Monomial Kahller-Based Quotient -- Unitary Mass-Bearing Set Of Discrete Energy Quanta

 When the Kahler-Based Quotient, that may be considered in such a given case here, to work to convey a tense of the dimensional-related flow, on account of the correlative kinetic transport, of which is here to be due to the directly corresponding Yukawa-Based incursion, of a correlative respective Legendre (co)homology,  to where the phenomenology that is here to be kinematically transferred, by the inferred Fourier-Related progression of the stated Legendre (co)homology, is of a Noether-Based mass-bearing cohesive set of discrete energy quanta, in which the earlier mentioned Kahler-Based Quotient, that may be described of, as working to bear a monomial expression of an inertial state of pulsation, will thereby often tend to result, to where this general type of a Ward-Cauchy-Related interaction, that is here to be incurred upon the herein inferred mass-bearing Hamiltonian Operator of such a given respective case, will thereby often work to imply the general proximal local physical condition, by which the Lagrangian-Based motion of such an inferred mass-bearing set of discrete energy, may therefore often tend to work to be directed in a holomorphic manner, into a unitary Lagrangian-Based path, over the durational course of a sequential series of group-related instantons. I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SINCERELY, SAM. 

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.

Legendre Homology, And Energy As Motion

 The general phenomenology of Legendre (co)homology, is directly eminent to the multiplicity of the mappable-tracing of the kinetic wave-tug -- that is here to be applied to the multiplicity of mass-bearing cohesive sets of discrete energy quanta, in so as to allow for matter to be in motion. SAMUEL ROACH.

Rate Of i*PI(del) Action And Rate Of Superstringular Vibration During BRST

The quicker that any one given arbitrary mass-bearing orbifold eigenset is to accelerate, when this is here to be taken in its relationship to both the motion and the existence of electromagnetic energy, -- the faster that the directly corresponding i*PI(del) action will tend to work to happen, to those composite superstrings of discrete energy permittivity that work to comprise the said respective orbifold eigenset of such a here stated case scenario, -- when this is here to be taken in respect to a lower Hodge Index as to the number of partition-based discrepancies, that are here to be proximal local to the general topological surface of the here stated superstrings, that are here to work to comprise the earlier mentioned orbifold eigenset.  Since homotopic residue is to be conserved; the less partition-based discrepancies that work to be directly affiliated with the general topological surface of those superstrings of discrete energy permittivity that work to comprise any one said given arbitrary mass-bearing orbifold eigengeset, the more of such mass-bearing strings that it will consequently take to comprise such a said eigenset.  The denser that any one given arbitrary orbifold eigenset is to be, the quicker that those composite strings -- that work to comprise such a said eigenset -- are consequently to need to vibrate, during each successive iteration of BRST, in which such a said mass-bearing orbifold eigenset is to be accelerating in its relationship to both the motion and the existence of electromagnetic energy.  This works to produce that general Hamiltonian operation, that is here to act as a fractal of momentum, -- that works to allow for the added thrust of accelerated mass-bearing phenomenology.  Again; it is the multiplicit Legendre homology, that works to allow for the kinematic motion of mass-bearing orbifold eigensets. Samuel David Roach.

