We establish the local well-posedness of the general Ericksen-Leslie system in liquid crystals with the initial velocity and director field in H 1 × H 2 b . In particular, we prove that the solutions of the Ginzburg-Landau approximation system converge smoothly to the solution of the Ericksen-Leslie system for any t ∈ (0, T * ) with a maximal existence time T * of the Ericksen-Leslie system.1991 Mathematics Subject Classification. AMS 35K50, 35Q30.

The Landau-de Gennes energy in nematic liquid crystals depends on four elastic constants L 1 , L 2 , L 3 , L 4 . In the case of L 4 = 0, Ball-Majumdar [2] found an example that the original Landau-de Gennes energy functional in physics does not satisfy a coercivity condition, which causes a problem in mathematics to establish existence of energy minimizers. At first, we introduce a new Landau-de Gennes energy density with L 4 = 0, which satisfies the coercivity condition for all Q-tensors and keeps most physical quantities of the original Landau-de Gennes density. Secondly, we prove that solutions of the Landau-de Gennes system can approach a solution of the Q-tensor Oseen-Frank system without using energy minimizers. Thirdly, we develop a new approach to generalize Nguyen-Zarnescu's converging result in [38] to the case of nonzero elastic constants L 2 , L 3 , L 4 .

Background and objectivesObstructive jaundice is common in patients with pancreaticobiliary malignancies. Preoperative biliary drainage (PBD) can alleviate cholestasis; however, no consensus has been reached on the impact of PBD on the incidence of surgery-related complications and patient survival. This study aimed to evaluate the effect among patients treated with PBD.MethodsThis retrospective study examined the clinical and follow-up prognostic data of 160 patients with pancreaticobiliary malignancies who underwent pancreaticoduodenectomy (PD) at Beijing Friendship Hospital, Capital Medical University, from January 2016 to July 2020. Outcomes were compared between patients who underwent PBD (PBD group) and those who did not (control group). Changes in biochemical indicators were evaluated before and after drainage in the PBD group. Between-group differences in inflammatory indicators after PD were assessed using the Wilcoxon signed-rank test. Postoperative complications were classified according to the Clavien-Dindo classification system. The effects of PBD and biliary drainage efficiency on postoperative complications were evaluated using the chi-square test and binary logistics regression. The Kaplan-Meier analysis was used for between-group comparison of survival analysis. Univariate and multivariate regression analyses were performed to identify prognostic factors of survival.ResultsTotal 160 patients were enrolled,the mean age of the study sample was 62.75 ± 6.75 years. The distribution of pancreaticobiliary malignancies was as follows: 34 cases of pancreatic head cancer, 61 cases of distal bile duct cancer, 20 cases of duodenal papilla cancer, 39 cases of duodenal ampullary cancer, and 6 cases of malignant intraductal papillary mucinous neoplasm (IPMN). PBD was performed in 90 of the 160 patients, with PBD performed using an endoscopic retrograde cholangiopancreatography (ERCP) approach in 55 patients and with percutaneous transhepatic cholangiography (PTC) used in the remaining 35 cases. The mean duration of drainage in the PBD group was 12.8 ± 8.8 days. The overall rate of complications was 48.05% (37/77) in the control group and 65.55% (59/90) in the PBD group with non-significant difference (χ2 = 3.527, p=0.473). In logsitics regression analysis, PBD was also not a risk factor for postoperative complications OR=1.77, p=0.709). The overall rate of postoperative complications was significantly higher among patients who underwent PBD for >2 weeks (χ2 = 6.102, p=0.013), with the rate of severe complications also being higher for this subgroup of PBD patients (χ2 = 4.673, p=0.03). The overall survival time was 47.9 ± 2.45 months, with survival being slightly lower in the PBD group (43.61 ± 3.26 months) than in the control group (52.24 ± 3.54 months), although this difference was not significant (hazard ratio (HR)=0.65, p=0.104).ConclusionIn patients with malignant biliary obstruction, PBD does not affect the incidence of postoperative complications after pancreaticoduodenectomy nor does it affect patient survival. Prolonged biliary drainage (>2 weeks) may increase the incidence of overall postoperative complications and severe complications.

BackgroundThe influence of body composition on the outcome of colorectal cancer surgery is controversial. The aim of this study was to evaluate the effects of visceral obesity and sarcobesity on the incidence of total and surgical complications after radical resection of colorectal cancer.MethodsWe collected a total of 426 patients who underwent elective radical resection of colorectal cancer at Beijing Friendship Hospital, Capital Medical University from January 2017 to May 2018. According to the inclusion and exclusion criteria, 387 patients were finally included. A CT scan at the level of the L3-L4 intervertebral disk was selected to measure the values of visceral fat area and skeletal muscle area. Multivariate analysis was used to explore the independent risk/protective factors affecting postoperative complications.Results128 (33.1%) patients developed complications, and 44 (11.4%) patients developed major complications. Among them, 111 patients developed surgical complications and 21 developed medical complications. Visceral fat area (Z = −3.271, p = 0.001), total fat area (Z = −2.613, p = 0.009), visceral fat area to subcutaneous fat area ratio (V/S, Z = −2.633, p = 0.008), and sarcobesity index (Z = −2.282, p = 0.023) were significantly associated with total complications. Visceral fat area (Z = −2.119, p = 0.034) and V/S (Z = −2.010, p = 0.044) were significantly associated with total surgical complications. Sarcobesity index, smoking, stoma, blood loss, surgery time, and American Society of Anesthesiology (ASA) score were selected as risk factors for total postoperative complications according to LASSO regression. Multivariate logistic regression analysis suggested that sarcobesity index was an independent risk factor for postoperative total complications and surgical complications. Subgroup analysis suggested that albumin level was an independent protective factor for postoperative total complications in male patients. Smoking, operative time, and sarcobesity index were independent risk factors, and cholesterol was an independent protective factor for total postoperative complications in female patients.ConclusionIncreased sarcobesity index is an independent risk factor for postoperative complications in patients with colorectal cancer, while visceral fat area is not. For female patients, smoking, operation time, and obesity index are independent risk factors for postoperative complications, while cholesterol is an independent protective factor. For male patients, serum albumin is an independent protective factor for postoperative complications.