As I have mentioned before, and as it is quite already known in physics -- when electromagnetic energy is to strike an electron, the said electron is here to have a tendency of jumping back-and-forth energy levels, in so as to release its residual kinetic energy in the form of a photon. As the just mentioned photon is in the process of being formed by the so-stated released residual kinetic energy of an electron, -- the directly corresponding electron that is here to be moving back-and-forth an energy level, in the process of indirectly working to form a discrete increment of light, that is in the form of an impending photon -- (the said electron) will here to tend to be re-bounding via the motion of a Ward-Supplemental-related manner, in the process of going from a condition of moving inward an energy level, into then going into a condition of moving outward an energy level. Such a re-bounding Fourier-related activity, that is here to work to involve a Ward-Supplemental process, is here to then involve a set of antiholomorphic Kahler conditions -- which, to an extent, is dependent upon the number of superstrings that work to comprise the overall electron, that is here to act as one respective overall orbifold eigenset, that is present at that given arbitrary electron's energy level and so forth, from within the given arbitrary atom of the said respective case. Such a set of antiholomorphic Kahler conditions, is to then to rise in so as to form a set of Lagrangian-based Chern-Simons singularities, -- of which will then bear a set of complex roots, depending upon the number of spatial dimensions that the said electron is to be going through, as it is here to be traveling in a back-and-forth manner over time.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Showing posts with label complex roots. Show all posts
Showing posts with label complex roots. Show all posts
Thursday, March 8, 2018
More About Discrete Residual Energy Released As Photon
Posted by
samsphysicsworld
at
2:01 PM
0
comments
Labels:
atom,
Chern-Simons,
complex roots,
electron,
energy,
Kahler conditions,
Lagrangian,
orbifold eigenset,
spatial dimensions,
Ward-supplemental
Monday, February 19, 2018
Majorana-Weyl-Invariant-Mode Becoming Entropic
Let us consider a given arbitrary orbifold eigenset, that is here to be undergoing a tense of superconformal invariance over an initial relatively transient duration of time. The said eigenset is then to here be consequently going through a state of Majorana-Weyl-Invariance. If the directly corresponding metrical flow of the motion of the said orbifold eigenset -- as it is here to be forming a set of Lagrangian-based Chern-Simons singularities, that are here to work to bear complex roots, to where this is to here to bear a non-trivial set of assymetric Ward-Supplemental-related antiholomorphic Kahler conditions -- that are eminently non hermitian over time, then as this general tense of a Fourier Transformation is to happen, the initially stated tense of a Majorana-Weyl-Invariant-Mode will spontaneously tend to work to become entropic, as it is here to tend to then to move out of the initially stated tense of superconformal invariance.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
10:35 AM
0
comments
Labels:
Chern-Simons,
complex roots,
hermitian,
Kahler condition,
Lagrangian,
Majorana-Weyl-Invariant-Mode,
orbifold eigenset,
superconformal invariance,
time
Monday, February 12, 2018
Shimmering In Tightly-Knit Locus
If the discrete energy quanta that work to comprise one given arbitrary orbifold eigenset, are to work to bear superstrings that bear complex Lagrangian-based roots that are of a Chern-Simons nature, that are here to work to bear a relatively anti chiral symmetry, when this is in terms of the tendency of their potential holomorphic fractal of angular momentum that these said superstrings are to bear upon one another, over the so-eluded-to proscribed evenly gauged Hamiltonian metric -- then, such a respective given arbitrary orbifold eigenset is more than likely to then be of a super conformal nature -- to where its directly corresponding eigenindices will then tend to have a nature of simply shimmering, at a relatively tightly-bound proximal locus over time.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
7:05 AM
0
comments
Labels:
Chern-Simons,
complex roots,
discrete energy quanta,
eigenindices,
Lagrangian,
orbifold eigenset,
proximal locus,
superconformal,
superstrings
Saturday, January 27, 2018
