... consider the q-extension ofthe generating function for the higher- order generalized Genocchi numbers and polynomials attached to χ The purpose of this paper is to present a systemic study of some ... numbers ofhigher order, ” Advances in Difference Equations, vol 2010, Article ID 309480, pages, 2010 V Kurt, “A further symmetric relation on the analogue ofthe Apostol-Bernoulli and the analogue of ... Difference Equations r r In the special case x 0, Gn,χ,q Gn,χ,q are called the nth generalized q-Genocchi numbers oforder r attached to χ Therefore, we obtain the following theorem Theorem 2.1 For r ∈...
... systemic study of some formulas ofthe twisted q-extension ofthe generalized Euler numbers and polynomials oforder k attached to χ On the Twisted q-Extension ofthe Generalized Euler Polynomials ... are called the nth generalized h, q -Euler polynomials oforder r attached r to χ In the special case x 0, En,χ,ζ,q r En,χ,ζ,q are called the nth generalized h, r -Euler r numbers oforder r By ... 1999 T Kim, “Some identities on the q-Euler polynomials ofhigherorder and q-Stirling numbers by the fermionic p-adic integral on Zp ,” Russian Journal of Mathematical Physics, vol 16, no 4,...
... polynomials and the generalized higher- order Euler polynomials The main purpose of this paper is to give the symmetry identities for the twisted generalized Euler polynomials ofhigherorder using the symmetric ... integral on Zp From these symmetric properties, we derive the symmetry identities for the twisted generalized Euler polynomials ofhigherorder In 14 , Kim gave the relation between the power sum polynomials ... Journal of Inequalities and Applications Comparing the coefficients on both sides of 2.17 and 2.18 , we obtain the following theorem which shows the relationship between the power sums and the twisted...
... n! 1.11 k Then the values of En,ζ x at x are called the ζ-Euler numbers oforder k When k 1, the polynomials or numbers are called the ζ-Euler polynomials or numbers The purpose of this paper ... of symmetry for the ζ-Euler polynomials ofhigherorder By using our identities of symmetry for the ζ-Euler polynomials ofhigher order, we can obtain many identities related to the Frobenius-Euler ... to the Frobenius-Euler polynomials ofhigherorder On the Symmetry for the ζ-Euler Polynomials ofHigherOrder Let w1 , w2 ∈ N with w1 ≡ mod and w2 ≡ mod Then we set R m Zm p w1 , w2 e w1 x1...
... polynomials attached to χ ofhigherorder Symmetric Properties for the Generalized Bernoulli Polynomials ofHigherOrder Let χ be the Dirichlet’s character with conductor d ∈ N Then we note that t ... Bn,χ x n tn n! 2.12 k Then the values of Bn,χ x at x are called the generalized Bernoulli numbers attached to χ oforder k When k 1, the polynomials of numbers are called the generalized Bernoulli ... ofthe Jangjeon Mathematical Society, vol 11, no 2, pp 191–198, 2008 ¨ 23 A Tekcan, A Ozkoc, B Gezer, and O Bizim, “Some relations involving the sums of Fibonacci ¸ numbers,” Proceedings of the...
... respectively, the ring of p-adic rational integers, the field of p-adic rational numbers and the p-adic completion ofthe algebraic closure of Qp The p-adic absolute value in Cp is 1/p When one talks of ... 1.16 The purpose of this paper is to give the distribution of extended higherorder q-Euler and q-Genocchi polynomials In 24 , Choi-Anderson-Srivastava have studied the q-extension ofthe Apostol-Euler ... polynomials oforder n, and the multiple Hurwitz zeta functions see 24 Actually, their results and definitions are not new see 18, 20 and the definition ofthe Apostol-Bernoulli numbers in their paper...
... about the integers There are higher- order logics that have been provided which contain the formulas of second -order logic but which not assume the same notion of models (i.e the integers) These ... individuals, a predicate of type (i ~ o) ~ o represents a set of sets of individuals, 248 of positive Horn clauses for first -order logic The formula on the left ofthe D in a higher- order definite clause ... below a brief exposition ofthe higher- order features of this language that we shall use in the examples in the later sections A fuller description ofthe language and ofthe logical considerations...
