[S1,Q15=MAC15(S1), P13=MAC13(S1,Q15)] [S2,Q25=MAC25(S2),P23=MAC23(S2,Q25)] [S4,Q46=MAC46(S4),P45=MAC45(S4,Q46)] Q36=MAC36(S1|S2|S3) P35=MAC35(S3, S1|S2, Q15, Q25, Q36) [S3, (S1|S2), Q15, Q25, Q36, P35] Q5B= MAC5B(S1|S2|S3|S4|S5) P56=MAC56(S5, (S1|S2|S3|S4),Q36,Q46,Q5B) [S5, (S1|S2|S3|S4),Q36, Q46, Q5B, P56] P6B=MAC6B(S6, ((S1|S2|S3|S4 |S5)| S7|S8),Q5B,Q7B,Q8B) [S6, ((S1|S2|S3|S4 |S5)| S7|S8),Q5...

• The entropy is a state function: S = S(state). Furthermore, it is additive; S12 = S1 + S2 for a system with subsystems 1 and 2. • Entropy is unchanged in a reversible state change. That is, S(f) = S(i) and so ∆S = 0. For a reversible state change, entropy increases: S(f) > S(i), and so ∆S > 0. In all cases, ∆S ≥ 0. • When heat is added to a system, then the entropy changes by an amount propor...

In this paper the third order long-range dependence (LRD) is de…ned in terms of the bispectrum and third order cumulants (bicovariances). Two particular non-Gaussian processes with second order LRD are considered together with their bispectra and bicovariances. AMS 2000 Subject Classi…cations: Primary 62M10, 37M10; secondary 62M15, 91B70. Dedicated to Endre Csáki and Pál Révész on the occasion ...

We give precise conditions under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0, X1]θ,p when Y0 is a closed subspace of codimension one. We then apply this result to nonharmonic Fourier series in Sobolev spaces Hs(−π, π) when 0 < s < 1. The main result: let E be a family of exponentials exp(iλnt) and E forms an unconditional basis in L2(−π, π). Then there...

It is generally believed that prokaryotic translation is initiated by the interaction between the Shine-Dalgarno (SD) sequence in the 5' UTR of an mRNA and the anti-SD sequence in the 3' end of a 16S ribosomal RNA. However, there are two exceptional mechanisms, which do not require the SD sequence for translation initiation: one is mediated by a ribosomal protein S1 (RPS1) and the other used le...

Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings s1 and s2 from the same alphabet and the goal is to find a mapping π between them so as to maximize the number of duos preserved. A duo is any two consecutive characters in a string and it is preserved in the mapping if its two consecutive ch...

Penelitian ini bertujuan untuk mengetahui kesesuaian lahan, penerapan dan pengembangan teknologi budidaya tambak sehingga potensi sumber daya yang tersedia dapat dimanfaatkan secara optimal lestari. Metode penelitian digunakan adalah metode survei yaitu mengumpulkan data dari sampel diambil acak terdiri 59 rumah tangga perikanan lahan menggunakan Sistem Informasi Geografis. Hasil menunjukkan ba...

Proof. Suppose z is in the RHS. Then, for some f ∈ Y X , z ∈ Sxfx for all x ∈ X. Hence for each x ∈ X there is y = fx so that z ∈ Sxy, so z is in the LHS. Suppose z is in the LHS. Then for each x ∈ X there is some y ∈ Y so that z ∈ Sxy. Hence for each x ∈ X the set Tx = { y : z ∈ Sxy } is not empty. By AC there is a function f ∈ Y x so that, for all x ∈ X, fx ∈ Tx. Hence, for all x ∈ X, z ∈ Sxf...