Showing posts with label Fourier. Show all posts
Showing posts with label Fourier. Show all posts

Tuesday, July 7, 2026

The NEXT

 When the i*PI(Del)Action is hermitian in delineation, its coupling with angular frequency, may often tend to work to facilitate, the formation of succinct charge. Furthermore; When the i*PI(Del)Action is hermitian in resonance, its coupling with angular frequency, may often tend to work to facilitate, the formation of resolute charge. 

When the i*PI(Del) Action is hermitian in delineation, its coupling with angular momentum, may often tend to work to facilitate, the formation of free-flowing entropy. Furthermore; When the I*PI(Del)Action is hermitian in resonance, its coupling with angular momentum, may often tend to work to facilitate, the formation of bogged down entropy. 

When the kinetic energy, of a Fourier-Related System, is to spontaneously couple, with its eminently corroborative angular frequency, in a hermitian manner, that this particular given arbitrary case scenario, is one in which the electromotive power, of which is directly pertinent to the Lagrangian-Based Drive, of such a cohesive system of wave-like phenomenology, is here to thence become spontaneously generated. Furthermore; When a superstring is to work to bear a hermitian coupling with its own angular frequency, this general process may often tend to facilitate, its ( the string’s) conversion, into holomorphic directed kinetic pure energy. 

When the i*PI(Del)Action is spurious in delineation, its coupling with angular frequency, may often tend to work to facilitate, the formation of an anharmonic tense, of transversal charge. Furthermore; When the i*PI(Del)Action is spurious in resonance, its coupling with angular frequency, may often work tend to work to facilitate, the formation of an anharmonic tense, of radial charge.

When the i*PI(Del)Action is spurious in delineation, its coupling with angular momentum, may often tend to work to facilitate, the formation of an anharmonic tense, of malignant transversal entropy. When the i*PI(Del)Action is spurious in resonance, its coupling with angular momentum, may often tend to work to facilitate, the formation of an anharmonic tense, of malignant radial entropy.

When there is here to be an equipoise, between the change in the direction and the change in the rate, of an accelerating kinematically propagated Hamiltonian Topological Manifold, it will subsequently tend to spontaneously tend to consequently follow, that the resultant charge delineation that will tend to follow, will have an enhanced probability, of having a respective equipoise, that is here to be eminently corroborative with this implicit case scenario, that is thence to expressively demonstrate, a reductional balance, between its directly associated spin-orbital momentum, when in covariant conjunction with its directly associated transversal momentum. 

Let’s initially consider, a spinning, kinematically propagated, mass-bearing, Hamiltonian Topological Manifold. As it is changing in its direction, relative to the motion of light, this general genus of a physical operation, tends to form a tense, of radial unitary heuristic-gauge magnetic potential. As such radial unitary heuristic-gauge magnetic potential, interacts, in a hermitian manner, with angular frequency, this tends to work to form radial-based  charge.

When the covariant-based positioning, of a spinning, kinematically propagated, mass-bearing, Hamiltonian Topological Manifold, is to spontaneously become erratic, the eminently corroborative, implicitly considered, radial-based charge, of which is here to become spontaneously generated, once it is to bear a hermitian coupling with the regional local angular frequency, will thereby tend to become spurious, in its spatial implication of delineation. 

When the covariant-based positioning, of the escalating Lagrangian-Based Expansion, of a kinematically propagated, mass-bearing, Hamiltonian Topological Manifold, is to spontaneously become erratic, the eminently corroborative, implicitly considered, transversal-based charge, of which is here to become spontaneously generated, once it to bear a hermitian coupling with the regional local angular frequency, will thereby tend to become spurious, in its spatial implication of delineation. 

When the escalating Lagrangian-Based Expansion, of a kinematically propagated, mass-bearing Hamiltonian Topological Manifold, is to bear its perturbation of speed, in a radial manner, it may tend to be said to work to bear, a Clifford charge translation. Furthermore; When the escalating Lagrangian-Based Expansion, of a kinematically propagated, mass-bearing Hamiltonian Topological Manifold, is to bear its perturbation of speed, in a transversal manner, it may tend to be said to work to bear, a Euclidean charge translation. 


