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  1. #1 JOURNALS?? 
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    Please help. I have mathematics and physics articles.
    and the journals does not acknowledge receipt of my papers.

    My papers on the following topics:

    Vector Product in > 3D
    New Integration Technique

    have been accepted by a few individual post graduates (proof of some of this is on the forum).

    I have also answered all the questions posed on my paper on:

    Non-Square Determinants.

    I need Einstein to vouch for me: look at his notebook on General Relativity: on the first page he states a 4D vector product formula that he didn't complete, so he must have thought it would be important. Doesn't it indicate that he might have changed his search to some method not requiring a 4D vector product?

    Other articles include:

    Graphical (approximate geometrical) Model for Nuclear Structure,

    Neutron Decay,

    Collatz (3x + 1) Conjecture,

    Riemann Hypothesis (I actually made progress)

    Simpler form for Electro Magnetic 4-force.


    It also matters what isn't there - Tao Te Ching interpreted.
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  3. #2 Re: JOURNALS?? 
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    Quote Originally Posted by talanum1
    Please help. I have mathematics and physics articles.
    and the journals does not acknowledge receipt of my papers.

    My papers on the following topics:

    Vector Product in > 3D
    New Integration Technique

    have been accepted by a few individual post graduates (proof of some of this is on the forum).

    I have also answered all the questions posed on my paper on:

    Non-Square Determinants.

    I need Einstein to vouch for me: look at his notebook on General Relativity: on the first page he states a 4D vector product formula that he didn't complete, so he must have thought it would be important. Doesn't it indicate that he might have changed his search to some method not requiring a 4D vector product?

    Other articles include:

    Graphical (approximate geometrical) Model for Nuclear Structure,

    Neutron Decay,

    Collatz (3x + 1) Conjecture,

    Riemann Hypothesis (I actually made progress)

    Simpler form for Electro Magnetic 4-force.
    I cannot offer you much comfort. The notion of a vector cross product in dimensions higher than 3 is already well-known. It comes up in treatments of differential forms. However, the kicker is that it is not a simple product of two objects but is a product of n-1 objects (so an ordinary binary operation in dimension 3). You can see this notion in Mike Spivak's little book Calculus on Manifolds Thus I think it lkely that your submission on a higher dimensional vector product will not make it past the desk of the editors.

    What is the nature of your new integration technique ? Unless it is very new, very different, and very rigorously proven it too will probably not make it past the editor.

    To which journals did you make your submission ? As an unsolicited article, they are under no obligation to send you any confirmation, and may or may not do so at their discretion.

    Generally speaking, mathematics journals receive more submittals than they can publish and select articles on the basis of the importance of the results contained in the article, importance as judged by the editors and the referees. Papers that are correct, but are not of sufficient importance or present results that a referee might find as "obvious" may not be accepted.

    I suggest that before you spend much time on a "non-square determinant" you take a hard look at what is already known about determinants and Grassman algebras in general. http://en.wikipedia.org/wiki/Exterior_power

    What you are going to find is that topics published in research mathematics journals are generally not topics that are readily understood by non-specialists, and that notions accessible to non-specialists have usually been investigated in a detail by the professionals already, leaving little left of a publishable nature.


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    Are the editors even Mathematicians? How do I get it solicited? I have the advice from
    a professor at University of South Africa to send the vector product article to a good journal
    - he checked it and wrote that the value would be in the newness of it. I sent this one to
    American Journal of Mathematics and earlier to Linear Algebra and it's Applications at
    Elsevier.

    The n -1 thing is considered (my generalisation is a product of 2 vectors in >3D) not the
    generalisation that fills up the determinant (you cannot find a vector orthogonal to two 4D
    vectors with this definition). They probably looked at the title and tossed it away, though
    I did say it is of 2 vectors in the title. The wedge product is the alternation of the vector
    product it has 13 instead of 31 in the 3D case.

    There is not much to the proof of the itegration technique, it is a three liner. I posted it
    last year on this forum. No one complained that it was already done or wrong.

    The specialisation may be necessary for some type of advance but there is much to be
    found that are rather basic, especially in Graph Theory, and there is almost nothing about
    2D patterns in general and superpositions/extensions of patterns.
    It also matters what isn't there - Tao Te Ching interpreted.
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  5. #4  
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    Quote Originally Posted by talanum1
    Are the editors even Mathematicians? How do I get it solicited? I have the advice from
    a professor at University of South Africa to send the vector product article to a good journal
    - he checked it and wrote that the value would be in the newness of it. I sent this one to
    American Journal of Mathematics and earlier to Linear Algebra and it's Applications at
    Elsevier.
    The editors of journals are not only mathematicians, they are generally very strong research mathematicians.

    If your result is really that good, you might try getting the professor who reviewed it for you to write a letter of recommendation for the piece and send it along with your draft.

    The American Journal of Mathematics is one of the best journals, and pieces selected for publication in that journal usually have to meet quite a high standard of originality and importance.

    The n -1 thing is considered (my generalisation is a product of 2 vectors in >3D) not the
    generalisation that fills up the determinant (you cannot find a vector orthogonal to two 4D
    vectors with this definition). They probably looked at the title and tossed it away, though
    Sure you can. In fact you can find a vector orthogonal to any 3-dimensional subspace that contains your two vectors.

    I did say it is of 2 vectors in the title. The wedge product is the alternation of the vector
    product it has 13 instead of 31 in the 3D case.
    What does it mean that "it has 13 instead of 31" ? The wedge product, also known as the exterior product, is a bit more general than the vector cross product. Take a look a the subject of Grassman algebras or exterior algebra, or just differential forms.

