All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., q = 1), does not modify anything to the second principle of thermodynamics, which therefore holds in the usual way. Moreover, some claims in the literature that this principle can be violated for specific anomalous systems (e.g., granular materials) can be shown ...

The Weak Reflection Principle for ω2, or WRP(ω2), is the statement that every stationary subset of Pω1 (ω2) reflects to an uncountable ordinal in ω2. The Reflection Principle for ω2, or RP(ω2), is the statement that every stationary subset of Pω1 (ω2) reflects to an ordinal in ω2 with cofinality ω1. Let κ be a κ+-supercompact cardinal and assume 2κ = κ+. Then there exists a forcing poset P whic...

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In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces H(R) and H−s(Rd). Keywords...

bert transform. Section 4 describes the algorithm Narayana, S., Sarkar, T. K., Adve, R., Wicks, M., and Vanused to implement this. In Section 5, a few numerical nicola, V., A Comparison of Two Techniques for the Interexamples are studied and comparisons made. polation/Extrapolation of Frequency Domain Responses, Digital Signal Processing 6 (1996), 51–67. 2. THE CAUCHY METHOD In this paper, a co...

where Xt= jBtjp and St = max 0 r t jBrjp. In the case p=1 the closed form for s 7! g (s) is found. This yields 1;q = (q(q+1)=2)( (1+(q+1)=q)) for all q > 0 . In the case p 6= 1 no closed form for s 7! g (s) seems to exist. The inequality above holds also in the case p = q+1 (Doob’s maximal inequality ). In this case the equation above (with K = p=2c ) admits g (s) = s as the maximal solution, a...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...