 

Tuesday, April 14, 2026

Metaphorical Thoughts

 Let’s say, that one were to figuratively liken, the multiplicity of space time fabric, to the multiplicity of language. One could then metaphorically consider: the nouns to be likened to the Hamiltonians, the verbs to be likened to the Lagrangians, the adjectives to be somewhat likened to the metric gauge, the adverbs to be somewhat likened to the heuristic gauge, and the prepositions to be likened to the re-calibration of Chern-Simons singularities. 

I will certainly continue with the suspense Later! ‘Till then, I hope you are having a good day, and make today the most phenomenal day of your life! Sincerely, Sam Roach (1989).

String theory is the metaphorical language of energy, and Fourier-Analysis is the metaphorical language of waves. Energy is both wave and particle based. This gives one an idea, as to Why Fourier-Analysis is so crucial to string theory. 

Entropy is energy of heat transfer per Kelvin Mole. Entropy that is conveyed in a De Rham manner, often tends to bear a benevolent physical nature. Whereas; Entropy that is conveyed in a Dolbeault manner, often tends to bear a malignant physical nature. Although at least some entropy is necessary, for various changes in physical states to occur, it is my theory, that even though it goes against the second “law” of thermodynamics, that it is possible, to be able to viably decrease, at least some of the scalar effectual presence, of the multiplicity, of malignant entropy. 

Harmonically propagated sound, often tends to work to bear a tense of consonant vibration. Whereas; Anharmonic associated propagated sound, often tends to bear a tense of dissonant vibration. Consonant vibration may often tend to facilitate, the generation of resonant pulsation. Whereas; Dissonant vibration may often tend to facilitate, the degeneration of resonant pulsation. One may think of resonant pulsation, in a way, as being the physical manifestation, of the inverse of isotropically stable thought frequency. 

Whenever a physical phenomenon is kinematically propagated and/or transferred through space (over a duration of time), this will inevitably work to involve a system of waves. Therefore; Whenever a time-related physical occurrence is to take place, such an occurrence will inextricably tend to work to involve, at least some sort of Fourier-Related System, since waves are thus involved. 

When one is dealing with a system of waves, that is taking place in Less than one discrete increment of time, one may, perchance, call this, a Laplacian-Related "activity," as taken from within the scope of a tightly-knit Fourier-Related situation. Remember: Fourier-Related Analysis, is the language of waves. 

Consider the following: Take a theoretical snapshot of a wave-based delineation, of a given arbitrary proscribed system of waves, over the course of one Planck-Related instance. Next; Take a theoretical snapshot of the wave-based delineation of the same system of waves, yet over the ensuing course of the proceeding Planck-Related instance. Keep going as such. Now; recursively display the respective sequential series, of the integrative set, that is of such theoretical snapshots, in the proscribed order that these were taken. This will give one a viable indication, as to the wave-related progression, if taken in the insinuated piecewise continuous manner eluded to, to where, this general procedure, will work to facilitate a knowledge, as to the eminently corroborative, given arbitrary Fourier-Related-Progression, that is here to be, of such a particular genus of a case scenario. When given in lieu of its Lagrangian-Based Drive, this will tend to work to refine, such a facilitation, as to understanding how such a wave-based system enfolds, to where the metaphorical artifacts of knowing how such a system is to proceed, is thus enhanced. 

Here is a procedural hint, in so as to facilitate being able to determine Chern-Simons Invariant gauge-actions, in general, for the arbitrary genus of case scenario, involving co-tangent bundle R3.:

1) Consider the trace depiction of the motion, that is of the eminently corroborative Hamiltonian Topological Manifold, being mathematically worked with here, as taken at a snapshot of its delineation, in terms of the mathematical physics description, that is here to describe the way that the minimal surface, that is implicitly mentioned here is to be mapped out — as a generic pattern of mappable oscillation.

2) Consider the given arbitrary, eminently involved mathematical physics expression, of kinematically propagational-related import, that is most relevant to the suitings, of such a respectively proscribed case scenario. 

3) Take both the first order integral, and, the second order integral, of the just mentioned expression of kinematically propagational-related import, in respect to a durational parameter of variable. 

