# Variable (mathematics)

In mathematics, a variable (from Latin variabilis, “changeable”) is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.[1]

Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation.

### Contents

• 1 History
• 2 Notation
• 3 Specific kinds of variables
• 3.1 Dependent and independent variables
• 3.2 Examples
• 3.2.1 Example: the ideal gas law
• 4 Moduli spaces
• 5 Conventional variable names

# 1 History

In ancient works such as Euclid’s Elements, single letters refer to geometric points and shapes. In the 7th century, Brahmagupta used different colours to represent the unknowns in algebraic equations in the Brāhmasphuṭasiddhānta. One section of this book is called “Equations of Several Colours”.[2]

At the end of the 16th century, François Viète introduced the idea of representing known and unknown numbers by letters, nowadays called variables, and the idea of computing with them as if they were numbers—in order to obtain the result by a simple replacement. Viète’s convention was to use consonants for known values, and vowels for unknowns.[3]

In 1637, René Descartes “invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c”.[4] Contrarily to Viète’s convention, Descartes’ is still commonly in use. The history of the letter x in math was discussed in a 1887 Scientific American article.[5]

Starting in the 1660s, Isaac Newton and Gottfried Wilhelm Leibniz independently developed the infinitesimal calculus, which essentially consists of studying how an infinitesimal variation of a variable quantity induces a corresponding variation of another quantity which is a function of the first variable. Almost a century later, Leonhard Euler fixed the terminology of infinitesimal calculus, and introduced the notation y = f(x) for a function f, its variable x and its value y. Until the end of the 19th century, the word variable referred almost exclusively to the arguments and the values of functions.

In the second half of the 19th century, it appeared that the foundation of infinitesimal calculus was not formalized enough to deal with apparent paradoxes such as a nowhere differentiable continuous function. To solve this problem, Karl Weierstrass introduced a new formalism consisting of replacing the intuitive notion of limit by a formal definition. The older notion of limit was “when the variable x varies and tends toward a, then f(x) tends toward L”, without any accurate definition of “tends”. Weierstrass replaced this sentence by the formula

{\displaystyle (\forall \epsilon >0)(\exists \eta >0)(\forall x);|x-a|<\eta \Rightarrow |L-f(x)|<\epsilon ,}(\forall \epsilon >0) (\exists \eta >0) (\forall x) ;|x-a|<\eta \Rightarrow |L-f(x)|<\epsilon,
in which none of the five variables is considered as varying.

This static formulation led to the modern notion of variable, which is simply a symbol representing a mathematical object that either is unknown, or may be replaced by any element of a given set (e.g., the set of real numbers).

# 2 Notation

Variables are generally denoted by a single letter, most often from the Latin alphabet and less often from the Greek, which may be lowercase or capitalized. The letter may be followed by a subscript: a number (as in x2), another variable (xi), a word or abbreviation of a word (xtotal) or a mathematical expression (x2i + 1). Under the influence of computer science, some variable names in pure mathematics consist of several letters and digits. Following René Descartes (1596–1650), letters at the beginning of the alphabet such as a, b, c are commonly used for known values and parameters, and letters at the end of the alphabet such as (x, y, z) are commonly used for unknowns and variables of functions.[6] In printed mathematics, the norm is to set variables and constants in an italic typeface.[7]

For example, a general quadratic function is conventionally written as {\textstyle ax^{2}+bx+c,}{\textstyle ax^{2}+bx+c,}, where a, b and c are parameters (also called constants, because they are constant functions), while x is the variable of the function. A more explicit way to denote this function is {\textstyle x\mapsto ax^{2}+bx+c,}{\textstyle x\mapsto ax^{2}+bx+c,}, which clarifies the function-argument status of x and the constant status of a, b and c. Since c occurs in a term that is a constant function of x, it is called the constant term.[8]

Specific branches and applications of mathematics have specific naming conventions for variables. Variables with similar roles or meanings are often assigned consecutive letters or the same letter with different subscripts. For example, the three axes in 3D coordinate space are conventionally called x, y, and z. In physics, the names of variables are largely determined by the physical quantity they describe, but various naming conventions exist. A convention often followed in probability and statistics is to use X, Y, Z for the names of random variables, keeping x, y, z for variables representing corresponding better-defined values.

