Hypercomplex Numbers
Induced Representations and Hypercomplex Numbers
... for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G = SL 2 ( R ...percomplex numbers. Thus, we investigate various hypercomplex ...
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On Cosets in Split Extensions of Hypercomplex Numbers
... The multiplication tables for the split extension of hypercomplex numbers were constructed by use of the Jonathan-Smith doubling formula. Cyclic subloops were then constructed. The results showed that the ...
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Embeddings of Almost Hermitian Manifold in Almost Hyper Hermitian Manifold and Complex (Hypercomplex) Numbers in Riemannian Geometry
... Further, an almost hyper Hermitian structure has been constructed on the tangent bundle TM with help of the Riemannian connection of an almost Hermitian structure on a manifold M then, w[r] ...
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Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks
... To this end, this paper explores a new way to improve/maintain the performance of these neural architectures while substantially reducing the pa- rameter cost (compression of up to 75%). In or- der to achieve this, we ...
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Cryptanalysis of HK17
... In December of 2017, NIST published the Round 1 submissions for the Post- Quantum Cryptography. Among all the candidate schemes, a key exchange called HK17 was proposed by Hecht and Kamlofsky [1]. Different from most of ...
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Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics
... We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) ...
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Associative Space Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory
... multicomponent hypercomplex numbers such as quaternions and octonions are widely used for the refor- mulation of quantum mechanics and field theory ...
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CONVOLUTION THEOREM AND AN ALTERNATIVE TO THE OCTONIONIC FOURIER TRANSFORM DEFINITION
... are hypercomplex numbers and can be considered as non-associative quaternions in some ...the hypercomplex, more specifically in the construction of the Fourier transform ...
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Remarks on Direct System Identification Using Hypercomplex–Valued Neural Network with Application to Time–Series Estimation
... of hypercomplex numbers for neural networks has attracted increasing attention from engineering re- search fields because it helps to learn to handle a wide variety of geometric objects and their ...
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Steerable filters generated with the hypercomplex dual tree wavelet transform
... A complete implementation of Kingsbury’s dual-tree hypercom- plex wavelet transform including Selesnick’s filter design has been given. A fully functional program for manipulating arrays of hypercomplex ...
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The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers
... r-Whitney numbers of the second kind, r-Whitney-Lah numbers, and the ordinary Lah ...r-Dowling numbers and the sums of row entries of the product of matrices containing the r-Whitney numbers ...
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Construction of the Transcomplex Numbers From the Complex Numbers
... The absence of all exceptions is extremely powerful in computation. It means that it is possible to construct compu- tational systems where all syntactically correct expressions are semantically correct. For example it ...
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Seeing Numbers
... prime number representations). Surprisingly enough, I never imagine a rect- angle of six rows and six columns of dots (or something), or a prism made of small cubes, four horizontal, three vertical, and three backwards. ...
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ALMOST HYPERCOMPLEX MANIFOLDS WITH HERMITIAN-NORDEN METRICS AND 4-DIMENSIONAL INDECOMPOSABLE REAL LIE ALGEBRAS DEPENDING ON ONE PARAMETER
... We generalize the obtained results in the three relevant classes by the following Theorem 2.1. Let (L, H, G) be a 4-dimensional almost hypercomplex manifold with Hermitian-Norden metrics. Then, the manifold (L, H, ...
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Brother Numbers
... Sometimes you may want to choose from among several long distance carriers when you make a call. Rates may vary depending upon the time and destination. To take advantage of low rates, you can store the access codes or ...
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Object a in Numbers
... rational numbers, something “lying beyond the infinite sequence of rationals” (Moore 1990: ...irrational numbers, irrational numbers cannot exist as numbers per se but only as a concept such ...
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An Approximation of Fuzzy Numbers Based on Polynomial Form Fuzzy Numbers
... fuzzy numbers with closer cores in comparison with the ones obtained from the other four ...fuzzy numbers, our method can approximate all the trapezoidal, triangular and m-degree polynomial form fuzzy ...
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An Introduction to the Theory of Numbers
... Ramanujan made the same conjecture but no progress towards a solution of the problem. About 1940 the problem appeared as an elementary (!!) problem in the Monthly. No solutions were offered. However in 1950 an incorrect ...
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Connection between Frustum of the cone with Jarasandha Numbers and Some Special Numbers
... This paper concerns with the problem of obtaining the radii of the bottom and top circles of the frustum and the height ‘h’ in connection with the Jarasandha number and some special numbers. Few different patterns ...
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The Distribution of Prime Numbers and Finding the Factor of Composite Numbers without Searching
... large numbers. Par- ticularly fast methods are available for numbers of special forms, such as Mersenne ...prime numbers from ...prime numbers remain open, such as Goldbach’s conjecture (that ...
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