The equivalent of 186,986 printed pages was downloaded (681.752 memory pages or hits) from 689 distinct visits each averaging 2.8 memory pages and 8 minutes, printed pages to hits ratio of 72.76, top referrals total 2,339,589, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 896, Top ten 479, Collected Evans / Morris 330(est), Collected scientometrics 210, MJE 97, F3(Sp) 88, Book of Scientometrics 82, Collected Eckardt / Lindstrom 77, Barddoniaeth 64, UFT88 63, Evans Equations 45, Autobiography volumes one and two 44, Collected Proofs 34, Engineering Model 25, Llais 22, UFT311 22, PECE 21, CV 18, CEFE 17, UFT321 15, SCI 13, PECE2 11, ADD 9, UFT313 12, UFT314 13, UFT315 12, UFT316 8, UFT317 9, UFT318 14, UFT319 15, UFT320 16, UFT322 11, UFT323 14, UFT324 24, UFT325 18, UFT326 7, UFT327 14, UFT328 12, UFT329 11, UFT330 14, UFT331 12, UFT332 16, UFT333 7, UFT334 5, UFT335 14, UFT336 18, UFT337 3, UFT338 7, UFT339 6, UFT340 5, UFT341 13, UFT342 8, UFT343 8, UFT344 6, UFT345 15, UFT346 10, UFT347 12, UFT348 14, UFT349 11, UFT351 14, UFT352 12, UFT353 13, UFT354 18, UFT355 13, UFT356 11, UFT357 8, UFT358 17, UFT359 11, UFT360 7, UFT361 8, UFT362 6, UFT363 10, UFT364 11, UFT365 9, UFT366 11, UFT367 17, UFT368 13, UFT369 12, UFT370 14, UFT371 8, UFT372 7, UFT373 7, UFT374 6, UFT375 4, UFT376 5, UFT377 8, UFT378 7, UFT379 5, UFT380 6, UFT381 8, UFT382 21, UFT383 18, UFT384 4, UFT385 6, UFT386 10, UFT387 8, 8, UFT388 11, UFT389 10, UFT390 11, UFT391 8, UFT392 22, UFT393 25 to date in December 2017. Fudan University China UFT88; Deusu search engine photographs; Free University Berlin UFT146, ECE Article; University of Regensburg overview, University of California Irvine UFT177; University of Delaware UFT116; International Peace Bureau Namibia general. Intense interest all sectors, updated usage file attached for December 2017.

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These examples would be very useful. What about gamma sup a sub mu nu, do non zero diagonal elemnets exist for this? These are very interesting developments. So I will revert to the original Lindstrom constraint, which is a fundamental equation of physics and mathematics.

To: EMyrone@aol.com, Sent: 11/12/2017 14:22:02 GMT Standard Time
Subj: Re: Eq. (42) of UFT298

I will give some examples for non-vanishing diagonal elements of the Christoffel connection in the text book I am preparing. I will see that I can finish the first chapter over the holidays and then will send it to you as a draft.

Horst

Am 10.12.2017 um 13:14 schrieb EMyrone:

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.

The commutator, torsion and curvature are antisymmetric in mu and nu so on the diagonal:

[D sub mu, D sub mu] = – [D sub mu , D sub mu] = 0

It is fine to use the original Lindstrom constraint.

To: EMyrone@aol.com, dwlindstrom@gmail.com
Sent: 11/12/2017 14:17:38 GMT Standard Time
Subj: Re: Hayley Hamilton Theorems

The fact that the Christoffel symbol is not a tensor should only play a role as far as tensor operations are involved. In the definiton of torsion, diagonal elements are allowed:

If Gamma ^rho _ {mu mu} not equal zero,

then Gamma ^rho _ {mu mu} – Gamma ^rho _ {mu mu} = 0,

that means T^rho_ {mu mu} = 0 as required by Cartan geometry.

The commutator is built from T ans R which are tensors.
One argument for staying at the original trace antisymmetry equation is that we otherwise would obtain too many equations. The spatial spin connections are determined completely by the antisymmetry equations of the field tensor.

Horst

Am 11.12.2017 um 14:54 schrieb EMyrone:

Many thanks, it looks as if this is an exposition on the trace of a rank three object. The Christoffel connection is not a tensor as you know, because it does not transform as tensor. I think that it is safe to assume that the trace of the mixed index connection gamma sup a sub mu nu is zero, so I will revert to your original trace antisymmetry equation. .

