分类： 数学 >> 数学物理 分类： 物理学 >> 基本粒子与场物理学 提交时间： 2023-02-08
In this paper, we present how to calculate the bounded from below or the vacuum stability of scalar potential for a general CP violating two-Higgs-doublet model by using the concepts of co-positivity and the gauge orbit spaces. Meanwhile, the semi-positive definiteness is prove for a class of 4th-order 2-dimensional complex tensor.
分类： 数学 >> 控制和优化 提交时间： 2023-02-01
The aim of this paper is first to establish a general prediction framework for turning (period) term structures in COVID-19 epidemic related to the implementation of emergency risk man#2;agement in the practice, which allows us to conduct the reliable estimation for the peak period based on the new concept of “Turning Period” (instead of the traditional one with the focus on “Turning Point”) for infectious disease spreading such as the COVID-19 epidemic appeared early in year 2020. By a fact that emergency risk management is necessarily to implement emergency plans quickly, the identification of the Turning Period is a key element to emergency planning as it needs to provide a time line for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible. As applications, the paper also discusses how this “Turning Term (Period) Structure” is used to predict the peak phase for COVID-19 epidemic in Wuhan from January/2020 to early March/2020. Our study shows that the predication framework established in this paper is capa#2;ble to provide the trajectory of COVID-19 cases dynamics for a few weeks starting from Feb.10/2020 to early March/2020, from which we successfully predicted that the turning period of COVID-19 epi#2;demic in Wuhan would arrive within one week after Feb.14/2020, as verified by the true observation in the practice. The method established in this paper for the prediction of “Turning Term (Period) Structures”, and associated criteria for the Turning Term Structure of COVID-19 epidemic is expected to be a useful and powerful tool to implement the so-called “dynamic zero-COVID-19 policy” ongoing basis in the practice.
分类： 数学 >> 控制和优化 提交时间： 2023-01-27
摘要：This paper deals with the uniform exponential stabilities (UESs) of two hybrid control systems consisting of wave equation and a second-order ordinary differential equation. Linear feedback law and local viscosity, and nonlinear feedback law and interior anti-damping are considered, respectively. Firstly, the hybrid system is reduced to a first order port-Hamiltonian system with dynamical boundary conditions and the resulting systems are then discretized by average central-difference scheme. Secondly, the UES of the discrete system is obtained without prior knowledge on the exponential stability of continuous system. The frequency domain characterization of UES for a family of contractive semigroups and discrete multiplier method are utilized to verify main results, respectively. Finally, the convergence analysis of the numerical approximation scheme is performed by the Trotter-Kato Theorem. Most interestingly, the exponential stability of the continuous system is derived by the convergence of energy and UES and this is a new idea to investigate the exponential stability of some complicate systems. The effectiveness of the numerical approximating scheme is verified by numerical simulation.
分类： 数学 >> 控制和优化 提交时间： 2023-01-27
摘要：In this note, Timoshenko beams with interior damping and boundary damping are studied from the viewpoints of control theory and numerical approximation. Especially, the uniform exponential stabilities of the beams are studied. The meaning of uniform exponential stability in this paper is two-fold: The first one is in the classical sense and also is concisely called exponential stability by many authors; The second one is that the semi-discretization systems, which are derived from an exponentially stable continuous beam by some semi-discretization schemes, are uniformly exponentially stable with respect to the discretized parameter. To investigate uniform exponential stability of continuous and discrete systems, five completely different methods, which are stability theory of port-Hamiltonian system, direct method of Lyapunov functional, perturbation theory of $C_{0}$-semigroup, spectral analysis of unbounded operator and frequency standard of exponential stability for contractive semigroup, are involved. Especially, a new method, which is based on the frequency domain characteristics of uniform exponential stability of $C_{0}$-semigroup of contractions, is established to verify the uniform exponential stability of semi-discretization systems derived from coupled system. The effectiveness of the numerical approximating algorithms is verified by numerical simulations.
