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A Characterization of Semilinear Surjective Operators and Applications to Control Problems  [PDF]
Edgar Iturriaga, Hugo Leiva
Applied Mathematics (AM) , 2010, DOI: 10.4236/am.2010.14033
Abstract: In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with Delay, etc.
Creative Mathematics Education  [PDF]
Edgar E. Escultura
Creative Education (CE) , 2012, DOI: 10.4236/ce.2012.31008
Abstract: Creativity and critical thinking are the core values of science. Since mathematics is its primary language, the student of mathematics must imbibe and consolidate them. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. Therefore, the student of mathematics must go through the twists and turns of the critique-recti- fication of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works.
Electromagnetic Treatment of Genetic Diseases  [PDF]
Edgar E. Escultura
Journal of Biomaterials and Nanobiotechnology (JBNB) , 2012, DOI: 10.4236/jbnb.2012.322036
Abstract: The paper offers an overview of quantum and macro gravity, two of the three pillars of the Grand Unified Theory (GUT), the other thermodynamics, developed in a series of papers since the solution of the gravitational n-body problem in 1997 (J. Nonlinear Analysis, A-Series: Theory, Methods and Applications, Vol. 30, No. 8, 1997, pp. 5021 - 5032) and consolidated in the paper, The Grand Unified Theory (J. Nonlinear Analysis, A-Series: Theory: Method and Applications, Vol. 69, No. 3, 2008, pp. 823 - 831). GUT is further advanced by the paper, The Mathematics of GUT (J. Nonlinear Analysis, A-Series: Theory: Method and Applications, Vol. 71, 2009, pp. e420 - e431) and the discovery of more natural laws in the course of analyzing and explaining the disastrous final flight of the Columbia Space Shuttle in 2004 (J. Nonlinear Studies, Vol. 14, No. 3, 2007, pp. 241 - 260). Qualitative modeling was the key to the development of GUT and its theoretical and practical applications. The relevant natural laws of GUT that provide the foundations of the Unified Theory of Evolution are stated. GUT provides the basis for the development of the electromagnetic engine and the Unified Theory of Evolution, its theoretical application, for the development of appropriate technology for electromagnetic treatment of genetic diseases such as cancer, systemic lupos erythematosus, diabetes, muscular dystrophy and mental disorder, the central focus of this paper.
A General Theorem on the Conditional Convergence of Trigonometric Series  [PDF]
Edgar A. Cohen Jr.
Open Journal of Discrete Mathematics (OJDM) , 2013, DOI: 10.4236/ojdm.2013.31003
Abstract: The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to group appropriately the terms of the series in order to show absolute divergence of the series, given the well-established result that the series as it stands is convergent.
The Logic and Fundamental Concepts of the Grand Unified Theory  [PDF]
Edgar E. Escultura
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.48A021
Abstract:

The grand unified theory (GUT) originated in mathematics with this question: why are there long standing unsolved problems in mathematics, e.g., Fermat’s conjecture (also known as Fermat’s last theorem (FLT))? The answer came quickly: its underlying fields—foundations and the real number system—are defective. In particular, formal logic is inapplicable to mathematics (language of science) and the real number system is inconsistent. Critique-rectification of these fields was undertaken leading to a new mathematical methodology and the consistent new real number system that provides the main mathematics of GUT. Similar question was posed in physics: why are there long standing problems, e.g., the gravitational n-body and turbulence problems? The answer: the present methodology, quantitative modeling is inadequate and the remedy is a new methodology—qualitative mathematics and modeling that solved these problems and provided the initial formulation of GUT. This paper presents the basic logic of GUT and its fundamental concepts, particularly, the superstring or fundamental building block of matter.

On the Decomposition of a Bounded Closed Interval of the Real Line into Closed Sets  [PDF]
Edgar A. Cohen
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.34058
Abstract:

It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets or a countably infinite family of such sets. In particular, for a closed interval of the real line endowed with the usual topology, we see that we cannot partition it into a countably infinite number of disjoint, nonempty closed sets. On the positive side, however, one can certainly express such an interval as a union of c disjoint closed sets, where c is the cardinality of the real line. For example, a closed interval is surely the union of its points, each set consisting of a single point being closed. Surprisingly enough, except for a set of Lebesgue measure 0, these closed sets can be chosen to be perfect sets, i.e., closed sets every point of which is an accumulation point. They even turn out to be nowhere dense (containing no intervals). Such nowhere dense, perfect sets are sometimes called Cantor sets.

