GAUGE-INSTITUTE
Pi
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
Gamma
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
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
The Universe is Riemannian 3-Sphere that Curves Positively with 93% Certainty
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
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
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
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
Space-Time Electrodynamics, and Magnetic Monopoles
The Aharonov-Bohm Magnetic Field is Non-Zero and the Electron Spirals towards the Center
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
Gravitational Waves and the Origin of Gravitation
The Sun's Orbit Radius, and Period
Regarding Response to American Mathematical Monthly Confusion about Circular Motion
Atom
Wave-Particle Duality: de Broglie Waves and Uncertainty
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
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
Neutrino
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 Energy, and Entropy of Photons and Electrons
Quantum Entropy & Temperature
Zero Point Energy, and Electromagnetic Entropy
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: 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
Electron’s Spin, Diffraction, and Radius
Einstein's Wave-Particle Fallacy: Radiation Is NOT a Mixture of Photons and Waves
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