Klingen $${\mathfrak {p}}^2$$ p 2 vectors for $$\mathrm{GSp}(4)$$ GSp ( 4 )

The Ramanujan Journal - We calculate the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $${\mathfrak {p}}^2$$ for all irreducible, admissible...     

Scheme to measure the expectation value of a physical quantity in weak coupling regime

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, ifthe coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointercan not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, whichmakes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurementmethod in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement,our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.     

Fabrication of Microporous Metal–Organic Frameworks in Uninterrupted Mesoporous Tunnels: Hierarchical Structure for Efficient Trypsin Immobilization and Stabilization

Hierarchically porous metal–organic frameworks (HP-MOFs) are promising in various applications. Most reported HP-MOFs are prepared based on the generation of mesopores in microporous frameworks, and the formed mesopores are connected by microporous channels, limiting the accessibility of mesopores for bulky molecules. A hierarchical structure is formed by constructing microporous MOFs in uninterrupted mesoporous tunnels. Using the confined space in as-prepared mesoporous silica, highly dispersed metal precursors for MOFs are coated on the internal surface of mesoporous tunnels. Ligand vapor-induced crystallization is employed to enable quantitative formation of MOFs in situ, in which sublimated ligands diffuse into mesoporous tunnels and react with metal precursors. The obtained hierarchically porous composites exhibit record-high adsorption capacity for the bulky molecule trypsin. The thermal and storage stability of trypsin is improved upon immobilization on the composites.     

Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials

Nonlinear Dynamics - Fatigue is inevitable in pipes conveying fluid due to unwanted vibration. Internal resonance occurs in such pipes due to pre-pressure. For the first time, the effects of...     

树状大分子接枝型聚合物色谱分离材料研究进展

随着色谱固定相制备技术和材料科学领域的不断发展,目前已经有大量修饰方法和新型材料被用于固相萃取、高效液相色谱以及离子色谱聚合物固定相填料的功能化修饰。其中聚酰胺-胺(PAMAM)树状大分子由于其独特的结构和性质,在色谱分离材料结构完善和性能提升中也发挥了重要的作用。该文主要综述了PAMAM树状大分子在以聚合物为基质的色谱分离材料修饰中的应用,并对其今后的发展进行了展望。     

气体压强对纳秒激光诱导空气等离子体特性的影响

环境气体的压强对激光诱导等离子体特性有重要影响.基于发射光谱法开展了气体压强对纳秒激光诱导空气等离子体特性影响的研究,探讨了气体压强对空气等离子体发射光谱强度、电子温度和电子密度的影响.实验结果表明,在10-100 kPa空气压强条件下,空气等离子体发射光谱中的线状光谱和连续光谱依赖于气体压强变化,且原子谱线和离子谱线强度随气体压强的变化有明显差别.随着空气压强增大,激光击穿作用区域的空气密度增加,造成激光诱导击穿空气几率升高,从而等离子体辐射光谱强度增大.空气等离子体膨胀区域空气的约束作用,增加了等离子体内粒子间的碰撞几率以及能量交换几率,并且使离子-电子-原子的三体复合几率增加,因此造成原子谱线OⅠ777.2 nm与NⅠ821.6 nm谱线强度随着气体压强增大而增大,在80 kPa时谱线强度最高,随后谱线强度缓慢降低.而离子谱线N Ⅱ 500.5 nm谱线强度在40 kPa时达到最大值,气体压强大于40 kPa后,谱线强度随压强增加而逐渐降低.空气等离子体电子密度均随压强升高而增大,在80 kPa后增长速度变缓.等离子体电子温度在30 kPa时达到最大值,气体压强大于30 kPa后,等离子体电子温度逐渐降低.研究结果可为不同海拔高度的激光诱导空气等离子体特性的研究提供重要实验基础,为今后激光大气传输、大气组成分析提供重要的技术支持.     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

The Applications of Order Reduction Methods in Nonlinear Dynamic Systems

Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper. First, the transient proper orthogonal decomposition (T-POD) method is introduced based on the high-dimensional nonlinear dynamic system. The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends. The efficiency of the T-POD method is verified via comparing with the results of the original system. Second, the polynomial dimensional decomposition (PDD) method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response. The numerical results obtained by the PDD method agree well with the Monte Carlo simulation (MCS) method. The results of the PDD method can approximate to MCS better with the increasing of the polynomial order. Meanwhile, the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.     

An effective interference suppression algorithm for visible light communication system based on DBSCAN

In order to improve the signal-to-noise ratio and mitigate the damage of noise to the communication quality,an effective interference suppression algorithm,which is based on the improved density-based spatial clustering of applications with noise algorithms,is proposed for visible light communication systems using the complementary metal–oxide–semiconductor image sensor as the receiver.Experimental results show that the algorithm can learn the region where the payload data is located,filter out the noise data,and greatly decrease the interference.The effect of the algorithm is also studied through bit error ratio performance.     

Spin-exchange relaxation of naturally abundant Rb in a K-Rb-21Ne self-compensated atomic comagnetometer

The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed,and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a large extra spinexchange broadening compared to pure 87Rb.This broadening mainly comes from the contribution of the equivalent reduction in the Rb spin-exchange rate.On this basis,an approximate relaxation model is proposed and experimentally demonstrated to be more accurate than that from a previous work.This study also provides a method for determining the properties of alkali-metal vapor cells.