منابع مشابه
Factorials of real negative and imaginary numbers - A new perspective
Presently, factorials of real negative numbers and imaginary numbers, except for zero and negative integers are interpolated using the Euler's gamma function. In the present paper, the concept of factorials has been generalised as applicable to real and imaginary numbers, and multifactorials. New functions based on Euler's factorial function have been proposed for the factorials of real negativ...
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This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a ‘geometric product’ of vectors in 2and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Reflections and rotations are analysed in terms of bilinear spinor transforma...
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We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems.
متن کاملRepresenting real numbers in a generalized numeration system
numeration systems An abstract numeration system (ANS) is given by a triplet S = (L,Σ, <) where L is a regular language over a totally ordered alphabet (Σ, <). By enumerating the words in L with respect to the radix order induced by <, we define a one-to-one correspondence: repS : N → L valS = rep −1 S : L → N. ANS: a generalization Most numeration systems satisfy the relation: m < n (usual ord...
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Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...
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ژورنال
عنوان ژورنال: ACM Transactions on the Web
سال: 2018
ISSN: 1559-1131,1559-114X
DOI: 10.1145/3265986