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sqlcode大模型中文英文回答：SQLCODE, short for Structured Query Language Code, is a code that identifies the type of error or warning that occurred during the execution of an SQL statement. It is a three-digit numeric code, where the first digit indicates the class of the error, the second digit indicates the subtype of the error, and the third digit indicates the specific error.SQLCODE values can be positive or negative. Positive values indicate a warning, while negative values indicate an error. The most common SQLCODE values are:0: No error or warning.100: Warning.200: Syntax error.300: Data type error.400: Constraint violation.500: Privileges error.600: System error.SQLCODE values can be used to identify the cause of an error or warning, and to take appropriate action to resolve the issue. For example, if a SQLCODE value of 200 is returned, it indicates that a syntax error occurred. The developer can then check the SQL statement for typos or other syntax errors.SQLCODE values can also be used to provide more information about an error or warning. For example, a SQLCODE value of 400 can be returned with a message that indicates the specific constraint that was violated. The developer can then use this information to determine how to resolve the issue.中文回答：SQLCODE，即结构化查询语言代码，是一个用于标识在执行 SQL 语句期间发生的错误或警告类型的代码。
将object强制转换成int效率测试今天阅读代码时发现下⾯这句代码string SqlCount ="select count("+ IndexField +") from "+ SqlTablesAndWhere;mandText = SqlCount;RecordCount = (int)cmd.ExecuteScalar();写过代码的都知道ExecuteScalar()是⼲什么的，它返回的是SQL语句执⾏结果集的第⼀⾏第⼀列，类型是object那么上⾯的代码强制转换是⼀定能成功的。
不过出于平时总听到或见到说尽量不要⽤强制转换，要⽤int.Parse或Convert.ToInt32之类的代替。
所以⼀直对(int)是避⽽远之，但在反编译微软System.Web库时发现⾥⾯很多地⽅还是⽤到了是直接⽤的(int),于是有我以下测试.测试代码1private static void Test3(int count) {int x;object y =4;DateTime dt1 = DateTime.Now;for (int i =0; i < count; i++){x = Convert.ToInt32(y);}DateTime dt2 = DateTime.Now;for (int i =0; i < count; i++){x = (int)y;}DateTime dt3 = DateTime.Now;//for (int i = 0; i < count; i++) //Parse只能将字符串转成int 这⾥跳过测试//{// x = int.Parse("4");//}//DateTime dt4 = DateTime.Now;Console.WriteLine("---------"+ (dt2 - dt1).ToString());Console.WriteLine("*********"+ (dt3 - dt2).ToString());//Console.WriteLine("*********" + (dt4 - dt3).ToString());Console.Read();}在控制台调⽤，传参100000000，执⾏结果为测试代码2private static void Test3(int count) {int x;string y ="4";DateTime dt1 = DateTime.Now;for (int i =0; i < count; i++){x = Convert.ToInt32(y);}DateTime dt2 = DateTime.Now;//for (int i = 0; i < count; i++)//{// x = (int)y; //⽆法将string转换成int//}DateTime dt3 = DateTime.Now;for (int i =0; i < count; i++) //Parse只能将字符串转成int 这⾥跳过测试{x =int.Parse(y);}DateTime dt4 = DateTime.Now;Console.WriteLine("---------"+ (dt2 - dt1).ToString());//Console.WriteLine("*********" + (dt3 - dt2).ToString());Console.WriteLine("*********"+ (dt4 - dt3).ToString());Console.Read();}同样在控制台调⽤，传参100000000，执⾏结果为测试代码3private static void Test3(int count) {int x;object y =4;DateTime dt1 = DateTime.Now;for (int i =0; i < count; i++){x = Convert.ToInt32(y);}DateTime dt2 = DateTime.Now;//for (int i = 0; i < count; i++)//{// x = (int)y; //⽆法将string转换成int//}DateTime dt3 = DateTime.Now;for (int i =0; i < count; i++) //Parse只能将字符串转成int 这⾥跳过测试{x =int.Parse(y.ToString());}DateTime dt4 = DateTime.Now;Console.WriteLine("---------"+ (dt2 - dt1).ToString());//Console.WriteLine("*********" + (dt3 - dt2).ToString());Console.WriteLine("*********"+ (dt4 - dt3).ToString());Console.Read();}同样在控制台调⽤，传参100000000，执⾏结果为其实做这些测试挺⽆聊的，还可能招来⼀⽚骂声，说什么要效率你⽤汇编，C或更进⼀步直接写机器码吧。
第十二届全国代数学术会议大会报告摘要Classical Yang-Baxter equation,its extensions and some related algebraicstructures白承铭南开大学Wefirst give a brief introduction to the classical Yang-Baxter equation which emphasizes the relationship between the tensor and operator forms.Then we give two approaches to extend the classical Yang-Baxter equation,motivated by the study of different topics like integrable systems,Rota-Baxter algebras and Lie bialgebras.Moreover,there are some interesting algebraic structures behind these two approaches.Representation type of algebras:Yesterday,today and tomorrow韩阳中国科学院数学与系统科学研究院Email:***********.cnOne task in representation theory of algebras is to classify all representations of an algebra.Before this,one needs to judge whether it is hopeful for an algebra to do so or not,namely,to determine the representation type of an algebra.In this survey,some concepts,results,ideas,methods,and problems on representation type of algebras are introduced.群环的代数K理论唐国平中科院研究生院数学科学学院报告将分为三个部分：1）本质循环群(具有指数有限的循环子群的群)的整群环的K理论。
PostgreSql扩展Sql-动态加载共享库（C函数）基于 psql (PostgreSQL) 10.4pg_language表定义了函数实现所使⽤的语⾔。
主要⽀持了C语⾔和SQL语句。
⼀些可选的语⾔包括pl/pgsql、tcl和perl。
ligang=# select lanname, lanispl, lanpltrusted, lanplcallfoid, laninline, lanvalidator from pg_language;lanname | lanispl | lanpltrusted | lanplcallfoid | laninline | lanvalidator----------+---------+--------------+---------------+-----------+--------------internal | f | f | 0 | 0 | 2246c | f | f | 0 | 0 | 2247sql | f | t | 0 | 0 | 2248plpgsql | t | t | 13198 | 13199 | 13200pg_proc表对函数进⾏了定义。
每⼀个函数在该表中都对应⼀个元组，包含函数名。
输⼊参数类型，返回类型以及对函数的定义(可能是⽂本，可能是⼀段编译型语句，也可能是对可执⾏代码的引⽤)。
编译过的函数可以静态地链接到服务器上，或者在存储在共享库内，当第⼀次使⽤该库时动态的载⼊。
ligang=# select proname,prolang, prorettype,proargtypes, prosrc,probin from pg_proc where proname like '%square%';proname | prolang | prorettype | proargtypes | prosrc | probin---------+---------+------------+-------------+----------------------------+--------------------square | 13201 | 23 | 23 | begin return $1 * $1; end; |squares | 13 | 23 | 23 | squares_return_int | $libdir/squares.so查看其数据类型ligang=# select oid , typname from pg_type where oid = 23;oid | typname-----+---------23 | int4(1 row)以下是⽰例函数：C: 与内建SQL类型等效的C类型intsquare_int (int x){return x * x;}把上⾯的函数编译成共享库⽂件，这样声明：CREATE FUNCTION square(int) RETURNS intAS '/path/to/square.so', 'square_int'LANGUAGE 'C';PL/PGSQL：ligang=# create function square(int) returns int as 'begin return $1 * $1; end;' LANGUAGE 'plpgsql';CREATE FUNCTIONligang=#ligang=#ligang=# select square(4);square--------16建⽴⽤户函数动态库新建代码#include "postgres.h"#include "fmgr.h"intsquare_int(int x){return x * x;}编译 - 添加共享库[ligang@yfslcentos71 include]$ gcc -I`pg_config --includedir-server` -c squares.c[ligang@yfslcentos71 include]$ gcc -shared squares.o -o squares.so[ligang@yfslcentos71 include]$ cp squares.so `pg_config --libdir`/Pg数据库装载ligang=# create function squares(int) returns int as '$libdir/squares.so', 'square_int' LANGUAGE 'c' STRICT;关于PG_MODULE_MAGIC为了确保不会错误加载共享库⽂件，从PostgreSQL 开始将检查那个⽂件的"magic block"，这允许服务器以检查明显的不兼容性。
it面试题库及答案IntroductionWith the rapid development of information technology, the demand for IT professionals has been increasing. As a result, IT interviews have become a crucial step in the hiring process. To succeed in an IT interview, it is essential to have a comprehensive understanding of commonly asked questions and well-prepared answers. This article aims to provide a detailed IT interview question bank along with sample answers.1. Technical Questions1.1 Programming Languages1.1.1 What is the difference between Java and Python?Java and Python are both popular programming languages but differ in various aspects. Java is a compiled language that runs on the Java Virtual Machine (JVM), while Python is an interpreted language. Java is mainly used for enterprise-level applications, while Python is known for its simplicity and readability. Additionally, Java requires explicit declaration of data types, while Python uses dynamic typing.1.1.2 What is object-oriented programming?Object-oriented programming (OOP) is a programming paradigm that organizes software design around objects that represent real-world entities. It emphasizes the concepts of encapsulation, inheritance, and polymorphism. OOP allows for modular and reusable code, making it easier to maintain and expand software systems.1.2 Database Management1.2.1 What is the difference between SQL and NoSQL databases?SQL (Structured Query Language) databases are relational databases that store and manage structured data in tables with predefined schemas. They are suitable for complex queries and transactions. NoSQL (Not only SQL) databases, on the other hand, are non-relational databases designed for handling large amounts of unstructured or semi-structured data. They provide flexible schemas and horizontal scalability.1.2.2 What is ACID in database