### 数学代写|数论作业代写number theory代考|A Personal Tribute

statistics-lab™ 为您的留学生涯保驾护航 在代写数论number theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数论number theory代写方面经验极为丰富，各种代写数论number theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|数论作业代写number theory代考|Anindita Balslev

The few lines that I am about to put on record here are not about the work of the young professor of mathematics who arrived at Aarhus University in Denmark in 1974 from the US, after being a visiting professor at SUNY Buffalo, New York and then at UCLA, California. It is important for my story to retrace the phase before that, when he was in France as a post-Doc fellow, associating with the Institut Henri Poincare and Institut des Hautes Etudes Scientific. Paris is, indeed, the place where we met and got married, Buffalo and Los Angeles being the birthplaces of our two children, Eva and Olav. Ever since, France and USA remain as important as Denmark and India in our lives where we have kept on returning over the years. We settled in Denmark, the country of his birth, and it is there that our children grew up. We enjoyed our annual visits to India and the occasional trips to France and USA; our common prayer was-Let noble thoughts come to us from all directions” (Rigveda).
Indeed, as we flew from one hemisphere to the other in these early years, I began to notice that India-the country where I was born-was embracing colossal changes while at the same time seeking to re-vitalize her ancient cultural heritage, whereas the Danish academia was resisting change especially in the fields of philosophy and religion with their view to sustain its virtually monolithic culture. Evidently students were ready to expand the horizon of knowledge by going beyond the rigid set of mono-cultural academic offerings, the system (rather, the few who control the system) was not.

Now more than four decades have passed by and despite that I have been with him during all that time, this is not an account about his colleagues or collaborators or students nor about the pros and cons of our work-situation in Denmark, where the opportunities and disappointments that awaited us were to be a part of the web of our lives.

Here, I am only seeking to share with the readers a few snapshots from the album of my life by recalling what Erik was like as my life companion, my closest friend, my spouse. It is easier said than done! Indeed, to capture the impact of such a deep companionship is no less subtle a job than to describe the smell of roses or jasmines, especially to those who have not smelt the scent of these flowers. It seems to be an overwhelming task, as I seek to express what Erik’s presence in my life has really meant for me.

## 数学代写|数论作业代写number theory代考|Our Friend, Our Colleague Erik Balslev

Unfortunately I was unaware of the fact that Erik Balslev had suddenly passed away, and that too only after three years. But I do remember Erik very well and I will remember him forever. Moreover, I do still feel him to be very close since we have known each other very well. We met each other during that famous academic year 1966-1967 of mathematical physics at the “Institut des Hautes Etudes Scientifiques” in Bures-sur-Yvette. This was an agreeable small but nice place located in a green domain situated in the south of Paris, next to the other well-known place for scientists, namely, the town of Orsay where there was an important science campus.

The fine fleur of mathematical physicists of the globe did find each other that year in that quiet French place. There was an exclusive gathering of famous people. I was a young Belgian mathematical or rather theoretical physicist who had printed in his head that he wanted to specialize in mathematical physics. There I came to meet David Ruelle, a Belgian researcher, who was already known to be a kind of a star in his field. He obtained his Ph.D. on the basis of work done in Zurich, Switzerland, as far as I remember. He already had a serious reputation as a well-known researcher, educated in the Zürich school for mathematical physics and was a picture example of somebody whom I strove to be. Also I do remember that our communication suffered a bit from our different Belgian linguistic origins. There are many jokes in our small Belgian country that describe these different language situations. Anyway that was the reason why my scientific attention did move a bit more in the direction of the other star in the field of mathematical physics, namely, in the direction of Daniel Kastler.

Unfortunately Daniel passed away very recently. I may take this occasion to express a salute of honor to this great and rich personality. Daniel was a French mathematical physicist and was a typical product of the French school. He was a person who had an important impact on the mathematics education and studies in his country. For centuries mathematical physics was a very popular subject in France, and it was considered at the universities as a very serious field of study as well. Daniel was an exponential example of a French and European mathematical physicist.

## 数学代写|数论作业代写number theory代考|Sergio Albeverio and Illia Karabash

The contribution by Sergio Albeverio and Illia Karabash considers the location of resonances of a Schrödinger Hamiltonian for a quantum mechanical particle in a potential generated by randomly placed points (delta-interactions) in the three-dimensional Euclidean space. The resonances are shown to be zeroes of random exponential polynomials, forming a point process in the complex plane. The detailed asymptotic properties of the locations of these resonances (at infinity in the complex plane) are discussed in general and particularly for the special case where the randomness (of the process of delta-interactions) is of the binomial type. In this case it is proven in particular that the counting function for the number of resonances in a sphere of radius $R$ divided by $R$ converges almost surely for $R$ converging to infinity to the random variable $\pi^{-1} V(Y)$, where $Y$ describes the location of the point interactions and $V(Y)$ is a “measure of size” associated with $Y$.

Thus, a stochastic version of the “Weyl-type asymptotics for resonances” is established (similarly as for the Weyl asymptotics of the number of eigenvalues of Laplace operators in bounded domains). For a general finite point process of deltainteractions, the decomposition of the random set of resonances into sequences with “logarithmic” asymptotics is studied. It it shown that this decomposition can be described by a finite number of real-valued random parameters. The behavior of the distributions of some of these parameters is also considered under the assumption that the intensity of the binomial process of delta-interactions grows to infinity.
This paper is related to interests of Erik Balslev, both through the concern with resonances and by the use of exponential polynomials, familiar in the study of location of zeroes of number-theoretical functions.

## 数学代写|数论作业代写number theory代考|Sergio Albeverio and Illia Karabash

Sergio Albeverio 和 Illia Karabash 的贡献考虑了量子力学粒子在三维欧几里得空间中随机放置的点（δ 相互作用）产生的势中的薛定谔哈密顿量的共振位置。共振显示为随机指数多项式的零点，在复平面中形成点过程。这些共振位置的详细渐近特性（在复平面中的无穷远处）一般会讨论，特别是对于随机性（δ相互作用过程的）是二项式的特殊情况。在这种情况下，特别证明了半径球体中共振数量的计数函数R除以R几乎肯定会收敛R向随机变量收敛到无穷大圆周率−1在(是)， 在哪里是描述点交互的位置和在(是)是与相关的“尺寸度量”是.

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## 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。