Explicit estimates of sums related to the Nyman–Beurling criterion for the Riemann Hypothesis

We give an estimate for sums appearing in the Nyman–Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the Möbius function. The bound is smaller than the trivial bound – essentially the number of terms – by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.     

正电子冲击下氦电离三重微分截面的理论计算

我们发展了一种正电子碰撞原子电离的畸变波Born近似方法， 在这个方法中，正负电子偶素通道通过一个ab initio的光学势附加到入射粒子和靶的相互作用势上，且通道对电离作用被第一次被考虑在正电子碰撞原子电离的过程中. 应用这个方法计算了在50 eV入射能量范围氦的电离的三重微分截面，计算结果和实验数据很好的符合.     

Explicit solutions and Darboux transformations of a generalized D-Kaup–Newell hierarchy

Nonlinear Dynamics - Darboux and Bäcklund transformations on integrable couplings are formulated and generalized. The generalization of the theory pertains to spectral problems where the...     

Optimal spectral phase control of femtosecond laser-induced up-conversion luminescence in Sm^3+:NaYF4 glass

The spectral phase of the femtosecond laser field is an important parameter that affects the up-conversion(UC)luminescence efficiency of dopant lanthanide ions.In this work,we report an experi-mental study on controlling the UC lmiiinescence efficiency in Sm^3+:NaYF4 glass by 800-nm femtosec-ond laser pulse shaping using spectral phase modulation.The optimal phase control strategy efficiently enhances or suppresses the UC luminescence intensity.Based on the laser-power dependence of the UC luminescence intensity and its comparison with the luminescence spectrum under direct 266-nm fem-tosecond lciser irradiation,we propose herein an excitation model combining non-resonant two-photon absorption with resonance-media ted three-photon absorption to explain the experimental observations.     

H2S gas sensor based on integrated resonant dual-microcantilevers with high sensitivity and identification capability

Detection of trace-level hydrogen sulfide (H₂S) gas is of great importance whether in industrial production or disease diagnosis. This research presents a novel H₂S gas sensor based on integrated resonant dual-microcantilevers which can identify and detect trace-level H₂S in real-time. The sensor consists of two integrated resonant microcantilever sensors with different functions. One cantilever sensor can identify H₂S by outputting positive frequency shift signals, while the other cantilever sensor will detect H₂S as a normally used cantilever sensor with negative frequency shifts. Combined the two cantilever sensors, the proposed gas sensor can distinguish H₂S from a variety of common gases, and the detection limit to H₂S of the sensor is as sensitive as below 1 ppb.     

System-size effect on the friction at liquid-solid interfaces

The friction at the liquid-solid interfaces is widely involved in various phenomena ranging from nanometer to micrometer scales. By the molecular dynamic(MD)simulation, the friction properties of liquid-solid interfaces at the molecular level are calculated via the Green-Kubo relation. It is found that the system size will influence the value of the friction coefficient, especially for the solid surfaces with the larger polar charge. The value of the friction coefficient decreases with the increase in the system size and converges at large system sizes. The large polar charge will lead to a significant friction coefficient. However, the diffusion of water molecules on this surface is almost a constant, indicating that the diffusion coefficient seems to be independent of the system size and polar charge. This work provides insights for the selection of the system size in modeling the frictional properties of hydrophobic/hydrophilic surfaces.     

Narrowband polarization entangled paired photons with controllable temporal length

Quantum networks strongly depend on the efficient interactions between flying photonic quantum bits and local long-lived atomic matter nodes. To achieve the efficient quantum interfaces between polarization-encoding photons and spin-encoding atoms, polarization-entangled paired photons with a bandwidth narrower than the natural linewidth of the atoms are highly required. In this paper, we review the generation of subnatural-linewidth polarization-entangled paired photons through spontaneous four-wave mixing with cold atoms, which is very suitable for the application of quantum networks.     

Asymmetric Hydrosilylation of Aromatic Ketones Catalyzed by an Economical and Effective Copper-Diphosphine Catalytic System in Air

In the presence of the inexpensive and non‐toxic polymethylhydrosiloxane, the combination of copper(II) acetate and a chiral diphosphine displayed high catalytic efficiency in the asymmetric hydrosilylation of a series of aromatic ketones in air atmosphere and at room temperature. (R)‐1‐Arylethanols were obtained with up to 99% yield and 93% enantiomeric excess. Meanwhile, the electron effect and steric hindrance of substituents on the aromatic ring had an interesting influence on both the yields and enantioselectivities. Furthermore, a possible mechanism was presented to explain the influence of some key factors on the reaction.