Báo cáo hóa học: "Research Article Maximal Regularity of the Discrete Harmonic Oscillator Equation" doc

... has discrete maximal regularity if Kf  I − TB ∗ f defines a bounded operator K ∈Bl p Z  ; X. As consequence of the definition, if 1.2 has discrete maximal regularity, then 1.2 has discrete ... representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterizatio...

Ngày tải lên: 22/06/2014, 11:20

... 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

... smoothness of reversible mapping 1.1 and the exponent of the small divisors condition. Moreover, we obtain a Gevrey normal form of the reversible mappings in a neighborhood of the union of the invariant ... Id  W −1 0    D s−5ρ,μr ×Π h ≤ c αρ τ2 , 2.26 where ·denotes the maximum of the absolute value of the elements of a matrix, W 0  diagρ −1 0...

Ngày tải lên: 21/06/2014, 07:20

... Problems This property of solutions is established i n the following theorem. Its proof combines the methodsofdeGiorgi[18], Landis [13], Moser [19], Serrin [20], and other mathemati- cians. Theorem 3.10. ... [2,Theorem8.1 (case (D)) and Theorem 9.1 (case (ND))]. Since our assumptions in the case (D)are slightly different from those in [2], we give a sketch of the proof. Proof(inthe...

Ngày tải lên: 22/06/2014, 22:20

... 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

... 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 Ministry of Education. References 1 P. ˇ Reh ´ ak, ... 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 l...

Ngày tải lên: 21/06/2014, 20:20

... state some condition and many lemmas which we need in the proof of the main theorem. In Section 3, we give the proof of the main result of the paper. 2. Preliminaries Let F  x, t    t 0 f  x, ... in R N . There are many results about it we can see 14–18. Because of the unboundedness of the domain, the Sobolev compact embedding does not hold. There are many met...

Ngày tải lên: 21/06/2014, 20:20

... and the following inequality holds for −∞ <r<s<t<∞, Γ t−r s f ≤ Γ t−s r fΓ s−r t f. 2.46 Proof. As in the proof of Theorem 2.1,weuseTheorem 1.4 instead of Theorem 1.3. Theorem ... we discuss the log-convexity of differences of the Popoviciu inequalities 1.4, 1.7, and 1.8. In the third section we introduce some mean value theorems and the Cauchy me...

Ngày tải lên: 22/06/2014, 02:20