Change in language - Revision history

Vulanovic at 11:24, 10 June 2009

2009-06-10T11:24:59Z

Vulanovic at 10:46, 10 June 2009

2009-06-10T10:46:23Z

Vulanovic at 10:43, 10 June 2009

2009-06-10T10:43:53Z

Vulanovic at 10:25, 10 June 2009

2009-06-10T10:25:40Z

Vulanovic at 10:17, 10 June 2009

2009-06-10T10:17:54Z

Vulanovic at 09:32, 10 June 2009

2009-06-10T09:32:34Z

KHBest: ergänzt

2008-06-02T09:12:31Z

ergänzt

KHBest at 19:23, 19 April 2007

2007-04-19T19:23:31Z

KHBest: erg

2007-04-19T19:16:34Z

erg

Altmann at 12:00, 26 July 2006

2006-07-26T12:00:56Z

@@ Line 87: / Line 87: @@
 (c) '''Reversible change''' if <math>k_t = A - Bt</math>, <math>C</math> = constant
-(4)<math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
+(4) <math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
 where <math>a, b</math> and <math>c</math> depend on <math>A, B</math> and <math>C</math>.

← Older revision		Revision as of 10:46, 10 June 2009
Line 15:		Line 15:
	(iv) lexicon decay or glottochronology (<math>\rightarrow</math>)		(iv) lexicon decay or glottochronology (<math>\rightarrow</math>)

−	The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beöthy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s findings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hasemann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Vulanović (~~2003~~), ~~Best~~ (~~2006~~). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.	+	The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beöthy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s findings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hasemann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Best (2006), Vulanović (2007), Vulanović, Baayen (2007). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.

@@ Line 188: / Line 188: @@
 '''Körner, H.''' (2004). Zur Entwicklung des deutschen (Lehn)Wortschatzes. ''Glottometrics 7, 25-49.''
-'''Kroch, A.S.''' (1989a). Function and grammar in the history of English: periphrastic do. In: Fasold, R.W., Schiffrin, D. (eds.), Language change and variation: 133-172. Amsterdam: Benjamins.
+'''Kroch, A.S.''' (1989a). Function and grammar in the history of English: periphrastic ''do''. In: Fasold, R.W., Schiffrin, D. (eds.), Language change and variation: 133-172. Amsterdam: Benjamins.
 '''Kroch, A.S.''' (1989b). Reflexes of grammar in patterns of language change. In: Fasold, R.W., Schiffrin, D. (eds.), ''Language change and variation: 199-244''. Amsterdam: Benjamins.
@@ Line 228: / Line 228: @@
 '''Sankoff, D.''' (1969). ''Historical linguistics as stochastic process.'' Montreal. Diss., McGill Univ., Montreal.
-'''Sankoff, D.''' (1971). Stochastic models for glottochronology. In: Hodson, F.R. et al. (eds.),  ''Anglo-Romanian Conference on Mathematics in the Archaeological and Historical Sciences. Mamaia, Romania, 1970.'' Edinburgh: Edinburgh Univ. Press, 1971. S.381-386.
+'''Sankoff, D.''' (1971). Stochastic models for glottochronology. In: Hodson, F.R. et al. (eds.),  ''Anglo-Romanian Conference on Mathematics in the Archaeological and Historical Sciences. Mamaia, Romania, 1970: 381-386.'' Edinburgh: Edinburgh Univ. Press.
 '''Sankoff, D.''' (1972). Lexical replacement processes. ''Computer Studies in the Humanities and Verbal Behaviour 4, 208-212.''
@@ Line 234: / Line 234: @@
 '''Tuldava, J.''' (1998). ''Probleme und Methoden der quantitativ-systemischen Lexikologie''. Trier: WVT.
-'''Vulanović, R.''' (2003). Fitting periphrastic 'do' in affirmative declaratives. QUALICO 2003, Atlanta.
+'''Vulanović, R.''' (2007). Fitting periphrastic ''do'' in affirmative declaratives. ''Journal of quantitative linguistics 14, 111-126''.
 '''Weinreich, U., Labov, W., Herzog, M.E.''' (1968). Empirical foundations for a theory of language change. In: Lehmann, W.P., Malkiel, Y. (eds.), ''Directions for historical linguistics: 95-188.'' Austin: University of Texas Press.
-'''Winter, W.''' (1971). Formal frequency and linguistic change. Some preliminary comments. ''Folia Linguistica 5, 55-61''.
+'''Winter, W.''' (1971). Formal frequency and linguistic change. Some preliminary comments. ''Folia linguistica 5, 55-61''.
 '''Zipf, G.K.''' (1946). Cultural-chronological strata in speech. ''Journal of abnormal and social psychology 41, 351-355.''

