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Optimal convex approximations of qubit states based on l1-norm of coherence 认领 引用
1
作者 Li-Qiang Zhang Yan-Dong Du Chang-Shui Yu 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第8期475-491,共17页
Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In t... Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In this paper,we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the l1-norm of coherence of the target quantum state,striving to make the prepared state and the target state as similar as possible.Here,we present the analytical solution for the optimal distance for any N given quantum states.We find that the optimal approximation problem for any N>4 quantum states can be transformed into an optimal approximation problem for no more than four quantum states,which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation.Ultimately,a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach. 展开更多
关键词 quantum information processing quantum resource theory quantum coherence optimal convex approximations
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Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises 认领 引用 被引量：1
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作者 Yanzhao Cao Jialin Hong Zhihui Liu 《Communications in Mathematical Research》 CSCD 2020年第2期113-127,共15页
The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises.The n... The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises.The noise term is approximated through the spectral projection of the covariance operator,which is not required to be commutative with the Laplacian operator.Through the convergence analysis of SPDEs with the noise terms replaced by the projected noises,the well-posedness of the SPDE is established under certain covariance operator-dependent conditions.These SPDEs with projected noises are then numerically approximated with the finite element method.A general error estimate framework is established for the finite element approximations.Based on this framework,optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are obtained.It is shown that with the proposed approach,convergence order of white noise driven SPDEs is improved by half for one-dimensional problems,and by an infinitesimal factor for higher-dimensional problems. 展开更多
关键词 Elliptic stochastic partial differential equation spectral approximations finite element approximations power-law noise
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Improved Analytical Approximations to the Scattering Solutions of the Schrdinger Equation with a Hyperbolical Potential 认领 引用 被引量：1
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作者 尤源 陆法林 +1 位作者 孙东升 陈昌远 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第9期315-319,共5页
Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalize... Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalized wavefunctions are presented. All data calculated by the above approximate analytical formula are compared with those obtained by using the numerical integration method in the scattering state cases. We find that this improved approximate formula is better than previous one since the calculated results are in good agreement with those exact ones. 展开更多
关键词 hyperbolic potential scattering solutions analytical approximations
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POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY 认领 引用 被引量：3
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作者 刘红霞 潘涛 《Acta Mathematica Scientia》 SCIE 2009年第1期111-128,共18页
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn... This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ... 展开更多
关键词 Scalar conservation laws with boundary vanishing viscosity approximations error estimate pointwise convergence rate transport inequality
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Operators of Approximations and Approximate Power Set Spaces 认领 引用 被引量：6
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作者 张贤勇 莫智文 舒兰 《Journal of Electronic Science and Technology of China》 2004年第2期94-96,共3页
Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, co... Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space. 展开更多
关键词 rough sets approximation operators operators of approximations power set space approximate power set spaces
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Generalized multi-layered granulations and approximations based on neighborhood systems under incomplete information systems 认领 引用
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作者 何明 冯博琴 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2005年第2期205-208,共4页
A generalized multi-layered granulation structure used by neighborhood systems is proposed. With granulated views, the concepts of approximations under incomplete information systems are studied, which are represented... A generalized multi-layered granulation structure used by neighborhood systems is proposed. With granulated views, the concepts of approximations under incomplete information systems are studied, which are represented by covering of the universe. With respect to different levels of granulations, a pair of lower and upper approximations is defined and an approximation structure is investigated, which lead to a more general approximation structure. The generalized multi-layered granulation structure provides a basis of the proposed framework of granular computing. Using this framework, the interesting and useful results about information granulation and approximation reasoning can be obtained. This paper presents some useful explorations about the incomplete information systems from information views. 展开更多
关键词 rough set approximations neighborhood systems granular computing
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A meshless algorithm with moving least square approximations for elliptic Signorini problems 认领 引用 被引量：1
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作者 王延冲 李小林 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第9期35-42,共8页
Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection ope... Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm. 展开更多
关键词 meshless method Signorini problem moving least square approximations convergence
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Basic belief assignment approximations using degree of non-redundancy for focal element 认领 引用 被引量：4
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作者 Yi YANG Deqiang HAN Jean DEZERT 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2019年第11期2503-2515,共13页
Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combinatio... Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches. 展开更多
关键词 BBA approximation Belief functions Evidence theory Focal element Non-redundancy
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The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations 认领 引用
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作者 Kamyar Hosseini Mousa Ilie +3 位作者 Mohammad Mirzazadeh Dumitru Baleanu Choonkil Park Soheil Salahshour 《Communications in Theoretical Physics》 SCIE CAS CSCD 2022年第7期21-29,共9页
