GAUGE-INSTITUTE

 

 

Gauge Institute Journal

 

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

 

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

Complex Delta Function, and the Fourier Transform: Cauchy Integral Formula is the Complex Fourier Integral Theorem

Jordan Lemma Proof

Delta Function, and Hilbert Transform

 

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, and the 2-D Fourier-Bessel Transform

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

Complex Delta Function, and the Fourier Transform: Cauchy Integral Formula is the Complex Fourier Integral Theorem

Circular and Spherical Delta Functions

Sturm-Liouville Expansions of the Delta Function

Linear Differential Equations Driven by Delta Functions

 

Integral Transforms

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, and the 2-D Fourier-Bessel Transform

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

 

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 & 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

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

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

 

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

 

Neutrino

The Neutrino Mixing Matrix

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

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

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

 

Wave-Particle

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

Proton’s Spin and Radius

Neutron’s Spin and Radius

 

Spin

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

 

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