Let {sij : i, j = 1,2, . . .} consist of i.i.d. random variables in C with Es11 = 0, E|s11| 2 = 1. For each positive integer N , let sk = sk(N) = (s1k, s2k, . . . , sNk) T , 1≤ k ≤K, with K =K(N) and K/N → c > 0 as N →∞. Assume for fixed positive integer L, for each N and k ≤K, αk = (αk(1), . . . , αk(L)) T is random, independent of the sij , and the empirical distribution of (α1, . . . , αK), ...

The full transformation semigroup TnTn is defined to consist of all functions from Xn={1,…,n}Xn={1,…,n} itself, under the operation composition. In \cite{JMH1}, for any αα in TnTn, Howie and denoted collapse by c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}. Let OnOn be order-preserving transformations CnCn decreasing on XnXn=under its natural order, respectively. E(On)E(On) set ide...

Laser and photocell quantum heat engines (QHEs) are powered by thermal light and governed by the laws of quantum thermodynamics. To appreciate the deep connection between quantum mechanics and thermodynamics we need only recall that in 1901 Planck introduced the quantum of action to calculate the entropy of thermal light, and in 1905 Einstein's studies of the entropy of thermal light led him to...

Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied separately. It is indeed natural to consider an integrated model in which a processor, when awake...

We give a simple straightforward and rigorous derivation that when the eigenvalues of one of the d = 9 (5, 3, 2) matrices in the SU(N) invariant supersymmetric matrix model become large (and well separated from each other) the ground-state wavefunction (resp. asymptotic zero-energy solution of the corresponding differential equation) factorizes, for all N > 1, into a product of supersymmetric h...

The Virasoro conjecture predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential operators which form a half branch of the Virasoro algebra. This conjecture was proposed by Eguchi, Hori and Xiong [EHX2] and also by S. Katz [Ka] (see also [EJX]). It provides a powerful tool in the computation of Gromov-Witten invariants. In [LT], the author...

OBJECTIVE To study the issues and dilemmas in prenatal diagnosis of Sickle cell anemia (SCA) and to evaluate the role of genetic modifiers in counseling the families. METHODS The authors studied the genotype in 47 individuals with increased HbS and three representative families were taken as an example for describing various issues which need to be sorted out for appropriate counseling. RES...