What Often Works To Form Antiholomorphic Kahler Conditions
Often, what works to form an antiholomorphic Kahler condition, is the following general case scenario: Let's say that an orbifold eigenset is to initially be traveling via a Rham cohomology -- in so that it is to bear both hermitian Lagrangian-based singularities, as well as working to bear hermitian metrical-based singularities, -- as such an orbifold eigenset is to be traveling through a given arbitrary Hamiltonian operand, that is traversed via a discrete Lagrangian-based path. At a given point in time, the said eigenset is to be enacted upon by a ghost-inhibitor -- that is then to work at helping to cause the just mentioned set of discrete energy quanta that operate in so as to perform one specific function, to bear a change in the course of its Fourier-based translation, that is here to involve a Ward-Supplemental perturbation in the course of the trajectory of the projection of its ensuing given arbitrary Lagrangian-related path, over a sequential series of group-related instantons. (As an ansantz, in only two spatial dimensions -- the orbifold eigenset of this case would just go back in the direction in which it had just originally come. Yet, in this, as well as in just about any other substringular case, the directly corresponding orbifold eigenset, as well as its given arbitrary path -- will involve more spatial dimenisons than this.) The more spatial dimensions that the said orbifold eigenset is to directly bear, as well as the more spatial dimensions that the path of the said orbifold eigenset is to bear -- the more complex roots that such a Ward-Supplemental perturbation may possibly work to involve. Such a Ward-Supplemental perturbation, that may be caused by such a said ghost-inhibitor -- may often work to cause the eminent presence of a set of antiholomorphic Kahler conditions.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
2:57 PM
0
comments
Labels:
complex roots,
dimensions,
eigenset,
Fourier,
ghost-inhibitor,
Hamiltonian,
hermitian,
Kahler conditions,
Lagrangian,
orbifold,
singularities,
Ward-supplemental
Wednesday, August 2, 2017
More As To Cohomological Generation
Let us initially consider an orbifold eigenset of one given arbitrary nature, that is to work to bear an ellongated pulse -- as it is to be accelerated through a Doubolt cohomology, that is to bear both a set of metrical-based Chern-Simons singularities that are to each to bear a set of complex roots, as well as to also bear a set of Lagrangian-based Chern-Simons singularities that are to each to bear a set of complex roots, -- as the so-stated Doubolt cohomology is to be able to be extrapolated as having a mappable-tracing, that is to bear a general index of Ward-Polarization, that is to be generating a respective cohomology, that is to bear a larger resultant scalar magnitude of the formation of Gliosis-Sherk-Olive ghosts than the resultant scalar magnitude of the formation of Nielson-Kollosh ghosts. So, the general condition of a net generation of cohomological residue -- that is to be formed by discrete quanta of energy that are to work together in so as to perform one common Hamiltonian operation -- will tend to form a significantly higher scalar amplitude of a Reimman scattering, that is of the norm-state-projections that such discrete energy is to strike in a Gliosis-based manner, -- than the relative quanta of the scalar amplitude of that overall Rayleigh-based scattering, that is of the Gliosis-Sherk-Olive ghosts that are to be scattered out of the condition of cohomological generation, -- that would otherwise happen if the correlative Hamiltonian-related group-related discrete energy that is to here to act as one quantum, would work to form, if it were to, instead, to act as a group-attractor of cohomological degeneration.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
1:44 PM
0
comments
Labels:
Chern-Simons,
cohomology,
complex roots,
discrete,
Doubolt,
energy,
Gliosis,
group-attractor,
GSO ghosts,
Rayleigh,
Reimman,
Ward-polarization
Monday, July 31, 2017
As To Nature Of A Certain Substringular Perturbation
