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Journal articles on the topic 'Rational tetrahedra'

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Published: 4 June 2021
Last updated: 31 January 2023

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1

Chisholm, C., and J. A. MacDougall. "Rational and Heron tetrahedra." Journal of Number Theory 121, no. 1 (November 2006): 153–85. http://dx.doi.org/10.1016/j.jnt.2006.02.009.

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2

Mazėtis, Edmundas, and Grigorijus Melničenko. "Rational cuboids and Heron triangles II." Lietuvos matematikos rinkinys 60 (December 5, 2019): 34–38. http://dx.doi.org/10.15388/lmr.b.2019.15233.

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We study the connection of Heronian triangles with the problem of the existence of rational cuboids. It is proved that the existence of a rational cuboid is equivalent to the existence of a rectangular tetrahedron, which all sides are rational and the base is a Heronian triangle. Examples of rectangular tetrahedra are given, in which all sides are integer numbers, but the area of the base is irrational. The example of the rectangular tetrahedron is also given, which has lengths of one side irrational and the other integer, but the area of the base is integer.
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3

Buchholz, Ralph Heiner. "Perfect pyramids." Bulletin of the Australian Mathematical Society 45, no. 3 (June 1992): 353–68. http://dx.doi.org/10.1017/s0004972700030252.

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This paper discusses rational edged tetrahedra, in 3, 4 and n dimensions, with rational volume. The main results are (i) a proof of the existence of infinitely many tetrahedra with rational edge-lengths, face-areas and volume and (ii) a proof that there exist dimensions for which all regular hypertetrahedra with rational edge-lengths have rational hypervolume.
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4

Chisholm, C., and J. A. MacDougall. "Rational tetrahedra with edges in arithmetic progression." Journal of Number Theory 111, no. 1 (March 2005): 57–80. http://dx.doi.org/10.1016/j.jnt.2004.07.009.

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5

Chisholm, C., and J. A. MacDougall. "Rational tetrahedra with edges in geometric progression." Journal of Number Theory 128, no. 2 (February 2008): 251–62. http://dx.doi.org/10.1016/j.jnt.2007.07.002.

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6

Kolpakov, Alexander, and Sinai Robins. "Spherical tetrahedra with rational volume, and spherical Pythagorean triples." Mathematics of Computation 89, no. 324 (December 17, 2019): 2031–46. http://dx.doi.org/10.1090/mcom/3496.

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7

CHAIR, NOUREDDINE, and CHUAN-JIE ZHU. "TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY." International Journal of Modern Physics A 06, no. 20 (August 20, 1991): 3571–98. http://dx.doi.org/10.1142/s0217751x91001738.

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Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.
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8

XU, GUOLIANG, CHANDRAJIT L. BAJAJ, and SUSAN EVANS. "C1 MODELING WITH HYBRID MULTIPLE-SIDED A-PATCHES." International Journal of Foundations of Computer Science 13, no. 02 (April 2002): 261–84. http://dx.doi.org/10.1142/s0129054102001084.

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We propose a new scheme for modeling a smooth interpolatory surface, from a surface discretization consisting of triangles, quadrilaterals and pentagons, by algebraic surface patches which are subsets of real zero contours of trivariate rational functions defined on a collection of tetrahedra and pyramids. The rational form of the modeling function provides enough degrees of freedom so that the number of the surface patches is significantly reduced, and the surface has quadratic recover property.
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9

Leininger, S., J. Fan, M. Schmitz, and P. J. Stang. "Archimedean solids: Transition metal mediated rational self-assembly of supramolecular-truncated tetrahedra." Proceedings of the National Academy of Sciences 97, no. 4 (February 4, 2000): 1380–84. http://dx.doi.org/10.1073/pnas.030264697.

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10

DURHUUS, BERGFINNUR, HANS PLESNER JAKOBSEN, and RYSZARD NEST. "TOPOLOGICAL QUANTUM FIELD THEORIES FROM GENERALIZED 6J-SYMBOLS." Reviews in Mathematical Physics 05, no. 01 (March 1993): 1–67. http://dx.doi.org/10.1142/s0129055x93000024.

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Given an associative algebra with a distinguished finite set of representations that is closed under a (deformed) tensor product, and satisfies some technical assumptions, we define generalized 6j-symbols, and show that they can be associated, in a natural way, with certain labeled tetrahedra. Given a 3-dimensional compact oriented manifold M with boundary ∂M = Σ we choose an arbitrary triangulation [Formula: see text] of M and exploit the above correspondence between 6j-symbols and labeled tetrahedra to construct a vectorspace UΣ and a vector Z(M) ∈ UΣ, independent of [Formula: see text], and fulfilling the axioms of a topological quantum field theory as formulated by Atiyah [11]. Examples covered by our approach are quantum groups corresponding to the classical simple Lie algebras as well as, expectedly, chiral algebras of 2-dimensional rational conformal field theories.
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11

EVANS, DAVID E., and YASUYUKI KAWAHIGASHI. "FROM SUBFACTORS TO 3-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND BACK: A detailed account of Ocneanu’s theory." International Journal of Mathematics 06, no. 04 (August 1995): 537–58. http://dx.doi.org/10.1142/s0129167x95000201.