# 3 Specific kinds of variables

It is common for variables to play different roles in the same mathematical formula, and names or qualifiers have been introduced to distinguish them. For example, the general cubic equation

{\displaystyle ax{3}+bx{2}+cx+d=0,}ax3+bx2+cx+d=0,
is interpreted as having five variables: four, a, b, c, d, which are taken to be given numbers and the fifth variable, x, is understood to be an unknown number. To distinguish them, the variable x is called an unknown, and the other variables are called parameters or coefficients, or sometimes constants, although this last terminology is incorrect for an equation, and should be reserved for the function defined by the left-hand side of this equation.

In the context of functions, the term variable refers commonly to the arguments of the functions. This is typically the case in sentences like “function of a real variable”, “x is the variable of the function f: x ↦ f(x)”, “f is a function of the variable x” (meaning that the argument of the function is referred to by the variable x).

In the same context, variables that are independent of x define constant functions and are therefore called constant. For example, a constant of integration is an arbitrary constant function that is added to a particular antiderivative to obtain the other antiderivatives. Because the strong relationship between polynomials and polynomial function, the term “constant” is often used to denote the coefficients of a polynomial, which are constant functions of the indeterminates.

This use of “constant” as an abbreviation of “constant function” must be distinguished from the normal meaning of the word in mathematics. A constant, or mathematical constant is a well and unambiguously defined number or other mathematical object, as, for example, the numbers 0, 1, π and the identity element of a group. Since a variable may represent any mathematical object, a letter that represents a constant is often called a variable. This is, in particular, the case of e and π, even when they represents Euler’s number and 3.14159…

Other specific names for variables are:

An unknown is a variable in an equation which has to be solved for.
An indeterminate is a symbol, commonly called variable, that appears in a polynomial or a formal power series. Formally speaking, an indeterminate is not a variable, but a constant in the polynomial ring or the ring of formal power series. However, because of the strong relationship between polynomials or power series and the functions that they define, many authors consider indeterminates as a special kind of variables.
A parameter is a quantity (usually a number) which is a part of the input of a problem, and remains constant during the whole solution of this problem. For example, in mechanics the mass and the size of a solid body are parameters for the study of its movement. In computer science, parameter has a different meaning and denotes an argument of a function.
Free variables and bound variables
A random variable is a kind of variable that is used in probability theory and its applications.
All these denominations of variables are of semantic nature, and the way of computing with them (syntax) is the same for all.

## 3.1 Dependent and independent variables

Main article: Dependent and independent variables
In calculus and its application to physics and other sciences, it is rather common to consider a variable, say y, whose possible values depend on the value of another variable, say x. In mathematical terms, the dependent variable y represents the value of a function of x. To simplify formulas, it is often useful to use the same symbol for the dependent variable y and the function mapping x onto y. For example, the state of a physical system depends on measurable quantities such as the pressure, the temperature, the spatial position, …, and all these quantities vary when the system evolves, that is, they are function of the time. In the formulas describing the system, these quantities are represented by variables which are dependent on the time, and thus considered implicitly as functions of the time.

Therefore, in a formula, a dependent variable is a variable that is implicitly a function of another (or several other) variables. An independent variable is a variable that is not dependent.[9]

The property of a variable to be dependent or independent depends often of the point of view and is not intrinsic. For example, in the notation f(x, y, z), the three variables may be all independent and the notation represents a function of three variables. On the other hand, if y and z depend on x (are dependent variables) then the notation represents a function of the single independent variable x.[10]

## 3.2 Examples

If one defines a function f from the real numbers to the real numbers by

{\displaystyle f(x)=x^{2}+\sin(x+4)}{\displaystyle f(x)=x^{2}+\sin(x+4)}
then x is a variable standing for the argument of the function being defined, which can be any real number.

In the identity

{\displaystyle \sum _{i=1}^{n}i={\frac {n^{2}+n}{2}}}{\displaystyle \sum _{i=1}^{n}i={\frac {n^{2}+n}{2}}}
the variable i is a summation variable which designates in turn each of the integers 1, 2, …, n (it is also called index because its variation is over a discrete set of values) while n is a parameter (it does not vary within the formula).

