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.

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.

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.

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 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 isinapplicable 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.

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.

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.

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).

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.

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).