4) Take the last three implicit values of kinematically propagational-related import, and add them together. 

5) Consider the just mentioned summation, as one whole group. 

6) Consider the directional attributes, that the gauge-action being considered, is inextricably to be taken in. 

7) Multiply the initial implicitly mentioned vector trace, by the latter mentioned grouping. 

8) Next; Multiply this whole thing, by 2/3 — since the reductional minimal surface is heuristically in two spatial dimensions, and the gauge-action is of co-tangent bundle R3. 

9) Divide the entirety of what has been described so far, at this point, by 4*PI. 

10) The result of this math, in many general cases, will facilitate an endeavor, to determine the vector value, of certain proscribed cases, in terms of finding the desirable Chern-Simons Invariant Gauge-Action, of what this is to be eminently corroborative to happen to be in the process of finding out, in lieu of acting to better understand that metaphorical grip hold of wave tug, whose alterations spew into charge and or entropy. 

In a metaphorical nutshell: The i*PI(Del)Action, amounts to being — Unitary heuristic-gauged magnetic potential. 

Whenever individually taken Chern-Simons Invariant gauge-actions are re-calibrated, unitary heuristic-gauged magnetic potential is generated. When such a respectively indicated potential is to couple with a discrete quantum of angular frequency, in at least a fairly hermitian manner, this will generally tend to form charge.,Yet; If, instead, such a respectively indicated potential is to couple with a discrete quantum of angular momentum, again, in at least a fairly hermitian manner, this will generally tend to form entropy. 

Here’s a nifty metaphor I recently thought of: The Higgs Field in physics is to mass, what the Ribosomes in biology are to protein!

The Majorana-Weyl-Invariant Field in physics is to mass, what the Golgi Apparatus in biology is to protein. 




Thursday, April 13, 2023

Correlative Flow Of Lorentz-Four-Contraction

 The Fourier of the i*PI(del) Action, is inversely analogous, to the corroborative flow, of the respective Lorentz-Four-Contraction. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

For super string-related phenomena, that are moving forward in time, the Ricci Flow may often be tantamount, to (-( (the secant of 45 degrees)^2)).  This amounts to “-2.”

Two different and distinct kinetically propagated covariant Kahler Manifolds, that are relativistically diffeomorphic, when in respect to one another, will often tend to work to bear, a relatively heightened tense of Gaussian Symmetry, over the general course of their eminently associated Fourier-Related-Progression.  

Back To Basics: A Lagrangian, is the actual motion of a system of energy. Any Trace that is mappable, may be represented or shown, as a distribution of a motion that has already happened, to where such a said  "trace," may be indicated, as a flat oscillation, that is inter-dependently related, to the eminently associated presence, of two spatial dimensions, as taken along a planar surface ( a surface, with a height and a width, yet no breath (since it is a "trace.")). A Lagrangian-Based-Trace, is the mappable-trace, of the actual motion of a system of energy, that has just moved through a region, to where the mapping of where it had moved, as it went through this region, may be shown by a representation, of how it had oscillated through that region, via the center of its density, to where this mapped-out path-like trace, is here to be shown, as a chord, that works to connect the flow of the bounds of the path, that the implicit eminently associated energy had happened to have taken, over the general course of its spatial delineation; To where the phenomenology of such a general tense of energy, when taken as a "thing" of topological stratum, is here to be directly appertaining, to the holonomic substrate, of such an inferred Hamiltonian Operator. (The actual "stuff" that works to move, in so as to work to form the stated Lagrangian; To where, the stated Hamiltonian Operator, may be perceived of, as being the "stuff," of the overall energy of a given arbitrary system.).

When the i*PI(Del) Action, operates in so as to exhibit, a relatively succinct flow, in the general process, of its kinematically displayed explication, this may often tend to be eminently associated, with a spontaneously smooth change, in its eminently associated Lorentz-Four-Contraction.  

The kinematic behavior of the Higgs Field, as working to form a mass-like phenomenology, may often tend to be facilitated into generative induction, by the net steady-state gauge-action, of the implicit recursively stable proximal local kinetic energy in equilibrium, that is here to tend to be helped into becoming a mass-like phenomenon, via the Higgs-Landau-Gisner Action. 


