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1  or Ca/Au/Bi mixtures to give 16-atom Friauf polyhedra.
2 of bridging ligands in soluble metal-organic polyhedra.
3 octahedra are completely surrounded by IO(3) polyhedra.
4 nd other topologies containing as many as 60 polyhedra.
5 ahedra, each of which is bonded to six IO(3) polyhedra.
6 iO(6) octahedron that is linked to six IO(3) polyhedra.
7 ional structure of corner-shared Al(BO3 )3 O polyhedra.
8 use any net change in the metal coordination polyhedra.
9 dral symmetry only in half of the individual polyhedra.
10 dues based on calculations with Voronoi-like polyhedra.
11 red static arrays of tiles, linked rings and polyhedra.
12 nt diol dehydratase is associated with these polyhedra.
13 lin inclusions but many fewer than wild-type polyhedra.
14  we construct a reference library of regular polyhedra.
15 nation common to smaller and higher-symmetry polyhedra.
16 he discs occupying the faces in the caveolar polyhedra.
17 shared atoms between two linked coordination polyhedra.
18 sional structure of corner-shared Mg(CO3)2F2 polyhedra.
19 sting of corner- and edge-shared UF9 and MF6 polyhedra.
20 produced diverse synthetic three-dimensional polyhedra.
21 engths was used for hierarchical assembly of polyhedra.
22 polyhedra and the relative lack of irregular polyhedra.
23 fullerene-topology cage built from 28 uranyl polyhedra.
24 orated into the self-assembled symmetric DNA polyhedra.
25 ations of that involve two different regular polyhedra.
26 s formed from linked M(O,F)(n) and P(O,F)(n) polyhedra.
27 can be cured and purified to yield colloidal polyhedra.
28 truncated octahedron, one of the Archimedean polyhedra.
29 shell cluster consisting of 68 uranyl peroxo polyhedra, 16 nitrate groups, and ~44 K(+) and Na(+) cat
30                          These metal-organic polyhedra act as supermolecular building blocks when the
31 y corner-sharing capped trigonal planar AgO4 polyhedra, AgO6 capped square pyramids, and AgO6 octahed
32                                Metal-organic polyhedra and frameworks (MOPs and MOFs) were prepared b
33 suited to the functional requirements of the polyhedra and has been either preserved or re-selected d
34 he basic structures for linking squares into polyhedra and networks (reticulation) are enumerated, an
35 bbons and tubes, three-dimensional crystals, polyhedra and simple finite two-dimensional shapes.
36  particular the abundance of regular Voronoi polyhedra and the relative lack of irregular polyhedra.
37 cavities in these double-shell metal-organic polyhedra and their inner/outer binding sites provide pe
38  synthesis of colloidal SnS cubes, spherical polyhedra, and sheets and demonstrate their activity for
39 ple for maximizing the yield of self-folding polyhedra; and (ii) shortest paths from 2D nets to 3D po
40  individually within cubic inclusion bodies (polyhedra, approximately 100 nm across), although two to
41 iency (AQE) of 6.1 % for OER compared to the polyhedra (AQE: 1.6 %) and SrTaO2 N polycrystals (AQE: 0
42 ents confirmed the internal cavities of such polyhedra are accessible.
43 , single-crystalline SrTaO2 N nanoplates and polyhedra are achieved selectively.
44 ayer of TiO(2) stoichiometry in which TiO(5) polyhedra are arranged into edge-shared structures, in c
45                                          The polyhedra are based on concentric shells of alternating
46 hombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular
47  also the fact that the 9-coordinated CeO(9) polyhedra are expected to be geometrically more complian
48                                              Polyhedra are formed during either aerobic or anaerobic
49 ous responses of single atoms and also major polyhedra are found to change greatly with increasing ex
50 cturally related to corundum, but the AlO(6) polyhedra are highly distorted, with the interatomic bon
51                              Uranyl peroxide polyhedra are known to self-assemble into complex closed
52               The edges of the Pt-rich PtNi3 polyhedra are maintained in the final Pt3Ni nanoframes.
53 nd faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical.
54 tructure, such that the side-by-side aligned polyhedra are offset by 158 degrees.
55                To achieve this, coordination polyhedra are parameterized as FSBs and a simple empiric
56 4, where topological low coordination number polyhedra are still observed around the critical cavity.
57 dra, including some Archimedean and Platonic polyhedra, arise spontaneously in elastic shells formed
58                    Natural protein crystals (polyhedra) armour certain viruses, allowing them to surv
59 e full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.
