Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

蛋白质-多糖复合体系在活性物质传递中的应用

蛋白质-多糖复合体系作为生物活性物质传递系统的壁材,有着人工合成聚合物或无机物等其他材料不可比拟的多重优势。本文就蛋白质和多糖之间的连接方式及蛋白质-多糖复合体系形成传递系统的多种形式进行了综述,以及对此领域的发展趋势进行了展望。结合蛋白质和多糖的结构特点,二者之间的链接方式分为非共价结合的物理共聚,和共价结合的美拉德偶联、化学交联、酶催化交联等方式,文中分别对各种连接方式的原理和机理,以及其影响因素做了深入阐述。以蛋白质-多糖复合体系为壁材对活性物质的传递形式大体上分成乳化系统、胶束、纳米凝胶、分子复合物以及壳核结构等系统。不同的活性物质的特征和传递需求,可针对性地选择合适结构的蛋白质和多糖种类以及二者的连接方式和传递系统的形式。并且,随着研究的逐步发展和推进,此领域的发展趋势朝着智能化和靶向性的方向进行。目前活性物质的蛋白质-多糖复合体系的传递系统,还依然面临着系统设计、评价和应用等多方面的挑战,这就要求我们在更全面更深入了解认识其对活性物质影响和功效的基础上,安全合理地设计和深入细致地评价活性成分的传递系统。     

Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

A Biosilification Fusion Protein for a ‘Self‐immobilising’ Sarcosine Oxidase Amperometric Enzyme Biosensor

Monomeric sarcosine oxidase (mSOx) fusion with the silaffin peptide, R5, designed previously for easy protein production in low resource areas, was used in a biosilification process to form an enzyme layer electrode biosensor. mSOx is a low activity enzyme (10–20 U/mg) requiring high amounts of enzyme to obtain an amperometric biosensor signal, in the clinically useful range <1 mM sarcosine, especially since the K_m is >10 mM. An amperometric biosensor model was fitted to experimental data to investigate dynamic range. mSOx constructs were designed with 6H (6×histidine) and R5 (silaffin) peptide tags and compared with native mSOx. Glutaraldehyde (GA) cross‐linked proteins retained ～5 % activity for mSOx and mSOx‐6H and only 0.5 % for mSOx‐R5. In contrast R5 catalysed biosilification on (3‐mercaptopropyl) trimethoxysilane (MPTMS) and tetramethyl orthosilicate (TMOS) particles created a ‘self‐immobilisation’ matrix retaining 40 % and 76 % activity respectively. The TMOS matrix produced a thick layer (>500 μm) on a glassy carbon electrode with a mediated current due to sarcosine in the clinical range for sarcosinemia (0–1 mM). The mSOx‐R5 fusion protein was also used to catalyse biosilification in the presence of creatinase and creatininase, entrapping all three enzymes. A mediated GC enzyme linked current was obtained with dynamic range available for creatinine determination of 0.1–2 mM for an enzyme layer ～800 nm.     

Thermally induced solid-state transformation of cimetidine. A multi-spectroscopic/chemometrics determination of the kinetics of the process and structural elucidation of one of the products as a stable N3-enamino tautomer

Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics.     

Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

Autonomous system for data collection: Location and mapping issues in post-disaster environment

Disaster relief requires many resources. Depending on the circumstances of each event, it is important to rapidly choose the suitable means to respond to the emergency intervention. A brief review of the conditions and means demonstrated the usefulness of an autonomous stand-alone machine for these missions. If many techniques and technologies exist, their relevant combination to achieve such a system presents several challenges. This communication tries to outline the possible achievement of an autonomous vehicle under these particular circumstances. This paper focuses on the specific working conditions and welcomes future contributions from robotics and artificial intelligence.In the necessarily limited scope of this article, the authors focus on a particularly critical aspect: location. Indeed, this machine is intended to evolve in heterogeneous and dangerous environment and without any outside contacts that could last up to several days. This blackout, due to the propagation difficulties of electromagnetic waves in the ground, induces an independence of the localisation process and makes the use of any radio navigation support system (GNSS), most of the time, impossible. The knowledge of the position of the system, both for navigation of the autonomous system (Rover) and location of targets (victims buried under debris) must be able to be estimated without contributions from external systems. Inertial classical techniques, odometer, etc., have to be adapted to these conditions during a long period without external support. These techniques also have to take into account that energy optimisation requests the use of low-power processors. Consequently, only poor computing capacity is available on-board.The article starts with a presentation of the context of a post-disaster situation as well as the main missions of Search and Rescue (SaR). It is followed by the analysis of autonomous navigation located in a post-earthquake situation. We will then discuss means to determine the attitude of the autonomous system and its position. The interest of hybridisation with external systems – whenever possible –, will be evaluated with a view to correcting deviations suffered by the system during its mission. Finally, prospects and future work are presented.