Relativistic Shape Of World-Sheets

Individually taken mass-bearing superstrings of discrete energy permittivity, tend to bear a toroidal world-sheet, -- when taken at an internal reference-frame.  However; those individually taken superstrings of discrete kinetic energy permittivity, tend to bear a conical world-sheet, -- again, when this is here to be taken at an internal reference-frame.  Discrete energy tends to happen in groups of discrete quanta, that operate to perform a specific function.  I name such "groups" as being, "orbifold eigensets."  Mass-bearing superstrings of discrete energy permittivity, tend to exist via a symplectic geometry (as a closed-looped geometry). Whereas; superstrings of discrete kinetic energy permittivity, tend to exist via a Khovanov geometry (an open-looped or an open-strand-related geometry).  It is those particular individually taken groups of superstrings, that are of the nature of discrete kinetic energy permittivity, that are here of a Khovanov geometry, of which are also here to be of a Legendre (co)homology, that are thence to act, in so as to work to spatially transfer those particular individually taken groups of superstrings, that are here to be of the nature of being a mass-bearing orbifold eigenset (to where this is of a symplectic-related cohomology), -- to where, even though such an inferred set of interdependent mass-bearing superstrings, are to tend to be super conformally invariant at an internal reference-frame, these are thus to be transferred through space over time at an external reference-frame, via a directly corresponding Lagrangian, via the covariant motion of the earlier inferred set of kinetic-based superstrings, that are here to act as a directly associated tense of a Legendre (co)homology.  Superstrings of discrete kinetic energy permittivity, tend to work to bear a conical-shaped world-sheet; whereas, a world-sheet that is of a discrete mass-bearing superstring, tends to be toroidal-shaped world-sheet.  Consequently; there often tends to be in nature -- at a level that is Poincare to a certain tense of a Ward-Cauchy-related scenario, -- a multiplicit set of interdependent conical-shaped world-sheet-based phenomenology, that are of a  kinetic energy-related nature, that act, in so as to drive the kinematic-related motion of a correlative multiplicit set of interdependent toroidal-shaped world-sheet-based phenomenology; -- in so as to help in the process of the transference of mass through space, over time. To Be Continued! Sincerely, Samuel David Roach.

Isotropic Stability And Tense Of Cohomology-Related Degeneration

If the cohomology that is here to be formed, by the motion of a set of one or more mass-bearing superstrings of discrete energy permittivity-- that are here to be moved along at a relatively external reference-frame, by a set of one or more superstrings that are of a Legendre homology --  is to bear such a condition, --  to where the said contingent set of superstrings of a Legendre homology, that are here to be in the inferred process of "tugging-along" the said set of mass-bearing superstrings, are to work to bear an isotropically unstable (co)homology, then, such a resultant cohomology, that is said here to have been formed by the earlier mentioned motion of the said set of one or more mass-bearing superstrings of discrete energy permittivity, that are to be operating in so as to perform one inferred common function, are then to tend to bear more of a degeneration of cohomology, than if, instead, the Legendre (co)homology that is here to be "tugging-along" the said mass-bearing set of superstrings, were to otherwise work to bear an isotropically stable condition.  Sincerely, Samuel David Roach.

Some Stuff As To Conical Legendre Homology

The more conical that a Legendre homology is to be, in the process of working to transport a mass-bearing orbifold eigenset through space, -- over a duration of time -- the greater will its ability tend to be, in so as to be able to then, to have a hightened scalar amplitude of being capable of transfering the earlier mentioned given arbitrary mass-bearing orbifold eigenset through space and time.  Sam.

Release Of Relative Yukawa Bearing

When the general Ward-Cauchy-related process is here to be going on, during which the residual kinetic energy of an electron is to be released in the form of a photon -- there is here to be one directly corresponding open-looped superstring of discrete energy permittivity, that is then to release the immediately prior state that it had had, when in terms of its relative Yukawa bearing upon the correlative respective electron, to where right after such a said general process is to occur -- the here just released correlative discrete quantum of a Legendre homology, is then to undergo the general process,  that is here to be directly involved with the activity of the Fujikawa Coupling,  which is here to happen via the manner of activity that is known of as being of the Green Function, -- in so as to ensue as to work to form one given arbitrary respective discrete quantum of electromagnetic energy.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Symplectic Versus Khovanov Knotting Equations

When one is to work to determine the knotting equations for a system of cohomology, to where these so-eluded-to equations are here to work to be describing a symplectic geometry, -- the main difference that there is, between the formulation of this said cohomology and the formulation of a Legendre homology, is that, when determining a cohomology, one is here to be converting a Minkowski space into a Hilbert space; whereas, -- when one is to work to determine the knotting equations for a system of a Legendre homology,  to where these so-eluded-to equations are here to work to be describing a Khovanov geometry, -- the formulation of this said general genus of homology is as such, to where one is to instead, to be converting a Hilbert space into a Minkowski space.  To Be Continued!  Sincerely, Samuel David Roach.