management?ACID (Atomicity, Consistency, Isolation, Durability) is a set of properties that ensure reliability and consistency in database transactions. Atomicity guarantees that a transaction is treated as a single unit of work, either fully completed or fully rolled back if any part fails. Consistency ensures that the database remains in a valid state before and after a transaction. Isolation prevents interference from concurrent transactions, and Durability guarantees that once a transaction is committed, its changes are permanent.2. Behavioral Questions2.1 Problem-Solving2.1.1 Describe a challenging technical problem you encountered and how you resolved it.2.1.2 Give an example of a time when you had to work under pressure to meet a tight deadline. How did you handle it?2.2 Communication Skills2.2.1 Explain a complex technical concept to someone without a technical background.2.2.2 Describe a situation where you had to communicate and collaborate with a team to solve a problem.3. Sample Answers1.1.1 Java and Python differ in their execution models and use cases. Java is a compiled language that runs on the JVM, allowing for high performance and platform independence. It is commonly used for building enterprise-level applications. In contrast, Python is an interpreted language known for its simplicity and readability. It is widely adopted in web development, scientific computing, and data analysis due to its ease of use and extensive library support.1.1.2 Object-oriented programming (OOP) is a software development paradigm that focuses on modular and reusable code. It organizes software design around objects, which are instances of classes representing real-world entities. OOP emphasizes encapsulation, where data and methods are bundled together within objects. It also enables inheritance, allowing classes to inherit attributes and behaviors from parent classes. Polymorphism, another key concept in OOP, allows objects to take on many forms and exhibit different behaviors based on the context. OOP enhances code reusability, maintainability, and scalability.2.1.1 In my previous role, I encountered a challenging technical problem where a critical database server went down, causing a major disruption inour production environment. I promptly identified the root cause, which was a disk failure. To resolve the issue, I replaced the faulty disk and restored the database from the latest backup. However, to minimize the downtime, I implemented a backup server configuration and utilized a replication mechanism to keep the data synchronized. This solution ensured both data integrity and high availability.2.1.2 Working under pressure to meet tight deadlines is a common occurrence in the IT industry. In one instance, I received a project with an unexpectedly shortened timeline due to unexpected client requirements. To handle the situation, I immediately prioritized the tasks, focusing on critical components and breaking down the project into manageable subtasks. I communicated with the team, delegating responsibilities and ensuring everyone was aware of the new timeline. By working overtime, maintaining constant communication, and efficiently managing resources, we successfully met the deadline without compromising the quality of the deliverables.2.2.1 Complex technical concepts can be challenging to explain to non-technical individuals. To overcome this, I often use analogies and relatable examples to help them grasp the idea. For instance, when explaining encryption, I compare it to sending secret messages using a lock and key. I describe how encryption algorithms scramble data (message) using a key (like a lock), making it unreadable to unauthorized parties. Only someone with the correct key can decrypt (unlock) and access the original message. This simplifies the concept and allows non-technical individuals to understand the fundamentals of encryption.2.2.2 Collaboration and effective communication are vital in solving complex technical problems. In a recent project, our team encountered a challenging software bug that affected the system's stability. To overcome this, we organized regular meetings to discuss and share ideas. Each team member had a specialized area of expertise, so we collaborated closely, actively listening to each other's suggestions and insights. By pooling our knowledge and skills, we successfully identified the root cause and implemented a comprehensive solution. This experience highlighted the importance of teamwork and effective communication in problem-solving.ConclusionThe field of information technology is vast and evolving, and IT interviews are designed to evaluate candidates' technical knowledge, problem-solving abilities, and communication skills. By familiarizing yourself with common IT interview questions and crafting thoughtful answers, you can increase your chances of success. Remember to adapt your answers based on your own experience and expertise. Good luck with your upcoming IT interviews!。
SQL注入资产谷歌语法介绍SQL注入是一种常见的网络攻击方式，攻击者通过在应用程序的输入字段中插入恶意的SQL语句来获取数据库中的信息或对数据库进行操作。
资产谷歌语法是一种用于在互联网上搜索敏感信息的技术，通过使用特定的语法，可以在谷歌搜索引擎中搜索到包含指定关键词的网页。
本文将探讨如何使用SQL注入技术来利用谷歌搜索引擎来搜索并获取敏感信息。
SQL注入基础知识回顾在继续探讨SQL注入资产谷歌语法之前，让我们回顾一下SQL注入的基础知识。
什么是SQL注入？SQL注入是指攻击者通过在应用程序的输入字段中插入恶意的SQL语句来实施攻击的一种安全漏洞。
当应用程序没有对用户输入的数据进行适当的验证和过滤时，攻击者可以通过构造特定的SQL语句来绕过应用程序的安全措施，获取数据库中的敏感信息，或者对数据库进行非法操作。
SQL注入的影响SQL注入攻击可能导致以下影响：1.泄露敏感信息：攻击者可以通过注入恶意的SQL语句来获取数据库中的敏感信息，如用户密码、信用卡号等。
2.篡改数据：攻击者可以修改数据库中的数据，如删除、更改或插入数据。
3.拒绝服务：攻击者可以利用SQL注入漏洞来执行高负载的查询，从而导致数据库性能下降甚至崩溃。
SQL注入资产谷歌语法实例SQL注入资产谷歌语法可以用于搜索特定的信息，如漏洞、用户名、密码、网站等。
下面是一些使用SQL注入资产谷歌语法的实例：1. 搜索数据库用户表使用以下谷歌语法可以搜索数据库用户表中的信息：site: inurl:user.php?id=这个语法将搜索包含user.php?id=的链接地址，然后返回与该语法匹配的网页结果，该地址可能是一个存在SQL注入漏洞的页面。
2. 搜索数据库中的敏感信息使用以下谷歌语法可以搜索数据库中的敏感信息：site: filetype:sql这个语法将搜索所有以.sql为扩展名的文件，这些文件通常包含数据库的备份或导出文件，在其中可能包含敏感信息。
sql lambda表达式摘要：1.SQL Lambda表达式的基本概念mbda表达式在SQL中的应用场景3.使用Lambda表达式的注意事项4.总结正文：SQL Lambda表达式是一种基于Java Lambda表达式的数据库查询技术。
在SQL查询中，Lambda表达式可以帮助我们更简洁、灵活地实现复杂的业务逻辑。
下面就让我们一起来了解SQL Lambda表达式的基本概念、应用场景以及使用注意事项。
1.SQL Lambda表达式的基本概念SQL Lambda表达式是基于Java 8中引入的Lambda表达式的一种数据库查询技术。
它允许你在SQL查询中使用简洁的匿名函数来替代传统的复杂SQL语句。
通过使用Lambda表达式，我们可以简化代码，提高可读性。
mbda表达式在SQL中的应用场景Lambda表达式在SQL中的应用场景主要包括以下几点：（1）筛选数据：使用Lambda表达式可以轻松地实现数据筛选，例如在SELECT语句中使用WHERE子句。
（2）排序数据：在ORDER BY子句中使用Lambda表达式，可以实现数据的排序。
（3）投影数据：使用SELECT子句和Lambda表达式，可以按照需求返回特定的字段。
（4）聚合函数：Lambda表达式可以与聚合函数（如COUNT、SUM、AVG等）结合使用，实现对数据的统计分析。
3.使用Lambda表达式的注意事项在使用Lambda表达式时，需要注意以下几点：（1）确保Lambda表达式的语法正确，避免出现拼写错误或其他语法问题。
（2）根据实际需求选择合适的操作符，如=、<>、>、<等，以实现所需的查询条件。
（3）在聚合函数中使用Lambda表达式时，需要确保传入的参数符合函数的参数要求。
4.总结SQL Lambda表达式为数据库查询带来了极大的便利，使我们可以用简洁的代码实现复杂的业务逻辑。
通过掌握Lambda表达式的基本概念、应用场景和使用注意事项，我们可以更好地利用这一技术，提高工作效率。
Golang SQLX预编译一、概述近年来，Golang语言在软件开发领域得到了广泛的应用。
作为一种高效、简洁和并发性能出色的编程语言，Golang在数据库操作方面也有着独特的优势。
SQLX是Golang中用于与关系型数据库交互的工具库之一，它提供了一套便捷、高效的API，能够帮助开发者轻松地与数据库进行交互。
本文将重点介绍SQLX中的预编译功能，探讨其优势和使用方法。
二、SQLX概述1. SQLX简介SQLX是Golang中用于与关系型数据库进行交互的工具库，它是对标准库database/sql的扩展。
SQLX提供了一套便捷的API，能够简化数据库操作，提高开发效率。
通过SQLX，开发者可以轻松地执行SQL查询、插入、更新和删除操作，同时还能够方便地映射查询结果到Golang的数据结构中。
2. SQLX优势SQLX相较于database/sql具有许多优势，包括更简洁的API、更加灵活的数据映射和更高效的数据库操作。
SQLX还提供了预编译SQL 语句的功能，能够帮助开发者提高查询的性能，减少数据库操作的开销。
三、预编译SQL语句1. 预编译概述预编译是指在执行SQL查询之前，先将SQL语句进行编译和优化，以便数据库在执行查询时能够更加高效地处理。
通过预编译，数据库可以缓存SQL查询的执行计划，避免重复解析和优化语句，从而提高查询的性能。
2. SQLX中的预编译SQLX提供了方便的预编译SQL语句的接口，开发者可以使用Preparex函数对SQL语句进行预编译，然后在执行查询时直接调用预编译的语句。
通过预编译，可以有效减少数据库操作的开销，提高查询的性能。
四、使用示例下面我们通过一个简单的示例来演示如何在Golang中使用SQLX进行预编译SQL语句。
```gopackage m本人nimport ("fmt""github/jmoiron/sqlx"_ "github/go-sql-driver/mysql")func m本人n() {// 连接数据库db, err := sqlx.Connect("mysql","username:passwordtcp(127.0.0.1:3306)/test")if err != nil {fmt.Println("数据库连接失败：", err)return}defer db.Close()// 预编译SQL语句stmt, err := db.Preparex("SELECT * FROM user WHERE id = ?")if err != nil {fmt.Println("预编译SQL语句失败：", err)return}defer stmt.Close()// 执行查询var user Usererr = stmt.Get(user, 1)if err != nil {fmt.Println("查询失败：", err)return}fmt.Println("查询结果：", user)}```在上面的示例中，我们首先通过sqlx.Connect函数连接到MySQL数据库，然后使用db.Preparex函数对SQL语句进行预编译。
淘宝数据库OceanBaseSQL编译器部分源代码阅读--解析SQL语法树OceanBase是阿⾥巴巴集团⾃主研发的可扩展的关系型数据库，实现了跨⾏跨表的事务，⽀持数千亿条记录、数百TB数据上的SQL操作。
在阿⾥巴巴集团下，OceanBase数据库⽀持了多个重要业务的数据存储。
包含收藏夹、直通车报表、天猫评价等。
截⽌到2013年4⽉份。
OceanBase线上业务的数据量已经超过⼀千亿条。
看起来挺厉害的,今天我们来研究下它的源码。
关于OceanBase的架构描写叙述有⾮常多⽂档。
这篇笔记也不打算涉及这些东西，仅仅讨论OceanBase的SQL编译部分的代码。
OceanBase是⼀个开源的数据库,托管在github上,。
本⽂讨论的源代码路径相应为：。