分类： 数学 >> 控制和优化 提交时间： 2023-01-27
摘要：In this paper, we investigate the uniform exponential stability of a semi-discrete scheme for a Schr "{o}dinger equation under boundary feedback stabilizing control in the natural state space $L^2(0,1)$. This study is significant since a time domain energy multiplier that allows proving the exponential stability of this continuous Schr "{o}dinger system has not yet found, thus leading to a major mathematical challenge to semi-discretization of the PDE, an open problem for a long time. Although the powerful frequency domain energy multiplier approach has been used in proving exponential stability for PDEs since 1980s, its use to the emph{uniform} exponential stability of the semi-discrete scheme for PDEs has not been reported yet. The difficulty associated with the uniformity is that due to the parameter of the step size, it involves a family of operators in different state spaces that need to be considered simultaneously. Based on the Huang-Pr "{u}ss frequency domain criterion for uniform exponential stability of a family of $C_0$-semigroups in Hilbert spaces, we solve this problem for the first time by proving the uniform boundedness for all the resolvents of these operators on the imaginary axis. The proof almost exactly follows the procedure for the exponential stability of the continuous counterpart, highlighting
the advantage of this discretization method.
分类： 数学 >> 数学（综合） 提交时间： 2023-01-14
In this paper, we present the characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces equipped with
the endograph metric. The conclusions in this paper significantly improve the corresponding conclusions given in our previous paper
H. Huang, Characterizations of endograph metric and $ Gamma$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84 .
The results in this paper are applicable to fuzzy sets in a general metric space. The results in our previous paper are applicable to fuzzy sets in the $m$-dimensional Euclidean space $ mathbb{R}^m$, which is a special type of metric space. Furthermore, based on the above results, we give the characterizations of relative compactness, total boundedness and compactness in a kind of common subspaces of general fuzzy sets according to the endograph metric. As an application, we investigate some relationship between the endograph metric and the $ Gamma$-convergence on fuzzy sets.
分类： 物理学 >> 气体、等离子体、放电物理 分类： 数学 >> 数学（综合） 提交时间： 2022-12-27
摘要：对三维向量场中的双曲环的不变流形，本文给出其柱坐标下的生长公式。其流形初始生长方向取决于 Poincaré 映射的 Jacobian 矩阵，文中给出这一矩阵在环上的演化公式。这一演化公式也适用于任意有限维的自治连续时间动力系统。本文构造有非莫比乌斯型、莫比乌斯型的鞍环，以及仿造的 X-环，以演示公式的使用方法。 对于真实的数值例子，取东方超环运行中的一磁场时间切片作为演示。
分类： 统计学 >> 数理统计学 分类： 数学 >> 统计和概率 分类： 计算机科学 >> 计算机应用技术 分类： 信息科学与系统科学 >> 信息科学与系统科学基础学科 提交时间： 2022-12-13
摘要：统计独立性是统计学和机器学习领域的基础性概念，如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具，而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用，概述了其基本概念定义、定理和性质，以及估计方法。介绍了Copula熵研究的最新进展，包括其在统计学的六个基本问题（结构学习、关联发现、变量选择、因果发现、域自适应和正态性检验等）上的理论应用。讨论了前四个理论应用之间的关系，以及其对应的深层次的相关性和因果性概念之间的联系，并将Copula熵的（条件）独立性度量框架与基于核函数和距离相关的同类框架进行了对比。简述了Copula熵在理论物理学、理论化学、化学信息学、水文学、气候学、气象学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、社会学、教育学、新闻传播学、法学、政治学，以及能源工程、土木工程、制造工程、可靠性工程、化学工程、航空航天、电子工程、通信工程、高性能计算、测绘遥感和金融工程等领域的实际应用。
分类： 数学 >> 控制和优化 提交时间： 2022-12-12
In this paper, we study the problem of integral input-to-state stabilization in different norms for parabolic PDEs with integrable inputs. More precisely, we apply the method of backstepping to design a boundary control law for certain linear parabolic PDEs with destabilizing terms and $L^r$-inputs, and establish the integral input-to-state stability in the spatial $L^p$-norm and $W^{1,p}$-norm, respectively, for the closed-loop system, whenever $p in 1,+ infty $ and $r in p,+ infty $. In order to deal with singularities in the case of $p in 1,2)$, we employ the approximative Lyapunov method to analyze the stability in different norms. Concerning with the appearance of external inputs, we apply the method of functional analysis and the theory of series to prove the unique existence and regularity of solution to the closed-loop system.