In the theory of polynomials, a polynomial of degree 2 is generally denoted as ax2 + bx + c, where a, b and c are called coefficients (they are assumed to be fixed, i.e., parameters of the problem considered) while x is called a variable. When studying this polynomial for its polynomial function this x stands for the function argument. When studying the polynomial as an object in itself, x is taken to be an indeterminate, and would often be written with a capital letter instead to indicate this status.

### 3.2.1 Example: the ideal gas law

Consider the equation describing the ideal gas law,

{\displaystyle PV=Nk_{B}T.}{\displaystyle PV=Nk_{B}T.}
This equation would generally be interpreted to have four variables, and one constant. The constant is {\displaystyle k_{B}}k_{B}, the Boltzmann constant. One of the variables, {\displaystyle N}N, the number of particles, is a positive integer (and therefore a discrete variable), while the other three, {\displaystyle P,V}{\displaystyle P,V} and {\displaystyle T}T, for pressure, volume and temperature, are continuous variables.
One could rearrange this equation to obtain {\displaystyle P}P as a function of the other variables,

{\displaystyle P(V,N,T)={\frac {Nk_{B}T}{V}}.}{\displaystyle P(V,N,T)={\frac {Nk_{B}T}{V}}.}
Then {\displaystyle P}P, as a function of the other variables, is the dependent variable, while its arguments, {\displaystyle V,N}{\displaystyle V,N} and {\displaystyle T}T, are independent variables. One could approach this function more formally and think about its domain and range: in function notation, here {\displaystyle P}P is a function {\displaystyle P:\mathbb {R} _{>0}\times \mathbb {N} \times \mathbb {R} _{>0}\rightarrow \mathbb {R} }{\displaystyle P:\mathbb {R} _{>0}\times \mathbb {N} \times \mathbb {R} _{>0}\rightarrow \mathbb {R} }.
However, in an experiment, in order to determine the dependence of pressure on a single one of the independent variables, it is necessary to fix all but one of the variables, say {\displaystyle T}T. This gives a function

{\displaystyle P(T)={\frac {Nk_{B}T}{V}},}{\displaystyle P(T)={\frac {Nk_{B}T}{V}},}
where now {\displaystyle N}N and {\displaystyle V}V are also regarded as constants. Mathematically, this constitutes a partial application of the earlier function {\displaystyle P}P.
This illustrates how independent variables and constants are largely dependent on the point of view taken. One could even regard {\displaystyle k_{B}}k_{B} as a variable to obtain a function

{\displaystyle P(V,N,T,k_{B})={\frac {Nk_{B}T}{V}}.}{\displaystyle P(V,N,T,k_{B})={\frac {Nk_{B}T}{V}}.}

# 4 Moduli spaces

Considering constants and variables can lead to the concept of moduli spaces. For illustration, consider the equation for a parabola,

{\displaystyle y=ax^{2}+bx+c,}{\displaystyle y=ax^{2}+bx+c,}
where {\displaystyle a,b,c,x}{\displaystyle a,b,c,x} and {\displaystyle y}y are all considered to be real. The set of points {\displaystyle (x,y)}(x,y) in the 2D plane satisfying this equation trace out the graph of a parabola. Here, {\displaystyle a,b}a,b and {\displaystyle c}c are regarded as constants, which specify the parabola, while {\displaystyle x}x and {\displaystyle y}y are variables.
Then instead regarding {\displaystyle a,b}a,b and {\displaystyle c}c as variables, we observe that each set of 3-tuples {\displaystyle (a,b,c)}(a,b,c) corresponds to a different parabola. That is, they specify coordinates on the ‘space of parabolas’: this is known as a moduli space of parabolas.

# 5 Conventional variable names

a, b, c, d (sometimes extended to e, f) for parameters or coefficients
a0, a1, a2, … for situations where distinct letters are inconvenient
ai or ui for the i-th term of a sequence or the i-th coefficient of a series
e for Euler’s number
f, g, h for functions (as in {\displaystyle f(x)}f(x))
i for the imaginary unit
i, j, k (sometimes l or h) for varying integers or indices in an indexed family, or unit vectors
l and w for the length and width of a figure
l also for a line, or in number theory for a prime number not equal to p
n (with m as a second choice) for a fixed integer, such as a count of objects or the degree of an equation
p for a prime number or a probability
q for a prime power or a quotient
r for a radius, a remainder or a correlation coefficient
t for time
x, y, z for the three Cartesian coordinates of a point in Euclidean geometry or the corresponding axes
z for a complex number, or in statistics a normal random variable
α, β, γ, θ, φ for angle measures
ε (with δ as a second choice) for an arbitrarily small positive number
λ for an eigenvalue
Σ (capital sigma) for a sum, or σ (lowercase sigma) in statistics for the standard deviation[11]
μ for a mean