最新的版本号为0.4，本⽂讨论的代码基于0.3版本号的OceanBase.眼下OceanBase的能解析的SQL还⽐較少，包含Select,Insert,Update,Delete,Show,Explain等.选择OceanBase 0.3 版本号进⾏学习。
基于⼏个原因：OceanBase 的⾼质量。
⾼可读性OceanBase 版本号低，没有历史负担OceanBase SQL解析相对简单。
更easy窥见全貌。
利于理解设计开发中要解决的主要问题。
与其它数据库的SQL解析部分进⾏对照，深⼊理解问题本质该部分主要功能包含了。
SQL语句解析，逻辑计划的⽣成。
物理操作符运算等。
⼊⼝：Ob Sq l类本部分的⼊⼝函数在ob_sql.h中,调⽤函数ObSql::direct_execute能够直接运⾏SQL语句,并返回结果集ObResultSet。
函数stmt_prepare⽤于解析要预编译的SQL语句,stmt_execute则⽤于运⾏Prepare过的SQL语句。
class ObSql{public:ObSql(){}~ObSql(){}int direct_execute(const common::ObString &stmt, ObResultSet &result)int stmt_prepare(const common::ObString &stmt, ObStmtPrepareResult &result);int stmt_execute(const uint64_t stmt_id, const common::ObArray<common::ObObj> params, ObResultSet &result);int stmt_close(const uint64_t stmt_id);};在0.4版本号中。
编译原理实践yacc(sql查询语句解析) 概述说明1. 引言1.1 概述本篇文章旨在介绍编译原理实践中使用Yacc工具对SQL查询语句进行解析的过程。
编译原理是计算机科学中的重要研究领域，主要涉及将高级语言转化为低级的机器语言，以便计算机能够理解和执行。
通过使用编译原理中的概念和技术，可以大大简化复杂语法的分析和解析过程，提高程序开发的效率。
1.2 文章结构本文共分为五个部分，每个部分都有其特定的内容和目标：- 引言：介绍本篇文章的背景和目的。
- 编译原理实践yacc：阐述编译原理及介绍Yacc工具在该领域中的应用。
- SQL查询语句解析过程：详细讲解SQL查询语句的基本结构、词法分析过程以及语法分析过程。
- Yacc工具的使用和配置：指导读者如何安装Yacc工具，并演示如何编写Yacc 源文件以及生成解析器代码并进行运行。
- 结论与展望：总结全文内容并提供未来可能的拓展方向。
1.3 目的本文目的在于通过对编译原理和Yacc工具在SQL查询语句解析中的应用进行介绍，帮助读者更好地理解编译原理的相关概念，并掌握使用Yacc工具进行语法分析和解析的方法。
通过实践演示和案例讲解，读者能够学会配置和使用Yacc 工具，并将其应用于自己感兴趣的领域。
以上为“1. 引言”部分内容的详细描述，请结合实际情况进行参考与调整。
2. 编译原理实践yacc2.1 什么是编译原理编译原理是计算机科学领域的一个重要分支，研究如何将高级程序语言转换为机器语言。
它涉及到编程语言的词法分析、语法分析和代码生成等多个方面。
通过编译原理，我们可以了解程序如何被解释和执行，从而能够更好地设计和优化程序。
2.2 Yacc介绍Yacc（Yet Another Compiler Compiler）是一款用于生成语法解析器的工具。
它是由AT&T贝尔实验室的Stephen C. Johnson在20世纪70年代开发的，并成为Unix操作系统环境下广泛使用的编译器工具之一。
Appendix:1. Mathematical vocabularyAAbelian group 交换群Absolute value 绝对值Absolute convergence 绝对收敛Accumulation point 聚点Acute angle 锐角Adjacent angles 邻角Adjoint matrix 伴随矩阵Algebra 代数Alternating series 交错级数Amplitude 振幅Analytic function 解析函数Angular velocity 角速度Approximation theory 逼近论Arc differential 弧微分Arithmetic root 算术根Associative law 结合律Auxiliary function 辅助函数Average velocity 平均速度Axiom of choice 选择公理BBall 球Banach algebra 巴拿赫代数Basic elementary function 基本初等函数Bell shaped curve 钟型曲线Bernoulli equation 贝努利方程Binomial expansion 二项展开式Bijection 双射Bivariate distributation 二元分布Block matrix 块矩阵;Borel set 波莱尔集Boundary curve 边界曲线Bounded function有界函数CCalculus 微积分Cardinal number基数Cartesian coordinates 笛卡尔坐标Cauchy inequality 柯西不等式Centre of a neighborhood 领域的中心Chain rule 链式法则Characteristic curve 特征曲线Chebyshev inequality 切比雪夫不等式Chord theory 弦理论Choas 混沌Closure 闭包Coefficient matrix 系数矩阵Cofactor 余子式Clockwise sense 顺针方向Collinear point 共线点Combinatorial programming 组合规划Commutation law 交换律Compact set 紧集Complement of event 补事件Complete space 完备空间Complex integral 复积分Composite function 复合函数Concave curve 凹曲线Conditional extreme values 条件极值Conjugate root 共轭根Connected component 连通分支Consistency theorem 相容性定理Continue function 连续函数Contractive mapping 压缩映射Converge series 收敛级数Converse sentence 逆命题Convex analysis 凸分析Corollary 推论Correlation coefficient 相关系数Cosine series 余弦级数Countable set 可数集Cover 覆盖Criterion of convergence 收敛准则Critical point 临界点Curvature 曲率Curve of second class 二次曲线Cyclic subgroup 循环子群Cylindrical surface 柱面DD’Alembert formula 达朗贝尔公式Decomposing subspace 可分解子空间Decreasing series 递减级数Definite integral 定积分Definition 定义Defined interval 定义区间Dense subset 稠密子集Dependent variable 因变量Derivative 导数Derivative function 导函数Determinant of matrix 矩阵的行列式Differential equation 微分方程Difference of set 差集Dimension number 维数Differential quotient 微商Direct product 直积Directional derivative 方向导数Discrete distribution 离散分布Disjoint events 不相交事件Divergent sequence 发散序列Dlliptic cone 椭圆锥面Domain 定义域Double integral 二重积分Duality principle 对偶原理EEdge 边Eigendistribution 特征分布Eigenvalue 特征值Elementary divisor 初等因子Elementary event 初等事件Elimination 消去法Ellipse 椭圆Empirical formula 经验公式End point 端点Entropy constant 熵常数Entry 元素Envelope 包络Equation of linear regression线性回归方程Equidistant 等距Equivalence class等价类Equivalent matrix 等价矩阵Equivalent infinitesimal 等阶无穷小Error term 误差项Estimation region 置信区间Euclidean space 欧几里德空间Euler function 欧拉函数Evolvent 渐近线Even function 偶函数Everywhere dense 处处稠密Exterior point 外点Expectancy 期望Explicit function 显函数Exponential function 指数函数Extension theorem 延拓定理Extremum with a condition 条件极值FFactor 因子，商，因素Factor group 商群Factorial 阶乘Fiber bundle 纤维从Fibonacci method 黄金分割法Field of direction 方向场Finite covering 有限覆盖Finite element method 有限元法First derivation 一阶导数Fully invariant subgroup 完全不变子群Fundamental system of solution 基础解系Fuzzy topology 模糊拓扑GGalois theory 伽罗华理论;Game matrix 对策矩阵Global(absolute) mximum 最大值Graph of a function 函数图形Gauss—Jordan elimination 高斯约当消元法Generalized inverse 广义逆Generating curve 母线Gradient 梯度Gravitational potential 引力势Greatest lower bound 下确界Group homomorphism 群同态Group isomorphism 群同构Group of permutations 置换群HHamilton equation 哈密尔顿方程Harmonic function 调和函数Hermite matrix 埃尔米特矩阵Hessian matrix 海塞矩阵Hilbert space 希尔伯特空间Homeomorphic 同胚Homogeneous linear equation齐次线性方程Horizontal plane 水平面Hybrid partial derivative 混合偏导数Hyperbolic 双曲线Hyperbolic function 双曲函数Hyperplane 超平面IIdeal 理想Idempotent 幂等元Identity 单位元Imaginary part 虚部Implicit difference equation 隐式微分方程Implicit function 隐函数Improper fraction 假分式Impossible event 不可能事件Incompatible event 不相容的事件Index theory 指标理论Induce mapping 诱导映射Inertial theorem 惯性定理Infimum 下确界Infinite point 无穷远点Infinitesimal of higher order 高阶无穷小Inflection point 拐点Inhomogeneous polynomial 非齐次多项式Injection 单射Integer 整数Integrable function可积函数Integration variable 积分变量Integration by parts 分部积分法Integration by substitution 换元积分法Intercept 截矩Interdependent 相互关联Interior 内部Intermediate term 中间项Interpolate 内插Interval 区间Invariant subspace不变子空间Inverse dependene 反比Invertible matrix 逆矩阵Isolated point 孤立点Isometric mapping 等距映射Isomorphism 同构Iterative process 迭代过程JJacobian matrix 雅克比矩阵Joint distribution 联合分布KKernel 核Kitchen drawer principle 抽屉原理LLabile point 不稳定点Lambda matrix -矩阵Laplacian operator 拉普拉斯算子Lattice 格Linear algebra 线性代数Linear transformation 线性变换Linear space 线性空间Local(relative) maximum 极大值Logarithm function 对数函数Logic 逻辑Lower semi-continuous 下半连续Lowest common multiple 最小公倍数MMajorization 优化Manifold 流形Mapping 映射Markov chain马尔科夫链Martingale 鞅Mathematical logic 数理逻辑Maximum value 极大值Measurable set 可测集Method of least squares 最小二乘法Metric space 度量空间Minimal value 极小值Minus 减，负号Module 模Moment 矩Monomial 单项式Monotone function 单调函数Multinomial expansion 多项式展开Multiobjective optimization 多目标优化Multiple 倍数，多重Multiplication 乘法NNarrow rectangle 窄矩形Negative definite quadratic form负定二次型Neighbourhood 邻域Nest 套Nilpotent matrix 幂零矩阵Norm 范数，模Normal plane 法平面Numerical Analysis数值分析OObjective function 目标函数Oblique triangle 斜三角形Octant 卦限Odd or even 奇或偶One-sided limits 单侧极限Open disk 开圆盘Operator algebra 算子代数Optimization 最优化Ordered set 有序集Ordinal number序数Orthogonal basis正交基Over field 扩张域PPair 偶，对Parabolic 抛物线Parallel 平行Parallelogram rule 平行四边形法则Paradoxical 悖论Parameter 参数Parametric equation 参数方程Partial ordered set 偏序集Partition 分割，分拆Pathological function 病态函数Pedal 垂足Period function 周期函数Permanency 不变性Permutation 排列，置换Perpendicular 垂线Perturbation 扰动Piecewise function 分段函数Poisson distribution 泊松分布Polynomial 多项式Postulate 公设Power series solution 幂级数解Prime number素数Primitive function 原函数Principle 原理Probability 概率Problem of fixed point 不动点问题Projection 射影Proportion 比例Proposition 命题Pure mathematics 基础数学QQuadrant 象限Quadratic form 二次型Quadric surface二次曲面Quasi-sphere 拟球Quaternary expression四进制表示Quotient 商RRadial 径向Radius of curvature 曲率半径Random process 随机过程Range 区域，值域Rank 秩Rational number 有理数Real analysis 实分析Reciprocal law 互反律，互逆律Rectifiable curve 可求长曲线Recurrence formula 递推公式Rectangular form 矩形Region 区域，范围Regular curve 正则曲线Representation 表示Riemann integral黎曼积分Root 根SSaddle point 鞍点Sample space 样本空间Scalar 标量，纯量Self—adjoint matrix 自共轭矩阵Separable space 可分空间Sequence 序列Similarity 相似性Sign function 符号函数Slope of the tangent line 切线的斜率Smooth curve光滑曲线Spectrum 谱Sphere 球面Spline interpolation 样条插值Square 平方，正方形Stable point 稳定点Stationary point驻点Statistical 统计量Step curve 阶梯曲线Stochastic variable 随机变量Superlinear 超线性Surface of revolution 旋转曲面Surjection 满射Symmetric transformation 对称变换TTabular 制表，列表Tangent 正切Tensor product 张量积Topological space 拓扑空间Torsion 挠率Total differential 全微分Trace 迹Transposed matrix 转置矩阵Trapezoid with curve edge 曲边梯形Trigonometric function 三角函数Trivial 平凡的Typical 典型的UUnbouded 无界的Uniform convergent 一致收敛Uniform motion 匀速运动Unitary operator酉算子Universal 范的, 通用的VVague set 模糊集Validity 有效性Variable 可变的Variation 变分Vector 向量Vertical asymptote 铅直渐近线Vertex 顶点V olume 体积V olute 螺线WWavelet analysis小波分析Weight number 权数Wreath product 