Geometry of String Theory Solitons

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by
Magnus Holm
Institute of Theoretical Physics
Chalmers University of Technology and Göteborg University – Göteborg 1999

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Abstract
In recent years there has been a dramatic progress in the understanding of the non-perturbative structure of various physical theories.
In particular string theory has been vastly developed during these years, where a lot of duality conjectures between the different string theories have arisen.
The introductory text of this thesis is an attempt to describe this development in short and to make a brief overview of the subject.
Special focus is put on solitonic solutions in various field theories, which is the corner stone for these duality conjectures.
The introduction of supersymmetry is also essential for the understanding of duality by its natural way of handling BPS-states through the algebra.
In string theory, which is not only a supersymmetric theory but also includes gravity, these studies are put together through the discovery of various p-brane solutions to the background field equations.
The geometrical structure of these solutions is studied in some of the papers in this thesis.
In a generalization to the treatment of p-branes as solutions which break the local vacuum symmetry, the theory of almost product structures (APS-theory) has arisen as the natural candidate to the study of the intricate geometry of these solutions.
The last two papers deal with this ansatz where it is also seen that APS-theory is the most natural way of treating all kinds of splitting of manifolds including fibrations, Yang-Mills theoryand Kaluza-Klein theory.
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399 comments to Geometry of String Theory Solitons

  • Andrea Rossi

    Eernie1:
    Thank you for your insight.
    As you know, I cannot disclose any particular related to what happens inside the reactor.
    Warm Regards,
    A.R.

  • eernie1

    Dear Andrea,
    Since we are in a holding pattern and have free time awaiting the results of the TPR, I would like to offer some reasons for my insistence that electron capture must be involved in at least a few mechanisms in LENR(not necessarily your effect). We know that in naturally occurring LENR(radioactivity) the most prevalent process involves either electron or positron emission in which many are triggered by electron capture. These processes produce energies which can be used for many purposes. Also we know that no stable atoms above Uranium are detected in nature. One reason for this is that when enough protons are present in a nucleus the positive fields attract the orbital electrons into the nucleus causing enough instabilities to cause decay to occur. When radioactive atoms are fully ionized their half lives are extended because of the absence of orbiting electrons. All these effects have been documented by experimental evidence.
    As atoms increase in proton number the inner electrons draw closer to the nucleus and in some cases pre Uranium atoms can under go electron capture spontaneously with emission of B- and B+ neutrinos and gammas of reduced energy. It is not difficult for me to envision a system where large external negative fields can be imposed on surrounding electron clouds to cause inner electrons to penetrate even stable isotopes of higher atomic number species such as the transition elements which possess volatile electron movements within their clouds. If there is an isomer present the penetrating electron can stimulate the excited nucleons further causing energy emissions. The number of possibilities for such configurations to be allowed can be large since the number of combinations of particles are enormous. This method seems to me to be much easier to attain than trying to force a proton into the nucleus or to create a neutron by combining an electron with a proton outside of the nucleus.
    Hopefully the TPR will be published before I can impose some other odd scenarios upon your readers.
    Good luck although I don’t think you need it to have a positive result.

  • Dear Andrea, what do you think of this future based on LERN? see the video.
    strength Rossiii
    https://www.youtube.com/watch?v=5fNXz6qMUeg

  • Andrea Rossi

    Silvio Caggia:
    That’ s pre- divulgation!
    Warm regards
    AR

  • silvio caggia

    Dear Steven N. Karels,
    Hands off “my” onion-cat! 😀

  • Andrea Rossi

    D. Travchenko:

    1- All scientific research and testing is only improved by having serious challengers, this is a normal part of the peer review process. I welcome those who are interested in science to come forward and volunteer their views, but objectively evaluate the theories and follow the facts as they are presented. Well- articulated debate is essential to further science and R&D efforts.
    2- I will continue to share my efforts to share the work I am doing and to make it as widely available as possible, but only at the appropriate time. Until then, I am not able to respond to those I have not worked with or those who are not directly involved in my research.
    3- I repeat: I am committed to my work for the development of the E-Cat and this must remain my focus. My sole focus.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Curiosone:
    I am committed to my research and the development of the E-Cat. This is my highest priority and it must remain my focus.
    I am not going to talk anymore about that thing.
    Warm Regards,
    A.R.