Chaos, Turbulence and Fractal: Theory and Applications  [PDF]
Edgar E. Escultura
International Journal of Modern Nonlinear Theory and Application (IJMNTA) , 2013, DOI: 10.4236/ijmnta.2013.23025
Abstract:

The paper identifies chaos, turbulence and fractal of quantum and macro gravity and studies their behavior, properties and applications based on the grand unified theory (GUT) and qualitative mathematics and modeling. Applications include devising electromagnetic engines, tornado aborter and terminator and technologies for electromagnetic treatment of genetic diseases such as cancer, systemic lupos erythematosus, diabetes and mental disorder without harm to normal cell and side effect. Typhoon in the Western Pacific which is turbulence is impossible to terminate and impractical to deflect but prediction can be improved because it follows the Northern Pacific Wind Cycle (Southern Pacific Wind Cycle in the Southern Hemisphere) and is affected by the temperature variation over the Philippine Deep and around Mayon Volcano. The electromagnetic engine uses the clean, inexhaustible, free dark matter, specifically, the energy of magnetic flux, in place of conventional fuel, e.g., fossil, nuclear and geothermal. The tornado aborter and terminator utilize the gravitational flux of the Earth, its vortex flux of superstrings as a cosmological vortex which is turbulence. The technologies for electromagnetic treatment of genetic diseases utilize electromagnetic waves based on resonance. All of them are GUT technologies because they are applications of GUT. Except for the magnetic train which is in operation the rest is still at the conceptual and research and development (R&D) phase but the theory is complete and the strategy for R&D are laid down in detail in the cited original papers.

Is Human Activity Linked to Climate Change?  [PDF]
Edgar E. Escultura
Atmospheric and Climate Sciences (ACS) , 2014, DOI: 10.4236/acs.2014.42031
Abstract: This paper establishes the link between human activity and climate change, e.g., more frequent and devastating typhoons, tornadoes, bushfires, droughts, floods and snowstorms and melting of the norther polar ice cap and recent occurrences of super typhoons and tornadoes. Qualitative mathematics and modeling(QMAM) explains this link and its remarkable verification based on the grand unified theory(GUT).
A Solution of a Problem of I. P. Natanson Concerning the Decomposition of an Interval into Disjoint Perfect Sets  [PDF]
Edgar A. Cohen Jr.
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.45024
Abstract:

In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.

Extending Electromagnetic Treatment to Infectious Diseases including the Ebola Virus  [PDF]
Edgar E. Escultura
Journal of Biomaterials and Nanobiotechnology (JBNB) , 2015, DOI: 10.4236/jbnb.2015.62010
Abstract: A blueprint for research and development for design and development of suitable electromagnetic treatment of genetic diseases (Escultura, Journal of Biomaterials and Nanobiotechnology, 3(2), 2012) known as genetic sterilization is applied to infectious diseases including viruses. It is based on the Grand Unified Theory (Escultura, Nonlinear Analysis, A-Series, 69(3), 2008) and the Unified Theory of Evolution (Escultura, The Journal of the Science of Healing Outcomes, 2015). Since every physical characteristic of living thing is determined by a gene, so is the undesirable symptom of a disease. For virus, its undesirable symptom is determined principally by the wavelength of the natural vibration of its gene as sequence of base materials which is equal to its measure as a segment of a double helix. Radiation with wavelength equal to this measure will resonate with it. Raising its intensity suitably will sterilize the gene, stop its spread and render it harmless to the host; then the disease is treated without harm to normal cells. Another treatment is establishing resonance with radiation of wavelength equal to the measure of the virus (protein strand with the gene) across; raising its intensity suitably will burn the virus without side effect (since it is much smaller than normal cells).
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