gauss apos s q binomial theorem and the triple product identity

Báo cáo toán học: "The q-Binomial Theorem and two Symmetric q-Identities" doc

Ngày tải lên : 07/08/2014, 07:21

... 1.2, and 1.3 In this section, we give 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 ... proofs of q- series identities, J Combin Theory Ser A, 99 (2002), 1–16 [6] G Gasper, Elementary derivations of summation and transformation formulas for q- series, In: Special Functions, q- Series and ... parts is equal to the number of partitions of n with the largest part at most 2m and with no repeated odd parts Theorem 2.1 was established by Chapman [5] in his proof of the q- identity ∞ q 2n−1...

8
313
0

Báo cáo toán học: "Hybrid Proofs of the q-Binomial Theorem and other identities" ppsx

Ngày tải lên : 08/08/2014, 14:22

... (q, q ; q )∞ (S2 0) q n +n = ; q ) ( q; q ) 4; q5 ) (q (q, q n n ∞ (S9 9) The equality of the three left sides of these equations once again easily follow from the summation formulae in Lemmas and ... [29], and similarly for other identities labelled below): ∞ (S1 4) q = , 4; q4 ) (q (q , q ; q )∞ n (S1 6) q n +n = (q ; q )n ( q; q )n+1 (q , q ; q )∞ (S9 4) ( q ; q )∞ n=0 ∞ n2 +2n n=0 ∞ ( q; q )∞ ... )∞ n=0 q n +n = , (q; q) n (q , q ; q )∞ Each of these identities had also previously been proven by Rogers [24] The equality of the three left sides of these equations easily follow from Theorem...

21
190
0

Girsanov’s theorem and the risk-neutral measure

Ngày tải lên : 18/10/2013, 03:20

... I ! = 0, this doesn’t really tell us anything useful about I Thus, P P we consider subsets of , rather than individual elements of e Distribution of B T If is constant, then n o Z T ... y2 dy (Substitute y = T + b) y = T + b = p 2T ,1 = 0: CHAPTER 17 Girsanov s theorem and the risk-neutral measure 191 fe We can also see that I B T = by arguing directly from the density formula ... is a martingale under IP 192 Lemma 1.54 (Baye s Rule) If X is F t-measurable and s t T , then f IE X jF s = Z s IE XZ tjF s : Proof: It is clear that Z 1s IE XZ tjF s is...

8
541
0

Báo cáo hóa học: " Some new identities on the twisted carlitz’s q-bernoulli numbers and q-bernstein polynomials" ppt

Ngày tải lên : 20/06/2014, 22:20

... derive some new identities for the twisted q- Bernoulli numbers and polynomials Final purpose of this paper is to give some relations 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 < Let us consider the nth twisted Carlitz s q- Bernoulli polynomials using ... http://www.journalofinequalitiesandapplications.com/content/2011/1/52 Acknowledgements The authors express their sincere gratitude to referees for their valuable suggestions and comments This paper was supported...

6
401
0

Ghana's biofuels policy: challenges and the way forward

Ngày tải lên : 05/09/2013, 16:10

... ethanol is about 97 per cent.) Based on these assumptions the demand for cassava for producing ethanol in 2015 and 2020 assuming further that only cassava will be used to meet this demand was estimated ... introduction of subsidies and incentives to boost the production of biofuels SNEP fell short of proposing any form of subsidies and or incentives after setting the targets In order to meet the set target ... biodiesel (Also EN 14214 was developed using rapeseed oil as the feedstock for the production of biodiesel) This is significant because vegetable oils differ in most cases significantly in their...

10
412
1

England’s opportunity, England’s character - Arnold, Mill, and the Union in the 1860s

Ngày tải lên : 01/11/2013, 07:20

... bring the heterogeneous whole under ﬁrmer pressure and control: so long as this mixed constitution of our nature possesses us, we pay it tribute and serve it; so soon as we possess it, it pays us ... Gladstone s legislative program, and it was on this issue that the deepest diﬀerences between English and Irish attitudes and practices revealed themselves.⁴⁵ Moreover, the land question became a discursive ... the viability of this view and, at the same time, argue that something other than this is just as important here For as Dewey suggests, the uses to which the essentializing historicist representation...

