@article{ZVMMF_2003_43_6_a1,
author = {R. V. Galiulin},
title = {Delone systems as a basis of geometry of the discrete world},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {790--801},
year = {2003},
volume = {43},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_6_a1/}
}
R. V. Galiulin. Delone systems as a basis of geometry of the discrete world. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 6, pp. 790-801. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_6_a1/
[1] Delaunay B. N., “Sur la sphere vide”, Proc.Internat. Math. Congress (Toronto, 1924), Univ.Toronto Press, 1928, 695–700
[2] Galiulin P. B., “Sistemy Delone”, Kristallografiya, 25:5 (1980), 901–908 | MR
[3] Agishtein M. E., Migdal A. A., “Kak uvidet nevidimoe. Eksperiment na displee”, Pervye shagi vychisl. fiz. Ser. Kibernetika, Nauka, M., 1989, 141–170
[4] Delone B. N., “Geometriya polozhitelnykh kvadratichnykh form”, Uspekhi matem. nauk, 1937, no. 3, 16–62
[5] Delone B. N., Dolbilin N. P., Ryshkov S. S., Shtogrin M. I., “Novoe postroenie teorii reshetchatykh pokrytii $n$-mernogo prostranstva ravnymi sharami”, Izv. AN SSSR Ser. Matem., 34 (1970), 298–307 | MR
[6] Delone B. N., Sandakova N. N., “Teoriya stereoedrov”, Tr. MI AN SSSR, 64, M., 1961, 28–51 | MR | Zbl
[7] Shtogrin M. I., Pravilnye razbieniya Dirikhle–Voronogo dlya vtoroi triklinnoi gruppy, Tr. MI AN SSSR, 123, M., 1973 | MR | Zbl
[8] Delone B. N., Dolbilin N. P., Shtogrin M. I., Galiulin R. V., “Lokalnyi kriterii pravilnosti sistemy tochek”, Dokl. AN SSSR, 227:1 (1976), 19–21 | MR | Zbl
[9] Medvedev N. N., Metod Voronogo–Delone i issledovanie struktury nekristallicheskikh sistem, Izd-vo SO RAN, Novosibirsk, 2000
[10] Galiulin R. V., “Kristallograficheskaya kartina mira”, Uspekhi fiz. nauk, 172:2 (2002), 229–233
[11] Bogomolov S. A., Vyvod pravilnykh sistem po metodu Fedorova, v. 1, Izd-vo Kubuch, L., 1932; т. 2, 1934
[12] Zassenhaus H., “Über einen algorithmus zur Bestimmung der Raumgruppen”, Commentaria Math. helvetici, 21 (1948), 117–141 | DOI | MR | Zbl
[13] Galiulin R. V., Matrichno-vektornyi sposob vyvoda fedorovskikh grupp, Dep. v VINITI, 1969
[14] Shtogrin M. I., Pravilnye razbieniya prostranstv postoyannoi krivizny i ikh prilozheniya, Avtoref. dis. ...dokt. fiz.-matem. nauk, MI RAN, M., 2000
[15] Engel P., Geometric crystallography, D. Reidel Publ. Co., Dordrecht, 1986
[16] Galiulin R. V., “Vysshaya kristallografiya almaza”, Materialovedenie, 1999, no. 6, 2–5
[17] Galiulin R. V., “Geometricheskaya teoriya kristalloobrazovaniya”, Kristallografiya, 43:2 (1998), 366–374
[18] Brave O., Kristallograficheskie etyudy, Klassiki nauki, M., 1974
[19] Delaunay B. N., “Neue Darstellung der geometrischen Kristallographie”, Z. Kristallogr., 84 (1933), 109–149
[20] Delone B. N., Padurov N., Aleksandrov A., Matematicheskie osnovy strukturnogo analiza kristallov, Gostekhteorizdat, M., 1934
[21] Henri N., Lonsdaly K., International tables for $\mathrm{X}$-ray crystallography, Kunoch Press, Birmingham, 1952
[22] Engel P., “Über wirkungsberaeichsteilungen von kubischer Symmetrie”, Z. Kristallogr., 157 (1981), 259–275 | DOI | MR
[23] Shtogrin M. I., “O konechnosti chisla tipov stereoedrov Dirikhle–Voronogo”, Tr. seminara po diskretnoi matem. i ee prilozheniyam, MGU, M., 1989, 115–116
[24] Shtogrin M. I., “O tsentrakh deistviya planigonov”, Matem. zametki, 44:2 (1988), 262–278 | MR
[25] Shubnikov A. V., “K voprosu o stroenii kristallov”, Izv. Imperatorskoi AN. Ser. 6, 10:9 (1916), 755–779
[26] Delone B. N., “Teoriya planigonov”, Izv. AN SSSR Ser. Matem., 23:3 (1959), 365–386 | MR | Zbl
[27] Kepler J., Harmonice mundi, Lincii, 1619
[28] Andreini A., “Sulle reti di poliedri regolari e semiregolari e sulle correspondenti reti correlative”, Mem. Soc. Italiana Scienze. Ser. 3, 14 (1905), 75–129
[29] Gratia D., “Kvazikristally”, Uspekhi fiz. nauk, 156:2 (1988), 347–364
[30] Andreev A. F., “Sverkhtekuchest, sverkhprovodimost i magnetizm v mezoskopike”, Uspekhi fiz. nauk, 168:6 (1998), 655–663
[31] Andreev A. F., “Mezoskopika i fundamentalnye svoistva prostranstva”, Priroda, 1998, no. 12, 3–10 | MR | Zbl
[32] Fedorov E. S., “Perfektsionizm”, Izv. SPb biol. lab., 8:1 (1906), 25–65; 2, 9–63
[33] Galiulin R. V., “Fedorovskie gruppy — universalnyi zakon prirody”, Priroda, 1991, no. 12, 20–36
[34] Lifshits A. M., Lozovik Yu. E., “Kvazidvumernye kristallicheskie klastery na sfere: metod topologicheskogo opisaniya”, Kristallografiya, 47:2 (2002), 214–223
[35] Smirnova I. M., Smirnov V. A., Geometriya, Prosveschenie, M., 2002
[36] Galiulin R. V., “Noneuclidean crystallography”, Science Spectra, 1998, no. 14, 54–60
[37] Kuzmenkov L. S., “Rost kristallov s sokhraneniem ikh podobiya”, Protsessy realnogo kristalloobrazovaniya, Nauka, M., 1977, 221–237
[38] Vlasov A. A., “K obobschennoi teorii plazmy i teorii tverdogo tela”, Vestn. MGU. Ser. fiz., 1946, no. 3–4, 63–96
[39] Antonyuk P. N., Galiulin R. V., Makarov B. C., “Kvazikristall — idealnyi kristall prostranstva Lobachevskogo”, Priroda, 1993, no. 7, 28–31 | MR
[40] Ivanenko D. D., Galiulin R. V., “Quasicrystal model of the universe”, Tr. XVII Mezhdunar. seminara po fiz. vysokikh energii, Protvino, 1995, 180–186
[41] Einasto J., Einasto M., Gotlober S. et al., “A 120-MPC periodicity in the three-dimensional distribution of galaxy superstructures”, Nature, 1997, no. 385, 139–141 | DOI