Thursday, April 6, 2023

Rotational Vibration Of Kahler Manifold

 The quicker that the recursively smooth rotational vibration, of a Noether-Based mass-bearing Kahler Manifold, is to be, of which here, is to be proximal local to an anti gravitational force --  the more likely that the Fourier-Related-Progression, of such a said Kahler Manifold, will consequently tend to be spontaneously tugged, into an escalating differentiable Clifford Expansion, of its net composite mass-bearing eigenstate. SINCERELY, SAMUEL DAVID ROACH. HELLO, UNIVERSITY OF MICHIGAN!

When a macroscopic Kahler Hamiltonian Operator, that works to exhibit a relatively high tense of inertial pliability, is to be spontaneously spinning and moving transversely at the same time, it may often, thereby, tend to have an enhanced capacity, of potentially being capable, of bending gravity waves. 

The stronger the elastic modulus of a metal, the greater the inertial pliability, that it tends to be capable of working, to potentially express.  

An accelerated Hamiltonian Operator, of which is to be spontaneously escalating in the rate of both its transversal and radial speed, in which such an implicit macroscopic compact topological manifold, is here to work to exhibit a relatively strong tense of the Kahler-Metric, may often tend to express an eminently harmonic inter-relation, between the escalation of its spin, when in conjunction with the escalation of its heuristic thrust. This is to where; There is here to be an eminently harmonic relationship being played out, in this general case, between the respectively implicit Clifford Expansion, when in conjunction with its eminently associated corroborating Euclidean Expansion. 

When the interface that is here to be present, between a given arbitrary particle-like phenomenon, And, a region of the Higgs Field, is to bear a hermitian tense of viable interaction, this general process, may often tend, to facilitate the spontaneous formation, of an isotropically stable mass. Furthermore; If the interface that is here to exist, between a given arbitrary particle-like phenomenon, And, a region of the Higgs Field, is not to bear a hermitian tense of viable interaction, this general process, may often tend, to facilitate the spontaneous formation, of an isotropically unstable mass, instead. 

When a given arbitrary kinematically propagated Kahler Hamiltonian Topological Manifold, is to recursively undergo the general physical operation, amidst the covariant action of its eminently corroborative kinetic transference through space-time-fabric, of altering from a relatively torsional condition, into a relatively more relaxed motion of elastic stress, back into a relatively torsional condition, over the span of a directly associated proscribed duration of time, it will often tend to possibly occur, that such a general type of an activity, may often tend to work to enhance the potential strength, of the eminently corroborative Fourier-Related-Progression, by being capable of enhancing the pseudo pressure of the associated applied homotopic transfer, that is here to be covariant in its piecewise continuous exertion, as the implicitly viable increase in resolute succinctness that is thereby facilitated into occurrence, by such a general physical operation, is here to work to tend to enhance the covariant wave-tug that is to be gauged upon the physical restraint, that is here to work to control the Flow of motion of the implicit team of mass-related discrete energy eigenstates, in so as to be able to tend to work at strengthening, both the angular frequency, and, the angular momentum, of the said team of mass-bearing energy, so that the motion of such a team of string-like phenomenology, may thereby have a strengthened motion over time. This is part of why increased torsion-based tensors, are often advantageous to motion.

Charge has more of a physical affinity, of being eminently corroborative, with a De  Rham cohomology, rather than with a Dolbeault cohomology. However; Entropy has more of a physical affinity, of being eminently corroborative, with a Dolbeault cohomology, rather than with a De Rham cohomology. 

The more ominous that the proximal local presence, of covariant cohesive Higgs Field eigenstates, is to be, as taken from within the general arena, of a given arbitrary region in space-time-fabric, that is otherwise relatively void, of anything other than vacuum-related potential eigenstates, it may therefore often tend to spontaneously occur, that such an implicit region, when incurred upon by covariant kinematically propagated kinetic eigenstates, will generally tend to generate the reductional facilitated formation, of a set of mass-bearing energy eigenstates. 

When the net hermitian spin-orbital momentum, of a recursively spinning mass-bearing Kahler Hamiltonian Topological Manifold, is gauge-invariant, this general process, may often tend to work to facilitate, the covariant proximal local presence, of an isotropically stable charge, over a venue of time.