The Motion Of Mass

Isotropically stable Legendre homology works at making a Yukawa Coupling upon Calabi-Yau spaces, in so as to tug these so-eluded-to mass-bearing spaces along the multi-various mappable-tracing of space and time -- over a sequential series of group-related instantons, -- in so as to work at helping to allow for the kinematic motion of matter over the course of time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Homologies And Norm-State-Projection Strike

 A superstring that works to bear a symplectic homology -- tends to form a Yukawa Coupling upon those norm-state-projections that these are to strike in a Gliosis-related manner, that is of more of an orthogonal manner, than the general tense of a Yukawa-based Coupling that a superstring that works to bear a Legendre homology is to bear upon those norm-state-projections that these are to strike in a Gliosis-related manner, -- because superstrings that work to bear a symplectic homology, tend to interact with less topological slippage upon the stratum that these are to work to bear a Yukawa-related coupling upon,  than superstrings that are to instead to work to bear a Legendre homology are to tug upon the correlative topological stratum that these are to come into a direct contact with.  This is, in part, because, superstrings that are of a symplectic homology, are of a closed-looped nature, that thereby work to interact with the norm-state-projections that these are to interact with, in a manner that is to tend to bear a stronger direct wave-tug-related angular drive in their directly corresponding holomorphic direction, whereas, superstrings that are of a Legendre homology, are of an open-looped nature, that thereby work to bear a stronger indirect wave-tug-related angular drive in their directly corresponding holomorphic direction.  This helps at working to describe as to why phenomenologies that are of abelian geometries, tend to form cohomology entities around the topological region of closed-looped superstrings of discrete energy permittivity -- whereas, phenomenologies that are of non abelian geometries, tend to form around the topological stratum of superstrings of discrete energy permittivity, -- that are of either of an open-looped or of an open-stand-related nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More As To Isotropically Stable Homology

When one is here to be dealing with a an isotropically stable Legendre homology, then -- if a directly corresponding superstring of discrete energy permittivity, is to consistently to be striking the norm-state-projections that it is to be coming into a Gliosis-related contact with, at a Ward-Cauchy-related  acute angle that is here to be under 30 degrees of subtention, it will tend to be in the process of degenerating more homology-related eigenindices than it is here to be generating.  Yet, if one is here to be dealing with an isotropically stable Legendre homology, in which the directly corresponding superstring of discrete energy permittivity is to consistently to be striking the norm-state-projections that it is to be coming into a Gliosis-related contact with, at a Ward-Cauchy-related acute angle that is here to be exactly 30 degrees of subtention, it will tend to be in the process of generating the same scalar magnitude of homology-related eigenindices as it is here to be degenerating.  Furthermore -- when one is here to be dealing with an isotropically stable Legendre homology, that is here to be directly corresponding to a superstring of discrete energy permittivity, that is here to consistently to be striking the norm-state-projections that it is to be coming into a Gliosis-related contact with, at a Ward-Cauchy-related acute angle of subtention that is to be from between 30 degrees and 90 degrees, it will then tend to be generating more homology-related eigenindices than it is here to be degenerating.  This is, in part, because -- since the Lagrangian as to the motion of discrete energy, through the path of the point commutator-related field in which the so-eluded-to physical norm-state-projections are to exist, is to be kinematically moving as a cross-product-related Hamiltonian operator, the sine of the angle by which such a so-eluded-to superstring is to strike those norm-state-projections in which it is to come into contact with, works, in part, to help in determining the generative conditions of its consequent correlative homology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Isotropically Stable Versus Isotropically Unstable Homology