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A full proof of Ocneanu’s theorem is given that one can produce a rational unitary polyhedral 3-dimensional topological quantum field theory of Turaev-Viro type from a subfactor with finite index and finite depth, and vice versa. The key argument is an equivalence between flatness of a connection in paragroup theory and invariance of a state sum under one of the three local moves of tetrahedra. This was announced by A. Ocneanu and he gave a proof of Frobenius reciprocity and the pentagon relation, which produces a 3-dimensional TQFT via the Turaev-Viro machinery, but he has not published a proof of the converse direction of the equivalence. Details are given here along the lines suggested by him.
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12

Jiang, Pengfei, Fuwei Jiang, Mufei Yue, Jing Ju, Chunling Xu, Rihong Cong, and Tao Yang. "Ca 2 PbGa 8 O 15 : Rational Design, Synthesis, and Structure Determination of a Purely Tetrahedra‐Based Intergrowth Oxide." Angewandte Chemie International Edition 58, no. 18 (April 23, 2019): 5978–82. http://dx.doi.org/10.1002/anie.201901373.

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13

Jiang, Pengfei, Fuwei Jiang, Mufei Yue, Jing Ju, Chunling Xu, Rihong Cong, and Tao Yang. "Ca 2 PbGa 8 O 15 : Rational Design, Synthesis, and Structure Determination of a Purely Tetrahedra‐Based Intergrowth Oxide." Angewandte Chemie 131, no. 18 (April 23, 2019): 6039–43. http://dx.doi.org/10.1002/ange.201901373.

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14

Li, Feng, Skandan Chandrasekar, Aftab Ahmed, and Anna Klinkova. "Interparticle gap geometry effects on chiroptical properties of plasmonic nanoparticle assemblies." Nanotechnology 33, no. 12 (December 28, 2021): 125203. http://dx.doi.org/10.1088/1361-6528/ac3f12.

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Abstract Chiral linear assemblies of plasmonic nanoparticles with chiral optical activity often show low asymmetry factors. Systematic understanding of the structure-property relationship in these systems must be improved to facilitate rational design of their chiroptical response. Here we study the effect of large area interparticle gaps in chiral linear nanoparticle assemblies on their chiroptical properties using a tetrahelix structure formed by a linear face-to-face assembly of nanoscale Au tetrahedra. Using finite-difference time-domain and finite element methods, we performed in-depth evaluation of the extinction spectra and electric field distribution in the tetrahelix structure and its dependence on various geometric parameters. The reported structure supports various plasmonic modes, one of which shows a strong incident light handedness selectivity that is associated with large face-to-face junctions. This works highlights the importance of gap engineering in chiral plasmonic assemblies to achieve g-factors greater than 1 and produce structures with a handedness-selective optical response.
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15

Müller, Iris M., Daniela Möller, and Christoph A. Schalley. "Rational Design of Tightly Closed Coordination Tetrahedra that are Stable in the Solid State, in Solution, and in the Gas Phase." Angewandte Chemie International Edition 44, no. 3 (December 29, 2004): 480–84. http://dx.doi.org/10.1002/anie.200461800.

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16

Parrinello, Michele. "Atomistic Modeling of Crystal Nucleation and Growth." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C39. http://dx.doi.org/10.1107/s2053273314099604.

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Understanding crystal growth from solution is crucial to control the development of crystal morphologies. Since the interaction of crystals with their environment occurs through their surface, their shape controls a wide variety of properties. This is particularly important not only in nanotechnology, where shape-function relations play a key role, but also in medicine where, e.g., changing the morphology of particles allows for a better targeting of cancer cells. In this work we combine experiments, molecular simulations and theory to examine the morphology of urea crystals grown in different solutions. In order to get a rational representation of all the possible habits we introduce a Shape Diagram in which the habit dependence on the relative growth rates is displayed. A wide portion of the habit space can be experimentally explored by varying the composition of the mother solution. By doing so we obtain morphologies ranging from the paradigmatic needle-like habit obtained in water to regular tetrahedra obtained in acetonitrile/biuret mixtures. By combining advanced molecular simulation techniques and theory we can predict urea steady state crystal habits and their dependence on additive concentration and/or supersaturation, paving the way towards a rational control of the habit of crystals grown from solution. We present also some other example of nucleation processes which will lead to some rather surprising results even in the case of humble NaCl. Finally we discuss some recent advances that allow us to calculate nucleation rates.
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17

Volkov, Sergey, Rimma Bubnova, Maria Krzhizhanovskaya, and Lydia Galafutnik. "The first bismuth borate oxyiodide, Bi4BO7I: commensurate or incommensurate?" Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 76, no. 6 (November 10, 2020): 992–1000. http://dx.doi.org/10.1107/s2052520620012640.

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The first bismuth borate oxyiodide, Bi4BO7I, has been prepared by solid-state reaction in evacuated silica ampoules. Its crystal structure [space group Immm(00γ)000] comprises litharge-related layers of edge-sharing OBi4 tetrahedra; the interlayer space is filled by I− and [BO3]3− anions. The wavevector, q = 0.242 (3)c*, is very close to the rational value of c*/4, yet refinement based on commensurate modulation faces serious problems indicating the incommensurate nature of the modulation. The I-/[BO3]3− anions are ordered in a complex sequence along [001], i.e. –<–BO3–BO3–I–I–> n = 28–I–I–I–<–BO3–BO3–I–I–> n = 28–BO3–BO3–BO3–, leading to a structural modulation. The principal feature of the latter is the presence of –I–I–I– and –BO3–BO3–BO3– sequences that cannot be accounted for in the a × b × 4c supercell. The thermal expansion of Bi4BO7I is weakly anisotropic (αa = 8, αb = 15 and αc = 17 × 10−6 K−1 at 500 K) which is caused by preferential orientation of the borate groups.
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18

Phillips, Anthony. "Comparing the dynamics of coordination polyhedra in a metal-cyanide framework." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C590. http://dx.doi.org/10.1107/s2053273314094091.