@@ Line 85: / Line 85: @@
-(c) '''Reversible change''' if <math>k_t = a´ - b´t</math>, <math>C</math> = constant
+(c) '''Reversible change''' if <math>k_t = A - Bt</math>, <math>C</math> = constant
 (4)<math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
-where <math>a, b, c</math> depend on <math>a´, b´</math> and <math>C</math>.
+where <math>a, b</math> and <math>c</math> depend on <math>A, B</math> and <math>C</math>.
 Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of <math>C</math> into consideration and used formula (4).
@@ Line 234: / Line 234: @@
 '''Tuldava, J.''' (1998). ''Probleme und Methoden der quantitativ-systemischen Lexikologie''. Trier: WVT.
-'''Vulanović, R.''' (2003). Fitting periphrastic do in affirmative declaratives. QUALICO 2003, Atlanta.
+'''Vulanović, R.''' (2003). Fitting periphrastic 'do' in affirmative declaratives. QUALICO 2003, Atlanta.
 '''Weinreich, U., Labov, W., Herzog, M.E.''' (1968). Empirical foundations for a theory of language change. In: Lehmann, W.P., Malkiel, Y. (eds.), ''Directions for historical linguistics: 95-188.'' Austin: University of Texas Press.

@@ Line 38: / Line 38: @@
 <math>pk_t</math> = a function of time (can also be a constant),
-C =  limit of change,
+<math>C</math> =  limit of change,
-t = time, t > 0,
+<math>t > 0</math>, time,
 and
@@ Line 47: / Line 47: @@
-This means that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants:
+This means that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants.
-'''(a) Complete change''' if C = 1 and <math>k_t = b</math> is constant
+'''(a) Complete change''' if <math>C = 1</math> and <math>k_t = b</math> is constant
-(2) <math>p=\frac{1}{1+ae^{-bt}}</math>
+(2) <math>p=\frac{1}{1+ae^{-bt}}</math>,
-where a is the integration constant. The result in (2) represents the so-called logistic curve used in different disciplines  for modeling growth phenomena.
+where <math>a</math> is the integration constant. The result in (2) represents the so-called logistic curve used in different disciplines  for modeling growth phenomena.
-'''Example'''. Since years represent large numbers hindering the fitting, one usually transforms the time intervals in a time variable beginning with t = 1. Often the cumulative frequencies are changed to cumulative proportions, or the proportions are ascertained from the occurrence of rival forms.
+'''Example'''. Since years represent large numbers hindering the fitting, one usually transforms the time intervals in a time variable beginning with <math>t = 1</math>. Often, the cumulative frequencies are changed to cumulative proportions, or the proportions are ascertained from the occurrence of rival forms.
-Complete change: The replacement of –{t} by –{st} in German 2nd person singular indicative present time with the verb “wollen”, shown by Best (2003a). The result of fitting is presented in Table 1 and Fig. 1. Here ft is the relative frequency of –{st}, pt is the computed relative frequency according to (2).
+Complete change: The replacement of –{t} by –{st} in German 2nd person singular indicative present tense of the verb “wollen”, shown by Best (2003a). The result of fitting is presented in Table 1 and Fig. 1. Here <math>f_t</math> is the relative frequency of –{st} and <math>p_t</math> is the computed relative frequency according to (2).
@@ Line 70: / Line 70: @@
-(b) '''Partial change''' if <math>k-t = b</math>  is constant, C is the asymptote
+(b) '''Partial change''' if <math>k-t = b</math>  is constant, <math>C</math> is the asymptote
 (3) <math>p=\frac{C}{1+ae^{-bt}}</math>
-and a is the integration constant.
+and <math>a</math> is the integration constant.
-Example. Partial change: Borrowings from Latin in  Hungarian
+Example. Partial change: Borrowings from Latin in  Hungarian.
 Beöthy and Altmann examined the borrowing from different langugages in Hungarian. The fate of Latin words is shown in Table 2 and Fig. 2. The fitting was performed for the cumulative values.
@@ Line 85: / Line 85: @@
-(c) '''Reversible change''' if <math>k_t</math> = a´ - b´t, C = constant
+(c) '''Reversible change''' if <math>k_t = a´ - b´t</math>, <math>C</math> = constant
 (4)<math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
-where a, b, c are simple functions of a´, b´and C.
+where <math>a, b, c</math> depend on <math>a´, b´</math> and <math>C</math>.
-Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. Past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of C into consideration and used formula (4).
+Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of <math>C</math> into consideration and used formula (4).
 <div align="center">[[Image:Tabelle33_CiL.jpg]]</div>