  • Curiosone

    Can you give more information about the corrupted persons that have , as you say, devastated your life 20 years ago and that could be behind this attack ?
    W.G.

  • DTravchenko

    Dear Andrea:
    1- will you be open to further peer reviewing after the publication of the report?
    2- will you be able to share your work and the work of your team with us, to make us better understand how an E-Cat is born?
    3- we have links to disclose who is paying for the attack made against you.
    From Russia, with love,
    D.T.

  • Andrea Rossi

    Steven N. Karels:
    1- I cannot give this information until the product is on the market
    2- see point 1
    3- would a man with 5 balls be considered a pin-ball?
    Warm Regards,
    A.R.

  • Steven N. Karels

    Dear Andrea Rossi,

    You referred to the “Mouse and Cat” design for eCat control. The Mouse provides stability, runs part of the time with a relatively low effective COP. The Cat provides the large amount of output power and spends portions of its time in a self-sustaining mode. Surely you must have considered a “Mouse, Cat and Tiger” configuration. Where the Cat controls the Tiger.

    1. Can you address this possible configuration?
    2. Would stability be an issue?
    3. Could not the “Mouse and Cat” subsystem be considered a “Big Mouse” to the Big Cat (Tiger)?

  • Andrea Rossi

    Bernie Koppenhofer:
    I have too much work to do to save enough of it for defending myself from a well organized libelling, made by direct and indirect competitors. I have nothing to add to what has been written on
    http://www.ingandrearossi.com
    I underline, confirm and repeat every single word of that site. The mafious system, based on corruption, that destroyed my work 20 years ago, is now terrorized that my incoming work could , if successful, put in evidence what they made 20 years ago.
    The falsities I have been reported of, regarding this pseudo- scientific broadcasting, speak for themselves ; every honest, sincere and intelligent person can understand perfectly what is behind those attacks, unleashed right before the publication of a neutral experiment whose results, positive or negative as they might be, will be anyway important.
    The experiment of the Third Indipendent Party has been made in a neutral place, not in the USA, not in Italy. I am not allowed to give any further information before the publication: obviously the precise location will be described in the report.
    Warm Regards,
    A.R.

  • Bernie Koppenhofer

    Dr Rossi: I am impressed by how positive you stay after the personal unscientific attacks by a “scientific” program. The editor of the program should be ashamed. Keep up your good very important t work. In this program it was said the tests were not being done in Sweden, can you confirm?

  • Andrea Rossi

    G. Parenti:
    No. There are no scientific bases to open a discussion. About the events that devastated my life 20 years ago, I confirm what is described in
    http://www.ingandrearossi.com
    I am making a very hard work, we are working for the diffusion of our plants, we are waiting for a dramatically important report regarding a long run test and I want not to be distracted from my work by things that will have no importance at all, either if the results of our work will be positive or if will be negative, as they might be.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Ravedoni Carlo:
    It violates the first and second thermodynamic principle.
    Warm Regards,
    A.R.

  • Ravedoni Carlo

    Signor Rossi buongiorno,
    Volevo segnalarLe (nel caso non ne fosse al corrente) un dispositivo inventato da un francese, Dumas appunto.

    Ecco qui il suo sito internet : http://leblogdejc.com/effetdumas/?page_id=165 (in English)
    http://leblogdejc.com/effetdumas (in francese).

    Si tratta di una palla in acciaio coperta da una semi sfera a una distanza di circa 1,6 mm. Alimentata da corrente che genera un sur più’ di potenza del 16 %.

    Su suo sito ci sono tutti gli appunti, e i piani per la fabbricazione del dispositivo, che Dumas mette a disposizione di tutti. Lo scopo del sig. Dumas è che chiunque si ritiene capace di sviluppare la sua invenzione, sia libero di farlo, a condizione che questo sviluppo ulteriore sia messo a disposizione di tutti. Non impedisce comunque la commercializzazione degli sviluppi futuri.

    Non so cosa se ne puo’ fare lei di questo dispositivo. Volevo solamente attirare la sua attenzione su cosa succede nel mondo.

    Approfitto dell’occasione per ringraziarla per il lavoro che sta svolgendo, e attendo con impazienza i risultati del test, che spero siano positivi.