分类： 数学 >> 代数与数论 提交时间： 2022-12-07
本文简要回顾了五度相生法的生律特征和音律计算的研究成果，推导和证明了五度相生法的上行五度音列和下行五度音列的分数式通项计算公式，结合两个分数式通项式证明了五度相生法的简易计算公式。利用这些公式可以直接计算任意位置上的音律，而无需从起始律开始链式计算中间的音律，依据简易计算公式可以把五度相生法的上行五度音列和下行五度音列合并为自变量为整数数轴的五度音列。本文利用简易计算公式得到了五度音列中每个音与起始音之间音程音分值的计算公式，依据一致分布的理论得到了五度音列的无穷个音分值在八度内是一致分布的结论。根据三间隔理论分析和图示了五声音阶、七声音阶、十二声音阶、京房六十律和钱乐之三百六十律的的不同音程数量和它们出现的次数。
分类： 数学 >> 数学物理 提交时间： 2022-12-07
摘要：In this article we employ classical tricks to give local and global well-posedness to MagnetoElasticity System. Different from many cases, we consider the equation which the magnetic field satisfies is Landau-Lifshitz system without viscidity, i.e. the Schrodinger flow. As is well known, people can not obtain ¨ global existence of Schrodinger flow at general cases. However, the reason why we do what others can not ¨ do is the Schrodinger flow with non-zero convection term.
分类： 数学 >> 数学（综合） 提交时间： 2022-12-04
摘要：本文通过严格数学分析找出了交叉熵过拟合的成因：边界样本的损失贡献比重大且随法向量
增长而加速增大、边界样本分布散乱，顺便理清了正则项的作用机理。
分类： 数学 >> 统计和概率 提交时间： 2022-11-13
摘要：医疗数据主要包括各类生物医学信号和医疗影像，专业医生可以通过医疗数据对患者身体状况做出判断。然而医疗数据的判读需要大量的人工成本且可能存在误判情况，因此有很多学者利用神经网络和深度学习进行医疗数据的分类和研究，进而提高医生工作效率和准确率、及早发现疾病实现早期诊断等，因此具有广泛的应用前景。但是传统神经网络存在能耗高、高延迟（计算速度慢）等缺点。文章介绍了近年来基于第三代神经网络——脉冲神经网络，利用医疗数据，如脑电信号、心电信号、肌电信号和磁共振图像等，在信号分类和疾病诊断等方面的研究，总结了脉冲神经网络相比于传统网络的优缺点，并展望了将来发展方向。
分类： 数学 >> 应用数学 提交时间： 2022-11-09
摘要：近年来，混合整数线性规划(MILP)被广泛用到对称密码的自动化分析中，并逐渐成为一个强有力的工具。在MILP方法中，一个核心的数学问题就是：对给定的Z2n上的高维离散点集S，如何利用尽可能少的不等式刻画它，简称整系数线性不等式完全刻画问题(FLIIIC problem)。该问题是NP-hard的。在这个工作中，我们是首次针对该问题给出了完整的求解理论。我们的方法从Plain集合出发，即由单个线性不等式确定的解集，揭示了其一系列内在属性，包括型、稀疏度、第一类退化、第二类退化，序、极小元、极大元、范数和界。在此基础上我们进一步给出了刻画Plain集合的一个充分必要条件，即集合S是Plain集合的充分必要条件是S集合是good集合。基于上述知识，对任意给定的子集S，我们提出了一个求解S的全部极小闭包和最优线性不等式完全刻画的算法。我们的算法非常高效且实用，可以应用到密码学中各种常见的S盒的刻画。据我们所知，这是首次给出了各种常见S盒的全部极小闭包，且我们得到的所有刻画结果都是目前最好的结果，尤其时在高维S盒刻画方面，我们的结果远优于国内外同行的结果。
分类： 数学 >> 应用数学 分类： 物理学 >> 交叉学科物理及相关领域的科学与技术 提交时间： 2022-11-04
