广义神经传播方程的整体吸引子

使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.     

基于有序介孔碳的氯离子选择性电极的制备及其在手持传感系统中的应用

以有序介孔碳(OMC)球为离子-电子转换层,制备了固态氯离子选择性电极,构建了基于离子敏感的场效应晶体管(ISFET)的手持式传感系统,用于检测人体血清中的氯离子。优化了OMC前驱体的碳化温度,探究了OMC形貌结构对电极传感性能的影响;电极柔性化制备后考察了其在手持系统中对氯离子的检测效果。结果表明,最优条件下,电极在5.12×10^-4~1.02 mol/L的浓度范围呈现线性响应,响应斜率为60 mV/decade。该柔性电极在手持传感系统中展现出高灵敏度和重现性,可用于人体血清样品中氯离子的检测,其回收率为96.3%~104.9%。     

Highly edge-connected factors using given lists on degrees

Let G be a 2k-edge-connected graph with and let for every . A spanning subgraph F of G is called an L-factor, if for every . In this article, we show that if for every , then G has a k-edge-connected L-factor. We also show that if and for every , then G has a k-edge-connected L-factor.     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

An Introduction to Influence Theory: Kinematics and Dynamics

Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their empirically determined relationships, from a more primitive model. It is postulated that there exist things, which are call particles, that influence one another in a discrete and directed fashion resulting in a partially ordered set of influence events. The problem of consistent quantification of the influence events is considered. Observers are modeled as particle chains (observer chains) as if an observer were able to track a particle and quantify the influence events that the particle experiences. From these quantified influence events, consistent quantification of the universe of events based on the observer chains is studied. Herein, the kinematics and dynamics of particles from the perspective of influence theory are both reviewed and further developed.     

Synthesis of nano‐sized magnetite mesoporous carbon for removal of Reactive Yellow dye from aqueous solutions

In this study, core‐shell structures of magnetite nanoparticles coated with CMK‐8 ordered mesoporous carbon (Fe₃O₄@SiO₂‐CMK‐8 NPs) have been successfully synthesized for the first time by carbonizing sucrose inside the pores of the Kit‐6 mesoporous silica. The nano‐sized mesoporous particles were characterized by X‐ray diffraction, Fourier transform‐infrared spectroscopy, scanning electron microscope, dynamic light scattering, vibrating‐sample magnetometer, Brunauer–Emmett–Teller (BET) and transmission electron microscopy instruments. The obtained nanocomposite was used for removal of Reactive Yellow 160 (RY 160) dye from aqueous samples. The N₂ adsorption–desorption method (at 77 K) confirmed the mesoporous structure of synthesized Fe₃O₄@SiO₂‐CMK‐8 NPs. Also, the surface area was calculated by the BET method and Langmuir plot as 276.84 m²/g and 352.32 m²/g, respectively. The surface area, volume and pore diameter of synthesized nanoparticles (NPs) were calculated from the pore size distribution curves using the Barrett–Joyner–Halenda formula (BJH). To obtain the optimum experimental variables, the effect of various experimental parameters on the dye removal efficiency was studied using Taguchi orthogonal array experimental design method. According to the experimental results, about 90.0% of RY 160 was removed from aqueous solutions at the adsorbent amount of 0.06 g, pH 3 and ionic strength = 0.05 m during 10 min. The pseudo‐second order kinetic model provided a very good fit for the RY 160 dye removal (R² = 0.999). The Langmuir, Freundlich, Temkin and Dubinin–Radushkevich models were applied to describe the equilibrium isotherms, and the Langmuir isotherm showed the best fit to data with the maximum adsorption capacity of 62.893 mg/g. Furthermore, the Fe₃O₄@SiO₂‐CMK‐8 NPs could be simply recovered by external magnet, and exhibited recyclability and reusability for a subsequent six runs.     

Highly edge-connected regular graphs without large factorizable subgraphs

We construct highly edge-connected $r$-regular graphs of even order which do not contain $r?2$ pairwise disjoint perfect matchings. When $r$ is a multiple of 4, the result solves a problem of Thomassen [4].     

Injective and automorphism-invariant non-singular modules

Every automorphism-invariant non-singular right A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring.     

三维位势问题的梯度边界积分方程的新解法

三维位势问题的边界元分析中,关于坐标变量的边界位势梯度的计算是一个困难的问题. 已有一些方法着手解决这个问题,然而,这些方法需要复杂的理论推导和大量的数值计算. 本文提出求解一般边界位势梯度边界积分方程的辅助边值问题法. 该方法构造了与原边界值问题具有相同解域的辅助边值问题,该辅助边值问题具有已知解,因此通过求解此辅助边值问题,可获得梯度边界积分方程对应的系统矩阵,然后将此系统矩阵应用于求解原边值问题,求解过程非常简单,只需求解一个线性系统即可获得原边值问题的解. 值得注意的是,在求解原边值问题时,不再需要重新计算系统矩阵,因此辅助边值问题法的效率并不很差. 辅助边值问题法避免了强奇异积分的计算,具有数学理论简单、程序设计容易、计算精度高等优点,为坐标变量梯度边界积分方程的求解提供了一个新的途径. 3个标准的数值算例验证了方法的有效性.