Generalized retarded integral inequalities

We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].Comment: Changes suggested by the referee don

Identification of rice chromosome segment substitution line Z322-1-10 and mapping QTLs for agronomic traits from the F₃ population

Chromosome segment substitution lines (CSSLs) are powerful tools to combine naturally occurring genetic variants with favorable alleles in the same genetic backgrounds of elite cultivars. An elite CSSL Z322-1-10 was identified from advanced backcrosses between a japonica cultivar Nipponbare and an elite indica restorer Xihui 18 by SSR marker-assisted selection (MAS). The Z322-1-10 line carries five substitution segments distributed on chromosomes 1, 2, 5, 6 and 10 with an average length of 4.80 Mb. Spikilets per panicle, 1000-grain weight, grain length in the Z322-1-10 line are significantly higher than those in Nipponbare. Quantitative trait loci (QTLs) were identified and mapped for nine agronomic traits in an F3 population derived from the cross between Nipponbare and Z322-1-10 using the restricted maximum likelihood (REML) method in the HPMIXED procedure of SAS. We detected 13 QTLs whose effect ranging from 2.45% to 44.17% in terms of phenotypic variance explained. Of the 13 loci detected, three are major QTL (qGL1, qGW5-1 and qRLW5-1) and they explain 34.68%, 44.17% and 33.05% of the phenotypic variance. The qGL1 locus controls grain length with a typical Mendelian dominance inheritance of 3:1 ratio for long grain to short grain. The already cloned QTL qGW5-1 is linked with a minor QTL for grain width qGW5-2 (13.01%) in the same substitution segment. Similarly, the previously reported qRLW5-1 is also linked with a minor QTL qRLW5-2. Not only the study is important for fine mapping and cloning of the gene qGL1, but also has a great potential for molecular breeding

Well-posedness of the Ericksen-Leslie system

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.Comment: 16 page

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

Microfluidic and Nanofluidic Cavities for Quantum Fluids Experiments

The union of quantum fluids research with nanoscience is rich with opportunities for new physics. The relevant length scales in quantum fluids, 3He in particular, are comparable to those possible using microfluidic and nanofluidic devices. In this article, we will briefly review how the physics of quantum fluids depends strongly on confinement on the microscale and nanoscale. Then we present devices fabricated specifically for quantum fluids research, with cavity sizes ranging from 30 nm to 11 microns deep, and the characterization of these devices for low temperature quantum fluids experiments.Comment: 12 pages, 3 figures, Accepted to Journal of Low Temperature Physic

Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry

The energy spectra and the corresponding two- component spinor wavefunctions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The $s-$wave ($\kappa = 0$ state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wavefunctions for this potential and other special types of this potential are obtained. Extension of this result to $\kappa \neq 0$ state is suggested.Comment: 18 page

Elastic properties of polycrystalline YBa_2Cu_3O_7: Evidence for granularity induced martensitic behavior

In this work we present the study of the elastic properties of polycrystalline samples of superconducting YBa_2Cu_3O_7 prepared by the sol-gel method. The quality of all samples was checked by x-ray diffraction and scanning electronic microscopy while their physical properties were verified by transport and magnetic measurements. The elastic study was performed using the standard pulse-echo technique through measuring the phase velocity and the attenuation of ultrasonic waves (in the range of a few MHz) as a function of temperature. We have focused this study on the low temperatures interval (T < 200K). The obtained results show a strong hysteretic behavior in the ultrasonic attenuation (in addition to usually observed hysteretic behavior for the velocity) which strongly supports the existence of a martensitic-like phase above the superconducting critical temperature T_C. We argue that this peculiar behavior can be attributed to the granularity present in the samples.Comment: Physica C (in press

Sexual violence against women and children in Chinese societies

This article provides a comprehensive overview of the reported patterns of sexual violence against women and children in China. It reviews the prevalence of and risk factors for various types of sexual violence and discusses community knowledge and perceptions of these violent acts. It also critically examines three major problems of sexual violence research in China. First, the diversity of findings and study methods reported by surveys and criminal reports reflects the problems in obtaining accurate figures on the scope of the problem. Second, precautions must be taken in reading studies on Chinese culture-specific risk factors for domestic violence. Third, the study of culture-specific factors should not focus solely on cultural factors in a vacuum but rather, should examine traditional culture in the context of modern societies and consensus international standards of human rights. Recommendations for future research are also discussed. © 2009 Sage Publications.postprin