Lambda calculus
Observable variable
Physical constant
Propositional variable

## EXCEL拼接SQL脚本

EXCEL拼接SQL脚本一&#xff1a;拼接sql二&#xff1a;时间格式问题三&#xff1a;插入Oracle数据库报&#xff1a;ORA-01861: 文字与格式字符串不匹配一&#xff1a;拼接sql 如图&#xff1a; 格式&#xff1a; “insert into product (ID,THING,DATE)values(’”&A2&a…...

## 自动截取基金定期报告的运行分析部分

#自动读取文件夹内的各基金报告pdf&#xff0c;提取里面的运行报告&#xff0c;并汇总保存到word表格 from pathlib import Path import pdfplumber import pandas as pd import docx p Path("E:/seasonreport/") #读取路劲FileList list(p.glob("*.pdf"…...

## MybatisPlus 分页功能实现

MyBatisPlus分页使用 1&#xff1a;设置分页拦截器作为Spring管理的bean package com.alibaba.config;import com.baomidou.mybatisplus.extension.plugins.MybatisPlusInterceptor; import com.baomidou.mybatisplus.extension.plugins.inner.PaginationInnerInterceptor; i…...

## ClearAi-照片优化增强软件，人工智能让模糊不清的人像照片瞬间高清美化

ClearAi只需您轻轻点击&#xff0c;即刻将您的老旧照片、像素不足照片、模糊或有损坏的照片变成高清并美化的照片&#xff01; ClearAi使用最先进的人工智能来去模糊降噪、修复和增强美化您想要的任何图像。完美重现您的旧时光&#xff0c;以令人惊叹的清晰高清画质赋予它们新…...

## Games101-Chapter11-Geometry（曲线和曲面）

【Explicit Geometry】 1.Point Cloud 不考虑物体有一个表面&#xff0c;仅仅是用点表示物体 list of points(x,y,z) 理论上来说可以表示任何几何 2.Polygon Mesh 那么在图形学中怎么表示模型的信息&#xff1f; 把空间中的点&#xff0c;纹理&#xff0c;法线坐标分别表示 …...

## 了解下RDF 容器元素

RDF 容器用于描述一组事物。举个例子&#xff0c;把某本书的作者列在一起。下面的 RDF 元素用于描述这些的组&#xff1a;<Bag>、<Seq> 以及 <Alt>。<rdf:Bag> 元素 <rdf:Bag> 元素用于描述一个规定为无序的值的列表。 <rdf:Bag>元素可包…...

## 2022年第十一届认证杯数学中国数学建模国际赛小美赛：C 题 对人类活动进行分类 建模方案及代码实现

2022年第十一届认证杯数学中国数学建模国际赛小美赛&#xff1a;C 题 对人类活动进行分类 建模方案及代码实现 1 题目 人类行为理解的一个重要方面是对日常活动的识别和监控。可穿戴活动识别系统可以在许多关键领域提高生活质量&#xff0c;如门诊监测、居家康复、跌倒检测等。…...

## 14.MongoDB系列之配置分片

1. 启动服务器 1.1 启动配置服务器 配置服务器是集群的大脑&#xff0c;保存着关于每个服务器包含哪些数据的所有元数据&#xff0c;因此&#xff0c;必须首先创建配置服务器。 由于资源限制&#xff0c;在同一机器上启动三个进程 # mkdir /home/mongo/cs1 # mkdir /home/mo…...

## openEuler iso x86_64 定制分析笔记

22.03 aarch64 ### BEGIN /etc/grub.d/10_linux ### menuentry Install openEuler 22.03-LTS --class red --class gnu-linux --class gnu --class os { linux /images/pxeboot/vmlinuz inst.stage2hd:LABELopenEuler-22.03-LTS-aarch64 ro inst.geoloc0 consoletty0 smm...