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The enormous amount of attention devoted to metal-organic framework materials over the past two decades has yielded substantial synthetic control over these materials, so that specific topologies can be explicitly engineered by carefully selecting metal and ligand "building blocks". The dynamic behaviour of these materials, however, remains far less predictable: yet it is this behaviour that is the key to understanding the highly anomalous thermodynamic properties of many framework materials. When studying these compounds crystallographically it is important to acknowledge the limitations of Bragg scattering, which by revealing only a space- and time-averaged structure can give an incomplete or even actively misleading picture of the material's dynamic behaviour. For this reason, complementary techniques, such as XAFS, that are sensitive to the local structure of materials are vitally important. We have studied the behaviour of a prototypical framework material exhibiting near-zero thermal expansion, tetramethylammonium copper(I) zinc(II) cyanide, by X-ray absorption spectroscopy at the Cu and Zn K edges in combination with total neutron and X-ray scattering, supported by reverse Monte Carlo and density-functional theory calculations, thus simultaneously modelling the long-range and local structure of this material. Our results resolve for the first time the individual flexibility of the copper and zinc coordination tetrahedra, suggesting substantially higher flexibility of both types of polyhedra than was previously thought. These results shed new light on the atomic origins of this material's flexibility, and explain the mobility of guest molecules through the framework structure. More generally, this methodology points the way to being able to choose framework components for their dynamic properties, and hence to the rational synthesis of flexible framework materials with targeted thermodynamic properties.
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19

Sadykov, N. M. "Cohomology of the rational “electric” tetrahedron relation." Functional Analysis and Its Applications 51, no. 2 (April 2017): 123–34. http://dx.doi.org/10.1007/s10688-017-0174-3.

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20

Brückner, Christian, Ryan E. Powers, and Kenneth N. Raymond. "Symmetry-Driven Rational Design of a Tetrahedral Supramolecular Ti4L4 Cluster." Angewandte Chemie International Edition 37, no. 13-14 (August 3, 1998): 1837–39. http://dx.doi.org/10.1002/(sici)1521-3773(19980803)37:13/14<1837::aid-anie1837>3.0.co;2-a.

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21

Battaglia, Fiammetta, and Elisa Prato. "Toric Geometry of the Regular Convex Polyhedra." Journal of Mathematics 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2542796.

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We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.
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22

Mao, Xiuhai, Anna J. Simon, Hao Pei, Jiye Shi, Jiang Li, Qing Huang, Kevin W. Plaxco, and Chunhai Fan. "Activity modulation and allosteric control of a scaffolded DNAzyme using a dynamic DNA nanostructure." Chemical Science 7, no. 2 (2016): 1200–1204. http://dx.doi.org/10.1039/c5sc03705k.

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We report a DNA nanotechnology-enabled approach for the rational design of an allosteric deoxyribozyme by precisely and dynamically controlling the nanometer-scale interactions of two catalytic centers within a well-defined tetrahedral DNA scaffold.
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23

BAJAJ, CHANDRAJIT L., GUOLIANG XU, ROBERT J. HOLT, and ARUN N. NETRAVALI. "NURBS APPROXIMATION OF A-SPLINES AND A-PATCHES." International Journal of Computational Geometry & Applications 13, no. 05 (October 2003): 359–90. http://dx.doi.org/10.1142/s0218195903001232.

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Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a parametric tensor-product NURBS form for A-patch surfaces. We concentrate on cubic A-patches, providing a C1-continuous surface that interpolates a given triangulation together with surface normals at the vertices. In many cases we can generate cubic trimming curves that are rationally parametrizable on the triangular faces of the tetrahedra; for the remaining faces we resort to using quadratic curves, which are always rationally parametrizable, to approximate the cubic trimming curves.
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24

Chen, Lizhen, Jie Shen, and Chuanju Xu. "A Unstructured Nodal Spectral-Element Method for the Navier-Stokes Equations." Communications in Computational Physics 12, no. 1 (July 2012): 315–36. http://dx.doi.org/10.4208/cicp.070111.140711a.

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AbstractAn unstructured nodal spectral-element method for the Navier-Stokes equations is developed in this paper. The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property. It allows arbitrary triangular and tetrahedral mesh, affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method. The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.
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25

Hu, Sheng, and Ming-Liang Tong. "Rational design and construction of the first tetrahedral net with photoluminescent Cu4I4 cubane cluster as the tetrahedral node." Dalton Transactions, no. 7 (2005): 1165. http://dx.doi.org/10.1039/b500015g.

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26

Abramczyk, Jacek. "Symmetric Free Form Building Structures Arranged Regularly on Smooth Surfaces with Polyhedral Nets." Symmetry 12, no. 5 (May 6, 2020): 763. http://dx.doi.org/10.3390/sym12050763.

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The article is an original insight into interdisciplinary challenges of shaping innovative unconventional complex free form buildings roofed with multi-segment shell structures arranged with using novel parametric regular networks. The roof structures are made up of nominally plane thin-walled folded steel sheets transformed elastically and rationally into spatial shapes. A method is presented for creating such symmetric structures based on the regular spatial polyhedral networks created as a result of a composition of many complete reference tetrahedrons by their common flat sides and straight side edges arranged regularly and symmetrically in the three-dimensional Euclidean space. The use of the regularity and symmetry in the process of shaping different forms of (a) single tetrahedral meshes and whole consistent polyhedral structures, (b) individual plane walls and complex elevations, (c) single transformed folds, entire corrugated shell roofs, and their structures allow a creative search for attractive rational parametric solutions using a few author’s parametric algorithms and their implementation as built-in commands of the AutoCAD visual editor or applications of the Rhino/Grasshopper program.
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27

Qi, Liang, Huacui Hou, Fei Ling, and Weihui Zhong. "The cinchona alkaloid squaramide catalyzed asymmetric Pictet–Spengler reaction and related theoretical studies." Organic & Biomolecular Chemistry 16, no. 4 (2018): 566–74. http://dx.doi.org/10.1039/c7ob02606d.

