Báo cáo hóa học: " Research Article Cauchy Means of the Popoviciu Type" pot

... arrive at a contradiction by using the same argument as in the latter part of proof of Theorem 1.1. This completes the proof of Theorem 1.2. 5. Applications Proof of Theorem 1.3. We shall divide our ... the proof of Theorem 5.1. Acknowledgments The authors thank the referees for reading the manuscript very carefully and making a number of valuable suggestions to impr...

Ngày tải lên: 21/06/2014, 05:20

... <s<r, then  u s 1  u s 2  ··· u s k  1/s ≥  u r 1  u r 2  ··· u r k  1/r . 2.1 Proof of Theorem 1.1. In our proof we often use the well-known fact that the scale of power means is ... inequality: ⎛ ⎝ n  j1  m  i1 a ij  p ⎞ ⎠ 1/p ≤ m  i1 ⎛ ⎝ n  j1 a p ij ⎞ ⎠ 1/p , 1.2 Journal of Inequalities and Applications 7 Case 5 0 <p<q<1.Ifm ≤ n, then...

Ngày tải lên: 21/06/2014, 07:20

... n r denotes the number of rows in the parity check matrix of the code, u k is the number of nonzero elements in the kth row of the parity check matrix and n iter is the number of iterations of the optimization ... as l ( S ( k )) = ( −1 ) u k +1 atanh ⎛ ⎝ u k  j=1 tanh ⎛ ⎝  r  k j  2 ⎞ ⎠ ⎞ ⎠ , (7) where r ( i ) = 2 σ 2 r ( i ) (8) is the LLR of the ith r...

Ngày tải lên: 21/06/2014, 08:20

... OFDM symbol of the first slot of each subframe. For the normal CP duration, the PHICH is also mapped into the first OFDM symbol of the first slot of each subframe. On the other hand, for the extended ... defining the control channels to resource element mapping. The size of the REG varies depending on the OFDM symbol number and antenna configuration [1]. The PCFIC...

Ngày tải lên: 21/06/2014, 11:20

... accelerate the convergence of the algorithm. The nature of the fixed point is determined by the char- acteristic values of the Jacobian matrix of partial derivatives evaluated at the fixed point. The ... right shows the histogram of the estimated parameters. The left column shows the time series of the estimated state functions of the hemodynamic respon...

Ngày tải lên: 21/06/2014, 20:20

... completes the proof of the theorem. Acknowledgment The authors are very grateful to the referees for their helpful comments and suggestions. 6 Fixed Point Theory and Applications The uniqueness of T ... 3791–3798, 2008. 17 D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of...

Ngày tải lên: 21/06/2014, 20:20

... solution of 5.19 if p ≥ 2. Acknowledgments This research is supported by the Grant 201/07/0145 of the Czech Grant Agency of the Czech Republic, and the Research Project MSM0022162409 of the Czech ... Similarly, as in the proof of Theorem 4.1, denote w k  r k ΦΔh k /h k  and let w k be a solution of 2.1 generated by another solution linearly independent of...

Ngày tải lên: 21/06/2014, 20:20

... problem depends on the structure of the boundary of the domain, the right hand side and the dimension n of the space R n . The classical Schr ¨ odinger equation in quantum mechanics has the form iΔu  x, ... the theorem holds up to l − 1 then we have u ∈ H l1 0 e −γt ,Q ∞ . By using analogous arguments in the proof of Lemma 4.4,withnotethat  f t s ∈ H l−s 0 e...

Ngày tải lên: 21/06/2014, 20:20

... ≤ G  u  T   P. 2.53 The rest of the proof is similar to that of Theorem 2.8, and the details are omitted. The proof is completed. Theorem 2.10. Assume that the function ft, u 0 , ,u n−1  ... discrete analysis. The cases when a time scale is equal to the real numbers or to the integers represent the classical theories of differential and of difference equations...

Ngày tải lên: 21/06/2014, 05:20

... Tt, the assumption c obviously holds. Acknowledgments The work was supported by the NSF of China, the Key Project of Chinese Ministry of Education, the NSF of Jiangxi Province of China, the ... completes the proof. Remark 2.6. For some general conditions which can ensure that the assumption c in Theorem 2.5 holds, we refer the reader to 17, Theorem 4.5. In...

Ngày tải lên: 21/06/2014, 05:20