A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment

Applications of Mathematics - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated...     

金属衬底在石墨烯化学气相沉积生长中的作用

以过渡金属为催化衬底的化学气相沉积法(Chemical Vapor Deposition，CVD)已经可以制备与机械剥离样品相媲美的石墨烯，是实现石墨烯工业应用的关键技术之一。原子尺度理论研究能够帮助我们深刻理解石墨烯生长机理，为实验现象提供合理的解释，并有可能成为将来实验设计的理论指导。本文从理论计算的角度，总结了各种金属衬底在石墨烯CVD生长过程中的各种作用与相应的机理，包括在催化碳源裂解、降低石墨烯成核密度等，催化加快石墨烯快速生长，修复石墨烯生长过程中产生的缺陷，控制外延生长石墨烯的晶格取向，以及在降温过程中石墨烯褶皱与金属表面台阶束的形成过程等。在本文最后，我们对当前石墨烯生长领域中亟需解决的理论问题进行了深入探讨与展望。     

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

On the $$\bar\partial$$ -problem and dressing method for the complex vector modified KdV equation

Theoretical and Mathematical Physics - Starting from a $$5\times 5$$ local matrix $$\bar\partial$$ -problem, we successfully use the $$\bar\partial$$ -dressing method to derive a hierarchy of...     

On Minimal Asymptotic Bases

Mathematical Notes - Let $$\mathbb N$$ denote the set of all nonnegative integers, and let $$A\subseteq\mathbb N$$ . Let $$h,n\in\mathbb N$$ , $$h\ge 2$$ and $$r_h(A,n)=\#\{(a_1,\dots,a_h)\in...     

LWE from non-commutative group rings

Designs, Codes and Cryptography - The Learning-With-Errors (LWE) problem (and its variants including Ring-LWE and Module-LWE), whose security are based on hard ideal lattice problems, has proven to...     

基于摩擦磨损的KDP晶体固结磨料抛光垫优化

本文通过固结磨料球与KDP晶体对磨的单因素试验探究固结磨料球中反应物种类、磨粒浓度、反应物浓度、基体硬度对摩擦系数、磨痕截面积和磨痕处粗糙度的影响,试验结果表明:KHCO₃固结磨料球对磨后磨痕对称性好,磨痕处的粗糙度值低;磨痕截面积随磨粒和反应物浓度的增加而增大,随基体硬度的增大而降低;磨痕处粗糙度随磨粒和反应物浓度的增加先降低后上升,随基体硬度的增大先上升后降低;摩擦系数受磨粒和反应物浓度影响不明显,随基体硬度的增大而降低。选择KHCO₃作为反应物,Ⅰ基体,磨粒浓度为基体质量的100%,反应物浓度为15%制备固结磨料球与KDP晶体对磨后的磨痕轮廓对称度好且磨痕处粗糙度值低,以该组分制备固结磨料垫干式抛光KDP晶体,可实现晶体表面粗糙度Sa值为18.50 nm,材料去除率为130 nm/min的高效精密加工。     

Polymer complexes. LXXVI. Synthesis,characterization, CT‐DNA binding,molecular docking and thermal studies of sulfoxine polymer complexes

Novel polymer complexes of 8‐hydroxyquinoline‐5‐sulfonic acid hydrate ( H ₂ L ) with Cu²⁺, Co²⁺ and Ni²⁺ chloride were prepared and characterized. Microanalysis, magnetic susceptibility, IR spectra, electron spin resonance, mass spectra, X‐ray, molar conductance, thermal, and UV–Vis spectra studies have been used to confirm the structure of the prepared polymer complexes. The molecular and electronic structures of the hydrogen bond conformers for ligand ( H ₂ L ) were optimized theoretically and the quantum chemical parameters were calculated. On the basis of elemental and IR data, the chemical structure of metal chelates commensurate that the tri‐dentate (H₂L) coordinate to metal chlorides through oxygen atom of phenolic OH and oxygen atom of SO₃‐H group by replacing H atoms and nitrogen of the quinoline ring. The magnetic studies suggested the octahedral geometrical structure for all produced polymer complexes with general formula {[ML (OH₂)₃] .xH₂O}_n (M = Cu²⁺, x = 1.; Co²⁺, x = 2 and Ni²⁺, x = 2) in molar ratio (1:1). Coats–Redfern and Horowitz–Metzger methods have been used for calculating the activation thermodynamic parameters of the thermal decomposition for H ₂ L and its polymer complexes. The interaction between H ₂ L and its transition metal complexes with the calf thymus DNA (CT‐DNA) was determined by UV–Vis spectra. Binding efficiency between H ₂ L with the receptors of the prostate cancer (PDB code 2Q7L Hormone) and the breast cancer (PDB code 1JNX Gene regulation) was studied by molecular docking. The inhibition behaviour of H ₂ L against the corrosion of carbon steel / HCl (2 M) solution was studied by weight loss, Tafel polarisation, electrochemical impedance spectroscopy (EIS) and electrochemical frequency modulation (EFM) techniques. The adsorption isotherm was found to be Friendlish isotherm. The morphology of inhibited carbon steel? s surface was studied using scanning electron microscope (SEM) and energy dispersive X‐ray spectroscopy (EDS).     

Cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction and HPLC–DAD analysis of ezetimibe and simvastatin in human plasma and urine

A new cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction (CA–HF–SLPME) followed by high‐performance liquid chromatography–diode array detection (HPLC–DAD) method was developed for simultaneous determination of ezetimibe and simvastatin in human plasma and urine samples. To prepare the CA–HF–SLPME device, the cetyl‐alcohol was immobilized into the pores of a 2.5 cm hollow fiber micro‐tube and the lumen of the micro‐tube was filled with 1‐octanol with the two ends sealed. Afterwards, the prepared device was introduced into 10 mL of the sample solution containing the analytes with agitation. Under optimized conditions, calibration curves plotted in spiked plasma and urine samples were linear in the ranges of 0.363–25/0.49–25 μg L^?1 for ezetimibe/simvastatin and 0.193–25/0.312–25 μg L^?1 for ezetimibe/simvastatin in plasma and urine samples, respectively. The limit of detection was 0.109/0.174 μg L^?1 for ezetimibe/simvastatin in plasma and 0.058/0.093 μg L^?1 for ezetimibe/simvastatin in urine. As a potential application, the proposed method was applied to determine the concentration of selected analytes in patient plasma and urine samples after medication and satisfactory results were achieved. In comparison with reference methods, the CA–HF–SLPME–HPLC–DAD method demonstrates considerable potential in the biopharmaceutical analysis of selected drugs.