Willem F Esterhuyse - Academia.edu (original) (raw)
Drafts by Willem F Esterhuyse
Abstract We resolve the negative sign in Maxwells equations by putting it in another context (... more Abstract
We resolve the negative sign in Maxwells equations by putting it in another context (the negative sign changes to positive). We also write two of Maxwells equations as one equation. We use the 4x3 determinant. The text uses my computation method for a nxm determinant. We develop a formalism using the 4-dimensional curl of the Electromagnetic potential. We use the scalar electric potential appended with the vector magnetic potential into the same vector.
We translate the article by Chiara Marletto into symbols of Structural Logic. Maybe someone can t... more We translate the article by Chiara Marletto into symbols of Structural Logic. Maybe someone can then find more consequences. The meaning of the symbols can be found in my other Article: "Introduction to Logical Structures.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
IJASR, 2021
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We disprove the Riemann Hypothesis using the equivalent statement of the problem involving the pr... more We disprove the Riemann Hypothesis using the equivalent statement of the problem involving the prime counting function.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information, it has to be chopped up. Just look at a kid playing with blocks with letters on them: he has to break up the word into letters to assemble another word. Within SrL we take as our "atoms" propositions with chopped up relations attached to them. We call the results: (incomplete) "structures". We play it safe by only allowing relations among propositions to be choppable. We will see whether this is the correct way of chopping up sentences (it seems to be).
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensiona... more We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is a quantum rotation: turn from state A to state B without visiting the in-between states) as measured along the circle if the Pp encounters a space point. The circle's infinity point stays at the north pole of the Riemann Sphere for any finite rotation since infinity-constant = infinity. Using this, Time can be defined if we require special particles to be in the particles of a clock. We go on to define photons and anti-photons. If we define anti-photons we are at a more efficient level of using resources (conservation of space implied by conservation of Energy). The model explains why photons have momentum. The reason why a photon can have variable frequency is also stated. The model assumes there are positive and negative events of spacetime and this is the reason why one can choose a zero point (for coordinates) anywhere. The model explains why light travels at a finite speed.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
We state Zermelo-Fraenkel Set Theory in the symbols of ref. [1]: Introduction to Logical Structur... more We state Zermelo-Fraenkel Set Theory in the symbols of ref. [1]: Introduction to Logical Structures. Several issues are explored. Symbols are more varied and focussed than words and can define more than words can. The logic shows the structure of a statement explicitly. Logical Structures is graphs with singly or doubly labelled vertices and edges (labelled with symbols). The double labeling is accomplished by specifying vertices to be enclosure symbols with letter content or without.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
Papers by Willem F Esterhuyse
We give a model for particles which explains why particle properties are quantised. We define pa... more We give a model for particles which explains why particle properties are quantised. We define particles as pictures. We define a pi-minus, electron, electron antineutrino and a proton. We prove the model for electrons. We aslo show how to construct antiparticles. We show why Gravity is fundamentally different from the other forces. The model predicts the Electromagnetic field of a free electron. The model also predicts that antimatter will have attractive gravity with matter. Three new particles are predicted. We prove a reason why only right handed anti-neutrinos are allowed. We also show how all the decay modes of the tauon arrise in this model.
We prove that fundamental particles cannot change flavour as is believed. Therefore the belief th... more We prove that fundamental particles cannot change flavour as is believed. Therefore the belief that down quarks can change to up quarks and electrons and electron anti-neutrinos is wrong.
Abstract We resolve the negative sign in Maxwell's equations by putting it in another context ... more Abstract
We resolve the negative sign in Maxwell's equations by putting it in another context (the negative sign changes to positive). We also write two of Maxwell's equations as one equation. We use the 4x3 determinant. The text uses my computation method for a nxm determinant. We develop a formalism using the 4-dimensional curl of the Electromagnetic potential. We use the scalar electric potential appended with the vector magnetic potential into the same vector.
