GAUGE-INSTITUTE
Pi
Pi, e, and
Gamma are Transcendental Numbers
All the
Pi-Squared Series and the Catalan Series
All the Pi-Cubed
Series and the Zeta(3) Series
The
College Mathematics Journal explains why Pi is a constant
Expansions of
a=tanA in powers of arctan(a)=A
Gamma
Pi,
e, and Gamma are Transcendental Numbers
The Gamma Constant,
and the Euler's Zeta Functions
The Gamma
Function Role in the Summation of the Catalan Series
Euler's Gamma is
Irrational and Sequentially Transcendental Number
The Geometry of
Exponentials, And Euler’s Gamma Expanded in Logarithms
Zeta(3)
Pi,
e, and Gamma are Transcendental
Numbers
All the Pi-Cubed
Series and the Zeta(3) Series
Zeta(3) is
Irrational and Sequentially Transcendental Number
Catalan Constant
Pi,
e, and Gamma are Transcendental
Numbers
The Gamma
Function Role in the Summation of the Catalan Series
All the
Pi-Squared Series and the Catalan Series
Catalan
Constant is Irrational and Sequentially Transcendental Number
Transcendental
Pi,
e, and Gamma are Transcendental
Numbers
Euler's Gamma is
Irrational and Sequentially Transcendental Number
Zeta(3) is
Irrational and Sequentially Transcendental Number
Catalan
Constant is Irrational and Sequentially Transcendental Number
Pi+e, and (Pi)e
are Sequentially Transcendental Numbers
Expansions of
a=tanA in powers of arctan(a)=A
Fermat
Fermat Last Theorem
Complete Statement
Geometry
The Curvature
in E^4 of a 3-Sphere, and of the Klein
Bottle
The
Universe is Riemannian 3-Sphere that Curves Positively with 93% Certainty
The Geometry of
Exponentials, And Euler’s Gamma Expanded in Logarithms
Expansions of
a=tanA in powers of arctan(a)=A
Chi-Squared
Goodness-of-fit test of the Riemann Hypothesis
Riemann’s
Formula for Count of the Primes: The effect of the Hypothesis Series
Power
Means Calculus: Product Calculus, Harmonic Mean Calculus, and Quadratic Mean
Calculus
The Fundamental Theorem of the Fractional Calculus,
and the Meaning of Fractional Derivatives
Hilbert’s
First Problem: Cantor’s Continuum Hypothesis
Rationals
Countability and Cantor’s Proof
Correction to
Rationals Countability and Cantor's Proof
Cantor’s Set and
the Cardinality of the Reals
Cardinality,
Measure, and Category
The
Continuum Hypothesis, The Axiom of Choice, and Non-Cantorian Theory
Well-Ordering
of the Reals, Equality of all Infinities, and the Continuum Hypothesis
THE
EQUALITY OF ALL INFINITIES: From the Natural Numbers to the Continuum
Cantor's
Paradoxical Diagonal Argument, and Transfinite Induction
Feynman Integral and Convolution Products
Riemannian
Trigonometric Series
Infinite
Series with Infinite Hyper-real Sum
Infinitesimal
Complex Calculus
Infinitesimal
Variational Calculus
Infinitesimal
Calculus of Random Walk and Poisson
Processes
Infinitesimal
Calculus of Random Signals and White
Noise
Analysis
The Mean Value
Theorem, and its Geometrical Meaning
Modulus Principles
for Analytic Functions
The infinite Series cos(x)
+cos(2x)+ cos(3x) +… is Sumless for any non-zero x
Infinitesimal
Complex Calculus
Delta Function of
a Complex Variable
Fourier
Transforms, and Fourier Integrals of a Complex Delta Function, and of an
Analytic Function
The Fourier-Bessel
Integral of the Polar Delta of a Complex Variable, and of an Analytic Function
The Fourier Series
of a Singular Function of a Complex Variable
Delta Function,
and Hilbert Transform
The Geometry of
Exponentials, And Euler’s Gamma Expanded in Logarithms
Residue Calculus
The Gamma
Function Role in the Summation of the Catalan Series
All the
Pi-Squared Series and the Catalan Series
All the Pi-Cubed
Series and the Zeta(3) Series
Space-Time
Electrodynamics, and Magnetic Monopoles
The
Aharonov-Bohm Magnetic Field is Non-Zero and the Electron Spirals towards the
Center
Space-Time
Curves and Surfaces
The Infinitesimal
Circulation Theorem
Circular and
Spherical Delta Functions
Infinitesimal
Variational Calculus
Infinitesimal
Elasticity, Variational Principles, and Castigliano Theorems
Infinitesimal
Calculus of Random Walk and Poisson
Processes
Einstein’s
Diffusion and Probability-Wave Equations of Random Walk and Poisson Processes
Evolution
Equations of Random Walk and Poisson
Processes
Infinitesimal
Calculus of Random Signals and White
Noise
The Fourier
Integral, and Delta Function Exponential Representations
The
Fourier Series of a Delta Function
Delta
