subpart q—welding cutting and brazing

... welding and oxy-acetylene welding (b) Torch brazing, furnace brazing, induction brazing, resistance brazing and dip brazing (c) The welding and brazing of carbon, carbon-manganese, and low and high ... information and guidance © Copyright STANDARDS AUSTRALIA / STANDARDS NEW ZEALAND Users of Standards are reminded that copyright subsists in all Standards Australia and Standards New Zealand publications ... STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND Australian/New Zealand Standard Pressure equipment — Welding and brazing qualification S E C T I O N S C O P E A N D G E N E R A L 1.1 SCOPE This Standard...

Ngày tải lên: 12/03/2014, 18:02

... welding and oxy-acetylene welding (b) Torch brazing, furnace brazing, induction brazing, resistance brazing and dip brazing (c) The welding and brazing of carbon, carbon-manganese, and low and high ... STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND Australian/New Zealand Standard Pressure equipment — Welding and brazing qualification S E C T I O N S C O P E A N D G E N E R A L 1.1 SCOPE This Standard ... prohibited This Standard unifies and revises the requirements for the qualification of welding and brazing procedures, welding and brazing personnel, and production test plates and welds, specified...

Ngày tải lên: 12/03/2014, 18:03

... Manzanera and Pardos, 1990), Q Shumardii (Bennett and Davies, 1986), Q acutissima (Ide and Yamamoto, 1986; Sato et al, 1987), Q serrata (Ide and Yamamoto, 1987) and Q lobata (Johnson and Walker, ... the ground) and from seedlings and trees of differ- ent ages (1-30-yr-old trees) For each treatment, 40-90 cuttings were used Cuttings were collected between May 20 and July 20 All cuttings were ... modified MurashigeSkoog (MS) medium (Murashige and Skoog, 1962), Schenk-Hildebrandt (SH) medium (Schenk and Hildebrandt, 1972), and WPM (Lloyd and McCown, 1980), supplemented with glutamine (200...

Ngày tải lên: 08/08/2014, 19:21

... BB carbon arc brazing .CAB diffusion brazing DFB dip brazing DB flow brazing FLB furnace brazing FB induction brazing IB infrared brazing .IRB resistance brazing RB torch brazing TB ... –oxyacetylene cutting OFC.A –oxyhydrogen cutting OFC.H –oxynatural gas cutting OFC.N –oxypropane cutting .OFC.P oxygen arc cutting AOC oxygen lance cutting LOC arc brazing AB block brazing ... arc cutting AAC carbon arc cutting .CAC gas metal arc cutting GMAC gas tungsten arc cutting GTAC metal arc cutting .MAC plasma arc cutting PAC shielded metal arc cutting SMAC Other cutting...

Ngày tải lên: 12/03/2014, 17:09

... eB(q)t k! and Gq (t) = Ek (q) k=0 tk = eE(q)t , k! where the symbol Bk (q) and Ek (q) are interpreted to mean that (B(q))k and (E(q))k must be replaced by Bk (q) and Ek (q) when we expanded the ... 1)n n=0 and |q i − 1|p ≤ |q − 1|p < 1, where i ∈ Z We easily see that if |q − 1|p < 1, then q x = for x = if and only if q is a root of unity of order pN and x ∈ pN Zp (see [16]) By (2.3) and (2.7), ... As q → in (4.6) and (4.7), we have Fq,χ (t, x) → Fχ (t, x) and Gq,χ (t, x) → Gχ (t, x), where Fχ (t, x) and Gχ (t, x) are the usual generating function of generalized Bernoulli and Euler numbers,...

Ngày tải lên: 18/06/2014, 22:20

... eB(q)t k! and Gq (t) = Ek (q) k=0 tk = eE(q)t , k! where the symbol Bk (q) and Ek (q) are interpreted to mean that (B(q))k and (E(q))k must be replaced by Bk (q) and Ek (q) when we expanded the ... 1)n n=0 and |q i − 1|p ≤ |q − 1|p < 1, where i ∈ Z We easily see that if |q − 1|p < 1, then q x = for x = if and only if q is a root of unity of order pN and x ∈ pN Zp (see [16]) By (2.3) and (2.7), ... As q → in (4.6) and (4.7), we have Fq,χ (t, x) → Fχ (t, x) and Gq,χ (t, x) → Gχ (t, x), where Fχ (t, x) and Gχ (t, x) are the usual generating function of generalized Bernoulli and Euler numbers,...

