On a class of projectively flat Finsler metrics

In this paper, we study a class of Finsler metrics composed by a Riemann metric $\alpha=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $\beta=b_i(x)y^i$ called general ($\alpha$, $\beta$)-metrics. We classify those projectively flat when $\alpha$ is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totally determined. Then a new group of projectively flat Finsler metrics is found

Large deviation principle for fractional Brownian motion with respect to capacity

We show that fractional Brownian motion(fBM) defined via Volterra integral representation with Hurst parameter $H\geq\frac{1}{2}$ is a quasi-surely defined Wiener functional on classical Wiener space,and we establish the large deviation principle(LDP) for such fBM with respect to $(p,r)$-capacity on classical Wiener space in Malliavin's sense

The contact mechanics and occurrence of edge loading in modular metal-on-polyethylene total hip replacement during daily activities

The occurrence of edge loading in hip joint replacement has been associated with many factors such as prosthetic design, component malposition and activities of daily living. The present study aimed to quantify the occurrence of edge loading/contact at the articulating surface and to evaluate the effect of cup angles and edge loading on the contact mechanics of a modular metal-on-polyethylene (MoP) total hip replacement (THR) during different daily activities. A three-dimensional finite element model was developed based on a modular MoP bearing system. Different cup inclination and anteversion angles were modelled and six daily activities were considered. The results showed that edge loading was predicted during normal walking, ascending and descending stairs activities under steep cup inclination conditions (≥55°) while no edge loading was observed during standing up, sitting down and knee bending activities. The duration of edge loading increased with increased cup inclination angles and was affected by the cup anteversion angles. Edge loading caused elevated contact pressure at the articulating surface and substantially increased equivalent plastic strain of the polyethylene liner. The present study suggested that correct positioning the component to avoid edge loading that may occur during daily activities is important for MoP THR in clinical practice

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results

Unraveling the role of ectopic thymic tissue in patients undergoing thymectomy for myasthenia gravis

Extended thymectomy has been considered the goal of surgery for myasthenia gravis (MG) mainly due to the existence of ectopic thymic tissue. Recently, ectopic thymic tissue has attracted increasing attention in patients with MG following thymectomy. However, the specific role of ectopic thymic tissue in patients with MG is still under debate. A systematic search of the literature was performed on PubMed and Medline according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISM) statement. Studies evaluating the rate of ectopic thymic tissue in patients with MG with or without thymoma were included. Extraction was performed for all eligible studies and the rate of ectopic thymic tissue at common locations was calculated. Eighteen out of fifty-nine studies were eligible for inclusion, of which ten studies reported the common locations of ectopic thymic tissue in mediastinal fat. Of these ten studies, the presence of ectopic thymic tissue was investigated in different anatomical locations in 882 patients, of whom, 509 patients (58%) have at least one positive location with the most common ones being anterior mediastinal fat, pericardiophrenic angles, aortopulmonary window, cervical region (pretracheal fat) and lateral to phrenic nerves. On the other hand, nine studies analyzed the influence of the presence of ectopic thymic tissue on the clinical outcomes of MG patients. Of these, six found that the presence of ectopic thymic tissue in MG patients is a significant predictor of poor outcome after thymectomy, however, the other three did not find a significance. Altogether, ectopic thymic tissue is likely to present in more than a half of patients undergoing thymectomy for MG. Besides, MG patients who have ectopic thymic tissue after thymectomy do not seem to have as good outcome as those who have not