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In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)

Today, most of the “big data” applications needs to compute data in real-time since the Internet develops quite fast and the users expect the get reactions from the applications simultaneously. This rule is valid for almost all types of applications. When a user interacts with a commercial website by looking a product, the website should be able to show her related products for increasing its conversion rates. For a CRM application, the users should be able to solve their problem using that application. And most the time, these actions need aggregation computations. The aim of our project is to provide a high-performance scalable computational engine that is flexible and can be adapted to any type of applications. The system collects the events with collection API and continuously processes them on the fly with using pre-aggregation rules submitted by Analysis API.

Lazaridou., et al 2017 proposed a framework for language learning that relies on multi-agent communication. The agents in the framework were setup in a referential game where they communicated about many images. In this paper, we propose an experiment where agents develop a private language for referring to specified sentences given a set of sentences. The challenge is for the agents to learn a method of distinguishing differences between sentences and to develop a shared language to be able to refer to particular sentences by those distinguishing features. We will evaluate the agents' ability to accurately identify and differentiate the sentences. In addition, we will identify patterns in the methods that the agents develop to refer to the different types of sentences.Keywords: Reinforcement learning, multi-agent coordination

Fred Brooks Jr. outlined four inherent problems in software engineering in his paper No Silver Bullet. Being written almost thirty years ago new technologies have been developed which have not been evaluated against these properties. This paper will be evaluating the features of NoSQL databases and look to see how they affect the problems, whether positively or negatively.

Vuong V. Trinh's CV

The usage of software has grown as computers become popular. There have emerged, both in academia and in the market, technological solutions for several areas, among them education. On the other hand, classroom teaching and learning continues to suffer from classical educational problems such as lack of student and teacher motivation and lack of clear educational goals. And although software supports learning across a range of disciplines and ages, children's audiences, especially in mathematics, have been little contemplated with the benefits that technological solutions can bring. Therefore, the use of pedagogical approaches, such as Bloom's Taxonomy and Formative Assessments, together with gamification techniques, such as Octalysis, can be used to develop a technological solution that contemplates this public. The present work aims to propose the development of a software to assist the teaching and learning of mathematics for children in the classroom.

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A proof of the improper integral that defines the gamma function that I have derived for \(R \geq 0\).

Curriculum Vitae of Yuri da Silva Villas Boas An Applied Mathematics Bachelors by the Federal University of Rio de Janeiro, with expertise in Finance and considerable experience in C++ searches for a position as IT.