圈积Xx—axis x轴Y Y—is axis y轴Yield function 产出函数Z Zero divisor 零因子Zero element 零元素Zero mearsure set 零测度集Zone 区域2. Writing Paper and ExampleA paper is to be written for solving problems in research and practices, which shows the author’sideas. Often it presents some applications in research and practices. It is an important form of idea and results of communication. Therefore, writing paper is a routine work for people to do research. Generally, they are published in some special journal or international conference.A paper often is composed of five parts, such as, title, authors’ names, abstract, American classification number, concrete contents, reference. First, title gives the research problem. Second, the authors’ names will be given in turns. Third, abstract, from its meaning, the problem is described and the main research results are given. American classification number shows the research range of this paper, by it, we can find the paper easily. The following part is the core of paper. It often includes three sections. Authors will illustrate the background of problems that be given in this paper. Then authors will give the idea, results and proofs of results. Finally, applications in research and practices are given. After the main content of the paper, reference is given. In reference, authors will list related materials used in this paper so that readers are convenient to learn it. In addition, at the end, author will give his e-mail address.English Paper ExampleBull. London Math. Soc. 36(2004)53-58 2004 London Mathematical SocietyGAPS BETWEEN CLASSES OF MATRIX MONOTONEFUNCTIONSFRANK HANSEN, GUOXIN JI AND TOMIYAMAABSTRACTThe class )(x P n of matrix monotone function of order n, defined on an interval I, is considered in this paper. Explicit examples are given to prove that if I is different from the whole real line, then )(x P n 1+ is a proper subset of )(x P n for each nature number n. The subhomogeneous C*-algebra are then characterized in term of matrix monotone functions.1．IntroductionAlmost seventy years have passed since Lowner[8] proposed the notation of operator monotone function .A real, continuous function R I f →: defined on a nontrivial interval I is said to be matrix monotone of order n if )()(y f x f y x ≤⇒≤ for any pair of self-adjointn n ⨯matrix x and y with eigenvalues in I . We denote by )(x P n the set of such functions.…2. The gaps between )(x P n and )(1x P n +For a positive integer n, let )(t g n be the polynomial defined by123121...31)(--+++=n n t n t t t g ……..(2).Following the notations in [3], we consider the matrix-valued function associated with )(t g n andgiven by nj i j i n n n j i t g t g M 1,)1())!1()(();(=-+-+=. The following lemma is an application of standardargument taken from the theory of moment problems for Hankel matrices. Lemma 1. The matrix )0;(n n g M is a positive definite. Proof : We set ...2,1,0,2111==⎰-k for dt t b kk , and we calculate that⎩⎨⎧+=-odd is k if evenis k if k b k 0)1(1. Hence we can write )(t g n as 1222210...)(--+++=n n n t b t b t b t g ,and we therefore obtain n j i b j i g j i j i n,...,2,1,,)!1()0(2)1(=-+=-+-+.Consequently, nj i j i n n b g M 1.2)()0;(=-+=.Now we take a vector n n C c c c c ∈=),...,,(21, and calculatedt t c dt t c c c c b c c g M ni i i j i i n i n j j i j n i nj j i n n 21111211111122121,))0;(⎰∑∑∑⎰∑∑-=--+-==--==-+==>=<. It follows that the matrix )0;(n n g M is positive semidefinite. Moreover, if 0)0;(=c g M n n , we see that011=∑=-ni i i tc , almost everywhere in [-1,1]. Since the left-hand side is a polynomial,it is identity zero on the interval [-1,1]. All entries of the vector c are therefore zero, and the matrix)0;(n n g M is positive definite.….3. Characterization of *C -algebras in terms of matrix monotone functions….Reference1. J. bendat and S. Sherman, Monotone and convex operator functions, Trans. Amer. Math.Soc. 79(1955) 58-71.2. O. Dobsch, Matrix funktionen beschrankter Schwankung, Math. Z. 43 (1973)353-388.3. W. Donoghue, Monotone matrix functions and analytic continuation (Springer, 1974).4.K. Lowner, Uber monotone Matrixfunktionen, Math. Z. 38(1934)177-216.….Frank Hansen Guoxing jiInstitute of Economics College of MathematicsUniversity of Copenhagen and informationStudiestrance 6 Shannxi Normal UniversityDK-1455, Copenhagen K Xi,an 710062Denmark P.R.Chinafrank.hansen@econ.ku.dk guoxiji@Jun TomiyamaDepartment of mathematics and PhysicsJapan Women,s UniversityMejirodai Bunkyo-kuJapanjtomiyama@fc.jwuac.jp英语数学论文的组成及写作要求1 Titile（标题）简短明了又能概括全篇中心内容标题要求：标题一般是一个名词短语或者加上介词on ;标题通常不写成句子或不定式短语，也不出现从句。
第39卷第5期 齐 齐 哈 尔 大 学 学 报（自然科学版） Vol.39,No.5 2023年9月Journal of Qiqihar University(Natural Science Edition)Sep.,2023保积3-Hom-李超代数的积结构关宝玲1，田馨心2，田丽军3，闫煦1，王春艳1，李艳君1，董红月1，汪禹淼1，蒋加欣1，赵芬芬1（1.齐齐哈尔大学 理学院，黑龙江 齐齐哈尔 161006；2.中山大学 数学学院，广州 510275；3.齐齐哈尔大学 通信与电子工程学院，黑龙江 齐齐哈尔 161006）摘要：把3-李代数的积结构推广到3-Hom-李超代数。
引入了保积3-Hom-李超代数上的积结构定义，给出了积结构存在的充分必要条件，得到一种特殊的积结构，严格积结构。
关键词：保积3-Hom-李超代数；积结构；严格积结构中图分类号：O152.5 文献标志码：A 文章编号：1007-984X(2023)05-0091-04Hom-李代数的概念是由HARTWIG 等[1]介绍的。
Hom-代数的结构最早出现在向量域上的李代数的拟形变和离散化领域，这些拟形变产生Hom-李代数，它是一个广义的李代数，它包含斜对称性和扭的Jacobi 等式。
Witt 代数和Virasoro 代数的一些q -形变中也有一个Hom-李代数的结构，它与离散的、形变的向量域和微积分学有着紧密联系[1-3]。
Hom-结构被引入到许多代数中，例如，Hom-李代数、Hom-结合代数、Hom-余代数、Hom-双代数、n -元Hom-Nambu-李代数、Hom-莱布尼兹代数和Hom-n -李超代数等等[4-11]。
三李代数最早哈密顿力学的NAMBU 推广[12]，三李超代数最早是由CANTARINI 介绍的[13]，3-Hom-李超代数是三李超代数的Hom-型推广。
GUAN 等[14]研究了3-Hom-李超代数的构造和诱导表示。
Ambiguous operators need parentheses -----------不明确的运算需要用括号括起Ambiguous symbol ''xxx'' ----------------不明确的符号Argument list syntax error ----------------参数表语法错误Array bounds missing ------------------丢失数组界限符Array size toolarge -----------------数组尺寸太大Bad character in paramenters ------------------参数中有不适当的字符Bad file name format in include directive --------------------包含命令中文件名格式不正确Bad ifdef directive synatax ------------------------------编译预处理ifdef有语法错Bad undef directive syntax ---------------------------编译预处理undef有语法错Bit field too large ----------------位字段太长Call of non-function -----------------调用未定义的函数Call to function with no prototype ---------------调用函数时没有函数的说明Cannot modify a const object ---------------不允许修改常量对象Case outside of switch ----------------漏掉了case 语句Case syntax error ------------------ Case 语法错误Code has no effect -----------------代码不可述不可能执行到Compound statement missing{ --------------------分程序漏掉"{"Conflicting type modifiers ------------------不明确的类型说明符Constant expression required ----------------要求常量表达式Constant out of range in comparison -----------------在比较中常量超出范围Conversion may lose significant digits -----------------转换时会丢失意义的数字Conversion of near pointer not allowed -----------------不允许转换近指针Could not find file ''xxx'' -----------------------找不到XXX文件Declaration missing ; ----------------说明缺少"；" houjiumingDeclaration syntax error -----------------说明中出现语法错误Default outside of switch ------------------ Default 出现在switch语句之外Define directive needs an identifier ------------------定义编译预处理需要标识符Division by zero ------------------用零作除数Do statement must have while ------------------ Do-while语句中缺少while部分Enum syntax error ---------------------枚举类型语法错误Enumeration constant syntax error -----------------枚举常数语法错误Error directive :xxx ------------------------错误的编译预处理命令Error writing output file ---------------------写输出文件错误Expression syntax error -----------------------表达式语法错误Extra parameter in call ------------------------调用时出现多余错误File name too long ----------------文件名太长Function call missing -----------------函数调用缺少右括号Fuction definition out of place ------------------函数定义位置错误Fuction should return a value ------------------函数必需返回一个值Goto statement missing label ------------------ Goto语句没有标号Hexadecimal or octal constant too large ------------------16进制或8进制常数太大Illegal character ''x'' ------------------非法字符xIllegal initialization ------------------非法的初始化Illegal octal digit ------------------非法的8进制数字houjiumingIllegal pointer subtraction ------------------非法的指针相减Illegal structure operation ------------------非法的结构体操作Illegal use of floating point -----------------非法的浮点运算Illegal use of pointer --------------------指针使用非法Improper use of a typedefsymbol ----------------类型定义符号使用不恰当In-line assembly not allowed -----------------不允许使用行间汇编Incompatible storage class -----------------存储类别不相容Incompatible type conversion --------------------不相容的类型转换Incorrect number format -----------------------错误的数据格式Incorrect use of default --------------------- Default使用不当Invalid indirection ---------------------无效的间接运算Invalid