메뉴 건너뛰기




Volumn 9, Issue 2, 2007, Pages 189-214

Mathematical aspects of the Periodic Law

Author keywords

Chemical elements; Information theory; Mathematical chemistry; Number theory; Order theory; Periodic Law; Set theory; Topology

Indexed keywords


EID: 34447262584     PISSN: 13864238     EISSN: 15728463     Source Type: Journal    
DOI: 10.1007/s10698-006-9026-6     Document Type: Article
Times cited : (18)

References (69)
  • 2
    • 84855937713 scopus 로고    scopus 로고
    • The Concepts of Periodicity and Hyperperiodicity: From Atoms to Molecules
    • In: Rouvray D.H., Kirby E.R. (Eds.) Research Studies Press: Taunton
    • Babaev E.V., Hefferlin R. (1996) The Concepts of Periodicity and Hyperperiodicity: From Atoms to Molecules. In: Rouvray D.H., Kirby E.R. (Eds.), Concepts in Chemistry. Research Studies Press: Taunton
    • (1996) Concepts in Chemistry
    • Babaev, E.V.1    Hefferlin, R.2
  • 4
    • 3042978330 scopus 로고
    • Der Bau der Atome und die physikalishen und chemishen Eigenschaften der Elemente
    • English translation in N. Bohr, Collected Works, J. R. Nielsen, Ed.; North-Holland: Amsterdam, 1977
    • N. Bohr. Der Bau der Atome und die physikalishen und chemishen Eigenschaften der Elemente. Zeitschrift für Physik 9: 1-67, 1922. English translation in N. Bohr, Collected Works, J. R. Nielsen, Ed.; North-Holland: Amsterdam, 1977
    • (1922) Zeitschrift Für Physik , vol.9 , pp. 1-67
    • Bohr, N.1
  • 5
    • 34447266287 scopus 로고    scopus 로고
    • Periodicity of the Chemical Elements and Nuclides: An Information Theoretic Analysis
    • In: King R.B. Rouvray D.H. (Eds) Nova: New York
    • Bonchev D. (2006) Periodicity of the Chemical Elements and Nuclides: An Information Theoretic Analysis. In: King R.B. Rouvray D.H. (Eds), The Mathematics of the Periodic Table Nova: New York
    • (2006) The Mathematics of the Periodic Table
    • Bonchev, D.1
  • 6
    • 84987067987 scopus 로고
    • How Similar is a Molecule to Another? An Electron Density Measure of Similarity between Two Molecular Structures
    • Carbó R., Leyda L., Arnau M. (1980) How Similar is a Molecule to Another? An Electron Density Measure of Similarity between Two Molecular Structures. International Journal of Quantum Chemistry 17: 1185-1189
    • (1980) International Journal of Quantum Chemistry , vol.17 , pp. 1185-1189
    • Carbó, R.1    Leyda, L.2    Arnau, M.3
  • 8
    • 2442583622 scopus 로고
    • The collected mathematical papers of Arthur Cayley
    • 1st ed. Cambridge University Press: Cambridge
    • A. Cayley. The collected mathematical papers of Arthur Cayley. Vol IX, 1st ed. Cambridge UniHersity Press: Cambridge, 1896. Internet: http://www.hti.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc= h;sid=0128b870e72ce32c3182761dac22f43e;q1=triangular%20numbers;rgn= full%20text;view=pdf;seq=00000001;idno=ABS3153.0009.001
    • (1896) , vol.9
    • Cayley, A.1
  • 10
    • 33845741627 scopus 로고
    • Solvtio Problematis ad Geometriam Sitvs Pertinentis
    • Opera Omnia. Series 1. Volume 7, pp. 1-10. Internet
    • L. Euler. Solvtio Problematis ad Geometriam Sitvs Pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8: 128-140, 1741. Opera Omnia. Series 1. Volume 7, pp. 1-10. Internet: http://www.eulerarchive.com/
