Showing posts with label homeomorphic. Show all posts
Showing posts with label homeomorphic. Show all posts

Tuesday, March 7, 2023

Homotopy Of Frequencies

 Two different kinematically flowing covariant, homeomorphic frequencies, often tend to bear an eminent  tense of homotopy, when in terms of their directly associated Fourier-Related-Progression.SAM ROACH.

A highly succinct, gauge-invariant, kinetically transferred, Kahler Hamiltonian Operator, that is proximal local, to a viably incurred, anti gravitational field, may often tend to work to exhibit, a venue of relatively strong,  Kahler-Based physical attributes, that may be described of, as being eminently related, to a general genus, of what may be termed of, as being extremal metrics.  

A kinetically impelled, Yau-Exact, Kahler Hamiltonian Operator, that works to bear a Euclidean-Based Expansion, that is here to be in sync, with its eminently associated Clifford-Based Expansion, may often tend to work to exhibit, a hermitian-related tense of acceleration.  

A kinetically transferred, Calabi-Yau field, when under the proximal local influence, of an anti gravitational force, that works to attenuate, the general covariant physical incursion, of an otherwise more applicable tense, of Gravitational Topological Variance, may, at times, tend to increase the potential probability, in which the implicit, eminently associated, kinematically propagated, Calabi-Yau Manifold, in question, may thereunto have an enhanced capability, of thereby spontaneously exhibiting, the general likings, of a covariant, diffeomorphic Kahler-Based field, as taken over a proscribed duration of time.  

A Modification Of My Understanding Of The DNA Molecule:

In a reverse-fractal metaphorical manner; The projected trajectory, of the heuristic unraveling, of a DNA molecule, works to involve an analogous dual characterization, that may be considered, in a way, to be akin, to working to exhibit the form of a Dolbeault cohomology, while yet spontaneously working to exhibit, the behavior of a P-Adic cohomology. Whereas -- In a reverse-fractal metaphorical manner; The projected trajectory, of the heuristic bringing together, of two different eminently associated strands of a corroborative DNA molecule, works to involve an analogous dual characterization, that may be considered, in a way, to be akin, to working to exhibit the form of a Dolbeault cohomology, while yet spontaneously working to exhibit, the behavior of an Etale cohomology, 

The stronger the Slater-Based Incursion is to be, the greater that the spontaneous covariant escalation of Cohomological Generation, consequently tends to be. Also; The stronger the Poincaré-Based Incursion is to be, the greater that the spontaneous covariant escalation of Cohomological De-generation, consequently tends to be. 

The more succinct that the corroborative Fourier-Related-Progression is to be, for an eminently associated, kinetically transferred Kahler Topological Manifold, the more likely that such an implicit Kahler Hamiltonian topological entity, that is here to behave as a team of mass-bearing discrete energy eigenstates, may often tend to be potentially capable of thereby working to potentially achieve, a consequentially resultant enhanced ability, of being facilitated into spontaneously escalating in its Lagrangian-Based Expansion, over a proscribed duration, in what will tend to be physically demonstrative here, as working to exhibit a relatively hermitian set of conditions. 

The more resolute that the corroborative Fourier-Related-Progression is to be, for an eminently associated, kinetically transferred Kahler Topological Manifold, the stronger that its directly related inertial-based pulsation may often tend to be, to where external forces may thereby find it relatively more difficult, to be able to impede the continued motion, of the stated Manifold.  

The more conformal invariant, that a given arbitrary, kinematically propagated Fadeev-Popov Trace eigenstate, is to be exhibited as working to express, the more steady-state, that the eminently associated, implicit discrete energy quantum, may often thereby tend to work to be demonstrative as being; To where, the more likely, that the  mentioned implicit discrete energy quantum, may thereby have the general tendency, of working to express a viable tense of corroborative gauge-invariance, to where such a stated eminently associated discrete quantum of energy, may thereby often tend to bear an enhanced tendency, of exhibiting the general Ward-Cauchy-Related physical feature, of a viable tense, of corroborative isotropic stability.  

A pulsating frequency, that works to bear, a corroborative dimensional-related wave-tug, may often tend to spontaneously work to exhibit, a resolute tense, of an eminently associated Fourier-Related-Progression. Whereas; A pulsating frequency, that works to bear, a corroborative durational-related wave-tug, may often tend to spontaneously work to exhibit, a succinct tense, of an eminently associated Fourier-Related-Progression. 