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An asymmetric Pictet–Spengler reaction between tryptamine derivatives and aldehydes has been developed using a cinchona alkaloid squaramide as the catalyst. The reaction produced tetrahedron-β-carbolines in good to excellent yields and ee values. A rational mechanistic pathway was proposed based on DFT calculations.
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28

Vaidya, Shefali, Apoorva Upadhyay, Saurabh Kumar Singh, Tulika Gupta, Subrata Tewary, Stuart K. Langley, James P. S. Walsh, Keith S. Murray, Gopalan Rajaraman, and Maheswaran Shanmugam. "A synthetic strategy for switching the single ion anisotropy in tetrahedral Co(ii) complexes." Chemical Communications 51, no. 18 (2015): 3739–42. http://dx.doi.org/10.1039/c4cc08305a.

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We have shown for the first time, by simply exploiting the hard/soft nature of ligands, single ion magnetic anisotropy of Co(ii) tetrahedral complexes can be switched (+ve to −ve orvice versa) rationally.
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29

Ciccariello, Salvino. "The correlation functions of the regular tetrahedron and octahedron." Journal of Applied Crystallography 47, no. 4 (August 1, 2014): 1445–48. http://dx.doi.org/10.1107/s1600576714014289.

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The expressions of the autocorrelation functions (CFs) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and (a + br 2)1/2, a and b being appropriate integers and r a distance. The CF expressions make the numerical determination of the corresponding scattering intensities fast and accurate even in the presence of a size dispersion.
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30

Oppel (née Müller), Iris M, and Kirsten Föcker. "Rational Design of a Double-Walled Tetrahedron Containing Two DifferentC3-Symmetric Ligands." Angewandte Chemie International Edition 47, no. 2 (January 2008): 402–5. http://dx.doi.org/10.1002/anie.200703789.

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31

Bakshi, Pradip K., Sergey V. Sereda, Osvald Knop, and Michael Falk. "Crystal chemistry of tetraradial species. Part 6. Embarras de richesses: lithium cation coordinated by eight O—H … phenyl bonds." Canadian Journal of Chemistry 72, no. 10 (October 1, 1994): 2144–52. http://dx.doi.org/10.1139/v94-272.

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Lithium tetraphenylborate tetrahydrate, [Li(OH2)4]BPh4 (LiTBw; tetragonal, I41/a, a = 27.566(2) Å, c = 12.228(2) Å, Z = 16) is remarkable in that the four H2O molecules coordinating the Li+ ion all form O—H …π hydrogen bonds to the phenyl groups of the anion. LiTBw thus appears to be the first reported example of such an exhaustive O—H …π coordination and can be described as a 3-dimensional, completely H-bonded polymer in which all the H2O hydrogens are bonded to phenyl groups and all the phenyl groups are involved in O—H … phenyl bonds. Six of the O—H … phenyl bonds are essentially normal and two are highly bent, possibly bifurcated. The existence of the H-bonds has been corroborated from variable-temperature FT-ir spectra of weakly deuterated LiTBw. The O—Li—O angles in the LiO4 coordination tetrahedron (of symmetry C1) exhibit large departures from the tetrahedral angle, two of the angles bisected by a quasi-S4 axis being 118.3° and 122.5°, respectively. An ab initio (6-31G*) investigation of the Li(OH2)4+ and Be(OH2)42+ cations has shown that such large O—M—O angles are to be expected even in the free ions and are thus not necessarily the result of packing effects. A detailed comparison with several Li(OH2)4+ and Be(OH2)42+ salts provides a rationale for the observed M(OH2)4n+ (M = Li, Be) geometries.
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32

Tian, Yiqiao, Yanyu Huang, Pan Gao, and Tianfeng Chen. "Nucleus-targeted DNA tetrahedron as a nanocarrier of metal complexes for enhanced glioma therapy." Chemical Communications 54, no. 68 (2018): 9394–97. http://dx.doi.org/10.1039/c8cc04021d.

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33

Zhang, De-Xiang, Hai-Xia Zhang, Tian Wen, and Jian Zhang. "Targeted design of a cubic boron imidazolate cage with sensing and reducing functions." Dalton Transactions 44, no. 20 (2015): 9367–69. http://dx.doi.org/10.1039/c5dt00639b.

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A cubic cationic cage is rationally designed by using tridentate boron-imidazolate ligands to link tetrahedral metal Zn(ii) centers, which displays excellent properties in the Cr2O72− exchange and can reduce Au3+ ions into Au nanoparticles directly.
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34

Liang, Li-Li, Jun Zhang, Shi-Bin Ren, Gen-Wu Ge, Yi-Zhi Li, Hong-Bin Du, and Xiao-Zeng You. "Rational synthesis of a microporous metal–organic framework with PtS topology using a semi-rigid tetrahedral linker." CrystEngComm 12, no. 7 (2010): 2008. http://dx.doi.org/10.1039/b925903a.

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35

Zhong, Yi-ning, Yan Zhang, Yun-qiong Gu, Shi-yun Wu, Wen-ying Shen, and Ming-xiong Tan. "NovelFeIIandCoIIComplexes of Natural Product Tryptanthrin: Synthesis and Binding with G-Quadruplex DNA." Bioinorganic Chemistry and Applications 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5075847.

