The Experts below are selected from a list of 75 Experts worldwide ranked by ideXlab platform
Edgar E. Escultura - One of the best experts on this subject based on the ideXlab platform.
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the mathematics of the grand unified theory
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Edgar E. EsculturaAbstract:Abstract This paper surveys the mathematics of GUT and highlights the author’s new Real Number System R ∗ which is a continuum, non-Archimedean and non-Hausdorff, but its subspace of decimals is countably infinite, discrete, Archimedean and Hausdorff. The paper also proves Goldbach’s conjecture in R ∗ and provides an overview of GUT and qualitative and computational models of many of the presently ill-defined physical concepts, e.g., gravity.
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revisiting the hybrid Real Number System
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Edgar E. Escultura, Gnana T Bhaskar, V Lakshmikantham, S LeelaAbstract:The hybrid Real Number System consisting of terminating and nonterminating decimals, dark Numbers, dual dark Numbers, involving the notions of personal infinities and the impersonal infinity has been discussed. Some algebraic properties of dark Numbers and dual dark Numbers are discussed.
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the new Real Number System and discrete computation and calculus
Neural Parallel & Scientific Computations archive, 2009Co-Authors: Edgar E. EsculturaAbstract:The paper points out the inconsistency and ambiguity of the field axioms of the Real Number System and notes that the only clearly defined and consistent mathematical model of the Real Numbers is the set of terminating decimal. Then it identifies present mathematics having global applications. They are continuous and discrete; the former meets the needs of the natural sciences since physical space is a continuum that pervades everything in nature and the latter of computing and applications since physical Systems are discrete. Then the base mathematical space over which mathematics is to be built called the new Real Number System is developed using three consistent axioms. This new mathematical space is a continuum, non-Archimedean and non-Hausdorff but contains the subspace of decimals which is discrete, Archimedean and Hausdorff. It introduces a new norm that has many advantages over the other norms of the Real Number System, especially, for purposes of computing.
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The grand unified theory
Nonlinear Analysis: Theory Methods & Applications, 2008Co-Authors: Edgar E. EsculturaAbstract:Abstract The paper presents an overview of the Grand Unified Theory, introduces the ten most important natural laws and surveys the mathematics involved in the Grand Unified Theory’s development and applications with more detail on the author’s recent contribution, the new Real Number System.
V Lakshmikantham - One of the best experts on this subject based on the ideXlab platform.
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revisiting the hybrid Real Number System
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Edgar E. Escultura, Gnana T Bhaskar, V Lakshmikantham, S LeelaAbstract:The hybrid Real Number System consisting of terminating and nonterminating decimals, dark Numbers, dual dark Numbers, involving the notions of personal infinities and the impersonal infinity has been discussed. Some algebraic properties of dark Numbers and dual dark Numbers are discussed.
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the hybrid Real Number System
Nonlinear Analysis: Hybrid Systems, 2007Co-Authors: V Lakshmikantham, Danny KovachAbstract:Abstract The origin of the concepts that we employ such as natural Numbers, rational and irrational Numbers, zero, infinity and the place value System among others originate in the Vedas, or Veda Samhitas to be correct [Veda Samhitas]. However, due to our second-hand reception from the Arabs and the belief that everything originated in Greece, this appears to have lost the original source and meaning [V. Lakshmikantham, S. Leela, J. Vasundhara Devi, The Origin and History of Mathematics, Cambridge Scientific Publishers, Cambridge, UK, 2005. [5] ]. As a consequence, the so-called rational thinking or logic that applies to concrete situations when employed for concepts that are beyond our sensory perceptions has created some paradoxes [E.E. Escultura, FTG XVII: The new mathematics and physics, J. Appl. Math. Comput. 138 (2003) 127–149; E.E. Escultura, FTG XXXIV. Foundations of analysis and the new arithmetic, Nonlinear Anal. Phenom. III (2006) (in press)]. It is therefore necessary to return to the origin to clearly understand the basis. In this paper, we plan to propose a hybrid Real Number System utilizing the original ideas so as to shed some light on the existing System and strengthen it.
Danny Kovach - One of the best experts on this subject based on the ideXlab platform.
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the hybrid Real Number System
Nonlinear Analysis: Hybrid Systems, 2007Co-Authors: V Lakshmikantham, Danny KovachAbstract:Abstract The origin of the concepts that we employ such as natural Numbers, rational and irrational Numbers, zero, infinity and the place value System among others originate in the Vedas, or Veda Samhitas to be correct [Veda Samhitas]. However, due to our second-hand reception from the Arabs and the belief that everything originated in Greece, this appears to have lost the original source and meaning [V. Lakshmikantham, S. Leela, J. Vasundhara Devi, The Origin and History of Mathematics, Cambridge Scientific Publishers, Cambridge, UK, 2005. [5] ]. As a consequence, the so-called rational thinking or logic that applies to concrete situations when employed for concepts that are beyond our sensory perceptions has created some paradoxes [E.E. Escultura, FTG XVII: The new mathematics and physics, J. Appl. Math. Comput. 138 (2003) 127–149; E.E. Escultura, FTG XXXIV. Foundations of analysis and the new arithmetic, Nonlinear Anal. Phenom. III (2006) (in press)]. It is therefore necessary to return to the origin to clearly understand the basis. In this paper, we plan to propose a hybrid Real Number System utilizing the original ideas so as to shed some light on the existing System and strengthen it.
S Leela - One of the best experts on this subject based on the ideXlab platform.
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revisiting the hybrid Real Number System
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Edgar E. Escultura, Gnana T Bhaskar, V Lakshmikantham, S LeelaAbstract:The hybrid Real Number System consisting of terminating and nonterminating decimals, dark Numbers, dual dark Numbers, involving the notions of personal infinities and the impersonal infinity has been discussed. Some algebraic properties of dark Numbers and dual dark Numbers are discussed.
Frank Rogers - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy gradient descent for the linear fuzzy Real Number System
AIMS Mathematics, 2019Co-Authors: Frank RogersAbstract:Many problems in education, finance, and engineering design require that decisions be made under uncertainty. In these fields, Machine Learning is often used to search for patterns and information from data. To find patterns in Fuzzy Data, Fuzzy Machine Learning techniques can be used. In this paper, we focus on solving and manipulating Fuzzy Nonlinear problems in the Linear Fuzzy Real (LFR) Number System using the Gradient Descent. The Gradient Descent is the most often used learning algorithm in Machine Learning. Thus, we propose the LFR Gradient Descent method for solving nonlinear equations in the LFR Number System.
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fuzzy nonlinear optimization for the linear fuzzy Real Number System
2009Co-Authors: Frank Rogers, Younbae JunAbstract:Quite a few problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made under uncertainty. In this paper, we focus on Fuzzy nonlinear optimization problems in the Linear Fuzzy Real (LFR) Numbers. The problems will consist of fuzzy constraints and objective functions, crisp constraints with a fuzzy objective function, or fuzzy constraints with a crisp objective function. In this paper, we propose LFR Newton’s method for solving nonlinear Systems and use it to solve optimization problems.