When the net hermitian angular momentum, of a recursively pulsating mass-bearing Kahler Hamiltonian Topological Manifold, is gauge-invariant, this general process, may often tend to work to facilitate, the covariant proximal local presence, of an isotropically stable resonant vibration, over a venue of time. 

Metric-Gauge eigenstates, generally tend to be physically coupled, to dimensional-related topological phenomenology, of which are here to be proximal local in linkage, to the venue of a hereupon eminently corroborative Kahler Hamiltonian Topological Manifold. This works to facilitate the reason, as to why metric-gauge eigenstates, tend to generally and primarily incur upon the basic phenomenology of angular momentum. Whereas; Heuristic-Gauge eigenstates, generally tend to be physically coupled, to the inverse frequency-related topological phenomenology, of which are here to be proximal local in linkage, to the venue of a hereupon eminently corroborative Kahler Hamiltonian Topological Manifold. This works to facilitate the reason, as to why heuristic-gauge eigenstates, tend to generally and primarily incur upon the basic phenomenology, of angular frequency. When both angular momentum & angular frequency, are incurred upon, in a Gliosis-Related manner, by the Gauge-Transformations, of the workings of the discrete energy impedance, that is here to work to help restrain the motion, of a given arbitrary Kahler Hamiltonian Topological Manifold, this will tend to allow for a more super conformal invariant internal reference-frame, at the central knotting, of the implicit team of energy's steady-state interdependent inter bounds. 






Wednesday, March 15, 2023

The Flow Of The Polyakov Action

 The Fourier of the i*PI(del) Action, is analogous to the time-related flow of the Polyakov Action. SINCERELY, SAMUEL DAVID ROACH. 

Homotopic Transfer may often happen, along the coni-axion of least resistance.

Homotopic Restraint may often happen, along a con-axion, that works to incur, a viable scalar magnitude of resistance.  

A Yau-Exact, De Rham Kahler Hamiltonians Operator, will often tend to have, the dual physical attribute, of working to bear, a relatively succinct and resolute tense, of a Fourier-Relative-Progression, as it is moving spatially.  

A viable perturbation, in the net light-cone-gauge eigenstate, of an eminently associated, given arbitrary Kahler Hamiltonian Operator, may often tend to be indicative, to the eminently associated presence, of a directly related Chern-Simons Singularity, that is here to be spontaneously incurred, upon the cohomology-related topology, that is here to be proximal local, to the externalized core-field-density, that is eminently associated, to the projected trajectory, of the Lagrangian-Based motion, of the stated Kahler Hamiltonian Operator.

A kinetically transferred, succinctly resolute, De Rham Kahler Hamiltonian Operator, may often tend to be spontaneously gauge-invariant, as it is propagated.  

Regions of the Rarita Structure, in which the general Higgs-Related Field, is harmonically distributed in delineation, may often tend to be spontaneously proximal local, to a tense of space-time-fabric, of which is hereby to consequently result, in working to exhibit, a relatively permeable “zone,”of eminently associated zero-point-energy-related indices, to where such an implicit genus, of a vacuum-like region in space-time-fabric, is hereunto to often tend to be less viscous, in its eminently related density of corroborative Hess States, than an otherwise analogous region in space and time, as taken along the Rarita Structure, that instead, is to exhibit an anharmonic distributional delineation, of correlatively associated Higgs Field-Related eigenstates, of which may often tend to spontaneously correspond, to a relatively more viscous tense of space-time-fabric, of which may often tend to be indicative, to the thereunto proximal local presence, of a general region, of corroboratively denser Hess States.  

Two different, kinematically propagated, covariant Calabi-Yau Manifolds, that are each proximal local, to the same tense of gravitational force, to where both of these implicit, kinetically transferred, Calabi-Yau topological manifolds, are both of the same spatial dimensionality, and, are here to be effected by the same tense of Lorentz-Four Contraction, may often tend to exhibit, a dual-state field, that is homeomorphic, in its innate expressed nature.  