    Ravedoni Carlo

  • GParenti

    Dr Andrea:
    We all understood that the attack against your person we saw in the last days has been a clownesque attempt to discredit your work using insults and using your vicissitudes of 20 years ago instead of a clean and honest scientific criticism; we all understood that this all was a frame up paid by your competitors. Nobody has been so stupid to take seriously this shameful frame up. Will you answer to their “arguments”?
    G. Parenti

  • Andrea Rossi

    Robert Curto:
    Thanks,
    Warm Regards,
    A.R.

  • Robert Curto

    Dr. Rossi, snow is removed from most roads, when a snow plow pushes it
    to the side of the road.
    On a city street you cannot do that, you cannot push the snow on top of
    the sidewalk.
    The snow is scooped up by a Front End Loader, loaded into a Truck and
    transported to a dump site, could be a river, or a large area.
    For example in Helsinki, Finland they need to remove 210,000 Truck Loads.
    I was wondering could E-Cat heat a big ‘bin’ that could be placed over a
    drain, located on every city block ?
    The Front End Loader could dump it’s load into the hot ‘bin’ and the snow would turn to water.
    You don’t have to boil the water, the ‘bin’ just has to be hot enough to melt
    the snow to water.
    Robert Curto
    Ft. Lauderdale, Florida
    USA

  • LMV

    Hi Andrea,

    Vietnamese government has delayed their plan to build 14 nuclear power stations. Maybe they are aware of your Hotcat development.

  • Andrea Rossi

    Steven N. Karels:
    Good idea.
    Warm Regards,
    A.R.

  • Steven N. Karels

    Dear Andrea Rossi,

    Have you considered continuous asphalt plants as an application for eCat technology? According to Wikipedia, they produce 500 Tonnes per hour of hot asphalt. Being a continuous constant load seems well suited for eCat technology. Typical asphalt temperatures are around the 200C region and are usually stored in Hot Storage before being shipped out. Conceptually, delivery truck could also be equipped with eCat units to maintain the asphalt temperature. Currently, maintaining temperature limits the distance deliveries can be made.

  • Andrea Rossi

    To our wonderful Readers:
    Congratulations and thank you for your intelligence. Useless to say to what I refer. You reaction gives evidence of the difference between intelligent people and clowns.
    God bless you all,
    Andrea Rossi

  • Wladimir Guglinski

    Joe wrote in May 27th, 2014 at 1:31 PM

    1) ——————————
    Concerning your question, my view is the following:
    Math does not create physics.
    Physics does not create math.
    But when devising a new approach, both have to be kept in mind. That is why I stated in my post to Magnus Holm that I used logical forms as a starting point. It is important to remember that logic is the foundation of our understanding of both math and physics. When working with logic, all the nonsense (“phantasmagoria”) is swept away. What remains is scientific truth.
    —————————————–

    COMMENT

    Yes, as the own Galileo had emphasized: the science cannot be divorced to the logic.

    2) ——————————–
    Do not worry, Wladimir. The physical elegance that you demand of a theory exists in my work. It is not as evident as in Quantum Ring Theory. But even you said that scientists would have to apply differential equations to your model in order that your model be complete. And differential equations can sometimes cloud the obvious physicality of a model.
    ——————————————-

    COMMENT

    I understand.
    Even because a correct mathematic approach can help the discovery of the true physical model, and to test it.

    regards
    wlad

  • Andrea Rossi

    Gherardo:
    Both. Without the help of God I could do nothing anyway.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Ing. Michelangelo De Meo:
    I do not deal with commercial issues.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Orsobubu:
    He,he,he…
    Do not worry: I will give information on this blog as soon as I will have notice of the publication, whatever the results. To hide a negative resultmixing it in the middle of minor things would be like to hidden an elephant behind a strawberry.
    Maybe somebody will get information about the publication before me, as it happened in past: I am not privileged, I will read the publication and will give information about it and I am in the USA, therefore in China they will read the publication 15 hours ahead of me. This is why I have been anticipated.
    Warm Regards,
    A.R.

  • Joe

    Wladimir,

    I thank you for reading my paper.

