Nowadays, most factories rely on machines to help boost up their production and process. Therefore, an effective machine condition monitoring system plays an important role in these factories to ensure that their production and process are running smoothly all the time. In this paper, a new and effective machine condition monitoring system using log-polar mapper, quaternion based thermal image ...

Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation AXB+CY D = E. Formulas are established for the extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a solution pair X = X1 +X2i+X3j+X4k and Y = Y1+Y2i+Y3j+Y4k to this equation. Moreover, necessary and sufficient cond...

We develop an efficient technique for computing values at s = 1 of Hecke L-functions. We apply this technique to the computation of relative class numbers of non-abelian CM-fields N which are abelian extensions of some totally real subfield L. We note that the smaller the degree of L the more efficient our technique is. In particular, our technique is very efficient whenever instead of simply c...

Facial expression recognition is an important technology in human-computer interaction. This study investigates a method for facial expression recognition using quaternion neural networks. A multi-layer quaternion neural network that conducts its learning using a quaternion back-propagation algorithm is employed to design the facial expression recognition system. The input feature vector of the...

A Riemannian manifold is said to be Kähler if the holonomy group is contained in U(n). It is quaternion Kähler if the holonomy group is contained in Sp(n)Sp(1). It is known that quaternion Kähler manifolds of dimension ≥ 8 are Einstein, so the scalar curvature s splits these manifolds according to whether s > 0, s = 0 or s < 0. Ricci flat quaternion Kähler manifolds include hyperkähler manifold...

This paper discusses quaternion L geometric weighting averaging working on the multiplicative Lie group of nonzero quaternionsH∗, endowed with its natural bi-invariant Riemannian metric. Algorithms for computing the Riemannian L center of mass of a set of points, with 1 ≤ p ≤ ∞ (i.e., median, mean, L barycenter and minimax center), are particularized to the case of H∗. Two different approaches ...

In an earlier paper [14] I have adumbrated amethod for establishing that the zeta-function of a Shimura variety associated to a quaternion algebra over a totally real field can be expressed as a product of L-functions associated to automorphic forms. Now I want to add some body to that sketch. The representation-theoretic and combinatorial aspects of the proof will be given in detail, but it wi...

Recently, solutions to inverse problems have been required in various engineering fields. The neural network inversion method has been studied as one of the neural network-based solutions. On the other hand, the extension of the neural network to a higher-dimensional domain, e.g., complex-value or quaternion, has been proposed, and a number of higher-dimensional neural network models have been ...

This paper presents an algorithm to average a set of quaternion observations. The average quaternion is determined by minimizing the weighted sum of the squared Frobenius norms of the corresponding attitude matrix differences, subject to the unit-norm constraint in the determined solution. Two cases are presented: one that incorporates scalar weights and one that incorporates general weights on...