Over an evenly-gauged Hamiltonian eigenmetric -- an isotropically stable open-looped superstring of discrete energy permittivity, may either: generate more homology-related eigenindices than it is to degenerate, or it may generate less homology-related eigenindices than it is to degenerate, or, it may sometimes generate as much homology-related eigenindices than it is to  degenerate.  Yet, -- over the same general genus of an evenly-gauged Hamiltonian eigenmetric -- an isotropically unstable open-looped superstring of discrete energy permittivity may only be able to either generate more homology-related eigenindices than it is to degenerate, or it may, instead, generate less homology-related eigenindices than it is to degenerate, -- to where an isotropically unstable superstring of discrete energy permittivity will never generate the same scalar magnitude of homology-related eigenindices as it is here to degenerate, over a definitive amount of viable time, -- otherwise, one would here to be dealing with an isotropically stable Legendre homology instead.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little As To Abelian Verus Non Abelian Groups

When one is dealing with a phenomenology that works to display a symplectic geometry -- such a so-eluded-to homology, that is thence formed by the interaction of the said string's topology with its immediately proximal norm-state-projections, is then to be directly corresponding to a closed-looped superstring of discrete energy permittivity, -- of which is here to be a cohomology, of which is here to have a grouping of abelian eigenindices, that work to form the structure of its homology-related framework, as this is proximal local to its external topological surface at the Poincare level.  Yet -- when one is dealing, instead, with a phenomenology that works to display a "Khovanov" geometry -- such a so-eluded-to homology, that is thence formed by the interaction of the said string's topology with its immediately proximal norm-state-projections, is then to be directly corresponding to either an open-looped superstring or an open-looped strand of discrete energy permittivity, -- of which is here to be a Legendre homology, of which is here to have a grouping of non abelian eigenindices, that work to form the structure of its homology-related framework, as this is proximal to its external topological surface at the Poincare level.  Furthermore, as I have inferred to before -- an abelian group works to form a direct wave-tug-related interaction with the respective phenomenology that it is to come into contact with, -- whereas, a non abelian group works to form an indirect wave-tug-related interaction with the respective phenomenology that it is to come into contact with.  Consequently, the process of the indistinguishably different recycling of non abelian groupings -- that work to form the homology-related shell of Legendre-related geometric phenomena -- are here to be recycled relatively more swiftly, whereas the process of the indistinguishably different recycling of abelian groupings -- that work to form the cohomology-related shell of symplectic-related geometric phenomena -- are here to be recycled relatively less swiftly.  Abelian groupings are brought into the Ward-Neumman bounds of the relatively proximal local region of a closed-looped genus of substringular phenomenology -- because, when a bosonic string is to interact with those norm-state-projections that it is to come into contact with, -- such a consequent interaction tends to be of a relatively orthogonal nature, -- whereas, non abelian groupings are brought into the Ward-Neumman bounds of the relatively proximal local region of either an open-looped or an open-strand genus of substringular phenomenology -- because, when a fermionic string is to interact with those norm-state-projections that it is to come into contact with, -- such a consequent interaction tends to be of a relatively oblique nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Three As To Solitons

