bernoulli numbers and σ1 n2k
Báo cáo hóa học: " Some new identities on the twisted carlitz’s q-bernoulli numbers and q-bernstein polynomials" ppt
... Bn,ξ = and n = 1, n > 1, (5) with the usual convention about replacing Bn by Bn,ξ (see [17-19]) Recently, several ξ authors have studied the twisted Bernoulli numbers and q -Bernoulli numbers ... of the twisted q -Bernoulli numbers and polynomials related to q-Bernstein polynomials From these properties, we derive some new identities for the twisted q -Bernoulli numbers and polynomials Final ... between the twisted Carlitz’s q -Bernoulli numbers and q-Bernstein polynomials On the twisted Carlitz ‘s q -Bernoulli numbers In this section, we assume that n Î ℤ+, ξ Î Tp and q ∈ Cp with |1 - q|p
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Báo cáo hóa học: " q-Bernoulli numbers and q-Bernoulli polynomials revisited" docx
... http://www.advancesindifferenceequations.com/content/2011/1/33 Page of q -Bernoulli numbers and q -Bernoulli polynomials revisited In this section, we perform a further investigation on the q -Bernoulli numbers and qBernoulli polynomials given ... approach to q -Bernoulli numbers and q -Bernoulli polynomials related to qBernstein polynomials Adv Differ Equ (2010) Article ID 951764 Kim, T, Rim, SH: Generalized Carlitz’s q -Bernoulli numbers in ... polynomials and correct its wrong properties, and rebuild the theorems of q -Bernoulli numbers and polynomials Redefinition For q Î ℂ with |q|
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Báo cáo hóa học: " Research Article A New Approach to q-Bernoulli Numbers and q-Bernoulli Polynomials Related to q-Bernstein Polynomials" pdf
... function related to the q -Bernoulli numbers and q -Bernoulli polynomials and give a new construction of these numbers and polynomials related to the second kind Stirling numbers and q-Bernstein polynomials ... q -Bernoulli polynomials at negative integers and are associated with q-Bernstein polynomials New Approach to q -Bernoulli Numbers and Polynomials Let N be the set of natural numbers and N∗ q -Bernoulli ... the nth generalized q -Bernoulli numbers and q -Bernoulli polynomials attached to χ and q-Bernstein polynomials From 2.16 , one has the following theorem Theorem 2.7 For n ∈ N∗ and |q| < 1, one has...
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Báo cáo hóa học: " Research Article Some Identities on the Generalized q-Bernoulli Numbers and Polynomials Associated with q-Volkenborn Integrals" docx
... formulae for the higher-order Carlitz’s type q -Bernoulli numbers and polynomials in the p-adic number field On the Generalized Higher-Order q -Bernoulli Numbers and Polynomials In this section, we assume ... pp 1798–1804, 2009 L Carlitz, “q -Bernoulli numbers and polynomials,” Duke Mathematical Journal, vol 15, pp 987–1000, 1948 L Carlitz, “q -Bernoulli and Eulerian numbers, ” Transactions of the American ... q -Bernoulli numbers associated with Daehee numbers, ” Advanced Studies in Contemporary Mathematics, vol 18, no 1, pp 41–48, 2009 16 Y Simsek, “Generating functions of the twisted Bernoulli numbers and...
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báo cáo hóa học:" Research Article Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials" pptx
... functions and related integrals,” Journal of Number Theory, vol 76, no 2, pp 320–329, 1999 T Kim, J Choi, and Y.-H Kim, “Some identities on the q-Bernstein polynomials, q-Stirling numbers and q -Bernoulli ... authors cf 8, and the f x n We have references given there For n ∈ N, write fn x n−1 I1 fn f l I1 f 2.3 l This identity is to derives interesting relationships involving Bernoulli numbers and polynomials ... Mathematics-Modelling and Simulation In press M Acikgoz and S Araci, “On the generating function of the Bernstein polynomials,” in Proceedings of the 8th International Conference of Numerical Analysis and Applied...
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Báo cáo sinh học: " Some results for the q-Bernoulli, q-Euler numbers and polynomials" ppt
... q -Bernoulli numbers and polynomials Duke Math J 15, 987–1000 (1948) [2] Carlitz, L: q -Bernoulli and Eulerian numbers Trans Am Math Soc 76, 332–350 (1954) [3] Kamano, K: p-adic q -Bernoulli numbers ... Carlitz’s q -Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions Appl Math Comput 215(3), 1185–1208 (2009) [12] Kim, T: On the analogs of Euler numbers and ... q-Euler numbers and polynomials related to the Bosonic and the Fermionic p-adic integral on Zp In this section, we provide some basic formulas for p-adic q -Bernoulli, p-adic q-Euler numbers and polynomials...