    • (1741) Commentarii Academiae Scientiarum Imperialis Petropolitanae , vol.8 , pp. 128-140
    • Euler, L.1
  • 13
    • 33845554294 scopus 로고
    • Confusion in the Periodic Table of the Elements
    • Fernelius W.C., Powell W.H. (1982) Confusion in the Periodic Table of the Elements. Journal of Chemical Education 59(6): 504-508
    • (1982) Journal of Chemical Education , vol.59 , Issue.6 , pp. 504-508
    • Fernelius, W.C.1    Powell, W.H.2
  • 17
    • 77956848589 scopus 로고
    • A short History of Greek mathematics
    • C. E. Stechert: New York
    • Gow G. (1923) A short History of Greek mathematics. C. E. Stechert: New York
    • (1923)
    • Gow, G.1
  • 19
    • 34447289769 scopus 로고    scopus 로고
    • Department of Mathematics University of Turku: Turku
    • Harju T. (2002) Lecture Notes on Graph Theory. Department of Mathematics University of Turku: Turku
    • (2002) Lecture Notes on Graph Theory
    • Harju, T.1
  • 20
    • 34447290965 scopus 로고    scopus 로고
    • The Heavy Elements
    • In: King R.B., Rouvray D.H. (Eds.) Nova: New York
    • Karol P.J. (2006) The Heavy Elements. In: King R.B., Rouvray D.H. (Eds.), The Mathematics of the Periodic Table Nova: New York
    • (2006) The Mathematics of the Periodic Table
    • Karol, P.J.1
  • 21
    • 21844523502 scopus 로고
    • Similarity and dissimilarity in posets
    • Klein D.J. (1995) Similarity and dissimilarity in posets. Journal of Mathematical Chemistry 18: 321-348
    • (1995) Journal of Mathematical Chemistry , vol.18 , pp. 321-348
    • Klein, D.J.1
  • 23
    • 0008767361 scopus 로고    scopus 로고
    • Prolegomenon on Partial Orderings in Chemistry
    • Klein D.J. (2000) Prolegomenon on Partial Orderings in Chemistry. MATCH 42: 7-21
    • (2000) MATCH , vol.42 , pp. 7-21
    • Klein, D.J.1
  • 25
    • 0002144317 scopus 로고
    • The Atom and the Molecule
    • Internet
    • G.N. Lewis. The Atom and the Molecule. Journal of the American Chemical Society 38: 762-786H 1916. Internet: http://dbhs.wvusd.k12.ca.us/webdocs/ Chem-History/Lewis-1916/Lewis-1916.html
    • (1916) Journal of the American Chemical Society , vol.38 , pp. 762-786
    • Lewis, G.N.1
  • 31
    • 0037666927 scopus 로고
    • Sootnoshenie svoistv s atomnym vesom elementov
    • Mendeleev D.I. (1869) Sootnoshenie svoistv s atomnym vesom elementov. Zh Russ Khim Obshch 1(2/3): 60-77 60-77
    • (1869) Zh Russ Khim Obshch , vol.1 , Issue.2-3 , pp. 60-77
    • Mendeleev, D.I.1
  • 32
    • 5244343431 scopus 로고
    • The Periodic Law of the Chemical Elements
    • Internet
    • D.I. Mendeleev, The Periodic Law of the Chemical Elements. Journal of Chemical Society 55H 634-656, 1889. Internet: http://web.lemoyne.edu/ ~giunta/mendel.html
    • (1889) Journal of Chemical Society , vol.55 , pp. 634-656
    • Mendeleev, D.I.1
  • 33
    • 0038727387 scopus 로고
    • Die Natur der chemischen Elemente als Function ihrer Atomgewichte
    • Meyer L. (1870) Die Natur der chemischen Elemente als Function ihrer Atomgewichte. Annalen der Chemie und Pharmarcie Supplementband 7: 354-364
    • (1870) Annalen Der Chemie Und Pharmarcie Supplementband , vol.7 , pp. 354-364
    • Meyer, L.1
  • 34
    • 0000481928 scopus 로고
    • The High Frequency Spectra of the Elements
    • Internet
    • H.G.J. Moseley. The High Frequency Spectra of the Elements. Phil. Mag, 1024, 1913. Internet: http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/ Moseley-article.html
