Interesting Stuff As To Grobner Bases

Let's consider what is meant to be determined as a Grobner Basis:

Let's say that one is to have a point particle.  It is theoretically to be of zero spatial dimensions.  Consequently; its surrounding spatial dimensionality, is theoretically here to be "infinite" in its number of spatial dimensions.  Next; one may take certain basic differential geometrical-related mathematical stipulations, about the dimensional relationships of certain spaces, that are here to be related to both the existence and the motion of such a theoretical point particle, both as to what may potentially be an element of what, what may be in union to what, what may intersect what, etc., -- based upon the basic mathematical operations of addition, division, multiplication, and subtraction.  Consequently; one may then work to determine an eigenbasis, that is here to work upon a given arbitrary space, in a Laplacian-related manner -- that is here to work to involve a stipulation, that involves the relationship of one point particle To a stipulation that involves the relationship of another point particle, -- to where the relationship that is here to work to involve the two inferred point particles, is then to be of either a Real Riemann Gaussian-related association, or of a Li-based Gaussian-related association.  Such a general tense of an eigenbasis, may then be utilized, to work to determine as to what actual point-like spaces are more likely to be relatively adjacent to other actual point-like spaces, -- given how such point-like spaces are here to be acting, over time. Such a general tense of an eigenbasis, may be thought of as a Grobner Basis.  Sincerely, Samuel David Roach.

Operators And Group Attractors, Part Two

As to those points that seem to "disappear" during the generally unnoticed duration of Ultimon Flow, these first-ordered point particles, if remaining in and of the same universal setting, reappear after at least one minimum valued discrete time increment of being gone, and, as well, these will then tend to reappear at at least the radius of a minimum-sized first-ordered point particle -- away from where these had appeared over the immediately subsequent iteration of group-related instanton.  Now, at the sub-stringular level, the so-stated "disappearing act" of a respective point particle, is only at the relative discrete region that is from within the immediate Ward-Neumman locus -- of what may here be described of as the "neighborhood" of the said point particle.  The said "disappearing act" of the so-stated point -- at the globally distinguishable realm -- is the result of the Fourier-based point commutation of point particles,  that have moved from an exact and linear status, to where these said points often tend to act in so as to work to change in their propagation of condensed oscillation, to where these particles are to then to tend to be translated into a different Gaussian tense, that would then be of a Li-based nature or of a Njenhuis-based nature, as compared to the directly subsequent tense of the here relative Real Reimmanian spacing that these had had -- immediately prior to the so-eluded-to change in their Gaussian-based propagation.  When the spacing of a set of one or more first-ordered point particles is altered in its predominant Gaussian-based format, that genus of extrapolation that would then tend to be applied, in so as to work to predict the detection of that set of point particles in the initial set of circumstances, will tend to not be sufficient as a genus of extrapolation -- that could otherwise work to predict the spacing of that selfsame set of first-ordered point particles, as these so-stated point particles are to then be of a different universal setting in the ensuing so-eluded-to case in "point."  Such a "disappearing act" will then work to form part of the rudiments -- as to that general activity that happens over time, in so as to integrate into both those superstringular entities and those substringular activities, that work to distinguish the Li-based Gaussian tense of one set of eigenstates that may be distinguished in one universal setting, towards a covariant extrapolation  that may be directed into working to determine those substringular activities and those substringular entities,  that may work here to distinguish the Li-based Gaussiain tense of one or more other sets of eigenstates that may be considered as part of one or more ulterior universal settings.  Often as well, one may occasionally be able to extrapolate the potential and/or the actual ebbing of one or more sets of eigenstates of one or more universal settings -- either into or out of another set of one or more universal settings, over time.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Worm-Hole Projections, the Last Part Of Session 12 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

Depending upon the manner of the trajectory of any one given arbitrary worm-wole that is to be formed, its projection often may or may not work to inter bind two different universal settings -- via the Fourier-based activity of the manner of the respective contorsioning that is to happen here, with whatever the said worm-hole in question would happen to be.  If the contorsioning of the Njenhuis-based Lagrangian-affiliated tensors, that are of the Doubolt-affiliated tense of that bending of  space-time-fabric that is to be utilized -- in so as to work to inter bind two different relatively distant spots in the  Continuum -- is to here work to bear a Li-based tense of Chern-Simons singularities, then, the so-eluded-to worm-hole will then often tend to work to interconnect two different settings that are likewise and respectively of two different universal settings.  Yet, if the contorsioning of the Njenhuis-based Lagrangian-affiliated tensors, that are of the Doubolt-affiliated tense of that bending of space-time-fabric that is to be utilized -- in so as to work to inter bind two different relatively distant spots in the Continuum -- is to work to bear a Li-based tense of hermitian  singularities instead, then, the so-eluded-of worm-hole will then often tend to work to interconnect two different settings that are likewise and respectively of the same universal setting.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.