Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function

In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1}!.     

Remarks to Heisenberg's Farm-Hall lecture on the critical mass of fast neutron fission

Heisenberg's estimate of the critical mass of an explosive nuclear chain reaction is discussed with a view to the future of world peace and a real effective treaty on non-proliferation.     

Uncertainty principles associated with the offset linear canonical transform

As a time‐shifted and frequency‐modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and optics. To study simultaneous localization of a signal and its OLCT, the classical Heisenberg's uncertainty principle has been recently generalized for the OLCT. In this paper, we complement it by presenting another two uncertainty principles, ie, Donoho‐Stark's uncertainty principle and Amrein‐Berthier‐Benedicks's uncertainty principle, for the OLCT. Moreover, we generalize the short‐time LCT to the short‐time OLCT. We likewise present Lieb's uncertainty principle for the short‐time OLCT and give a lower bound for its essential support.     

Reassignment of the Stockwell spectrogram

The recently developed Stockwell spectrogram provides a multi-scale time-frequency representation of a signal. Due to the Heisenberg's inequality, however, the unavoidable blurring of time and frequency information may conceal important signal structures. Here, we propose to use the reassignment method to improve the readability of the Stockwell representation. An numerical example is presented to illustrate its effectiveness in practice. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel uncertainty principles associated with 2D quaternion Fourier transforms

The quaternion Fourier transform has been widely employed in the colour image processing. The use of quaternions allow the analysis of colour images as vector fields. In this paper, the right-sided quaternion Fourier transform and its properties are reviewed. Using the polar form of quaternions, two novel uncertainty principles associated with covariance are established. They prescribe the lower bounds with covariances on the products of the effective widths of quaternionic signals in the space and frequency domains. The results generalize the Heisenberg's uncertainty principle to the 2D quaternionic space.     

Time‐dependent photon statistics in variable media

We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, which describes a generic model of variable media in the case of multiparameter squeezed input photon configuration. The corresponding probability amplitudes and photon statistics are also derived in the Schrödinger picture in an abstract operator setting of the quantum electrodynamics; a comparison discussion is made in Heisenberg's picture as well. The unitary transformation and an extension of the squeeze/evolution operator are introduced formally. The time‐dependent photon probability amplitudes with respect to the Fock basis are indeed derived in an operator form. Further, explicit expressions for the matrix elements of the displacement and squeeze operators are derived in terms of hypergeometric functions and solutions of a certain Ermakov‐type system. In the Supporting Information , we provide a computer algebra verification of the derivation of the Ermakov‐system and of the solutions of the Heisenberg equations.     

Zaremba's problem for elliptic equations in the neighborhood of a singular point or in the infinity

In the present paper the behavior of solutions of the mixed Zaremba's problem in the neighborhood of a boundary point and at infinity is studied. In part I of this paper[4] the concept of Wiener's generalized solution of Zaremba's problem was introduced and the so called Growth Lemma for the class of domains, satisfying isoperimetric condition, was proven. In part II regularity criterion for joining points of Neumann's and Dirichlet's boundary conditions is formulated. Generalized solution in unlimited domains as a limit of Zaremba's problem's solutions in a sequence of limited domains is introduced and a regularity condition allowed to obtain an analogue of Phragmen-Lindeloeff theorem for the solutions of Zaremba's problem. Main results of the present paper are formulated in terms of divergence of Wiener's type series.     

Use of Halley's Method in the Nonlinear Finite Element Analysis

Halley's method is a higher order iteration method for the solution of nonlinear systems of equations. Unlike Newton's method, which converges quadratically in the vicinity of the solution, Halley's method can exhibit a cubic order of convergence. The equations of Halley's method for multiple dimensions are derived using Padé approximants and inverse one-point interpolation, as proposed by Cuyt. The investigation of the performance of Halley's method concentrates on eight-node volume elements for nonlinear deformations using Staint Venant-Kirchhoff's constitutive law, as well as a geometric linear theory of von Mises plasticity. The comparison with Newton's method reveals the sensibility of Halley's method, in view of the radius of attraction but also demonstrates the advantages of Halley's method considering simulation costs and the order of convergence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

