Essay Abstract

Newton's equivalence principle states that the motion of a body solely under the influence of gravity is independent of the composition and internal structure of the body. Isotropy and Equivalence are both rejected for a more common sense approach which is justified by a non-problematic solution to the 100ky glacial cycle, based on 'plane of rotation anisotropic high energy density non-baryonic matter' at the core of heavenly bodies creating additional ocean and atmospheric tides. Should CERN's quest for the Higgs Boson become fruitless, I present nothing less than a contingency hypothesis which has the potential to seamlessly replace the current science ethos.

Author Bio

I'm a former Scientific Officer at the UK's Royal Aircraft Establishment, home of the Farnborough Airshow. I have pursued a 'jigsaw puzzle methodology' of research since childhood due my early recognition of an underlying problem within the fundamentals of physics. Only now with this essay contest can this research be given to others for critical scrutiny and hopefully some mutual enlightenment.

Download Essay PDF File

My apologies for the hiccup in the essay sentence: "The Antarctic landmass and Greenland allow for this settling of snow and ice which brings global cooling which then leads to Arctic sea ice to forming more readily". I should have asked my mother who did the PDF conversion for me to proof-read it too!

Note that the North American landmass is also important of course for the northern hemisphere due it being so large with prevailing rains compared to the southern hemisphere's circular sea island continent of Antarctica. Would the moisture laden clouds reach the southern landmass as easily as Greenland? I doubt it, hence another contributing factor to the 400,000 year cycle, the underlying 200,000 year 3D orbital cycle of up and down which either enters the earth's southern or northern hemisphere first into the Sun's exotic plane of influence.

    I just had a thought! The distribution of the earth's crust embedded exotic comets would also be critical to extra surface tides due to the either northern or southern hemisphere entry into the sun's exotic plane of influence. The Indian sub-continental plate is a prime candidate for a low angle exotic comet impact. The formerly unexplained high speed of 'drift' into the Asian plate creating the Himalayas now has an answer.

    Is the moon *really* moving away from the earth or is the earth simply moving more towards Jupiter for instance? The Hidden Exotic Matter (HEM) hypothesis opens up a mulitude of new possibilities to explore.

    7 days later

    The Higgs discovery only confirms the particle theory of physics and *doesn't* detract from the alternative view of planetary motion given in the essay.

      The Hidden Exotic Matter Hypothesis gives an alternative solution to the Moon's recession and moving away at around 3.7cm per year. The Moon is likely to have been created with a slow spin rate and quickly stopped altogether. The build-up of exotic comets on the far side, unshielded by the Earth, would give it an asymmetry which becomes apparent when in high inclination, either above or below the Earth's equatorial plane. It can be modelled as if a large exotic matter object is still descending to the HEM lunar core, on the far side, half-hidden from the Earth. In reality, many small exotic comets would be descending. I've estimated the gravitational influence of exotic matter to exotic matter attraction to be approximately 15,000 times Earth's surface gravity. This is the identical underlying process to the precession of the planets and also the cause of the 1,470 year millennial cycle of our weather imo. The present woes of the UK's jet stream positioning can perhaps be attributed to it.

        According to the Holy Bible, God said "Let there be light," and there was light. God never said, "Let there be a spark." Almighty God never spent $10 billion making a particle. Only 3,000 scientists would be so gluttonistically stupid enough to spend that amount of money looking for it. The scientists have not actually found the particle as yet. They are just sure it must be in one of the still photographs taken from running the televised tape of the particle collisions backwards that shows all of the approximately 3 trillion sparks they were able to create. They are relying on the flawed law of averages in order to prove that a picture of the particle's pathway exists in among the mass of accumulated data somewhere and they will helpingly add an arrow to the photograph pointing to where exactly the particle is supposed to be once the computer locates it. They can never show the actual photograph of the particle because it is a particle and it is invisible as are all particles. The fact that each one of the sparks and each one of the particles causing the sparks will have to differ in some way not only from every other spark and every other particle created by CERN, but each spark and each particle will also have to be different in some infinitesimal way from every other spark and every other particle that has ever been created anywhere, or that will ever be created anywhere else in the future, totally eludes all scientists everywhere. We live in one Universe once. There can only ever be one of anything once. There was only one of anything once in the past. There will only be one of anything once in the future.