Sent: 10/12/2017 17:01:49 GMT Standard Time
Subj: Re: Eq. (42) of UFT298

Myron, I concur. This is the first instance of the trace being mentioned that I am aware of. The invariant nature of the Trace function I think stems from the Hayley-Hamilton theorems which looks at the eigenvalues for the characteristic equation associated with an equation set. There may be some ambiguity in applying trace invariance to a form structure such as Gamma sum a sub mu sub nu when summed along the a – nu axis. There should be no difficulty however in the tensorial representation, Gamma sup rho sub mu sub nu. In this case we should get twelve trace equations, as shown in the attached. Note that not all of the equations are independent.

Doug

=

On Dec 10, 2017, at 5:14 AM, EMyrone wrote:

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.

It would be very interesting to explore the consequences of this analysis for the commutator method that defines the curvature and torsion as in UFT99. That method defines the Riemannian torsion and curvature simultaneously. The Riemannian definitions can be transformed into Cartan curvature and torsion using the tetrad, as is well known. The well known fundamental hypothesis of ECE makes the field tensor directly proportional to Cartan torsion. So in this definition, all diagonal elements are zero, as well as the trace. In the definition being developed by Doug from metric compatibility, it is not proven that the trace is zero. However the vector valued torsion two form defined by the first Maurer Cartan structure equation: T = D ^ q = d ^ q + omega ^ q is by definition antisymmetric, so all its diagonal elements are zero. The second Maurer Cartan structure equation defines the vector valued curvature two form: R = D ^ omega = d ^ omega + omega ^ omega in minimal notation. The Riemannian and Cartan curvature and torsion transform into each other as is well known. So the commutator method of UFT99 is equivalent to the fundamental structure equations of differential geometry. Metric compatibility does not enter into the commutator method, so metric compatibility is giving a new species of torsion. Trace antisymmetry comes from the connection, scalar and vector antisymmetry come from the field tensor. The safest thing to do is to use the original Lindstrom constraint.

Sent: 10/12/2017 19:07:34 GMT Standard Time
Subj: more from the tetrad postulate

Myron,Horst:
Here are some thoughts on metric compatibility, the tetrad postulate, and trace invariance that I’ve been working on. I will also append a section on total antisymmetry of the gamma connection and how that reduces equation complexity.

Doug=

gammainvariance-1.pdf

Many thanks, it looks as if this is an exposition on the trace of a rank three object. The Christoffel connection is not a tensor as you know, because it does not transform as tensor. I think that it is safe to assume that the trace of the mixed index connection gamma sup a sub mu nu is zero, so I will revert to your original trace antisymmetry equation. .

Sent: 10/12/2017 17:01:49 GMT Standard Time
Subj: Re: Eq. (42) of UFT298

Myron, I concur. This is the first instance of the trace being mentioned that I am aware of. The invariant nature of the Trace function I think stems from the Hayley-Hamilton theorems which looks at the eigenvalues for the characteristic equation associated with an equation set. There may be some ambiguity in applying trace invariance to a form structure such as Gamma sum a sub mu sub nu when summed along the a – nu axis. There should be no difficulty however in the tensorial representation, Gamma sup rho sub mu sub nu. In this case we should get twelve trace equations, as shown in the attached. Note that not all of the equations are independent.

Doug

=

On Dec 10, 2017, at 5:14 AM, EMyrone wrote:

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.