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Tryptanthrin is one of the most important members of indoloquinoline alkaloids. We obtained this alkaloid fromIsatis. Two novelFeIIandCoIIcomplexes of tryptanthrin were first synthesized. Single-crystal X-ray diffraction analyses show that these complexes display distorted four-coordinated tetrahedron geometry via two heterocyclic nitrogen and oxygen atoms from tryptanthrin ligand. Binding with G-quadruplex DNA properties revealed that both complexes were found to exhibit significant interaction with G-quadruplex DNA. This study may potentially serve as the basis of future rational design of metal-based drugs from natural products that target the G-quadruplex DNA.
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36

Alekseytsev, Anatoliy Victorovich, and Natalia Sergeevna Kurchenko. "Shape Synthesis for Skeletal Structures Using а Genetic Algorithm and Delaunay Tetrahedron Partition." Applied Mechanics and Materials 736 (March 2015): 134–39. http://dx.doi.org/10.4028/www.scientific.net/amm.736.134.

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Method of searching for rational shapes of skeletal structures based on the use of Delaunay tetrahedron partition algorithms with constraints and evolutionary modeling has been developed. Topology of load-bearing rod system is synthesized on specified multitude of nodes at fixed number of rods. Established structures are considered redundant and are optimized by means of excluding individual members. Optimization is performed with the modified genetic algorithm pursuant to criterion of minimum weight of structure. An example of synthesis of rectangular rod structure showing performance of suggested approach in terms of shape synthesis of trusses has been given.
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37

Korohodska, A. N., G. N. Shabanova, O. M. Tychyna, and N. B. Deviatova. "Calculation and evaluation of temperatures and eutectic compositions of multicomponent sections of the CaO—Al2O3—Fe2O3—Cr2O3 system." Scientific research on refractories and technical ceramics 120 (December 30, 2020): 120–25. http://dx.doi.org/10.35857/2663-3566.120.11.

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The predicted service temperatures and eutectic compositions of the polycomponent sections of the CaO—Al2O3—Fe2O3—Cr2O3 system were calculated and evaluated. According to the results of geometrical topological studies of this system, the CaAl2O4—CaFe2O4—CaCr2O4—Ca4Al2Fe2O10 tetrahedron has the largest relative volume and the smallest degree of asymmetry. However, the composition of this tetrahedron includes two compounds that do not have hydraulic activity; this will adversely affect the cement strength. Presence of CaFe2O4 will significantly reduce the composition melting point, that why the CaAl2O4—Ca12Al7O33—CaCr2O4—Ca4Al2F2O10 tetrahedron is of more interest. The calculations result of temperatures and eutectic compositions of triple and tetra-component sections of the CaAl2O4—Ca12Al7O33—CaCr2O4—Ca4Al2F2O10 region of the CaO—Al2O3—Fe2O3—Cr2O3 system are presented. The phases that make up this tetrahedron are highly likely to exist in the CaO—Al2O3—Fe2O3—Cr2O3 system, which will allow us to develop a stable technology for the oil-well cementing materials based on calcium-ferro-alumina chromate cement without special techniques for ensuring high accuracy of the starting components dosage. The paper presents graphic images of the liquidus surface of polycomponent sections of optimal region of system. Selected areas are the most suitable for producing oil-well binding materials with an elevated temperature in application. It was found that, composite materials based on this system can be used at temperatures above 1350 °C. Based on the analysis of temperatures and eutectics compositions of polycomponent section, the use of rational area compositions for producing high-temperature resisting oil-well cement has been proved.
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38

Chun, Hyungphil, Woojeong Bak, Keunil Hong, and Dohyun Moon. "A Simple and Rational Approach for Binodal Metal–Organic Frameworks with Tetrahedral Nodes and Unexpected Multimodal Porosities from Nonstoichiometric Defects." Crystal Growth & Design 14, no. 4 (March 6, 2014): 1998–2002. http://dx.doi.org/10.1021/cg500116f.

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39

Ovchinnikov, Alexander, and Svilen Bobev. "Electronic stabilization by occupational disorder in the ternary bismuthide Li3–x–y In x Bi (x ≃ 0.14, y ≃ 0.29)." Acta Crystallographica Section C Structural Chemistry 76, no. 6 (May 20, 2020): 585–90. http://dx.doi.org/10.1107/s2053229620006439.

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A ternary derivative of Li3Bi with the composition Li3–x–y In x Bi (x ≃ 0.14, y ≃ 0.29) was produced by a mixed In+Bi flux approach. The crystal structure adopts the space group Fd\overline{3}m (No. 227), with a = 13.337 (4) Å, and can be viewed as a 2 × 2 × 2 superstructure of the parent Li3Bi phase, resulting from a partial ordering of Li and In in the tetrahedral voids of the Bi fcc packing. In addition to the Li/In substitutional disorder, partial occupation of some Li sites is observed. The Li deficiency develops to reduce the total electron count in the system, counteracting thereby the electron doping introduced by the In substitution. First-principles calculations confirm the electronic rationale of the observed disorder.
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40

Tang, Xiaowen, Junjie Wang, Nan Zhao, Qingzhu Zhang, and Wenxing Wang. "Theoretical study on the hydrolytic step in the biotransformation of β-hexachlorocyclohexane degraded by haloalkane dehalogenase LinB." Canadian Journal of Chemistry 95, no. 7 (July 2017): 729–35. http://dx.doi.org/10.1139/cjc-2016-0653.

