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Acta Mathematica Sinica,English Series 2024年第6期40卷 1521-1532页

作者： Peng Cheng LI Dong He PEI Xin ZHAO School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024P.R.China Department of Mathematics Harbin Institute of TechnologyWeihai 264209P.R.China School of Mathematics and Statistics Qingdao UniversityQingdao 266071P.R.China

In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski *** is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike ***,we show a new geometric invariant to characterise singularities of the focal ***,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.

关键词： Evolutes focal surfaces spacelike framed curves singularities

A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent singularities

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1364-1382页

作者： Jake L. Nkeck Department of Mathematics University of Buea Buea Cameroon

The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

关键词： singularities Finite Element Methods Heat Equation Predictor-Corrector Algorithm

Spin-valley Hall phenomena driven by Van Hove singularities in blistered graphene

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npj Computational Materials 2020年第1期6卷 27-34页

作者： M.Umar Farooq Arqum Hashmi Tomoya Ono Li Huang Department of Physics Southern University of Science and TechnologyShenzhenGuangdong 518055China Center for Computational Sciences University of TsukubaTsukubaIbaraki 305-8577Japan Kansai Photon Science Institute National Institutes for Quantum and Radiological Science and Technology(QST)Kyoto 619-0215Japan Department of Electrical and Electronic Engineering Kobe UniversityKobe 657-8501Japan

Using first-principles calculations,we investigate the possibility of realizing valley Hall effects(VHE)in blistered graphene *** show that the Van Hove singularities(VHS)induced by structural deformations can give ri... 详细信息

关键词： graphene valley singularities

On variance of exponents for isolated surface singularities with modality ≤ 2 In Memory of Professor Philip Wagreich

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Science China Mathematics 2014年第1期57卷 31-41页

作者： YAU Stephen S.T. ZUO HuaiQing Department of Mathematical Science Tsinghua University Mathematical Sciences Center Tsinghua University

Using the theory of the mixed Hodge structure one can define a notion of exponents of a *** 2000,Hertling proposed a conjecture about the variance of the exponents of a ***,we prove that the Hertling conjecture is tru... 详细信息

关键词： singularities modality exponents

EXPERIMENTAL ANALYSIS FOR singularities IN CRACK NORMAL TO BIMATERIAL INTERFACE

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Acta Mechanica Solida Sinica 1998年第2期11卷 180-186页

作者： Kang Yilan Wang Shibin Wang Yangen Tianjin Univ Dept Mech Tianjin 300072 Peoples R China Ryerson Polytech Inst Toronto ON M5A 2K3 Canada

Three kinds of the model of crack normal to the bimaterialinterface are studied by an experimental method. The highly sensitivemoire interferometry technique is employed to obtain the displacementfields near the crack tip. The singularities of the three kinds ofmodel are determined and analyzed by the experimental method andcompared and discussed.

关键词： singularities crack normal to interface experimental analysis

APPLICATION OF PARA-FOURIER INTEGRAL OPERATORS TO PROPAGATION OF NONLINEAR singularities

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Science China Mathematics 1990年第9期33卷 1060-1071页

作者：仇庆久 Department of Mathematics Nanjing University Nanjing 210008 PRC

In this paper, the author applies the Egorov Theorem for paradifferential operators established by the theory of para-Fourier integral operators to reduce microlocally paradifferential operators with the principal type. This reduction is used to study the propagation of singularities for solutions to nonlinear differential equations in the lower frequency range.

关键词： (principal type) paradifferential operators (adjoint) para-Fourier integral operators microlocal reduction propagation of singularities with lower frequency.

ON THE singularities OF COMPOSITION OF ENTIRE FUNCTIONS

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Analysis in Theory and Applications 2005年第4期21卷 370-376页

作者： A.P.Singh R.Sharma University of Jammu India

Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.

关键词： asymptotic values critical values entire functions singularities wandering domain

Deceleration Parameter Q(Z) and Examining If a Joint DM-DE Model Is Feasible, with a Revisit to the Question of Cosmic singularities

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Journal of High Energy Physics, Gravitation and Cosmology 2016年第3期2卷 362-382页

作者： Andrew Beckwith Department of Physics Chongqing University Chongqing China

This paper is a revisit to a 2011 document, with the addition of results pertinent to singularities in the case of a single repeating universe, as well as when the multiverse voids the necessity of a classical GR singularity. When a classical singularity does not exist, it impacts the formation of a massive graviton for reasons brought up, and allows for reacceleration of the universe due to massive gravitons. The existence of massive gravitons would also affect initial entropy, and also lead to the datum, that a calculated inflaton may re-emerge after fading out in the aftermath of inflation. The inflaton may be a contributing factor, with non-zero graviton mass, in reacceleration of the universe a billion years ago. The inflaton is a source of reacceleration of the universe, especially if the effects of a re-emergent inflaton are in tandem with the appearance of macro effects of a small graviton mass, leading to a speed up of the rate of expansion of the universe one billion years ago, at red shift value of Z ~ 0.423. We find that the graviton being massless or massive directly affects graviton contributions to reacceleration of the universe, with other phenomenological consequences. Finally we give our own counterpart as to how much space-time should be transferred to the present cosmological inflationary cycle which may permit preservation of Planks constant value and support Corda’s brilliant “gravity’s breath” document.

关键词： Inflaton Non Zero Graviton Mass Emergent Structure BBN singularities

Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple singularities

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Journal of Applied Mathematics and Physics 2019年第7期7卷 1572-1598页

作者： Hyunju Kim Department of Mathematics North Greenville University Tigerville SC USA

In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0?space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.

关键词： Mapping Method Non-Uniform Rational B-Spline (NURBS) Galerkin Approximation Isogeometric Analysis Multiple singularities

Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint singularities in Weighted Hölder Spaces

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Applied Mathematics 2014年第17期5卷 2779-2785页

作者： Oleksandr Karelin Anna Tarasenko Institute of Basic Sciences and Engineering Hidalgo State University Pachuca Mexico

In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.

关键词： Endpoint singularities Weighted Holder Space Weighted Lebesgue Spaces Relation between Norms Boundedness