    • (1913) Phil. Mag , pp. 1024
    • Moseley, H.G.J.1
  • 35
    • 0038389344 scopus 로고    scopus 로고
    • What and How Physics Contributes to Understanding the Periodic Law
    • Ostrovsky V.N. (2001) What and How Physics Contributes to Understanding the Periodic Law. Foundations of Chemistry 3: 145-182
    • (2001) Foundations of Chemistry , vol.3 , pp. 145-182
    • Ostrovsky, V.N.1
  • 37
    • 0021467019 scopus 로고
    • A Chemical Scale for Crystal-Structure Maps
    • Pettifor D.G. (1984) A Chemical Scale for Crystal-Structure Maps. Solid State Communications 51(1): 31-34
    • (1984) Solid State Communications , vol.51 , Issue.1 , pp. 31-34
    • Pettifor, D.G.1
  • 38
    • 34248527314 scopus 로고
    • The Structures of Binary Compounds: I. Phenomenological Structure Maps
    • Pettifor D.G. (1986) The Structures of Binary Compounds: I. Phenomenological Structure Maps. Journal of Physics C: Solid State Physics 19: 285-313
    • (1986) Journal of Physics C: Solid State Physics , vol.19 , pp. 285-313
    • Pettifor, D.G.1
  • 39
    • 0024055661 scopus 로고
    • Structure Maps for Pseudobinary and Ternary Phases
    • Pettifor D.G. (1988a) Structure Maps for Pseudobinary and Ternary Phases. Materials Science and Technology 4: 675-692
    • (1988) Materials Science and Technology , vol.4 , pp. 675-692
    • Pettifor, D.G.1
  • 40
    • 0002060936 scopus 로고
    • Structure Maps in Magnetic Alloy Design
    • Pettifor D.G. (1988b) Structure Maps in Magnetic Alloy Design. Physica B 149: 3-10
    • (1988) Physica B , vol.149 , pp. 3-10
    • Pettifor, D.G.1
  • 41
    • 0030269781 scopus 로고    scopus 로고
    • Phenomenology and Theory in Structural Prediction
    • Pettifor D.G. (1996) Phenomenology and Theory in Structural Prediction. Journal of Phase Equilibria 17(5): 384-395
    • (1996) Journal of Phase Equilibria , vol.17 , Issue.5 , pp. 384-395
    • Pettifor, D.G.1
  • 43
    • 0141460650 scopus 로고    scopus 로고
    • An Earth Scientist's Periodic Table of the Elements and their Ions
    • Railsback L.B. (2003) An Earth Scientist's Periodic Table of the Elements and their Ions. Geology 31(9): 737-740
    • (2003) Geology , vol.31 , Issue.9 , pp. 737-740
    • Railsback, L.B.1
  • 48
    • 21044432110 scopus 로고    scopus 로고
    • 2005 From Trees (Dendrograms and Consensus Trees) to Topology
    • Restrepo G., Villaveces J.L. (2005a) From Trees (Dendrograms and Consensus Trees) to Topology. Croatica Chemica Acta 78: 275-281
    • (2005) Croatica Chemica Acta , vol.78 , pp. 275-281
    • Restrepo, G.1    Villaveces, J.L.2
  • 49
    • 22944432413 scopus 로고    scopus 로고
    • Trees (dendrograms and consensus trees) and their topological information
    • Subhash C. Basak and Indira Ghosh Proceedings of the Pune, India, 8-12 January 2005. Pune
    • G. Restrepo, E.J. Llanos and J.L. Villaveces. Trees (dendrograms and consensus trees) and their topological information, Subhash C. Basak and Indira Ghosh, Proceedings of the Fourth Indo-US Workshop on Matehmatical Chemistry, 39-62, Pune, India, 8-12 January 2005. Pune, 2005b
    • (2005) Fourth Indo-US Workshop on Matehmatical Chemistry , pp. 39-62
    • Restrepo, G.1    Llanos, E.J.2    Villaveces, J.L.3
  • 50
    • 22944458875 scopus 로고    scopus 로고
