理想弹塑性固体Riemann问题的解结构与初值条件

针对理想弹塑性固体材料的一维Riemann问题,在不考虑真空的情况下,讨论其所有可能存在的解结构,给出每一种解结构下对应的初值条件且证明该系列初值条件的完备性,即任意给定的物理量初值均有且只有一种解结构与之对应.基于该理论,在设计精确或近似理想弹塑性Riemann问题求解器时,可以依据初值条件对任意物理量初值直接判断其对应的解结构,从而提高求解器的精度和效率.数值试验验证了该系列初值条件的正确性和有效性.     

Sommerfeld-type integrals for discrete diffraction problems

Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As a result, explicit solutions are obtained in terms of recursive relations (for the Green’s function), algebraic functions (for the half-line problem), or elliptic functions (for the right angle problem).     

大型公共建筑工程质量保险纯费率厘定研究——基于GLM及GAM的实证比较分析

为准确地厘定大型公共建筑工程质量的保险纯费率,通过文献分析及调研,对影响大型公共建筑工程质量的因素进行了研究,提炼出11项保险费率因子。以46栋竣工于1993—2016年的大型公共建筑为工程数据集,在频率-强度法基础上,基于Poisson、Negative Binomial、Gamma、Inverse Gauss等分布的假设,利用广义线性模型及广义可加模型建立了8个工程质量保险纯费率厘定模型,通过比较选择最优模型,并对模型进行了验证。结果表明,所建模型可用于大型公共建筑工程质量保险纯费率厘定。     

饮用水中三氯甲烷与其他氯消毒副产物在活性炭上的吸附竞争研究

通过等温吸附实验,探究了三氯甲烷（CHCl₃）与二氯一溴甲烷（CHBrCl₂）、二氯乙酸（Cl₂CHCOOH）在活性炭上的竞争吸附关系,同时探究了在低浓度条件下CHBrCl₂和Cl₂CHCOOH浓度变化对活性炭吸附CHCl₃的影响。实验结果表明,活性炭吸附CHCl₃和CHBrCl₂符合Freundlich模型,对Cl₂CHCOOH的吸附符合Langmuir模型;活性炭对3种消毒副产物均为优先吸附,吸附能力由大到小依次为CHBrCl₂、CHCl₃、Cl₂CHCOOH;低浓度条件下,活性炭对消毒副产物的吸附效果随体系中物质种类的增加而降低;低浓度条件下,Cl₂CHCOOH的浓度变化对CHCl₃的吸附效果影响不大,但吸附效果随水体中CHBrCl₂浓度的升高而降低。     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One

By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$.     

Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(\cdot )$-Laplacian in a Variable Exponent Sobolev Space

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(\cdot )$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.     

网吧消防安全问题及其治理

网吧作为新兴事物备受人们的青睐,但由于场所内部及管理存在的问题导致火灾隐患重重,网吧发生的火灾事故造成的财产损失及人员伤亡逐年上升,通过对网吧消防安全上存在的问题进行分析,提出相应的预防措施和管理对策.     

奇摄动非线性系统Robin边值问题的多种层性质

通过研究一类具有转向点的二阶非线性系统Rob in边值问题的奇摄动.在适当的假设条件下,利用微分不等式方法得到了解的存在性和渐近估计.