    Concerning your question, my view is the following:
    Math does not create physics.
    Physics does not create math.
    But when devising a new approach, both have to be kept in mind. That is why I stated in my post to Magnus Holm that I used logical forms as a starting point. It is important to remember that logic is the foundation of our understanding of both math and physics. When working with logic, all the nonsense (“phantasmagoria”) is swept away. What remains is scientific truth. And physics as it stands today has a lot of nonsense. In fact, that is in part what got me started. I did not create anything new here, I just cleaned up what was already there. In part, I used old approaches such as “form versus substance” and “static versus dynamic”. I ended up with two conceptual forms that I combined in a novel (but still logical) way. The result is an equation of which the function that you see in my paper is only a small part. And since that function seems to be viable as a descriptor of fermion masses, it would mean that the rest of my equation would be valid in describing other physical phenomena.

    So what are these two conceptual forms that I used?
    As I have already stated in my post to Magnus Holm, I will save that for another time if and when the scientific community will be interested in my work. Suffice it to say that both conceptual forms are very well attested in history as math tools in describing physical reality. They are still used today. One form exists in both classical and modern physics, as well as in engineering. And the other form exists as a very practical tool in navigation.

    Do not worry, Wladimir. The physical elegance that you demand of a theory exists in my work. It is not as evident as in Quantum Ring Theory. But even you said that scientists would have to apply differential equations to your model in order that your model be complete. And differential equations can sometimes cloud the obvious physicality of a model.

    All the best,
    Joe

  • orsobubu

    Andrea, just a curiosity. I was lurking for the previous announcement
    about the first third-party-report, published in JONP on may 19, 2013.
    I noted that some readers were faster then you on the news:
    ——
    Enrico Billi
    May 19th, 2013 at 11:27 PM

    Third party report published! I cross the fingers for you Andrea Rossi!

    http://arxiv.org/ftp/arxiv/papers/1305/1305.3913.pdf
    ——
    Italo R.
    May 20th, 2013 at 12:20 AM

    Finally, the REPORT!!
    It is GREAT!!

    http://ecat.com/files/Indication-of-anomalous-heat-energy-production-in-a-reactor-device.pdf
    ——
    Todd Burkett
    May 20th, 2013 at 12:26 AM

    Congratulations !
    On the 3rd party report!
    Are you pleased?
    ——
    Andrea Rossi
    May 20th, 2013 at 1:25 AM

    Dear Todd Burkett:
    IThank you. This is one of the most important days of my life.
    Warm Regards,
    A.R.
    ——
    The anticipation appeared buried deep inside the article “Electrical catalyst” by
    Tadej Bajda on May 11th, 2013, counting the record number of 834 comments.
    Do you plan to make the announcement yourself, this time?

    As always, beware, dear readers: I think Andrea Rossi will publish a brand new dedicated hystorical article if the report will be positive
    but it will appear again lost in the middle of another old article if it will be negative.

  • Dear Andrea, if the tests are positive (I hope so!) and the hot Cat works, will be immediately sold and marketed?
    To what extent is the industrialization?
    when do you think we will see the first Hot Cat in Italy?
    is ready for the commercial network?
    thanks

  • Gherardo

    Dott.Rossi,
    looking backward to the beginning, but with the understanding of the following researches, to you think the very first e-cat was more a serendipity success out of a methodological work or the due result of hard work?
    To explain better my question, I do remember that the solution came out of some instinct but also many trials. Were you lucky and got early results or had to go through all planned possibilities?
    Gherardo

  • Wladimir Guglinski

    Joe wrote in May 25th, 2014 at 10:31 PM

    Magnus Holm,

    I thank for responding to my question.

    It is true that particular masses of the Standard Model are a great mystery.

    Magnus Holm, I humbly provide to you for your examination and judgment, if you are so inclined, a paper that I wrote and just uploaded to the Internet a few days ago that solves the mystery of fermion masses.

    My paper (abridged version):
    https://drive.google.com/file/d/0B_rhNc9hA61_TEtWOGhRNEljQ0k/edit?usp=sharing
    ——————————————

    Dear Joe,
    I read your article, but even if your theory is correct, and it describes mathematically the fermion masses, however a fundamental question remains:

    what are the physical mechanisms underlying the mathematical description?

    Is the matter only a manifestation of mathematical equations with no physical reality ?