If an orbifold eigenset is to be altered out of a tense of Majorana-Weyl-Invariance -- into a net unitary-based holomorphic path, that is to be brought into a tense of working to bear an abrasive cohomological generation, then, such a perturbation out of the said state of Majorana-Weyl-Invariance -- is to be of a Rayleigh state of a scattering-based mode. Yet, if such an alteration out of a tense of Majorana-Weyl-Invariance -- into a unitary-based holomorphic path, is to be brought into a tense of working to bear a tightly-knit cohomological generation, then, such a perturbation out of the said state of Majorana-Weyl-Invariance -- is to be of a Reimman state of a scattering-based mode. In so long as those eigenstates that work to form the resultant set of those complex roots, that work to form any potential either metrical-based and/or Lagrangian-based Chern-Simons singularities, are to act in so as to be of a high tense of a Ward-Caucy-related state of bearing little to no eigenindices of oscillation-based distortion, then, the so-eluded-to tense of scattering will then tend to be of a Reimman-based nature.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
9:36 AM
0
comments
Labels:
Chern-Simons,
complex roots,
distortion,
eigenindices,
Lagrangian,
Majorana-Weyl-Invariance,
metrical,
orbifold eigenset,
Rayleigh,
Reimman,
scattering
Friday, July 21, 2017
Cyclic Permutations Involving Ward-Supplemental-Based Paths
Let us initially consider an orbifold eigenset, that is to be traveling through an initially considered discrete Lagrangian-based path. Let us say, that all of the sudden -- the said orbifold eigenset, is to be effected by the Chern-Simons-based condition of a Ward-Supplemental-based perturbation, upon the topological stratum of the holonomic substrate of the said orbifold eigenset. This will then work to cause the said eigenset, to ensue at attaining an antiholomorphic Kahler condition. Let us say that the said orbifold eigenset, is to be traveling through six spatial dimensions plus time, in this general respective given arbitrary case. So, there are actually quite a number of possibilities as to what exactly are to be the arrangement -- of those respective complex roots, that are to here to be directly associated with the here resultant antiholomorphic Kahler-based Lagrangian path. Let us next say, that the said eigenset is to then to reverberate back into one of its original parameters of homomorphism, in so as to then to work to attain an antiholomorphic Kahler-based condition, -- that may be attributed to it in the meanwhile. This to, is to be associated with one of a number of a potential sets of arrangements of those respective complex roots, that are to here to be directly associated with the here resultant antiholomorphic Kahler-based Lagrangian path. Let us next consider this general genus of activity to repeat -- in an analogous but cyclical permutative manner -- to where, over a relatively spread-out group-metric, the same Lagrangian-based paths are Not to be identically mapped-out in the same fashion -- but in such a manner, to where there are here to be an iterative cycle of a set of similar but different combinations of complex roots, that are to work here in so as to help at working to form similar but different combinations of the resultant antiholomorphic Kahler-related Lagrangian-based paths.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
9:35 AM
0
comments
Labels:
Chern-Simons,
complex roots,
cyclic permutation,
holonomic substrate,
Kahler conditions,
Lagrangian-based paths,
orbifold eigenset,
topological stratum
Wednesday, July 19, 2017
Degenerative Cohomologies
Any one said given arbitrary degenerative cohomology, will tend to be exclusively of a Doubolt nature. Such a respective said general tense of a degenerative cohomological index, will tend to be both of an attenuated pulsation, as well as the condition that such a general genus of a cohomological metric -- will always tend to bear metrical-based Chern-Simons singularities, in the form of the directly corresponding complex roots, that are to be correlative to the corresponding perturbation in the Fourier translation of those eigenstates -- that have to had here just increased in the scalar magnitude of their metrical instability, over time. Fourier-based transformations, that are to involve a degenerative cohomological index -- will often tend to also work to bear what would here be the presence of Lagrangian-based Chern-Simons singularities, that will here have more to do with an assymptotic approximation to what would otherwise be of a Rham-based cohomological index, than if the resultant Lagrangian-based path were to instead to be of a hermitian-based nature -- due to the general Ward-Cauchy-based condition, that such a degeneration will often tend to bear such a dampening of the metrical-based singularities -- that will as well help at working to cause the formation of a set of potential complex Lagrangian-based roots, via the resultant space-time translation that would here be imbued upon the holonomic substrate of the correlative Hamiltonian operand, that would thus be potentially formed over time, to where such Njenhuis singularities are here to be formed by the resultant Ward-Supplemental motion of the external core-field-density-related eigenindices of the respective Calabi-based manifold -- that had just been translated into a directly corresponding antiholomorphic Kahler condition, upon what would have initially been the presence of a relatively Njenhuis topological substrate of Hamiltonian operand space-time-fabric phenomenology.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
1:01 PM
0
comments
Labels:
attenuated,
Chern-Simons,
cohomologies,
complex roots,
dampening,
eigenstates,
energy,
Hamiltonian operand,
Kahler,
Lagrangian,
metrical,
Njenhuis,
Ward-supplemental
Tuesday, July 18, 2017
Multidimensional Kahler-Metric And Instability In Proximal Local Field
Let us initially consider an orbifold eigenset -- that is to here to be comprised of the holonomic substrate of the Ward-Cauchy-based phenomenology of bosonic superstrings, that are to here to be moving through ten spatial dimensions plus time -- through a relatively discrete Lagrangian, over time. Let us next say, that the so-stated orbifold eigenset is to soon be perturbated into then working to bear an antiholomorphic Kahler condition. The potential resulting Ward-Supplemental "reverberation" of the so-eluded-to topological substrate, that is of the said orbifold eigenset, may then tend to work to bear significantly more potential complex roots, as to the mappable-tracing of the resultant potential world-sheets -- that is related to what I mean of as to the potential mapping-out of the Lagrangian-based path of the so-eluded-to "reverberation," that will here be of the so-stated Kahler-Metric, -- than if the said orbifold eigenset were to, instead, be traveling through only three spatial dimensions, plus time, -- in the process of working to undergo the Kahler-Metric in a Gliosis-based manner, in such a way that would then be initiated upon those superstrings that are to here to work to comprise the said orbifold eigenset. This would then work to mean, that the more spatial dimensions that an orbifold eigenset is to be traveling through -- in the process of going through an antiholomorphic Kahler condition -- the more of a tendency that there will then be, of the condition of there then being a higher scalar magnitude of the proximal local related topological instability of the directly corresponding Hamiltonian operand that is to here to be considered at the Poincare level, in the process of the perturbation of the resultant mapped-out Lagrangian-based path, than if there were, instead, to be an antiholomorphic Kahler condition that were to be traveling through fewer spatial dimensions, over time. I will continue with the suspense later!
To Be Continued! Sincerely, Samuel David Roach.
To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
5:30 PM
0
comments
Labels:
antiholomorphic,
complex roots,
instablility,
Kahler-Metric,
Lagrangian-based path,
orbifold eigenset,
perturbation,
strings,
Ward-Cauchy
Saturday, May 13, 2017
More As To Kahler-Based Roots
Let us consider an orbifold eigenset, -- that is to initially be in an anharmonic perturbative Ward-Caucy-based condition of kinematic reverberation -- as it is going through a correlative entropic Fourier-related transformation. Let us next say, that a group-attractor is to then to be introduced into the proximal local region, in which the said orbifold eigenset is to be of the general condition of being in an initially anharmonic scattered condition. Next, let's say that the correlative group-attractor that had just become Yukawa to the Ward-Caucy region, in which the so-stated orbifold eigenset was to here be differentiating in a chaotic manner -- is to help at working to cause a general genus of wave-tug, that is to then to work to cause a harmonic scattering of the eigenindices of the eigenstates of the said orbifold eigenset -- to where there is to then be the Wess-Zumino condition of a Reimman scattering of the core-field-density of the Gliosis-based topological sway of such eigenstates, that are here to be at the Poincare level. Let's then say, that over an ensuing relatively transient sequential series