... discussion ofthe role ofhigher education in economic development and specific actions taken by the institutions oftheHigher Education Alliance for the Rock River Region (HEARRR): Northern Illinois ... increase the value placed on education within the region The Role ofHigher Education in Economic Development Page of 12 Examples of P-20 initiatives ofthe Alliance institutions include the following: ... work together to attract students into critical programs • The members ofthe Alliance match instructional programs to the economic growth needs ofthe region In the past three years, they have...
... Possible Negative Effects ofHigher Education Expansion The history ofthe development of formal education, both in terms of participation rates and the lengthening of study-time has gone hand ... between, on the one hand, the actual state and status ofthe academic sector and, on the other hand, the cultural representation of academia and the social strategies related to the social representation ... Essentially the positive demand shocks increase wages so the observed wage effect is the combination ofthe demand shock and the effect of increased graduates in the area Moretti controls for a host of...
... as a means of saving money A Strategy Vacuum? Yet, given the harsh reality ofthe politics of HE’ and the voting power ofthe better-off, the White Paper proposals may yet run into the sand, ... merely the continuation of a very slow recognition that the taxpayer has other priorities and burdens in society than financing the major part ofthe cost ofhigher education for the better-off ... vacuum that the HEIs then fail to fill since they themselves are split as their leaders (the Vice-Chancellors gathered at Universities UK as the trade body’) squabble over whether the tuition...
... features None ofthe other known C splice variants are encoded with the same N-terminus as Ca1 and Cb1 and it is not expected that they undergo the same type of modifications Thus, they may harbor ... targeting ofthe C The latter has recently been demonstrated in that the N-terminal residues 1–39 are required for localization of A-kinase interaction protein in the nucleus [15] Despite these reports, ... cells with characteristics of post-mitotic neurons ofthe central nervous system [19], express six novel mRNA species ofthe PKA Cb gene; these variants lack exon The Cb forms lacking exon were...
... evolution of one ofthe most diverse osteichthyan groups, the Teleostei, and since the testing ofthe monophyly ofthe otophysan, ostariophysan and otocephalan fishes is one ofthe aims ofthe present ... support the monophyly of this taxon are the enlargement ofthe basal elements ofthe pectoral fin, the unique arrangement ofthe scales, the interlocking mechanism, and the presence of a single ... are the closest living relatives of teleosts, the amiids ofthe genus Amia, or both these fishes and the lepisosteids ofthe genera Lepisosteus and Atractosteus, that is, the members ofthe three...
... the existence of periodic solutions for the higherorder difference equation x(n + k) = g(x(n)) − f (n, x(n − τ (n)) We show the existence of periodic solutions by using Schauder’s fixed point theorem, ... fixed point theorem 1 Introduction and main results Let R denote the set ofthe real numbers, Z the integers and N the positive integers In this article, we investigate the existence of periodic ... obtained existence theorem for single and multiple positive periodic solutions of (1.3) Our aim of this article is to study the existence of periodic solutions for the higherorder difference equations...
... positive integers The purpose of this article is to consider the existence of positive periodic solution of higher- order functional difference equation (2), we will remove the constrains on a ... remove the unreasonable assumption l = w Based on a fixed point theorem in a cone, a new sufficient condition is established for the existence of positive periodic solutions for higher- order functional ... completely continuous This completes the proof We can easily obtain the following result Lemma The fixed point of T in K is a positive periodic solution of (2) Main result Let ϕ(s) = max{f (n,...
... (3:8) then (1.1) is oscillatory or tends to zero as t ® ∞ Proof The proof ofthe corollary is similar to the proof of Corollary 3.3 and so it is omitted From the above results on the oscillation of ... (2:13) then every solution of (1.1) is oscillatory or tends to zero as t ® ∞ Proof The proof ofthe corollary is similar to the proof of Corollary 2.8 and so it is omitted Example 2.11 Consider the ... http://www.advancesindifferenceequations.com/content/2011/1/45 Page of 10 From the above results on the oscillation of odd -order differential equation and Lemma 2.5, we can easily obtain the following results regarding the oscillation of evenorder neutral...