Study of weak solutions for parabolic equations with nonstandard growth conditions

AbstractThe authors of this paper study the existence and uniqueness of weak solutions of the initial and boundary value problem for ut=div((uσ+d0)|∇u|p(x,t)−2∇u)+f(x,t). Localization property of weak solutions is also discussed

Mass transfer and boson cloud depletion in a binary black hole system

Ultralight boson is one of the potential candidates for dark matter. If exists, it can be generated by a rapidly rotating black hole via superradiance, extracting the energy and angular momentum of the black hole and forming a boson cloud. The boson cloud can be affected by the presence of a companion star, generating fruitful dynamical effects and producing characteristic gravitational wave signals. We study the dynamics of the boson cloud in a binary black hole system, in particular, we develop a framework to study the mass transfer between two black holes. It is found that bosons occupying the growing modes of the central black hole can jump to the decaying modes of the companion black hole, resulting in cloud depletion. This mechanism of cloud depletion is different from that induced by the resonant perturbation from the companion

Blood preoperative neutrophil-to-lymphocyte ratio is correlated with TNM stage in patients with papillary thyroid cancer

OBJECTIVE: To predict the American Joint Cancer Committee tumor-node-metastasis stage in patients with papillary thyroid carcinoma by evaluating the relationship between the preoperative neutrophil-to-lymphocyte ratio and the tumor-node-metastasis stage. METHODS: We retrospectively examined 161 patients with a diagnosis of papillary thyroid carcinoma. The Neutrophil-to-Lymphocyte Ratio was calculated according to the absolute neutrophil counts and absolute lymphocyte counts on routine blood tests obtained prior to surgery and patients with a Neutrophil-to-Lymphocyte Ratio of 2.0 or more were classified as the high NLR group, while those with a Neutrophil-to-Lymphocyte Ratio less than 2.0 were classified as the low Neutrophil-to-Lymphocyte Ratio group. Clinicopathological variables, which were stratified by the Neutrophil-to-Lymphocyte Ratio, were analyzed. A multivariate analysis was performed to determine factors that affect the Neutrophil-to-Lymphocyte Ratio. The association between the Neutrophil-to-Lymphocyte Ratio and the TNM stage in patients ≥45 years of age was analyzed using the Spearman rank correlation. RESULTS: Various blood indices, including hemoglobin, platelet and thyroid-stimulating hormone levels in the two groups showed no significant differences. Lymph node metastasis, multifocality and tumor size exhibited significant differences in the two groups (p=0.000, p=0.000 and p=0.035, respectively). Correlation analysis indicated that a higher preoperative Neutrophil-to-Lymphocyte Ratio was observed in patients with lymph node metastasis, larger tumor size and multifocality (r=0.341, p=0.000; r=0.271, p=0.000; and r=0.182, p=0.010, respectively). For patients ≥45 years of age, the number of patients with an advanced TNM stage in the high NLR group was higher than that in the low Neutrophil-to-Lymphocyte Ratio group (p=0.013). A linear regression analysis showed that the preoperative Neutrophil-to-Lymphocyte Ratio was positively correlated with the American Joint Cancer Committee tumor-node-metastasis stage (rho=0.403, p=0.000). CONCLUSION: The preoperative Neutrophil-to-Lymphocyte Ratio was closely related to the stage of papillary thyroid carcinoma. The increase in the preoperative Neutrophil-to-Lymphocyte Ratio contributed to the advanced tumor-node-metastasis stage of papillary thyroid carcinoma patients ≥45 years of age