以便每个明文翻译成唯一的密文。这防止了模糊性，并确保在解密过程中原始数据能够准确恢复。总之，injective函数的概念是数学的一个基本方面，渗透到计算机科学、密码学和数据管理等多个学科中。通过确保不同的输入产生不同的输出，injective函数帮助维护数据的完整性和唯一性，使其在理论和实际应用中不可或缺。随着我们继续探索数学及其应用的深度，理解injective函数的重要性无疑将增强我们的理解，使我们能够自信地解决更复杂的问题。