On the Cauchy problem for Gross-Pitaevskii hierarchies

The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n,$ $n \geq 1.$ We prove local existence and uniqueness of solutions in certain Sobolev type spaces $\mathrm{H}^{\alpha}_{\xi}$ of sequences of marginal density operators with $\alpha > n/2.$ In particular, we give a clear discussion of all cases $\alpha > n/2,$ which covers the local well-posedness problem for Gross-Pitaevskii hierarchy in this situation.Comment: 17 pages. The referee's comments and suggestions have been incorporated into this version of the pape

Habitat differentiation and conservation gap of Magnolia biondii, M. denudata, and M. sprengeri in China

The flower buds of Magnolia biondii, M. denudata, and M. sprengeri are the materials of Xinyi, a traditional Chinese medicine. The harvest of flower buds and habitat fragmentation caused by human disturbance heavily threatens the natural regeneration and survival of these three Magnolia species. With the aim to support the conservation and improve the effectiveness of conservation, we performed an assessment on habitat suitability, influences of environmental variables on habitat suitability, and the conservation gap of these three Magnolia species, based on the Maxent modeling method. The results indicated that: (1) altitude, annual mean temperature, extreme temperature, temperature fluctuation, annual precipitation, and extreme precipitation are the most influential environmental variables for the distribution of M. sprengeri, M. biondii, and M. denudata; (2) obvious habitat differentiations were observed among M. biondii, M. denudata, and M. sprengeri. M. sprengeri tends to be located in further northern areas with higher altitudes, lower temperatures, and lower precipitation compared to M. biondii and M. denudata; and (3) a large proportion of suitable habitats have been left without protection. Woodland and forest shared the largest area out of the suitable habitats. However, grassland, agricultural land, residential land, and mining and industry areas also occupied large areas of suitable habitats

Nonexistence for mixed-type equations with critical exponent nonlinearity in a ball

AbstractIn this work, we consider the following isotropic mixed-type equations: (0.1)y|y|α−1uxx+x|x|α−1uyy=f(x,y,u) in Br(0)⊂R2 with r>0. By proving some Pohozaev-type identities for (0.1) and dividing Br(0) naturally into six regions Ωi(i=1,2,3,4,5,6), we can show that the equation (0.2)yuxx+xuyy=sign(x+y)|u|2u with Dirichlet boundary conditions on each natural domain Ωi has no nontrivial regular solution in Br(0)

Use of whole-exome sequencing to identify novel monogenic gene mutations and genotype–phenotype correlations in Chinese Han children with urolithiasis

The incidence of urolithiasis (UL) in children has been increasing. Although the pathogenesis of pediatric UL is controversial and remains unclear, multiple monogenic causes of UL have been identified. We aim to investigate the prevalence of inherited UL causes and explore the genotype–phenotype correlation in a Chinese pediatric group. In this study, we analyzed the DNA of 82 pediatric UL patients using exome sequencing (ES). The data of metabolic evaluation and genomic sequencing were subsequently analyzed together. We detected 54 genetic mutations in 12 of 30 UL-related genes. A total of 15 detected variants were described as pathogenic mutations, and 12 mutations were considered likely pathogenic. Molecular diagnoses were made in 21 patients with pathogenic or likely pathogenic variants. Six novel mutations that were not previously reported were identified in this cohort. Calcium oxalate stones were detected in 88.9% cases (8/9) with hyperoxaluria-related mutations, while 80% of individuals (4/5) with cystinuria-causing defects were diagnosed with cystine stones. Our study highlights the significant genetic abnormalities in pediatric UL and demonstrates the diagnostic power of ES for screening patients with UL

Demonstration of laser-produced neutron diagnostic by radiative capture gamma-rays

We report a new scenario of time-of-flight (TOF) technique in which fast neutrons and delayed gamma-ray signals were both recorded in a millisecond time window in harsh environments induced by high-intensity lasers. The delayed gamma signals, arriving far later than the original fast neutron and often being ignored previously, were identified to be the results of radiative captures of thermalized neutrons. The linear correlation between gamma photon number and the fast neutron yield shows that these delayed gamma events can be employed for neutron diagnosis. This method can reduce the detecting efficiency dropping problem caused by prompt high-flux gamma radiation, and provides a new way for neutron diagnosing in high-intensity laser-target interaction experiments