• Korean Journal of Crystallography
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• v.16 no.1
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• pp.11-20
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• 2005

Six basic symmetries and five Bravais lattices existing in the two-dimensional lattice are derived and then ten two-dimensional point groups are classified by each of five Bravais lattices. Finally seventeen two-dimensional space groups belonging to the ten point groups are studied.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.883-914
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• 2001

We present a survey of research results obtained for infra-nilmanifolds, their fundamental groups and some of their generalizations. This is presented from two different approaches and covers achievements obtained during the past four decades and showing a remarkable amount of mathematical interdisciplinarity. We go more in depth concerning the existence and construction of polynomial structures for these manifolds and groups, a direction where significant progress was made in the past few years. The bounded-degree polynomial structures developed by the authors triggered a number of challenging open problems. Also, their study already has lead to some interesting results concerning e.g. Anosov diffeomorphisms and expanding maps.

• Korean Journal of Crystallography
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• v.3 no.2
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• pp.129-132
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• 1992

The multiplicity factor, which is defined as the number of different planes in a form having identical interplanar spacing and identical intensity, is tabulated here for the eleven Laue groups on the basis of their symmetries.

• Korean Journal of Crystallography
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• v.12 no.1
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• pp.1-4
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• 2001

Single crystals of strontium barium metaborate, Sr/sub 1.36/Ba/sub 1.64/(B₃O/sub 6/)₂, were grown for the first time by the high-temperature-solution-growth technique, and a detailed structure analysis was carried out with the space group R3c. The metaborate (B₃O/sub 6/)/sup 3-/ anion planar groups in the title compound form infinite layers parallel to (001) plane, and Sr and Ba atoms are alternatively placed between the layers and are octahedrally coordinated by six O(2) atoms in the neighbouring anion rings.

• Korean Journal of Crystallography
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• v.4 no.1
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• pp.25-35
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• 1993

Tetra-tert-butyl-tetrapropionycalix (4) arena (C56H7208) is Triclinic, space group Pl, with a=13.664(5), b=17.585(5), c=12.863(2)A, a=109.33(2), B=111.97(2), γ=76.45(3) ˚, Z=2, V=2684.08A3, D, =1.152g/cm3, Dm=1.15g/cm3. The intensity data were collected on an Enraf-Nonius CAD-4 Diffractometer with a graphite monochromated Mo-Ka radiation. The structure was solved by direct methods and refined by leastsquares methods. The final R factor was 0.084 for 2561 observed reflections. The configuration of the molecule from the X-ray crystallographic investigation has the partial cone conformation, three tort-butylphenyls are down and a tort-butylphenyl is up. Three propionyloxy groups direct toward the exterior of the macrocycle cavity.

• Korean Journal of Crystallography
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• v.10 no.1
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• pp.66-70
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• 1999

The calix[4]arene molecule adopting the 1,3-alternate conformation forms a square cavity, and two pair phenyl rings lying above and below a least-square plane defined by the four bridging methylene groups in the calix[4]arene are widened upwards and downwards, respectively, from central axis, which leads to O1-O4=4.064 and O2-O3=3.864 . Two propyloxy groups are stabilized with all trans conformations, but the rather short azacrown ether chain with two oxygen atoms includes cis/trans conformations with O1-C35=2.906 . Therefore the cavity does not seem to be big enough to form a host-guest complex.

• Korean Journal of Crystallography
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• v.10 no.2
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• pp.130-135
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• 1999

The title compound consisting of a calix[4]arene molecule with four phenyl rings bridged by four methylene groups and arranged alternately in anti-orientation fashion, two 25,27-bis(1-pro-pyloxy) groups attached on the two lower rims of calix[4]arene, and crown-6 chain attached on the other set of lower rims of calix[4]arene offers a big cavity inside a molecule which might possess a potential for forming host-guest complexes. The molecular packing is accomplished by van der Waals forces.

• Korean Journal of Crystallography
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• v.14 no.1
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• pp.13-15
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• 2003

For all primitive centric space groups in the triclinic, monoclinic and orthorhombic systems, either phase 0 or π can be allocated to three different kinds of reflections in order to specify the origin at one of the eight centers of symmetry. and the same holds for all primitive acentric space groups belonging to the point group 222. If these phased reflections are used as a basic set, more and more phased reflections with better accuracy could emerge in the process of direct methods.

• Korean Journal of Crystallography
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• v.13 no.2
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• pp.73-81
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• 2002

Triclinic system에는 2개의 point group들 1,(equation omitted), 그리고 monoclinic system에는 3개의 point groups, 2, m, 2/m 가 있는데/sup 1)/ point group들 1, 2, m은 polar point group이고 이 중의 1, 2는 enantiomorphous point group이며 point group들 (equation omitted)와 2/m은 centric point group으로 Laue group이라 일컬어진다./sup 2-4)/ 본 해설문에서는 point group들 1, (equation omitted)에서 나오는 2개의 space group들과 point group들 2, m, 2/m에서 유도되는 13개의 space group들의 좌표들을 유도하였다 . Monoclinic system에서는 unique axis b 만을 다루었고, 그리고 space group No. 14은 3가지로 해석하였으며 나머지는 standard space group만을 다루었다. 모든 space group diagram은 “International Tables for Crystallography, Volume A edited by Theo Hahn, Third revised edition published for The International Union of Crystallography by Kluwer Academic Publishers, 1992”에 기재되어 있다.

• Applied Microscopy
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• v.47 no.4
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• pp.223-225
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• 2017

Cryo-electron microscopy (cryo-EM) is arguably the most powerful tool used in structural biology. It is an important analytical technique that is used for gaining insight into the functional and molecular mechanisms of biomolecules involved in several physiological processes. Cryo-EM can be separated into the following three groups according to the analytical purposes and the features of the biological samples: cryo-electron tomography (cryo-ET), cryo-single-particle reconstruction, and cryo-electron crystallography. Cryo-tomography is a unique EM technique that is used to study intact biomolecular complexes within their original environments; it can provide mechanistic insights that are challenging for other EM-methods. However, the resolution of reconstructed three-dimensional (3D) models generated by cryo-ET is relatively low, while single-particle reconstruction can reproduce biomolecular structures having near-atomic resolution without the need for crystallization unless the samples are large (>200 kDa) and highly symmetrical. Cryo-electron crystallography is subdivided into the following two categories according to the types of samples: one category that deals with two-dimensional (2D) crystalline arrays and the other category that uses 3D crystals. These two categories of electron-crystallographic techniques use different diffraction data obtained from still diffraction and continuous-rotation diffraction. In this paper, we review crystal-based cryo-EM techniques and focus on the recently developed 3D electron-crystallographic technique called microcrystal-electron diffraction.