Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure

We consider the propagation of broad optical beams through slab waveguides with a purely quadratic nonlinearity and containing linear and nonlinear long-period quasi-phase-matching gratings. An exact Floquet analysis on the periodic, plane-wave solution shows that the periodicity can drastically alter the growth rate of the modulational instability but that it never completely removes the instability. The results are confirmed by direct numerical simulation, as well as through a simpler, approximate theory for the averaged fields that accurately predicts the low-frequency part of the spectrum.Comment: 10 Pages, 13 figures (some in two parts) new version has some typos removed and extra references and explanation adde

Smooth minimal genera for small negative classes in CP2#nCP2 with n⩽9

AbstractThe smooth minimal genera for ξ∈H2(CP2#nCP2,Z) are determined completely when n⩽9 and 0>ξ2>−16. In particular, we find that ξ is represented by an embedded 2-sphere when 0>ξ2>−n−7 and n⩽9

First R and I Lights and Their Photometric Analyses of GSC 02393-00680

We obtained complete $R$ and $I$ light curves of GSC 02393-00680 in 2008 and analyzed them with the 2003 version of the W-D code. It is shown that GSC 02393-00680 is a W-type shallow contact binary system with a high mass ratio $q=1.600$ and a degree of contact factor $f=5.0$. It will be a good example to check up on the TRO theory. A period investigation based on all available data suggests that the system has a small-amplitude period oscillation ($A_3=0.^{d}0030$; $T_3=1.92$years). This may indicate it has a moderate mass close third body, which is similar to XY Leo

Mutant spectrum of dengue type 1 virus in the plasma of patients from the 2006 epidemic in South China

SummaryThe aim of the present study was to explore the mutant spectrum of dengue type 1 virus (DENV-1) within individuals during the 2006 dengue epidemic in South China. A 513-bp fragment including most of domain III of the envelope (E) gene was amplified directly from clinical samples, then cloned and sequenced. A total of 89 clones from six patients (range 11–17 clones per patient) were sequenced. Genetic diversity was calculated using MEGA 4 package. The total number of nucleotide mutations was 113 (3.7%) within the sequenced 513-bp E gene, with a range of 15 (3%) to 24 (4.7%) within individual viral populations, harboring more non-synonymous than synonymous mutations. The extent of sequence diversity varied among patients, with the mean diversity ranging from 0.19% to 0.32%, and the mean pairwise p-distance ranging from 0.34% to 0.65%. No genome-defective virus was detected in any clone in this study. Purifying selection may be the main driving force for the intrahost evolution: the mean dN/dS ratio was 0.532. Our findings contribute to the understanding of the genetic variation of DENV-1 in South China