A model for nuclear structure is presented. With the model, we are able to compute J and parity, ... more A model for nuclear structure is presented. With the model, we are able to compute J and parity, and it predicts (postdicts) these correctly for all isotopes. Also proved is that neutrons fill in the extra dimensions. It is also explained why the orbitals of the Shell Model has the k/2 (k an odd Natural Number) subscript that they have - something left unexplained by the Shell Model. The model explains the magic numbers for nuclei. B(5, 5) is shown to be exceptional and it is predicted it will behave like Li(3, 4). So is Fe(26, 31): it is predicted to act chemically like Cr(24, 29) except where mass enters the equation. Also: Co(27, 32) will act chemically like Fe(26, 28) except when mass comes into play. No coincidence that they share similar magnetic properties. It is a fact that Co was found together with Fe in the meteoric iron of Tuthankamen's dagger. It is seen that nucleons sometimes do not fill only the lowest energy orbitals. We compute the spin speed of H-1 using the experimentally obtained charge radius of the proton and use the speed to find a minimum radius for Li(3, 3) and use the Li(3, 3) radius to compute the radius of Li(3, 4) as 2*r_Li(3, 3) and test this value against the one obtained from L = mvr. The values are in fair agreement (they differ by 7 in the most significant digits). We can see people using our pictures to compute other values like quadrupole moments and binding energies. Our pictures show why the nuclear magnetic moment of Li(3 ,4) is larger than that of Li(3, 3).
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
Abstract We resolve the negative sign in Maxwells equations by putting it in another context (... more Abstract
We resolve the negative sign in Maxwells equations by putting it in another context (the negative sign changes to positive). We also write two of Maxwells equations as one equation. We use the 4x3 determinant. The text uses my computation method for a nxm determinant. We develop a formalism using the 4-dimensional curl of the Electromagnetic potential. We use the scalar electric potential appended with the vector magnetic potential into the same vector.
We translate the article by Chiara Marletto into symbols of Structural Logic. Maybe someone can t... more We translate the article by Chiara Marletto into symbols of Structural Logic. Maybe someone can then find more consequences. The meaning of the symbols can be found in my other Article: "Introduction to Logical Structures.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
IJASR, 2021
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We disprove the Riemann Hypothesis using the equivalent statement of the problem involving the pr... more We disprove the Riemann Hypothesis using the equivalent statement of the problem involving the prime counting function.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information, it has to be chopped up. Just look at a kid playing with blocks with letters on them: he has to break up the word into letters to assemble another word. Within SrL we take as our "atoms" propositions with chopped up relations attached to them. We call the results: (incomplete) "structures". We play it safe by only allowing relations among propositions to be choppable. We will see whether this is the correct way of chopping up sentences (it seems to be).
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensiona... more We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is a quantum rotation: turn from state A to state B without visiting the in-between states) as measured along the circle if the Pp encounters a space point. The circle's infinity point stays at the north pole of the Riemann Sphere for any finite rotation since infinity-constant = infinity. Using this, Time can be defined if we require special particles to be in the particles of a clock. We go on to define photons and anti-photons. If we define anti-photons we are at a more efficient level of using resources (conservation of space implied by conservation of Energy). The model explains why photons have momentum. The reason why a photon can have variable frequency is also stated. The model assumes there are positive and negative events of spacetime and this is the reason why one can choose a zero point (for coordinates) anywhere. The model explains why light travels at a finite speed.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
We state Zermelo-Fraenkel Set Theory in the symbols of ref. [1]: Introduction to Logical Structur... more We state Zermelo-Fraenkel Set Theory in the symbols of ref. [1]: Introduction to Logical Structures. Several issues are explored. Symbols are more varied and focussed than words and can define more than words can. The logic shows the structure of a statement explicitly. Logical Structures is graphs with singly or doubly labelled vertices and edges (labelled with symbols). The double labeling is accomplished by specifying vertices to be enclosure symbols with letter content or without.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We give a model for particles which explains why particle properties are quantised. We define pa... more We give a model for particles which explains why particle properties are quantised. We define particles as pictures. We define a pi-minus, electron, electron antineutrino and a proton. We prove the model for electrons. We aslo show how to construct antiparticles. We show why Gravity is fundamentally different from the other forces. The model predicts the Electromagnetic field of a free electron. The model also predicts that antimatter will have attractive gravity with matter. Three new particles are predicted. We prove a reason why only right handed anti-neutrinos are allowed. We also show how all the decay modes of the tauon arrise in this model.
We prove that fundamental particles cannot change flavour as is believed. Therefore the belief th... more We prove that fundamental particles cannot change flavour as is believed. Therefore the belief that down quarks can change to up quarks and electrons and electron anti-neutrinos is wrong.
Abstract We resolve the negative sign in Maxwell's equations by putting it in another context ... more Abstract
We resolve the negative sign in Maxwell's equations by putting it in another context (the negative sign changes to positive). We also write two of Maxwell's equations as one equation. We use the 4x3 determinant. The text uses my computation method for a nxm determinant. We develop a formalism using the 4-dimensional curl of the Electromagnetic potential. We use the scalar electric potential appended with the vector magnetic potential into the same vector.
