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%。     

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.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

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.     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.     

Estimates of densities for Lévy processes with lower intensity of large jumps

We obtain general lower estimates of transition densities of jump Lévy processes. We use them for processes with Lévy measures having bounded support, processes with exponentially decaying Lévy measures for large times and for processes with high intensity of small jumps for small times.     

On analyticity of the ‐Stokes semigroup for some non‐Helmholtz domains

Consider the Stokes equations in a sector‐like C ³ domain . It is shown that the Stokes operator generates an analytic semigroup in for . This includes domains where the ‐Helmholtz decomposition fails to hold. To show our result we interpolate results of the Stokes semigroup in and L ² by constructing a suitable non‐Helmholtz projection to solenoidal spaces.