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Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers
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作者 杨薇 程雪苹 +1 位作者 金桂鸣 王佳楠 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期170-178,共9页
We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota b... We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one. 展开更多
关键词 nondegenerate solitons variable coefficients coupled nonlinear Schr?dinger equations Hirota bilinear method
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Atomic coherence in nondegenerate four-wave mixing 被引量:2
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作者 左战春 孙江 +5 位作者 刘霞 米辛 俞祖和 姜谦 傅盘铭 吴令安 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第4期1042-1046,共5页
Two-photon resonant nondegenerate four-wave mixing (NFWM) with the addition of a coupling field in Ba atomic vapour has been studied. We find that coherence of the atomic level transitions leads to suppression of th... Two-photon resonant nondegenerate four-wave mixing (NFWM) with the addition of a coupling field in Ba atomic vapour has been studied. We find that coherence of the atomic level transitions leads to suppression of the NFWM signal, giving rise to a dip with a linewidth that is linearly proportional to the intensity of the coupling field. 展开更多
关键词 nondegenerate four-wave mixing electromagnetically induced transparency
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Path Integral Formalism for Nondegenerate Parametric Amplifiers in Entangled State Representation
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作者 FANHong-Yi LIChao +1 位作者 LIUQiu-Yu AlfredWiinsche 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期998-1002,共5页
We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
关键词 path integral entangled states nondegenerate parametric amplifier
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Intrinsic polarization conversion and avoided-mode crossing in X-cut lithium niobate microrings
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作者 谭泽林 张检发 +4 位作者 朱志宏 陈伟 邵铮铮 刘肯 秦石乔 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期398-403,共6页
Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology... Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology of waveguide cross section and scattering. Here, we study the polarization conversion mechanism in 1-THz-FSR X-cut lithium niobate microrings with multiple-resonance condition, that is the conversion can be implemented by birefringence of waveguides,which will also introduce an avoided-mode crossing. In the experiment, we find that this mode crossing results in severe suppression of one sideband in local nondegenerate four-wave mixing and disrupts the cascaded four-wave mixing on this side. Simultaneously, we propose one two-dimensional method to simulate the eigenmodes(TE and TM) in X-cut microrings, and the mode crossing point. This work will provide one approach to the design of polarization converters and simulation for monolithic photonics integrated circuits, and may be helpful to the studies of missed temporal dissipative soliton formation in X-cut lithium niobate rings. 展开更多
关键词 polarization conversion BIREFRINGENCE nondegenerate four-wave mixing
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Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control
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作者 TAHRI Mohamed BENKHEDDA Hanane BENAISSA Abbes 《Journal of Partial Differential Equations》 CSCD 2021年第3期201-223,共23页
In this paper,we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary.We proved the polynomial decay result with an estimation of the decay r... In this paper,we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary.We proved the polynomial decay result with an estimation of the decay rates.Our result is established using the frequency-domain method and Borichev-Tomilov theorem. 展开更多
关键词 nondegenerate wave equation fractional boundary control Frequency domain method Optimal polynomial stability
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Effects of Atomic Coherence and Injected Classical Field on Chaotic Dynamics of Non-degenerate Cascade Two-Photon Lasers 被引量:1
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作者 ZHANG Ya-Jun HUANG Hong-Bin +1 位作者 YANG Peng XIE Xia 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2X期288-294,共7页
Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into th... Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations. 展开更多
关键词 nondegenerate cascade two-photon laser chaos bifurcation injected classical field atomic coherence
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关于沪市A股市场规模效应的实证研究
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作者 王萍 《运筹与管理》 CSCD 2006年第2期119-123,共5页
本文是用上证180指数的180支样本股票所产生的数据和Robert Fernholz提出的新方法来验证规模效应在沪市A股市场的存在性。
关键词 流通市值 规模效应 pathwise mutually nondegenerate 半鞅 局部时
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A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES
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作者 J.M. Soriano C. Ding 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期535-540,共6页
It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.