pointer addition ------------------指针相加无效Irreducible expression tree -----------------------无法执行的表达式运算Lvalue required ---------------------------需要逻辑值0或非0值Macro argument syntax error -------------------宏参数语法错误Macro expansion too long ----------------------宏的扩展以后太长Mismatched number of parameters in definition ---------------------定义中参数个数不匹配Misplaced break ---------------------此处不应出现break语句Misplaced continue ------------------------此处不应出现continue语句Misplaced decimal point --------------------此处不应出现小数点Misplaced elif directive --------------------不应编译预处理elifMisplaced else ----------------------此处不应出现else houjiumingMisplaced else directive ------------------此处不应出现编译预处理elseMisplaced endif directive -------------------此处不应出现编译预处理endifMust be addressable ----------------------必须是可以编址的Must take address of memory location ------------------必须存储定位的地址No declaration for function ''xxx'' -------------------没有函数xxx的说明No stack ---------------缺少堆栈No type information ------------------没有类型信息Non-portable pointer assignment --------------------不可移动的指针（地址常数）赋值Non-portable pointer comparison --------------------不可移动的指针（地址常数）比较Non-portable pointer conversion ----------------------不可移动的指针（地址常数）转换Not a valid expression format type ---------------------不合法的表达式格式Not an allowed type ---------------------不允许使用的类型Numeric constant too large -------------------数值常太大Out of memory -------------------内存不够用houjiumingParameter ''xxx'' is never used ------------------能数xxx没有用到Pointer required on left side of -> -----------------------符号->的左边必须是指针Possible use of ''xxx'' before definition -------------------在定义之前就使用了xxx（警告）Possibly incorrect assignment ----------------赋值可能不正确Redeclaration of ''xxx'' -------------------重复定义了xxxRedefinition of ''xxx'' is not identical ------------------- xxx的两次定义不一致Register allocation failure ------------------寄存器定址失败Repeat count needs an lvalue ------------------重复计数需要逻辑值Size of structure or array not known ------------------结构体或数给大小不确定Statement missing ; ------------------语句后缺少"；"Structure or union syntax error --------------结构体或联合体语法错误Structure size too large ----------------结构体尺寸太大Sub scripting missing ] ----------------下标缺少右方括号Superfluous & with function or array ------------------函数或数组中有多余的"&"Suspicious pointer conversion ---------------------可疑的指针转换Symbol limit exceeded ---------------符号超限Too few parameters in call -----------------函数调用时的实参少于函数的参数不Too many default cases ------------------- Default太多(switch语句中一个)Too many error or warning messages --------------------错误或警告信息太多Too many type in declaration -----------------说明中类型太多houjiumingToo much auto memory in function -----------------函数用到的局部存储太多Too much global data defined in file ------------------文件中全局数据太多Two consecutive dots -----------------两个连续的句点Type mismatch in parameter xxx ----------------参数xxx类型不匹配Type mismatch in redeclaration of ''xxx'' ---------------- xxx重定义的类型不匹配Unable to create output file ''xxx'' ----------------无法建立输出文件xxxUnable to open include file ''xxx'' ---------------无法打开被包含的文件xxxUnable to open input file ''xxx'' ----------------无法打开输入文件xxxUndefined label ''xxx'' -------------------没有定义的标号xxxUndefined structure ''xxx'' -----------------没有定义的结构xxxUndefined symbol ''xxx'' -----------------没有定义的符号xxxUnexpected end of file in comment started on line xxx ----------从xxx行开始的注解尚未结束文件不能结束Unexpected end of file in conditional started on line xxx ----从xxx 开始的条件语句尚未结束文件不能结束Unknown assemble instruction ----------------未知的汇编结构houjiumingUnknown option ---------------未知的操作Unknown preprocessor directive: ''xxx'' -----------------不认识的预处理命令xxx Unreachable code ------------------无路可达的代码Unterminated string or character constant -----------------字符串缺少引号User break ----------------用户强行中断了程序Void functions may not return a value ----------------- Void类型的函数不应有返回值Wrong number of arguments -----------------调用函数的参数数目错''xxx'' not an argument ----------------- xxx不是参数''xxx'' not part of structure -------------------- xxx不是结构体的一部分xxx statement missing ( -------------------- xxx语句缺少左括号xxx statement missing ) ------------------ xxx语句缺少右括号xxx statement missing ; -------------------- xxx缺少分号houjiumingxxx'' declared but never used -------------------说明了xxx但没有使用xxx'' is assigned a value which is never used ----------------------给xxx赋了值但未用过Zero length structure ------------------结构体的长度为零。
关系代数（RelationAlgebra）与SQL语句的对应关系SQL语句的执⾏⼀般是先翻译为关系代数再被执⾏的（能有效提⾼执⾏速度），所以我们有必要了解关系代数与SQL语句间的对应关系。
就像⾼中代数由+-*/和数字组成，关系代数是由union、intersection、join等运算符和关系实例组成的。
关系代数有五个基础运算符，这五个基础运算符能派⽣出其他组合运算符。
它们分别是：选择（σ， selection）、投影（π， projection）、叉乘（x， cross-product）、差（-, set-difference）和并（υ, union）它们和SQL语句的对应关系为：选择（σ， selection）相当于SQL语句中的where，表⽰选出满⾜⼀定条件的⾏。
如：σ rating>8 (S2）相当于 select * from S2 where rating>8;投影（π， projection）相当于SQL语句中的select。
distinct，表⽰选择哪些列。
注意：投影是会去重的！如：π sname,rating (σ rating>8 (S2）)相当于 select sname, rating from S2 where rating>8;叉乘（x， cross-product）相当于SQL语句中的from，表⽰穷举所有集合两边元素的组合量如: AxB 相当于 select * from A, B; 注意：叉乘时两个集合不能有重名列差（-, set-difference）R-S返回所有在R中⽽不在S中的元组并（υ, union）RυS返回包含在R中或在S中的所有元组注意：并、交、差都要求两个关系实例是并相容的。
并相容指：1. 两个关系实例字段数相同 2. 对应字段类型、取值范围相同合成运算符：合成运算符是由基础运算符组合派⽣⽽来的，算是⼀种速记标志。
交(∩, intersection) R∩S返回既在R中⼜在S中的元组。
sql lambda表达式摘要：1.SQL 与Lambda 表达式的概述2.SQL Lambda 表达式的特点3.SQL Lambda 表达式的使用场景4.SQL Lambda 表达式的语法5.SQL Lambda 表达式的优势与局限性正文：1.SQL 与Lambda 表达式的概述SQL（Structured Query Language，结构化查询语言）是一种用于管理关系型数据库的编程语言。
它可以用于查询、插入、更新和删除数据库中的数据，还可以用于创建和修改数据库表结构。
Lambda 表达式是一种简洁的匿名函数表示形式，常用于编程语言中。
它们都可以提高代码的可读性和简洁性。
当SQL 与Lambda 表达式结合时，可以实现更简洁、更易读的SQL 查询语句。
2.SQL Lambda 表达式的特点SQL Lambda 表达式具有以下特点：- 匿名：Lambda 表达式不需要显式声明函数名，可以直接在SQL 语句中使用。
- 简洁：Lambda 表达式可以简化复杂的逻辑表达式，使SQL 语句更简洁易读。
- 功能强大：Lambda 表达式支持各种逻辑操作，如过滤、排序、分组等。
- 与SQL 完美融合：SQL Lambda 表达式可以与SQL 的其他关键字（如SELECT、FROM、WHERE 等）结合使用，实现复杂的查询需求。
3.SQL Lambda 表达式的使用场景SQL Lambda 表达式适用于以下场景：- 复杂的逻辑查询：当SQL 查询语句中需要使用复杂的逻辑表达式时，可以使用Lambda 表达式简化代码。
- 临时性函数：当需要对查询结果进行临时性计算时，可以使用Lambda 表达式定义一个匿名函数。
- 高级聚合函数：在使用窗口函数、分组、排序等高级功能时，Lambda 表达式可以提供更简洁的语法。
4.SQL Lambda 表达式的语法SQL Lambda 表达式的基本语法如下：```SELECT column1, column2,...FROM table_nameWHERE some_column = Lambda(parameters)```其中，`parameters`可以是一个或多个表达式，用逗号分隔。
SQL Extensions and Algebras for Object-OrientedQuery LanguagesCarolina Culik,Randall Mack and Dave ShewchunContents1Introduction3 2Query Languages32.1What is a Query Language? (3)2.1.1Purpose (3)2.1.2Characteristics (3)2.1.3Design (4)2.2RELOOP (5)2.2.1Syntax (6)2.2.2Accessing Nested Structures (7)2.2.3Constructing New Entities (8)2.2.4Nested Structures (8)2.2.5Some Additional RELOOP Facilities (9)2.2.6Aggregate Operators (10)2.3OSQL (10)2.3.1Syntax (11)2.3.2Referencing Objects Through Keys (11)2.3.3Using Functions in Queries (12)2.3.4Accessing Nested Data (12)2.3.5Aggregate Functions (13)3Algebras for Object-oriented Database Systems133.1An Algebra for EXTRA/EXCESS (13)3.1.1The EXTRA Data Model (13)3.1.2The EXCESS Query Language (14)3.1.3The Algebra (14)3.1.4Operators (14)3.1.5Examples (16)3.2An Algebra for ENCORE (16)3.2.1The ENCORE Data Model (16)3.2.2Operators (17)12Culik,Mack and Shewchun3.3An Algebra for RELOOP (19)3.3.1RELOOP (19)3.3.2The O2Data Model (19)3.3.3Algebra Operators (19)3.3.4Example (20)3.4An Algebra for OODAPLEX (21)3.4.1OODAPLEX Data Model (21)3.4.2OODAPLEX Queries (21)3.4.3OOAlgebra (22)3.4.4OOAlgebra Operators (22)3.4.5Examples (23)3.5Conclusions (24)4Overall Conclusions25SQL Extensions and Algebras for OODBMS3 1IntroductionThe query language used to access a database and the underlying algebra form one of the most important components of a database management system.We will discuss the issues involved in the design of a query language,examine several SQL-like query languages and review several possible algebras for the object-oriented model.The emphasis in this paper is on practical,user-friendly models.Query languages which are attempts at extending SQL to the object-oriented model were chosen because of the large population of users already familiar with SQL,as well as its simplicity and formal basis.2Query LanguagesIn this section we introduce the concept of a query language,explaining some of the issues which affect its design and use.We analyze in depth the query languages RELOOP for the O2[CDLR89] object-oriented database management system(OODBMS)and OSQL[FAC+89]for Iris OODBMS.2.1What is a Query Language?2.1.1PurposeQuery languages are used for four main purposes[BCD89].1.for interactive queries2.to access the database from a programming language3.for simple