A model for nuclear structure is presented. With the model, we are able to compute J and parity, ... more A model for nuclear structure is presented. With the model, we are able to compute J and parity, and it predicts (postdicts) these correctly for all isotopes. Also proved is that neutrons fill in the extra dimensions. It is also explained why the orbitals of the Shell Model has the k/2 (k an odd Natural Number) subscript that they have - something left unexplained by the Shell Model. The model explains the magic numbers for nuclei. B(5, 5) is shown to be exceptional and it is predicted it will behave like Li(3, 4). So is Fe(26, 31): it is predicted to act chemically like Cr(24, 29) except where mass enters the equation. Also: Co(27, 32) will act chemically like Fe(26, 28) except when mass comes into play. No coincidence that they share similar magnetic properties. It is a fact that Co was found together with Fe in the meteoric iron of Tuthankamen's dagger. It is seen that nucleons sometimes do not fill only the lowest energy orbitals. We compute the spin speed of H-1 using the experimentally obtained charge radius of the proton and use the speed to find a minimum radius for Li(3, 3) and use the Li(3, 3) radius to compute the radius of Li(3, 4) as 2*r_Li(3, 3) and test this value against the one obtained from L = mvr. The values are in fair agreement (they differ by 7 in the most significant digits). We can see people using our pictures to compute other values like quadrupole moments and binding energies. Our pictures show why the nuclear magnetic moment of Li(3 ,4) is larger than that of Li(3, 3).
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
IOSR Journal of Mathematics, 2022
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information,
IOSR Journal of Mathematics, 2022
We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Log... more We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very
We explain why Anyons have-e/3 charge. We assume Anyons are Electrons confined to a plane. The mo... more We explain why Anyons have-e/3 charge. We assume Anyons are Electrons confined to a plane. The model predicts Anyons have no magnetic moment.
Russian Journal of Mathematical Research. Series A, 2018
This paper disproves the Riemann hypothesis by generalizing the results from Titchmarsh's book Th... more This paper disproves the Riemann hypothesis by generalizing the results from Titchmarsh's book The Theory of the Riemann Zeta-Function to rearrangements of conditionally convergent series that represent the reciprocal function of zeta. When one replaces the conditionally convergent series in Titchmarsh's theorems and consequent proofs by its rearrangements, the left hand sides of equations change, but the right hand sides remain invariant. This contradiction disproves the Riemann hypothesis.
We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mat... more We show how to use Logical Structures (of ref. [1]) in a variety of settings. It is of use in mathematics to show explicit formal reasoning, and especially important in detective work and arguing in a court of law. It is also useful to express knowledge so that someone else can check the correctness of the Structures before and after executing any operators. It is also useful in solving logical puzzles (for pleasure or as a test of mental competence). What we need to do is to fix our thinking to a commonly agreed on symbolisation (words and letters are not clear, precise, varied and focused enough). Logical Structures are graphs with singly or doubly labelled vertices and labelled (by symbols) edges. The levels of reasoning are of special importance and are made explicit. They are of great help in reasoning correctly. We prove AND introduction, and other "axioms" of propositional logic using properties of Attractors and Stoppers. Other axioms of propositional logic can also be proved. We note that all the axioms of Zermelo-Fraenkel set theory can be expressed entirely in symbols of Structural Logic.
Language Arts & Disciplines, Introduction to Logical Structures, Jan 15, 2013
JOURNAL OF ADVANCES IN PHYSICS, 2019
We introduce a definition of Time and Photons from four Axioms. Basically you take a 4-dimensiona... more We introduce a definition of Time and Photons from four Axioms. Basically you take a 4-dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is an quantum rotation: turn from state A to state B without visiting the in between states) as measured along the circle, every time the Pp encounters a space point. Space fluctuates and expands so this does not give a static circle Pp. The…
We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensiona... more We introduce a definition of Time and Photons from four Axioms. Basically, you take a 4dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is a quantum rotation: turn from state A to state B without visiting the in-between states) as measured along the circle if the Pp encounters a space point. The circle's infinity point stays at the north pole of the Riemann Sphere for any finite rotation since infinity-constant = infinity. Using this, Time can be defined if we require special particles to be in the particles of a clock. We go on to define photons and anti-photons. If we define anti-photons we are at a more efficient level of using resources (conservation of space implied by conservation of Energy). The model explains why photons have momentum. The reason why a photon can have variable frequency is also stated. The model assumes there are positive and negative events of spacetime and this is the reason why one can choose a zero point (for coordinates) anywhere. The model explains why light travels at a finite speed.