GAUGE-INSTITUTE

Gamma

The Gamma Constant, and the Euler's Zeta Functions

The Gamma Function Role in the Summation of the Catalan Series

Volume of x-Dimensional Set

Euler's Gamma is Irrational and Sequentially Transcendental Number

Zeta(3)

All the Pi-Cubed Series and the Zeta(3) Series

Zeta(3) is Irrational and Sequentially Transcendental Number

Catalan Constant

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

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

Fermat

Fermat Last Theorem Complete Statement

Geometry

Volume of x-Dimensional Set

The Universe is Riemannian 3-Sphere that Curves Positively with 93% Certainty

Poincare

Poincare Conjecture Proof

Riemann Hypothesis

Riemann Zeta Function: the Riemann Hypothesis Origin, the Factorization Error, and the Count of the Primes

Chi-Squared Goodness-of-fit test of the Riemann Hypothesis

Riemann’s Formula for Count of the Primes: The effect of the Hypothesis Series

Riemann Hypothesis Proof

Power Means Calculus

Power Means Calculus: Product Calculus, Harmonic Mean Calculus, and Quadratic Mean Calculus

Fractional Calculus

The Fundamental Theorem of the Fractional Calculus, and the Meaning of Fractional Derivatives

Infinity

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

Non-Cantorian Set Theory

Cardinality, Measure, and Category

Khintchine’s Constant Fallacy, and the Geometric Mean of the Coefficients of Continued Fraction Expansion

The Continuum Hypothesis, The Axiom of Choice, and Non-Cantorian Theory

The Continuum Hypothesis

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

Integration

Feynman Integral and Convolution Products

Lebesgue Integration

Riemannian Integration

Riemannian Trigonometric Series

Jordan Lemma Proof

Ito Integral

Infinitesimal Calculus

Infinitesimals

Infinitesimal Calculus

Infinite Series with Infinite Hyper-real Sum

Infinitesimal Complex Calculus

Infinitesimal Vector Calculus

Infinitesimal Variational Calculus

Infinitesimal Calculus of Random Walk and Poisson Processes

Infinitesimal Calculus of Random Signals and White Noise

Complex Calculus

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

Jordan Lemma Proof

Delta Function, and Hilbert Transform

Residue Calculus

The Gamma Function Role in the Summation of the Catalan Series

Pi Series

All the Pi Series

All the Pi-Squared Series and the Catalan Series

All the Pi-Cubed Series and the Zeta(3) Series

Vector Calculus

Infinitesimal Vector Calculus

4-Space Curl is a 4-Vector

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

Variational Calculus

Infinitesimal Variational Calculus

Infinitesimal Elasticity, Variational Principles, and Castigliano Theorems

Random Calculus

Infinitesimal Calculus of Random Walk and Poisson Processes

Einstein’s Diffusion and Probability-Wave Equations of Random Walk and Poisson Processes

Ito Integral

Evolution Equations of Random Walk and Poisson Processes

Infinitesimal Calculus of Random Signals and White Noise

Delta Function

The 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

Integral Transforms

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

Fourier Series

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

Series Expansions

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 Solitons

Optical Soliton, and Propagating Delta Function

Delta Function and Optical Catastrophe Models

Electrodynamics

Space-Time Electrodynamics, and Magnetic Monopoles

The Aharonov-Bohm Magnetic Field is Non-Zero and the Electron Spirals towards the Center

Relativity

Black Holes Follow From Newton's Gravitation Alone, Not From the Paradoxical Schwarzschild Metric of General Relativity

The Invariance of the Energy-Momentum Under the Lorentz Transformation

Gravitational Waves Do Not Propagate at Light Speed. And Mercury’s Perihelion Precession Does Not confirm General Relativity

A Hypothesis that Dark Matter is Regular Matter, Invisible, since it Moves Faster Than Light

Einstein’s General Relativity is Electromagnetic

Faster Than Light Motion

Mass Conversion into Neutrino Energy

Gravitation

Supermassive Black Holes DO NOT Evaporate in Hawking's Radiation because Gravitational Mass/Energy Converts into Neutrinos. NOT into Photons

Black Holes Follow From Newton's Gravitation Alone, Not From the Paradoxical Schwarzschild Metric of General Relativity