    Is the phantasmagoric scientific method proposed by Heisenberg the final answer for the puzzles of the physical reality existing in the Universe?

    regards
    wlad

  • Andrea Rossi

    Fabio82:
    I have not idea of the date of the publication, because it does not depend on me. The domestic E-Cat productionis not possible without a safety certification.
    Warm Regards,
    A.R.

  • Fabio82

    Dear Andrea, do you have any idea about the time between the publication of the third independent party report and the beginning of mass production and the e cat commercialisation?
    Warm regards
    Fabio

  • Andrea Rossi

    Robert Curto:
    Thank you.
    You did not send the link, but we can also Google.
    Warm regards,
    A.R.

  • Robert Curto

    Dr. Rossi and Readers, Google:
    OTEC
    Scroll down and click on:
    World’s largest OTEC power plant planned for China
    Robert Curto
    Ft. Lauderdale, Florida
    USA

  • Andrea Rossi

    Koen Vandewalle:
    1- yes
    2- we do not give information in positive or negative about the reactor operation
    3- The E-Cat has never been an easy to manufacture thing, but maybe you are right: easiness is a relative concept.
    Warm Regards,
    A.R.

  • Koen Vandewalle

    Andrea,
    A Gas-Cat, is that
    1. An E-cat device that is heated by burning some kind of fuel.
    2. An E-Cat device using a mix of Ni-powder and a gas that flows and is repeatedly cooled and heated ?

    You are teaming up with very good scientist, apparently developing theoretical and/or numerical models.
    If I understand the theory and answers from Magnus Holm, that are very well written, it seems to be way too complex to develop a model that is usefull to enhance the E-cat beyond COP’s that make other energy sources somewhat pointless.

    In case that your answer about the Gas-Cat is “2”, then a Carnot cycle may generatie the best outcome.

    A last question, for now, that comes into my mind: does the E-Cat remain an easy to manufacture device, or has it become very complex, and eventually multi-stage ?

    Kind Regards,
    Koen

  • Andrea Rossi

    Steven N. Karels:
    Interesting, we will take deeper information about this.
    Warm regards,
    A.R.

  • Steven N. Karels

    Dear Andrea Rossi,

    OTEC use the lower temperature of deep water versus the relatively hot water near the ocean’s surface. The surface water pressure is reduced and the colder water used to cool the hot vapors into distilled water. The eCat would generate the electrical power to pump the water and to reduce the pressure.

  • Andrea Rossi

    Tom Conover:
    I do not know when the report of the hird Independent Party will be published, therefore I am not able to answer you.
    We must be patient. This report will have a strong importance, whatever the results, positive or negative as they might be.
    Warm Regards,
    A.R.

  • Tom Conover

    Dear Andrea,

    On 1/20/14 Frank asked if you would also be publishing an internal report of your own internal long-term testing at some point. You replied on 1/20/14 that “Yes, it will be published after the report of the third indipendent party.”

    As we draw closer to this moment, can you comment on the timeframe that might be realistic for the publication of the internal report that many of us that are also interested in? (+/-) 🙂

    Thank you so very much!

    Tom Conover

  • eernie1

    Dear Magnus,
    It is not surprising that many adhoc explanations are proffered for the description of physical spaces because of the complexities inherent in our limited ability to visualize multidimensional manifolds. Empirical evidence available to me suggests that I reside in a 4 dimensional Riemannian symmetry space since almost all of the visible or mental forms that I can perceive are spherical or spheroidal in three dimensional space with the other dimension time a non Abelian factor since it can only proceed in one direction(forward). When we describe particles, atoms, celestial bodies, nucleon configurations(tear drop),electron orbits and indeed the universe itself, spherical geometries are used. We also see other manifolds in a limited way in the toroidal forms of the magnetic fields of the Earth and the behavior of sun spots under the influence of its magnetic field. We also postulate the various non spherical positions of electron orbitals containing higher quantum numbers as distortions from symmetrical spheres. I feel that because of these complexities, the use of analogy in attempting to explain physical conceptions is one of the most important tools we have. When Bohr conceived his model of the atom, even though it contained a few questionable properties, it instigated the development of modern chemistry and electronic devices such as semiconductors. Perhaps a clever analogy for space forms can do the same for the next level of physical science.
    Thank you for responding to my previous blogs. These discussions bring me much pleasure.
    Regards.