摘要：伪随机数发生器（PRNG）广泛应用于许多领域，尤其是在密码应用中。设计欠佳的PRNG生成的序列将导致其密钥较弱从而可能泄漏被隐藏的信息。基于Golomb对理想伪随机序列的假设和FIPS 140-2随机性检验准则，本文首次提出了一种改进伪随机序列伪随机性能的新方法。其次，用广义同步定理、Henon映射、logistic映射和tube射构造了一个新的8维混沌广义同步系统（8DCGSS）。然后使用8DCGSS设计了一个混沌PRNG（CPRNG）。CPRNG的密钥空间大于2^{1117}。用FIPS 140-2随机性测试规范和广义FIPS 140-2随机性测试规范分别检测了CPRNG、Matlab PRNG、RC4算法和m序列分别生成的1000条20 000比特长的密钥流的通过率，应用广义FIPS 140-2随机性测试规范分别评估了改进的密钥流流的通过率（伪随机性）。用FIPS 140-2和广义FIPS 140-2伪随机性测试规范分别评估了4个PRNG产生的1000条100 000比特长的密钥流和1000条1 000 000比特长的密钥流和改进的密钥流的通过率。结果表明，本文的方法能够显著提高四个PRNGs生成的密钥流的伪随机性。m序列伪随机数发生器生成的长度小于100 000比特的密钥流的伪随机性能不佳。
分类： 信息科学与系统科学 >> 系统工程方法论 分类： 数学 >> 应用数学 提交时间： 2022-10-30
摘要：多因素影响分析是经济数量分析的重要内容，有多种方法，其中，结构分解分析（SDA）在投入产出技术应用中被广泛使用。本文对SDA的缺陷做了深入说明，全面阐述新提出的多因素多阶影响分析（MMIA）技术。首先，定义了多因素影响分析和多因素多阶影响分析的基本概念，其次，阐明了多因素多阶影响分析与泰勒级数展开的关系，再次，提出了正向分析和逆向分析的概念和技术，最后，对MMIA在投入产出技术框架下的几个应用做了简要说明。
分类： 数学 >> 离散数学和组合数学 提交时间： 2022-10-24
摘要：Let f(n) be the maximum number of edges in a graph on n vertices in which no two cycles have the same length. Erd¨os raised the problem of determining f(n). Erd¨os conjectured that there exists a positive constant c such that ex(n, C2k) ≥ cn1+1/k. Haj´os conjecture that every simple even graph on n vertices can be decomposed into at most n/2 cycles. We present the problems, conjectures related to these problems and we summarize the know results. We do not think Haj´os conjecture is true.
分类： 数学 >> 离散数学和组合数学 提交时间： 2022-10-22
The set of all non-increasing nonnegative integers sequence π = (d(v1), d(v2), ..., d(vn)) is denoted by NSn. A sequence π ∈ NSn is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NSn is denoted by GSn. A graphical sequence π is potentially H-graphical if there is a realization of π containing H as a subgraph, while π is forcibly H-graphical if every realization of π contains H as a subgraph. Let Kk denote a complete graph on k vertices. Let Km −H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of Km). This paper summarizes briefly some recent results on potentially Km −G-graphic sequences and give a useful classification for determining σ(H, n).
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