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MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS
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作者 陈彬 高永帅 +1 位作者 郭玉劲 吴越 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期984-996,共13页
This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers... This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously. 展开更多
关键词 decaying nonlinearity L~2-subcritical MINIMIZERS bounded domains mass concentration
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L^p Boundedness of Commutators of Calderón-Zygmund Singular Integral Operators 被引量:8
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作者 邓东皋 颜立新 《数学进展》 CSCD 北大核心 1998年第3期259-269,共11页
本文证明了当b∈BMO时,具有弱核的CalderónZygmund奇异积分算子的交换子[b,T]f=bT(f)-T(bf)是Lp(1<p<∞)有界的.一个等价的命题是双线性算子gT(f)-fT(g)∈H1,只... 本文证明了当b∈BMO时,具有弱核的CalderónZygmund奇异积分算子的交换子[b,T]f=bT(f)-T(bf)是Lp(1<p<∞)有界的.一个等价的命题是双线性算子gT(f)-fT(g)∈H1,只要f∈Lp,g∈Lq,1<p<∞,1p+1q=1. 展开更多
关键词 交换子 HARDY空间 奇异积分算子 L^P有界性
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Pacman Renormalization in Siegel Parameters of Bounded Type
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作者 Carlos Antonio Marin-Mendoza Rogelio Valdez-Delgado 《Advances in Pure Mathematics》 2023年第10期674-693,共20页
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorial... A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant. 展开更多
关键词 Siegel Parameters Pacman Renormalization bounded Type Continued Fraction
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An Example of a Bounded Potential q(x) on the Half-Line, for Estimates of A(α) Amplitude
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作者 Herminio Blancarte 《Applied Mathematics》 2023年第2期130-149,共20页
We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schr&#246;dinger Equation, and show us ... We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schr&#246;dinger Equation, and show us the Estimates of the A(α) amplitude. 展开更多
关键词 The Amplitude A(α) as a Function of the Phase α Estimates of the A(α) Amplitude A bounded Potential on the Half Line
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Error reachable set based stabilization of switched linear systems with bounded peak disturbances
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作者 Xinxin Shang Songlin Zhuang +1 位作者 Tianyu Tan Yang Shi 《Journal of Automation and Intelligence》 2023年第2期87-98,共12页
This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clock... This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results. 展开更多
关键词 bounded peak disturbances Persistent dwell-time Reachable set minimization Stability and stabilization Switched systems
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Theoretical investigation of excited dipole bound states of alkali-containing diatomic anions
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作者 连艺 肖利丹 +2 位作者 边丽丽 徐海峰 闫冰 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第5期389-393,共5页
Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic st... Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules. 展开更多
关键词 ANIONS dipole bound states alkali-metal-containing diatomic molecules
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Chiral bound states in a staggered array of coupled resonators
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作者 金伍林 李静 +2 位作者 卢竞 龚志瑞 周兰 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期124-130,共7页
We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two ty... We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained. 展开更多
关键词 bound states two-level small atom coupled-resonator array CHIRALITY
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Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM
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作者 Hongke CAI Yaqin MAO +2 位作者 Xuanhao ZHU Yunfei FU Renjun ZHOU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第3期391-406,共16页
Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These ... Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells. 展开更多
关键词 TRMM minimum bounding rectangle minimum circumscribed ellipse
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Coulomb-assisted nonlocal electron transport between two pairs of Majorana bound states in a superconducting island
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作者 王浩迪 任俊潼 +1 位作者 吕海峰 柯莎莎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第5期275-279,共5页
We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majoran... We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majorana bound state(MBS)is coupled to one lead via a quantum dot with resonant levels.In this device,the nonlocal correlations can be induced in the absence of Majorana energy splitting.We find that the negative differential conductance and giant current noise cross correlation could be induced,due to the interplay between nonlocality of MBSs and dynamical Coulomb blockade effect.This feature may provide a signature for the existence of the MBSs. 展开更多
关键词 Majorana bound states superconducting island current cross correlation
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Holevo bound independent of weight matrices for estimating two parameters of a qubit
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作者 牛畅 郁司夏 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期137-143,共7页
Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly... Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed. 展开更多
关键词 quantum metrology quantum Fisher information Holevo bound quantum multi-parameter estimation
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Iterative physical optics method based on efficient occlusion judgment with bounding volume hierarchy technology
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作者 Yang Su Yu-Mao Wu Jun Hu 《Journal of Electronic Science and Technology》 EI CAS CSCD 2024年第1期1-12,共12页
This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the ... This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios. 展开更多
关键词 bounding volume hierarchy Cavity scattering Iterative physical optics(IPO)
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Interface state-based bound states in continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system
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作者 杨嘉玲 史奥芊 +2 位作者 彭宇宸 彭鹏 刘建军 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第8期288-293,共6页
We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by ... We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system.We extensively classify and study these BICs and BCR modes,which exhibit high-quality(high-Q)factors,in different regions relative to the interface of the system.These BICs and BCR modes with a high-Q factor have been studied in detail based on distinctive structural parameters and scattering theory.The outcomes of this research break the periodic limitation of interface state-based BICs,and realize more and higher symmetry interface state-based BICs and BCR modes.Moreover,we can control the region where light is captured by adjusting the frequency,and show that the Q factor of BICs is more closely related to the ordinal number of rings and the rotational symmetry number of the system. 展开更多
