• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.439-449
• /
• 2019

In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between "CM" and "IM". In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials P[f] and P[g] generated by meromorphic functions f and g, respectively. Our results generalize the results due to S. Lin and W. Lin, and H.-Y. Xu and Y. Hu.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.189-201
• /
• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• The Korean Journal of Rheology
• /
• v.10 no.4
• /
• pp.202-216
• /
• 1998

Improved version of previous 'Orthotropic' closure approximation, termed 'ORW' has been numerically developed using new homogeneous flow data. Previous 'Orthotropic' closure approximation, i.e., ORF or ORL showed non-physical oscillation for interaction coefficient $C_1$<0.001 at simple shear flow. It also shows non-physcial oscillation and under-prediction compared with 'Distribution Function Calculation' at non-homogeneous flow of center-gated disk. These phenomena are mainly due to the flow data of 'Distribution Function Calculation' which were used for least-square optimization. ORW obtained by fitting flow data of low interaction coefficient does not show non-physical oscillation and results in reasonably good behaviors at non-homogeneous flows as well as homogeneous flows. Fitting function forms have not been found to improve overall behaviors. It has been found that considering all the eigenvalues of orientation tensor (including the third eigenvalues) might end up with a better closure approximation than just considering the first and second eigenvalues. It is, however, very important and yet difficult to select appropriate function forms of eigenvalues. Numerical simulation including coupling and in-plane velocity gradient effects were performed for injection mold filing process with a film-gated strip and a center-gated disk using ORW and various other closure approximations for comparisons. Although ORW is in excellent agreement with 'Distribution Function Calculation', the predicted results seem to have consistent error in comparison with experimental data. The diffusivity term with constant interaction coefficient might have to be further investigated in order to accurately describe orientation states.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.717-734
• /
• 1996

For a scalar rational function, the spectral data consisting of zeros and poles with their respective multiplicities uniquely determines the function up to a nonzero multiplicative factor. But due to the richness of the spectral structure of a rational matrix function, reconstruction of a rational matrix function from a given spectral data is not that simple.

• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.419-428
• /
• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• Geomechanics and Engineering
• /
• v.13 no.3
• /
• pp.517-533
• /
• 2017

In this paper, with a graphical approach, a series of stability charts for homogeneous slopes with benches are presented based on the upper bound limit analysis theory and strength reduction technique. The objective function of the slope safety factor $F_s$ is optimized by the nonlinear sequential quadratic programming, and a substantial number of examples are illustrated to use the stability charts for homogeneous slopes with benches driven by only the action of the soil weight. These charts can be applied to quick and accurate estimations of the stability status of homogeneous slopes with benches. Moreover, the failure modes and the formula for safety factor Fs of homogeneous slopes with benches are provided to illustrate the stability analysis of slopes with benches, which is validated by samples.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.9C
• /
• pp.853-858
• /
• 2006

TMHMM(Tied Mixture Hidden Markov Model) is an important approach to reduce the number of free parameters in speech recognition. However, this model suffers from a degradation in recognition accuracy due to its GPDF (Gaussian Probability Density Function) clustering error. This paper proposes a clustering algorithm, called HCNN(Homogeneous Centroid Neural network), to cluster acoustic feature vectors in TMHMM. Moreover, the HCNN uses the heterogeneous distance measure to allocate more code vectors in the heterogeneous areas where probability densities of different states overlap each other. When applied to Korean digit isolated word recognition, the HCNN reduces the error rate by 9.39% over CNN clustering, and 14.63% over the traditional K-means clustering.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.23 no.2
• /
• pp.165-173
• /
• 2010

In this paper, the dynamic stiffness of scaled boundary finite element method(SBFEM) was analytically derived to represent the non-homogeneous space. The non-homogeneous parameters were introduced as an expotential value of power function which denoted the non-homogeneous properties of analysis domain. The dynamic stiffness of analysis domain was asymptotically expanded in frequency domain, and the coefficients of polynomial series were determined to satify the radiational condition. To verify the derived dynamic stiffness of domain, the numerical analysis of the typical problems which have the analytical solution were performed as various non-homogeneous parameters. As results, the derived dynamic stiffness adequatlly represent the features of the non-homogeneous space.

• Korean Journal of Computational Design and Engineering
• /
• v.12 no.3
• /
• pp.220-232
• /
• 2007

Current geometric modeling and analysis are commonly based on B-Rep modeling and a finite elements method respectively. Furthermore, it is difficult to represent an object whose material property is heterogeneous using the B-Rep method because the B-Rep is basically used for homogeneous models. In addition, meshes are required to analyze a property of a model when the finite elements method is applied. However, the process of generating meshes from B-Rep is cumbersome and sometimes difficult especially when the model is deformed as time goes by because the topology of deforming meshes are changed. To overcome those problems in modeling and analysis including homogeneous and heterogeneous materials, we suggest a unified modeling and analysis method based on implicit representation of the model using R-function which is suggested by Rvachev. For implicit modeling of an object a distance field is approximated and blended for a complex object. Using the implicit function mesh-free analysis is possible where meshes are not necessary. Generally mesh-free analysis requires heavy computational cost compared to a finite elements method. To improve the computing time of function evaluation, we utilize GPU programming. Finally, we give an example of a simple pipe design problem and show modeling and analysis process using our unified modeling and analysis method.

• Journal of the korean society of oceanography
• /
• v.32 no.2
• /
• pp.75-84
• /
• 1997

Relation between the length scale and the wall proximity function in the Mellor-Yamada level 2.5 turbulence closure model has been investigated through various experiments using a range of wall proximity functions. The model performance has been evaluated quantitatively by comparing with laboratory data for wind-driven flow (Baines and Knapp, 1965) and for open-channel flows without and with adverse wind action (Tsuruya, 1985). Comparison shows that a symmetric wall proximity function used by Blumberg and Mellor(1987) gives rise to current profiles with better accuracy than asymmetric wall proximity functions considered. It is noted that in modelling homogeneous flows the length scale 1= 0.31${\|}$z${\|}$(1+z/h) can be used with tolerable accuracy.