Complete hyperbolic lattices derived from tessellations of type {4g, 4g}

Queiroz Catia Quilles; Benedito Cintya W.; Interlando J. Carmelo; Palazzo Reginaldo

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Complete hyperbolic lattices derived from tessellations of type {4g, 4g}

机译：源自{4g，4g}类型的镶嵌的完整双曲格

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摘要

Regular tessellations of the hyperbolic plane play an important role in the design of signal constellations for digital communication systems. Self-dual tessellations of type {4g, 4g} with g = 2(n), 3 . 2(n), and 5 . 2(n) have been considered where the corresponding arithmetic Fuchsian groups are derived from quaternion orders over quadratic extensions of the rational. The objectives of this work are to establish the maximal orders derived from {4g, 4g} tessellations for which the hyperbolic lattices are complete (the motivation for constructing complete hyperbolic lattices is their application to the design of hyperbolic lattice codes), and to identify the arithmetic Fuchsian group associated with a quaternion algebra and a quaternion order.

机译：双曲平面的规则镶嵌在数字通信系统的信号星座设计中起着重要作用。类型为{4g，4g}且g = 2（n），3的自对偶镶嵌。 2（n）和5。已经考虑了2（n），其中相应的算术Fuchsian组是从有理数的二次扩展上的四元数阶推导而来的。这项工作的目的是建立从{4g，4g}棋盘格中得出的最大阶数，对于这些棋盘格来说，双曲晶格是完整的（构造完整双曲晶格的动机是将其应用于双曲晶格代码的设计），并确定与四元数代数和四元数阶相关的算术Fuchsian群。

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《Journal of algebra and its applications》 |2016年第8期|共28页
作者
Queiroz Catia Quilles; Benedito Cintya W.; Interlando J. Carmelo; Palazzo Reginaldo;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Hyperbolic geometry; arithmetic Fuchsian group; quaternion order;

机译：双曲几何;算术Fuchsian群;四元数阶;

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1. Complete hyperbolic lattices derived from tessellations of type {4g, 4g} [J] . Queiroz Catia Quilles, Benedito Cintya W., Interlando J. Carmelo, Journal of algebra and its applications . 2016,第8期

机译：源自{4g，4g}类型的镶嵌的完整双曲格
2. Danish type gelsolin related amyloidosis: 654G-T mutation is assoicated with a disease pathogenetically and clinically similar to that caused by the 654G-A mutation (familial amyloidosis of the Finnish type) [J] . Carl Peter J Maury, Mikko Lijestrom, Gudrun Boysen Journal of Clinical Pathology . 2000,第2期

机译：丹麦凝溶胶蛋白相关的淀粉样变性病：654G-T突变与在疾病上和临床上与654G-A突变引起的疾病（芬兰型家族性淀粉样变性）相关
3. Photoconductivity of the Single Crystals Pb4Ga4GeS12 and Pb4Ga4GeSe12 [J] . Hadj Bellagra, Oksana Nyhmatullina, Yuri Kogut, Proceedings . 2020,第1期

机译：单晶Pb4ga4ges12和Pb4ga4gese12的光电导
4. A 4GS/s Time-Interleaved RF ADC in 65nm CMOS with 4GHz Input Bandwidth [C] . Matt Straayer, Jim Bales, Dwight Birdsall, IEEE International Solid-State Circuits Conference . 2016

机译：具有4GHz输入带宽的65nm CMO中的4GS / s时间交错的RF ADC
5. Pokeweed antiviral protein interacts with plant translation initiation factors eIF4G and eIFiso4G. [D] . Wang, Melan. 2004

机译：商陆抗病毒蛋白与植物翻译起始因子eIF4G和eIFiso4G相互作用。
6. Danish type gelsolin related amyloidosis: 654G-T mutation is associated with a disease pathogenetically and clinically similar to that caused by the 654G-A mutation (familial amyloidosis of the Finnish type) [O] . C. P. Maury, M. Liljestrom, G. Boysen, 2000

机译：丹麦凝溶胶蛋白相关淀粉样变性病：654G-T突变与在疾病上和临床上与654G-A突变引起的疾病（芬兰型家族性淀粉样变性）相关
7. High pressure matrix-assisted laser desorption/ionization fourier transform mass spectrometry for minimization of ganglioside fragmentation11Abbreviations: Gangliosides are abbreviated according to the system of L. Svennerholm 1–3 as follows: GM1, Galβ1 → 3GalNAcβ1 → 4(Neu5NAcα2 → 3) Galβ1 → 4Glcβ1 → 1′Cer; GD1a, Neu5NAcα2 → 3Galβ1 → 3GalNAc β1→ 4(Neu5NAcα2 → 3)Galβ1 → 4Glcβ1 → 1′Cer; GT1b, Neu5NAcα2 → 3Galβ1 → 3GalNAcβ1 → 4(Neu5NAcα2 → 8Neu5NAcα2 → 3) Galβ1 → 4Glcβ1 → 1′Cer; GQ1b, Neu5NAcα2 → 8Neu5NAcα2 → 3Galβ1→3 GalNAcβ1 → 4 (Neu5NAcα2 → 8Neu5NAcα2 → 3)Galβ1 → 4Glcβ1 → 1′Cer; QP1 (in this case is a mixture of QP1b and QP1c), QP1b, Neu5NAcα2 → 8Neu5NAcα2 → 8 Neu5NAcα2 → 3 Galβ1 → 3GalNAcβ1 → 4(Neu5NAcα2 → 8Neu5NAcα2 → 3) Galβ1 → 4Glcβ1 → 1′Cer and QP1c, Neu5NAcα2 → 8Neu5NAcα2 → 3Galβ1→3 GalNAcβ1→ 4 (Neu5NAcα2 → 8 Neu5NAcα2 → 8Neu5NAcα2 → 3)Galβ1→ 4 Glcβ1 → 1′Cer. [O] . O’Connor Peter B, Mirgorodskaya Ekaterina, Costello Catherine E 2002

机译：最小化神经节苷脂碎片的高压基质辅助激光解吸/电离傅里叶变换质谱法11缩写：根据L. Svennerholm 1-3的系统，神经节苷脂的缩写如下：GM1，Galβ1→3GalNAcβ1→4（Neu5NAcα2→3） Galβ1→4Glcβ1→1′Cer; GD1a，Neu5NAcα2→3Galβ1→3GalNAcβ1→4（Neu5NAcα2→3）Galβ1→4Glcβ1→1'Cer; GT1b，Neu5NAcα2→3Galβ1→3GalNAcβ1→4（Neu5NAcα2→8Neu5NAcα2→3）Galβ1→4Glcβ1→1'Cer; GQ1b，Neu5NAcα2→8Neu5NAcα2→3Galβ1→3GalNAcβ1→4（Neu5NAcα2→8Neu5NAcα2→3）Galβ1→4Glcβ1→1'Cer; QP1（在这种情况下是QP1b和QP1c的混合物），QP1b，Neu5NAcα2→8Neu5NAcα2→8Neu5NAcα2→3Galβ1→3GalNAcβ1→4（Neu5NAcα2→8Neu5NAcα2c→3）Galβ1→4GlcNA12→8'Ner5NAcα2→8' 3Galβ1→3GalNAcβ1→4（Neu5NAcα2→8Neu5NAcα2→8Neu5NAcα2→3）Galβ1→4Glcβ1→1'Cer。

Complete hyperbolic lattices derived from tessellations of type {4g, 4g}

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