scholarly journals The Metod for Research of Isomorphism of Indecomposable Hypercomplex Number Systems.

2017 ◽  
Vol 39 (3) ◽  
pp. 61-76
Author(s):  
Ya.A. KALINOVSKY ◽  
◽  
Yu.E. BOYARINOVA ◽  
Keyword(s):  
Hypercomplex Number ◽  
Number Systems

scholarly journals On the structure of hypercomplex number systems

1905 ◽  
Vol 6 (2) ◽  
pp. 172-172 ◽  
Author(s):  
Saul Epsteen ◽  
J. H. Maclagan-Wedderburn
Keyword(s):  
Hypercomplex Number ◽  
Number Systems

scholarly journals Use of Methods for Generating Isomorphic Hypercomplex Number Systems to Increase the Efficiency of Multiplying Hypercomplex Numbers

2018 ◽  
Vol 40 (5) ◽  
pp. 27-40
Author(s):  
Ya.A. Kalinovsky ◽  
◽  
Yu.E. Boyarinova ◽  
Ya.V. Khitsko ◽  
A.S. Sukalo ◽  
...  
Keyword(s):  
Hypercomplex Numbers ◽  
Hypercomplex Number ◽  
Number Systems

Method of Selecting Hypercomplex Number Systems for Modeling Digital Reversing Filters of the 3rd and 4th Orders

2019 ◽  
Vol 41 (4) ◽  
pp. 03-18
Author(s):  
J.A. Kalinovsky ◽  
◽  
Y.E. Boyarinova ◽  
J.V. Khitsko ◽  
◽  
...  
Keyword(s):  
Hypercomplex Number ◽  
Number Systems

ASSOCIATIVE MEMORY IN QUATERNIONIC HOPFIELD NEURAL NETWORK

2008 ◽  
Vol 18 (02) ◽  
pp. 135-145 ◽  
Author(s):  
TEIJIRO ISOKAWA ◽  
HARUHIKO NISHIMURA ◽  
NAOTAKE KAMIURA ◽  
NOBUYUKI MATSUI
Keyword(s):  
Neural Network ◽  
Associative Memory ◽  
Energy Function ◽  
Hopfield Neural Network ◽  
Input Output ◽  
Stable States ◽  
Hypercomplex Number ◽  
Number Systems

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

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