Let us initially consider one given arbitrary Ward-Cauchy-related phenomenon, that is here to be a soliton.  Let us consider the condition, that, in order for it to be a "soliton," it is to not be compact -- to where it is here to conform to the Ward-Cauchy-related condition, that it is to bear a tense of diffeomorphisrm.  Since the said soliton is to work to bear diffeomorphisrm, it is to bear a manifold, complex here if you will, that is to have both a smooth and an isomorphic homeomorphic topological contour -- to where one could theoretically try to here, act in so as to extrapolate a Laplacian-related cohomological mappable-tracing, along the Minkowski-related plane of its external topological surface, at the Poincare level -- in such a manner, to where there would here be the condition of one to not to have any Lagrangian-based Chern-Simons spurs to be detected.  This would then work to mean here, in this given arbitrary general case,  that the absolute value of the Beti number would not vary, and, in so long as such a soliton is here to be of a Noether-related tense of phenomenology, such a consistent absolute value of the Beti number, would be of the same absolute value of an even integer per group-related instanton, in so long as both the constraints as to being -- that such a said phenomenon is to be a soliton, as well as the constraint, that the said phenomenon does not become tachyonic here at all.  Yet, if the absolute value of the Beti number is to either decrease or to increase spontaneously, then, the soliton will no longer be a soliton -- it will then be of a compact nature, that will to be either losing or to be gaining a certain number of spatial dimensions, spontaneously.  If such an initially stated soliton, that is to change into not being a soliton, in such a manner -- to where there is not only a change in the compactification of its correlative dimensionality, yet also to where -- the topological strands of the said superstring are to expand, in terms of the scalar amplitude of their Ward-Neumman bounds, over a relatively transient evenly-gauged Hamiltonian eigenmetric, -- then, there is then to be a Clifford-Expansion in the size of the core-field-density of such a phenomenon, that is here to have perturbated from being a soliton into Not being a soliton.  Furthermore, if such a change is here to work to convert an initial Legendre homology into a symplectic homology, over time -- then, such a change will almost certainly work to alter the initial complex manifold M, -- into then being of a Real Reimman manifold, instead.  If such an alteration in the type of phenomenon that is being discussed, is to work to bear a set of one or more Laplacian-based Chern-Simons Lagrangian-related topological spurs, then, the said phenomenon is to no longer be of a flat Ricci curvature.  Let us still stay, though, that the flow of such so-eluded-to phenomenon will work to displace a holomorphic vector field.  Such A Change In Ward-Cauchy-Conditions Is One General Manner Of How One Given Arbitrary Eigenstate Of A Nijenhuis Holographic Spacing, May Work To Convert Into A Real Reimman Hilbert Space, Thus Working To Convert The Soliton Into A Cohomological-Based Compact Calabi-Yau Space, Which Is Then No Longer A Soliton.  This may often be able to happen, when there is a significant dissonance of the tendencies of the push and tug of gravitational waves, in such a manner -- to where the "best-fit-curve" as to how such a phenomenon as to what was initially a soliton -- is to behave, is then to bear a perturbative alteration, in both the display and in the scalar amplitude of its "phenotypical" correlative proximal local altering cotangent bundle.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Perturbative In Delineation

The general condition as to the electrodynamic scattering of the multiplicit Legendre-related energy, that is here to be delineated by a tense of the generation of the multiplicit Lagrangian of electromagnetic superstrings, of which are of discrete energy permittivity -- through which such a so-eluded-to generation of energy is of an electromotive nature -- tends to be of more of a perturbative nature, -- than the general condition as to the kinetic energy scattering of the multiplicit Legendre-related energy, that is here to be delineated by a generation of the multiplicit Lagrangian of mass-bearing superstrings, of which are of discrete energy permittivity -- through which such a so-eluded-to generation of energy is not of an electromotive nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Polarity Of Legendre Homology

Let us initially consider a tense of a discrete overall quantum of Legendre homology, that is here to be delineated by the generation of the Lagrangian-related activity of an electromagnetic source.  Next, let us say that the voltage (energy per charge) that is to be directly associated with the said electromagnetic source, is to be of a positive polarity. This will then mean -- that the directoral-related angular momentum of the earlier mentioned delineated Legendre homology, will be directed as a cross-product-related operation of kinetic energy, -- to where the kinetic energy that is here to be produced by the said electromagnetic source (in the form of voltage, or, energy per charge), will here be directed relatively outward.  However, -- if the voltage is to, instead, to be directly associated with a negative polarity, then, this will mean -- that the directoral-related angular momentum of the so-eluded-to Legendre homology, will then, in this ulterior case, be directed as a dot-product-related operation of kinetic energy, -- to where the kinetic energy that is here to be produced by the said electromagnetic source (in the form of voltage, or, energy per charge), will here be directed relatively inward.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Entropic Photons And Isotropic Instability

