Distribusi sampling eksak dari populasi normal

Penulisan skripsi ini membabas penurunan beberapa distribusi sampling eksak dari populasi normal dengan menggunakan latar belakang kalkulus..Jadi tentunya menggu nakan theorema theorema dalam kalkulus seperti theorema Liebnitz tentang mendifferensialkan suatu integral, tbeo-rema.pengubaban variabel dalam integral Banda, dll. Ada beberapa metode penurunan distribusi sampling eksak. Beberapa diantaranya yang akan diperkenalkan ada - lab 1. Metode Geometri 2, Metode Analitik 3. Metode Fungsi Karakteristik. Dalam pemakaiannya, metode metode diatas kadang-kadang di gunakan sejalan, dalam anti digunakan bersama-sama

Formal representation and proof for cooperative games

In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist. For mechanised theorem proving, the research introduces the field to a new application domain with a large user base; more specifically, the researchers are collaborating with developers working on state-of-the-art theorem provers. For economics, the research will provide tools for handling a hard class of problems; more generally, as the first application of mechanised theorem proving to centrally involve economic theorists, it aims to properly introduce mechanised theorem proving techniques to the discipline.\u

Arboreslenle dalam graph

Arborescence graph adalah suatu pohon (tree) yang mempunyai sebuah akar dan tidak mempunyai cycles. Berdasar theorema dan definisi, akan dibahas bentuk matriks arborescence•juga dibahas• perhitungan banyaknya arborescence dalam graph serta dapat menentukan bobot minimal graph arborescence

The lost proof of Fermat's last theorem

This work contains two papers: the first entitled "Euler's double equations equivalent to Fermat's Last Theorem" presents a marvellous "Eulerian" proof of Fermat's Last Theorem, which could have entered in a not very narrow margin, i.e. in only a few pages (less than 13). The second instead, entitled "The origin of the Frey elliptic curve in a too narrow margin" provides a proof, which is not elementary (25 pages): It is in various ways articulated and sometimes the author use facts with are proven later, but it is still addressed in an appropriate manner. This proof is however conditioned by presence of a right triangle (very often used by Fermat in his elusive digressions on natural numbers) or more precisely from a Pythagorean equation, which has a role decisive in the reconstruction of the lost proof. Regarding the first paper, following an analogous and almost identical approach to that of A. Wiles, I tried to translate the aforementioned bond into a possible proof of Fermat's Theorem. More precisely, through the aid of a Diophantine equation of second degree, homogeneous and ternary, solved at first not directly, but as a consequence of the resolution of the double Euler equations that originated it and finally in a direct I was able to obtain the following result: the intersection of the infinite solutions of Euler's double equations gives rise to an empty set and this only by exploiting a well known Legendre Theorem, which concerns the properties of all the Diophantine equations of the second degree, homogeneous and ternary. I report that the "Journal of Analysis and Number Theory" has made this paper in part (5 pages) available online at http://www.naturalspublishing.com/ContIss.asp?IssID=1779Comment: 39 pages, 1 figure- The double equations of Euler and the two fundamental theorems of this work are equivalent to the Fermat Last Theorem. The main goal is to rediscover what Fermat had in mind (no square number can be a congruent number). Also with the method of Induction, discovered by Fermat, we obtain a full proof of FLT. arXiv admin note: text overlap with arXiv:1604.0375

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Nonlocal Hardy type inequalities with optimal constants and remainder terms

Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha}{2}}\dif x \dif y \le \mathcal{C}_{N,\alpha, 0}\int_{\R^N} \abs{\varphi}^2,] and of its combinations with the Hardy inequality by Beckner [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, 1} \int_{\R^N} \abs{\nabla \varphi}^2,] and with the fractional Hardy inequality [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, s} \mathcal{D}_{N, s} \int_{\R^N} \int_{\R^N} \frac{\bigabs{\varphi (x) - \varphi (y)}^2}{\abs{x-y}^{N+s}}\dif x \dif y] where (I_\alpha) is the Riesz potential, (0 < \alpha < N) and (0 < s < \min(N, 2)). We also prove the optimality of the constants. The method is flexible and yields a sharp expression for the remainder terms in these inequalities.Comment: 9 page