        The Newtonian calculated inclination cycle of the Moon is 1800 years but it is assumed that with the HEM hypothesis at high inclination the Earth and Moon experience an additional accelerating force of attraction which increases the speed of the Moon's orbit and so gives the climate data figure of 1470 years. The Moon precesses despite it's apparent lack of spin with the HEM hypothesis.

        The effect of the Millennial cycle is enhanced due to the Moon's highly asymmetric exotic matter build-up on the far side due it's non-spinning formation.

        To summarise the theorised shape of exotic matter within the Earth, Moon and Sun:

        The Earth's hidden exotic core has a counter-intuitive rugby ball shape which is standing on end so that the Moon sees a larger x-section when traversing the equatorial plane and coincides with baryonic high tide raising forces on the millennial scale. The Sun is the opposite in having a larger x-sectional area seen at high inclinations, so that the Earth experiences extra exotic tide raising forces during the glacial period which gives global cooling due to the runaway albedo effect.

        Perhaps the Earth's exotic matter core is this shape due to a very high spin rate caused by the exotic comet impact creation of the Moon for example?

        • [deleted]

        • Post #10

        Dear Alan,

        I found your essay surprising, in part because I expected an Archimedes screw to make an appearance at any time. This was something very different. I do know that there are still discoveries to be made by science. So I should try to keep an open mind about such things as hills of exotic matter and the influence of exotic matter on planetary movements, that I know nothing about. The essay ended too soon as it was easy to read and I was enjoying it. I got to the end thinking ?OK and ?maybe and then thought but he hasn't mentioned the Archimedes screw yet! Did I miss it? I will have to wait until next year for another fascinating and perhaps equally surprising instalment. Good luck. I hope you get lots of appreciative readers as the competition progresses.

          Hi Georgina,

          Thank you very much for reading my essay and giving such encouraging comments. The shortness of the essay is just my style unfortunately. I'd like to expand on the ideas within this discussion forum if anyone is keen enough. Btw, it's still the Archimedes screw idea with exotic matter! It's simply matter which is anisotropic as opposed to Newton's isotropic matter. A bit like a two hidden core supermagnets which attract with around 15000 times the force of baryonic matter at planetary scales. It's a directional force as opposed to a force with eminates in all directions equally which therefore contradicts the notion of a space-time 'fabric'. The basics are childs play. The rewards from pursuing this line of enquiry are staggering. I never thought it would solve so much as it seems to be doing. I'm adamant that the ice age conundrum is much better served by this hypothesis. The subject in itself has a long history and can seem complicated to the uninitiated. How many cutting edge physicists know about the 5 problems with the current sunlight-only model? Not many I suspect. How many would be willing to suspect that a fundamental problem with the very first assumptions in the foundations of physics is the key to a new solution? Just one?? Only me?? I'm sure the penny will drop with someone else one day soon. I just hope it's before the CERN team throw their hands up in the air about the nature of Dark Matter though. That'd be another couple of years to wait!

          Oops!! I've made a mistake when calculating the figure of 15,000 times baryonic matter interaction. I'd assumed that the Earth's 360 mile innermost core was composed of exotic matter(!). This guesstimate fits with the estimated number and size of incident exotic comets but certainly isn't strong enough for additional planetary tidal forcing. If the central very innnermost core of exotic material is assumed to be just 1 km in diameter, keeping to a sphere shape for simplicity for now, then the estimated figure is now 1.4 million times that of normal matter. This figure appears more appropriate especially when considering the amount of physical space available when quantum modelling of particle structures. But now the question is: "Where has all the exotic comet material gone to over the Earth's lifetime??". I assume that it must have annihilated and generated the internal heat of the planet! The same thing must be happening inside the sun. The model of superhot nuclear fusion is *wrong*. It's slow cold fusion. The central very innermost cores of the Earth and Sun are likely to have been original matter from the implosion event of the initial fractal-like structures of creation. They aren't from an amalgamation starting from scratch. Maybe there is a rate of build-up of exotic comet influx against a rate of annihilation.

          This hypothesis is still in the creation phase. The pieces are still being fitted together with remarkable consistency. Please bare with me.

          Thanks Alan for an interesting set of ideas - although I second Georgina's complaint that you could have expanded on your meanings, giving examples, references etc. Yes I remember the Archemides screw idea - very clever though I objected to its application at the time! What I particularly enjoyed in this heat wave here is reference to the ice ages!