The Deflection of Light by the Sun Follows From Newton's Gravitation Alone, And Does Not Confirm General Relativity

Gravitational Waves and the Origin of Gravitation

Hulse-Taylor Pulsar Periastron Precession is due to Magnetic Attraction propagating at light-speed, by Electromagnetic Waves

Supernova Models indicate that the Neutrino is the Quantum of Gravitational Radiation. The Origin of Gravitation is the Transition between the d-quark energy level, and the u-quark energy level of a Nucleon

The Sun's Orbit Radius, and Period

American Mathematical Monthly claims that in a Circular Motion, the Radial Acceleration is zero, there is no Gravitational Force, the Earth does not orbit the Sun, and the Sun’s Mass is Zero

Regarding Response to American Mathematical Monthly Confusion about Circular Motion

Atom

Wave-Particle Duality: de Broglie Waves and Uncertainty

The Composite Photon

Zero Point Energy, and the Charge-Radiation Equation in Bohr's Atom

Radiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom

The Neutron as a Collapsed-Hydrogen Atom: Zero Point Energy & Nuclear Binding Energy, X Rays & Gamma Rays, Nuclear Forces & Bonding, Neutronic Electrons Orbitals, and Neutron Stars

Radiation Power Equilibrium as key to Nuclear Forces

Radiation-Reaction Forces in the Hydrogen Atom, and in the Neutron

The Electron and Proton Orbits in the Hydrogen Atom

The Proton Spectrum in the Hydrogen Atom

Hydrogen Atom

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

Molecules

Why the Van der Waals Interaction is Determined Empirically, And How it Can NOT be Determined from the Schrödinger Equation

Neutrino

The Neutrino Mixing Matrix

Neutrino-less Double Beta Decay violates Angular Momentum Conservation

Quantum Mechanics

The Aharonov-Bohm Magnetic Field is Non-Zero and the Electron Spirals towards the Center

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 Entropy Constant k, The Radiation Constant h, The Quantized 2nd Law, The Quantized Temperature, & The Temperature Quantum

The Energy, and Entropy of Photons and Electrons

The Composite Photon

Quantum Entropy & Temperature

Zero Point Energy, and Electromagnetic Entropy

The Entropy Constant k, The Radiation Constant h, The Quantized 2nd Law, The Quantized Temperature, & The Temperature Quantum

The Energy, and Entropy of Photons and Electrons

Magnetic Monopoles

Space-Time Electrodynamics, and Magnetic Monopoles

What are Dirac Magnetic Monopoles, Where Are They, and What They Mean

Zero Point Energy

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

The Casimir Effect Fallacy: Casimir's Zero Point Energy has Infinite Mass, is not Conserved, and is Falsely based on Euler’s Formula. The Fallacy No Journal Accepted, that Resonates to No End in Journals

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

Gravitational Waves Do Not Propagate at Light Speed. And Mercury’s Perihelion Precession Does Not confirm General Relativity

Zero Point Energy Does not Imply Planck's Radiation Law, and Does Not Replace the Quantum Assumption

The Deflection of Light by the Sun Follows From Newton's Gravitation Alone, And Does Not Confirm General Relativity

Black Holes Follow From Newton's Gravitation Alone, Not From the Paradoxical Schwarzschild Metric of General Relativity

The Energy, and Entropy of Photons and Electrons

Wave-Particle

Wave-Particle Duality: de Broglie Waves and Uncertainty

Photon’s Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon

The Composite Photon

Electron’s Spin, Diffraction, and Radius

Proton’s Spin and Radius

Neutron’s Spin and Radius

Einstein's Wave-Particle Fallacy: Radiation Is NOT a Mixture of Photons and Waves

Spin

Photon’s Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon

The Composite Photon

Electron’s Spin, Diffraction, and Radius

Proton’s Spin and Radius

Neutron’s Spin and Radius

Physical Units & Constants

Non-Physical Unit Systems in General Relativity, and in Quantum Field Theory

The Fine Structure Constant and the Paradoxical Natural Units

Feynman Integral

Feynman Integral and Convolution Products

Weak Mixing

The Weak Mixing Matrix

The Neutrino Mixing Matrix

High Energy Physics

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