一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

牛磺酸通过调控AKT/GSK-3β通路抑制结直肠癌细胞侵袭转移

观察糖原合酶激酶-3β(GSK-3β)在牛磺酸(Tau)抑制结直肠癌(CRC)侵袭转移中的作用,探讨Tau抑制结直肠癌侵袭转移分子机制。选用人结直肠癌SW480和HT29细胞为研究对象,用浓度为40～200 mmoL Tau处理细胞;Transwell小室和细胞划痕愈合实验检测细胞侵袭、迁移能力,Western blot检测细胞EMT标志性蛋白(E-cadherin, N-cadherin, Vimentin),基质金属蛋白酶2/7(MMP2/7)和AKT/GSK-3β通路相关蛋白水平。与正常对照组比较,Tau可浓度依赖性抑制CRC细胞侵袭和迁移,上调CRC上皮标志物E-cadherin表达,下调EMT间质标志物N-cadherin, Vimentin和MMPs表达;降低AKT和p-AKT水平,提高PTEN,GSK-3β及p-GSK-3β表达水平(P<0.05)。与p-EGFP-GSK-3β或Tau组比较,p-EGFP-GSK-3β+Tau组细胞迁移和侵袭数量有显著性降低(P<0.01);与Tau组或p-EGFP-GSK-3β组比较,p-EGFP-GSK-3β+Tau组E-Cadherin、GSK-3β蛋白表达有显著升高(P<0.01),而N-Cadherin, Vimentin,β-Catenin, MMP2/7和AKT蛋白表达均有显著降低(P<0.01)。牛磺酸可通过调控AKT/GSK-3β通路抑制结直肠癌细胞侵袭转移。     

广义Fermat型微分与微差分方程整函数解的存在性与形式

利用Nevanlinna值分布理论,主要讨论了几类广义Fermat型微分与微差分方程有限级超越整函数解,得到了二阶微分、微差分方程整函数解的存在性条件以及解的具体形式,所获定理推广了之前的结果,并举例说明了结果的精确性。     

Insights into the efficient charge separation over Nb2O5/2D-C3N4 heterostructure for exceptional visible-light driven H2 evolution

Two-dimensional carbon nitride(2 D-C₃ N₄)nanosheets are promising materials in photocatalytic water splitting,but still suffer from easy agglomeration and fast photogene rated electron-hole pairs recombination.To tackle this issue,herein,a hierarchical Nb₂ O₅/2 D-C₃ N₄ heterostructure is precisely constructed and the built-in electric field between Nb₂O₅ and 2 D-C₃ N₄ can provide the driving force to separate/transfer the charge carriers efficiently.Moreover,the strongly Lewis acidic Nb₂O₅ can adsorb TEOA molecules on its surface at locally high concentrations to facilitate the oxidation reaction kinetics under irradiation,resulting in efficient photogene rated electrons-holes separation and exceptional photocatalytic hydrogen evolution.As expected,the champion Nb₂O₅/2 D-C₃N₄ heterostructure achieves an exceptional H2 evolution rate of 31.6 mmol g^-1 h^-1,which is 213.6 times and 4.3 times higher than that of pristine Nb₂O₅ and2 D-C₃N₄,respectively.Moreover,the champion heterostructure possesses a high apparent quantum efficiency(AQE)of 45.08%atλ=405 nm and superior cycling stability.Furthermore,a possible photocatalytic mechanism of the energy band alignment at the hetero-interface is proposed based on the systematical characterizations accompanied by density functional theory(DFT)calculations.This work paves the way for the precise construction of a high-quality heterostructured photocatalyst with efficient charge separation to boost hydrogen production.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

基于抛光基材的热蒸镀铜箔生长高平整单层石墨烯薄膜

在石墨烯的化学气相沉积工艺中,铜箔是决定石墨烯薄膜质量的重要因素。传统铜箔由于制备工艺的限制,存在大量的缺陷,导致石墨烯薄膜的成核密度较高。本工作选用抛光铝板、抛光不锈钢板、微晶玻璃和SiO₂/Si作为基材,用热蒸镀法制备了不同粗糙度的铜箔,并详细讨论了以该系列铜箔生长高平整度石墨烯薄膜的条件及铜箔对石墨烯薄膜品质的影响。实验结果表明,铜箔以(111)取向为主,与基材分离后,表面具有纳米级平整度。在生长石墨烯后,从SiO₂/Si剥离的铜箔成核密度是4种基材中最小的。同时,从SiO₂/Si剥离的铜箔晶体结构变化最不明显,具有良好的结晶性,表面几乎不存在铜晶界缺陷。当压强为3 000 Pa,氢气和甲烷流速分别为300 mL/min和0.5 mL/min时,可以获得约1 mm横向尺寸的石墨烯单晶晶畴。     

水热法制备二氧化锡/钨酸铋复合光催化材料及其催化活性研究

本文用水热法制备了正交晶系的纳米球状结构的二氧化锡和正交晶系的由片状聚集成球状结构的钨酸铋,并且对二者进行了复合,制备出了二氧化锡/钨酸铋复合光催化材料。采用X射线衍射(XRD)、扫描电子显微镜(SEM)、比表面积测试仪(BET)、紫外可见分光光度计等技术对复合样品的结构、形貌、比表面积、孔容孔径和光学性质进行了表征。用碘钨灯模拟太阳光,分别以二氧化锡、钨酸铋和二氧化锡/钨酸铋复合材料为催化剂降解罗丹明B(RhB),研究所制备的二氧化锡/钨酸铋复合材料的光催化活性。光催化90 min时二氧化锡、钨酸铋和二氧化锡/钨酸铋对罗丹明B的降解率分别是9%、22%和30%。实验结果表明,在可见光下,二氧化锡/钨酸铋复合材料的光催化活性要高于单一的二氧化锡和钨酸铋。     

初中数学不同课型阅读教学的实践探究

数学学习有别于其他学科的学习,使得数学阅读也有其独特性,它需要阅读者有较强的数学思维能力,在数学阅读过程中,学生不仅要知道数学概念、规则等的自然语言,也要知道它的数学语言所表达的含义,还要理清它的结构、数学思想、积累的经验.     

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.