• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1255-1274
• /
• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.2
• /
• pp.269-278
• /
• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Kyungpook Mathematical Journal
• /
• v.59 no.1
• /
• pp.125-134
• /
• 2019

Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known results.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.277-303
• /
• 2021

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).

• International Journal of Computer Science & Network Security
• /
• v.23 no.8
• /
• pp.40-48
• /
• 2023

Speech Emotions recognition has become the active research theme in speech processing and in applications based on human-machine interaction. In this work, our system is a two-stage approach, namely feature extraction and classification engine. Firstly, two sets of feature are investigated which are: the first one is extracting only 13 Mel-frequency Cepstral Coefficient (MFCC) from emotional speech samples and the second one is applying features fusions between the three features: Zero Crossing Rate (ZCR), Teager Energy Operator (TEO), and Harmonic to Noise Rate (HNR) and MFCC features. Secondly, we use two types of classification techniques which are: the Support Vector Machines (SVM) and the k-Nearest Neighbor (k-NN) to show the performance between them. Besides that, we investigate the importance of the recent advances in machine learning including the deep kernel learning. A large set of experiments are conducted on Surrey Audio-Visual Expressed Emotion (SAVEE) dataset for seven emotions. The results of our experiments showed given good accuracy compared with the previous studies.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.1
• /
• pp.194-204
• /
• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

• Journal of Korea Multimedia Society
• /
• v.14 no.6
• /
• pp.742-751
• /
• 2011

This paper presents a robust 3D model hashing dependent on key and parameter by using heat kernel signature (HKS), which is special shape feature descriptor, In the proposed hashing, we calculate HKS coefficients of local and global time scales from eigenvalue and eigenvector of Mesh Laplace operator and cluster pairs of HKS coefficients to 2D square cells and calculate feature coefficients by the distance weights of pairs of HKS coefficients on each cell. Then we generate the binary hash through binarizing the intermediate hash that is the combination of the feature coefficients and the random coefficients. In our experiment, we evaluated the robustness against geometrical and topological attacks and the uniqueness of key and model and also evaluated the model space by estimating the attack intensity that can authenticate 3D model. Experimental results verified that the proposed scheme has more the improved performance than the conventional hashing on the robustness, uniqueness, model space.

• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.115-129
• /
• 2016

Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. [9] evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, $Erd\acute{e}lyi$-Kober and Saigo operators, associated with multivariable H-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.11
• /
• pp.1036-1042
• /
• 2013

In this paper, an elderly assistance system is developed based on Xenomai, a real-time development framework cooperating with the Linux kernel. A Kinect sensor is used to recognize the behavior of the elderly and A-star search algorithm is implemented to find the shortest path to the person. The mobile robot also generates a trajectory using a digital convolution operator which is based on a Bezier curve for smooth driving. In order to follow the generated trajectory within the control period, we developed real-time tasks and compared the performance of the tracking trajectory with that of non real-time tasks. The real-time task has a better result on following the trajectory within the physical constraints which means that it is more appropriate to apply to an elderly assistant system.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.81-105
• /
• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.