Inter-Binding(s) Between Linked Cohomology-Related World-Sheets

 When the inter-binding(s) between linked cohomology-related world-sheets is (are) hermitian, the inferred net flow of curvature, of which is here to interdependently exist from amongst the proximal local presence of such world-sheets, is thence to often tend to work to bear a relatively smooth homotopy. SAMUEL ROACH. 

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. 

Hermitian Cox Ring -- Hermitian Composite Del Pezzo Spaces

 The more Hermitian that the flow of the Laplacian-Based curvature of a given arbitrary Ward-Cauchy-Related Cox-Ring is to be, the more Hermitian that the correlative individually taken linkages that are here to be present, as amongst the directly corresponding Del Pezzo Spaces, of which are here to help to work to comprise, such a stated respective given arbitrary Ward-Cauchy-Related Cox Ring. SAM ROACH. (1989).

Part Five As To Solitons

If one were to initially take a soliton, that is here to be kinematic in its interdependence with its environment -- via a Fourier Transformation, that is here to work to involve an evenly-gauged Hamiltonian eigenmetric -- while then spontaneously, such an initially said phenomenology, is to move into a Ward-Cauchy-related field, that works to eminently involve the directly corresponding presence of more than 26 spatial dimensions plus time, then, -- the initially said soliton, will, at this point in duration, no longer be a soliton.  This is because, flat space is only capable of having the eminent presence of up to 26 spatial dimensions plus time.  In order for a soliton to be a soliton, by definition, -- it is to always work to bear a flat Ricci curvature.  So, if any given arbitrary phenomenology is to work to bear more than 26 spatial dimensions plus time -- then, it may no longer, at this point in duration, work to bear a flat Ricci curvature. 
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Course 2, Session 1

What is a line? A line is a curvature that goes straight in whichever direction you consider it going in. If the line were ideal and not a segment, then it would go infinitely in either direction. Since the universe that we are dealing with is limited, it is finite. Anything that is finite as a discrete size. Therefore, any line that is physical is limited, and thereby finite. Thus, there are no physical lines with infinite length. This means that there is actually no ideal line. Lines are segments.

In our previous course, we discussed that phenomena is constantly in flux. Organization allows life, and life proves a relative degree of order. In order for order to proceed from physical flux and reassociations, there must be a set of physical points that are flush for every eigenstate of encasement. Each point particle of such a flush array must have a counterpart that allows each to lock in as a stabilized action. Otherwise, the flush orientation would just be a transient coincidental array and THAT would not happen. The counterpart would associate here due to an attraction due to wave supplementation. The flush array of Real points mentioned here is an example of a one-dimensional string. Its counterpart is the Fock Space association of the string.

Strings are physical. These are relatively optimum and necessarily, yet these are not ideal. Strings are small, yet these also have thickness. These are straight, yet these are not infinite in flushness. Strings are temporary per iteration, yet these hold near position for a slightly longer metric than the adjacent point commutators, although these subsequently speed up for a brief while.

Every string in the substringular has segments that make it up. Each of these segments is a separation from space as it normally is, and I call these “partitions.” Each of these “partitions” encodes for a string in the realm that we would detect them. Each of these globally distinguishable strings has one aberration from flushness. The aberration from the flushness of the globally distinguishable strings is equal to the thickness of one point particle. In the substringular, the partition is smaller than the string that it encodes for. The strings in the substringular keep flush top to bottom in the world-tube/general world-sheet that these iterate in.

SESSION 3 OF COURSE 1 (Curvature)

Draw a line. It goes from one spot to another. Usually, when people refer to something as a "line", what they really mean is a straight line. Although truly straight lines are hard to draw in a sketch, these do exist in nature to a high degree of precision. With a compass, you can draw a line that is perfectly straight up to the precision of the thickness of that line. What may vary on a smaller scale is the thickness of the line due to your drawing utensil, or the smoothness of the straight edge that you used. When you use lines, you are involved with linear geometry. How do you determine if something is in a straight line? Take three of the points you are considering. Get out your straight edge. Try to have all three points even with the edge of the straight edge. If the points aren't all along the edge, then the points do not describe a line. Thus, the points are not linearly distributed.
A line describing a simple function does not change in curvature. Let's say that you had a horizontal x-axis and vertical y-axis. One line is perfectly vertical. This line has no real curvature. It could be said that its curvature is infinite, except that you can not divide by zero. Slope is the word used to indicate what a curvature is. Slope is equal to vertical change (rise) over horizontal change (run). If something rises with no run, then its slope is (something/0), which you can either look at as absolutely infinite or as a slope whose curvature is fictitious, since one can not divide by zero. A horizontal slope is zero, since (0/anything that is not zero or imaginary) is zero. A slanted line among these axes is real and non-zero, yet, if it remains constantly linear, then the curvature does not change. If a line is displaced, then it no longer is the same line. Such a change would have a change in curvature, yet this would be a different function, and what we discussed above was a constant function.
For instance, the identity function is a line where x=y all of the time, when you are talking about an x--y plane. If the line is constantly this function, then its curvature will not change. I will mention later of many functions where the curvature changes. You may even have a case where there are many axes for the dimensions of the particle, and there may be a straight line where each parameter for each axis is incremented to the same degree at each detectable level of measurement. This would be an even greater type of identity function.
A line may appear straight even when it isn't. It may be constantly in one plane, appearing to go in only one direction while it actually is jointal in many segments. This may be indicated by a change in the morphological appearance or texture that is shown by looking at the object. Sometimes, by distinguishing SINGULARITIES in segments of something's appearance, you may discuss how an object is not straight.