Function, the Fourier Transform, and Fourier Integral Theorem
Delta Function,
the Laplace Transform, and Laplace Integral Theorem
Delta Function,
and Hilbert Transform
Polar
Delta Function, the 2-D Fourier-Bessel Transform, and the 2-D Fourier-Bessel
Integral
Radial
Delta Function, and the 3-D Fourier-Bessel Transform
Periodic Delta
Function and Dirichlet Summation of Fourier Series
Periodic Delta Function
and Fejer-Cesaro Summation of Fourier Series
Periodic Delta
Function and Poisson Integral for Abel Summation of Fourier Series
Periodic Delta
Function and Expansion in Legendre Polynomials
Delta Function and
Expansion in Hermite Functions
Delta Function
and Expansion in Laguerre Functions
Periodic Delta
Function and Expansion in Chebyshev Polynomials
Periodic Delta
Function and Expansion in Bessel Functions
Delta Function of
a Complex Variable
Fourier
Transforms, and Fourier Integrals of a Complex Delta Function, and of an
Analytic Function
The Fourier-Bessel
Integral of the Polar Delta of a Complex Variable, and of an Analytic Function
Circular and
Spherical Delta Functions
Sturm-Liouville
Expansions of the Delta Function
Linear
Differential Equations Driven by Delta Functions
Delta
Function and the Poisson Summation Formula
Delta
Function, the Fourier Transform, and Fourier Integral Theorem
Fourier
Transforms, and Fourier Integrals of a Complex Delta Function, and of an
Analytic Function
The Fourier-Bessel
Integral of the Polar Delta of a Complex Variable, and of an Analytic Function
Delta Function,
the Laplace Transform, and Laplace Integral Theorem
Delta Function,
and Hilbert Transform
Polar
Delta Function, the 2-D Fourier-Bessel Transform, and the 2-D Fourier-Bessel
Integral
Radial
Delta Function, and the 3-D Fourier-Bessel Transform
Riemannian
Trigonometric Series
Periodic Delta
Function and Dirichlet Summation of Fourier Series
Periodic Delta
Function and Fejer-Cesaro Summation of Fourier Series
Periodic Delta
Function and Poisson Integral for Abel Summation of Fourier Series
Fourier
Series Convergence in the Mean, and Parseval’s Theorem
The Fourier Series
of a Singular Function of a Complex Variable
Periodic Delta
Function and Expansion in Legendre Polynomials
Delta Function and
Expansion in Hermite Functions
Delta Function
and Expansion in Laguerre Functions
Periodic Delta
Function and Expansion in Chebyshev Polynomials
Periodic Delta
Function and Expansion in Bessel Functions
Sturm-Liouville
Expansions of the Delta Function
Optical
Soliton, and Propagating Delta Function
Delta
Function and Optical Catastrophe Models
Electrodynamics
It
is a World full of Magnetic Monopoles
Space-Time
Electrodynamics, and Magnetic Monopoles
The
Aharonov-Bohm Magnetic Field is Non-Zero and the Electron Spirals towards the
Center
Electro-Magnetic Radiation
The
Photon’s Electric and Magnetic Energies Densities are Equal
Magnetism
It
is a World full of Magnetic Monopoles
The Magnetic Neutrino
Gravitation
May Be Sum of Misaligned Atomic Magnets,
Neutrino May Be the Magnetic Radiation Quantum
The Invariance of
the Energy-Momentum Under the Lorentz Transformation
A
Hypothesis that Dark Matter is Regular Matter, Invisible, since it Moves Faster Than Light
Einstein’s
General Relativity is Electromagnetic
Mass
Conversion into Neutrino Energy
Gravitation
The Magnetic Neutrino
Gravitation
May Be Sum of Misaligned Atomic Magnets,
Neutrino May Be the Magnetic Radiation Quantum
The
Deflection of Light by the Sun Follows From Newton's Gravitation Alone
Gravitational
Waves and the Origin of Gravitation
The Sun's
Orbit Radius, and Period
Regarding
Response to American Mathematical Monthly Confusion about Circular Motion
Hydrogen Atom
It
is a World full of Magnetic Monopoles
Radiation
Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton
Atom
The Electron and
Proton Orbits in the Hydrogen Atom
The Proton
Spectrum in the Hydrogen Atom
Zero Point
Energy, and the Charge-Radiation Equation in Bohr's Atom
Radiation-Reaction
Forces in the Hydrogen Atom, and in the Neutron
Atom
It
is a World full of Magnetic Monopoles
Gravitation
May Be Sum of Misaligned Atomic Magnets,
Neutrino May Be the Magnetic Radiation Quantum
Radiation
Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton
Atom
Radiation Power Equilibrium as key to Nuclear Forces
Molecules
Electron
It is a World full of Magnetic Monopoles