programming tasks4.to simplify complicated programming tasksHowever,these four modes of use do not apply equally to all query languages.In general,object-oriented query languages are intended to merge smoothly with the programming language.This means that a programmer should be able to access the database directly from the host language, removing the need to use the query language for this purpose.On the other hand,traditional SQL embeddings only permit modification of the database through SQL queries and the lack of close ties between the two languages will preclude using SQL for programming shortcuts.Despite the variety of uses to which a query language can be put,we will concentrate on its aptness for phrasing interactive queries.From the perspective of object-oriented query languages, that is certainly the most fundamental application.Any other purpose can be seen as more of a useful side-effect.2.1.2CharacteristicsAn ad hoc query language should have several characteristics:it should be possible to simply and concisely express reasonable queries;the run-time system should be able tofind a good strategy for obtaining the result;and it should be independent of any specific application.As well,the interactive query language need not be as powerful as a complete programming/query language combination.Simplicity is more important.4Culik,Mack and Shewchun2.1.3DesignThere are many issues involved in the design of a query language.A sample of some of the more critical ones might be[BCD89]:•Should encapsulation be supported?•What form will the answer take?•Will the query language be integrated into the host language?•Should queries be explicitly typed?From the point of view of an ad hoc query language for an OODBMS,we can provide tentative answers to these questions.EncapsulationEncapsulation is the concept of packaging a set of methods with any given item of data,where only the methods will be visible to the user.Essentially this notion is just abstract data types as applied to an object-oriented language,and current wisdom says that the use of abstract data types is a good thing.From this we can see that for queries buried in a programming language,encapsulation is a must.However,for interactive queries it is not so obvious.The main reason for encapsulation(to enforce modularity in programs)does not apply here.It is also easy to come up with examples where encapsulation would significantly hamper the user.For example[BCD89],a user does not want to query a stack through push and pop operations,he wants to be able to see the entire stack.It appears that the best approach would be to enforce encapsulation for embedded queries,but relax this restriction at the interactive level.Form of the AnswerThere are essentially three options for how to represent/store the value returned from a query.1.Queries can only return information in the form in which it currently exists in the database.2.Query results belong to a meta-class which has pre-defined methods permitting displayingand printing.3.A new class and methods permitting access to all of itsfields are dynamically defined forevery query result.Option one is too restrictive for many purposes.Option three requires more overhead than most OODBMS’s can spare.This leaves option two as the most reasonable compromise,but re-using the results can cause problems if encapsulation is enforced.We see a tradeoffbetween encapsulation and the power/efficiency of the language.SQL Extensions and Algebras for OODBMS5 Embedding the Query LanguageThe most important thing to remember about this topic is that one of the major objectives in the design of OODBMS’s is to remove the impedance mismatch found with relational systems. Assuming that problem is avoided,we have one remaining choice.Whether to make the query language a subset of the programming language,or merely ensure that it mixes well enough that calls from within the programming language are natural.While either is acceptable it would appear that making the query language a subset of the programming language would be ing this approach,there is no need for the programmer to learn two distinct languages.Learning the programming language is sufficient.TypingSimilar to the discussion on encapsulation,wefind that explicit typing is good for embedded queries,but bad for ad hoc queries.Explicitly typing embedded queries improves the correctness of a program.For an interactive user however,correctness is not quite as big an issue.Since the type can be inferred from the structure/class,we do not need to declare an explicit type with the query.This will increase the clarity and ease the creation of new,ad hoc queries.2.2RELOOPThe Altair research group in Rocquencourt,France,is currently implementing O2[CDLR89],an object-oriented database management system(OODBMS).O2supports two languages,each one adding data description and data manipulation to an existing programming language.These pro-gramming languages,when coupled with the database management facilities,solve the traditional impedance mismatch problem.However,they do not provide a very nice way in which to query a database.Therefore,to compete with relational systems,the Altair group is implementing RELOOP,an interactive query language designed to allow users to specify reasonable queries easily and concisely.RELOOP is being implemented on top of the O2OODBMS.O2supports all of the standard object-oriented features.Its support of complex objects is in the form of providing three minimal set constructors:sets,lists and tuples.All of these constructors can be applied to each other. For example,the user can create sets of sets,tuples with set valuedfields,etc.O2also has one additional distinctive feature–its values.Values differ from objects in the following ways[BCD89]:•Values do not obey object-oriented principles.•Their structures are very similar to objects,but they are visible to the user whereas objects are encapsulated.•Values have no identity.•Values are manipulated by operators,not by methods.For instance,the‘.’operator allows for the extraction of afield from its tuple,like in SQL. Iteration is possible over a set value,and two list values can be concatenated.A Sample O2Database Schema6Culik,Mack and Shewchun Person=[name:[f-name:String,l-name:String],age:Integer,address:[city:String,zipcode:Integer]]Woman=[name:[f-name:String,l-name:String],age:Integer,sex:String,address:[city:String,zipcode:Integer]]Woman is a subclass of person.Man=[name:[f-name:String,l-name:String],age:Integer,sex:String,address:[city:String,zipcode:Integer]]Man is a subclass of person.Family=[name:String,mother:Woman,father:Man,children:{Person}]All thefields of the above classes can be accessed through methods such as the following.name:Person⇒[first-name:String,last-name:String]address:Person⇒[city:String,zipcode:String]age:Person⇒Integeris-child-of:Person×Person⇒Booleanspouse:Woman⇒Manspouse:Man⇒Womanname:Family⇒Stringmother:Family⇒Womanfather:Family⇒Manchildren:Family⇒{Person}Note that these methods allow complete access to all data;thus,there is no reason to violate encapsulation.The following is a presentation of the features of the RELOOP language[CDLR89].All example queries access a sample database implemented on the above defined database schema.2.2.1SyntaxSince most potential users of the query language know SQL,the designers of RELOOP decided to make the language SQL-like.Consequently,RELOOP queries will feature the select from where block.SQL Extensions and Algebras for OODBMS7 We begin with a simple query illustrating the syntactical differences between RELOOP and SQL.Q1:What are the names of the minors?select name(p)from p in Personwhere age(p)<18Basically,the query can be read and understood much like an SQL query.The select clause defines the result(the names of some persons).The from clause says where to get the information. Note that in this case,“Person”is a special set value,so it is legal to define the variable p as ranging over the set and representing one of its elements.The where clause specifies the conditions that must be satisfied.Thefirst obvious difference from SQL is the specification of“name(p)”instead of“”in the select clause.The designers believe that the functional notation is easier to read.Another advantage of this notation is that it is used both for operators and methods,so inexperienced users do not need to