          But seriously I often wondered at gravity's action through matter layers of different density. How does it 'work' ? It is as if matter is both transparent to gravity and not transparent to it! I think the action of rotating nodes in my Beautiful Universe (BU) theory explains that puzzle nicely, and at the same time explains the Holographic Principle in a physical way. The rotating nodes locked up in the envisaged polyhedral patterns making up matter form a 3D linkage. Gravity is the extension of this rotation into the nodes making up the extended ether surrounding matter. So when another piece of matter causes these nodes to untwist see Fig. 18 of my (BU) 2005 paper it acts on the surface nodes of matter and the effect is resisted within matter internally. It needs to be worked out!

            Thank you Vladimir for appreciating some of the ideas that I'm presenting for the first time. The essay could have done with some expansion, agreed, but I wanted to keep to the absolute nub of the argument of which I'm trying to convey. In addition, my methodology was destined to conclude with a zen-like picture of how everything works, so it's still in an abstract phase. I assume you must be in the east states because here in the UK where the jet stream has dropped bringing wet chilly weather, we're *preying* for a heatwave. It's more likely to be the millennial cycle rather than the ice age incidentally.

            You say "It is as if matter is both transparent to gravity and not transparent to it!", and yes, I totally agree that this needs some clarification. I did look at your website and the diagrams looked very familiar. I haven't fully absorbed your BU theory but agree that it's the kind of modelling that is needed. How do you feel about the concept of saturated maximum energy density matter who's gravitational attraction is dependent on it's x-sectional area, rather than the amount of material?? This assumes that the surface can't emit any more force carrying particles and is at it's maximum limit, so therefore it doesn't matter how much material is behind it at that moment relative to another body of maximum energy density material. This is at the crux of my idea for additional exotic matter tidal forcing.

            I even had the idea that the Artic basin is the impact site of the proto-moon collision and that the event tipped the Earth by 90 degrees and kept in place by the orbit of the newly formed satellite.

            The Spring Tides can now be also be thought of as additional exotic matter tides due to the moon lying along the equatorial plane. The moon and the sun are aligned every two weeks which result in spring tides; tides that are 20% higher than normal. The exotic matter hypothesis now adds another dimension. It's the same idea as gravity 'kicks' explained by Prof Cox as the mechanism needed to understand the Saturn's rings and the sheperding effects of it's moons. He failed to explain how this could be managed without violating Newtonian laws incidentally(!).

            ! I had another thought too w.r.t the 'missing' exotic comet build-up in the Earth's core which I talked about earlier. If the moon's calculated 1800 year orbit is now reduced to 1470 years, which fits with the field data, doesn't it mean that the Earth's 100,000 year glacial cycle is similarly over estimated?? The planet should speed up during the non-interglacial period which we appear to be still in and so would drastically reduce the figure to something more like 50,000 years wouldn't it?? Possible? More thought needed on this one..

            My latest thoughts:

            They're *all* amalgamations of 'isotropic saturated matter'. The galactic centre, the stars and the planet exotic matter cores. It's isotropic, but not as we know it. It radiates attractive force carrying particles equally in all directions from it's surface, but is dependent on size of surface areas to determine force of interaction between two exotic matter bodies. Note that the underlying Archmides screw analogy still applies, so matter is really anisotropic, which is seen at the quantum level.

            The moon was created from the collision of another early planet with the earth. This left the incoming planet as a moon after the impact event, which tilted both bodies by 90 degrees so that each kept the other in this on-end configuration. The earth's and the moon's exotic matter cores shaped like central bulging disks were tipped onto their ends. The orbit of the two then changed the shape of the conglomerate cores and moulded them into rugby ball shapes. When the moon is on the earth's equator the surface area 'seen' by both is at a maximum and so gives the extra 20% tidal kick. I've done a quick sketch for illustration purposes. See attached.

            The rate of exotic matter comet impacts is likely to be much higher in the past due to remnants from the 'big bang' implosion event. When all this debris is consumed by stars then only supernovae remnants are a source of incoming exotic comets.