The Proton and its Quarks Rotations and
Energies
The Composite Electron with Compton
Radius
The Electron’s Charge Sign Indicates
Electron’s Self-Rotation
An Electron with Compton
Radius Rotates at Speed 260km/s, and Frequency 10^20c/s
Electron’s
Spin, Diffraction, and Radius
The Electric
Forces within the Compton Radii of the Proton, and the Electron are Very Strong
Proton
Gravitation
May Be Sum of Misaligned Atomic Magnets,
Neutrino May Be the Magnetic Radiation Quantum
The Proton and its
Quarks Rotations and Energies
An Electron
with Compton Radius Rotates at Speed 260km/s, and Frequency 10^20c/s
The Electric
Forces within the Compton Radii of the Proton, and the Electron are Very Strong
Neutron
The Electric
Forces within the Compton Radii of the Proton, and the Electron are Very Strong
Photon’s Spin, Diffraction, and
Radius. The One Photon Hypothesis, and Stopped Photon
The Quantum Optics
of a Photon Composed of Two Circulating Subelectrons
Quark
The Proton and its
Quarks Rotations and Energies
An Electron
with Compton Radius Rotates at Speed 260km/s, and Frequency 10^20c/s
The Electric
Forces within the Compton Radii of the Proton, and the Electron are Very Strong
Neutrino
The Magnetic Neutrino
Gravitation
May Be Sum of Misaligned Atomic Magnets,
Neutrino May Be the Magnetic Radiation Quantum
Neutrino-less
Double Beta Decay violates Angular Momentum Conservation
Quantum Mechanics
Quantum
Entanglement is Paradoxical
The Quantum Optics
of a Photon Composed of Two Circulating Subelectrons
The Aharonov-Bohm
Magnetic Field is Non-Zero and the Electron Spirals towards the Center
Wave-Particle
Duality: de Broglie Waves and Uncertainty
American Journal of
Physics claims that h approaching
zero does not imply Classical Mechanics
EPR, and the Paradoxical
Axiomatic Quantum Mechanics
What are
Dirac Magnetic Monopoles, Where Are They, and What They Mean
The
Energy, and Entropy of Photons and Electrons
Quantum
Entanglement
Quantum Entanglement is
Paradoxical
EPR, and the Paradoxical
Axiomatic Quantum Mechanics
Quantum Optics
The Quantum Optics
of a Photon Composed of Two Circulating Subelectrons
Photon’s
Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon
Quantum Entropy
& Temperature
Zero Point
Energy, and Electromagnetic Entropy
The Energy, and Entropy of
Photons and Electrons
Magnetic
Monopoles
It
is a World full of Magnetic Monopoles
Space-Time
Electrodynamics, and Magnetic Monopoles
What are
Dirac Magnetic Monopoles, Where Are They, and What They Mean
Zero
Point Energy: Planck Radiation Law
Zero Point
Energy: Thermodynamic Equilibrium and Planck Radiation Law
Zero Point
Energy, and the Charge-Radiation Equation in Bohr's Atom
Zero Point
Energy, and Electromagnetic Entropy
Zero Point Energy
Does not Imply Planck's Radiation Law, and Does Not Replace the Quantum
Assumption
American Journal of
Physics Claims that a Harmonically Oscillating mass has Zero Point Energy
Zero Point Energy
Does Not Generate Gravitation
Einstein Errors
Einstein's
Wave-Particle Fallacy: Radiation Is NOT a Mixture of Photons and Waves
The Invariance of
the Energy-Momentum Under the Lorentz Transformation
Einstein’s
General Relativity is Electromagnetic
Zero
Point Energy Does not Imply Planck's Radiation Law, and Does Not Replace the
Quantum Assumption
The Energy, and Entropy of
Photons and Electrons
Wave-Particle
Duality: de Broglie Waves and Uncertainty
Photon’s
Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon
Einstein's
Wave-Particle Fallacy: Radiation Is NOT a Mixture of Photons and Waves
The Proton and its
Quarks Rotations and Energies
The Composite
Electron with Compton Radius
The
Electron’s Charge Sign Indicates Electron’s Self-Rotation
An Electron
with Compton Radius Rotates at Speed 260km/s, and Frequency 10^20c/s
Photon’s
Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon
Electron’s
Spin, Diffraction, and Radius
Non-Physical
Unit Systems in General Relativity, and in Quantum Field Theory
The Fine Structure Constant and the Paradoxical
Natural Units
Feynman
Integral and Convolution Products
Entangled Simultaneous
Measurement and Elementary Particle Representations
Elementary Particle Mixing
for Maximum Channel capacity in measured Decays
Extension of Lorentz
Group Representations for Chiral Fermions
The W Mediated Weak Decay
as an Information Channel