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báo cáo hóa học:" Some results for the q-Bernoulli, q-Euler numbers and polynomials" ppt
... q -Bernoulli numbers and polynomials Duke Math J 15, 987–1000 (1948) [2] Carlitz, L: q -Bernoulli and Eulerian numbers Trans Am Math Soc 76, 332–350 (1954) [3] Kamano, K: p-adic q -Bernoulli numbers ... Carlitz’s q -Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions Appl Math Comput 215(3), 1185–1208 (2009) [12] Kim, T: On the analogs of Euler numbers and ... q-Euler numbers and polynomials related to the Bosonic and the Fermionic p-adic integral on Zp In this section, we provide some basic formulas for p-adic q -Bernoulli, p-adic q-Euler numbers and polynomials...
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Báo cáo toán học: " Some results for the q-Bernoulli, q-Euler numbers and polynomials" doc
... non-positive integers can be represented by the q -Bernoulli, q-Euler numbers, and polynomials q -Bernoulli, q-Euler numbers and polynomials related to the Bosonic and the Fermionic p-adic integral on ℤp ... known formulas by using several results of q -Bernoulli, q-Euler numbers, and polynomials By using generating functions of q -Bernoulli, q-Euler numbers, and polynomials, we also present the q-analogues ... generating functions of q -Bernoulli, q-Euler numbers, and polynomials In the complex case, we shall explicitly determine the generating function Fq(t) of qBernoulli numbers and the generating function...
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Báo cáo hóa học: " Research Article Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers" pdf
... polynomials and numbers are called the twisted q -Bernoulli polynomials and numbers, respectively When k and q 1, the polynomials and numbers are called the twisted Bernoulli polynomials and numbers, ... respectively When k 1, q 1, and ζ 1, the polynomials and numbers are called the ordinary Bernoulli polynomials and numbers, respectively Many authors have studied the twisted q -Bernoulli polynomials ... twisted p-adic q-integral on Zp and extend our result to the twisted q -Bernoulli polynomials and numbers Finally, we derive some various identities related to the twisted q -Bernoulli polynomials Multivariate...
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Báo cáo toán học: "Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers" ppt
... to (2.2) and (2.3) we have D1 (p) = det and D2 (p) = det p+1 p+1 p+1 p p+1 = p(p + 1) , = p2 (p + 1)(p + 5) , 12 and as before we see that −p−1 D1 (−p) and −p−2 D2 (−p) occur in (1.3) and (1.8), ... This is indeed the case, and there is a close relationship with the degenerate Bernoulli numbers These numbers (in fact, polynomials) were first studied by Carlitz [3], and can be defined by the ... first kind and bn the Bernoulli number of the second kind Recall that the Bernoulli numbers of the second kind are defined by the generating function (6.1) For properties of Stirling numbers see,...
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Numbers and Operations Review
... – NUMBERS AND OPERATIONS REVIEW – Practice Question The number –16 belongs in which of the following sets of numbers? a rational numbers only b whole numbers and integers c whole numbers, ... factor shared by 28 and 21 Practice Question What are the common factors of 48 and 36? a 1, 2, and b 1, 2, 3, and c 1, 2, 3, 6, and 12 d 1, 2, 3, 6, 8, and 12 e 1, 2, 3, 4, 6, 8, and 12 Answer c ... Median, and Mode To find the average, or mean, of a set of numbers, add all of the numbers together and divide by the quantity of numbers in the set mean ϭ sum of numbers in set ᎏᎏᎏ quantity of numbers...
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Tài liệu Lab 10.2.5 Well-Known Port Numbers and Multiple Sessions docx
... another command prompt Step Start a fourth Telnet session to router by opening another command prompt Step 10 Check the number of sessions on the host a Open another command prompt on the host and type ... port numbers 3-5 CCNA 2: Routers and Routing Basics v 3.0 - Lab 10.2.5 Copyright 2003, Cisco Systems, Inc Erasing and reloading the router Enter into the ... with the proper IP address, subnet mask and default gateway Step Allow HTTP access to the router a Allow HTTP access by issuing the ip http server command in global configuration mode Step Use...