38
386
0

leapfrogging india s information technology industry and the internet docx

Ngày tải lên : 18/03/2014, 11:20

42
373
0

Learning from My Mother’s Voice Family Legend and the Chinese American Experience pptx

Ngày tải lên : 29/03/2014, 04:20

... had its own set of stories and legends that sustain its people and nurture its children As groups immigrate to other lands, they cherish these stories and legends while creating new ones of their ... rebelliousness against feudal rulers of China is similar to the rebelliousness of Chinese immigrants against the unjust and racist policies of the United States Many immigrants defied the rules that they ... acknowledged their equality with men, the contrasts between the peasants and nobility, and the contrasts between men and women In worship of gods and goddesses, the sun and moon have come to symbolize the...

178
223
0

Monetary Policy in the Eurozone: Evaluating the European Central Bank’s interest rate decisions and the needs of member states using a Taylor rule ppt

Ngày tải lên : 29/03/2014, 13:20

... area countries have implications on various additional economic issues such as competitiveness and debt dynamics These issues, and the implications of the ECB s interest rate decisions, were explained ... levels of 2% does not necessarily apply to all the euro area countries, it does seem that the stress levels have increased since mid-2007 V Risks and Mitigations One major risk is the use of the ... conditions” and thus can be used as “a benchmark to assess policy decisions.” 66 VI Implications One of the major potential implications of these various stress levels and lasting differences between...

41
513
0

báo cáo hóa học:" Research Article Browder’s Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces" doc

Ngày tải lên : 21/06/2014, 11:20

... Browder s Theorems and Some Results in IFNS In this section, we discuss the idea of fuzzy type of some Browder s fixed point theorems in intuitionistic fuzzy normed space by 26, 27 As a consequence ... Nonlinear Science and Its Applications, vol 3, no 2, pp 96–109, 2010 13 R Saadati, S Sedghi, and N Shobe, “Modified intuitionistic fuzzy metric spaces and some fixed point theorems,” Chaos, Solitons and ... Theory and Applications is, we can deal with such situations by modelling the inexactness through the intuitionistic fuzzy norm Schauder 18 introduced the fixed point theorem, and since then several...

11
313
0

Báo cáo sinh học: "Research Article A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials" docx

Ngày tải lên : 21/06/2014, 16:20

... some symmetric properties of them Furthermore, using these symmetric properties of them, we can obtain some relationships between the twisted q- Bernoulli numbers and polynomials and between the ... Equations Acknowledgments The authors express Their sincere gratitude to referees for their valuable suggestions and comments This work has been conducted by the Research Grant of Kwangwoon University ... integers,” Russian Journal of Mathematical Physics, vol 11, no 1, pp 71–76, 2004 T Kim, “Power series and asymptotic series associated with the q- analog of the two-variable p-adic L-function,” Russian...

13
357
0

Báo cáo hóa học: " Research Article On the Distribution of the q-Euler Polynomials and the q-Genocchi Polynomials of Higher Order" docx

Ngày tải lên : 22/06/2014, 03:20

... 1.16 The purpose of this paper is to give the distribution of extended higher order q- Euler and q- Genocchi polynomials In 24 , Choi-Anderson-Srivastava have studied the q- extension of the Apostol-Euler ... complex number q ∈ C or a p-adic number q ∈ Cp If q ∈ C, one normally assumes |q| < If q ∈ Cp , one normally assumes |1 − q| p < We use the notation x − qx , 1 q q x q x − q q , 1.5 cf 1–5, ... j ∞ ql j w m k−1 m m m lm m q q wm q −1 q m lm m 1 q q q wm m q −1 m lm m q q wm q n n l n l −1 l qlm L Jang and T Kim Now we consider the following generating functions: ∞ k k Fq,w t En ,q, w...

9
287
0

Báo cáo toán học: " Character Polynomials, their q-analogs and the Kronecker product" potx

Ngày tải lên : 08/08/2014, 01:20

... ν⊢b Substituting in this the expansion s /ν = s /ν , s s = λ⊢a+c s , s s s λ⊢a+c we get hb ∗ s /δ = s , s s s , s s s s µ⊢a ν⊢b λ⊢a+c = s /λ , s s /δ , s s s = µ⊢a ν⊢b λ⊢a+c s /δ ... that equation 1.12 gives   h1 s2 1 [X − 1] = det h2  h3  = h2 h1 − h3 − h1 h1 + h1 h1 and equation 3.15 gives U(2,1) = s2 s1 s s + s1 1 s1 s s − (s3 s + s( 2,1) s + s1 3 s ) − s1 s1 s s ... s2 ,1 = s2 ,1 +s1 ,2 +s1 ,1,1 +s0 ,2,1 +s0 ,3 = s2 ,1 s1 ,2 +s1 ,1,1 s1 ,1,1 s2 ,1 = since s1 2 = s1 2 = So we have = here (2) Setting n = in equation 4.16 gives s2 ,2 ∗ s3 ,1 = s3 ,1 + s2 ,2 + s2 ,1,1 + s1 ,2,1...

