Extremal problems for a matching and any other graph

For a family of graphs \F, a graph is called \F-free if it does not contain any member of \F as a subgraph. The generalized Tur\'an number \ex(n,K_r,\F) is the maximum number of $K_r$ in an $n$-vertex \F-free graph and \ex(n,K_2,\F)=\ex(n,\F), i.e., the classical Tur\'an number. Let $M_{s+1}$ be a matching on $s+1$ edges and $F$ be any graph. In this paper, we determine \ex(n,K_r, \{M_{s+1},F\}) apart from a constant additive term and also give a condition when the error constant term can be determined. In particular, we give the exact value of \ex(n,\{M_{s+1},F\}) for $F$ being any non-bipartite graph or some bipartite graphs. Furthermore, we determine \ex(n,K_r,\{M_{s+1},F\}) when $F$ is color critical with $\chi(F)\ge \max\{r+1,4\}$. These extend the results in [2,11,18]

The effect of metabolic syndrome on postoperative complications and long-term survival of patients with colorectal cancer

BackgroundMetabolic syndrome (MetS) is associated with poor prognosis in many cancers. However, the relationship between metabolic syndrome and overall survival (OS) in patients with colorectal cancer (CRC) remains unclear. We aimed to comprehensively analyze whether MetS could affect postoperative complications and long-term survival in patients with CRC.MethodsWe included patients who underwent CRC resection at our center between January 2016 and December 2018. Bias was reduced through propensity score matching analysis. Patients with CRC were divided into the MetS and non-MetS groups based on whether they had MetS. Univariate and multivariate analyses were used to identify risk factors affecting OS.ResultsWe included 268 patients; among them, 120 were included for further analysis after propensity score matching. There were no significant between-group differences in the clinicopathological features after matching. Compared with the non-MetS group, the MetS group had a shorter OS (P = 0.027); however, there was no significant between-group difference in postoperative complications. Multivariate analysis revealed that MetS (hazard ratio [HR] = 1.997, P = 0.042), tumor-node-metastasis stage (HR = 2.422, P = 0.003), and intestinal obstruction (HR = 2.761, P = 0.010) were independent risk factors for OS.ConclusionsMetS affects the long-term survival of patients with CRC without affecting postoperative complications

Efficacy of radiation plus transarterial chemoembolization and lenvatinib in hepatocellular carcinoma with portal vein tumor thrombus

BackgroundWe aimed to investigate the efficacy of a novel regimen, external beam radiation (RT) combined with trans arterial chemoembolization (TACE) and lenvatinib (LEN), in the treatment of hepatocellular carcinoma (HCC) with portal vein tumor thrombus.MethodsWe prospectively observed 102 participants from three tertiary medical centers in China between October 2018 and October 2020, who chose either RT plus TACE and LEN (RT-TACE-LEN) or TACE and LEN (TACE-LEN). LEN (12 mg or 8 mg daily) was administrated orally and continued until progression or intolerable side effects were noted. TACE was given one day after administration of LEN, and RT began within 4 weeks after the first TACE. The median dose/fraction of RT was 50 Gy/25 fractions (range: 45-60 Gy/25 fractions). Overall survival and progression free survival were compared between two groups, and complications were assessed.ResultsBoth 51 patients received RT-TACE-LEN and TACE-LEN, respectively. Most patients had tumor size> 5 cm (73.8%) and tumor number≥ 2 (69.9%). The overall incidence of toxicities was significantly higher in RT-TACE-LEN group than TACE-LEN group (100% vs. 64.7%, p< 0.001), but incidences of grade 3-4 toxicities were comparable (54.9% vs. 49.0%, p= 0.552). Both median overall survival (22.8 vs. 17.1 months, p= 0.031) and median progression-free survival (12.8 vs. 10.5 months, p= 0.035) were significantly longer after RT-TACE-LEN treatment than TACE-LEN.ConclusionsThe addition of RT to TACE and LEN was safe, and might improve clinical outcomes of patients with advanced HCC, which needs conformation from further studies