Ngày tải lên: 20/06/2014, 04:20

... q-Bernoulli and p-adic q-Euler polynomials The padic q-Bernoulli and p-adic q-Euler polynomials in q x are defined by means of the bosonic and the fermionic p-adic integral on ℤp : [x + z]k dμ1 (z) and ... http://www.advancesindifferenceequations.com/content/2011/1/68 Page of 16 where the symbol Bk(q) and Ek(q) are interpreted to mean that (B(q))k and (E(q))k must be replaced by B k (q) and E k (q) when we expanded the one on the right, respectively ... (1991) doi:10.1016/0022-314X(91)90048-G 11 Choi, J, Anderson, PJ, Srivastava, HM: Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions...

Ngày tải lên: 20/06/2014, 21:20

... twisted carlitz’s q-bernoulli numbers and q-bernstein polynomials Journal of Inequalities and Applications 2011 2011:52 Submit your manuscript to a journal and benefit from: Convenient online submission ... + 1)n − 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 ... 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 purpose...

Ngày tải lên: 20/06/2014, 22:20

... of Inequalities and Applications 2011, 2011:64 http://www.journalofinequalitiesandapplications.com/content/2011/1/64 ∞ Fq (t, x) = (α) En,q (x) n=0 Page of tn n! (8) By (5) and (8), we get ∞ ... Inequalities and Applications 2011, 2011:64 http://www.journalofinequalitiesandapplications.com/content/2011/1/64 Page of Theorem is important to study the relations between q-Bernstein polynomials and ... Journal of Inequalities and Applications 2011, 2011:64 http://www.journalofinequalitiesandapplications.com/content/2011/1/64 Page of Let n, k Î ℤ+ with n > k Then, by (16) and Corollary 6, we have...

Ngày tải lên: 20/06/2014, 22:20

... particular, by (1) and (2), we get qDq (t, 1) − Dq (t) = t (7) Thus, by (7), we have qBn,q (1) − Bn,q = 1, if 0, if n = 1, n > 1, (8) and n n l−1 q Bl,q l Bn,q (1) = l=0 (9) Therefore, by (4) and (6)-(9), ... Acikgöz, Erdal and Araci derived some results by using Theorems 1-3 Hence, the other results are incorrect Now, we redefine the generating function of q-Bernoulli numbers and polynomials and correct ... 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 by Acikgöz...

Ngày tải lên: 20/06/2014, 22:20

... Govil and Gupta 10 have introduced a new type of q-integrated Meyer-Konig-Zeller-Durrmeyer operators, and their results are ¨ closely related to the study of q-Bernstein polynomials and q-Genocchi ... the Euler and the Genocchi numbers and polynomials,” Advanced Studies in Contemporary Mathematics (Kyungshang), vol 20, no 1, pp 23–28, 2010 T Kim, “A note on the q-Genocchi numbers and polynomials,” ... polynomials,” Journal of Inequalities and Applications, vol 2007, Article ID 71452, pages, 2007 S.-H Rim, S J Lee, E J Moon, and J H Jin, “On the q-Genocchi numbers and polynomials associated with...

Ngày tải lên: 21/06/2014, 05:20

... 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 We ... numbers and Carlitz’s q-Bernoulli numbers,” Abstract and Applied Analysis in press 15 T Kim, L.-C Jang, and H Yi, “A note on the modified q-Bernstein polynomials,” Discrete Dynamics in Nature and ... 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 polynomials...

Ngày tải lên: 21/06/2014, 07:20

... xr dμq x1 · · · dμq xr 2.36 By 2.35 and 2.36 , one obtains the following corollary 12 Journal of Inequalities and Applications Corollary 2.8 For r ∈ N and n ∈ Z , one has n 0,r βn,q x l n 0,r ... dμq x1 q ⎧ ⎨1, if n ⎩0, if n > 1, 1, 2.48 and h,1 β0,q Zp q h−2 x1 dμq x1 h−1 h−1 q 2.49 14 Journal of Inequalities and Applications h,1 From 2.46 and 2.48 , one can derive the recurrence relation ... 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 that q...

Ngày tải lên: 21/06/2014, 07:20

... 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, ... and βn,ζ,q βn,ζ,q are called the twisted q-Bernoulli numbers of order k When k 1, the polynomials and numbers are called the twisted q-Bernoulli polynomials and numbers, respectively When k and ... x1 ··· xk x1 ··· xk By 2.11 and 2.12 , we obtain the following theorem ζ n n 2.12 k k q,ζ Journal of Inequalities and Applications Theorem 2.3 For n ∈ Z , k ∈ N and ζ ∈ Tp , one has n n l l...