The multiplicity of Mass, may often tend to be the equipoise, between the covariant steady-state Lagrangian-based eigenstates of meter, in implicit conjunction with the force of gravity, over time.  

When a mass-bearing Kahler Hamiltonian (Operator), is “driven,” to become spontaneously spatially translated, backwards in time, the eminently associated net gauged action, that is here to be directly associated, with its discrete energy impedance, will tend to become reversed, in the relative direction, of its holomorphic wave-tug.  

The more spatial dimensions that a Ward-Cauchy topological manifold is to exhibit, the more of a complex manifold that it may often tend to be expressed of as.  

The stronger that the incursion of heuristic gravitational force, that is here to be spontaneously imparted, upon a Kahler Hamiltonian (Operator), the more heightened that the potential probability may often tend to be, that there could possibly be an increased incursion, in the Poincaré-Based Incursion, that may often tend to be corroborative in its eminent proximal local effect, upon the topological field, of the earlier stated Kahler Hamiltonian (Operator). 

The Tensor-Related intricacies, in the Slater-Based Incursion, that is here to be physically applied, upon the holonomic substrate, of an eminently associated, Hamiltonian (Operator), may often tend to be directly corroborative, to the spontaneous proximal local covariant presence, of tensor-related intricacies, that are of the eminently effected escalation-based physical attributes, of the viably contingent Lagrangian-Based Expansion, that is here to be physically translated, by the directly associated kinetic motion of spatial transference, that the implicitly operated upon Hamiltonian (Operator), is to be in the general process of undergoing, as it is to be increasingly moving at an enhanced rate, over the general course, of its eminently associated, Fourier-Related-Progression.  

A harmonically spinning, non perturbative Calabi-Yau Manifold, that is Kaluza-Klein, in its abelian light-cone-gauge nature, will often tend to work to bear, an eminently associated non escalating i*PI(Del) Action, that is here to be viably corroborative, to what may tend to be directly associated, with the likings of a steady-state charge delineation, over the general course of its Lagrangian.  

In a viable sense, one may often tend to think of the i*PI(Del)Action, as the holonomic Lagrangian-Related flow, of the superstring-related exchange of homotopic residue, when in terms of the harmonic re-calibration, of the proximal local Chern-Simons Invariant gauge-actions.  

Thursday, February 16, 2023

The Poisson Integral -- De Rahm Cohomology

 The Fourier-Related-Progression of a De Rahm cohomological mappable-tracing, tends to be more aptly describable, when in lieu of a potentially eminent tense, of the mathematically applicable implementation, of a piecewise continuous Poisson Integral, than the Fourier-Related-Progression of a Debault cohomological mappable-tracing, is able to mathematically afford. TO BE CONTINUED! SAM.

Tuesday, February 14, 2023

Fourier-Related-Progression And Inertia

 The stronger the Fourier-Related-Progression of a given arbitrary Noether-Based mass-bearing Hamiltonian Operator is to be, the greater that its resultant inertia will consequently often tend to be. SAM ROACH. 

Thursday, February 9, 2023

Complex/Riemann-Based Fourier-Related-Progression

 Let us initially consider a Noether-Based mass-bearing Hamiltonian Operator, that is here to be in the process, of being physically transferred through space, over a certain proscribed duration to time.

The physical action, that is here to be of the directly associated Majorana-Weyl-Invariant-Mode, is to be eminently working to express, the likings of a Complex Fourier-Related-Progression. Whereas; The wave-tug-related action, that is here to be incurred by the directly associated Legendre Homology, in so as to work to physically transport the core-field-density, that is of the earlier inferred cohesive set of mass-bearing eigenstates, is here to be eminently working to express, the likings of a Real Riemannian-Based Fourier-Related-Progression. THANK YOU! TO BE CONTINUED! SAM ROACH. 

Complex Fourier-Related-Progression

 Complex Fourier-Related-Progression, is tantamount to Fourier-Related Conformal Invariant Progression. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH.(1989).