## 第一章 动态规划 状态压缩DP

1、基本概述 状态压缩dp和状态机一样&#xff0c;都是一种特殊的状态表示方式。状态机用一系列小状态表示某一状态。状态压缩dp用二进制数进行表示。虽然看代码起来时间复杂度比较高&#xff0c;但是很多的情况都给剪枝掉了。 状态压缩的题目主要分成两种 棋盘式&#xff08;…...

## Oracle SQL执行计划操作（2）——索引相关操作

2. 索引相关操作 该类操作与SQL语句执行计划中通过索引访问表中数据的路径和方式相关，主要包括索引访问类相关操作。根据不同的具体SQL语句及其他相关因素，以下各操作可能会出现于相关SQL语句的执行计划。 1）INDEX UNIQUE SCAN 进行一个索引唯一扫描。顾名思义，唯一索引…...

## HTML5期末大作业：基于html+css+javascript+jquery实现藏族文化15页【学生网页设计作业源码】

&#x1f389;精彩专栏推荐 &#x1f4ad;文末获取联系 ✍️ 作者简介: 一个热爱把逻辑思维转变为代码的技术博主 &#x1f482; 作者主页: 【主页——&#x1f680;获取更多优质源码】 &#x1f393; web前端期末大作业&#xff1a; 【&#x1f4da;毕设项目精品实战案例 (10…...

## SQLServer 常用函数汇总

SYSDATETIME() 系统时间GETDATE() 当前时间CHARINDEX ( expressionToFind , expressionToSearch [ , start_location ] ) --可用来当做Contains函数expressionToFind &#xff1a;目标字符串&#xff0c;就是想要找到的字符串&#xff0c;最大长度为8000 。 expressionToSearc…...

## 阿里分布式事务seata

(一) seata 介绍 Seata 是一款阿里开源的分布式事务解决方案&#xff0c;致力于提供高性能和简单易用的分布式事务服务。Seata 将为用户提供了 AT、TCC、SAGA 和 XA 事务模式&#xff0c;为用户打造一站式的分布式解决方案这里演示学习使用SpringCloud/SpringBoot集成配置了Sea…...

## HBase Shell启动缓慢及操作耗时长的原因分析与解决

1.现象 在内网搭了一个 hbase-2.2.6&#xff08;hadoop-2.7.3&#xff09;的环境&#xff0c;使用的是其内置的 zookeeper-3.4.10&#xff0c;16010端口对应的 web界面可以正常访问&#xff0c;且各项功能正常。 在使用 hbase shell的过程中&#xff0c;首先是 hbase shell启…...

## 2021.06青少年软件编程（Python）等级考试试卷（三级）

2021.06青少年软件编程（Python）等级考试试卷（三级） 一、单选题(共25题，每题2分，共50分) 1.关于open()函数的参数，下列描述正确的是？（ D ） A. "w+" 以十六进制格式打开一个文件只用于写入 B. "r+"打开一个文件用于读写。文件指针将会放在文件…...

## FromBottomToTop第十二周项目博客

FromBottomToTop第十二周项目博客 本周项目计划 设计整体架构&#xff0c;收集素材&#xff0c;制作出静态界面部分 项目进展 已完成游戏整体架构设计已完成游戏界面、背景音乐等素材的收集正在进行静态界面部分的制作游戏整体架构 框架类及核心类 Activity的实现类MainGameAct…...

## 【Java8 新特性 3】Supplier简介，java视频直播技术架构

Supplier persionSupplier Person::new; Arrays.asList(“a”,“b”,“c”).forEach(e->System.out.println(e)); 在Java8中增加的接口Supplier&#xff0c;最适合用于表示工厂。带有Supplier的方法&#xff0c;通常应该限制输入工厂的类型参数使用有限制的通配符类型&am…...

## C#报错：Could not find any resources appropriate for the specified culture or the neutral culture

WinForm程序报错&#xff0c;提示&#xff1a; Could not find any resources appropriate for the specified culture or the neutral culture 代码&#xff1a; object obj ResourceManager.GetObject("btn_bg_down", resourceCulture); 资源文件都在的&#…...

