Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

In this study, Brillouin optical time-domain analysis (BOTDA) sensing technology was utilized for monitoring settlement in a similarity model of a highway subgrade. As contact winding cannot be used for an optical fiber that is buried directly in soil, uncoupling between. the fiber and the soil can occur. Thus, an optical-fiber-embedded beam (OFEB) was developed, and a method for measuring and calculating the beam deformation was proposed. A calibration test and a test on a similarity model of a subgrade were carried out to investigate the applicability and monitoring accuracy of the OFEB. It was concluded that the OFEB can accurately measure beam deflection, where the maximum relative error between measurements by the optical fiber and a displacement transducer was approximately 5%. The OFEB was embedded directly into a similarity model of a subgrade to monitor settlement. The deflection deformation of the OFEB was found to be close to the subgrade settlement over a certain settlement range with a relative error below 8.1%. Thus, the OFEB can be used to realize measure large-range distributed settlement in a subgrade. A numerical simulation was performed to identify appropriate beam dimensions and material design parameters, thereby extending the measurement range before decoupling of the OFEB and soil occurs. The enhancement of the measurement range and accuracy of the OFEB based on the preliminary experiments carried out in this study enables further investigation of settlement monitoring.

Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China¹. There are more than one hundred cases outside of China, affecting a dozen of countries globally². The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed³. Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days ^4,5. However, major factors such as transportation and cultural customs have not been weighed enough. Our model is not set out for precise prediction of the number of infected cases, rather, it is meant for a glance of the dynamics under a public epidemic emergency situation and of different contributing factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

The supramolecular based macrocyclic amphiphiles have attracted great attention in the field of drug delivery due to their unique self-assembling nature. Therefore, these macrocycles are used as nanocarriers for the delivery of poor water soluble drugs, and also for those which have lower permeability, and cannot cross the barrier to reach the desired site. Herein, we design and synthesized a new supramolecular amphiphilic macrocycle to overcome these problems. The macrocycle was synthesized in two steps. In first step 4-hydroxybenzaldehyde was treated with 1-bromotetradecane to obtain a derivatized product which was then treated with resorcinol to cyclize and get calix(4)resorcinarene based supramolecular amphiphilic macrocycle. The synthesized macrocycle and intermediate products were characterized by Mass spectrometry, IR and 1H-NMR spectroscopic techniques. The amphiphile was screened for biocompatibility studies, vesicles formation, and then Amphotericin-B was loaded in the supramolecular amphiphile based vesicles and was characterized for shape, size, homogeneity, surface charge, drug entrapment, in-vitro release profile and stability through atomic force microscopy (AFM), Zetasizer, HPLC and FT-IR. Amp-B loaded macrocycle based vesicles were investigated for in-vivo bioavailability in rabbits. The synthesized macrocycle was nontoxic in cancer cells, hemo-compatible and safe in mice. The drug-loaded macrocycle based vesicles appeared spherical, nano-ranged, and homogeneous in size with negative surface charge and were able to load an increased amount of drug. The vesicles are stable upon storage and when incubated with gastric simulated fluid. Amp-B increased oral bioavailability was achieved when delivered in synthesized macrocycle based vesicles. These results point out that the synthesized supramolecular amphiphile is an efficient nanocarrier to enhance the oral bioavailability of lipophilic drugs