Ngày tải lên: 21/06/2014, 07:20

... Jang, S.-D Kim, D.-W Park, and Y.-S Ro, “A note on Euler number and polynomials,” Journal of Inequalities and Applications, vol 2006, Article ID 34602, pages, 2006 L.-C Jang and T Kim, “On the distribution ... function for q-Euler numbers and its derivatives,” Journal of Mathematical Analysis and Applications, vol 339, no 1, pp 598–608, 2008 13 T Kim, “On the analogs of Euler numbers and polynomials associated ... Jang, and S.-H Rim, “New q-Euler numbers and polynomials associated with p-adic q-integrals,” Advanced Studies in Contemporary Mathematics, vol 15, no 2, pp 243–252, 2007 23 W Kim, Y.-H Kim, and...

Ngày tải lên: 21/06/2014, 16:20

... field of number theory and mathematical physics, zeta functions and l-functions interpolating these numbers in negative integers have been studied by Cenkci and Can , Kim 4–12 , and Ozden et al 16–18 ... physics, and so on see 3–18 The purpose of this paper is to give a new construction of the q-extensions of Euler numbers and polynomials It is expected that new constructed q-Euler numbers and polynomials ... n! En,q tn n! tn n! n ∞ n 2.4 From 2.1 and 2.3 , we can easily derive the following equation: Fq t, By 2.4 and 2.5 , we see that E0,q n l n l Fq t 2.5 and ql El,q En,q Therefore, we obtain the...

Ngày tải lên: 21/06/2014, 18:20

... q-Euler numbers and its derivatives,” Journal of Mathematical Analysis and Applications, vol 339, no 1, pp 598–608, 2008 27 T Kim and S.-H Rim, “New Changhee q-Euler numbers and polynomials associated ... x s ··· nh 4.4 for all s ∈ C and Re x > We note that ζw s, x is analytic function in the whole complex h,q h,q 1,q s-plane and ζw s, ζw s We also remark that if w and h 1, then ζ1 s, x ζq s, ... L-functions and p-adic q-integrals,” Journal of the Korean Mathematical Society, vol 44, no 1, pp 1–10, 2007 L.-C Jang, S.-D Kim, D.-W Park, and Y.-S Ro, “A note on Euler number and polynomials,”...

Ngày tải lên: 21/06/2014, 22:20

... Choi, P J Anderson, and H M Srivastava, “Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function,” Applied Mathematics and Computation, ... pp 44–56, 2007 L Jang and T Kim H Ozden, I N Cangul, and Y Simsek, “Remarks on sum of products of h, q -twisted Euler polynomials and numbers,” Journal of Inequalities and Applications, vol 2008, ... for their valuable suggestions and comments References L.-C Jang, S.-D Kim, D.-W Park, and Y.-S Ro, “A note on Euler number and polynomials,” Journal of Inequalities and Applications, vol 2006,...

Ngày tải lên: 22/06/2014, 03:20

... suggestions and comments and Professor Paolo E Ricci for his cooperations and helps This work was supported by Jangjeon Research Institute for Mathematical Science(JRIMS2005005-C00001) and Jangjeon ... simple and useful for deriving many interesting identities related to q-Genocchi numbers By this reason, we consider q-Genocchi numbers and polynomials which are different Our q-Genocchi numbers and ... (see [1]), Cenkci et al have studied q-Genocchi numbers and polynomials and p-adic q-Genocchi measures Starting from T Kim, L.-C Jang, and H K Pak’s construction of q-Genocchi numbers [7], they...

Ngày tải lên: 22/06/2014, 18:20

... q)∞ which is symmetric in a and b Note that the special case z = of (1.2) has also appeared in the literature (see Stockhofe [9] and Pak [8, 2.2.4]) Rewrite the left-hand side of (1.3) as (z; q)n ... due to Andrews, Jim´nez-Urroz, and Ono [4] Here we describe Chapman’s proof e Proof of Theorem 2.1 We shall construct an involution σ on P1 such that σ preserves |λ| while interchanging (λ) and ... combinatorial proofs of the q-binomial theorem and Theorems 1.2 and 1.3 Our combinatorial proof of the q-binomial theorem is based on Theorem 2.1, and is essentially the same as that of Alladi...

Ngày tải lên: 07/08/2014, 07:21