of instantons, that the so-stated orbifold eigenset is to then to be tugged-out of its so-eluded-to relatively tightly-knit tense of a Majorana-Weyl-Invariant-Mode, -- to where it is to then be propagated with an even acceleration, across a smoothly harmonic oscillatory-based path. Let's next consider, that the said orbifold eigenset is of a mass-bearing integration of Yau-Exact eigenstates, that are to here to work together, in so as to form a discrete Hodge-Index of Reimman-based gravitational eigenindices, that are here to be propagated in a hermitian manner, over the ensuing duration of a sequential series of group-related instantons. Such an orbifold eigenset will tend to not bear -- neither any metrical-based Chern-Simons singularities, nor any Lagrangian-based Chern-Simons singularities. In so long as there is no eminent collision here, that would otherwise act in so as to work to help at forming the Cevita condition of what would here be a resultant Rayleigh scattering of such a Yau-Exact tense of a mass-bearing radiation, the harmonic flow of the composite eigenindices -- that had worked to comprise the said orbifold eigenset, will not spontaneously tend to bear any complex Kahler-based roots.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
3:34 PM
0
comments
Labels:
Chern-Simons,
complex roots,
eigenstates,
Fourier,
instantons,
Kahler-Metric,
Majorana-Weyl-Invariant-Mode,
orbifold eigenset,
Ward-Caucy
Thursday, May 11, 2017
Cohomologies And Kahler-Based Roots
When a cohomology is of a Rham-based nature -- it tends to work to produce Real Reimmanian Kahler-based roots, -- yet, when a cohomology is of a Doubolt-based nature, -- it tends to work to produce complex Kahler-based roots.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
Posted by
samsphysicsworld
at
10:39 AM
0
comments
Labels:
cohomology,
complex roots,
Doubolt,
Kahler-Metric,
Real Reimmanian,
Rham
Tuesday, February 14, 2017
Reverberations And The Kahler-Metric, Part Four Of Four
Let us initially consider a set of three relatively adjacent electrons, that are to initially reverberate through one general Stoke's-related Lagrangian-based Hamiltonian operand, -- in a reiterative manner that is to maintain its general tense of velocity, in a relatively transient duration of group-related metric. Let us next consider that, after the reverberation that I have just generally described, is to have reverberated a certain discrete number of times in a back-and-forth manner, -- to where the general plane of reverberation is to then adjust in a vibratory oscillation-based manner, by a Ward-Caucy-related degree of orphoganation. Let us next say that, once the general plane of orphoganation of the so-eluded-to set of three orbifold eigensets is to then reverberate in that so-eluded-to Stoke's-based Minkowski-related plane of regional eigenindices, this will happen to where these orbifold eigensets will act as eigenstates, of which are of a sequential series of back-and-forth reiterations that are to work here to bear a relatively constant velocity. Let us then consider that the second inferred rate of reverberation that is to here exist in the second said tense of orphoganation is to bear both the same general manner of a Noether-based flow, and as well as also working to bear the same general manner of Majorana-Weyl-Invariance in its holomorphic tense of directoral-based flow, as the initial tense of reverberation that was to exist in the initial tense of orphoganal-based back-and-forth flow was to bear -- in both its general manner of Noether-based flow and the same general manner of its Majorana-Weyl-Invariance, -- over what may here be described of as a tense of a metrical-based reverse-fractal of a "Sterling Approximation" of the tense of the flow of the second stated genus of reverberation in relation to the flow of the first stated genus of reverberation. The Lagrangian-based Kahler quotients that are to here be used to compare the Yukawa-based interactions of the general Kahler-Metric eigenstates of the second said reverberative state, will then tend to bear complex roots -- when this is taken in relation to the first said reverberative state, and vice-versa, when the so-stated reverberations are to be compared to each other in an isomorphic manner -- that is to here be metrically overlapped as a conjugate dual group-metric, -- in which the trivial permutations are to here be omitted. I will continue with the suspense later! To Be Continued! Samuel David Roach.