关键词 Autonomous system continuation methods TRAJECTORY nondegenerate critical point zero point stationary trajectory stable trajectory asymptotically stable Morse inequalities
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Continuous variable entanglement generation in coupled cavities
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作者 潘桂侠 肖瑞杰 周玲 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第1期98-103,共6页
We investigate continuous variable entanglement produced in two distant coupled cavities, in which two four-level atoms are driven by classical fields respectively. Under the large detuning condition, an effective Ham... We investigate continuous variable entanglement produced in two distant coupled cavities, in which two four-level atoms are driven by classical fields respectively. Under the large detuning condition, an effective Hamiltonian containing the square of the creation (annihilation) operator of the cavity field is derived. Due to the nonlinearity, entanglement formally created by the beam splitter type interaction is transformed into the nondegenerate parametric down conversion type. Employing the operator algebraic method, we study the time evolution of the entanglement condition, and show that the system provides us an advantage in achieving a larger photon number with better entanglement. We also discuss the dissipation of the cavities affecting the entanglement. 展开更多
关键词 continuous variable entanglement coupled cavities nondegenerate parametric down conversion cavity dissipation
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COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OFΔ(3,3,k)
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作者 M.Ashiq Q.Mushtaq 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期363-370,共8页
Let q be a prime power. By PL(Fq) the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphis... Let q be a prime power. By PL(Fq) the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △(3, 3, k) = (u, v: u^3 = v^3 = (uv)^k = 1〉on PL(Fq), where q ≡ ±1(modk). Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △(3, 3, k) on PL(Fq). The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by (u^-v^-)^k. In this way, they get △(3, 3, k) as permutation groups on PL(Fq). 展开更多
关键词 Coset diagrams conjugacy classes nondegenerate homomorphism projec tire line and triangle groups
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A two-mode squeezed light based on a double-pump phase-matching geometry
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作者 Xuan-Jian He Jun Jia +3 位作者 Gao-Feng Jiao Li-Qing Chen Chun-Hua Yuan Wei-Ping Zhang 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第7期337-345,共9页
We theoretically investigate the frequency-nondegenerate and frequency degenerate squeezed lights with a four-wave mixing process(4WM)driven by two pump fields crossing at a small angle.Different from a 4WM process dr... We theoretically investigate the frequency-nondegenerate and frequency degenerate squeezed lights with a four-wave mixing process(4WM)driven by two pump fields crossing at a small angle.Different from a 4WM process driven by a single pump field,the refractive index of the corresponding probe field,np,can be converted to a value that is greater than 1 or less than 1 by an angle adjustment.In the new region with np<1,the bandwidth of the gain is relatively large due to the slow change in the refractive index with the two-photon detuning.In this region with an exchange of the roles of the pump and probe beams,the frequency degenerate and spatial nondegenerate twin beams can be generated,which has potential application in quantum information and quantum metrology. 展开更多
关键词 four-wave mixing phase matching frequency degenerate and spatial nondegenerate metrology
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On C^(1 ,α) Regularity for Monge- Ampre Equation
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作者 胡云姣 保继光 《Northeastern Mathematical Journal》 CSCD 2000年第1期46-50,共5页
In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both deg... In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both degenerate and nondegenerate cases. 展开更多
关键词 Global C 1 1/4 regularity Monge Ampère equation degenerate and nondegenerate cases
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Some Results on Completly Restricted Lie Superalgebras 被引量:1
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作者 陈良云 孟道骥 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2005年第2期191-196,共6页
This paper is devoted to the study of completely restricted Lie superalgebras. We give some sufficient and necessary conditions for both completely restricted Lie superalgebras and strongly completely restricted Lie s... This paper is devoted to the study of completely restricted Lie superalgebras. We give some sufficient and necessary conditions for both completely restricted Lie superalgebras and strongly completely restricted Lie superalgebras. Some other important results on completely restricted Lie superalgebras are also obtained. 展开更多
关键词 completely restricted Lie superalgebras strongly completely restricted Lie superalgebras nondegenerate Killing form.
