• Kyungpook Mathematical Journal
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• 제64권3호
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• pp.395-405
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• 2024

In this paper we define a matrix sequence called the Pell matrix sequence whose elements consist of Pell numbers. Using a positive parameter k, we generalize the Pell matrix sequence to a k-Pell matrix sequence and using two parameters s, t we generalize them to (s, t)-Pell matrix sequences. We give the basic properties of these matrix sequences. Then, using these properties we obtain exponential representations of the Pell matrix sequence and its generalizations in different ways.

• East Asian mathematical journal
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• 제39권1호
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• pp.23-27
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• 2023

In this paper, we derive the some identities which are related to the multifactorial numbers and the Catalan numbers. We utilize the fundamental theorem of Riordan matrix to obtain those identities.

• 대한수학회논문집
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• 제35권2호
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• pp.533-546
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• 2020

Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the 2-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called 2-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.

• 대한수학회보
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• 제48권4호
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• pp.725-736
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• 2011

By using the Lyapunov functional method, stochastic analysis, and LMI (linear matrix inequality) approach, the mean square exponential stability of an equilibrium solution of uncertain stochastic Hopfield neural networks with delayed is presented. The proposed result generalizes and improves previous work. An illustrative example is also given to demonstrate the effectiveness of the proposed result.

• 대한수학회논문집
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• 제31권3호
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• pp.603-611
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• 2016

In this paper, we show that if $\mathcal{A}$ is a differential subalgebra of Banach algebras $\mathcal{B}({\ell}^r)$, $1{\leq}r{\leq}{\infty}$, then solutions of the infinite dimensional linear system associated with a matrix in $\mathcal{A}$ have its p-exponential stability being equivalent to each other for different $1{\leq}p{\leq}{\infty}$.

• 한국축산식품학회지
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• 제37권1호
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• pp.147-152
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• 2017

A bioluminescent Lactobacillus plantarum (pLuc2) strain was constructed. The luminescent signal started to increase during the early exponential phase and reached its maximum in the mid-exponential phase in a batch culture of the strain. The signal detection sensitivity of the strain was the highest in PBS (phosphate buffered saline), followed by milk and MRS broth, indicating that the sensitivity was influenced by the matrix effect. The strain was used in millet seed fermentation which has a complex matrix and native lactic acid bacteria (LAB). The luminescent signal was gradually increased until 9 h during fermentation and abolished at 24 h, indicating that the strain could be specifically tracked in the complex matrix and microflora. Therefore, the bioluminescent labeling system can be used for monitoring LAB in food and dairy sciences and industries.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권9호
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• pp.2991-3007
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• 2022

Two dimensional locality preserving projections (2D-LPP) is an improved algorithm of 2D image to solve the small sample size (SSS) problems which locality preserving projections (LPP) meets. It's able to find the low dimension manifold mapping that not only preserves local information but also detects manifold embedded in original data spaces. However, 2D-LPP is simple and elegant. So, inspired by the comparison experiments between two dimensional linear discriminant analysis (2D-LDA) and linear discriminant analysis (LDA) which indicated that matrix based methods don't always perform better even when training samples are limited, we surmise 2D-LPP may meet the same limitation as 2D-LDA and propose a novel matrix exponential method to enhance the performance of 2D-LPP. 2D-MELPP is equivalent to employing distance diffusion mapping to transform original images into a new space, and margins between labels are broadened, which is beneficial for solving classification problems. Nonetheless, the computational time complexity of 2D-MELPP is extremely high. In this paper, we replace some of matrix multiplications with multiple multiplications to save the memory cost and provide an efficient way for solving 2D-MELPP. We test it on public databases: random 3D data set, ORL, AR face database and Polyu Palmprint database and compare it with other 2D methods like 2D-LDA, 2D-LPP and 1D methods like LPP and exponential locality preserving projections (ELPP), finding it outperforms than others in recognition accuracy. We also compare different dimensions of projection vector and record the cost time on the ORL, AR face database and Polyu Palmprint database. The experiment results above proves that our advanced algorithm has a better performance on 3 independent public databases.

• 대한수학회보
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• 제15권1호
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• pp.35-41
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• 1978

• International Journal of Aeronautical and Space Sciences
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• 제11권1호
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• pp.10-18
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• 2010

The purpose of this paper deals with direct multiple-shooting method (DMS) to resolve helicopter maneuver problems of helicopters. The maneuver problem is transformed into nonlinear problems and solved DMS technique. The DMS method is easy in handling constraints and it has large convergence radius compared to other strategies. When parameterized with piecewise constant controls, the problems become most effectively tractable because the search direction is easily estimated by solving the structured Karush-Kuhn-Tucker (KKT) system. However, generally the computation of function, gradients and Hessian matrices has considerably time-consuming for complex system such as helicopter. This study focused on the approximation of the KKT system using the matrix exponential and its integrals. The propose method is validated by solving optimal control problems for the linear system where the KKT system is exactly expressed with the matrix exponential and its integrals. The trajectory tracking problem of various maneuvers like bob up, sidestep near hovering flight speed and hurdle hop, slalom, transient turn, acceleration and deceleration are analyzed to investigate the effects of algorithmic details. The results show the matrix exponential approach to compute gradients and the Hessian matrix is most efficient among the implemented methods when combined with the mixed time integration method for the system dynamics. The analyses with the proposed method show good convergence and capability of tracking the prescribed trajectory. Therefore, it can be used to solve critical areas of helicopter flight dynamic problems.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.