Real Algebra

1996 ◽  
pp. 29-60
Author(s):  
Carlos Andradas ◽  
Ludwig Bröcker ◽  
Jesús M. Ruiz
Keyword(s):  
Real Algebra

Determinação aproximada de chuvas intensas no leste do paraná através da estatística e da álgebra pseudo real / Approximate determination of heavy rain in east paraná through statistics and pseudo real algebra

2021 ◽  
Vol 4 (3) ◽  
pp. 2966-2976
Author(s):  
Carlos Pereira De Novaes
Keyword(s):  
Heavy Rain ◽  
Approximate Determination ◽  
Real Algebra

Este artigo foi elaborado para se mostrar como se pode utilizar a álgebra pseudo-real em correlações usando dados de precipitações intensas de localidades da região leste do Estado do Paraná, de forma a se obter equações de chuvas intensas aproximadas para uso em engenharia de recursos hídricos e aqui vamos analisar uma equação aproximada geral de chuvas intensas para esta região com dados de chuvas intensas obtidas no livro Chuvas Intensas no Brasil correlacionando-as através do uso da estatística pseudo real com as latitudes, as longitudes e as precipitações médias anuais obtidas pela internet.

scholarly journals Landau’s theorem for slice regular functions on the quaternionic unit ball

2017 ◽  
Vol 28 (03) ◽  
pp. 1750017 ◽  
Author(s):  
Cinzia Bisi ◽  
Caterina Stoppato
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Analogous Result ◽  
Open Unit ◽  
Open Unit Ball ◽  
Slice Regular Functions ◽  
New Approach ◽  
The Real ◽  
Regular Functions ◽  
Real Algebra

During the development of the theory of slice regular functions over the real algebra of quaternions [Formula: see text] in the last decade, some natural questions arose about slice regular functions on the open unit ball [Formula: see text] in [Formula: see text]. This work establishes several new results in this context. Along with some useful estimates for slice regular self-maps of [Formula: see text] fixing the origin, it establishes two variants of the quaternionic Schwarz–Pick lemma, specialized to maps [Formula: see text] that are not injective. These results allow a full generalization to quaternions of two theorems proven by Landau for holomorphic self-maps [Formula: see text] of the complex unit disk with [Formula: see text]. Landau had computed, in terms of [Formula: see text], a radius [Formula: see text] such that [Formula: see text] is injective at least in the disk [Formula: see text] and such that the inclusion [Formula: see text] holds. The analogous result proven here for slice regular functions [Formula: see text] allows a new approach to the study of Bloch–Landau-type properties of slice regular functions [Formula: see text].

Differentiable functions on algebras and the equation grad (w) = M grad (v)

1992 ◽  
Vol 122 (3-4) ◽  
pp. 353-361 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Second Order ◽  
Frobenius Algebra ◽  
Constant Matrix ◽  
Second Order Differential Equations ◽  
Differentiable Functions ◽  
Open Set ◽  
Finite Dimensional ◽  
Taylor Expansions ◽  
Second Derivatives ◽  
Real Algebra

SynopsisLet U be a convex open set in a finite-dimensional commutative real algebra A. Consider A-differentiable functions f: U → A. When they are C2 as functions of their real variables, their A-derivatives are again A-differentiable, and they have second-order Taylor expansions. The real components of such functions then have second derivatives for which the A-multiplications are self-adjoint. When A is a Frobenius algebra, that condition (a system of second-order differential equations) actually forces a real function on U to be a component of some such f. If v is a function of n real variables, and M is a constant matrix, then the requirement that M∇(u) should equal ∇(w) for some w usually falls into this setting for a suitable A, and the quite special properties of such v, w can be deduced from known properties of A-differentiable functions.

scholarly journals More on real algebra in scott's model

1986 ◽  
Vol 30 (3) ◽  
pp. 277-291 ◽  
Author(s):  
Philip Scowcroft
Keyword(s):  
Real Algebra

scholarly journals Some properties of integration of real-valued function over a fuzzy interval

2021 ◽  
Vol 8 (12) ◽  
pp. 9-13
Author(s):  
M. A. Shakhatreh ◽  
◽  
A. M. Al-Shorman ◽  
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Interval Analysis ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Mathematical Concepts ◽  
Fuzzy Distance ◽  
Real Algebra ◽  
Fuzzy Interval

One of the most fundamental concepts in fuzzy set theory is the extension principle. It gives a generic way of dealing with fuzzy quantities by extending non-fuzzy mathematical concepts. There are a few examples, including the concept of fuzzy distance between fuzzy sets. The extension approach is then methodically applied to real algebra, with considerable development of fuzzy number operations. These operations are computationally appealing and generalized interval analysis. Although the set of real fuzzy numbers with extended addition or multiplication is no longer a group, it retains many structural qualities. The extension concept is demonstrated to be particularly beneficial for defining set-theoretic operations for higher fuzzy sets. We need some definitions related to our properties before we can create the properties of integration of a crisp real-valued function over a fuzzy interval. It is our goal in this article to develop and demonstrate certain characteristics of a real-valued function over a fuzzy interval in order to broaden the scope of the notion of integration of a real-valued function over a fuzzy interval. Some of these characteristics are linked to the operations of extended addition and extended subtraction, while others are not.

scholarly journals Inequalities Characterizing Linear-Multiplicative Functionals

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Włodzimierz Fechner
Keyword(s):  
Hausdorff Spaces ◽  
Multiplicative Functional ◽  
Real Algebra ◽  
Multiplicative Functionals

We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operatorsT:CX→CY, whereXandYare compact Hausdorff spaces.

Sign in / Sign up

Export Citation Format

Share Document