GAUGE-INSTITUTE

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__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

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

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

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__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

**Relativity
& Gravitation**

The Meaning of the Michelson-Morley Experiment

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

Gravitational Waves and the Origin of Gravitation

The Sun's Orbit Radius, and Period

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

__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

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__

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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

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

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

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