            The Late Heavy Bombardment is a clue to this new way of thinking imo.Attachment #1: Exotic_Cores.jpg

            This model predicts that after the creation of the moon, tidal strength would have gradually increased due to the morphing of the conglomerate exotic cores into rugby ball shapes. Please see diagram attached.Attachment #1: Exotic_Core_Morphing.jpg

            The moon's creation via the current Giant impact hypothesis has many problems.

            [quote]The giant impact hypothesis is the currently-favoured scientific hypothesis for the formation of the Moon.[3] Supporting evidence includes: the identical direction of the Earth's spin and the Moon's orbit,[4] Moon samples which indicate the surface of the Moon was once molten, the Moon's relatively small iron core, lower density compared to the Earth, evidence of similar collisions in other star systems (which result in debris disks), and that giant collisions are consistent with the leading theories of the formation of the solar system.

            There remain several questions concerning the best current models of the giant impact hypothesis, however. The energy of such a giant impact is predicted to heat Earth to produce a global 'ocean' of magma; yet there is no evidence of the resultant planetary differentiation of the heavier material sinking into Earth's mantle. At present, there is no self-consistent model that starts with the giant impact event and follows the evolution of the debris into a single moon. Other remaining questions include: when did the Moon lose its share of volatile elements; and why Venus, which also experienced giant impacts during its formation, does not host a similar moon.[end quote]

            The exotioc very innermost core hypothesis seems to help in an explanation imo. The core of the moon would be lost to the bigger exotic core of the earth, taking most of the iron with it. The impact collision would have to be modelled totally differently and therefore likely to produce an event at a lower temperature, hence solving the 'magma ocean' conundrum.Attachment #1: Giantimpact.gif

            The compositional problems suggest to me that there was no second proto-planet Theia, only an exotic comet impact which stayed with the core of earth but whose energy ejected surface matter into orbit.

            [quote]There are a number of compositional inconsistencies that need to be addressed.

            The ratios of the Moon's volatile elements are not explained by the giant impact hypothesis. If the giant impact hypothesis is correct, they must be due to some other cause.[16]

            The presence of volatiles such as water trapped in lunar basalts is more difficult to explain if the Moon was caused by an impact which would entail a catastrophic heating event.[17]

            The iron oxide (FeO) content (13%) of the Moon, which is intermediate between Mars (18%) and the terrestrial mantle (8%), rules out most of the source of the proto-lunar material from the Earth's mantle.[18]

            If the bulk of the proto-lunar material had come from the impactor, the Moon should be enriched in siderophilic elements, when, in fact, it is deficient in those.[19]

            The Moon's oxygen isotopic ratios are essentially identical to those of Earth.[2] Oxygen isotopic ratios, which may be measured very precisely, yield a unique and distinct signature for each solar system body.[20] If Theia had been a separate proto-planet, it probably would have had a different oxygen isotopic signature than Earth, as would the ejected mixed material.[21]

            The Moon's titanium isotope ratio (50Ti/47Ti) appears so close to the Earth's (within 4 ppm), that little if any of the colliding body's mass could likely have been part of the Moon.[22][end quote]

            The last titanium isotope analysis is greatly in favour of the exotic comet hypothesis instead of Theia imo.

            I've made a new connection: The 45 degree angle of impact to create the moon deduced from simulation modelling and the 45 degree anomaly of the 360 mile diameter innnermost core! Seismic evidence for distinct anisotropy in the innermost inner core and Giant impact hypothesis

            [quote]Astronomers think the collision between Earth and Theia happened at approximately 4.53 Gya; about 30-50 million years after the Solar System began to form. In astronomical terms, the impact would have been of moderate velocity. Theia is thought to have struck the Earth at an oblique angle when the latter was nearly fully formed. Computer simulations of this "late-impact" scenario suggest an impact angle of about 45° and an initial impactor velocity below 4 km/s.[10] Theia's iron core would have sunk into the young Earth's core, and most of Theia's mantle accreted onto the Earth's mantle, however, a significant portion of the mantle material from both Theia and the Earth would have been ejected into orbit around the Earth. This material quickly coalesced into the Moon (possibly within less than a month, but in no more than a century). Estimates based on computer simulations of such an event suggest that some twenty percent of the original mass of Theia would have ended up as an orbiting ring of debris, and about half of this matter coalesced into the Moon.

