INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.

The Tricomi and Frankl Problems for Generalized Chaplygin Equations in Multiply Connected Domains

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.

Convex hull theorem for multiply connected domains in the plane with an estimate of the quasiconformal constant

For any multiply connected domain Ω in ?2, let S be the boundary of the convex hull in H 3 of ?2Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on ?S = ?Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.

Oblique Derivative Problem for Quasilinear Mixed (Lavrentév-Bitsadze) Equations of Second Order in Two Connected Domains

In this article, we first give the representation of solutions for the oblique derivative problem of mixed （Lavrentév-Bitsadze） equations in two connected domains, afterwards prove the uniqueness of solutions of the above problem. Moreover, we prove the solvability of oblique derivative problem for quasilinear mixed （Lavrentév-Bitsadze） equations of second order, and obtain a priori estimates of solutions of the above problem. The above problem is an open problem proposed by Rassias.

An Expansion Theorem for an Eigenvalue Problem of an Arbitrary Multiply Connected Domain with an Eigenparameter in a General Type of Boundary Conditions

The object of this paper is to establish an expansion theorem for a regular right- definite eigenvalue problem with an eigenvalue parameter λ which is contained in the Schrodinger partial differential,equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain in R^n(n≥2).We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.

Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries

In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture.We prove,for some special connected fractal domains,the sharp estimate for second term of counting function asymptotics,which implies that the weak form of the Weyl- Berry conjecture holds for the case.Finally,we also study a naturally connected fractal domain,and we prove,in this case,the weak Weyl-Berry conjecture holds as well.

中国碳市场与电力市场间的风险溢出效应研究——基于BK溢出指数模型

研究碳市场与电力市场间的风险溢出效应,对于有效防范碳金融风险以及国家节能减排战略的稳步推进具有重要意义。本文基于广义方差分解谱构建溢出指数,从频域视角考察中国碳市场与电力市场在短、中、长期的静态溢出和时变溢出,并根据溢出指数构建溢出网络,探究风险的中心与演化。结果表明:中国碳市场与电力市场之间的风险溢出短期>中期>长期,且存在一定的波动性和不确定性,受宏观经济状况影响较大。发电企业接收到的风险量与火电装机比例有关,发电企业输出风险的能力与发电量有关。在短期,碳市场属于风险净接收方,而在中长期,碳市场属于风险净溢出方。基于上述结论提出了相关政策建议。

REMARKS ON JOHN DISKS

Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.

LiDAR signal denoising based on connected domains

The streak tube imaging light detection and ranging （LiDAR） is a new type of waveform sampling laser imaging radar whose echo signals are stripe images with a high frame rate. In this study, the morphological and statistical characteristics of stripe signals are analyzed in detail. Based on the concept of mathematical morphology denoising, connected domains are constructed in a noise- containing stripe image, and the noise is removed using the difference in connected domains area between signals and noises. It is shown that, for stripe signals, the proposed denoising method is significantly more efficient than Wiener filtering.

Covering Theorems on Two Classes of Quasi-conformal Mappings

In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.

Simple Proofs of Upper and Lower Envelopes of Van Der Pauw’s Equation for Hall-Plates with an Insulated Hole and Four Peripheral Point-Contacts

For plane singly-connected domains with insulating boundary and four point-sized contacts, C0 …C3, van der Pauw derived a famous equation relating the two trans-resistances R01,23, R12,30 with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.

IMPROVED DELAUNAY TRIANGULATION FOR TRIMMED NURBS SURFACE

An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.

The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic Degeneracy

This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness and existence of solutions are proved by a new method.

Linear Connectivity, Schwarz–Pick Lemma and Univalency Criteria for Planar Harmonic Mapping

In this paper, we first establish a Schwarz-Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.

中国的房地产周期及其与信贷周期的交互影响动态

解绑房地产对经济发展的桎梏是新发展阶段下释放内需潜力、培育发展动力的先决条件。基于TVP-FAVAR模型构造房地产周期指数,从时域和频域双重维度对中国房地产周期的波动特征及其与信贷周期之间的影响动态展开系统分析。研究结果表明:首先,中国房地产市场整体呈现出以3—4年为主的周期波动,但2016年后开始呈现出周期弱化且下行持续期延长的新特征。其次,房地产周期与信贷周期的交互影响主要集中于低频长周期成分且存在明显的状态依赖性特征,在房地产周期处于繁荣阶段时,其对信贷周期的正向反馈效应较为突出,而在房地产周期处于紧缩阶段时,信贷周期对房地产周期的逆向调控效应则更为明显。因此,立足于新发展阶段,房地产调控需更加关注多尺度周期的叠加特征,构建长短期差异化的房地产调控机制,增强后疫情时代的房地产市场韧性,实现全体人民“住有所居”。

中国经济周期波动的行业叠加及其与政策周期的时频关联

综合运用连续小波变换与频域连通性等方法,探究中国经济周期波动特征和各个行业领域不同频率波动成分的叠加机理,检验不同频域内经济周期与政策周期的交互影响动态。研究表明,经济周期由不同频率波动成分叠加谐振而成,其中4年左右的主周期波动主要由工业、农业、建筑业、金融业与房地产业复合驱动形成,在全球金融危机及新冠肺炎疫情时期,2年左右的短周期波动相对凸显且主要由批发零售业、住宿餐饮业与交通运输业等驱动形成;财政政策周期(货币政策周期)主要在高频(低频)波动成分上对经济周期产生短期(长期)影响效应,而经济周期对经济政策周期的溢出影响则均集中于低频波动成分。这些研究为新时期协调运用各类宏观调控政策实施定向精准调控,进一步完善宏观调控跨周期设计与调节机制,从行业叠加和时频关联视角提供了有益的经验依据和政策启示。

Carleson Measures on Planar Sets

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets