On almost pseudo m-projectively symmetric manifolds

Singh, Jay Prakash; Lalmalsawma, C.

doi:10.30755/nsjom.06728

Cited by 5 publications

(8 citation statements)

References 9 publications

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“…In passing, we draw the reader's attention to the fact that the elements of E A (and also E A ) are either all integers or half-integers, so we can talk of the nature of any of the elements as being an integer or half-integer by just referring to any other element. With this last observation in mind, one can easily show that, max A − J l 0, if both J 0 and max A are integers or half-integers 1 2 , if only one of the pair ( J 0 , max A) is half-integer, (14) since all the elements of A are less or equal to max A . Thus, when max A < J 0 , min E A = J m = 0, if both J 0 and max A are integers or half-integers 1 2 , if only one of the pair…”

Section: Max a < Jmentioning

confidence: 97%

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On the composition of an arbitrary collection of SU(2) spins: an enumerative combinatoric approach

Gyamfi¹,

Barone²

2018

J. Phys. A: Math. Theor.

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The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)[1] is a natural setting for spin composition, and easily leads to very general analytic formulae -many of which hitherto not present in the literature. Based on it, we propose three general methods for computing spin multiplicities; namely, 1) the multi-restricted composition, 2) the generalized binomial and 3) the generating function methods. Symmetric and anti-symmetric compositions of SU (2) spins are also discussed, using generating functions. Of particular importance is the observation that while the common Clebsch-Gordan decomposition (CGD) -which considers the spins as distinguishable -is related to integer compositions, the symmetric and anti-symmetric compositions (where one considers the spins as indistinguishable) are obtained considering integer partitions. The integers in question here are none other but the occupation numbers of the Holstein-Primakoff bosons.The pervasiveness of q−analogues in our approach is a testament to the fundamental role they play in spin compositions. In the appendix, some new results in the power series representation of Gaussian polynomials (or q−binomial coefficients) -relevant to symmetric and antisymmetric compositions -are presented. a

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Section: Max a < Jmentioning

confidence: 97%

“….}. The coupling of these angular momenta will give rise to a multiset [1,14] E A of angular momenta, which we indicate as…”

Section: Coupling Of An Arbitrary Collection Of Angular Momentamentioning

confidence: 99%

On the composition of an arbitrary collection of SU(2) spins: an enumerative combinatoric approach

Gyamfi¹,

Barone²

2018

J. Phys. A: Math. Theor.

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“…Some basic definitions in multiset theory. The definitions in this subsection are either taken from [3,7,8,9,18,28,29,30,31] or adapted with more expository note. Definition 2.1.…”

Section: Concept Of Multisetsmentioning

confidence: 99%

“…Multisets are very important structures applicable in real-life situations such as in database queries, information retrieval on the web, multicriteria decision making, knowledge representation in database systems, biological systems, membrane computing, musical note, frequency, chemical compositions, processes in an operating system, etc [21,23,28]. In mathematics, the prime factorisation of an integer n > 0 is a multiset whose elements are primes [31].…”

Section: Introductionmentioning

confidence: 99%

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Synopsis of the Notions of Multisets and Fuzzy Multisets

2019

Ann. Commun. Math.

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This paper is an attempt to summarize the basic concepts of the theories of multiset and fuzzy multiset. We begin by describing multisets and the operations between them with some related results. In the same vein, the basic concepts of fuzzy multiset theory as well as the operations between fuzzy multisets are buttressed in relation to multiset theory. Finally, we present some properties of fuzzy multisets with some related results.

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