Sunday, December 18, 2022

Heuristic Maintenance Of A Smooth Homotopy

When the multiplicity of the Fourier-Related-Progression, that is hereupon to be eminently associated, with the kinematic motion, of a directly corresponding Hamiltonian Operator, is thence to work to map-out a hermitian cohomology-related field of path-based curvature, it may therefore consequently tend to be said, in the general process, by which the respective Lagrangian-Based spatial translation, that is of this inferred "team" of discrete energy quanta, is thereupon to often have a consequentially heightened probability, of working to express the heuristic maintenance, of a relatively smooth homotopy. SAMUEL.

Tuesday, October 4, 2022

Stoke's-Based Hermitian Homeomorphic Region-Related Curvature

 The Fourier-Related-Progression of a Stoke's-Based hermitian homeomorphic region-related curvature, of which is here to work to bear a recursively smooth covariant vibrational oscillation, when such an inferred kinematically delineated distribution, of an operational set of cohesively nodal states or integrable "cells," is here to work to bear a Noether-Based symmetry, when in conjunction with its eminent externalized Ward-Cauchy-Related environment, will, more often than not, tend to work to bear the general characteristic, of exhibiting the display, of a net functional homotopic-related eigenstate, as this stated functional homotopic-related eigenstate, is here to quite often tend to behave, as an oscillating planar region, when this is to be considered, at a region which is Poincare, to the vantage-point of the topological surface, of the holonomic substrate, of the earlier stated region-related curvature. SAMUEL ROACH. 

Sunday, August 21, 2022

Relating To Conically Driven Tense Of Angular Momentum

 A given arbitrary Hamiltonian Operator, that is here to be exhibiting the display of a unitary Lagrangian, will often tend to have a more conically driven tense of angular momentum, than the motion of the otherwise analogous Fourier-Related-Progression, of such a respective inferred general genus of a Hamiltonian Operator, that is, instead, to be exhibiting the display of a binary Lagrangian. Furthermore; A given arbitrary Hamiltonian Operator, that is here to be exhibiting the display of a binary Lagrangian, will often tend to have a more conically driven tense of angular momentum, than the motion of the otherwise analogous Fourier-Related-Progression, of such a respective inferred general genus of a Hamiltonian Operator, that is, instead, to be exhibiting the display of a tertiary Lagrangian. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

Thursday, July 14, 2022

Diffeomorphic Field Of Space-Time-Fabric Traveled Through -- Hermitian Cohomological Translation

 When a given arbitrary Noether-Based Hamiltonian Operator, is to be spatially transferred through a diffeomorphic field of space-time-fabric, the cohomological mappable-tracing of the projected trajectory, that the Lagrangian-Based motion of such a stated Hamiltonian is to work to form, will consequently have the general tendency, of working to bear a directly associated hermitian cohomological spatial translation, as this is here to be taken, over the durational course of the respective Fourier-Related-Progression, in which such a stated Hamiltonian Operator, is here to be in the process of being kinematically proximal local, to such a respective diffeomorphic field of space-time-fabric. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (PHS 1989).

Friday, June 17, 2022

A Tense Of Magnetic Abrasion

 When the Fourier-Related-Progression, that is to be appertaining to the co-determinable co-differentiable relationship, that is here to be amongst the respective covariant field-density, that is to be latent between the general stratum of two relatively adjacent given arbitrary different and distinct covariant harmonic hermitian gauge-invariant propagated projected cohomological structures, are thence to bear the exhibition, of a  Lagrangian-Based tense, of a Ward-Parallel nature, when this is in retrospect to one another, the correlative respective Hamiltonian Operators, of which are here to be working to eminently facilitate the formation, of such an inferred dual tense of cohomology, may often, at times, work to bear a proximal local condition, in which there is here to be, the exhibited display, of a covariant  spontaneous tense of magnetic abrasion, towards one another. I WILL CONTINUE WITH THE SUSPENSE LATER!  SINCERELY, SAMUEL DAVID ROACH. (1989).

Friday, May 6, 2022

Back To Basics: Covariant Cohesive Sets Of Mass-Bearing Discrete Energy Quanta -- Covariant Cohomological Structures -- Covariant Lagrangian-Based Paths

 Kinematic Fourier-Related covariant Noether-Based mass-bearing cohesive sets of discrete energy quanta, are often to tend to work to bear respective covariant cohomological structures, to where these will, as well, often tend to bear covariant Lagrangian-Based paths. TO BE CONTINUED! SAM ROACH.