## win10蓝屏：终止代码：CRITICAL_PROCESS_DIED

1.硬件驱动问题Win X打开设备管理器-扫描检测硬件改动看是否有硬件驱动问题&#xff08;黄色标识&#xff09;&#xff0c;有的话更新或卸载重装2.查看蓝屏原因使用软件&#xff1a;BlueScreenViewWinX - 时间查看器window日志-系统&#xff1a;红色错误标识为系统错误问题3.一…...

## jmeter压力测试（windows,linux）

1、启动jmeter&#xff0c;打开界面工具&#xff0c;添加一个线程组&#xff0c;添加驱动 2、添加一个JDBC Connection Configuration&#xff0c;连接池配置文件。右键线程组【添加】--【配置元件】- -【JDBC Connection Configuration】 2.1配置数据库信息 3、右键线程组【添…...

<span οnclick"show()"><?php foreach($choice as$key>$value){ ?><label><input name"choice" type"radio" value"<?php echo$key?>"><?php echo \$value; ?></label>   &l…...

## 工作一年的java程序员薪资，纯干货

1 JVM的内存区域布局 java代码的执行步骤有三点 java源码文件->编译器->字节码文件字节码文件->JVM->机器码机器码->系统CPU执行 JVM执行的字节码需要用类加载来载入&#xff1b;字节码文件可以来自本地文件&#xff0c;可以在网络上获取&#xff0c;也可以实时…...

## arduino的pinMode()函数

pinMode() 1 说明 通过pinMode()函数&#xff0c;你可以将Arduino的引脚配置为以下三种模式&#xff1a; 输出(OUTPUT)模式输入(INPUT)模式输入上拉&#xff08;INPUT_PULLUP&#xff09;模式 &#xff08;仅支持Arduino 1.0.1以后版本&#xff09; 在输入上拉&#xff08;…...

## Android使用其他应用打开文件

public class MapTable {/*** -- MIME 列表 --*/public static final String[][] MIME_MapTable {// --{后缀名&#xff0c; MIME类型} --{".3gp", "video/3gpp"},{".3gpp", "video/3gpp"},{".aac", "audio/x-mpeg&…...

## k8s常用命令

k8s常用命令get 获取资源列表 [rootk8s-node1 mytestyaml]# kubectl get pod NAME READY STATUS RESTARTS AGE nginx-deployment-85ff79dd56-8f8s2 1/1 Running 0 30s nginx-deployment-85ff79dd56-nmhvr 1/1 R…...

## 【数据分析软件】【Weka】第一课：超easy安装教程

weka Data Science author&#xff1a;zoxiii 0. Weka官网 1. 双击下载的安装包&#xff0c;开始安装&#xff0c;点击【Next】 2. 同意协议&#xff0c;点击【I Agree】 3. 选择组件&#xff0c;直接【Next】 4. 选择安装位置&#xff0c;这里我修改到了D盘&#xff0c;点击…...

## weka java包_weka 机器学习调用的jar包实现的源码 - 下载 - 搜珍网

weka/weka/.classpathweka/.projectweka/.settings/weka/.settings/org.eclipse.jdt.core.prefsweka/bin/weka/bin/WekaTest/weka/bin/WekaTest/BinC45ModelSelection.classweka/bin/WekaTest/C45ModelSelection.classweka/bin/WekaTest/C45PruneableClassifierTree.classweka...

## 2.服务器负载均衡

1.服务器负载均衡概述 负载均衡基本概念 实服务器&#xff1a;处理业务流量的实体服务器&#xff0c;客户端发送的服务请求最终是由实服务器处理的。 实服务器组&#xff1a;由多个实服务器组成的集群&#xff0c;对外提供特定的一种服务。 虚拟服务器&#xff1a;实服务器组…...

## Spring Boot 引入jar 包中的 controller

【问题】 Spring Boot 引入jar 包中的 controller 【解决】 默认情况下 Spring Boot 在启动时, 只会扫描启动类对应的包以及子包进行装配&#xff0c; 因此jar包中的controller与主应用的包名保持一致即可。通过import注解引入对应的controller bean对象&#xff0c;在主程序…...

## w讠ndows Boot Manager,Win10电脑无法开机提示Windows boot manager的解决方案

Windows10系统电脑无法开机&#xff0c;且出现Windows boot manager界面&#xff0c;并提示\Boot\BCD 0xc000000f&#xff0c;这是怎么回事呢&#xff1f;其实&#xff0c;该问题是BCD文件丢失或损坏导致的。下面&#xff0c;系统城小编就分享下该问题的具体解决方案。解决方案…...