@@ Line 32: / Line 32: @@
 (1) <math>dp_t=k_tp_t(C-p_t)dt\quad\quad</math>,
-<math>p_t</math> = proportion of new forms
+where
-<math>pk_t</math> = a function of time (can also be a constant)
+<math>p_t</math> = proportion of new forms,
-C =  limit of change
+<math>pk_t</math> = a function of time (can also be a constant),
-t > 0, time
+C =  limit of change,
-<math>dp_t</math>  = change of the proportion
+t = time, t > 0,
-telling that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants:
+<math>dp_t</math>  = change in the proportion.

@@ Line 132: / Line 132: @@
 '''Best, K.-H.''' (2003d). Zum Wandel von Idiolekten. ''Naukovyj Visnyk Černivec’koho Universytetu, Vypusk 165-166, 36-43.''
-'''Best, K.-H.'''(2003e). Zur Entwicklung von Wortschatz und redefähigkeit bei Kindern. ''Göttinger Beiträge zur Sprachwissenschaft 9, 7-20.''
+'''Best, K.-H.'''(2003e). Zur Entwicklung von Wortschatz und Redefähigkeit bei Kindern. ''Göttinger Beiträge zur Sprachwissenschaft 9, 7-20.''
-'''Best, K.-H.'''(2006). Wortlängen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 23-49.''
+'''Best, K.-H.''' (2006a). Zum Computerwortschatz im Deutschen. ''Naukovyj Visnyk Cernivec’koho Universytetu: Hermans’ka filolohija. Vypusk 289, 10-24.''
-'''Best, K.-H.'''(2006). Quantitative Untersuchungen zu den Jiddismen im Deutschen. ''Jiddistik-Mitteilungen 36, 1-14.''
+'''Best, K.-H.'''(2006b). Italianismen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 77-86.''
-'''Best, K.-H.'''(2006). ''Quantitative Linguistik - Eine Annäherung.'' 3., stark überarbeitete und ergänzte Auflage. Göttingen: Peust & Gutschmidt.
+'''Best, K.-H.'''(2006c). ''Quantitative Linguistik - Eine Annäherung.'' 3., stark überarbeitete und ergänzte Auflage. Göttingen: Peust & Gutschmidt.
-'''Best, K.-H.'''(2006). Italianismen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 77-86.''
+'''Best, K.-H.'''(2006d). Quantitative Untersuchungen zu den Jiddismen im Deutschen. ''Jiddistik-Mitteilungen 36, 1-14.''
-'''Best, K.-H.''' (?). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)
+'''Best, K.-H.'''(2006e). Wortlängen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 23-49.''
 '''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungsprozessen im Deutschen. ''Folia Linguistica Historica 31-41.''

← Older revision		Revision as of 19:23, 19 April 2007
Line 139:		Line 139:

	'''Best, K.-H.'''(2006). ''Quantitative Linguistik - Eine Annäherung.'' 3., stark überarbeitete und ergänzte Auflage. Göttingen: Peust & Gutschmidt.		'''Best, K.-H.'''(2006). ''Quantitative Linguistik - Eine Annäherung.'' 3., stark überarbeitete und ergänzte Auflage. Göttingen: Peust & Gutschmidt.
		+
		+	'''Best, K.-H.'''(2006). Italianismen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 77-86.''