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The hydrolytic process of LinB-catalyzed biotransformation of a notorious contaminant β-HCH was investigated in atomistic detail with a combined quantum mechanics/molecular mechanics approach. The Boltzmann-weighted averaging method amended by disproportionate effect analysis was showed to capture the fluctuation of a single molecule enzyme reaction. With the potential barriers of 18.7 and 2.6 kcal/mol, two elementary steps that refer to formation and decomposition of a tetrahedral intermediate are involved in the hydrolytic reaction, respectively. Polarized by Glu132, His272 serves as a proton carrier along the whole hydrolysis reaction. The electrostatic influence analysis highlighted residue Leu248 as a possible mutation target for rational design of LinB in enzyme modification. Further spatial location analysis provided explanation for the opposite effect of Asn38 toward the two elementary steps. Getting insight into the catalytic details and the structure and function of LinB can enrich the knowledge of it and promote its application in bioremediation of chlorinated hydrocarbon pollutants.
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41

Szostak, Michal, and Guangchen Li. "Non-Classical Amide Bond Formation: Transamidation and Amidation of Activated Amides and Esters by Selective N–C/O–C Cleavage." Synthesis 52, no. 18 (May 15, 2020): 2579–99. http://dx.doi.org/10.1055/s-0040-1707101.

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In the past several years, tremendous advances have been made in non-classical routes for amide bond formation that involve transamidation and amidation reactions of activated amides and esters. These new methods enable the formation of extremely valuable amide bonds via transition-metal-catalyzed, transition-metal-free, or metal-free pathways by exploiting chemoselective acyl C–X (X = N, O) cleavage under mild conditions. In a broadest sense, these reactions overcome the formidable challenge of activating C–N/C–O bonds of amides or esters by rationally tackling nN → π*C=O delocalization in amides and nO → π*C=O donation in esters. In this account, we summarize the recent remarkable advances in the development of new methods for the synthesis of amides with a focus on (1) transition-metal/NHC-catalyzed C–N/C–O bond activation, (2) transition-metal-free highly selective cleavage of C–N/C–O bonds, (3) the development of new acyl-transfer reagents, and (4) other emerging methods.1 Introduction2 Transamidation of Amides2.1 Transamidation by Metal–NHC Catalysis (Pd–NHC, Ni–NHC)2.2 Transition-Metal-Free Transamidation via Tetrahedral Intermediates2.3 Reductive Transamidation2.4 New Acyl-Transfer Reagents2.5 Tandem Transamidations3 Amidation of Esters3.1 Amidation of Esters by Metal–NHC Catalysis (Pd–NHC, Ni–NHC)3.2 Transition-Metal-Free Amidation of Esters via Tetrahedral Intermediates3.3 Reductive Amidation of Esters4 Transamidations of Amides by Other Mechanisms5 Conclusions and Outlook
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42

Ejarque, Daniel, Teresa Calvet, Mercè Font-Bardia, and Josefina Pons. "Synthesis of a Heterometallic [Zn2Ca] Pinwheel Array Stabilized by Amide-Amide Synthons." Inorganics 10, no. 8 (August 14, 2022): 118. http://dx.doi.org/10.3390/inorganics10080118.

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The rational design of heterometallic compounds bearing s-block metal ions have been a difficult task for chemists owing to their lack of preferential geometries. However, some strategies, such as the design of coordinating pockets with different sizes and/or donor atoms, have offered great results. In this work, this strategy has been tested using Ca(II) as an s-block metal ion and a compound previously obtained by our group with the formula [Zn3(μ-ACA)6(4-phpy)2], which contains tetrahedral N,O- and octahedral O-coordinating pockets as a model structure. From this work, the corresponding heterometallic compound with the formula [Zn2Ca(μ-ACA)6(4-phpy)2]·EtOH (1) has been successfully synthesized, and fully characterized, and its crystal structure has been elucidated. Furthermore, we have compiled all the crystal structures containing [Zn2M] pinwheel secondary building units (SBUs), where M stands for an s-block metal ion, and the observed tendencies, as well as the promising applications as template SBUs for the preparation of 1D–3D coordination polymers, have been discussed. Finally, solid-state UV-Vis and photoluminescence have been recorded and compared with the homometallic [Zn3(μ-ACA)6(4-phpy)2] compound.
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43

Rochlitz, Raphael, Marc Seidel, and Ralph-Uwe Börner. "Evaluation of three approaches for simulating 3-D time-domain electromagnetic data." Geophysical Journal International 227, no. 3 (August 4, 2021): 1980–95. http://dx.doi.org/10.1093/gji/ggab302.

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SUMMARY We implemented and compared the implicit Euler time-stepping approach, the inverse Fourier transform-based approach and the Rational Arnoldi method for simulating 3-D transient electromagnetic data. We utilize the finite-element method with unstructured tetrahedral meshes for the spatial discretization supporting irregular survey geometries and anisotropic material parameters. Both, switch-on and switch-off current waveforms, can be used in combination with direct current solutions of Poisson problems as initial conditions. Moreover, we address important topics such as the incorporation of source currents and opportunities to simulate impulse as well as step response magnetic field data with all approaches for supporting a great variety of applications. Three examples ranging from simple to complex real-world geometries and validations against external codes provide insight into the numerical accuracy, computational performance and unique characteristics of the three applied methods. We further present an application of logarithmic Fourier transforms to convert transient data into the frequency domain. We made all approaches available in the open-source Python toolbox custEM, which previously supported only frequency-domain electromagnetic data. The object-oriented software implementation is suited for further elaboration on distinct modelling topics and the presented examples can serve for benchmarking other codes.
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44

Geng, Haibin, Xinxin Ding, Hao Du, Jiaxin Shi, Changyong Li, and Xiaoke Li. "Application of Self-Compacting Steel Fiber Reinforced Concrete for Pervious Frames Used for River Revetment." Applied Sciences 12, no. 20 (October 17, 2022): 10457. http://dx.doi.org/10.3390/app122010457.