    There is not much to the proof of the itegration technique, it is a three liner. I posted it
    last year on this forum. No one complained that it was already done or wrong.
    I haven't seen this technique, but if you can do it in only 3 lines I would infer that an editor might consider it to be either trivial or obvious. There is not much call for publication of integration techniques.

    The specialisation may be necessary for some type of advance but there is much to be
    found that are rather basic, especially in Graph Theory, and there is almost nothing about
    2D patterns in general and superpositions/extensions of patterns.
    There are journals devoted to graph theory and journals that publish quite a bit of graph theory along with other mathematics. You are wrong in thinking that graph theorists are not specialists in their own right, with some rather sophisticated techniques. I think you underestimate the sophistication of the subject and the depth required for a result to be considered interesting, novel and important.

    .
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  6. #5  
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    Quote Originally Posted by talanum1
    Are the editors even Mathematicians? How do I get it solicited? I have the advice from
    a professor at University of South Africa to send the vector product article to a good journal
    - he checked it and wrote that the value would be in the newness of it. I sent this one to
    American Journal of Mathematics and earlier to Linear Algebra and it's Applications at
    Elsevier.

    The n -1 thing is considered (my generalisation is a product of 2 vectors in >3D) not the
    generalisation that fills up the determinant (you cannot find a vector orthogonal to two 4D
    vectors with this definition). They probably looked at the title and tossed it away, though
    Part of your problem is that you sent an article to a truly high level professional research journal. The editors are quite busy and don't have the time or the charter to handle submittals from well-meaning amateurs. It would be rather like somehow getting your personal automobile onto the track during a grand prix race -- the drivers have their hands full with their own race cars. In addition to that aspect, it may be the case that they are receiving too many such submittals to be able to provide responses to all submitters.

    I suggest that perhaps you might try posting your idea on this forum, and we can give you a bit of advice once the details are in evidence.
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    Quote: Sure you can. In fact you can find a vector orthogonal to any 3-dimensional subspace that contains your two vectors.

    Please be more clear: would this orthogonal vector be in 4D? Or are you saying you can get a 4D vector and a vector
    orthogonal to any 3D subspace? The second sentence is not the same thing: mine are orthogonal in nD to two nD vectors.

    The 13, 31 comes from the indices of the vector components with positive sign (v_2u_3 etc.) after doing the product:

    23_13_12 for the wedge product

    23_31_12 for the cross product.

    They are therefore just similar products.

    The indice numbers may be extended into larger dimensions using number triangles:

    23_42
    ___34

    13_41 times (-1) on the components
    ___34

    12_41
    __24

    12_31 times (-1) on the components
    ___23

    for the 4D vector product.

    Where the first number triangle determines the rest (replace 2 with 1, 3 with 2, 4 with 3, each in the previous
    triangle), and triangle 1 extends as:

    2342__2562__2782_...
    __34__5336__7338_...
    ______4564__4784_...
    ________56__7558_...
    ____________6786_...
    ______________78_...

    It must be significant that this produces the orthogonality property, and the other properties of the 3D case. The algebra of this does not get worse and worse like the complex-quaternions-octonions sequence of algebras.

    Quote: I suggest that perhaps you might try posting your idea on this forum, and we can give you a bit of advice once the details are in evidence

    I did post the main result (see December last year). But there are more interesting things in proving the properties. I can post another summary, maybe someone can add meaningful results. I may post all of it on a web page (blog place?): the forum does not handle spaces well.

    The definition of the non-square determinant does respect the + - + - pattern of the square case and is compatible with the square case properties. It comes from the nD vector product in a natural way. Which is another reason for the nD product being natural.

    Why can't someone quote a proven reason for non-square determinants to be impossible?

    Can't they publish just the main result of the integration thecnique? Any advance must be publishable, otherwise we are shooting ourselves in the foot. It may be obvious in hindsight but not trivial since you can solve the integal of e^(t^2) with it (without the power series), (see post last year).
    It also matters what isn't there - Tao Te Ching interpreted.
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    Quote: Sure you can. In fact you can find a vector orthogonal to any 3-dimensional subspace that contains your two vectors.

    I take it then that the second sentence is what you meant by "sure you can"?

    Is there a reason why mathematics should favour 3 dimensions?
    It also matters what isn't there - Tao Te Ching interpreted.
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  9. #8  
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    Quote Originally Posted by talanum1
    Quote: Sure you can. In fact you can find a vector orthogonal to any 3-dimensional subspace that contains your two vectors.

    I take it then that the second sentence is what you meant by "sure you can"?

    Is there a reason why mathematics should favour 3 dimensions?
    I have no idea what you mean by mathematics favoring 3 dimensions. Mathematics deals with spaces of whatever dimension you might like, including infinite-dimensional spaces.

    Sometimes problems are particularly hard in a specific dimension. The Poincare conjecture in dimension 3 was extremely hard and was only solved very recently. It was solved in dimension 5 an above about forty years ago, in dimension 4 about 20 years ago. Dimensions 1 and 2 are quite easy.
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    I can't post the article now (the blog place does not behave well). If anyone wants it please send me your email adress. I have two derivations (a new one following from the determinant expansion of the cross product found at Geometric Algebra at Wikipedia). It is in RTF format. Wedge product and then Hodge contraction require more than 2 vectors in the product in 4D and larger (if it is to contract to just a vector not a k-vector).

    It leads to non-square determinants. I haven't found a reason to exclude it (after much advice on where to search for one).
    It also matters what isn't there - Tao Te Ching interpreted.
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  11. #10  
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    The derivation of the "nD Shift Permutation Vector Product" is at: http://www.physicsforums.com/.

    Navigate to Linear & Abstract Algebra, then look at the tread: "Finding a vector orthogonal to others" and scroll down. The file as an atachment to one of the replies.
    It also matters what isn't there - Tao Te Ching interpreted.
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