The Experts below are selected from a list of 2685 Experts worldwide ranked by ideXlab platform
Guido Van Hooydonk - One of the best experts on this subject based on the ideXlab platform.
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symmetry breaking how vector calculus can violate the Associative Law of addition
2003Co-Authors: Guido Van HooydonkAbstract:Standard vector calculus based upon properties of non-composite particles violates the Associative Law of addition when applied to composite particles. The proof starts with a redistribution of number 1 as 1 = x + x, where x = 1-x. Physical unit hydrogen mass m is redistributed as m=m +M, with M = m −m. With the Associative Law of addition, species H can occur naturally in 2 forms: an atom state H, related to the standard distribution x+(1-x) and an anti-atom state or anti-hydrogen -state, related to the mirror of the equivalent distribution of H or −x +(1+x). The difference between the 2 forms of species H, both with total mass m, lies in their reduced mass: (a) m(1-m/m) = m/(1+m/M), the Bohr value for the H-state and (b) its super-symmetrical equivalent m(1+m/m) for the anti-H or -state The ratio is 1.0011 known as an anomaly for me but an equivalent solution gives 2 proton radii, a problem for bound state QED theory as well as for experimentalists. Consequences for CERN-based artificial anti-hydrogen experiments are given.
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symmetry breaking how vector calculus can violate the Associative Law of addition
2003Co-Authors: Guido Van HooydonkAbstract:Standard vector calculus based upon properties of non-composite particles violates the Associative Law of addition when applied to composite particles. The proof starts with a redistribution of number 1 as 1 = x1 + x2, where x2 = 1-x1.Physical unit hydrogen mass mH is redistributed as mH=me +Mp, with Mp = mH -me. With the Associative Law of addition, species H can occur naturally in 2 forms: an atom state H, related to the standard distribution x1+(1-x1) and an anti-atom state or anti-hydrogen H-state, related to the mirror of the equivalent distribution of H or -x1 +(1+x1).The difference between the 2 forms of species H, both with total mass mH, lies in their reduced mass: (a) me(1-me/mH) ≡ me/(1+me/Mp), the Bohr value for the H-state and (b) its super-symmetrical equivalent me(1+me/mH) for the anti-H or H-state The ratio is 1.0011 known as an anomaly for me but an equivalent solution gives 2 proton radii, a problem for bound state QED theory as well as for experimentalists. Consequences for CERN-based artificial anti-hydrogen experiments are given.
Mustafa Demirci - One of the best experts on this subject based on the ideXlab platform.
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the generalized Associative Law in vague groups and its applications ii
2006Co-Authors: Mustafa DemirciAbstract:As a continuation of Part I, vague integral powers of elements in vague groups and their representation properties are introduced in this paper. Thereafter, some rudimentary algebraic properties of vague integral powers of elements, obtained from the generalized vague Associative Law formulated in Part I, are established.The present paper particularly provides the abstract foundations of integral powers and multiples of real numbers in vague arithmetic. For this reason, special attention is also paid to the calculation of integral powers and multiples of real numbers in vague arithmetic, and some practical applications related to the discrete structure of measurement instruments are also given.
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the generalized Associative Law in smooth groups
2005Co-Authors: Mustafa DemirciAbstract:In this paper, assuming a multiplicative symbol for smooth groups, successive products in smooth groups are introduced as a counterpart to the products of a finite number of elements in classical group theory, and then a generalized Associative Law in smooth groups is formulated by means of successive products. Various elementary properties of successive products are established, and some applications of the generalized Associative Law in smooth groups are given.
Noam Zeilberger - One of the best experts on this subject based on the ideXlab platform.
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A sequent calculus for a semi-Associative Law
2018Co-Authors: Noam ZeilbergerAbstract:We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-Associative Law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.
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a sequent calculus for a semi Associative Law
2017Co-Authors: Noam ZeilbergerAbstract:We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-Associative Law (equivalently, tree rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. One combinatorial application of this coherence theorem is a new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice Y_n. Elsewhere, we have also used the sequent calculus and the coherence theorem to build a surprising bijection between intervals of the Tamari order and a natural fragment of lambda calculus, consisting of the beta-normal planar lambda terms with no closed proper subterms.
Zeilberger Noam - One of the best experts on this subject based on the ideXlab platform.
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A sequent calculus for a semi-Associative Law
2019Co-Authors: Zeilberger NoamAbstract:This article is an extended version of a paper presented at FSCD 2017.International audienceWe introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-Associative Law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$
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A sequent calculus for a semi-Associative Law
2019Co-Authors: Zeilberger NoamAbstract:We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-Associative Law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.Comment: This article is an extended version of a paper presented at FSCD 2017. [v2: minor rev] arXiv admin note: text overlap with arXiv:1701.0291
Hiroshi Oike - One of the best experts on this subject based on the ideXlab platform.
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an algebraic proof of the Associative Law of elliptic curves
2017Co-Authors: Kazuyuki Fujii, Hiroshi OikeAbstract:In this paper we revisit the addition of elliptic curves and give an algebraic proof to the Associative Law by use of MATHEMATICA. The existing proofs of the Associative Law are rather complicated and hard to understand for beginners. An ‘‘elementary” proof to it based on algebra has not been given as far as we know. Undergraduates or non-experts can master the addition of elliptic curves through this paper. After mastering it they should challenge the elliptic curve cryptography.