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention,in the last decades.The main aim of the current investigation is to consider the time-fr... Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention,in the last decades.The main aim of the current investigation is to consider the time-fractional Sharma–Tasso–Olver–Burgers(STOB)equation in the Caputo–Fabrizio(CF)context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method(HAM)and the Laplace transform.The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition forφ(x,t;u)as the kernel and giving some theorems.To illustrate the CF operator effect on the dynamics of the obtained solitons,several two-and threedimensional plots are formally considered.It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context. 展开更多
关键词 time-fractional Sharma-Tasso-Olver-Burgers equation Caputo-Fabrizio context mixed approach existence and uniqueness valid approximations
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Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens 认领 引用 被引量：1
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作者 A.Yildirim A.Gokdogan +1 位作者 M.Merdan V.Lakshminarayanan 《Chinese Physics Letters》 SCIE EI CAS CSCD 2012年第7期99-102,共4页
An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed,using the multi-step differential transform method based o... An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed,using the multi-step differential transform method based on the classical differential transformation method.Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the precision and effectiveness of the proposed method.Results are given in explicit and graphical forms. 展开更多
关键词 method Approximation convergent
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The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations 认领 引用
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作者 FINZEL Kati BULTINCK Patrick 《物理化学学报》 SCIE CAS CSCD 北大核心 2018年第6期650-655,共6页
In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potentia... In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy. 展开更多
关键词 The Influence of the Exchange-Correlation Functional the Non-Interacting Kinetic Energy Density Functional Approximations
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Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces 认领 引用 被引量：2
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作者 何金苏 李冲 《Journal of Southeast University(English Edition)》 CAS 2001年第1期70-72,共3页
The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly uniqu... The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.  展开更多
关键词 best approximation RS set strong uniqueness
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Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D 认领 引用 被引量：1
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作者 L.Giraud A.Haidar Y.Saad 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第3期276-294,共19页
In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schu... In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported. 展开更多
关键词 Hybrid direct/iterative solver domain decomposition incomplete/partial factorization Schur approximation scalable preconditioner convection-diffusion large 3D problems parallelscientific computing High Performance Computing.
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ON INVARIANT RANDOM APPROXIMATIONS 认领 引用
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作者 Ismat Beg Naseer Shahzad 《Analysis in Theory and Applications》 1996年第3期68-72,共5页
A result regarding invariant random approximation is proved.
关键词 ON INVARIANT RANDOM APPROXIMATIONS
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CONTINUOUS AND DISCRETE N-CONVEX APPROXIMATIONS 认领 引用
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作者 D.Legg D.Townsend 《Analysis in Theory and Applications》 1992年第4期28-34,共7页
We show that the best L_p-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations.The techniques of the proof are then used to show the existence of near interpolants... We show that the best L_p-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations.The techniques of the proof are then used to show the existence of near interpolants to discrete n-convex data by continuous n-convex functions if the data points are close. 展开更多
关键词 CONTINUOUS AND DISCRETE N-CONVEX APPROXIMATIONS
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PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 认领 引用 被引量：1
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作者 A. Bensebah F. Dubeau J. Gelinas 《Analysis in Theory and Applications》 1997年第3期78-90,共13页
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th... A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given. 展开更多
关键词 PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS ODE
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Notes on Rough Set Approximations and Associated Measures 认领 引用 被引量：4
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作者 YAO Yiyu 《浙江海洋学院学报（自然科学版）》 2010年第5期399-410,共12页
We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,i... We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented. 展开更多
关键词 Accuracy measures Granularity Rough set approximations Roughness
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Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models 认领 引用 被引量：1
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作者 Qianli Di 《Open Journal of Modelling and Simulation》 2022年第4期349-390,共42页
In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Expo... In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance. 展开更多
关键词 Latent Force Model COVID-19 Quasi-Monte Carlo Approximations
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Diffusion approximations for multiclass queueing networks under preemptive priority service discipline 认领 引用
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作者 戴万阳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第10期1331-1342,共12页
We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the system... We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems. Such queueing networks appear typically in high-speed integrated services packet networks about telecommunication system. In the network, there is a number of packet traffic types. Each type needs a number of job classes （stages） of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service. Moreover, there is no inter-routing among different traffic types throughout the entire network. 展开更多
关键词 queueing network preemptive priority heavy traffic semimartingale re-flecting Brownian motion fluid model diffusion approximation Lyapunov function
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ASYMPTOTIC APPROXIMATIONS OF R-STIRLING NUMBERS 认领 引用
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作者 C. B. Corcino L. C. Hsu E. L. Tan 《Analysis in Theory and Applications》 1999年第3期13-25,共13页
Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Te... Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Temme[13], to put the integral representations in volved into a form on which we can apply the saddle point 展开更多
关键词 Math ASYMPTOTIC APPROXIMATIONS OF R-STIRLING NUMBERS
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