	'''Best, K.-H.''' (?). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)		'''Best, K.-H.''' (?). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)

@@ Line 1: / Line 1: @@
 '''1.	Problem and history'''
-Everything in language changes. The complete complex of causes can not be ascertained; we are interested in the general processes of change and its course, whatever the entity con¬cerned. There are four aspects treated in this volume, for which models could be set up:
+Everything in language changes. The complete complex of causes can not be ascertained; we are interested in the general processes of change and its course, whatever the entity concerned. There are four aspects treated in this volume, for which models could be set up:
 Qualitative change
@@ Line 15: / Line 15: @@
 (iv)	lexicon decay or glottochronology (<math>\rightarrow</math>)
-The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beö¬thy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s find¬ings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hase¬mann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Vulanović (2003). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.
+The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beöthy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s findings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hasemann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Vulanović (2003), Best (2006). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.
@@ Line 114: / Line 114: @@
 '''Bailey, Ch.J.N.''' (1973). ''Variation and linguistic theory.'' Arlington: Center for Applied Lin-guistics.
-'''Beöthy, E., Altmann, G.''' (1982). Das Piotrowski-Gesetz und der Lehnwort¬schatz. ''Zs. für Sprachwissenschaft 1, 171-178.''
+'''Beöthy, E., Altmann, G.''' (1982). Das Piotrowski-Gesetz und der Lehnwortschatz. ''Zs. für Sprachwissenschaft 1, 171-178.''
 '''Best, K.-H.''' (1983). Zum morphologischen Wandel einiger deutscher Verben. In: Best, Kohlhase (eds.) 1983: 107-118.
@@ Line 126: / Line 126: @@
 '''Best, K.H.''' (2003a). “Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes.” ''Glottometrics 6, 9-34.''
-'''Best, K.-H.''' (2003b). Wie verläuft Sprachwandel? ''Naukovij Visnik Černivec´kogo Univeristetu 155, 86-94.''
+'''Best, K.-H.''' (2003b). Wie verläuft Sprachwandel? ''Naukovyj Visnyk Černivec´koho Universytetu 155, 86-94.''
 '''Best, K.-H.''' (2003c). Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes. ''Glottometrics 6, 9-34.''
@@ Line 134: / Line 134: @@
 '''Best, K.-H.'''(2003e). Zur Entwicklung von Wortschatz und redefähigkeit bei Kindern. ''Göttinger Beiträge zur Sprachwissenschaft 9, 7-20.''
-'''Best, K.-H.''' (2004). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)
+'''Best, K.-H.'''(2006). Wortlängen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 23-49.''
 '''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungsprozessen im Deutschen. ''Folia Linguistica Historica 31-41.''

@@ Line 128: / Line 128: @@
 '''Best, K.-H.''' (2003b). Wie verläuft Sprachwandel? ''Naukovij Visnik Černivec´kogo Univeristetu 155, 86-94.''
-'''Best, K.-H.''' (2003c). “Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes.” ''Glottometrics 6, 9-34.''
+'''Best, K.-H.''' (2003c). Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes. ''Glottometrics 6, 9-34.''
 '''Best, K.-H.''' (2003d). Zum Wandel von Idiolekten. ''Naukovyj Visnyk Černivec’koho Universytetu, Vypusk 165-166, 36-43.''
 '''Best, K.-H.'''(2003e). Zur Entwicklung von Wortschatz und redefähigkeit bei Kindern. ''Göttinger Beiträge zur Sprachwissenschaft 9, 7-20.''
 '''Best, K.-H.''' (2004). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)
-'''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungs¬prozessen im Deutschen. ''Folia Linguistica Historica 31-41.''
+'''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungsprozessen im Deutschen. ''Folia Linguistica Historica 31-41.''
 '''Best, K.-H., Beöthy, E., Altmann, G.''' (1990). Ein methodischer Beitrag zum Piotrowski-Gesetz. ''Glottometrika 12, 115-124.''
@@ Line 144: / Line 145: @@
 '''Best, K.-H., Zhu, Jinyang''' (2006). Sprachwandel im Chinesischen. ''Archiv orientální 74, 203-214.''
 '''Brainerd, B.''' (1983). A stochastic model for language change. In: Brainerd, B. (ed.): ''Historical linguistics: 25-49''. Bochum: Brockmeyer.