trace-equations.pdf

The equivalent of 188,191 printed pages was downloaded (686.145 megabytes) from 2,339 downloaded memory files (hits) and 653 distinct visits each averaging 3.5 memory pages and 8 minutes, printed pages to hits ratio 28.82, top referrals total 2,339,363, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 845; Top ten 408, Collected Evans / Morris 297(est), Collected scientometrics 175, MJE 92, Principles of ECE 81, Barddoniaeth 80, F3(Sp) 77, Collected Eckardt / Linstrom 63, UFT88 57, Autobiography volumes one and two 40, Evans Equations 33, Collected Proofs 31, PECE 28, CV 18, CEFE 16, UFT311 16, UFT321 14, SCI 12, PECE2 8, ADD 7, UFT313 11, UFT314 13, UFT315 12, UFT316 8, UFT317 9, UFT318 13, UFT319 14, UFT320 15, UFT322 11, UFT323 13, UFT324 22, UFT325 17, UFT326 7, UFT327 13, UFT328 12, UFT329 11, UFT330 12, UFT331 9, UFT332 16, UFT333 7, UFT334 5, UFT335 14, UFT336 17, UFT337 3, UFT338 7, UFT339 6, UFT340 5, UFT341 13, UFT342 8, UFT343 8, UFT344 6, UFT345 15, UFT346 10, UFT347 12, UFT348 14, UFT349 11, UFT351 14, UFT352 12, UFT353 12, UFT354 17, UFT355 12, UFT356 10, UFT357 7, UFT358 15, UFT359 10, UFT360 7, UFT361 8, UFT362 6, UFT363 7, UFT364 10, UFT365 6, UFT366 8, UFT367 16, UFT368 13, UFT369 4, UFT370 13, UFT371 8, UFT372 6, UFT373 6, UTF374 6, UFT375 3, UFT376 4, UFT377 7, UFT378 7, UFT379 5, UFT380 4, UFT381 8, UFT382 20, UFT383 16, UFT384 3, UFT385 6, UFT386 10, UFT387 8, UFT388 8, UFT389 10, UFT390 11, UFT391 8, UFT392 22, UFT393 24 to date in December 2017. University of Bristol general. Intense interest all sectors, updated usage file attached for December 2017.

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This server could not verify that you are authorized to access the document requested. Either you supplied the wrong credentials (e.g., bad password), or your browser doesn’t understand how to supply the credentials required.

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Myron, I concur. This is the first instance of the trace being mentioned that I am aware of. The invariant nature of the Trace function I think stems from the Hayley-Hamilton theorems which looks at the eigenvalues for the characteristic equation associated with an equation set. There may be some ambiguity in applying trace invariance to a form structure such as Gamma sum a sub mu sub nu when summed along the a – nu axis. There should be no difficulty however in the tensorial representation, Gamma sup rho sub mu sub nu.In this case we should get twelve trace equations, as shown in the attached. Note that not all of the equations are independent.

Doug

trace-equations.pdf

On Dec 10, 2017, at 5:14 AM, EMyrone wrote:

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.

This is a note on conservation of vector antisymmetry in MZ theory, before starting work on its application to chemical shift theory in ESR and NMR using the magnetic dipole potential and dipole field. The results in UFT393 for the electric dipole potential and field are already highly interesting and equivalent to a kind of shielding. The chemical shift is due to the various nuclear magnetic dipole moments in an atom or molecule. These produce magnetic fields which oppose the applied field, and result in a well known spectrum – ESR or NMR, which is 80% of chemistry. The shivering due to the vacuum affects this spectrum in a measurable way.

a394thpapernotes5.pdf

Agreed with the missing cos(theta). Eq. (39) is always true. The magnetic flux density is an axial vector which is equivalent to an antisymmetric tensor using eq. (40). So from Eq. (38):

<B> sub ij = (curl A sub 0 – <omega> x A sub 0) sub ij

is antisymmetric. In MZ theory, B, omega and A sub 0 are all known, so Eq. (38) is always true. I will give more details in the next note before proceeding to the MZ theory of the magnetic potential and field.

To: EMyrone@aol.com
Sent: 07/12/2017 14:37:12 GMT Standard Time
Subj: Re: 394(2): Application of Antisymmetry

It seems that a factor of cos(theta) has been lost in eq. (30). resolving for (delta r)^2 gives the two last equations of the protocol for omega_r and omega_theta.
Why is there a particular consideration of antisymmetry for <B> in eqs. (39-42)? I thought that the antisymmetry laws apply for (38) as usual.

Horst

Am 28.11.2017 um 15:00 schrieb EMyrone:

This note applies conservation of scalar and vector antisymmetry to the shivering electric and magnetic dipole fields. In the given approximations the mean eletric dipole spin connections are given by Eqs. (16) and (17) and the mean magnetic dipole spin connections by Eqs. (34) and (35). They are both directly proportional to the mean square fluctuations in the vacuum. So there is a close similarity with Lamb shift theory.

394(2).pdf

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.