A perturbed Whittaker-Kotel?nikov-Shannon sampling theorem

The sampling theorem of Whittaker (1915) [31], Kotel?nikov (1933) [25] and Shannon (1949) [28] gives cardinal series representations for finite L²-Fourier transforms at equidistant sampling points. Here we investigate the situation when the Fourier transform is replaced by a perturbed one. Thus the kernel of the transform will be of the form exp(−ixt)+ε(x,t), instead of exp(−ixt) in the unperturbed case. The perturbed kernel arises from first order eigenvalue problems with rank one perturbations.     

一类连续半鞅的极大不等式

本文主要研究了一类连续半鞅的极大不等式.利用伊藤公式和Lenglart控制定理,得到了它们的极大不等式,推广了文献[9]的主要结果.     

纳米银刻蚀比色法检测褪黑激素

该文构建了一种基于氯金酸刻蚀球形纳米银检测褪黑激素的简单、高灵敏比色探针。纳米银可被氯金酸氧化刻蚀为Ag+,同时还原生成的纳米金沉积在刻蚀后的纳米银表面,导致其溶液的吸光度降低和颜色增强(由黄色变为橘黄色)。当向体系中加入褪黑激素时,氯金酸被还原,抑制了纳米银的刻蚀,从而使得溶液吸光度增加和颜色变浅。结果显示,在0.1 nmol/L~1.0 mmol/L范围内,褪黑激素浓度对数值(lgC)与其吸光度改变值(ΔA)呈良好的线性关系,线性方程为ΔA=0.049 8+0.516lgC,相关系数(R2)为0.996 4,检出限为0.09 nmol/L。该方法成功应用于人体尿液和葡萄中的褪黑激素的测定。     

3D printing for aqueous and non-aqueous redox flow batteries

Additive manufacturing technologies, generally grouped under the name of 3D printing, are experiencing an explosion of interest during the last few years. The possibility of fast prototyping enabled by 3D printing has been recognized as a crucial booster for device fabrication and general scientific advancements. In this review, attention is focused on the latest developments in the field of redox flow batteries which are, similar to other energy related devices, characterized by the recent adoption of 3D printing methods for the fabrication of key components. Whether simply to investigate flow phenomena, test new designs or fabricate final-product components with custom features, the use of 3D printing can critically drive this field of research towards better performing energy-storage systems. The latest and most representative examples of redox flow battery studies will be discussed, categorized in relation to the electrolyte used and whether the devices are employed in aqueous or non-aqueous applications.     

Nonextensive entropies derived from Gauss? principle

Gauss? principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles.     

Electronic transport properties of carbon chains between Au and Ag electrodes: A first-principles study

We report first-principles calculations of the current-voltage characteristic and the conductance of carbon-based molecular wires with different length capped with sulfur ends between two metallic electrodes made of different metals. The optimized molecular structure of carbon chain in the junction is presented on the structure of polyyne. The conductance of the polyyne wires shows oscillatory behavior depending on the number of carbon atoms (triple bonds). Current rectification is found and rectification direction presents inversion with the odd and even number of carbon atoms.     

q-Strategy spatial prisoner?s dilemma game

We generalize the usual two-strategy prisoner?s dilemma game to a multi-strategy game, in which the strategy variable s is allowed to take q different fractional values lying between 0 and 1. The fractional-valued strategies signify that individuals are not absolutely cooperative or defective, instead they can adopt intermediate strategies. Simulation results on 1D and 2D lattices show that, compared with the binary strategy game, the multi-strategy game can sustain cooperation in more stringent defective environments. We give a comprehensive analysis of the distributions of the survived strategies and we compare pairwise the relative strength and weakness of different strategies. It turns out that some intermediate strategies survive the pure defection because they can reduce being exploited and at the same time benefit from the spatial reciprocity effect. Our work may shed some light on the intermediate behaviors in human society.     

On Hardy?s paradox, weak measurements, and multitasking diagrams

We discuss Hardy?s paradox and weak measurements by using multitasking diagrams, which are introduced to illustrate the progress of quantum probabilities through the double interferometer system. We explain how Hardy?s paradox is avoided and elaborate on the outcome of weak measurements in this context.     

On Kre?n's formula

Kre?n's formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Kre?n's formula.     

On non-strong jumping numbers and density structures of hypergraphs

Estimating Turán densities of hypergraphs is believed to be one of the most challenging problems in extremal set theory. The concept of ‘jump’ concerns the distribution of Turán densities. A number α∈[0,1) is a jump for r-uniform graphs if there exists a constant c>0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Turán density of F is at least α+c. A fundamental result in extremal graph theory due to Erd?s and Stone implies that every number in [0,1) is a jump for graphs. Erd?s also showed that every number in [0,r!/r^r) is a jump for r-uniform hypergraphs. Furthermore, Frankl and Rödl showed the existence of non-jumps for hypergraphs. Recently, more non-jumps were found in [r!/r^r,1) for r-uniform hypergraphs. But there are still a lot of unknowns regarding jumps for hypergraphs. In this paper, we propose a new but related concept-strong-jump and describe several sequences of non-strong-jumps. It might help us to understand the distribution of Turán densities for hypergraphs better by finding more non-strong-jumps.