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Bounds on Fractional-Based Metric Dimension of Petersen Networks
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作者 Dalal Awadh Alrowaili Mohsin Raza Muhammad Javaid 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2697-2713,共17页
The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we st... The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity. 展开更多
关键词 Metric dimension local fractional metric dimension Petersen network local resolving neighborhoods
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Lipschitz Estimates for Commutators of N-dimensional Fractional Hardy Operators 被引量:8
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作者 ZHENG QING-YU Fu ZUN-WEI 《Communications in Mathematical Research》 CSCD 2009年第3期241-245,共5页
In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q ... In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = (α+β)/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p(R^n) is obtained. 展开更多
关键词 COMMUTATOR n-dimensional fractional Hardy operator Lipschitz function Herz space
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Application of the Algorithm of Fractional Dimension to Extraction Image Edge
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作者 Qiang Luo Qingli Ren 《稀有金属材料与工程》 SCIE EI CAS CSCD 北大核心 2006年第A03期605-606,共2页
The idea of fractional dimension was stated in brief firstly.Then,adopting the fractional statistical similar principle, the method of the least square minimum error was applied to evaluate the fractional dimension of... The idea of fractional dimension was stated in brief firstly.Then,adopting the fractional statistical similar principle, the method of the least square minimum error was applied to evaluate the fractional dimension of per image pixel depending on the fractional property of image.And the image edge is extracted by magnitude of fractional dimension of image pixel.We presented the algorithm of the local fractional dimension,which made the rule of window size and sentencing the fractional dimension of edge.Although this algorithm was waste time,it is better than the classical ones in extraction edge and anti-jamming. 展开更多
关键词 fractional dimension image edge fractional Brownian random field
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THE FRACTIONAL DIMENSION IDENTIFICATION METHOD OF CRITICAL BIFURCATED PARAMETERS OF BEARING-ROTOR SYSTEM
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作者 赵玉成 袁树清 +1 位作者 肖忠会 许庆余 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第2期141-146,共6页
The stable problem of rotor system, seen in many fields, has been cared for more. Nowadays the reasons of most losing stability are caused by nonlinear behaviors This presents higher requirements to the designing of m... The stable problem of rotor system, seen in many fields, has been cared for more. Nowadays the reasons of most losing stability are caused by nonlinear behaviors This presents higher requirements to the designing of motor system : considering nonlinear elements, avoiding the unstable parameter points or regions where nonlinear phenomena will be presented. If a family of time series of the unknown nonlinear dynamical system cart only be got ( may be polluted by noise), how to identify the change of motive properties at different parameters? In this paper, through the study of Jeffcott rotor system, the result that using the figures between the fractional dimension of rime-serial and parameter can be gained, and the critical bifurcated parameters of bearing-rotor dynamical system can be identified. 展开更多
关键词 fluid film bearing-rotor system BIFURCATION fractional dimension
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Fractional-dimensional approach for excitons in Ga As films on AlxGa(1-x)As substrates
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作者 武振华 陈蕾 田强 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第3期375-379,共5页
Binding energies of excitons in GaAs films on AlxGal-xAs substrates are studied theoretically with the fractional- dimensional approach. In this approach, the real anisotropic "exciton + film" semiconductor system ... Binding energies of excitons in GaAs films on AlxGal-xAs substrates are studied theoretically with the fractional- dimensional approach. In this approach, the real anisotropic "exciton + film" semiconductor system is mapped into an effective fractional-dimensional isotropic space. For different aluminum concentrations and substrate thicknesses, the exci- ton binding energies are obtained as a function of the film thickness. The numerical results show that, for different aluminum concentrations and substrate thicknesses, the exciton binding energies in GaAs films on AlxGal_xAs substrates all exhibit their maxima with increasing film thickness. It is also shown that the binding energies of heavy-hole and light-hole excitons both have their maxima with increasing film thickness. 展开更多