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Aimed at improving the production efficiency of tetrahedron-like pervious frames for the river revetment, self-compacting steel fiber reinforced concrete (SFRC) was applied to strengthen the tensile resistance of concrete to remove conventional steel bars used as reinforcement. The workability and mechanical properties of self-compacting SFRC were experimentally studied with the volume fraction of steel fiber changed from 0.4% to 1.2%, and the rational volume fraction of 0.8% was determined for producing the pervious frames. Based on the flow-induced orientation of the steel fibers in the fresh mix, the casting process of self-compacting SFRC was optimal from one inclined rod to other two inclined rods and the horizontal rods of the pervious frame. The loading capacities of pervious frames during lifting and stacking were respectively detected by the simulation tests on the testing machine, which ensure the safety of pervious frames lifted six layers together and stacked for nineteen layers. By testing groups of pervious frames throwed in and then salvaged from the river, the quality of pervious frames without any damage was observed. Finally, the pervious frames were successfully applied in an engineering project for the river revetment.
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45

Yang, Yao, Yin Xiong, Megan E. Holtz, Xinran Feng, Rui Zeng, Gary Chen, Francis J. DiSalvo, David A. Muller, and Héctor D. Abruña. "Octahedral spinel electrocatalysts for alkaline fuel cells." Proceedings of the National Academy of Sciences 116, no. 49 (November 14, 2019): 24425–32. http://dx.doi.org/10.1073/pnas.1906570116.

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Designing high-performance nonprecious electrocatalysts to replace Pt for the oxygen reduction reaction (ORR) has been a key challenge for advancing fuel cell technologies. Here, we report a systematic study of 15 different AB2O4/C spinel nanoparticles with well-controlled octahedral morphology. The 3 most active ORR electrocatalysts were MnCo2O4/C, CoMn2O4/C, and CoFe2O4/C. CoMn2O4/C exhibited a half-wave potential of 0.89 V in 1 M KOH, equal to the benchmark activity of Pt/C, which was ascribed to charge transfer between Co and Mn, as evidenced by X-ray absorption spectroscopy. Scanning transmission electron microscopy (STEM) provided atomic-scale, spatially resolved images, and high-energy-resolution electron-loss near-edge structure (ELNES) enabled fingerprinting the local chemical environment around the active sites. The most active MnCo2O4/C was shown to have a unique Co-Mn core–shell structure. ELNES spectra indicate that the Co in the core is predominantly Co2.7+ while in the shell, it is mainly Co2+. Broader Mn ELNES spectra indicate less-ordered nearest oxygen neighbors. Co in the shell occupies mainly tetrahedral sites, which are likely candidates as the active sites for the ORR. Such microscopic-level investigation probes the heterogeneous electronic structure at the single-nanoparticle level, and may provide a more rational basis for the design of electrocatalysts for alkaline fuel cells.
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46

Gao, Lu, Liying Liu, Yunfei Tian, Qianfan Yang, Peng Wu, Chunhai Fan, Qiang Zhao, and Feng Li. "Probing the Formation Kinetics and Thermodynamics with Rationally Designed Analytical Tools Enables One-Pot Synthesis and Purification of a Tetrahedral DNA Nanostructure." Analytical Chemistry 93, no. 18 (April 22, 2021): 7045–53. http://dx.doi.org/10.1021/acs.analchem.1c00363.

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47

Yeniyol, M. "Characterization of a Mg-rich and low-charge saponite from the Neogene lacustrine basin of Eskisşehir, Turkey." Clay Minerals 42, no. 4 (December 2007): 541–48. http://dx.doi.org/10.1180/claymin.2007.042.4.10.

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AbstractThe saponite examined occurs as two 0.1 m thick layers in a Pliocene sequence consisting of dolomite and dolomitic marl. To characterize this material, mineralogical and structural analyses (XRD, SEM and FTIR), thermal analyses (DTA, TG) and chemical analyses (ICP-ES) were performed. From XRD patterns of randomly-oriented powder samples, the first basal reflection appears as an asymmetric and broad peak with d001 values varying between 16.55 and 17.32 Å. In oriented and air-dried samples, this reflection occurs between 14.45 and 16.42 Å and is fairly symmetrical with FWHM of 2.7º2θ. Oriented and ethylene glycol-solvated samples produce a rational series of basal reflections, where 001 occurs at ~17.8 Å as an intense, narrow (1.1º2θ) and fairly symmetrical reflection. Upon solvation with glycerol, the 001 reflection shifts to ~18.7 Å.The chemical composition of this saponite is similar to stevensite. However, the structural formula of Na0.114Ca0.013K0.003(Mg2.957Al0.004Fe0.028Ti0.004)(Si3.826Al0.174)O10(OH)2 indicates that vacancies in the octahedral sheet do not exist. The negative layer charge arises nearly entirely from the substitutions in the tetrahedral sheet, with the net layer charge of –0.148, smaller than for common smectites.Due to the XRD characteristics and particularly the layer-charge distribution, it was concluded that this mineral is a Mg-rich saponite with low layer charge. The saponite was formed by direct precipitation in an alkaline lake environment from Mg- and Si-rich solutions at high pH.
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48

de Gelder, R., and A. Janner. "Remarkable features in lattice-parameter ratios of crystals. I. Orthorhombic, tetragonal and hexagonal crystals." Acta Crystallographica Section B Structural Science 61, no. 3 (May 13, 2005): 287–95. http://dx.doi.org/10.1107/s0108768105006968.

