• Korean Journal of Mathematics
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• 제28권4호
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.

• Bulletin of the Korean Chemical Society
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• 제17권4호
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• pp.314-321
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• 1996

Isoxazolidine derivatives 7 and 8 were synthesized from N-benzyl-C-(2-benzyloxyethyl)nitrones by 1,3-dipolar cycloaddition with ethyl crotonate. The isoxazolidine derivatives were converted to β-amino acid esters 9a and 9b by reduction with zinc in acetic acid. The β-amino acid esters were reacted with methylmagnesium bromide to give the 2-azetidinones (13a, 13b). The benzyl group of 2-azetidinones were removed by Birch reduction. The products were oxidized with PDC to give 3-[1-(t-butyldimethylsilyloxy)ethyl]-4-carboxymethyl-2-azetidinone derivatives (2a, 2c).

• Bulletin of the Korean Chemical Society
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• 제19권3호
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• pp.335-339
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• 1998

Syntheses of carbapenam skeletons were achieved from 3-benzyloxypropanal through 1,3-dipolar cycloaddition. 3-Benzyloxypropanal was reacted with N-hydroxyglycine ester to give C-(2-benzyloxyethyl)-N-alkoxycarbonylmethylnitrone (6). 1,3-Dipolar cycloaddition of the nitrone with ethyl crotonate gave 3-(2-benzyloxyethyl)isoxazolidine (7). Compound 7 was transformed to 4-(2-hydroxyethyl)-2-azetidinone (11). Compound 11 was converted to 4-(2-iodoethyl)-2-azetidinone (13) or 4-phenylthiocarbonylmethyl-2-azetidinone (16) which was cyclized to give 6-(1-hydroxyethyl)carbapenam-3-carboxylate (14, 17).

• 대한수학회보
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• 제58권2호
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• pp.315-326
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• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• 대한수학회논문집
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• 제37권3호
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• pp.705-718
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• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1053-1071
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• 2022

The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

• 대한수학회지
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• 제59권5호
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• pp.997-1013
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• 2022

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some 4 × 4 and 6 × 6 Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.

• 호남수학학술지
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• 제45권1호
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• pp.130-145
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• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• 한국정밀공학회지
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• 제12권8호
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• pp.114-121
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• 1995

This paper describes a method which uses rail curves for blending surfaces. Blending surface between the free form surfaces which have the flexible shapes and are widely used today is investigated. The rail curves give blending surface continuty through Pointwise interpola- tion. It is the point in this paper that the blending surfaces give a good flexibility to modeling of base free form surfaces. Using rail curves for simple base surfaces, complicated models can be designed. Also this blending surfaces can be used for path generation in compoud surfaces.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.