Existence of translating solutions to the flow by powers of mean curvature on unbounded domains

In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain. This problem comes from the study of mean curvature flow and its generalization, the flow by powers of mean curvature. Our approach is a modified version of the classical Perron method, where the solutions to the minimal surface equation are used as sub-solutions and a family auxiliary functions are constructed as super-solutions.Comment: 30 page

Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension

In the present paper, we investigate the dynamics of a Bose-Einstein condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both analytically and numerically. We focus on the self-trapping state and the effect of the system dimension. Under the tight-binding approximation we obtain an analytical criterion for the self-trapping state of BEC using time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of the BEC cloud is obtained accordingly and verified by directly solving the discrete Gross-Pitaevskii equation (GPE) numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the lattices.Comment: 8pages, 9 figure

KIR2DL2/2DL3-E(35) alleles are functionally stronger than -Q(35) alleles.

KIR2DL2 and KIR2DL3 segregate as alleles of a single locus in the centromeric motif of the killer cell immunoglobulin-like receptor (KIR) gene family. Although KIR2DL2/L3 polymorphism is known to be associated with many human diseases and is an important factor for donor selection in allogeneic hematopoietic stem cell transplantation, the molecular determinant of functional diversity among various alleles is unclear. In this study we found that KIR2DL2/L3 with glutamic acid at position 35 (E(35)) are functionally stronger than those with glutamine at the same position (Q(35)). Cytotoxicity assay showed that NK cells from HLA-C1 positive donors with KIR2DL2/L3-E(35) could kill more target cells lacking their ligands than NK cells with the weaker -Q(35) alleles, indicating better licensing of KIR2DL2/L3(+) NK cells with the stronger alleles. Molecular modeling analysis reveals that the glutamic acid, which is negatively charged, interacts with positively charged histidine located at position 55, thereby stabilizing KIR2DL2/L3 dimer and reducing entropy loss when KIR2DL2/3 binds to HLA-C ligand. The results of this study will be important for future studies of KIR2DL2/L3-associated diseases as well as for donor selection in allogeneic stem cell transplantation

Plasma level of M-CSF was independently related to 30-day survival in patients with suspected sepsis, and correlated to pathogen load: A prospective cohort study.

The purpose of our study was to screen the plasma cytokines to find possible indicators of disease progression and prognosis of patients with infection. With a prospective cohort study, selected patients were divided into sepsis group and non-sepsis group. Demographic and clinical information were collected. Blood samples were tested for the levels of plasma cytokines and metagenomic next-generation sequencing (mNGS). 30-day follow-up information was recorded, and data was analyzed by SPSS22.0 (SPSS Inc, Chicago, IL). A total of 95 patients were selected. After propensity score matching of age and gender, 36 patients with sepsis and 36 with non-sepsis were enrolled. 30-day follow-up data exhibited that 41 patients died and 31 survived. Patients with sepsis and 30-day death had higher plasma levels of cytokines, including macrophage-stimulating factor (M-CSF), monocyte chemoattractant protein-3 (MCP-3), etc., than patients with non-sepsis and 30-day survival, respectively. M-CSF > 8.21pg/ml was an independent risk factor for 30-day death, and the reads of pathogens in mNGS reports was positively correlated with the plasma concentrations of various cytokines, including M-CSF

3-[2-Chloro-4-(trifluoro­meth­yl)phen­oxy]benzoic acid

The asymmetric unit of the title compound, C14H8ClF3O3, comprises two independent mol­ecules. The rings in each molecule are connected together via O—H⋯O hydrogen bonds to form classical hydrogen-bonded carb­oxy­lic acid dimers. The dihedral angles between the benzene rings are 80.7 (1) and 68.7 (1)°

5-Meth­oxy-1,3,4-thia­diazol-2(3H)-one

The three mol­ecules in the asymmetric unit of the title compound, C3H4N2O2S, are connected via N—H⋯O hydrogen bonds, forming layers normal to [001]. The rings of the mol­ecules are approximately planar, with r.m.s. deviations of 0.0051 (1), 0.0044 (1) and 0.0111 (1) Å