## Complete Guide for Spring Boot Actuator

You are here to learn about Spring Boot Actuator for collecting metrics about your production grade applications. Spring Boot Actuator is sub-project of Spring Boot and it is one of the nice feature that adds great value to the Spring Boot applications. L...

## Native Boot 从一个 VHD 引导系统的相关说明

Native Boot 是 Windows 7 和 Windows Server 2008 R2 提供的一个新的功能&#xff0c;它允许从一个 VHD 文件引导一个操作系统&#xff0c;但是需要注意的是目前的 Windows 7 Beta 下 Native Boot 所提供的 Boot From a VHD 是有一定要求的&#xff0c;故 gOxiA 一直测试从 VH…...

## boot repair

Boot Info Script cfd9efe Boot-Repair extra info [Boot-Info 26Apr2016] Boot Info Summary: > No boot loader is installed in the MBR of /dev/sda.> Grub2 (v2.00) is installed in the MBR of /dev/sdb and looks at sector 1 of the same hard drive for...

## [附源码]计算机毕业设计JAVA校园摄影爱好者交流网站

[附源码]计算机毕业设计JAVA校园摄影爱好者交流网站 项目运行 环境配置&#xff1a; Jdk1.8 Tomcat7.0 Mysql HBuilderX&#xff08;Webstorm也行&#xff09; Eclispe&#xff08;IntelliJ IDEA,Eclispe,MyEclispe,Sts都支持&#xff09;。 项目技术&#xff1a; SSM …...

## 什么是PCI总线？

Q&#xff1a;什么是PCI总线&#xff1f; A&#xff1a;PCI&#xff08;Peripheral Component Interconnect&#xff09;外设部件互联标准的缩写&#xff0c;PCI是Intel公司1991年推出的一种局部总线。从结构上看&#xff0c;PCI是CPU和原来的系统总线之间插入的一级总线&…...

## java 数字金字塔,含详细解说

/*需求&#xff1a;数字金字塔 第i行 空格数量 左边的数字 右边的数字| 1 | i1 3个 1到1 0(没有数字)| 121 | i2 2个 1到2 1到1| 12321 | i3 1个 1到3 2到1| 123…...

## 奇妙生活-神奇数字-9的故事

987654321 * 9 08888888889 987654321 * 18 17777777778 987654321 * 27 26666666667 987654321 * 36 35555555556 987654321 * 45 44444444445 987654321 * 54 53333333334 987654321 * 63 62222222223 987654321 * 72 71111111112 987654321 * 81 80000000001 9876...

## Python案例：查询城市天气并绘制最高气温与最低气温折线图

Python案例：查询城市天气并绘制最高气温与最低气温折线图 一、解决思路 比如要查询“泸州”的天气。 1、首先获取泸州的城市代码 http://toy1.weather.com.cn/search?cityname=泸州 其中“?cityname=泸州 ”是查询字符串。 在返回的数据里，看第一项数据的ref值，其开头…...

## ubuntu 基于ffmpeg和Visual GDB 实现本地推流功能

ubuntu 上下载ffmpeg的相关组件 并且安装安装如下 1 ./configure --prefix/usr/local/ffmpeg2 --enable-shared --enable-libmp3lame --enable-libvorbis --enable-gpl --enable-version3 --enable-nonfree --enable-pthreads --enable-libfaac --enable-libopencore-amrnb --e…...

## Hibernate锁机制 悲观锁和乐观锁

Hibernate锁机制 悲观锁和乐观锁 文章分类:Java编程 今天就是元旦了&#xff0c;闲着没事&#xff0c;写点东西发上来&#xff01;1、Pessimistic Locking 悲观锁&#xff1b;pessimistic [,pesimistik] adj. 悲观的&#xff0c;厌世的&#xff1b;悲观主义的2、Optimistic Lo…...

## mysql那本书适合初学者_适用于初学者MySQL和数据库编程

mysql那本书适合初学者Dave Stokes使用MySQL已有15年以上&#xff0c;自2010年以来一直担任其社区经理。在今年的All Things Open中&#xff0c;他将为MySQL 初学者介绍数据库编程 。 在这次采访中&#xff0c;他预览了他的演讲&#xff0c;并分享了一些有用的资源&#xff0c…...

