Solutions of the Equation of a Spinorial Yamabe-type Problem on Manifolds of Bounded Geometry

We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler–Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hijazi inequality for the underlying spin manifold.     

New open modified Newton Cotes type formulae as multilayer symplectic integrators

New modified open Newton Cotes integrators are introduced in this paper. For the new proposed integrators the connection between these new algorithms, differential methods and symplectic integrators is studied. Much research has been done on one step symplectic integrators and several of them have obtained based on symplectic geometry. However, the research on multistep symplectic integrators is very poor. Zhu et al. [1] studied the well known open Newton Cotes differential methods and they presented them as multilayer symplectic integrators. Chiou and Wu [2] studied the development of multistep symplectic integrators based on the open Newton Cotes integration methods. In this paper we introduce a new open modified numerical method of Newton Cotes type and we present it as symplectic multilayer structure. The new obtained symplectic schemes are applied for the solution of Hamilton’s equations of motion which are linear in position and momentum. An important remark is that the Hamiltonian energy of the system remains almost constant as integration proceeds. We have applied also efficiently the new proposed method to a nonlinear orbital problem and an almost periodic orbital problem.     

Open source capillary electrophoresis

Open source paradigm is becoming widely accepted in scientific communities and open source hardware is finding its steady place in chemistry research. In this review article, we provide the reader with the most up‐to‐date information on open source hardware and software resources enabling the construction and utilization of an “open source capillary electrophoresis instrument”. While CE is still underused as a separation technique, it offers unique flexibility, low‐cost, and high efficiency and is particularly suitable for open source instrumental development. We overview the major parts of CE instruments, such as high voltage power supplies, detectors, data acquisition systems, and CE software resources with emphasis on availability of the open source information on the web and in the scientific literature. This review is the first of its kind, revealing accessible blueprints of most parts from which a fully functional open source CE system can be built. By collecting the extensive information on open source capillary electrophoresis in this review article, the authors aim at facilitating the dissemination of knowledge on CE within and outside the scientific community, fosters innovation and inspire other researchers to improve the shared CE blueprints.     

Using open‐tubular capillary electrochromatography with part‐coating column for binding constants determination of β2‐adrenergic receptor with seven drugs

An open‐tubular capillary electrochromatography method has been developed for the determination of binding constants between β₂‐adrenergic receptor (β₂‐AR) and seven drugs. β₂‐AR was oriented immobilized onto one part of inner surface of capillary via microwave‐assisted technical synthesis. According to the linear relationship between coating length and the apparent mobility of analyte, the binding constant (K_b) can be obtained by related theories and equations. The order of K_b values between drugs such as adrenaline hydrochloride, norepinephrine bitartrate, and propranolol hydrochloride with β₂‐AR is well consistent with that reported in the literature. By the method, K_b values between four extracts of Radix Paeoniae Rubra and β₂‐AR were also successfully obtained. Subsequently, computer models were applied to interpret the CEC experiments. And the results proved to be in good agreement with the method. The work, herein, demonstrates the potential of the method in drug‐receptor affinity interactions evaluation and screening of lead compounds from natural sources.     

Open Resonator System for Automatic and Precise Dielectric Measurement at Millimeter Wavelengths

As low loss dielectric materials, ZnS, MgF₂, MgAl₂O₄ and quartz ceramic have a very important application at millimeter frequencies. However, there is little information about their dielectric properties in the millimeter wavelength band. To obtain their dielectric properties, an automatic open resonator measurement system at Ka-band is designed and constructed. The importance on the precision determination of cavity length over a broad band and the checking of a measurement system are emphasized and their solutions are put forward in this paper for the first time so far as we know. The solutions of above problems ensure the credibility and high accuracy of our measurement system. The certified measurement system after a series of checking is used to measure the above materials. Lots of measurement results show that the standard deviation of measurement error is less than 0.154% in permittivity and 20.42% in loss tangent. Meanwhile, some experimental summaries on the open resonator technique are provided. Software that controls the measurement system is developed and it improves the testing efficiency greatly.     

MRI methodological development of intervertebral disc degeneration: a rabbit in vivo study at 9.4 T

Intervertebral disc (IVD) degeneration is a complex process characterized by biochemical and structural changes in both the nucleus pulposus and the anulus fibrosus. In this study, we were able to obtain in vivo magnetic resonance (MR) images of the rabbit spine, with several MR imaging (MRI) contrasts (ρ, T₁ and T₂). We quantified several parameters (T₂, apparent diffusion coefficient, disc height and area) to differentiate between healthy and degenerative IVDs and to characterize the degeneration process. To our knowledge, there has not been any previous in vivo study of rabbit IVDs at high-field MRI (9.4 T).A custom radio frequency (RF) coil for 9.4 T was designed to match rabbit IVD morphology, to study the degeneration in vivo on a model of human lumbar disease. Our new probe, a custom half-birdcage-type coil, obtains the necessary exploration depth while meeting the requirements for signal homogeneity and sensitivity of the study. This design addresses some of the difficulties with constructing RF coils at high field strengths.     

带开口磁环的周期永磁聚焦系统的2维模拟

 由于目前常用的磁聚焦系统设计方法不能直接计算带有非轴对称开口磁环的磁系统,因此在行波管磁系统实验测试基础上,提出了双面带极靴的开口磁环体积等效概念：将开口磁环等效为相等体积磁性材料的2维轴对称磁环,两者都双面带极靴时轴上的磁场值相等。使用2维电磁计算软件FEMM计算了采用该等效模型后的周期磁聚焦系统的轴上磁场值,计算结果与带有开口磁环的实际系统测试值符合良好,两者相差仅3×10^-3 T。该2维等效模型能代替开口磁环进行计算。     

Relaxation dynamics in a stochastic bosonic Josephson junction

We consider a bosonic Josephson junction in the Bose-Hubbard two-mode approximation where some of the parameters are corrupted by physically meaningful noise processes and study the corresponding relaxation dynamics towards its equilibrium state. We show with numerical simulations that this model can essentially capture all the important features observed in a recent experiment regarding the relaxation dynamics in one-dimensional bosonic Josephson junctions, namely the damped oscillations of the population imbalance and the relative phase, as well as the large final coherence factor. We expect that this work will further motivate research about the origin of relaxation mechanism in these systems.     

Low-cost automated capillary electrophoresis instrument assembled from commercially available parts

A CE instrument that can be assembled from commercially available components with minimal construction effort is described. Except for the electronic control circuitry no specially made parts are required. It is based on a flexible design of microfluidic, electropneumatic, and electronic sections and different configurations can easily be implemented. Automated injection into the capillary is performed hydrodynamically by the application of a pressure for a controlled length of time. The performance of the device was tested with a contactless conductivity detector by separating different metal ions. In addition, nine metal cations related to the quality of honey were separated in 2.3 min and four honey samples were analysed quantitatively to demonstrate the applicability of the method.