More Hermitian Lagrangian-Based Motion -- Less Superstring-Related Fractal Of "Turbulence"

 The more hermitian of a Lagrangian-Based motion, that is here to be exhibited, by the Fourier-Based kinematic spatial transference, of a respective given arbitrary Noether-Based mass-bearing cohesive set of discrete energy quanta, the less of a superstring-related fractal of "turbulence," that such a stated mass-bearing cohesive set of discrete energy quanta, will consequentially tend to be displaying, as this is to be taken, at the correlative Ward-Cauchy-Related reference-frame, that is here to be at a level that is Poincare, to the general region, that is immediately external, to the core-field-density of such an inferred "team" of mass-bearing energy. TO BE CONTINUED! SINCERELY, SAMUEL ROACH.

Thursday, May 5, 2022

Fourier-Related Kinematic Flow -- Cohomological Mappable-Tracings -- Covariant Lagrangian-Based Paths

 When the Fourier-Related kinematic flow, of multiple cohomological mappable-tracings, are here to bear an operationally eminent relationship with one another, one may consequently say, that these stated cohomological mappable-tracings, are here to work to bear covariant Lagrangian-Based paths. SAM.

Tuesday, April 5, 2022

Dissipation Of The Embroidery Of Electrodynamic Rays -- Function Of P-Adic Cohomology-Related Operation

 The general kinematic activity, which is of the dissipation of that initially embroidered topological manifold, that is here to initially be of a respective braided structural tense of cohomology, of which is to subsequently be acted upon in the general inferred manner, to where the correlative unsheathing of such a general tense, of certain of such respectively incurred upon kinematically covariant propagated electrodynamic rays, in a way, may often be eminent in its association, with a particular given arbitrary genus, of the general function, of certain ulterior forms, of kinematically covariant propagated p-adic cohomology-related operations, which are often to act, over the general durational course, that may be surmised by the mathematical workings of a correlative Fourier-Transformation, in so as to often tend to kinematically act to undo, the potentially proximal adjutant presence, of a covariant kinematically propagated co-tangentially imparted Etale cohomology of topological manifold, of which is here to have had a relatively high probability, of working to bear a spontaneously Gliosis interaction, with the inversely considered general genus of a respective cohomology-related structural projection, as the initially inferred moving sheathed cohomology, is here to subsequently work to bear a tense of becoming unsheathed. SAMUEL ROACH.

Saturday, March 19, 2022

Holomorphic/Anti-Holomorphic Odd Parity Of Vibrational Oscillation -- Spontaneous Ensuing Tachyonic Flow

 When the Betti Number, of which is here to be eminently associated, with a relationship, involving the vibrational symmetry of a superstring of discrete energy permittivity, is to remain odd -- during both BRST Quantization and its immediately ensuing Regge Action -- then, this general tense of an inferred associated gauged symmetry, will thereby tend to work to be indicative, of the reductional physical condition, to where the directly corresponding superstring of discrete energy permittivity, of which I have been discussing here in this case, is thereby, over the same implied durational course of a Fourier Transformation,  to consequently tend to work to bear a respective Holomorphic/Anti-Holomorphic odd parity of vibrational-related oscillation, to where this general tense of a gauge-like action, will thereby have the general tendency, of working to help in causing such a herein mentioned superstring of discrete energy permittivity, to proceed, in so as to consequentially work to bear, a spontaneously ensuing tense, of a tachyonic flow. I WILL CONTINUE WITH THE SUSPENSE LATER! SAMUEL DAVID ROACH.

Thursday, February 24, 2022

How Cohomology Works To Form Charge

 A kinetically symmetrical flowing braided Noether cohomology, that both works to form a hermitian Lagrangian, as well as also working to involve the covariant proximal local presence of kinematically transferred mass-bearing eigenstates, of which are here to tend to work to bear a spin-orbital nature, generally works to form charge. As this is here to be taken, over the durational course of a directly associated Fourier-Related-Progression, this generally works to form the phenomenology, of electromotive current, as measured via amperage. TO BE CONTINUED LATER! SAM ROACH.