Posted by
samsphysicsworld
at
11:35 AM
0
comments
Labels:
complex roots,
eigenstates,
holomorphic,
Kahler-Metric,
Noether Flow,
orbifold eigensets,
strings,
Yukawa
Saturday, January 21, 2017
More As To Real Versus Njenhuis Doubolt Cohomologies
The lower that the genus is, that is to here be directly associated with the Fourier-based activity of a Rham-based cohomology -- that is to then be formed into a Doubolt-based cohomology -- via the kinematic-based formation of a relatively low genus of an eigenstate of a Chern-Simons singularity, the more that there tends to be the proximal local Ward-Caucy-based condition of the state of homotopic torsional eigenindices, -- that are to here to bear Real Reimmanian or euclidean roots, instead of then working to bear Njenhuis or complex roots. Furthermore -- the higher that the genus is, that is to here be directly associated with the Fourier-based activity of a Rham-based cohomology -- that is to then be formed into a Doubolt-based cohomology -- via the kinematic-based formation of a relatively high genus of an eigenstate of a Chern-Simons singularity, the more that there tends to be the proximal local Ward-Caucy-based condition of the state of homotopic torsional eigenindices, -- that are to here bear Njenhuis or complex roots, instead of then working to bear Real Reimmanian or euclidean roots. I will continue with the suspense later! To Be Continued! Sincerely, Sam Roach.
Posted by
samsphysicsworld
at
8:21 AM
0
comments
Labels:
cohomology,
complex roots,
Doubolt,
Fourier,
homotopic torsional eigenindices,
Rham,
Ward-Caucy
Friday, January 13, 2017
Alternative Kahler Conditions
Let us initially consider one given arbitrary orbifold eigenset, that is moving in a reverberation -- via a relatively rectangular Lagrangian-based path, that moves at its corners towards the relative left -- as the said respective orbifold eigenset will work here to keep iterating in this case scenario, as a holonomic substrate that acts in a manner that is cyclical as a Hamiltonian operator that behaves in a permutative tense, per each succeeding individually taken cycle of such a so-eluded-to reverberation. Let us as well, consider that -- at an external reference frame -- the self-same orbifold eigenset is to reverberate from going into the relative "up" directorial-based direction towards then going into the relative "down" directorial-based direction, as a tensor that is behaving as such a so-eluded-to metrical-gauge-based Hamiltonian operator, over the course of the same group-metric in which such a said eigenset is to be moving via an iterative entity of reverberation, that cycles to the relative left at each succeeding corner of its Fourier-based flow, at what would here be more of an internal-based reference frame. As eluded-to before in earlier posts, that group-attractor that is most Yukawa to the course of action that is here to be utilized, in so as to work to allow for the just mentioned "up-and-down" tensoric reverberation, acts in a chiral-based manner -- in so as to help in working to allow for the said "upward" motion of the so-stated orbifold eigenset, whereas, that self-same group-attractor that is most Yukawa to the course of action that is here to be utilized, in so as to work to allow for the just mentioned "up-and-down" tensoric reverberation, acts in an antichiral-based manner -- in so as to help in working to allow for the said "downward" motion of the said orbifold eigenset. Again as eluded-to before, the so-stated relative chiral tendency will tend to work to form torsional eigenindices, that bear singularities that are of Real Reimmanian roots, while the so-stated relative antichiral tendency will tend to work to form torsional eigenindices, that bear complex roots. This alteration of the so-stated orbifold eigenset, from first going into the relative norm-to-forward-holomorphic direction, while then going into the relative norm-to-reverse-holomorphic direction -- will tend to work to form an antiholomorphic Kahler condition, that is proximal localized to certain superstrings that are Yukawa to that Ward-Caucy-based environment -- that is just external to the immediate internal reference frame of the left-tending reverberative flow of the said orbifold eigenset of this given arbitrary respective case.
I will continue with the suspense later! To Be Continued! Samuel David Roach.
I will continue with the suspense later! To Be Continued! Samuel David Roach.
Posted by
samsphysicsworld
at
2:46 PM
0
comments
Labels:
complex roots,
Fourier,
Kahler conditions,
Njenhuis,
orbifold eigenset,
permutation,
strings,
Yukawa
Subscribe to:
Posts (Atom)