## java多线程（四）—— 乐观锁和悲观锁

java多线程&#xff08;四&#xff09;—— 乐观锁与悲观锁 我们在学习java多线程的过程中&#xff0c;总是听到别人说什么乐观锁和悲观锁&#xff0c;那到底什么是乐观锁&#xff1f;什么是悲观锁呢&#xff1f;我们在多线程的并发编程中会遇到对共享资源的操作&#xff0c;而…...

## 碰到问题：ISG 2000 和 SSG 550M的配置不同

ISG 2000 和 SSG 550M的配置方式竟然有所不同&#xff0c;郁闷转载于:https://blog.51cto.com/413657/1261380...

## ISG FootBalls Live

ISG FootBalls Live...

## Juniper ISG1000 HA环境下出现inoperable修复过程

9月17日晚&#xff0c;对防火墙的不正常的HA状态进行了修复&#xff0c;过程如下&#xff1a; 1、 检查中发现该主设备的E2/1口down状态&#xff0c;通过对比的方法&#xff0c;发现光模块工作不正常&#xff0c;与E2/4口&#xff08;空闲口&#xff09;的光模块进行了调换后&…...

## Isg2000 HA配置步骤

Isg2000 HA配置步骤环境&#xff1a;备用isg2000有配置。1.主&#xff1a; isg2000>set interface e3 zone ha isg2000-> set nsrp cluster id 1 isg2000(M)-> set nsrp vsd id 0 isg2000(M)-> set nsrp vsd-group id 0 priority 50 &#xff08;优先级小的是mas…...

## ISG pwnme100 poc 学习

ISG pwnme100 poc 学习 背景 最近在学习ISG2015比赛的 FlappyPig 的writeup&#xff08;http://bobao.360.cn/learning/detail/702.html&#xff09;&#xff0c;对其中的pwn比较感兴趣&#xff0c;因此查阅了部分资料后对poc进行了研究。 其中在csdn上海枫的专栏&#xff0…...

## 稿最全，面中率最高，C++经典面试题（八）

28题&#xff1a;内存的分配方式有几种? 【参考答案】 一、从静态存储区域分配。内存在程序编译的时候就已经分配好&#xff0c;这块内存在程序的整个运行期间都存在。例如全局变量。 二、在栈上创建。在执行函数时&#xff0c;函数内局部变量的存储单元都可以在栈上创建&a…...

## ISG-1000网络安全配置

Juniper网络公司集成式安全网关&#xff08;ISG&#xff09;是一种专用安全解决方案&#xff0c;它采用了第四代安全ASIC GigaScreen3&#xff0c;以及高性能微处理器&#xff0c;能够提供无与伦比的防火墙和性能。Juniper网络公司 ISG 1000 和 ISG 2000 非常适合因需要运行VoI…...

## 动态AOP 自动以标签 源码解析

Spring AOP 是一个简化版的AOP 实现&#xff0c;并没有提供完整的AOP功能&#xff0c;通常情况下&#xff0c;Spring AOP 是能够满足我们日常开发过程中的大多数场景的&#xff0c;但在某些情况下&#xff0c; 我们可能需要使用Spring AOP 范围外的某些AOP 功能。 AspectJ是一…...

## Flutter 安装踩坑记录 HTTP host https://pub.dev/ is not reachable.

Flutter安装踩坑记录安装Flutter SDK参考链接安装Flutter SDK Windows安装 flutter官网下载flutter sdk包 2.解压到C盘除去program file相关的目录&#xff08;最好自己创建一个新的目录&#xff0c;因为放在program file等目录需要特殊的权限&#xff0c;会出现问题&#xf…...

## 在网上看别人去韩国的日记

https://bbs.hupu.com/17335264.html 去了趟首尔&#xff0c;说一下自己的主观感受。 由 yo655321 发表在虎扑步行街步行街主干道 https://bbs.hupu.com/bxj 行程朋友帮忙在天津报的自由行团&#xff0c;五天四晚一下午免税店&#xff0c;四天自由行&#xff0c;住五花酒店&am…...

...