60 ormulate the generation of dense packings of polyhedra as an optimization problem, using an adaptive
61 onent microscopic shells buckle into various polyhedra, as observed in many organelles.
62 single-crystalline nanoboxes of gold: hollow polyhedra bounded by six [100] and eight [111] facets.
63 hows that monodisperse, atomically smooth Ag polyhedra can self-assemble into uniform interparticle g
64 ties from those of the initial metal-organic polyhedra can thus lead to new metal-organic polyhedra w
65                                              Polyhedra, complex topological objects, a nanomechanical
66    The structure consists of REO6 and REO2F4 polyhedra connected by Si4O10 sheets with a previously u
67                      It is proposed that the polyhedra consist of AdoCbl-dependent diol dehydratase (
68                                          DNA polyhedra consist of an internal void bounded by a well-
69 tachment of cucurbit[n]uril to metal organic polyhedra constitutes a promising vehicle for the develo
70  method of positioning the dividing plane in polyhedra construction, and (iv) the set of structures u
71 led edges characteristic of wild-type AcMNPV polyhedra, contained fractures, and occluded few virions
72 tructure can be viewed as nested, concentric polyhedra, containing a total of five forms of Archimede
73  such as porous organic cages, metal-organic polyhedra, covalent organic frameworks and zeotype mater
74               Using the precision of Voronoi Polyhedra/Delauney Tessellations to identify contacts, t
75 th Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) enca
76                                Metal-organic polyhedra-discrete molecular architectures constructed t
77 ar proteins by approximating them to various polyhedra (dodecahedron, truncated octahedron, icosahedr
78 -prepared Sr2 Ta2 O7 nanoplates and SrTaO2 N polyhedra form by flux-assisted nitridation of the nanop
79 olds of Wigner-Seitz cells with many-faceted polyhedra, forming an important bridge between the simpl
80 d to study the chemical bonding in the boron polyhedra found in other structures including neutral bi
81 these PF mutants exhibited the traits of few polyhedra (FP) mutants; however, no large DNA insertions
82 ace geometry during the self-assembly of DNA polyhedra from branched DNA nanomotifs (tiles).
83 e self-folding of submillimeter-scale higher polyhedra from two-dimensional nets.
84 ting, the possibility of buckling into other polyhedra has not been explored.
85  metallosupramolecular cages known as M12L24 polyhedra have been adapted to serve as nanometer-scale
86 sses comprising continuously linked [AlO(x)] polyhedra have been prepared in only a few systems under
87           It is also shown that only 11 such polyhedra have faces that are regular polygons; these po
88 res, in contrast to the corner-shared TiO(6) polyhedra in bulk.
89                                       Simple polyhedra in crystalline compounds are often deformed du
90 nalogous to the condensation of coordination polyhedra in oxide frameworks.
91 c interference zones are limited to isolated polyhedra in the 1, 2 and 4 positions and the alpha face
92 ; and (ii) shortest paths from 2D nets to 3D polyhedra in the configuration space are important for r
93 re relationship and the role of flexible VOx polyhedra in the structural switching process.
94  features edge-sharing between the Ti and Bi polyhedra, in contrast to the dominant corner-linking of
95 tion metal compounds composed of homoanionic polyhedra, including nitrides, oxides, and fluorides.
96      We show here that irregular and regular polyhedra, including some Archimedean and Platonic polyh
97 the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer
98 recting the self-assembly of uranyl peroxide polyhedra into closed clusters.
99 cture adopted by the SnS cubes and spherical polyhedra is expanded along the a and b axes and contrac
100 ecules embed CPV particles inside infectious polyhedra is not known.
101 on, the rearrangement of the Fe coordination polyhedra is unique such that all available FeOn units (
102                                        These polyhedra lacked the beveled edges characteristic of wil
103 comprises bicapped trigonal prismatic PuS(8) polyhedra linked in chains through edge-sharing interact
104               A ring consisting of 40 uranyl polyhedra linked into five-membered rings and 16 nitrate
105  or channels lined with fluoride ions, metal polyhedra, M(O,F)(n), linked through vertex, edge, or fa
106 de), to modulate the growth of metal-organic polyhedra (MOP) crystals.
107 he synthesis of this series of metal-organic polyhedra (MOPs) employs sulfate-capped oxygen-centered
108                                Metal-organic polyhedra (MOPs) have been incorporated into silica nano
109                                Metal-organic polyhedra (MOPs) or frameworks (MOFs) based on Cr(3+) ar
110 oublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecu
111  shape measures analysis of the coordination polyhedra of a host of transition metal complexes with b
112 enyl) links to yield five highly crystalline polyhedra of general formula [NH2(CH3)2]8[Fe12O4(-)(SO4)
113          We have determined the structure of polyhedra of the baculovirus Autographa californica mult
114 Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2.
