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Βαρθολομαίος Αθανασιάδης
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1 41 3 Vol 41 No Journal of Jiangxi Normal UniversityNatural Science May Dirichlet 1 * Dirichlet Dirichlet a s Borel Borel Dirichlet Borel O A DOI /j cnki issn ln n/λ Dirichlet ln + σ n /λ Dirichlet Borel Mx f= sup fx + iy -!< y < +! Dirichlet mx f= max σ n e -λ n s n N Borel Mx f = sup f x + iy -!< y < +! 5-7 mx f = max Z n e -λ n s n N 1 fs Re s > 0 Dirichlet Laplace- Stieltjes ln + ln + Mx f ln 1 /x= +! x 0 + fs Re s > 0 1 Ur= r ρr ρr Dirichlet i ρr= +! f s= Z n e -λ n s r +! s = x + iy 1 ii ln UR/ln Ur= 1R = r1 + r +! 0 = λ 0 < λ 1 < λ < < λ n +!Z n 1 /ln Ur ΩA P ln + ln + Mx f ln U1 /x= 1 x 0 + n 0 EZ n > 01 fs Re s > 0 ρ1 /x d U1 /xfs d σ = d E Z n E Z n < +! fs Re s > 0 fs= MS0107 NJZY16017 Yqgdufe A G Laplace-Stieltjes kongcoco@ hotmail com σ n e -λ n s U1 /x

2 3 Dirichlet 53 a C 1 ε > 0 Z= Z 1 Z! C n ln nxim s - y < ε fs= a = 1 x 0 + ln U1 /x μ n B n = PZ -1 n B n n N + B n B n s = iy fsρ1 /x Borel C n B n μ n B n fsborel nxim s - y < ε fs = a fs - a Δy s = s Re s > xim s - y < ε H 1 = φs C φsre s > 0 φs ρ1 /x φ H 1 1 ε > 0 ln nxim s - y < ε f = φ = 14 x 0 + ln U1 /x s = iy fs Borel 1 5 Z n Ω A P! C n! B n supe Z n 0 n <! C= sup Z n 1 n /n < +! a s n! Z n E Z n! n a s Dirichlet 3 7 ln ln n ln λ n = l < 1 5 ln ln Mx f = 1 x 0 + ln 1/x n +! ln Uλ n ln + σ n = fzz < 1 a j zj = 1 qfz a j z1 j q r0 < r < 1 q o1 Tr f < q Nr 1 + j = 1 f - a j qn r f+ oln r Tr f f 1 J μ 4 6 μ Jμ dr 1 - r k <! ln K c n Z n = c n n = fsre s > 0 N + 1 N + = Pc n! N+1 = U1 /x s = iy fs1! Borel Borel C n Bn N + Γc n! N+1 = Z 1 Z n ΩA P C n B n c n e λ n s B n! C n B = Z 1 Z Z 1 Z! C n Z j B j B j j 1 n 0 n 0 N + σ- B! B n Z -1 B= Z j B j j 1 n 0 B! n 0 n 0 N + = j =1 Z -1 B j A B n Z -1 Β A Z μb= PZ -1 B B! B n B! B n n 0 μb= P Z B= μ j B j j = 1! C n! B n μ C n B n μ n 5 Dirichlet 1 5iy 0 y R f sborel Ωδ > 0 ln xim s - y < ε fs= a = 1 x 0 + ln U1 /x iy 1 Borel φ H 1 iy f s Borel 1 k = sup PZ n = c c C n N + < 1 c 0 1N > ln c / 0 ΩZ n 0 = c n n = N + 1 N + n = N+1 Z Z n N X n e -λ n s + iy 1 Borel

3 ρ1 /xj = 1 3 g 0 z f 0 s ρ1 /x H = f 0 s Borel 5 PH= 0 Y = c 1 c c j Cj N + c 1 c c N Γc n! N+1 Q = Z 1 Z Y HZ 1 Z Z N Γ c n! N+1 Z 1 Z Y H Q PH PQ= μi Y = iy 0 1 α f s= 3 Γc n! N+1 c j1 c j c jn Γc n! N+1 j = 1 φ j 1 Dirichlet H 1 j = 1 δ > 0nx y 0 δ f = φ j 35 ρnx y 0 δ N! C jn e -λ n n Z n 0 e -λ n s = φ j ln ln Mx f = 1a s = N+1 x 0 + ln U1 /x ρ ψ j s= Z n 0 - c jn e -λ n s + φ j s j = 1 ln Uλ n ln + σ n = 1 nx y 0 δ f 0 s= ψ j s ρ1 /x δ 0 π / Zs y 0 δ= eπiy 0 -s/δ e πiy 0 -s/δ ln Uλ n ln + σ n 1 - e πiy 0 -s/δ e πiy 0 -s/δ ln ln Mx f 1 7 Δt 0 δ = s Re s = x > 0Im s - x 0 + ln 1 /x y 0 < δ z < 1 X n = Z n σ n Sz y 0 δ= iy 0 - δ π ln z + 槡 z + z z ln Uλ n ln + σ n = z < 1 Δt 0 δ 6 k 0 1 k +! ln Uλ nk ln + σ nk g 0 z= fsz y 0 δ g j z= ψ j Sz k y 0 δz < 1 nr g 0 z = ln Uλ nk ln + σ g i z ρ1 /z 7 Nr nk > 0 g 0 z = g j z 1 - rnr g 0 z = 1 k! n k E X k! nk α a s g j z Nr g 0 z= g j z Ω X nk X nkl X nkl α n kl n k l +! ln U ( λ n ln + Z n α kl ln U ( λ nkl ln + σ nkl X nkl α kl l +! ln Uλ nkl ln + σ nkl = kl k +! ln Uλ nkl ln + σ nkl = α Z ne -λ ns m! I Yμ 1 dz 1 μ dz μ m dz m m > N= m! I Yμ N+1 dz N+1 μ m dz m I Γcn N! +1 μ 1 dz 1 μ N dz N m! N μ n Z n = c jn j n = μ! n = N+1dZ N+1 μ m dz m K N ε 5 ln Uλ n ln + σ n 1 ln ln Mx f x 0 + ln U1 /x = ln ln Mx f α 1 a s x 0 + ln U1 /x 7