百度关注度对股票收益率的影响——基于VEC模型的实证分析

基于百度指数所提供关键词搜索数据,构建百度看涨指数和百度看跌指数,形成了百度关注度.依据2017.2-2019.2的上证指数收益率数据,利用VEC模型和格兰杰因果检验,分析了百度关注度对股票收益率的影响.结果表明,投资者关注度是股票市场的格兰杰原因,百度看涨指数以0.4%的比例正面影响收益率,百度看跌指数以0.7%的比例负面影响收益率.而脉冲响应分析发现了投资者关注度对股票收益率的影响较持久,而后者对前者的波动十分敏感.最后,结合上述所得到的结论,基于投资者和监管者的立场分别给出了不同的有效建议.     

The β-Extension of the Multivariable Lagrange Inversion Formula

We show that Gessel's combinatorial proof of the multivariable Lagrange inversion formula can be given a ,β-extension, which generalizes Foata and Zeilberger's, β-extension of MacMahon's master theorem. Moreover, we show that there is no need to use Jacobi's identity in the derivation of the Lagrange formula. Finally, combining Gessel's method and ours, we obtain a new proof of Jacobi's identity.     

Silnikov's orbit in coupled Duffing's systems

The existence of Silnikov's orbit is demonstrated in coupled Duffing's equation using Melnikov's method and Geometrical singular perturbation theory. The numerical simulations are also given for a special coupled Duffing's system.     

中国地方政府财政民生支出效率实证分析

利用DEA方法计算出2009-2013年5年间全国31个省份财政民生支出资金配置的综合技术效率、纯技术效率、规模效率三种效率值,分析出各省份政府财政民生支出所处规模报酬阶段.结果显示:大部分省份的政府财政民生支出DEA得分在0.9以上,说明虽然效率没有达到最优水平,但是总体来说效率水平还是比较高的.另外,各省市财政民生产出存在较大的差异,东部地区综合产出水平高于中西部地区,其中,西部地区效率最低,改进空间最大.     

Zermelo in the mirror of the Baer correspondence, 1930–1931

Around 1931 Zermelo had an extended correspondence with the young Reinhold Baer concerning the edition of Cantor's collected works. Some of the letters also deal with Skolem's paradox and Gödel's first incompleteness theorem. Whereas Zermelo's letters are lost, most of Baer's letters are contained in the Zermelo Nachlass. Besides giving insight into Zermelo's reaction to Skolem's and Gödel's results, the letters also demonstrate Baer's clear understanding of the behavior of models of set theory and of the relevance of Gödel's first incompleteness theorem.     

对外投资创新、优势产业国际化与轨道交通全产业链海外发展

中国的优势产业具备国际化发展的条件,中国作为一个经济大国,拥有完备的产业体系、齐全的产业门类、大量的人才、充足的外汇储备和稳定的政治环境.为了加快中国优势产业的国际化发展,需要对"对外投资与合作"进行创新.轨道交通产业是中国的优势产业,结合该产业的国际化发展案例,分析了中国优势产业通过对外投资创新进行发展.研究认为,轨道交通产业的国际化发展,可以创造性地运用BT(建设-移交)、PPP、EPC等"对外投资与合作"模式.根据对外投资与合作的现状,以及中国高铁的实际案例,就"推进中国优势产业国际化"和"创新对外投资与合作方式"提出了有关建议.     

Permanence as a principle of practice

The paper discusses Peano's argument for preserving familiar notations. The argument reinforces the principle of permanence, articulated in the early 19th century by Peacock, then adjusted by Hankel and adopted by many others. Typically regarded as a principle of theoretical rationality, permanence was understood by Peano, following Mach, and against Schubert, as a principle of practical rationality. The paper considers how permanence, thus understood, was used in justifying Burali-Forti and Marcolongo's notation for vectorial calculus, and in rejecting Frege's logical notation, and closes by considering Hahn's revival of Peano's argument against Pringsheim's reading of permanence as a logically necessary principle.     

On the structure of linear semigroups

Green's Lemma [1, Lemma 2.2] is one of the most important theorems in the theory of semigroups. The main purpose of this note is to establish a generalized Green's Lemma and a generalized Clifford and Miller's Theorem [1, p. 59] in linear semigroups. A generalized Green's Lemma describes the behavior of certain mappings between two distinct D-classes.