Báo cáo toán học: "FASTER AND FASTER CONVERGENT SERIES FOR ζ(3)" doc

... (a 3 ), (b 3 ), (H 1 ), (H 2 ) and the following conditions hold true: (b + ) b(t) ≥ 0 for t ≥ 0. (f + ) f(x, t) ≥ 0 for x ∈ Ω and t ≥ 0. (g + ) g(x, t) ≥ 0 for x ∈ ∂Ω and t ≥ 0. (f 2 ) + There exist ... < p ∗ (x) for x ∈ ¯ Ω and lim inf t→0 |F (x,t)| |t| r 1 (x) < +∞ uniformly for x ∈ Ω. (g 5 ) There exists r 2 ∈ C 0 ( ¯ Ω) such that 1 < r 2 (x) < p ∗ (x) for...

Ngày tải lên: 20/06/2014, 21:20

... conclusion is straightforward to determine. Since tr(D 4 ) =  n i=1 d 4 i and tr(A 2 D 2 ) =  n i=1 d 3 i , it suffices to find tr(ADAD) and tr(A 4 ). For the former expression, note that for each i = ... edges of the form i ∼ j where d i = 2 and d j = 3, and 3n−5a 2 edges of the form i ∼ j where d i = 3 = d j = 3. We find that  i∼j d i d j = 27n−21a 2 and  i∼j (d i + d j − 2) =...

Ngày tải lên: 07/08/2014, 21:20

... +2)!(n +1) 2 (2n +1) 2 . For s =3 we have ζ(3) = ∞  n=0 (−1) n 72  4n n  3n n  { 6120n +5265n 4 + 13761n 2 + 13878n 3 + 1040 (4n + 1)(4n +3)(n + 1)(3n +1) 2 (3n +2) 2 }, and so on. References [A] ... 2 For s =2 we obtain ζ(3) = 1 4 ∞  n=1 (−1) n−1 56n 2 − 32n +5 (2n − 1) 2 1  3n n  2n n  n 3 where ... certify combinatorial identities,Jour.Amer.Math.Soc.3 (1990), 147-158. [Z] D...

Ngày tải lên: 07/08/2014, 06:20

... provide the ground for enabling proactive handling of problematic situations, i.e. identifying and handling issues that could undermine the performance of the system before these actually ... Learning and predicting the performance is also the target of the cognitive controller built using multilayer feed-forward neural network [13]. The controller performs this task for differen...

Ngày tải lên: 20/06/2014, 20:20

... right-continuous, and thus, is continuous. By (11) and (14), we have ηk ≤ f u (0, x) ≤ k, and so −(1 −η) k ≤ f u (0, x) −k ≤ 0 for every 10 Figure 1: Infinite beam on nonlinear and non-uniform elastic ... C q (R) if u ∈ C q (R) for q = 0, 1, 2, . . (F2) f(u, x) ·u ≥ 0, and f u (u, x) ≥ 0 for every u, x ∈ R. (F3) For every υ ≥ 0, sup x∈R, |u|≤υ   ∂ q f ∂u q (u, x)   <...

Ngày tải lên: 20/06/2014, 20:20

... exists m ≥ 0 such that β(t) ≥ ϕ ∗ for all t ∈ I − and β  (t) = m ≥ max y ≤max I β f(t, β(t), y) for a.a. t ∈ I 0 . Therefore, α and β are lower and upper solutions for problem (1).  Example 5 ... that β (t) ≥ k(t) for all t ∈ I − and β  (t) = m ≥ max y ≤max I β(t) f(y) for all t ∈ I 0 . (25) So we deduce from (24) and (25) that α and β are lower and upper solutions...

Ngày tải lên: 20/06/2014, 20:20

... uniform decomposition. Dyadic decomposition divides the input signal bandwidth into the logarithmic set of bandwidths, whereas the uniform decomposition divides it into the uniform set of bandwidths. ... frequency subbands of the frame. Each frame of speech signal is decomposed (uniformly/dyadic) into different frequency subbands using discrete wavelet transform (DWT) and each subband...

Ngày tải lên: 20/06/2014, 20:20

... signal x with a random waveform and randomly under-sample the result in time-domain. The random convolution is performed through a random pre-modulation in the Fourier domain and the signal thus ... a set of m indices chosen independently and uniformly at random from {1, . . . , N w }, and y = A c Ω α ∈ C m . For some universal constants C > 0 and γ > 1, if the number of mea...

Ngày tải lên: 20/06/2014, 20:20

... (1:3), and the precipitate was filtered and recrystallized from DMF and water. A mixture of the acids 3a–k and 4a–c (1 mmol), and phosphorus oxychloride (5 mL) was heated under reflux for 3 ... filtered, dried, and recrystallized from a mixture of ethanol and water. The compounds obtained 5a–k and 6a–c were reacted with 10 mL NaOH (20%) and 10 mL of ethanol under refl...

Ngày tải lên: 20/06/2014, 20:20

... designed and carried out the experiments and wrote the first draft of the manuscript. JHA analyzed the properties and helped draft the manuscript. KNH and KSH detailed the original idea and modified ... distance between the target and substrate was about 50 mm. The substrates were cleaned with acet- one and isopropyl alcohol for 10 min each and then rinsed with deionized wat...

Ngày tải lên: 20/06/2014, 21:20