When a given arbitrary Kähler Hamiltonian Topological Manifold, of which is here to be imparted upon, by an eminently associated Slater-Based Incursion, is thence to spontaneously work to bear a corroborative angular frequency, that is here to be symmetrically magnified, in a respectively recursive manner, over a proscribed duration of time, it may often tend to consequently follow, that the earlier stated Kahler Hamiltonian Topological Manifold, will thereby often become spontaneously transversely accelerated, in a respectively probable proportionality, that is here to be eminently in covariant corroboration, with the implicit pseudo description, of the Slater Induced wave amplification, of which is here to be in regards to the eminently associated escalating Lagrangian-Based Expansion, that is here to be kinematically propagated, in what will generally tend to be expressed of as, in both a wave-based manner, And, in a particle-based manner. 

Harmonically re-calibrating Chern-Simons Invariant gauge-actions, tend to couple the i*PI(del) Action with angular frequency, working to produce the stuff of charge. 



Monday, January 16, 2023

Homeomorphic Field That Is Also Homotopic

 A given arbitrary Noether-Based homeomorphic gauge-invariant set, of two different highly Kahler Hamiltonian Operators, of which are here to be kinematically morphologically interdependent, as taken at the Poincare level, to the Gliosis-Based Riemann surface, that is of their so-eluded-to relatively smooth externalized Gaussian core-field-density, may often be construed of here, as being a dual homotopic state, of a kinetically driven pair of geometrically symmetrical covariant interchanging energy eigenstates. SAMUEL DAVID ROACH.

Friday, January 6, 2023

Covariant Kahler Manifolds -- Same Genus -- Interdependently Co-Differentiable Homeomorphic Field

 Two different and distinct covariant Kahler Manifolds, that work to bear the same genus of topological structure, may often tend to work to bear an interdependently co-differentiable homeomorphic field. SINCERELY, SAMUEL DAVID ROACH. 

Wednesday, October 12, 2022

Isometry -- Heuristically Homeomorphic; Asymmetry -- Inversely Homeomorphic

 Isometrical homotopic curvatures often tend to be heuristically homeomorphic. Whereas; Asymmetrical homotopic curvatures often tend to be inversely homeomorphic. SINCERELY, SAMUEL ROACH.

Thursday, October 6, 2022

Adjacent Quantized Light-Cone-Gauge Eigenstates

 Adjacent quantized light-cone-gauge eigenstates, often tend to bear a homeomorphic nature in relation to one another. 'TILL NEXT TIME! TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

Monday, June 27, 2022

Recursively Smooth Covariant Interaction -- Potential Hermitian Coupling

 When the covariant interaction between two different given arbitrary Hamiltonian Operators is recursively smooth, the potential Yukawa Coupling, that may often be interdependently formed amongst these two respective said Hamiltonian Operators, may have the general tendency, of working to bear a respectively homeomorphic hermitian nature. TO BE CONTINUED! SINCERELY, SAM ROACH. 

Sunday, May 22, 2022

Resonant Vibration Of A Quantum Of Discrete Energy Impedance

 When all of the second-order light-cone-gauge eigenstates, of which are here to work to comprise the workings, of one given arbitrary respective individually taken first-order light-cone-gauge eigenstate, are here to bear a homeomorphic harmonization of their vibrational oscillation, this general genus of a kinematic process, will often tend to help, in working to allow, for such an inferred quantum of discrete energy impedance, to consequently have a heightened capacity, of resulting in working to form, a tense of resonant vibration. I WILL CONTINUE WITH THE SUSPENSE LATER1 O BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

Monday, April 18, 2022

Homeomorphic Field -- Orientable Superstring -- Grassman Constant

 The general homeomorphic field, that is thence to be intrinsically latent, to the general tense of asymmetry, of which is here to be directly corresponding to the gauge-like coupling, that is here to be most associated, with the innately incurred interaction, of which is here to be impelled, as amongst the region that is in-between a given arbitrary orientable superstring of discrete energy permittivity,  as taken in conjunction with its directly corresponding respective counter string (of discrete energy permittivity), may thereby respectively be perceived of, as being related to the general tense of an emulation of the Betti Action, of which is here to bear an eminent association, with the reductional workings of the Grassman Constant. 'TILL NEXT TIME; TO BE CONTINUED! (PINCKNEY HIGH SCHOOL, 1989). SINCERELY, SAMUEL DAVID ROACH. 

