Most of my web pages are of material from books I have read. This started with providing summaries for the students in my courses at San Jose State University. Originally these were in the form of hard copy paper handouts. This form required my having to brings copies to class several times to make sure everyone got their copy. When the internet became available it was a relief for me. I no longer had to keep extra copies of handouts. Up to that time my office was buried in old copies of course handouts. With the internet everything for the courses was online.

However along the way I had some original thoughts and carried out some original analysis. There are quite a number of these on my website.

Latest things at the Bottom of List
• Gestation periods and animal scale
• The General Paths of Hurricanes
• The General Paths of Tornadoes
• Explanation of the Higher Proportion of Male Births Among Humans
• Explanation of the Nuclear Magic Numbers
• Human Culture as God
• Digit Sum Arithmetic
• The Average Curvature of Curves
• Infinitely Iterated Exponentiation
• Explanation of the Rotation Periods of the Planets
• Derivation of a Bode-type Relation for the Planets
• Longevity and Animal Scale
• The Structure of the Mandelbrot Set
• Explanation of the Nature of the Consumption Function in Economics
• Extensions of the Central Limit Theorem
• The Distribution of Sample Statistics
• A Generalization of the Gauss-Bonnet Theorem
• Backwards Bending Supply Curves and the Impact of Taxes or Subsidies on Prices
• The Nature of the Nuclear Force
• Evidence of Alpha Particle Substructures in Nuclei
• The Nature of Mass Deficits in Nuclei
• Method of Estimation of the Parameters of a Stable Distribution
• The Nature of Trends in Average Global Temperature
• Blue is not a Primary Color, Violet is
• The Nature of Climate
• Social Cost of Monopoly Pricing
• Estimating the Parameters of a Bent Line in Regression Analysis
• Cycles and Trends in Average Global Temperature and Their Projection
• Confidence Limits on the Forecasts and Backcast of Average Global Temperature Based Upon Its Trend and Cycles Over the Past 128 Years
• The Decline of Summertime Arctic Sea Ice Is Not Due to Global Factors But Due to Developments in North Siberia and the Artic Oscillation
• A Multitude of Analyses Concerning Polyhedra
• The Nature of Mass as the Warping (Curvature) of Space This notion connects the formulas from the Special Theory of Relativity on the apparent contraction of length in the direction of motion and the increase in mass.
• Neutrons repel each other, as do protons. Nuclei are held together by spin pairing (neutron-neutron, proton-proton and neutron-pronton) and the attractions between neutrons and protons.

  The repulsion of like nucleons and the attraction of unlike nucleons is explained by the proton and neutron each possessing a charge with respect to the nuclear strong force and those charges being of opposite sign. If that charge for the proton is taken as unity the best estimate of the charge of a neutron is −2/3. This estimate is based upon regression analyses that explain upwards of 99.9 percent of the variation in the binding energy of nuclides.