            The Earth would have gained significant amounts of angular momentum and mass from such a collision. Regardless of the speed and tilt of the Earth's rotation before the impact, it would have experienced a day some five hours long after the impact, and the Earth's equator and the Moon's orbit would have become coplanar in the aftermath of the giant impact.[end quote]

            I suspect that the exotic comet impactor is still buried in the innermost core at a 45 degree angle and is non-symmetrical.Attachment #1: MoonImpactor.jpg

            I found a reference to this double peak in real climate data, Millennial-scale storminess variability in the northeastern United States during the Holocene epoch

            [quote]The pacing of storminess maxima derived from the various North Atlantic palaeoclimate records suggest a quasi-periodic cycle of 3,000 yr. Spectral analysis of our New England storminess time series reveals significant spectral power in a broad, double peak centred at a period of 3,070 yr. A similar double peak exists in the power spectrum of the GISP2 time series of aerosol deposition. Monte Carlo simulations show that the likelihood of obtaining comparable results from a composite of arbitrary lake sediment records (produced by randomly rearranging the events identified in each individual time series) is less than 1%.[end quote]

            The moon's exotic core interaction with the earth's exotic core 'slug' is likely to tilt the thick end of the wedge into the opposite hemisphere every cycle. This would have the effect of stirring the mantle more vigorously in this new hemisphere and so cause a magnetic pole reversal.

            Here's another important recent paper on the subject (19 Mar 2012) Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter-Saturn tidal frequencies plus the 11-year solar dynamo cycle

            [quote]...The demonstrated geometrical synchronicity between solar and climate data patterns with the proposed solar/planetary harmonic model rebuts a major critique (by Smythe and Eddy, 1977) of the theory of planetary tidal influence on the Sun. Other qualitative discussions are added about the plausibility of a planetary influence on solar activity. [end quote]

            The quasi-decadal ocean climate cycle can now be directly linked with the solar sunspot cycle of 11 years. Exotic matter interaction across the solar system creates a solar core wobble of tilt which affects the surface area 'seen' by the earth-moon system. The inclination cycles of the planets and their irregular exotic cores creates the subtle changes in tidal ocean strengths on this low end of the scale. All is now in place for a complete understanding and prediction of the earth's weather and climate. The climate model should start with the correct simulation modelling of the creation of the moon imo. The rest is future history.Attachment #1: SunspotCycle.jpg

            My latest thoughts:

            Distance is *not* an issue with exotic matter on planetary scales. The plane of rotation band of influence diminishes with distance on the solar scale. This has the ability to solve the spiral galaxy curve conundrum imo. It's why galaxies are in all directions and higgledy-piggledy. Exotic gravity doesn't easily exist between galaxies.

              Our planets are bound by exotic gravity. The sun contributes a planar exotic gravity band and overall the Milky Way diminishes outwards towards plane of rotation. This sets a natural maximum size for single galaxy formation. Much larger ones are coalitions. The model assumes that gravity particles which travel around a 4D universal hypersphere during the structural/energy build phase create Dark Energy, an apparent repulsive effect between galaxies. Clusters are created by irregularities in the universal sphere. This model assumes a geometrically perfect build and collapse just before the 'big bang'. (See my previous essay for clarification)

              Alan,

              Sorry for the delay to respond and thanks for your message - yes I live in Tokyo where summer is really muggy.

              BU theory is long overdue for a shorter more mathematical description - I think I had better do that, and the next step is modelling it.

              In BU there is no fixed amount of energy per node or area or volume. That allows electromagnetic intensity to occur in any one ether node or cluster of nodes. Its been some time since I have thought about it I think there must be a maximum limit of such density, though.

              Good luck with your research - zen thoughts are fine but they need to be conceptually tightened and cast in clear terms. In fact that is the Japanese planning modus operandi for new projects. Strart with fluid undefined ideas and then decide on one specific clear plan.

              Vladimir

              • [deleted]

              • Post #33

              Einstein's relativity is based on the early ideas and work on capillary action. His first paper was on this subject. Unfortunately for him, the Torsion balance used successfully to determine density variations in the earth's crust and referenced in his paper *IS NOT* sufficient to counter the exotic matter hypothesis!