115 le, we entropically reshape the coordination polyhedra of the particles in the system, a change that
116 d that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres.
117 loying pre-selected 0-periodic metal-organic polyhedra or 2-periodic metal-organic layers, SBBs or SB
118  unique relationship between edge-transitive polyhedra or layers and minimal edge-transitive 3-period
119 n into more elaborate building units (namely polyhedra or layers) to (i) elucidate the unique relatio
120                              Millimeter-size polyhedra-patterned with logic devices, wires, and solde
121 ed RE clusters are replaced by metal-organic polyhedra, peripherally functionalized so as to have the
122 ded virions (odv-e25, odv-e66, odv-e18), and polyhedra (polyhedrin/granulin, p10, pp34, and fp25k).
123 erefore, remarkable that both AcMNPV and CPV polyhedra possess identical crystal lattices and crystal
124 n be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca
125 cosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611.
126 eometries, those containing 24 and 28 uranyl polyhedra, respectively, show that the capsules-like clu
127       Clusters built from 32 uranyl peroxide polyhedra self-assemble and crystallize within 15 min af
128 ected at distances suggesting that Am and Fe polyhedra share corners in geometries ranging from bent
129 emely tetragonally elongated octahedron; the polyhedra share oxide vertexes.
130  face, thus resulting in well-structured DNA polyhedra/STV complexes.
131 ells with two elastic components buckle into polyhedra such as dodecahedra, octahedra, tetrahedra, an
132 and empty (no RNA) capsids were found inside polyhedra, suggesting a spontaneous RNA encapsidating pr
133 ree-dimensional arrangement of Ca(-COO, -OH) polyhedra supporting one-dimensional pores with aperture
134 ed by the disruption of connectivity between polyhedra (TaO6 octahedra or TaO7 bipyramids) at the par
135 he structure into 'natural tiles' or Voronoi polyhedra that are metastable and, consequently, tempora
136  for one-step self-assembly of wireframe DNA polyhedra that are more massive than most previous struc
137                            The 4 of these 11 polyhedra that are not known to have been published prev
138 ined in terms of the "cross-bracing" between polyhedra that occurs as a result of the phase transitio
139 f Tl tetrahedra along c are constructed from polyhedra that share opposed like edges, and these are i
140 dic anion-vacancy order to generate multiple polyhedra that together with cation order produce a pola
141 ahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the t
142           Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equi
143 tegy based on space-filling tessellations of polyhedra to create three-dimensional reconfigurable mat
144     The starting material, crystalline PtNi3 polyhedra, transforms in solution by interior erosion in
145  the connection of isolated LnO(6)(H(2)O)(3) polyhedra (tricapped trigonal prism) through the mellita
146 the capsid changes from spherical to faceted polyhedra, two modes are necessary to accomplish the con
147 gands and building blocks of condensed metal polyhedra, we recently reported a one-dimensional nickel
148 bound together: self-assembled symmetric DNA polyhedra were used to organize proteins in 3D space.
149  triperoxide or uranyl dihydroxidediperoxide polyhedra, were only realized within the last decade.
150                         Bi stabilizes the Ti-polyhedra, which are synergistically stabilized by the b
151 ructure of corner-shared MgO4, PO4, and TeO6 polyhedra, which form a [TeMg3P2O14]infinity framework.
152 ar capsids than wild type and more irregular polyhedra, which tend to be larger than in the wild type
153        Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral.
154                   We investigated 145 convex polyhedra whose assembly arises solely from their anisot
155 us, truncated tetrahedral and heterocuboidal polyhedra, whose pore size and functionality can be syst
156 polyhedra can thus lead to new metal-organic polyhedra with distinct properties (including size and s
157 ent here suggests that we can design faceted polyhedra with diverse symmetries by coassembling opposi
158 s with architectures that resemble different polyhedra with icosahedral symmetry.
159  of still more classes of convex equilateral polyhedra with polyhedral symmetry.
160                                Metal-organic polyhedra with surface-exposed organic groups have been
161            Self-assembly of millimeter-scale polyhedra, with surfaces patterned with solder dots, wir
162 nt network of As(V)/P coordinated to Fe(III) polyhedra, with varying amounts of Ca bound directly and
163  the smallest cytoplasmic polyhedrosis virus polyhedra yet characterized, which we failed to solve at

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