An analysis of the formation of the Tajik vowel system by Shinji Ido

By Shinji Ido

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Wlul imply wlv, then v is called a greatest common factor of Ul, U2, ... , U/. Next we continue to study the field M(M). Take {bo, ... , bq } C M(M) with bq =1= 0 and write q B(z,w) = Lbj(z)w j . 16) j=O Assume q ::; p. 17) where 8 j , Tj (1 ::; j ::; m) and 8 m +! are polynomials in w whose coefficients are rational functions of { aj} and {bj }. 18) F(z, w)A(z, w) + G(z, w)B(z, w) = Tm(z, w). 3. GROWTHS OF MEROMORPHIC FUNCTIONS 29 Obviously, Tm is a greatest common factor of A and B. , Tm E M(M} - {O}, then we say that A(z, w} and B(z, w} are coprime polynomials in w.

0. Then Nl = No - El = N - E is open in N. A thin analytic subset E2 of Nl exists such that 'IjJ is locally biholomorphic on N2 = Nl - E 2. Then D = 'IjJ(Eo U El U E 2) has measure zero in cm-l. Also N~ = 'IjJ(N2) is open in cm-l. Note that N' = 'IjJ(N) = N~ U D and N~ - D differ by sets of measure zero fromN~. The intersection C m (OJ r) n sUPPILj has (2m - 2)-dimensional Hausdorff measure zero. Then 'IjJ-l(W) = ({w} C(Ojp(w))) n N, X wE Cm-l(Ojr) and for almost all wE Cm-l(Oj r) we have 'IjJ-l(W) = ({w} X qOjp(w)]) nsuPPILj.

Then Q (q-2u+n)Tf(f) $ 'LNf(r,aj)-ONRam(r,f) j=O +lO log { (;) 2m-l holds for any ro ;~~ } + 0(1) < r < p < R, where 0 2':: 1 is the Nochka constant. Proof. 48, and w. l. o. , assume lIajll = 1 for j = 0, ... , q. (j) II ' CHAPTER 1. NEVANUNNA THEORY 56 which yields where c is a positive constant. 48, we obtain q Lw(aj)mf(r,aj) j=O < (n+l)Tf(r)-NRam(r,f) +llog { (;/m-l ;~R:} + 0(1). 1) and the properties of the Nochka weights, we have q Lmf(r,aj) j=O < (2u-n+l)Tf(r)-ONRam(r,f) and, hence, the theorem follows from this and the first main theorem.

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