UNIQUENESS THEOREM, DIFFERENCE POLYNOMIALS, DIFFERENTIAL POLYNOMIALS

2016, Uniqueness of meromorphic functions and q -difference polynomials sharing small function, To appear in Bull.. 2009, Diophantine approximation and Nevanlinna the-ory, Arithmetic Geo[r]

The authors declare that they have no competing interests.Received: 24 July 2011 Accepted: 6 December 2011 Published: 6 December 2011References1. Hayman, WK: Meromorphic Functions. Clarendon Press, Oxford (1964)2. Yang, L: Value Distribution Theory. Springer/Science Press, Berlin/Beijing (1993)3. Ya[r]

independent and L1 , ..., LN +1 , Lj , j ∈ {N + 2, ..., q + 1} are linearly dependent, wegetLj = b1j L1 + b2j L2 + ... + bN +1j LN +1 , bkj = 0, k = 1, ..., N + 1, j = N + 2, ..., q + 1;Lj (f˜) = b1j L1 (f˜) + b2j L2 (f˜) + ... + bN +1j LN +1 (f˜), j = N + 2, ..., q + 1;˜ = b1j L1 (G)˜ + b2j L2 (G)˜[r]

ncf (z + c) − ncf (z),n+1cf (z)=ncf (z + c) − ncf (z), n = 1, 2, In gen-eral, we use the notation C to denote the field of complex numbers.Currently, there has been an increasing interest in studying difference eq uations inthe complex plane. Halburd and Korhonen [4,5] established a versi[r]

ncf (z + c) − ncf (z),n+1cf (z)=ncf (z + c) − ncf (z), n = 1, 2, In gen-eral, we use the notation C to denote the field of complex numbers.Currently, there has been an increasing interest in studying difference eq uations inthe complex plane. Halburd and Korhonen [4,5] established a versi[r]

⎡⎢⎣fmk1wikXγkfIn⎤⎥⎦1/γ,2.11and taking i →∞in 2.11, we can get the inequality 2.2. T he proof of Theorem 2.1 is thuscompleted.2.2. Jensen Type Inequalities Involving Difference SubstitutionExchange the ith row and jth row in nth unit matrix E, then this matrix, written Ei[r]

|≤ lognδ1 logn  2nn1≤ cδlogn  2,2.27we get the result want to be proved by a simple modification of the proof of Lemma 2.2.Weomit the details. The proof of Theorem 1.2 is complete.AcknowledgmentsThe research was supported by the National Natural Science Foundition of China no.9[r]

in 2009.References1 T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288–299,2002.2 T. Kim, “On the symmetries of the q-Bernoulli polynomials,” Abstract and Applied Analysis, vol. 2008,Article ID 914367, 7 pages, 2008.3 T. Kim, “Symmetry p-[r]

following advantages: a. oDCB with b.p.¼180°C can be used to prevent nozzle clogging and provide a reliable jetting of the printhead b. the second component, mesitylene, with lower boiling point of 165°C of the solvent mixture, with a lower surface tension, is used to achieve optimum wetting and spr[r]

tnn!.2.12Then the values of Bkn,χx at x  0 are called the generalized Bernoulli numbers attached toχ of order k. When k  1, the polynomials of numbers are called the generalized Bernoullipolynomials or numbers attached to χ.Letw1,w2∈ N. Then we setKm, χ; w1,w2dXmm

Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2008, Article ID 270713, 19 pagesdoi:10.1155/2008/270713Research ArticleCongruences for Generalizedq-Bernoulli PolynomialsMehmet Cenkci and Veli KurtDepartment of Mathematics, Akdeniz University, 07058 Antalya, TurkeyCorres[r]

with any c2> 2 for n ≥ n (c2).58 E. A. RAKHMANOVWe also note (without proof) that log N in the estimate above and in (1.8)may be replaced with log2+n2/Nwhich is somewhat better if n/N is small.Moreover, it is possible to prove that this logarithmic factor may be in effectonly in a small neig[r]

Hindawi Publishing CorporationEURASIP Journal on Advances in Signal ProcessingVolume 2009, Article ID 963254, 14 pagesdoi:10.1155/2009/963254Research ArticleStabilization of 2D NSHP Recursive Digital Filters withGuaranteed Stability Using PLSI PolynomialsK. R. Santhi,1M. Ponnavaikko,2and N. Gangatha[r]

n=0 if n > 0.(1:2)The q-extension of the following recurrence formula for the Bernoulli numbers isgiven byB0,q=1andq(qB +1)n− Bn,q=1ifn =10ifn >1(1:3)with the usual convention of replacingBnqby Bn,q(see [2,4]).Rim et al. Advances in Difference Equations 2011, 2011:34http://www.[r]

Kim et al. Journal of Inequalities and Applications 2011, 2011:64http://www.journalofinequalitiesandapplications.com/content/2011/1/64Page 6 of 7Author details1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Korea2Department ofMathematics, Hannam University, Daejeon 3[r]

2)(M4+ D4) scalings. The general pattern should be apparent by now. We seethat the growth of the number of operations (the high order term, that is) is governed by M and notby A or S. A major goal of complexity theory is the understanding of computational requirementsas problem sizes increase, and n[r]

2Département demathématiques, Université Evry Val d’Essonne, Bd. F1. Mitterrand, 91025 Evry Cedex, FranceAuthors’ contributionsCoresponding author raised the problem and make a sequence to appoach the problem. AB carried out the q-Bernoulli poynomials studies, participated in the making new construc[r]

on funcional compuesta.Recibido 2000/03/22. Revisado 2001/05/10. Aceptado 2001/05/14.MSC (2000): 39B05, 39B12, 39B22.(E(a, b, c))1501Mohamed AkkouchiIntroductionIn this note, we are concerned by the following problem:1.1 Problem: Let a, b, c be three real numbers. Determine all functionsf : R −→ R s[r]

solely within the bubble regime.Images obtained during this investigation were analyzedand compared based on the primary process parameters oflaser energy, beam diameter, and ink-film thickness. To en-hance our understanding of bubble formation, a theoreticalmodel was also developed using a simple fo[r]