understand the difference between objects and values.For instance,to get thefirst name of a person,wefirst have to apply the“name”method on a “Person”object,and then use thefield extract operator to obtain the result.Clearly,the expression first-name(name(p))is easier to read and use than the expression name(p).first-name.Second,RELOOP introduces a new keyword,“in”in the from clause.Any expression which results in a set value can be used in the from clause.Therefore,in the case of complex expressions, a separator between the variable name and its domain makes the query easier to read.Finally,a select from where block result will always be a set value.This results from the fact that users are usually trying to retrieve a collection of database entities.However,if the user knows that they are extracting a single item from the database,they may use the RELOOP operator“extract”to get the unique item in a set.2.2.2Accessing Nested StructuresThe following query shows how to access data in a nested structure.Q2:Find the Families where the husband lives in Waterloo.select ffrom f in Familywhere city(address(husband(f)))=”Waterloo”The expression in the where clause can be seen as a path within the object composition hierarchy.For each family,we apply to it the husband method which returns a Man object.We then apply the address method to the Man object,and thenfinally the city operator to extract the cityfield from the address.We can access any data in the database using some such expression. The result of the query is a set of database objects.The next section will illustrate how the user can create new entities in the select clause.8Culik,Mack and Shewchun2.2.3Constructing New EntitiesThe following query shows how to construct tuple values.Q3:Find thefirst name and age of the minors.select[name:f-name(name(p)),age:age(p)]from p in Personwhere age(p)<18The tuple operator[]allows the construction of tuple values.It takes as argumentsfield names and their descriptions.A description can be made through any valid RELOOP expression. Therefore,as we will see later,this feature allows us to build nested structures.As mentioned earlier,the result of a query is always a set value.Therefore,since the above select clause constructs tuples,thefinal answer to the query will be of the following type:{[name: String,age:Integer]}2.2.4Nested StructuresIn this section we will illustrate both how to create nested structures and how toflatten nested ones.Thefirst query shows how to construct aflat structure from a nested one.Q4:Find the mother of every child.select[child:child,mother:mother(f)]from f in Familychild in children(f)An interesting observation is that it is valid to define a variable domain in the from clause through the application of a method on a previously defined variable.In fact,any RELOOP expression which returns a set value can be used for this purpose.This feature allows the user access to all levels of a nested structure,and thus,allows easy unnesting.The last two queries show,conversely,how to build nested structures fromflat ones.Q5:Associate with each woman her minor children’sfirst names,assuming that a woman may appear in different families.make-method minors(woman:mom)select f-name(name(child))from f in Familychild in children(f)where age(child)<18andmother(f)=momselect[mother:mom,children:minors(mom)]from mom in WomanSQL Extensions and Algebras for OODBMS9 The sets of minor children that we wish to construct are not database entities,therefore,they must be constructed.One way in which we can accomplish this is to create a method on the Woman class which will collect the appropriate set of children.The above method examines every child in every family and picks those that are under18years of age and whose mother is the method’s argument.Once the method is complete,we only need to build a simple query that creates a tuple result from which we call the method.Therefore,the type of thefinal result is{[mother:Woman, children:{String}]}In this example,the nesting was done on an object.However,often we work with values instead of objects.Since we cannot use methods on values,we mustfind another way of formulating the above query.The following is an alternate RELOOP expression for the above query which can deal with both objects and values.select[mother:mom,children:select f-name(name(child))from f in Familychild in children(f)where age(child)<18andmother(f)=mom]from mom in WomanThe only difference between the two formulations is that in the latter wefind the body of the method where the method was previously called.It is unclear from the literature written on RELOOP whether recursive calls to methods are permitted.2.2.5Some Additional RELOOP FacilitiesWe conclude our discussion of RELOOP by introducing two of the language’s facilities,the collapse operator,and the set constructor.The collapse operatorflattens a set of sets.For example,collapse({{1,2},{2,3}})={1,2,3}The set constructor{}builds a set value from its arguments.The following two queries illustrate the uses of these facilities.Q6:Find the people that have at least one child.select mother(f)from f in Familywhere children(f)={}unionselect father(f)from f in Familywhere children(f)={}This queryfirstfinds all the women and then all the men that have at least one child,and then it merges the results.The union of the results is possible because women and men are both persons.10Culik,Mack and Shewchun Using the collapse operator,we can also use a different query formulation to obtain the same result.collapse(select{mother(f),father(f)}from f in Familywhere children(f)={})In this query,for each family with more than one child,a set containing a mother and a father is constructed.Therefore,the result of this query is a set of sets.The collapse operatorflattens the result into just one set.An interesting observation is that this query does not use an instruction such as“distinct”to avoid duplicate values.This is because of the fact that we are manipulating sets in the select clause,and thus duplicates(and order)have no meaning.2.2.6Aggregate OperatorsAggregate operators,like those we are familiar with in SQL(sum,avg,...),are not yet implemented,but will be available in thefinal version of RELOOP.2.3OSQLHewlett-Packard Laboratories are currently developing the Iris[FAC+89]object-oriented database management system(OODBMS).Iris is a research prototype of a next generation DBMS,intended to meet the needs of new and emerging applications.Currently,one of the three interactive interfaces that is provided by Iris is Object SQL(OSQL) [FAC+89].OSQL is an object-oriented extension of SQL.A Sample OSQL Database SchemaPerson=(first-name Charstring required,last-name Charstring required,age Integer,city Charstring),Employee=(first-name Charstring required,last-name Charstring required,age Integer,city Charstring,company Charstring,salary Integer),Employee is a subclass of person.All thefields in the above classes can be accessed through property functions such as the following.first-name:Person⇒Charstringlast-name:Person⇒Charstringage:Person⇒Integercity:Person⇒Charstringcompany:Employee⇒Charstringsalary:Employee⇒IntegerNote that the above property functions allow complete access to all data;thus,there is no reason to violate encapsulation.The following is a presentation of the features provided by OSQL[FAC+89].Example queries access a sample database implemented on the above database schema.2.3.1SyntaxOSQL basically adheres to the SQL query format,but its syntax differs more from SQL than that of RELOOP.For example,consider the following simple query:Q1:What are thefirst names of the minors?Select distinctfirst-name(p)for each Person pwhere age(p)<18;An obvious difference is that the from keyword has been replaced by for each.We will see further differences in OSQL syntax in subsequent sections,especially shortcuts we can make in a query formulation when calling functions from the query.OSQL does provide SQL’s“distinct”operator which eliminates duplicates,while RELOOP does not.