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    I Is there any matrix equivalent for the Clifford product?

    Well, the question is in the title.
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    I What is the proper matrix product?

    It says in any textbook (for example, in classical text «Theory of matrices» by P. Lankaster) on matrix theory that matrices form an algebra with the following obvious operations: 1) matrix addition; 2) multiplication by the undelying field elements; 3) matrix multiplication. Is the last one...
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    I Which class of functions does 1/x belong to?

    For historical reasons the hyperbola always was considered to be one of the «classical» curves. The function, obviously, does not belong to C0. Apparently, is does not fit L2 or any other Lp? What is the smallest class?
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    I Principal difference between complex numbers and 2D vectors revisited

    I know this topic was raised many times at numerous forums and I read some of these discussions. However, I did not manage to find an answer for the following principal question. I gather one deals with the same set in both cases equipped it with two different structures (it is obvious if one...
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    Review of modern non-equilibrium thermodynamics theories

    Looking for thorough serious comparative review of modern generalisations of classical non-equilibrium thermodynamics of continua. I have heard about several such generalisations: 1) rational mechanics by Truesdell, Coleman, Noll. 2) extended thermodynamics by Müller (and Ruggeri). 3) the...
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    I Can the cross product concept be completely replaced by the exterior product?

    Do we really need concept of cross product at all? I always believed cross product to be sort of simplification of exterior product concept tailored for the 3D case. However, recently I encountered the following sentence «...but, unlike the cross product, the exterior product is associative»...
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    Is there place for higher order derivatives in mechanics?

    The building of theoretical mechanics can be constructed using only the first and the second derivatives (those of coordinates in case of kinematics: velocity and acceleration and those of energy in case of dynamics: force and gradient thereof). It is obviously unavoidable if one wants to deal...
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    Analogies between temperature and time in thermodynamics

    Looking through the book of abstracts for «XXI International Conference on Chemical Thermodynamics in Russia (RCCT-2017)» I came across the abstract of talk given by Peter Atkins (University of Oxford) titled «Thoughts about thermodynamics» (you'll find the whole abstract at the end of the...
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    I What is difference between transformations and automorphisms

    Could you please help me to understand what is the difference between notions of «transformation» and «automorphism» (maybe it is more correct to talk about «inner automorphism»), if any? It looks like those two terms are used interchangeably. By «transformation» I mean mapping from some set...
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    Can't find the home page for specific journal (non-trivial case)

    For the first time in my lime I am not able to find home page for well-known and respected western periodical. I am looking for the paper titled «Définition covariante des équilibres thermodynamiques» by J. M. Souriau published in Supp. Nuovo Cimento, 1, I , 4 (1966) pp. 203-216 (given the fact...
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    I Did Paul Dirac say anything about Bohmian mechanics?

    Could you, please, give me reference to any paper or talk by Paul Dirac where he expresses his views about or give comments to the de Broglie-Bohm theory (Bohmian mechanics)?
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    I Are there relations that are valid for any field?

    I use the word «field» in purely algebraic sense here. Sometimes, when reading textbooks I encounter sentences like «Although the formulae in this section derived for the field of real numbers, they remain valid for complex numbers field as well». Or even more general variant of it: «...remain...
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    I Nice intro to connections between algebra and geometry

    Connections between algebraic structures and geometries are mentioned in almost any course of modern geometry or algebra. There are monographs dedicated to the subject. Unfortunately, the books, I managed to find, are written for professional mathematicians. I am looking for a book that focuses...
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    A Concept of duality for projective spaces and manifolds

    I firstly learned about duality in context of differentiable manifolds. Here, we have tangent vectors populating the tangent space and differential forms in its co-tangent counterpart. Acting upon each other a vector and a form produce a scalar (contraction operation). Later, I run into the...
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    A Why are conics indistinguishable in projective geometry?

    It is said that curves of the second order which we usually refer to as ellipse, parabola and hyperbola, i. e. conics, are all represented on projective plane by closed curves (oval curve), which means there is no distinction between them. Why is it? Projective space can, in principle, be...
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    I Why only normal subgroup is used to obtain group quotient

    Hello! As far as I know any subgroup can, in principle, be used to divide group into bundle of cosets. Then any group element belongs to one of the cosets (or to the subgroup itself). And such division still is not qualified as a quotient. Yes, the bundle of cosets in this case will be...
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    Is there any proper way to print threads?

    Sort of printable versions of thread pages or script optimising thread being sent to printer on-the-fly. Is there anything like that on this forum?
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    Key difference between two real and single complex variable?

    Notion of differentiability (analyticity) for function of complex variable is normally introduced and illustrated by comparison with function of single real variable. It is stated that there are infinite number of ways to approach any given point of complex plane where function is defined, not...
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    Does phrase «Space over vector field» make any sense?

    I met in several sources (textbooks) phrase «Space can be constructed over any field». But it is always illustrated with linear space over scalar field (or sometimes over ring). Does it make any sense to talk about spaces over vector fields? What kinds of spaces are they? What about tensor...