40
288
0

the beginner's guide to broadband and the wireless internet (2006)

Ngày tải lên : 26/10/2014, 21:29

... Electronics Ltd Linksys product photos and screenshots copyright © and courtesy of Linksys Microsoft product screenshots reprinted with permission from Microsoft Corporation MSN Messenger, Microsoft, ... Performance and Maintenance and then select Power Options Action Change the settings for Turn off hard disks as well as System standby and System hibernates (Fig 3) Set these to several hours or Never ... The Beginner s Guide to Broadband and Wireless Internet Section 9: Switching Broadband Providers Essential Information The speed of broadband services continues to rise and the cost continues...

256
274
0

ward - the devil's casino; friendship, betrayal, and the high-stakes games played inside lehman brothers (2010)

Ngày tải lên : 03/11/2014, 13:49

... Adam; Steve was Hoss, and Joe, for obvious reasons was Little Joe " She said Chris, "the leader always the first in, was Pa " Neporent came up with the idea because Lessing, the chubbiest of the ... mortgage assets from government-owned asset management company Resolution Trust Corporation (RTC) stock, which was responsible for liquidating the assets of insolvent savings and loans (S& Ls) in the ... bonds, and tax shelters (which paid less commission) There was much less upside in this, so the Shearson brokers never gelled with their Lehman counterparts Meanwhile, irking the American Express...

249
233
0

Buying up the world japan’s outbound ma spree and the bid for value

Ngày tải lên : 06/12/2015, 23:03

... lessons have they learned from their previous successful (and not-so-successful) cross-border transactions? What pitfalls should be avoided in various stages of the deal and post-merger process? ... succeeds, the owner claims all the benefits If it fails, the owner sustains all the losses Lack of control, and the negative consequences this entails, is perhaps the most frightening scenario for the ... opportunities as soon as they arise explains why some Japanese firms buy first and consider the details later “In certain industries and types of business, there are only so many players you can...

29
233
0

East Asia’s Dynamic Development Model and the Republic of Korea’s Experiences

Ngày tải lên : 25/04/2016, 08:16

... Conditions for the East Asian Approach Over thousands of years, East Asia has formed its own social system based on these principles Its characteristics can be summarized as business-government ... prosperity and some misfortunes, such as the economic sluggishness in China until the 197 0s, the prolonged Japanese recession of the 199 0s, and the financial crises in 1997 Undeniably, the East ... Economics and Business The Yin- Yang theory can be applied to basic supply and demand theory The supply curve corresponds to Yang and the demand curve corresponds to Yin, because the supply curve has...

58
278
0

Virtually live blogs and the performance of identity

Ngày tải lên : 16/10/2015, 15:36

... Princess Cheri s submissives brought this role-play to the extreme, by de-humanising themselves as animals (a dog and a pig) in the service of the ‘Goddess’ they worshipped One of the submissives, ... of the other, and this is the essence of the selfing process Further, Mead s concept of self is delineated by the “I” and the “me” such that the creative “I” is the individual s response to the ... with these questions, vis-à-vis other blog performances, forms the backbone of this thesis These questions are tackled from two main perspectives – from my position as blog viewer and as a blogger...

117
384
0

Báo cáo toán học: "Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang and D. Sarason " docx

Ngày tải lên : 05/08/2014, 15:20

10
427
0

Neewa the Wonder Dog and the Ghost Hunters! Volume One: The Indian Medicine Woman's Mystery Revealed

Ngày tải lên : 07/11/2012, 09:09

... imaginations when it comes to seeing ghosts There are always stories in the newspapers about people seeing ghosts in the desert or mountains They see a shadow and think it s a ghost Their imagination ... into my shin to make sure I reach down to pet her as she loses her balance and stumbles over her oversized paws Neewa s nose starts sniffing the air She smells dinner and sits perfectly straight ... with quaking aspen, and green mosses that smell like morning due Only after it rains does the desert come alive with budding flowers, grasses and the wonderful desert smells of wet sage and sand...

18
485
0