(RELOOP select statements automatically eliminate duplicates).2.3.2Referencing Objects Through KeysObjects may be referenced directly rather than indirectly,through their keys.Interface variables may be bound to objects on creation or retrieval and may then be used to refer to the objects in subsequent statements.The following OSQL expression creates an instance of the person object.Create Person(first-name,last-name,age,city)instancep1(John,Doe,25,Waterloo);Q2:Find the age of the person with identifier p1.Select age(p1);First we create a new person and then give this person the unique identifier p1.We can then use the identifier when we want to refer to its object as in the above select clause.Notice that no such feature is provided in RELOOP.2.3.3Using Functions in QueriesUser-defined functions and Iris system functions may appear in where and select clauses to give concise and powerful retrieval.For example,let us define the function Marriage as,Create function Marriage(Person p)⇒<Person spouse,Charstring date>forward;(forward specifies that the function implementation will be specified later.)This function returns a compound result–the spouse and the date of the marriage.We have already seen the use of a function in the select clause in the previous section.The following example shows how a function is invoked in the where clause.Q3:Find Bob’s wife and the date on which they where married.Select s,dfor each Person s,Charstring dwhere<s,d>=Marriage(Bob);Here we are comparing every combination of a Person object and a character string to the result of the Marriage function when applied to the Person Object“Bob”.Note that the above example demonstrates that OSQL permits queries to range over infinite domains.The above query can be abbreviated to:Select each Person s,Charstring dwhere<s,d>=Marriage(Bob);Or even more simply to:Select Marriage(Bob);The last two query formulations stray from the SQL select from where block.Thefirst abbreviation combines the two keyword phrases Select and for each into one“Select each”phrase.The second abbreviation does not explicitly specify the type of its result,but implies that it will be of the form of the result of the Marriage function.Notice that these types of syntactical shortcuts are not possible in RELOOP.2.3.4Accessing Nested DataAs in RELOOP,the expression in the where clause can be seen as a path within the object composition hierarchy.All data in the database can be accessed using an expression such as the following:Q4:Find all families where the husband lives in Waterloo.Select ffor each Family fwhere city(husband(f))=“Waterloo”2.3.5Aggregate FunctionsSeveral aggregate functions have already been implemented in OSQL.In previous sections we saw functions defined on individual objects.There is also a need for functions over multi-sets(sets containing duplicates).The following query illustrates the use of the function“average”.Q5:Find the average salary of all employees.Select yfor each Real ywhere y=Average(select Salary(x)for each Employee x);The nested select function returns a mult-set of values which is used as input to the Average function.Iris semantics are such that nested select statements and function calls are equivalent in re-trievals.Thus,given a function,EmpSal(),that returns the salaries of all employees,the above query could be rewritten by replacing the nested select statement with a call to Empsal.As mentioned earlier,aggregate operators have not yet been implemented in RELOOP but will be available in thefinal version.It will be interesting to see how a query such as the above will be implemented since the RELOOP select statement eliminates duplicates.3Algebras for Object-oriented Database SystemsOne of the strong points for the relational database model is the existence of a formal algebra for query processing and optimization.Attempts are now being made to develop a similar algebra for object-oriented database systems.This section will examine four such algebras:an algebra for the EXTRA DDL and EXCESS DML[VD91],an algebra for the ENCORE data model[SZ],an algebra for RELOOP[CDLR89],and OOAlgebra,an algebra for OODAPLEX[Day].3.1An Algebra for EXTRA/EXCESS3.1.1The EXTRA Data ModelIn the EXTRA data model[VD91]complex objects are defined as complex structures.These structures are built from tuple,multiset,and array type constructors.Multisets are sets with duplicates.Arrays are one-dimensional only,and of variable length.Methods can also be defined for a structure as a sequence of EXCESS statements.Object identity is supported with the ref keyword which specifies a reference to an extant object(ie:an OID).In this way,ref can actually be viewed as another type constructor.Inheritance is handled by allowing one structure to inherit another, which causes all attributes and methods of the structure being inherited to become attributes and methods in the new structure.Any inherited attribute or method can be overridden in the new structure definition.Multiple inheritance is also allowed.3.1.2The EXCESS Query LanguageThe EXCESS query language allows for both querying and updating of the database.Any structure defined in EXTRA can be fully manipulated by EXCESS.EXCESS can also be extended with user-defined functions and operators written in the E language.As an example,consider the following EXCESS query whichfinds the names of the children of all employees who work for a department on the secondfloor.range of E is Employeesretrieve()from C in E.kidswhere E.dept.floor=2Here,Employees has been created in EXTRA to be a set of Employee structures(objects). The“.”notation is used to access the properties of a complex structure.3.1.3The AlgebraThe EXCESS/EXTRA algebra is formally defined as a set of n-ary operators that operate on a set of objects,and are closed with respect to this set of objects.Elements of this set of objects are called“structures”.A structure contains two components,a schema and an instance.A schema is a digraph with the nodes representing one of the four type constructors(multisets,tuples,arrays, or refs)or a simple scalar value,and the edges representing a“component of”relationship.So, a schema is just a digraph representation of a structure defined in the EXESS DDL.Since the algebra operates on different“sorts”(different type constructors),it is referred to as a“multi-sorted”algebra.3.1.4OperatorsThe EXTRA/EXCESS algebra contains a large number of operators to handle the various features of the EXCESS query language.Instead of having all operators work on sets,as is done in many algebras,different operators are defined for each of the four“sorts”within the algebra.Multiset OperatorsThere are eight operators for multisets:1.Additive Union:Combines two multisets and does not eliminate duplicates.2.Set Creation:Creates a new multiset with a single member.3.Set Apply:Apply an algebraic expression to all members of the multiset,replacing themwith the result of the expression.4.Grouping:Partition a multiset based an algebraic expression.5.Duplicate Elimination:Convert a multiset to a regular set.6.Difference:Subtract the cardinality of set members to determine the result cardinality.7.Cartesian Product:The regular set-theory Cartesian product.8.Set Collapse:Takes a multiset of multisets and returns the union of the member multisets. Tuple OperatorsThere are four operators for tuples:1.Projection:The same as the relational projection except it works only on a single tuple.2.Concatenation:Concatenates two tuples.3.Field Extraction:Extracts a singlefield from a tuple.Unlike projection,the result is thefield,not a1-tuple.4.Creation:Create a new1-tuple.Array OperatorsThere are nine operators for tuples:1.Creation:Create a single element array.2.Array Extract:Extract a single element from an array.3.Subarray:Extract a range of elements from an array and place them in a new array.4.Array Concatenation5.Array Apply6.Array Collapse7.Array Difference8.Duplicate Elimination9.Cartesian ProductThe last six operators are the same as the corresponding set operators except that they preserve order.OID OperatorsRecall that EXTRA/EXCESS OIDs are just references to objects which exist in the database independent of the objects which reference them.There are two operators for OIDs:1.Dereference:Dereference an OID node within a schema.The OID node is replaced by whatit referenced.2.Reference:This operator creates an OID for its operand and then inserts this new OID intoa schema.PredicatesThere is one additional operator within the algebra to handle predicates called COMP.A predicate is specified with the COMP operator and it returns its input exactly if the predicate is true,or nothing if the predicate is false.Predicates may only appear in this COMP operator.。
