quinta-feira, 8 de maio de 2014

Paraconsistent Mathematics - Differenttial and Integral

An Introduction to Paraconsistent Integral Differential Calculus: With Application Examples
            http://www.scirp.org/journal/PaperInformation.aspx?PaperID=44593

In this paper we show that it is possible to integrate functions with concepts and fundamentals of Paraconsistent Logic (PL). The PL is a non-classical Logic that tolerates the contradiction without trivializing its results. In several works the PL in his annotated form, called Paraconsistent logic annotated with annotation of two values (PAL2v), has presented good results in analysis of information signals. Geometric interpretations based on PAL2v-Lattice associate were obtained forms of Differential Calculus to a Paraconsistent Derivative of first and second-order functions. Now, in this paper we extend the calculations for a form of Paraconsistent Integral Calculus that can be viewed through the analysis in the PAL2v-Lattice. Despite improvements that can develop calculations in complex functions, it is verified that the use of Paraconsistent Mathematics in differential and Integral Calculus opens a promising path in researches developed for solving linear and nonlinear systems. Therefore the Paraconsistent Integral Differential Calculus can be an important tool in systems by modeling and solving problems related to Physical Sciences.
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Da Silva Filho, J. I. (2014) An Introduction to Paraconsistent Integral Differential Calculus: With Application Examples. Applied Mathematics, 5, 949-962. doi: 10.4236/am.2014.56090.
 
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Paraconsistent Mathematics and Dark Energy

Dark Energy Calculations Using the Paraquantum Gamma Factor (γPψ) on the Relativistic Energy Equation

A Paraconsistent Logic (PL) is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoretical structure. Paraquantum Logic (PQL) is based on a type of PL denominated Paraconsistent Annotated Logic with annotation of two values (PAL2v). The PAL2v have a representative Lattice of four vertices (Lattice FOUR) where are made interpretations with construction of Paraquantum Logical Model and equations capable computation values extract of Observable Variable measurements. The studies of the PQL are based on propagation of Paraquantum logical states ψ in a Paraquantum Universe represented by PQL-Lattice of four vertices. These studies of PQL are based in two Paraquantum factors: the Paraquantum Gamma Factor (γPψ) that has his action in the measurements of Observable Variables in the Physical world and the Paraquantum Factor of quantization hψ, which has his action in the Paraquantum Universe. In this paper we analyze the application of Paraquantum Gamma Factor γPψ and its intrinsic characteristics that add important information into the equation of Einstein’s relativistic Energy (E = MC2). In this article were made several calculations to demonstrate the effects of applying the Paraquantum Gamma Factor (γPψ) in relativistic energy equation. It is found that the factors of using the Paraquantum Logical Model make an adjustment in the equation of Einstein’s relativistic Energy and identify related values with recent results found for the Dark Energy and dark matter. In the Paraquantum/Relativistic Energy equation the γPψ appears as an important factor of transition between the relativistic universe and the Newtonian Universe. The results suggest that its use would be very important in the interpretation of the behavior of other astronomical factors as the cosmological constant and gravitation.
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Da Silva Filho, J.I. (2014) Dark Energy Calculations Using the Paraquantum Gamma Factor (γPψ) on the Relativistic Energy Equation. Journal of Modern Physics, 5, 319-334. http://dx.doi.org/10.4236/jmp.2014.56042
 
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Paraconsistent Mathematics and Derivative


Paraconsistent Differential Calculus (Part II): Second-Order Paraconsistent Derivative

http://www.scirp.org/journal/PaperInformation.aspx?PaperID=45616


The Paraconsistent Logic (PL) is a non-classical logic and its main property is to present tolerance for contradiction in its fundamentals without the invalidation of the conclusions. In this paper, we use the PL in its annotated form, denominated Paraconsistent Annotated Logic with annotation of two values-PAL2v. This type of paraconsistent logic has an associated lattice that allows the development of a Paraconsistent Differential Calculus based on fundamentals and equations obtained by geometric interpretations. In this paper (Part II), it is presented a continuation of the first article (Part I) where on the Paraconsistent Differential Calculus is given emphasis on the second-order Paraconsistent Derivative. We present some examples applying Paraconsistent Derivatives at functions of first and second-order with the concepts of Paraconsistent Mathematics.

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Da Silva Filho, J.I. (2014) Paraconsistent Differential Calculus (Part II): Second-Order Paraconsistent Derivative. Applied Mathematics, 5, 1222-1231. doi: 10.4236/am.2014.58107.
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Paraconsistent Mathematics

Paraconsistent Differential Calculus (Part I): First-Order Paraconsistent Derivative
A type of Inconsistent Mathematics structured on Paraconsistent Logic (PL) and that has, as the main purpose, the study of common mathematical objects such as sets, numbers and functions, where some contradictions are allowed, is called Paraconsistent Mathematics. The PL is a non-Classical logic and its main property is to present tolerance for contradiction in its fundamentals without the invalidation of the conclusions. In this paper (part 1), we use the PL in its annotated form, denominated Paraconsistent Annotated Logic with annotation of two values—PAL2v for present a first-order Paraconsistent Derivative. The PAL2v has, in its representation, an associated lattice FOUR based on Hasse Diagram. This PAL2v-Lattice allows development of a Para-consistent Differential Calculus based on fundamentals and equations obtained by geometric interpretations. In this first article it is presented some examples applying derivatives of first-order with the concepts of Paraconsistent Mathematics. In the second part of this work we will show the Paraconsistent Derivative of second-order with application examples.
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Da Silva Filho, J. I. (2014) Paraconsistent Differential Calculus (Part I): First-Order Paraconsistent Derivative. Applied Mathematics, 5, 904-916. doi: 10.4236/am.2014.56086.
 
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