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The investigation of the lattice-parameter ratios of tetrahedral and hexagonal–rhombohedral inorganic compounds, as reported by Constant & Shlichta [(2003), Acta Cryst. A59, 281–282], has been extended to the structural data found for organic and metal-organic compounds (CSD), for bio-macromolecular crystals (PDB) and for inorganic materials (ICSD). In this first part of the series, the frequency distribution of orthorhombic, tetragonal and hexagonal crystals is presented. The results obtained confirm the existence of sharp peaks as a function of the ratios of lattice parameters and reveal additional exponential components, decaying for large and small values of these ratios. Practically all the important peaks occur at ratios which correspond to lattices having metric tensors with rational entries, the so-called integral lattices. The exponential component is interpreted as expressing a general statistical distribution which is valid for the generic crystal lattices, i.e. those normally considered. The exponential fraction dominates the peaked component in the organic and metal-organic cases, is less important for bio-macromolecular crystals and is much less important than the sharp peaks for inorganic crystals. Remarkable is the crystallographic relevance of the isometric hexagonal lattice, characterized by the axial ratio c/a = 1 and first observed in the molecular form of a protein. In the frequency distribution of 12 117 inorganic hexagonal crystals, the highest peak of 937 crystals occurs for c = a. In the hexagonal case of the bio-macromolecules the most important peak of 422 crystals is observed near the ideal h.c.p. (hexagonal closed packing) ratio of (8/3)1/2.
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49

Kumar, Manoj, Monika Bhardwaj, Poonam Yadav, Divya Vashishth, Sulekha Chahal, Sunita Dalal, and Sudhir Kumar Kataria. "A review on distribution, properties, genetic organization, immobilisation and applications of urease." Journal of Applied and Natural Science 14, no. 4 (December 19, 2022): 1413–29. http://dx.doi.org/10.31018/jans.v14i4.3668.

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Urease, a nickel-containing metalloenzyme is getting remarkable attention due to a diverse range of applications for mankind. Urease plays a magnificent role in various field like agriculture, analytical, geological phenomena, beverage industry and is an important diagnostic tool. Urease is mainly present in bacteria, fungi, plants and invertebrates and its manifestation in specific genera may open new vistas for its taxonomic position. Various qualitative and quantitative assays are also reported for the estimation of urease enzyme. Urease based biosensors utilizing green synthesis on nanoparticles are also trending. Recently developed inhibitors against urease were discussed in the review. Inhibitory mechanisms involving the structural similarity of the substrate through modification or derivatization can also help in rational drug design by two possible competitive ways either by mimicking monodentate urea binding or binding as a tetrahedral intermediate. Immobilisation of urease through gel entrapment, using non-covalent and covalent protein tags, cross linkage, covalent bonding, using composite films, Teflon, co-precipitation and coating on nanoparticles is also reported. This review also comprised of various application of urease including enhancement of fertility in the soil, cell to cell organization, protection to predators, treatment of various bladder related diseases and infections, analysis of urea and heavy metal ions, biocementation, pollution control by bioleaching of heavy metals and making beverages urea and ethyl carbamate free. As researchers have a keen interest in urease enzyme at present, most of its aspects were incorporated in the article to make it helpful to the scientific community for further research related to the development of new inhibitors and add on applications of urease for the upliftment of the human as well as environment.
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50

Liu, Zhantao, Alex Chien, Shuo Wang, Zihao Lin, Jue Liu, Yifei Mo, and Hailong Chen. "Insights into the Crystal Structure of Halide Solid Electrolytes and Li Diffusion." ECS Meeting Abstracts MA2022-02, no. 4 (October 9, 2022): 390. http://dx.doi.org/10.1149/ma2022-024390mtgabs.

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Lithium halides with general formula Li3MX6 (M = metals such as Y, In, Yb or Sc; X = Cl or Br) have attracted significant attention because of their promising room temperature conductivities and high oxidative stability[1]. Li-ion mobility in these halides is strongly affected by the synthesis method and parameters. In Li3YCl6 with a hexagonal-close-packed (hcp) anion framework, the ionic conductivity is commonly observed to decrease with increased crystallinity. While in Li3YBr6 with a face-centered-cubic (fcc) anion framework, the ionic conductivity increases with increased crystallinity. So far there is no clear explanation for such opposite trends in these two otherwise very similar crystal structures. Ab initio molecular dynamics (AIMD) simulation[2] suggested higher ionic conductivity and lower activation energy in Li3YCl6 than inLi3YBr6, which also does not agree well with the experimental observation that Li3YBr6 commonly shows higher conductivity than Li3YCl6. Above-mentioned unexplained observations and inconsistencies imply that likely some critical structural features of these halides that strongly impact ionic diffusion are not yet explored nor taken into consideration. Here, we report our recent findings in the crystal structure of Li3YCl6 and Li3YBr6 and the design, synthesis and electrochemical testing of a few new halide compounds designed based on the new findings. The crystal structures are investigated with using ex situ and in situ synchrotron X-ray diffraction (XRD) and neutron diffraction (ND). Our study[3] demonstrated that the discrepancies between simulated and experimental results in Li3YBr6-type structure is partly caused by the grain boundary. Through PDF data analysis, we provide experimental evidences of cation local ordering in ab plane and stacking fault along c-direction in Li3YBr6-type structure. The lower ionic conductivity in low crystallinity is owing to the blockage of Li diffusion channel along c-direction caused by the stacking fault. Moreover, a new tetrahedral Li-site is identified, which may be critical in understanding the Li diffusion behaviors. Via rationally tuning Li occupancies at the tetrahedral and octahedral sites, low Li diffusion barriers can be achieved, which is in consistence with theoretical calculation results. [1] T. Asano, A. Sakai, S. Ouchi, M. Sakaida, A. Miyazaki, S. Hasegawa, Advanced Materials 2018, 30, 1803075. [2] S. Wang, Q. Bai, A. M. Nolan, Y. Liu, S. Gong, Q. Sun, Y. Mo, Angewandte Chemie International Edition 2019, 58, 8039-8043. [3] Z. Liu, S. Ma, J. Liu, S. Xiong, Y. Ma, H. Chen, ACS Energy Letters 2021, 6, 298-304.
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