On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports

In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum integers with fields of coefficients of characteristic zero. This also solves completely the classification problem proposed by Melvyn Nathanson and Yang Wang concerning the solutions, with semigroup supports which are not prime subsemigroups of ℕ, to these functional equations for the case of rational field of coefficients. As a consequence, we obtain some results for other problems raised by Nathanson concerning maximal solutions and extension of supports of solutions to these functional equations in the case where the semigroup supports are not prime subsemigroups of ℕ.

THE USE OF SLOPE HOISTING PLANTS TO CREATE THE CONDITIONS FOR CIRCULAR TRAFFIC OF DUMP TRUCKS

The purpose of this article is to develop and substantiate rational designs of slope hoisting systems for dump trucks in the open pit mines. In order to reduce the time losses associated with idle mileage in the transport cycle, it is proposed to use the slope hoisting plants only for hauling down the empty trucks. The basic arrangements of slope hoisting systems have been analyzed. A rational field of using them has been determined. The lack of experience in operation of slope hoisting systems with multi-rope friction winders, the possibility of reducing a friction ratio due to freezing and wetting the rope leave no chance to recognize this technical solution to be reliable. The article presents the results of the design study and determination of parameters of a hoister with a reeving system of suspension of one platform to haul down the 130-ton trucks. The developed hoisting plant consists of the main parts as follows: two 1-65.6/0.8 single-drum hoisters; a platform for transporting the truck; a headframe for placing the deflection sheaves; two deflection sheaves; two inclined rail tracks to move the platform. The article proposes the new technical solutions for hoisting plants with two platforms, which are alternately used for hauling down the empty trucks. The developed technology promotes improvement of the operational performance of dump trucks in the open pit mines.

Chaff, wheat, filters, and bubbles: a discussion on fake news, journalism, credibility, and affections at network times

This paper seeks to situate historically the production of what is now called “fake news” and points out the misconception of establishing a dividing line in which the traditional press would be the sole source for reliable information, even though it was and still is the origin of much untrue or biased information. It criticizes the methods of the fact-checking agencies, which end up selling a false idea of objectivity. But above all, it points out the need to deepen the discussion about credibility at a time when reference information standards are challenged and beliefs seem to be allowed to prevail over the evidences. If arguments are useless in face of convictions, and if journalism is more than never necessary, the way to recover its role would have to be sought outside the rational field, in order to deactivate the affections that lead to the formation of bubbles refractoryto all criticism.Este artigo procura situar historicamente a produção do que hoje se chama “fake news” e assinala o equívoco de se estabelecer uma linha divisória na qual a imprensa tradicional seria a exclusiva fonte para a informação confiável, mesmo porque ela própria foi e continua a ser a origem de muita informação inverídica ou deturpada. Critica os métodos das agências de checagem, que acabam por vender uma falsa ideia de objetividade. Mas, principalmente, aponta a necessidade de um aprofundamento da discussão sobre credibilidade, em um tempo em que os padrões da informação de referência são contestados e as crenças parecem autorizadas a prevalecer sobre as evidências. Se os argumentos são inúteis diante das convicções, e se apesar disso o jornalismo é mais do que nunca necessário, a saída para recuperar o seu papel precisaria ser buscada fora do campo racional para depois recuperá-lo, de modo a desativar os afetos que levam à formação das bolhas refratárias a qualquer crítica.Este artículo busca situar históricamente la producción de lo que hoy se llama “fake news” y señala el equívoco de establecer una línea divisoria en la que la prensa tradicional sería la única fuente para la información confiable, incluso porque ella misma fué y sigue siendo el origen de mucha información falsa o engañosa. Critica los métodos de las agencias de chequeo, que acaban por vender una errónea idea de objetividad. Pero, principalmente, apunta la necesidad de una profundización de la discusión sobre credibilidad, en un tiempo en que los parámetros de la información de referencia son contestados y las creencias parecen autorizadas a prevalecer sobre las evidencias. Si los argumentos son inútiles ante las convicciones, y si a pesar de ello el periodismo sigue siendo necesario, la salida para recuperar su papel necesitaría ser buscada fuera del campo racional, para desactivar los afectos que llevan a la formación de las burbujas refractarias a cualquier crítica.

ABSTRACT REAL NUMBERS

In this paper we represent a result of our study in field of analysis , that is, an abstraction of the system of real numbers. We start by defining a set of positive elements in a countable infinite (denumerable) field and, hence, we obtain a linearly ordered field which we call a field of rational elements or a rational field. After that we may introduce irrationals elements in our rational field. And, at last we have a system of real abstract numbers.

On faithful quasi-permutation representations of groups of order p5

For a finite group [Formula: see text], we denote by [Formula: see text] the minimal degree of faithful permutation representations of [Formula: see text], and denote by [Formula: see text] and [Formula: see text], the minimal degree of faithful representation of [Formula: see text] by quasi-permutation matrices over the rational field [Formula: see text] and the complex field [Formula: see text], respectively. In this paper, we calculate [Formula: see text], [Formula: see text] and [Formula: see text] for the groups of order [Formula: see text], where [Formula: see text] is an odd prime.

Nonvanishing of Central Values of L-functions of Newforms in S2(Γ0(dp2)) Twisted by Quadratic Characters

We prove that for d ∊ {2, 3, 5, 7, 13} and K a quadratic (or rational) field of discriminant D and Dirichlet character 𝜒, if a prime p is large enough compared to D, there is a new form f ∊ S2Γ0(dp2)) with sign (+1) with respect to the Atkin–Lehner involution wp2 such that L( f ⊗ 𝜒, •)≠ 0. This result is obtained through an estimate of a weighted sum of twists of L-functions that generalises a result of Ellenberg. It relies on the approximate functional equation for the L-functions L( f ⊗ 𝜒, · ) and a Petersson trace formula restricted to Atkin–Lehner eigenspaces. An application of this nonvanishing theorem will be given in terms of existence of rank zero quotients of some twisted jacobians, which generalises a result of Darmon and Merel.

Mediated Recognition and the Quest for a Common Rational Field of Discussion in Three Early Medieval Dialogues

Using interpretative resources from contemporary recognition theory with a special focus on the notion of mediated recognition, this paper discusses the nature and degree of methodological agreement as manifested in three twelfth-century dialogues. The first source to be considered was written by Gilbert of Crispin, and known as Disputatio Christiani cum Gentili (Disputation of Christian with a Pagan), ca. 1093. The second source was composed by the Christian convert Peter Alfonsi, whose dialogue Dialogi contra Iudaeos (Dialogue against the Jews) was written about 1110. The third source to be considered is Peter Abelard’s treatise Collationes, a dialogue with three participants and the narrator, written between 1127 and 1132. In particular, the paper discusses the role of reason, the principles of argument, and the potentially-shared set of rules these dialogues employ, thereby bringing the agreement among conflicting parties into focus. In this respect, the novel interpretative approach based on recognition theory also differs markedly from the standard reading of apologetic texts, which usually emphasizes conflict and disagreement.

An application of the -adic analytic class number formula

We propose an algorithm to verify the$p$-part of the class number for a number field$K$, provided$K$is totally real and an abelian extension of the rational field$\mathbb{Q}$, and$p$is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.

Submodule of free Z-module

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are different.