GAUGE-INSTITUTE
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
Circular Complex Delta Function
Delta Function, and Hilbert Transform
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, 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, Complex Fourier Transform, and Fourier Integral Theorem
Circular and Spherical Delta Functions
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
Fourier Series Convergence in the Mean, and Parseval’s Theorem
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
Optical Soliton, and Propagating Delta Function
Delta Function and Optical Catastrophe Models
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 Duality: de Broglie Waves and Uncertainty
American Journal of Physics claims that h approaching zero does not imply Classical Mechanics
Photon’s Spin, Diffraction, and Radius. The One Photon Hypothesis, and Stopped Photon
Electron’s Spin, Diffraction, and Radius
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