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# 数学代写|数学分析作业代写Mathematical Analysis代考|Baiburin and E. Providas

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## 数学代写|数学分析作业代写Mathematical Analysis代考|Definitions and Preliminary Results

Let X, Y be complex Banach spaces. Let P : X → Y denote a linear operator and D(P ) and R(P ) its domain and the range, respectively. An operator P is called an extension of the operator P0 : X → Y if D(P0) ⊆ D(P ) and P u = P0u, for all u ∈ D(P0). An operator P : X → Y is called correct if R(P ) = Y and the inverse operator P −1 exists and is continuous on Y .

We say that the problem P u = f , f ∈ Y, is correct if the operator P is correct.The problem P u = f with a linear operator P is uniquely solvable on R(P ) if the corresponding homogeneous problem P u = 0 has only a zero solution, i.e. if ker P = {0}. The problem P u = f is said to be everywhere solvable on Y if it admits a solution for any f ∈ Y .
Throughout this paper, we use lowercase letters and brackets to designate vectors and capital letters and square brackets to symbolize matrices. The unit and zero matrices are denoted by I and [0], respectively, and the zero column vector by 0.
The set of all complex numbers is specified by C. If ci ∈ C, i = 1, . . . , n, then we write c = (c1,…,cn) ∈ Cn. By Cn[0, 1], we mean the space of continuous vector functions f = f (x) = (f1(x), . . . , fn(x)) with norm

f Cn = f1(x)+f2(x)+···+fn(x), f (x) = maxx∈[0,1]|f (x)|.

## 数学代写|数学分析作业代写Mathematical Analysis代考|Main Results

Let the operator $P$ associated with problem (1) be defined as
\begin{aligned} P y &=y^{\prime}(x)-A y(x)-\sum_{i=0}^{m} G_{i}(x) \int_{0}^{1} H_{i}(t) y(t) d t, \ D(P) &=\left{y(x) \in C_{n}^{1}[0,1]: \sum_{i=0}^{m} A_{i} y\left(x_{i}\right)+\sum_{j=0}^{s} B_{j} \int_{\xi_{j}}^{\xi_{j+1}} C_{j}(t) y(t) d t=\mathbf{0}\right}, \end{aligned}
where $A, A_{i}, B_{j}$ are $n \times n$ constant matrices and $G_{i}(x), H_{i}(x), C_{j}(x)$ are variable $n \times n$ matrices with elements continuous functions on $[0,1]$; the points $x_{i}, \xi_{j}$ satisfy the conditions $0=x_{0}<x_{1}<\cdots<x_{m-1}<x_{m}=1,0=\xi_{0}<\xi_{1}<\cdots<\xi_{s}<$ $\xi_{s+1}=1$. Note that the operator $P$ is an extension of the minimal operator $P_{0}$ defined by
\begin{aligned} P_{0} y=& y^{\prime}(x)-A y(x) \ D\left(P_{0}\right)=&\left{y(x) \in C_{n}^{1}[0,1]: y\left(x_{i}\right)=\mathbf{0}, \int_{\xi_{j}}^{\xi_{j+1}} C_{j}(t) y(t) d t=\mathbf{0}\right.\ &\left.\int_{0}^{1} H_{i}(t) y(t) d t=\mathbf{0}, i=0, \ldots, m, j=0, \ldots, s\right} \end{aligned}

## 数学代写|数学分析作业代写Mathematical Analysis代考|Conclusions

We have studied a class of nonhomogeneous systems of $n$ linear first-order ordinary Fredholm type integro-differential equations subject to general multipoint and integral boundary constraints. We have established sufficient solvability and uniqueness criteria and we have derived a ready to use exact solution formula. The method proposed requires the knowledge of a fundamental matrix of the corresponding homogeneous system of first-order differential equations. The solution process can be easily implemented to any computer algebra system.

## 数学代写|数学分析作业代写MATHEMATICAL ANALYSIS代考|DEFINITIONS AND PRELIMINARY RESULTS

f Cn = f1X+f2X+···+fnX， FX = maxx∈0,1|fX|.

## 数学代写|数学分析作业代写MATHEMATICAL ANALYSIS代考|MAIN RESULTS

\begin{aligned} P y &=y^{\prime}(x)-A y(x)-\sum_{i=0}^{m} G_{i}(x) \int_{0}^{1} H_{i}(t) y(t) d t, \ D(P) &=\left{y(x) \in C_{n}^{1}[0,1]: \sum_{i=0}^{m} A_{i} y\left(x_{i}\right)+\sum_{j=0}^{s} B_{j} \int_{\xi_{j}}^{\xi_{j+1}} C_{j}(t) y(t) d t=\mathbf{0}\right}, \end{aligned}
where $A, A_{i}, B_{j}$ are $n \times n$ constant matrices and $G_{i}(x), H_{i}(x), C_{j}(x)$ are variable $n \times n$ matrices with elements continuous functions on $[0,1]$; the points $x_{i}, \xi_{j}$ satisfy the conditions $0=x_{0}<x_{1}<\cdots<x_{m-1}<x_{m}=1,0=\xi_{0}<\xi_{1}<\cdots<\xi_{s}<$ $\xi_{s+1}=1$. Note that the operator $P$ is an extension of the minimal operator $P_{0}$ defined by
\begin{aligned} P_{0} y=& y^{\prime}(x)-A y(x) \ D\left(P_{0}\right)=&\left{y(x) \in C_{n}^{1}[0,1]: y\left(x_{i}\right)=\mathbf{0}, \int_{\xi_{j}}^{\xi_{j+1}} C_{j}(t) y(t) d t=\mathbf{0}\right.\ &\left.\int_{0}^{1} H_{i}(t) y(t) d t=\mathbf{0}, i=0, \ldots, m, j=0, \ldots, s\right} \end{aligned}

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。