    • Ranking Regions Through Cluster Analysis and Posets
    • Restrepo G., Brüggemann R. (2005c) Ranking Regions Through Cluster Analysis and Posets. WSEAS Trans Inf Sci Appl 2: 976-981
    • (2005) WSEAS Trans Inf Sci Appl , vol.2 , pp. 976-981
    • Restrepo, G.1    Brüggemann, R.2
  • 54
    • 0013060588 scopus 로고    scopus 로고
    • On the Extension of Quantum Similarity to Atomic Nuclei: Nuclear Quantum Similarity
    • Robert D., Carbó-Dorca R. (1998) On the Extension of Quantum Similarity to Atomic Nuclei: Nuclear Quantum Similarity. Journal of Mathematical Chemistry 23: 327-351
    • (1998) Journal of Mathematical Chemistry , vol.23 , pp. 327-351
    • Robert, D.1    Carbó-Dorca, R.2
  • 57
    • 0039138989 scopus 로고
    • A short account of the history of mathematics
    • Macmillan and co: London Internet
    • W. W. Rouse. A short account of the history of mathematics. Macmillan and co: London, 19H9. Internet: http://www.hti.umich.edu/cgi/t/text/ pageviewer-idx?c=mhistmath;cc=umhistmath;sid=0128b870e72ce32c3182 761dac22f43e;q1=triangular%20numbers;rgn=full%20text;view=pdf;seq= 00000001;idno=ACA1117.0001.001
    • (1919)
    • Rouse, W.W.1
  • 61
    • 1842785309 scopus 로고    scopus 로고
    • Numerical Classification of the Chemical Elements and its relation to the Periodic System
    • Sneath P.H.A. (2000) Numerical Classification of the Chemical Elements and its relation to the Periodic System. Foundations of Chemistry 2: 237-263
    • (2000) Foundations of Chemistry , vol.2 , pp. 237-263
    • Sneath, P.H.A.1
  • 63
    • 34447293393 scopus 로고
    • Periodic Classification and Electronic Configuration of Elements
    • Sugathan K.K., Menon T.C.K. (1956) Periodic Classification and Electronic Configuration of Elements. Current Science 25: 85
    • (1956) Current Science , vol.25 , pp. 85
    • Sugathan, K.K.1    Menon, T.C.K.2
  • 65
    • 22944484113 scopus 로고    scopus 로고
    • Chemotopological Study of the Fourth Period Monohydrides
    • Uribe E.A., Daza M.C., Restrepo G. (2005) Chemotopological Study of the Fourth Period Monohydrides. WSEAS Trans Inf Sci Appl 2: 1085-1090
    • (2005) WSEAS Trans Inf Sci Appl , vol.2 , pp. 1085-1090
    • Uribe, E.A.1    Daza, M.C.2    Restrepo, G.3
  • 66
    • 1842785317 scopus 로고    scopus 로고
    • Química y Epistemología: Una relación esquiva
    • Revista Colombiana de Filosofía de la Ciencia 2-3
    • J.L. Villaveces. Química y Epistemología: Una relación esquiva. Revista Colombiana de Filosofía de la Ciencia 1: 2-3, 9-26, 2000
    • (2000) , vol.1 , pp. 9-26
    • Villaveces, J.L.1
  • 67
    • 34447279790 scopus 로고    scopus 로고
    • Personal communication
    • J. L. Villaveces. Personal communication, 2004
    • (2004)
    • Villaveces, J.L.1
  • 68
    • 34447279386 scopus 로고    scopus 로고
    • A Pythagorean Approach to Problem of Periodicity in Chemical and Nuclear Physics
    • In: Maruani J., Lefebvre R., Br̈ndas E.J. (Eds.) Kluwer: Dordrecht
    • Weise D. (2003) A Pythagorean Approach to Problem of Periodicity in Chemical and Nuclear Physics. In: Maruani J., Lefebvre R., Brändas E.J. (Eds.), Advanced Topics in Theoretical Chemical Physics. Kluwer: Dordrecht
    • (2003) Advanced Topics in Theoretical Chemical Physics
    • Weise, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.