Realistic rendering of participating media like clouds requires multiple anisotropic light scattering. This paper presents a propagation approximation for light scattered into M direction bins, which reduces the “ray effect” problem in the traditional “discrete ordinates” method. For a regular grid volume of n3 elements, it takes O(M n3 log n + M2 n3) time and O(M n3 + M2) space. This document ...

We show that random 3-SAT formulas with poly(log n) · n3/2 = n3/2+o(1) clauses can be efficiently certified as unsatisfiable. This improves a previous bound of n3/2+ε clauses. There ε > 0 is a constant.

The significance of DNA ethylation at the central hydrogen-bonding site (N3) of thymine was investigated using an in vitro DNA replication system. The system utilized a primed template in which the 3'-end of the primer is eight nucleotides away from N3-ethyldeoxythymidine (N3-Et-dT), present at template position 26 from the 3'-end. The 34-nucleotide template corresponds to a specific DNA sequen...

We study the periodic solutions of the generalized Abel equation x′ = a1A1(t)x 1+a2A2(t)x 2+a3A3(t)x n3 , where n1, n2, n3 > 1 are distinct integers, a1, a2, a3 ∈ R, and A1, A2, A3 are 2π-periodic analytic functions such that A1(t) sin t,A2(t) cos t, A3(t) sin t cos t are πperiodic positive even functions. When (n3−n1)(n3−n2) < 0 we prove that the equation has no nontrivial (different from zero...

The flexible zwitterionic dicarboxylate ligand 1,4-bis(4-carboxylato-1-pyridinium)butane (bcpb) assumes different conformations to collaborate with pseudohalides in various coordination modes to produce coordination polymers in which distinct anionic motifs with mixed carboxylate and pseudohalide bridges are interlinked by the cationic butylenebis(pyridinium) tethers. The Cu(II) compound, [Cu2(...

We show that a necessary and sufficient condition for the existence of a Kp ,2q factorization of the symmetric complete tripartite digraph K~1,n2,n3 is (i) ni = n2 = n3 == 0 (mod p) for p = q, (ii) ni = n2 = n3 == 0 (mod dp'q'(p' + 2q')) for p =Iq and p' odd, (iii) ni = n2 = n3 == 0 (mod dp'q'(p' + 2q')/2) for p =Iq and p' even, where d = (p, q), p' = p/d, q' = q/d.

Metabolic syndrome (MS) is characterised by accumulation of CVD risk factors. The use of very long chain n-3 polyunsaturated fatty acids (VLC n3 PUFA) could potentially benefit MS by reducing risk factors. To better understand the possible VLC n3 PUFA benefits, the literature was systematically reviewed for randomised controlled trials (RCT) that published effects of VLC n3 PUFA on MS patients....