Sunday, August 1, 2021

Binary Legendre-Related (Co)Homology

 When a Noether-Based binary Legendre-Related (co)homology, is to work to spatially transport an isotropically stable mass-bearing cohesive set of discrete energy quanta, such a said binary Legendre-Related (co)homology, will consequently tend to work to involve a set of two kinematic symmetrically covariant cohesive groupings, each of which are here to be comprised of by a set of one or more cohesively acting open-looped superstrings of discrete kinetic energy permittivity, that are here to be subtended on either side of the stated isotropically stable mass-bearing cohesive set of discrete energy quanta, that are consequently to often tend to work to bear a covariant field, that is here to work to bear the dual nature, of acting as a homomorphic field, that is also acting as a homeomorphic field. THANK'S FOR READING! (1989). I WILL CONTINUE WTIH THE SUSPENSE LATER! TO BE CONTINUED! SINCERELY, SAM.

Saturday, July 31, 2021

More; As To "Homeomorphic" Field -- Betti Action

 The "homeomorphic" field, that is here to exist between a superstring and its directly corresponding counter string, when the inferred discrete string-related energy is orientable, during the Betti Acton, is a mappable-relationship, that is here to work to bear an exacting tense of asymmetric configuration. SAM.

Friday, July 30, 2021

Difference Between A Homomorphic Field And A Homeomorphic Field

 The difference between the general characteristic that works to describe a homomorphic field, and, the general characteristic that works to describe a homeomorphic field, is that a homomorphic field is a configured mappable symmetric field, that is isotropically stable, (to where it is here to work to bear a tense of group action), -- whereas, a homeomorphic field, may either be a field that is comprised of two or more different metric-related spatial eigenstates, that work to bear the same tense of a hermitian distribution, at their respective individually taken delineations; Or, it may also be thought of as being a mappable relationship, between two different structural configurations, that are here to both work to bear the same tense of a hermitian distribution, at their respective individually taken delineations. Sam Roach.

Tuesday, July 27, 2021

A Refinement -- As To Diffeomorphic/Homeomorphic Field

 A diffeomorphic field, is a field -- in which all of the component eigenstates, that work to comprise such a said field, are here to work to bear the Same Type Of A Covariant Distribution, at their individually taken delineations, as this is here to be taken, along the Riemann surface, of such an inferred topological manifold, that is here to work to bear the general characteristic, of behaving as exhibiting the nature of such a diffeomorphic field. 

Whereas; a homeomorphic field, may be:

1) A Fourier-Related field, in which the time-related flow between two or more different metric-related spatial eigenstates, that are here to work to comprise such a said field, are here to work to bear the same tense of a hermitian distribution, at their respective individually taken delineations. OR;

2) A Laplacian-Related field, in which the non-time-related flow, (as in metaphorically acting, as a "snapshot" of a traceable flow, of what is here to be going on in such a general type of a case), between two or more different metric-related spatial eigenstates, that are here to work to comprise such a said field, are here to work to bear the same tense of a hermitian distribution, at their respective individually taken delineations. OR;

3) A mappable relationship, that is to be configured, between two different structures, of which are here to both work to bear the same tense of a hermitian distribution, at their respective individually taken delineations. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAMUEL.


Saturday, July 24, 2021

Heuristic Electrons -- Flat Ricci Curvature -- Calabi-Yau-Manifold

The general Noether-Based heuristic field of a given arbitrary electron, that is here to be moving in a homeomorphic manner through time and space -- to where the gravitational field that is proximal local to the effectual motion of such a said electron, is here to be of a smooth Ricci Flow, to where the said gravitational field is here to work to be exhibiting a flat Ricci Curvature, -- is a prime example of a Ward-Cauchy-Related field, that is here to be displaying the proximal local presence, of a mass-bearing cohesive set of discrete energy quanta, that is here to be of the general nature of being correlative to a tense of a Yau-Exact Calabi-Yau-Manifold.

I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SINCERELY, SAM.

