• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.119-125
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• 2015

In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.13-20
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• 2020

A commutative ring R with unityis called EM-Hermite if for each a, b ∈ R there exist c, d, f ∈ R such that a = cd, b = cf and the ideal (d, f) is regular in R. We showed in this article that R is a PP-ring if and only if the idealization R(+)R is an EM-Hermite ring if and only if R[x]/(xⁿ⁺¹) is an EM-Hermite ring for each n ∈ ℕ. We generalize some results, and answer some questions in the literature.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.220-225
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• 2007

This paper is a continuation of the recent development on the hermite-based divergence free basis function and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square cavity with temperature difference across the two sides. The basis functions for the velocities consist of the hermite function and its curl. However, the basis for the temperature are the hermite function and its gradienst. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x- and y-derivatives. Numerical results for the streamlines, the temperatures, the x-velocities and the y-velocities show good agreements with those of De vahl Davis[7].

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.129-140
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• 1998

A numerical method is proposed to optimize automotive cam profiles. An acceleration curve of a cam follower motion is described by Hermite spline curves. Because of the intrinsic characteristics of the Hermite curve, it is possible to design an acceleration curve with arbitrary shape. Design variables in the optimization problem are location of control points which define the acceleration curve. Objective function includes dynamic performances as well as kinematic properties of a valve train. Similar optimization procedure was also performed using Polydyne cam profile synthesis method. Optimized profiles using the Hermite curve are proved to be superior to those using the Polydyne method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.805-823
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• 2019

We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in ${\mathbb{R}}^{2,1}$, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve $C^1$ Hermite interpolation problems in ${\mathbb{R}}^{2,1}$, for an admissible $C^1$ Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.

• Journal of Ocean Engineering and Technology
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• v.23 no.5
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• pp.1-8
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• 2009

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.585-596
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• 2000

We developed a macro for prediction and classification using profection pursuit regression based on Friedman (1984b) and Hwang, et al. (1994). In the macro, the order of the Hermite functions can be selected automatically. In projection pursuit regression, we compare several smoothing methods such as super smoothing, smoothing with the Hermite functions. Also, classification methods applied to German credit data are compared.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.707-716
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• 2015

Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].