  • Andrea Rossi

    Frank Acland:
    1- no, I consider it an integration that can be convenient in specific situations
    2- that maybe one of the specific situations
    Warm Regards,
    A.R.

  • Frank Acland

    Dear Andrea,

    It’s fascinating that you have a big effort to combine solar with the E-Cat.

    1. Do you consider this a more efficient alternative to natural gas or grid electricity?

    2. Or is it an alternative when the above sources are not available?

    Happy Memorial Day!

  • Joe

    Magnus Holm,

    I thank for responding to my question.

    It is true that particular masses of the Standard Model are a great mystery. From Wikipedia, in the article titled “List of unsolved problems in physics”, in the category titled “High energy physics/particle physics”, it reads,

    “Generations of matter
    Why are there three generations of quarks and leptons? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of Yukawa couplings)?”

    Again in Wikipedia, in the article titled “Generation (particle physics)”, it reads,

    “It is hoped that a comprehensive understanding of the relationship between the generations of the leptons may eventually explain the ratio of masses of the fundamental particles, and shed further light on the nature of mass generally, from a quantum perspective.”

    Magnus Holm, I humbly provide to you for your examination and judgment, if you are so inclined, a paper that I wrote and just uploaded to the Internet a few days ago that solves the mystery of fermion masses. I developed a function that uniquely determines the mass ratios of charged fermions. This means nine predicted masses to almost five significant figures (off by only 2 at the fifth significant figure). (The uncharged neutrino is a slightly different matter and I did not include it for specific reasons.) I started developing this function from only logical forms in the year 2006. I did not work backwards from present data in the Standard Model. I finally applied my function to the information in the Standard Model twelve months ago and it worked. Between 2006 and 2013, I frankly had no doubt that it would work since the logic was as solid as I could imagine it to be. (I will leave the details of the logic involved for another time.) The good news is that my function ultimately confirms the standard view of the masses of the quarks that were attained by scientists.

    My paper is only one page in length (excluding the title page). It is an abridged version of a four-page paper which offers more proof. I would appreciate your opinion on it. It is very simple to understand, and the function itself can be easily graphed. (Here is the trick. Overlap three curves on the graph: one with positive q; one with negative q; and one with q = 0. The points where the positive q and negative q curves overlap is where the masses are identical (obviously) and therefore are particle-antiparticle pairs of second and third generations of any of the three families of charged fermions. The first generation of particle-antiparticle pairs is found at the unique points where all three q curves overlap.)

    My paper (abridged version):
    https://drive.google.com/file/d/0B_rhNc9hA61_TEtWOGhRNEljQ0k/edit?usp=sharing

    All the best,
    Joe

  • Andrea Rossi

    Frank Acland:
    This vast undertaking comes from the necessity to see the future of the E-Cat projected in all the most convenient fields.
    Warm Regards,
    A.R.

  • Dear Joe,

    Particle masses is probably the biggest enigma out there. Even if it really was the Higgs Boson of the Standard Model that was detected in LHC we still have no clue on how to calculate the particle masses theoretically. This is something a fundamental theory would be able to. Having said that I also attacked the Standard Model of not being fundamental, but it is the best we have so far.

    Best regards,
    Magnus

  • Frank Acland

    Dear Andrea:

    You have mentioned recently working on using natural gas as relatively inexpensive input for the E-Cat, so it’s interesting now that you are doing R&D combining the E-Cat with solar plants — what is the reason for this vast undertaking?

    Many thanks,

    Frank Acland

  • Dear eernie1,

    Thank you for your questions. Regarding M-Theory there are many interpretations, one of them is that D-Branes, those p-Branes with open ended strings attached, are multiverses and the attached strings are particles in our D3-brane universe. One should understand, though, that the extra dimensions of these theories allow for so many solutions that we can more or less create what fields we like in the 4-dimensional subspace that describes our visible universe. When it comes to choices of internal spaces it is very adhoc and one usually look at spaces that break enough supersymmetry to represent the particle families of the Standard Model and with isometry groups containing the U(1)xSU(2)xSU(3) Gauge Fields. Calabi-Yau is a good candidate for this.

    Best regards,
    Magnus

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