4 3 Dirichlet 55 ln Uλ n ln + σ n 1 ln ln Mx f ln 1 /x 1 ln U1 /x X = x > ln U1 /x ε lk > 0 n > K - λn - ln 1 /1 -ε n = - ln n ln n ε/1 -ε 1 Z n e -λ n x = σ n X n e -λ n x X n σ n e -λ n X exp mx f X n exp n =0 mx f ( X 0 + exp N = 1 ( ε ln n ln n - 1 -ε x 1 + ln U1 /x ( ( - λ n x λ n x ln U1 /x Cn 1 + ln U1/X a s mx f ( X 0 + Cn exp ( - σln nln n ε/1-ε x δ = 1 + ln U1 /x ε δln 1 - ε > 3 T = exp 3 /δ 1 -ε ε Mx f MX f X 0 + C K -1 n + N = 1 C 1 n > T n MX f ( MX f ( + K n T Cn 1 - δ B+ C T 1 a s t 1 -δ d t K - δ T - δ ln + ln + f x + iy 0 1 a s x 0 + ln U1 /x Palay-Zygmund Z n Dirichlet y R iy f s ρ1 /xborel ε Ω /Εε > 0 a C ln xim s - y < ε f s= a = 1 x 0 + ln U1 /x PE= ln ln n ln λ n < 1 / 4 Dirichlet Borel Ωy R δ > 0 φ H 1 4 Dirichlet y R iy f s ρ1 /xborel 4 y R iy f s ρ1 /xborel B+ C 1 1 Dirichlet Dirichlet M 004 B1 a s Dirichlet J ln Mx f ln MX f+ ln B+ - δln T = 01 33A ln MX f+ ln B+ - δ3 /δ 1 -ε/ε 3Sun Daochun Yu Jiarong On the distribution of values of random Dirichlet series J Chin Ann of Math B ln ln Mx f x 0 + ln 1 /x ln ln Mx f 1 a s 4 Dirichlet x 0 + ln 1 /x J Dirichlet 5 Dirichlet 35 J ln λ n = Dirichlet ln Uλ n ln + σ n J A A y 0 R 7 Dirichlet J ln + ln + f x + iy = 1 a s 9 x 0 + ln U1 /x

5 The Study on Provincial Technology Innovation Spillover Effect under FDI and Governmental Support ZHOU Xuan TAO Changqi * School of Statistics Jiangxi University of Finance and Economics Nanchang Jiangxi China AbstractThrough using the spatial econometric model and the panel threshold model the empirical study is done on the non-linear threshold effect of FDI and governmental support as well as the spatial correlation of technological innovation capability index variable The results show that GOV FDI and provincial technology innovation spillover effect have strong spatial autocorrelation Their impact strength expresses as double threshold and triple threshold respectively The keys to efficient spillover of provincial technology innovation are optimizing the spatial structure of government support and foreign investment when GOV and FDI are coupled Key wordsprovincial technology innovationgovernmental supportfdispatial spilloverthreshold characteristics 55 8Xu Hongyan Kong Yinying Wang Hua The approximation problem of Dirichlet series with regular growth J Journal of Computational Analysis and Applications Huo Yingying Kong Yinying On the generalized order of Dirichlet series J Acta Mathematica Scientia B Kong Yinying Yang Yan On the growth properties of the Laplace-Stieltjes transform J Complex Variables and Elliptic Equations On the growth of Laplace-Stieltjes transforms and the singular direction of complex analysis M Laplace-Stieltjes J The Random Dirichlet Series of Infinite Order Dealing with Small Function JIN Qiyu 1 KONG Yinying * 1 School of Mathematical Science Inner Mongolia University Hohhot Neimonggu China School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou Guangdong China AbstractThe infinite order function is used to study the value distribution of the random Dirichlet series It is concluded that for random Dirichlet series of infinite order in the right half plane every point iy is almost surely a strong Borel point without finite exceptional small functions which extended some results of Borel points Key wordsrandom Dirichlet seriessmall functionsstrong Borel point

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