Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

高效液相色谱手性固定相法拆分BETTI碱及其衍生物对映体

在纤维素三（3,5-二甲基苯基氨基甲酸酯）（Chiralcel OD-H）和Pirkle型(R, R)-Whelk-O1手性柱上对手性氨基酚1-(α-氨基苄基)-2-萘酚（Betti 碱）及其衍生物1-(α-苄氨基苄基)-2-萘酚和1-(α-哌啶基苄基)-2-萘酚对映体分离进行了研究，分别考察了在正己烷流动相中，碱性添加剂、醇类添加剂的种类和浓度对手性拆分的影响。结果表明：溶质在Chiralcel OD-H柱上的分离效果好，而在(R, R)-Whelk-O1手性柱上只有1-(α-苄氨基苄基)-2-萘酚部分分离。研究了空间立体结构因素对手性分离的影响，初步探讨和比较了溶质在这2种手性柱上的手性识别机理。发现对(R, R)-Whelk-O1柱，溶质与固定相之间的吸引作用很小，而对于Chiralcel OD-H柱，溶质在手性空腔中的空间适应性很可能是手性识别的关键。     

Ultra-broadband piezoelectric energy harvesting via bistable multi-hardening and multi-softening

Nonlinear Dynamics - An electromechanical coupled distributed parameter model is derived for a broadband piezoelectric energy harvester with nonlinear magnetic interaction and...     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

Heterointerface Engineering of ZnO/CdS Heterostructures through ZnS Layers for Photocatalytic Water Splitting

Solar-driven water splitting to produce clean and renewable hydrogen offers a green strategy to address the energy crisis and environmental pollution. Heterostructure catalysts are receiving increasing attention for photocatalytic hydrogen generation. ZnO/ZnS/CdS and ZnO/CdS heterostructures have been successfully designed and prepared according to two different strategies. By introducing a heterointerface layer of ZnS between ZnO and CdS, a Z scheme charge-transfer channel was promoted and achieved superior photocatalytic performance. A highest hydrogen generation rate of 156.7 μmol g⁻¹ h⁻¹ was achieved by precise control of the thickness of the heterointerface layer and of the CdS shell. These findings demonstrated that heterostructures are promising catalysts for solar-driven water splitting, and that heterointerface engineering is an effective way to improve the photocatalytic properties of heterostructures.     

Inverse spectral problems for non-self-adjoint Sturm–Liouville operators with discontinuous boundary conditions

This paper deals with the inverse spectral problem for a non-self-adjoint Sturm–Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential q is known a priori on a subinterval $$ \left[ b,\pi \right] $$ with $$b\in \left( d,\pi \right] $$ or $$b=d$$, then $$h,\,\beta ,\,\gamma $$ and q on $$\left[ 0,\pi \right] $$ can be uniquely determined by partial spectral data consisting of a sequence of eigenvalues and a subsequence of the corresponding generalized normalizing constants or a subsequence of the pairs of eigenvalues and the corresponding generalized ratios. For the case $$b\in \left( 0,d\right) $$, a similar statement holds if $$\beta ,\,\gamma $$ are also known a priori. Moreover, if q satisfies a local smoothness condition, we provide an alternative approach instead of using the high-energy asymptotic expansion of the Weyl m-function to solve the problem of missing eigenvalues and norming constants.     

Amides and Heparin‐Like Polymer Co‐Functionalized Graphene Oxide Based Core @ Polyethersulfone Based Shell Beads for Bilirubin Adsorption

Excessive bilirubin in the body of patient with liver dysfunction or metabolic obstruction may cause jaundice with irreversible brain damage, and new type of adsorbent for bilirubin is under frequent investigation. Herein, graphene oxide based core @ polyethersulfone‐based shell beads are fabricated by phase inversion method, amides and heparin‐like polymer are introduced to functionalize the core‐shell beads. The beads are successfully prepared with obvious core‐shell structure, adequate thermostability and porous shell. Clotting times and protein adsorption are investigated to inspect the hemocompatibility property of the beads. The adsorption of bilirubin is systematically investigated by evaluating the effects of contacting time, initial concentration and temperature on the adsorption, which exhibits improved bilirubin adsorption amount for the beads with amides contained cores or/and shells. It is worth believing that the amides and heparin‐like polymer co‐functionalized core‐shell beads may be utilized in the field of hemoperfusion for bilirubin adsorption.     

G-Frame and Riesz Sequences in Hilbert Spaces

G-frames generalize frames in Hilbert spaces. The literatures show that g-frames and frames share many similar properties, while they behave differently in redundancy and perturbation properties. Interestingly, g-frames have been extensively studied, but g-frame sequences have not. This problem is nontrivial since a g-frame and a frame both involve all vectors in the same Hilbert space, while a g-frame sequence and a frame sequence do not. They involve different linear spans. Using the synthesis and Gram matrix methods, we in this paper characterize g-frame sequences and g-Riesz sequences; obtain the Pythagorean theorem for g-orthonormal systems. These results recover several known results and lead to some new results on g-frames.     

Delay driven Hopf bifurcation and chaos in a diffusive toxin producing phytoplankton‐zooplankton model

This paper deals with a diffusive toxin producing phytoplankton‐zooplankton model with maturation delay. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are studied. Explicit results are derived for the properties of bifurcating periodic solutions by means of the normal form theory and the center manifold reduction for partial functional differential equations. Numerical simulations not only agree with the theoretical analysis but also exhibit the complex behaviors such as the period‐3, 5, 6, 7, 8, 11, and 12 solutions, cascade of period‐doubling bifurcation in period‐2, 4, quasi‐periodic solutions, and chaos. The key observation is that time delay may control harmful algae blooms (HABs). Moreover, numerical simulations show that the chaotic states induced by the period‐doubling bifurcation are purely temporal, which is stationary in space and oscillatory in time. The investigations may provide some new insights on harmful phytoplankton blooms.