Thursday, July 15, 2021

Homeomorphic Noether-Based Current -- Stronger Electrical Current

 The more homeomorphic that the Noether-Based Current is to be, as appertaining to the flow of a given arbitrary covariant set of electrons, as such a said flow of electrons (electricity) -- which is here to be physically transferred, through a respective given arbitrary electrical circuitry -- the stronger that the consequentially resultant directly corresponding current of electricity will therefore tend to be. (SAM).

Even more intrinsically: The more homomorphic that the Noether-Based Current is to be, as appertaining to the flow of a given arbitrary covariant set of electrons, as such a said flow of electrons (electricity) -- which is here to be physically transferred, through a respective given arbitrary electrical circuitry -- the stronger that the consequentially resultant directly corresponding current of electricity will therefore tend to be. (SAM).

Thursday, July 8, 2021

De Rham Cohomology/Dolbeault Cohomology -- Homeomorphic Field

 A given arbitrary Hamiltonian Operator, that works to form a De Rham cohomology, will tend to have a higher potential of working to form a homeomorphic field, -- than the chances of a given arbitrary Hamiltonian Operator, that works to form a Dolbeault cohomology, will. SINCERELY, SAM ROACH. 

Homeomorphic Field -- Group Action -- Homomorphic Field

 A homeomorphic field, that is formed by a cohesive set of energy eigenstates, that all act together in unison as one entity, is of the nature of being a genus of a homomorphic field. Therefore; a homeomorphic field, that is here to bear a cohesive set of energy eigenstates, that are here to work to form a tense of group action, to where the motion of the inferred Hamiltonian Operator of such a respective case, (the mentioned respective set of energy eigenstates), is here to display a relatively strong tense of isotropic stability, is of the nature of being a genus of a homomorphic field. I WILL CONTINUE WITH THE SUSPENSE LATER!  SAM ROACH. (1989).

Friday, June 25, 2021

Homeomorphic Set Of Energy Quanta — Net Homeomorphic Exhibition Of Dispersed CSI

 Whenever a Noether-Based mass-bearing cohesive set of discrete energy quanta, that is here to remain kinematically differentiating in a homeomorphic manner, over a durational span of time, is to alter in the directly associated exhibition of its correlative respective Chern-Simons Invariants, the consequently resultant flow, of that general net dispersion, that is here to be directly corresponding with the tangential flow, of the inferred expended eigenstates, of which are here to be directly associated, with the proximal local process, of such a given arbitrary respective case, in which the said Chern-Simons Invariants are here to be generated, will also often tend to work to bear a tense of a Homeomorphic-Related flow, over the span of time, of which is here to be analogously in sync, with the respective homeomorphic flow, that is here it be of the said cohesive set of discrete energy quanta. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. 

Thursday, June 24, 2021

Braided Cohomology -- Net Dolbeault Cohomology

 Whenever two different and distinct homeomorphic planes of force, of which are here to initially work to form, two different and distinct individually taken mappable-tracings, that are here to be of a De Rham cohomology-related nature, -- are to spontaneously be braided together in their cohomology-related structure, in a Nijenhuis manner, this general genus of a gauged-action, will consequently tend to result, in working to form a net overall cohomology, that is here to be of a Dolbeault-Related nature. SAMUEL.

Wednesday, June 23, 2021

Linked Gauged-Action Between String And Counter String -- Homeomorphic Field -- Orientable Superstring

 The stronger that the linkage is to be, in the proximal local gauged-action, that is here to exist, between a given arbitrary superstring of discrete energy permittivity, and its directly corresponding counter string of discrete energy permittivity, -- there will thereby tend to be present, an increased chance of an occurrence, in which the field that is here to exist, in-between the said string and its immediately correlative counter string, will consequently result in tending to work to bear a homeomorphic nature -- to where there will therefore tend to be a greater probability, in which the mentioned superstring of such a given arbitrary respective case, will consequently tend to work to bear a greater probability, of resulting in being of an orientable nature. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAM.(1989).

Tuesday, June 22, 2021

Braided Cohomology-Related Planes -- Net Homeomorphic Cohomology

 When two different distinct homeomorphic cohomology-related planes of force, are to be braided in a purely hermitian manner, the consequently formed net plane of force implied here, will therefore often tend to work to form, an overall net homeomorphic cohomology-related plane of force. SAMUEL (1989).