• The so-called neutron stars cannot be composed entirely of neutrons. There are some things being observed but they are not composed of entirely of neutrons because neutrons repel each other. No nuclide cantains more of an excess of neutrons than 60. There probably has not been one shred of evidence that the entities being observed are composed of neutrons from the time that Fritz Zwicky conjectured their existence.
• A neutron can form a spin pair bond with one other neutron and with one proton. The same applies for a proton. This leads to chain of modules involving two neutrons and two protons. These alpha modules are equivalent to alpha particles in terms of the binding energy of the nucleus they are are in. Thus nuclei are composed of alpha modules linked together in rings.
• The Correspondence Principle says that for quantum analysis of a physical system to be valid its limit as the energy (or other parameters) increases without bound must be compatible with the classical analysis of the system. I argue that the correspondence must be with the spatial and time averaged value of the results of the limit. No observations take place at an instant or at a point. Any observation requires an energy transfer and no energy is transferred at an instant or at a point. The observed world is a world of time and spatial averages. The solutions to the Schroedinger equations are probabaility density functions and thus so are their limits when energy increases without bound. They must correspond then with some probability density function for the classical system. But the classical system is deterministic and no are obviously involved. The one probability density function that makes sense for a deterministic system is the time-spent probability density distribution. For one dimensional system it can be proven analytically that the spatially averaged limit of the quantum theoretical analysis based upon a Schroedinge equation converges to the time-apent probability density distribution of classical analysis. The quantum analysis of two and three dimensional systems is based upon the separation-of-variables assumption and is not compatible with classical analysis and the Correspondence Principle.
• If a particle or system of particles with a generic charge is executing a periodic path then the expected value of its effect is equal to that of a static charge with a distributed charge density equal to the product of the generic charge times the time-spent probability density. The generic charge may be mass (gravitational charge), electrical charge or the charge associated with the nuclear strong force. When the periodic path is being executed quadrillions of times per second, as in atomic or nuclear systems, what is observed is the blurred image of such distributed charges.
• The Larmor proposition that accelerated point charges radiate electromagnetic waves is irrelevant in a world of spatially distributed charges.
• The Correspondence Principle says that for quantum analysis of a physical system to be valid its limit as the energy (or other parameters) increases without bound must be compatible with the classical analysis of the system. I argue that the correspondence must be with the spatial and time averaged value of the results of the limit. No observations take place at an instant aor at a point. Any observation requires an energy transfer and no energy is transferred at an instant or at a point. The observed world is a world of time and spatial averages. The solutions to the Schroedinger equations are probabaility density functions and thus so are their limits when energy increases without bound. They must correspond then with some probability density function for the classical system. But the classical system is deterministic and no are obviously involved. The one probability density function that makes sense for a deterministic system is the time-spent probability density distribution. For one dimensional system it can be proven analytically that the spatially averaged limit of the quantum theoretical analysis based upon a Schroedinge equation converges to the time-apent probability density distribution of classical analysis. The quantum analysis of two and three dimensional systems is based upon the separation-of-variables assumption and is not compatible with classical analysis and the Correspondence Principle.
• If a particle or system of particles with a generic charge is executing a periodic path then the expected value of its effect is equal to that of a static charge with a distributed charge density equal to the product of the generic charge times the time-spent probability density. The generic charge may be mass (gravitational charge), electrical charge or the charge associated with the nuclear strong force. When the periodic path is being executed quadrillions of times per second, as in atomic or nuclear systems, what is observed is the blurred image of such distributed charges.
• An extended answer to what holds a nucleus together is given in Nucleus.
• The existence of subshells0 within nuclear shells.
• The arithmetic of magic numbers such as 142857.
• The Principle of Least Action in mechanics is misleading. The dynamics of a system are not determined in order to minimize action; they involve response to forces and that incidentally happens to minimize action. For more see Minimization principles.
• A Short, Simple but Irrefutable Proof that the Copenhagen Interpretation is a Misinterpretation of Quantum Analysis Based upon Schroedinger's Equation
• The explanation of the binding energies of halo neutrons and especially halo protons.
• The Regularities and Irregularities of the Binding Energies of Alpha Module Nuclides
• The Statistical Explanation of the Binding Energies of Nuclides Based Upon a Three-Way Classification of Nucleon Shell Occupancies
• Minimum Energy Nuclear Composition and Nuclear Stability
• Positron emission and protons not paired with neutrons (Version 2)
• Positron emission and protons not paired with neutrons
• Two General Theorems Concerning the Coefficient Sums of Polynomials over a Field
• Some general properties of polynomials over a field
• Some Interesting General Properties of Polynomials
• Quotients and Remainders in Digit Sum Arithmetic
• Weighted Summations of Polynomial Coefficients and Remainders
• Divisibility and Remainders for Polynomials over a Field
• Six Lemmas on the Remainders for the Division of Polynomials
• The Net Sum of a Decimal Representation of a Number Resulting From an Alternation of Addition and Subtraction
• A Sensible Model for the Confinement and Asymptotic Freedom of Quarks
• The Wave Function from Schrödinger's Equation is Related to the Time Spent by the System in its Allowable States
• An Exponential of a Purely Imaginary Matrix and the Trigonometric Identities
• The relative extrema of the solution to a generalized Helmholtz equation
• Binding Energy per Nucleon and Nuclide Size
• The Masses and Binding Energies of Nuclides as a Function of their Quarkic Composition
• A Sensible Model of Quark Confinement and Asymptotic Freedom
• Some Remarkable Properties of Polynomials
• A Plausible Connection between the Binding Energy of a Composite Object and the Potential Energy Lost Upon its Formation
• Quantum Theory and the Nature of Quantun Reality
• A Testing of the Conventional Model of Nuclear Structure Which Involves the So-Called Strong Force
• The Nature of the So-Called Nuclear Strong Force
• The Horrendous Financial Cost of a Nicotine Addiction
• The Existence of a Magnetism-like Force Associated with the Motion of Any Charged Particles
• The Analogue of the Magnetic Field for the Nucleonic Force Field
• The Spin Pairing of Nucleons Due to the Magnetic Fields Generated by their Spinnings
• A property of the Solution of a Generalized Helmholtz Equation of Any Dimension
• The Solution of a Generalized Helmholtz Equation of Two Dimensions
• The Solutions to theTime-Independent Schroedinger Equation and their Relationship to the Classical Time-Spent Probability Distributions
• The Nature and History of the Bayes Rule for Computing Inverse Probabilities
• Aage Bohr and Dan Mottelson in their work on the rotations of nuclei discovered a quantization of nuclear rotation energy which is equivalent to the following quantization of nuclear angular momentum

  Jω = h(I(I+1))^½

  where J is the moment of inertia of the nucleus, ω is the rate of rotation in radians per second, h is Planck's Constant divided by 2π and I is an integer.

  This formula implies the extremely high rate of rotation for a deuteron of several billion trillion rotations per second. However the measured magnetic moment of a deuteron implies a rate of rotation of 1/137th of that amount. This is still extremely high but is based upon an empirical measurement.

  It is consistent with the Bohr-Mottelson formula more properly being

  Jω = q(I(I+1))^½I(I+1)

  where q is the quantum constant for the nuclear force field. The quantum constant for a force field is inversely proportional to its dimensionless coupling constant. The coupling constant for the electromagnetic field is approximately 1/137 and that of the nuclear force approximately 1. Therefore

  q/h ≅ (1/137)/(1/1) ≅ 1/137

  Planck's constant is therefore the quantum constant only for the electromagnetic field.