This document presents the mechanised proofs of two popular theorems attributed to Augustin Louis Cauchy Cauchy’s Mean Theorem and the Cauchy-Schwarz Inequality.

Recognizing human facial expression and emotion by computer is an interesting and challenging problem. In this paper we propose a method for recognizing emotions through facial expressions displayed in video sequences. We introduce the Cauchy Naive Bayes classifier which uses the Cauchy distribution as the model distribution and we provide a framework for choosing the best model distribution as...

We formulate an elementary condition on an involutive quantaloidQ under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of Q-enriched categories. For such quantaloids, which we call Cauchy-bilateral quantaloids, it follows that the Cauchy completion of any symmetric Q-enriched category is again symmetric. Examples include Lawver...

A completion of a Cauchy space is obtained without the T2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called s-maps form a subcategory CHY′ of CHY. A completion functor is defined for this subcategory. The completion subcategory of CHY′ turns out to be a bireflective subcategory of CHY′. This t...

Recognizing human facial expression and emotion by computer is an interesting and challenging problem. In this paper we propose a method for recognizing emotions through facial expressions displayed in video sequences. We introduce the Cauchy Naive Bayes classifier which uses the Cauchy distribution as the model distribution and we provide a framework for choosing the best model distribution as...

In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results. AMS Classific...

We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For every suitable choice of a real subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case we get a volume Cauchy formula. In the Clifford algebra case, the choice of the ...

ABSTRACT. We extend a recent result on third and fourth-order Cauchy-Euler equations by establishing the Hyers-Ulam stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one. We...

Flexible job-shop scheduling problem (FJSP) has been well known as one of the most difficult NP-hard combinatorial optimization problems. This problem FJSP is an extension of job-shop scheduling problem (JSP) which is to create a sequence of operations satisfying the precedence relationship together with assignment of time and resources for each operation. Thus, the FJSP model is closer to the ...

criticism of public extension services has resulted in various countries seeking alternative approaches for provision of these services. in all these approaches, extension personnel are the key factors to the success of the implementation. today, agricultural extension services in turkey bear the responsibility of the ministry of food, agriculture and livestock. a number of non-public extension...