关键词 bound states in the continuum below continuum resonance modes high-quality factors
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Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings
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作者 江孝伟 方彬 占春连 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期393-400,共8页
Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Current... Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future. 展开更多
关键词 bound state in the continuum Goos-Hänchen shift dielectric compound grating material asymmetry
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A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow
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作者 Hao Li Xiangxiong Zhang 《Communications on Applied Mathematics and Computation》 EI 2024年第1期113-141,共29页
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple boun... For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field. 展开更多
关键词 Finite difference MONOTONICITY bound-preserving Discrete maximum principle Passive convection Incompressible flow Total variation bounded limiter
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Oriented Bounding Box Object Detection Model Based on Improved YOLOv8
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作者 ZHAO Xin-kang SI Zhan-jun 《印刷与数字媒体技术研究》 CAS 北大核心 2024年第4期67-75,114,共10页
In the study of oriented bounding boxes(OBB)object detection in high-resolution remote sensing images,the problem of missed and wrong detection of small targets occurs because the targets are too small and have differ... In the study of oriented bounding boxes(OBB)object detection in high-resolution remote sensing images,the problem of missed and wrong detection of small targets occurs because the targets are too small and have different orientations.Existing OBB object detection for remote sensing images,although making good progress,mainly focuses on directional modeling,while less consideration is given to the size of the object as well as the problem of missed detection.In this study,a method based on improved YOLOv8 was proposed for detecting oriented objects in remote sensing images,which can improve the detection precision of oriented objects in remote sensing images.Firstly,the ResCBAMG module was innovatively designed,which could better extract channel and spatial correlation information.Secondly,the innovative top-down feature fusion layer network structure was proposed in conjunction with the Efficient Channel Attention(ECA)attention module,which helped to capture inter-local cross-channel interaction information appropriately.Finally,we introduced an innovative ResCBAMG module between the different C2f modules and detection heads of the bottom-up feature fusion layer.This innovative structure helped the model to better focus on the target area.The precision and robustness of oriented target detection were also improved.Experimental results on the DOTA-v1.5 dataset showed that the detection Precision,mAP@0.5,and mAP@0.5:0.95 metrics of the improved model are better compared to the original model.This improvement is effective in detecting small targets and complex scenes. 展开更多
关键词 Remote sensing image Oriented bounding boxes object detection Small target detection YOLOv8
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Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity
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作者 Hans-Peter Morsch 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第2期562-573,共12页
Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix... Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected. 展开更多
关键词 Quantum Field Theory of Fermion and Boson Fields Hadrons and Leptons Described as bound States of Relativistic Fermions and Bosons Leading to a Total Energy Equal to Zero
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Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search
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作者 Xiao Liu Pingting Lin +2 位作者 Fan Bu Shaoling Zhuang Shoudao Huang 《CES Transactions on Electrical Machines and Systems》 EI CSCD 2024年第1期32-42,共11页
The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regressi... The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems. 展开更多
关键词 Generator optimization Gaussian Process Regression(GPR) Conditional Likelihood Lower bound Search(CLLBS) Constraint improvement expectation(CEI) Finite element calculation
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Qualitative and quantitative analysis of characteristic free and bound phenolics in three colored quinoas
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作者 Jianxin Song Dezhi Gao Xiaodong Wang 《Journal of Polyphenols》 2024年第2期78-86,共9页
Quinoa is a good source of phenolics,which both exist as free and bound forms.In order to mark clear the characteristic free and bound phenolics in different quinoa samples,in this study,characteristic free and bound ... Quinoa is a good source of phenolics,which both exist as free and bound forms.In order to mark clear the characteristic free and bound phenolics in different quinoa samples,in this study,characteristic free and bound phenolics in three colored quinoas including WQ(white quinoa),RQ(red quinoa)and BQ(black quinoa)were investigated.Result showed a total of 14 phenolics both acted as free and bound form were analyzed in three colored quinoas(WQ,RQ and BQ).Gallic acid,vanillic acid,epicatechin,p-coumaric acid and quercetin existed both as free and bound forms were common phenolics in quinoas.The highest total free phenolics(238.10 mg/kg)and bound phenolics(3377.75 mg/kg)were presented in WQ and RQ,respectively.It indicated WQ and RQ were respectively good source of free and bound phenolics.Moreover,characteristic free and bound phenolics in three colored quinoas could be well analyzed by principal component analysis(PCA),indicating it was an effective and reliable method in distinguishing three colored quinoas based on their characteristic free and bound phenolics,respectively. 展开更多
关键词 QUINOA free phenolics bound phenolics PCA
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基于Bounding Box的车辆行为标注
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作者 雷承学 申彩英 +1 位作者 王佳馨 于睿烨 《现代车用动力》 2024年第3期1-5,60,共6页
针对目前自动驾驶汽车行为预测对目标行为标注准确率低及压线行驶行为无法标注问题,首先通过建立车辆包围盒(Bounding Box)将车辆的形状描述出来,随后通过Bounding Box 4个顶点与车道线的相交关系来判断目标车是否有换道行为。对于无车... 针对目前自动驾驶汽车行为预测对目标行为标注准确率低及压线行驶行为无法标注问题,首先通过建立车辆包围盒(Bounding Box)将车辆的形状描述出来,随后通过Bounding Box 4个顶点与车道线的相交关系来判断目标车是否有换道行为。对于无车道线的情况,首先通过自车轨迹左右拓展出虚拟车道线,通过Bounding Box与虚拟车道线的关系判断目标车是否有切入自车道的行为,随后进行标注。通过Bounding Box对目标行为进行标注可以将标注的准确率提高至80%,并且可以将压线行驶行为标注出来,为后续行为预测模型训练打下良好的基础。 展开更多
关键词 换道行为 车辆包围盒 切入自车道 虚拟车道线
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Completeness of bounded model checking temporal logic of knowledge
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作者 刘志锋 葛云 +1 位作者 章东 周从华 《Journal of Southeast University(English Edition)》 EI CAS 2010年第3期399-405,共7页
In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge... In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system's reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed. 展开更多
关键词 bounded model checking temporal logics of knowledge multi-agent system
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