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Tài liệu Lab 10.2.5 Well Known Port Numbers and Multiple Sessions pptx
... number of sessions on the host a Open a command prompt on the host and type netstat /? at the DOS prompt b What options are available for the netstat command? ... access by issuing the ip http server command in global configuration mode Step Use the workstation browser to access the router a Open a browser on Host and type http://ip-address of Router GAD ... information from the privileged exec command mode GAD# copy running-config startup-config Step Configure the host with the proper IP address, subnet mask and default gateway Step Allow HTTP access...
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Tài liệu Random Numbers part 1 ppt
... initializing, and then generating, “random numbers. ” In ANSI C, the synopsis is: #include #define RAND_MAX void srand(unsigned seed); int rand(void); You initialize the random number ... distinguish uniform deviates from other sorts of random numbers, for example numbers drawn from a normal (Gaussian) distribution of specified mean and standard deviation These other sorts of deviates ... Knuth [1] Then try [2] Only a few of the standard books on numerical methods [3-4] treat topics relating to random numbers Bratley, P., Fox, B.L., and Schrage, E.L 1983, A Guide to Simulation...
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Báo cáo khoa học: ˚ cDNA cloning and 1.75 A crystal structure determination of PPL2, an endochitinase and N-acetylglucosaminebinding hemagglutinin from Parkia platycephala seeds potx
... conserved strands b3 and b4 (Fig 4A, boxed), and the hydrogen bond network between residues Asp120 and Gly121 and Val74 (Fig 4A,B) [33], are also conserved in PPL2 On the other hand, the largest ... bond, and Asp125 and Tyr183 would contribute to the stabilization of the oxazolinium intermediate [45] In PPL2, these residues correspond to Asp125, Glu127 and Tyr182 (Figs and 4A) Asp125 and Glu127 ... present in the reaction mixture (3.93, 4.84 and 5.58 min) matched those of the standard carbohydrates GlcNac, (GlcNac)2 and (GlcNac)3 (3.86, 4.84 and 5.58 min, respectively) This result demonstrated...
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Báo cáo khoa học: Crystal structures of the human SUMO-2 protein at 1.6 A and 1.2 A resolution ppt
... and human ubiquitin (h_Ubiquitin) Secondary structure elements of SUMO-2 are shown above the sequences with a-helices and b-strands depicted as red cylinders and green arrows, respectively, and ... between Asp16 and Arg36, which is seen in the 1.6 A model The amino acids are shaded in red, green and blue for acidic, neutral and basic polar residues, and in yellow for prolines and glycines ... red and magenta, respectively, and nonpolar residues are shown in green The views in (C–F) are similar to that of Fig 3A and those of (A) and (B) are rotated 180° about the horizontal axis and...
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algebraic numbers and fourier analysis - salem
... Ph and y j = Pth, and, since I a ;" + cq*n I < 2, Take now for m the smallest integer such that h being a positive integer such that ~ l + ~ ! + ' ' + y k - < i l + Since a = 7-I and and the numbers ... the definitions and the results (though elementary) borrowed from algebra and from number theory I wish to express my thanks to Dr Abram L Sachar, President of Brandeis University, and to the Department ... THEOREM set o all numbers having the preceding property is denumerable PROOF We again write A& = 4, + en where a, is an integer and c, I = (1 XOn 11 We have and, since we have and an easy calculation...
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introduction to p-adic numbers and p-adic analysis - a. baker
... CONGRUENCES AND MODULAR EQUATIONS Proposition 1.4 The set Z/n with the operations + and × is a commutative ring and the n n function πn : Z −→ Z/n is a ring homomorphism which is surjective (onto) and ... first summand is {±1} and the second can be taken to be Now for a general n we have n = pr1 pr2 · · · prs s where for each i, pi is a prime with and ri p1 < p < · · · < p s Then the numbers pi ... (a) ≡ r p2r−1 p Then there exists a ∈ Z such that f (a ) ≡ p2r+1 and a ≡ a r p and a ∈ Z, CHAPTER The p-adic norm and the p-adic numbers Let R be a ring with unity = 1R Definition 2.1 A function...
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quant session 2 (classroom)- 75 questions - numbers and inequalities - solutions
... IN NUMBERS statement (1) let's just PICK A WHOLE BUNCH OF NUMBERS WHOSE GCF IS and watch what happens let's try to make the numbers diverse say, and 6 and 8 and 10 10 and 12 and 10 and 14 and ... 3, 2, and and share only as a factor and share only as a factor and share only as a factor and share only as a factor There are four positive integers, therefore, that are both less than and share ... between m and r, imagine m and r both starting out at 12, and 'sliding' equally in opposite directions, with r moving to the right and m moving to the left (you can't slide r to the left and m to...
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