              [quote]A variation of the earlier invention, the Torsion balance, the Eötvös pendulum, designed by Hungarian Baron Loránd Eötvös, is a sensitive instrument for measuring the density of underlying rock strata. The device measures not only the direction of force of gravity, but the change in the force of gravity's extent in horizontal plane. It determines the distribution of masses in the Earth's crust. The Eötvös torsion balance, an important instrument of geodesy and geophysics throughout the whole world, studies the Earth's physical properties. It is used for mine exploration, and also in the search for minerals, such as oil, coal and ores. The Eötvös pendulum was never patented, but after the demonstration of its accuracy and numerous visits to Hungary from abroad several instruments were exported worldwide, and the richest oilfields in the United States were discovered by Eötvös' Pendulum. The Eötvös pendulum was used to prove the equivalence of the inertial mass and the gravitational mass accurately, as a response to the offer of a prize. This was used later by Albert Einstein as aid in setting out the theory of general relativity...

              Eötvös' law of capillarity (weak equivalence principle) served as a basis for Einstein's theory of relativity. (Capillarity: the property or exertion of capillary attraction of repulsion, a force that is the resultant of adhesion, cohesion, and surface tension in liquids which are in contact with solids, causing the liquid surface to rise - or be depressed...)[end quote]

              Alan,

              There are so many variables not yet fully understood that affect gravity. Even to consider our place in the galaxy, some 25,000 to 28,000 LYs from the galactic core and those things that perturb sun and planets like the spiral arm rotation, our 225 million year orbit with varying massive objects in our path, and they talk of Gliese 710 approaching. All could impact gravity to some degree. Even orthodox views of gravity are not understood.

              You're going to pass on your studies to posterity?

              Jim

                Hi Jim,

                Yes, I like the sentence "Even orthodox views on gravity are not understood". Too true. Thank you for the in depth appreciation of the gravity problem we currently have. I'm adamant that the exotic matter element is missing from the mental pictures and calculations. This very first mis-assumption has confused everything imo.

                Yes, I've finished my research as far I can go on my own now. These two essays are my legacy. Someone will take up the mantle someday soon, I'm sure.

                All the best,

                Alan

                17 days later

                Sun surrounded by dark matter, claim scientists

                [quote]LONDON: Scientists have claimed that the Sun is surrounded by dark matter, a phenomenon first proposed in the 1930s by a Swiss astronomer. Researchers from the University of Zurich have developed a new theory - and built a simulation of the Milky Way to test their mass-measuring method before applying it to real data, the 'Daily Mail' reported. "We are 99 per cent confident that there is dark matter near the Sun," lead author Silvia Garbari was quoted as saying by the paper.[end quote]

                How long before they realise it *must be* at it's centre I wonder?

                  [quote]"Another possibility is a single dark matter component with an *anisotropic* velocity distribution, undergoing inelastic scattering, and possibly also elastic scattering as well. Detailed modelling will be needed to see which possibilities are viable.4"

                  7 days later

                  Hi Alan

                  I agree the Parthanon stands above pretty Hard Rock. I do like the exotic, but I didn't find any exotic stuff there. A nice bit of free thinking, but it seem you may need a deeper evidence pool to pattern match it with. I did just post a whole heap of helpful hot links to Hope Hu and He (but 'Her' not He). I hope they help.

                  Is your Archimedes screw anything like Frank Mackinson's helical gravity model? If the model is capable of being tapered at each end and can still hold water I've found a close representation of it as a soliton, formed from one of my toroidal scale invariant fractals, but translating to leave a spiral path. This has analogies wityh my Helical CMBR asymmetry model also posted there (providing the falsified solution to galaxy bars, also [still] evident in some disc galaxies).

                  Great to read your original ideas again.

                  Do try to get your head round my quite dense essay, but I warn you, it takes much focus and slow absorption to follow the logical kinetic path.

                  Best of luck

                  Peter

                  Hi Peter,

                  Yes, Frank and I have made that connection in Abraham's essay discussion. The details are still quite abstract in my analysis, but I have a very solid argument to make with regard to the ice age data and how it fits with the tidal model of Jupiter as the main driver of our weather on the 100kyr scale. Frank was gracious enough to recognise this as a new approach. I'd appreciate it if you read that interchange of ideas to give you an idea of where I'm at.

                  Thank you for the compliment. There *is* potential for us to collaborate, but I'd need you to understand the ice age data analysis and it's problems first. Maybe FQXi members can solve the whole shabang, who knows?

                  Kind regards,

                  Alan