Surveillance of Schistosoma japonicum Infection in Domestic Ruminants in the Dongting Lake Region, Hunan Province, China

Background: Schistosomiasis japonica is prevalent in Asian countries and it remains a major public health problem in China. The major endemic foci are the marsh and lake regions of southern China, particularly the Dongting Lake region bordering Hunan and Hubei provinces, and the Poyang Lake region in Jiangxi province. Domestic ruminants, especially bovines, have long been considered to play a major role in the transmission of Schistosoma japonicum to humans. Methods and Findings: A miracidial hatching technique was used to investigate the prevalence of S. japonicum infections in domestic ruminants and field feces collected from two towns located to the south and east of Dongting Lake, Hunan province, between 2005 and 2010. The overall prevalence of infection was not significantly reduced from 4.93 % in 2005 to 3.64 % in 2008, after which it was maintained at this level. Bovines comprised 23.5–58.2 % of the total infected ruminants, while goats comprised 41.8–76.5%. Infection rates in cattle and goats were significantly higher than those found in buffalo in most study years. The prevalence in buffalo younger than three years was significantly higher than that in those aged over three years. All the positive field samples of feces were derived from bovines in Nandashan. In Matang Town, 61.22 % of the positive field feces were from bovines, while the rest were from goats. The positive rates for field feces were approximately the same in April and November/October. Conclusions: The present study found that bovines and goats are major sources of S. japonicum infection in the Dongtin

A Comparative Study on Rock Properties in Splitting and Compressive Dynamic Tests

The dynamic properties of rock in splitting (tensile) and compressive tests are the focus of rock dynamic mechanics research. In this study, a split Hopkinson pressure bar (SHPB) apparatus was used to assess the comparability and strain rate effect of rock samples under two kinds of load conditions. With an increase in impact velocity under compression and splitting (tensile) tests, the strain rate of the samples increased continuously. The rock properties and strain rate in the two kinds of samples exhibited clear similarities: the dimensionless stress-strain curves of the rock samples were similar under the same strain rates. The peak strength and elastic modulus of the two kinds of samples increased with an increase in the strain rate. The number of cracks increased from intergranular to transgranular failure. The rack initiation value of the two kinds of samples was close at the same strain rate and declined with an increase in the strain rate as evidenced by a power function

Maximum cliques in a graph without disjoint given subgraph

The generalized Turan number ex(n, Ks, F) denotes the maximum number of copies of Ks in an n -vertex F -free graph. Let kF denote k disjoint copies of F. Gerbner et al. (2019) [8] gave a lower bound for ex(n, K3, 2C5) and obtained the magnitude of ex(n, Ks, kKr). In this paper, we determine the exact value of ex(n, K3, 2C5) and described the unique extremal graph for large n. Moreover, we also determine the exact value of ex(n, Kr, (k + 1)Kr) which generalizes some known results

A Novel Shape Finding Method for the Main Cable of Suspension Bridge Using Nonlinear Finite Element Approach

The determination of the final cable shape under the self-weight of the suspension bridge enables its safe construction and operation. Most existing studies solve the cable shape segment-by-segment in the Lagrangian coordinate system. This paper develops a novel shape finding method for the main cable of suspension bridge using nonlinear finite element approach with Eulerian description. The governing differential equations for a three-dimensional spatial main cable is developed before a one-dimensional linear shape function is introduced to solve the cable shape utilizing the Newton iteration method. The proposed method can be readily reduced to solve the two-dimensional parallel cable shape. Two iteration layers are required for the proposed method. The shape finding process has no need for the information of the cable material or cross section using the present technique. The commonly used segmental catenary method is compared with the present method using three cases study, i.e., a 1666-m-main-span earth-anchored suspension bridge with 2D parallel and 3D spatial main cables as well as a 300-m-main-span self-anchored suspension bridge with 3D spatial main cables. Numerical studies and iteration results show that the proposed shape finding technique is sufficiently accurate and operationally convenient to achieve the target configuration of the main cable