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Certifying the Global Optimality of Quartic Minimization over the Sphere 被引量:1
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作者 Sheng-Long Hu 《Journal of the Operations Research Society of China》 EI CSCD 2022年第2期241-287,共47页
The quartic minimization over the sphere is an NP-hard problem in the general case.There exist various methods for computing an approximate solution for any given instance.In practice,it is quite often that a global o... The quartic minimization over the sphere is an NP-hard problem in the general case.There exist various methods for computing an approximate solution for any given instance.In practice,it is quite often that a global optimal solution was found but without a certification.We will present in this article two classes of methods which are able to certify the global optimality,i.e.,algebraic methods and semidefinite program(SDP)relaxation methods.Several advances on these topics are summarized,accompanied with some emerged new results.We want to emphasize that for mediumor large-scaled instances,the problem is still a challenging one,due to an apparent limitation on the current force for solving SDP problems and the intrinsic one on the approximation techniques for the problem. 展开更多
关键词 Quartic minimization Tensor SPHERE Global optimality Elimination method Critical points EIGENVECTORS Determinant nondegenerate Characteristic polynomial SDP relaxations Moment matrix Flatness POSITIVSTELLENSATZ Nonnegative polynomial Sums of squares Duality
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A HOPF INDEX THEOREM FOR A REAL VECTOR BUNDLE 被引量:1
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作者 FENGHUITAO GUOENLI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第4期507-518,共12页
The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.
关键词 Super-twisted signature operator nondegenerate section in the sense of Bott Hopf index theorem Euler characteristic
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Nondegenerative ML-sequences over ring Z/(2~e)
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作者 YANG Junhui and ZHAI QibinInstitute of Software , Chinese Academy of Sciences , Beijing 100080, China State Key Laboratory of Information Security , Beijing 100080, China 《Chinese Science Bulletin》 SCIE EI CAS 1999年第17期1557-1561,共5页
The so-called quasi-period of an ML-sequence has been introduced. It is noted that an ML-sequence may degenerate in the sense that it has the quasi-period shorter than its period, and the problem of constructing the n... The so-called quasi-period of an ML-sequence has been introduced. It is noted that an ML-sequence may degenerate in the sense that it has the quasi-period shorter than its period, and the problem of constructing the nondegenerative ML-sequences has been solved by giving a criterion for nondegenerative primitive polynomials. 展开更多
关键词 nondegenerate ML-sequence quasi-period.
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Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria
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作者 JoséDaniel López-Barrientos 《Journal of the Operations Research Society of China》 EI 2014年第4期395-421,共27页
This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The sy... This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The system is assumed to be a nondegenerate diffusion.We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation.We also ensure the convergence of a sequence of such solutions,of the corresponding sequence of policies,and,ultimately,of the PIA. 展开更多
关键词 Ergodic payoff criterion Zero-sum stochastic differential games Policy iteration algorithm nondegenerate diffusions Poisson equation Schäl convergence Bias game
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Zero Product Determined Jordan Algebras, II
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作者 Mateja Grasic 《Algebra Colloquium》 SCIE CSCD 2015年第1期109-118,共10页
The Albert algebra and the Jordan algebra of a nondegenerate symmetric bilinear form are shown to be zero product determined.
关键词 zero product determined Jordan algebra Albert algebra Jordan algebra ofa nondegenerate symmetric bilinear form
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Limit theorems for a supercritical branching process with immigration in a random environment 被引量:10
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作者 WANG YanQing LIU QuanSheng 《Science China Mathematics》 SCIE CSCD 2017年第12期2481-2502,共22页
Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normaliz... Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n. 展开更多
关键词 branching process with immigration random environment almost sure convergence nondegeneration Lpconvergence and moments large and moderate deviations central limit theorem
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