As a general condition -- when there is to be that Fourier-related activity, in which photons are to scatter upon other phenomenology, these said photons, -- of which are discrete quanta of electromagnetic energy -- temporarily become of an entropic nature.  This just mentioned Ward-Cauchy-related manner of activity, is related to the state of affairs, to where  -- the general multiplicit Legendre homology -- that is delineated by the generation of that symplectic homology, that is of the nature of photons (photons work to form closed-looped strings), is to be of a homology that is of an isotropically unstable nature.  This means -- that the generation of the homology of those closed-looped phenomology -- that are of discrete quanta of electromagnetic energy, over time, works to delineate the general open-looped homology, that is of that plain kinetic energy, -- that is here of such a general genus, to where it is related to the presence of Tesla energy.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Path-Related Bundle And Legendre Homology

Let us initially consider a mass-bearing orbifold eigenset -- which is a set of mass-bearing discrete quanta of energy, that operate in so as to perform one specific function, over a sequential series of group-related instantons -- that may be be described of via a Fourier Transform, that is of an evenly-gauged Hamiltonian eigenmetric.  The directly corresponding mass-bearing superstrings of discrete energy permittivity, that work to comprise the said mass-bearing orbifold eigenset, are each, individually taken, as working to bear a symplectic homology -- which may be described of as being cohomological entities.  The generation of the Lagrangian of such cohomological entities works here, in so as to help in the delineation of superstrings that are here, individually taken, to exhibit a tense of working to bear a Legendre homology.  What I am describing here -- is that the generation of the actual motion of the closed-strings that are of a mass-bearing nature -- works to help here at delineating the proximal local presence of isotropically stable superstrings, that are here of the nature of plain kinetic energy.  The so-eluded-to multi-dimensional delineation of the said Legendre homology, of which is here of the nature of being a tense of plain kinetic energy -- is to work to bear a path-related bundle, that is here to work to involve the proximal local presence of the condition of Chern-Simons Invariants.  Let's next say that each general directoral-related partial function, that is correlative to the said path-related bundle -- is to be expressed in this given arbitrary case -- as one quadratic-based equation.  Let us next say that the said path-related bundle is here to involve the presence of eight covariant, codeterminable, and codifferentiable spatial parameter-related physical dimensions -- that may be expressed in a manner as being of a product of eight of such so-eluded-to directoral-based quadratic equations, -- as to here to be appertaining to working to help at describing the Lagrangian-based path of the earlier-mentioned Legendre homology, that is of a multidimensional open-loop of substringular topological stratum.  If one were to then to consider the product of four of the eight of such directoral-related equations, that are here to help at working to describe the path-related bundle of such a Legendre-related superstring -- as it is to here to be working to exhibit the attributes of the Ward-Cauchy-related conditions of its correlative Chern-Simons Invariants -- and, if one were to then to take the overall expression of the said Chern-Simons Invariants of such a Legendre homology in the said exhibition of the so-eluded-to eight spatial dimensions, and if one were to then to divide this expression by the product of the earlier-mentinioned respective given arbitrary path-related bundle of the respecitve given arbitrary four directoral-related equations, -- this will then tend to indicate, what would here amount to an attenuation of the dimensional-related pulsation of the said correlative Legendre-related homology.  Such an attenuation of dimensional-related pulsation, will then work to form the presence of a set of one or more proximal local metric-based Chern-Simons singularities that are of a dampening nature, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Partition-Based Discrepancies And Legendre Homology

The lower that the number of partition-based discrepancies, that are here to exist from within the Ward-Neumman bounds of those individually taken superstrings -- that work to comprise a mass-bearing orbifold eigenset, is to tend to be -- the higher that the spatial dimensionality of the resultant generation of the delineated Legendre-related superstrings, will then tend to be.  Likewise -- the higher that the number of partition-based discrepancies, that are here to exist from within the Ward-Neumman bounds of the individually taken superstrings, that work to comprise a mass-bearing orbifold eigenset, is to tend to be -- the lower that the spatial dimensionality of the resultant generation of the delineated Legendre-related superstrings, will then tend to be.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.