关键词 exciton binding energy GaAs film fractional-dimensional approach
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New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation 被引量:2
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作者 Zhiyun Zeng Xiaohua Liu +1 位作者 Yin Zhu Xue Huang 《Journal of Applied Mathematics and Physics》 2022年第2期333-346,共14页
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the co... In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions. 展开更多
关键词 Exact Traveling Wave Solutions (2 + 1)-dimensional Time-fractional Zoomeron Equation The New Mapping Approach The New Extended Auxiliary Equation Approach
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Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method
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作者 M. Nurul Islam M. Ali Akbar 《Journal of Applied Mathematics and Physics》 2018年第1期90-102,共13页
In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precise... In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical system changes in time. In order to determine the solutions a suitable transformation is considered to transmute the equations into a simpler ordinary differential equation (ODE) namely fractional complex transformation. We then use the modified simple equation (MSE) method to obtain new and further general exact wave solutions. The MSE method is more powerful and can be used in other works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical physics. The affect of obtaining parameters for its definite values which are examined from the solutions of two dimensional and three dimensional time-fractional Schrodinger equations are discussed and therefore might be useful in different physical applications where the equations arise in this article. 展开更多
关键词 MODIFIED SIMPLE EQUATION (MSE) METHOD fractionAL Differential EQUATION Nonlinear Evolution Equations Higher dimensional Schrodinger EQUATION Traveling Wave Transformation
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基于超声分层应变成像技术评价苓桂气化方改善射血分数保留心力衰竭早期大鼠心肌功能的研究 被引量:1
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作者 李知轩 杨晨光 +2 位作者 石玉姣 乔文博 董国菊 《环球中医药》 CAS 2024年第6期1007-1013,共7页
目的基于超声分层应变成像技术评价苓桂气化方改善射血分数保留心力衰竭(heart failure with preserved ejection fraction,HFpEF)早期大鼠心肌功能。方法40只SPF级SHR大鼠随机分为HFpEF模型组、恩格列净组、苓桂气化方低剂量组和苓桂... 目的基于超声分层应变成像技术评价苓桂气化方改善射血分数保留心力衰竭(heart failure with preserved ejection fraction,HFpEF)早期大鼠心肌功能。方法40只SPF级SHR大鼠随机分为HFpEF模型组、恩格列净组、苓桂气化方低剂量组和苓桂气化方高剂量组,10只WKY大鼠为空白组。采用高盐高脂高糖饮食及腹腔注射链脲佐菌素建立HFpEF早期大鼠模型,各组予相应干预9周后测量左室舒张末期内径、左室舒张末期后壁厚度、舒张早期血液速度/舒张早期二尖瓣环间隔侧组织多普勒频谱、左室射血分数以及左室心内膜下心肌整体纵向应变、中层心肌整体纵向应变、心外膜下心肌整体纵向应变、心内膜下心肌整体圆周应变、中层心肌整体圆周应变和心外膜下心肌整体圆周应变。酶联免疫吸附法测定血清B型脑尿钠肽。马松染色观察心肌组织病理变化。结果与模型组比较,恩格列净组心内膜下心肌整体纵向应变、中层心肌整体纵向应变和心内膜下心肌整体圆周应变明显升高(P<0.05),苓桂气化方低剂量组心内膜下心肌整体纵向应变和中层心肌整体纵向应变明显改善(P<0.05),苓桂气化方高剂量组心内膜下心肌整体纵向应变、中层心肌整体纵向应变和中层心肌整体圆周应变明显提升(P<0.05)。苓桂气化方低剂量组和苓桂气化方高剂量组心肌细胞间隙变窄,胶原纤维沉积减少。结论苓桂气化方能提高HFpEF早期模型大鼠心内膜下心肌整体纵向应变、中层心肌整体纵向应变、中层心肌整体圆周应变,改善左室重构和收缩功能。超声分层应变成像技术可以无创、定量、敏感检测HFpEF早期大鼠左室壁心肌改变。 展开更多
关键词 射血分数保留心力衰竭早期 二维超声斑点追踪技术 分层应变 苓桂气化方剂 心肌功能
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RT-3DE参数与射血分数保留心衰患者可溶性致癌抑制因子2水平及心功能分级的交互关系
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作者 郭倩倩 李斌 +1 位作者 王月丽 于玮 《医学影像学杂志》 2024年第10期30-34,共5页
目的探讨实时三维超声心动图(RT-3DE)参数与射血分数保留心衰(HFpEF)患者血清可溶性致癌抑制因子2(sST2)水平及心功能相关性。方法选取80例HFpEF患者作为HFpEF组,依据美国纽约心脏病协会(NYHA)分级分为:Ⅱ级(14例)、Ⅲ级(48例)、Ⅳ级(18... 目的探讨实时三维超声心动图(RT-3DE)参数与射血分数保留心衰(HFpEF)患者血清可溶性致癌抑制因子2(sST2)水平及心功能相关性。方法选取80例HFpEF患者作为HFpEF组,依据美国纽约心脏病协会(NYHA)分级分为:Ⅱ级(14例)、Ⅲ级(48例)、Ⅳ级(18例),另选择100例同期于我院体检的健康志愿者作为对照组,采用酶联免疫吸附测定法检测所有患者的血清sST2水平,所有患者均行常规超声心动图和RT-3DE检查,记录左心室6、12、16节段到达收缩期最小容积时间最大差异值标准化值(TmsvDif%)、标准差标准化值(TmsvSD%)和左心室射血分数(LVEF)、左心室收缩末容积(LVESV)、左心室舒张末容积(LVEDV);分析各RT-3DE参数与血清sST2水平及心功能之间的相关性。结果不同心功能分级HFpEF患者LVEF均明显低于对照组,且心功能等级越高LVEF越低,差异有统计学意义(P<0.05);不同心功能分级HFpEF患者LVEDV、LVESV明显高于对照组,且心功能等级越高LVEDV、LVESV越高,差异有统计学意义(P<0.05);不同心功能分级HFpEF患者Tmsv 6-SD%、Tmsv12-SD%、Tmsv16-SD%及Tmsv 6-Dif%、Tmsv 12-Dif%、Tmsv 16-Dif%较对照组均明显延长,且心功能等级越高,患者左心室6、12、16节段TmsvSD%和TmsvDif%时间越长,差异有统计学意义(P<0.05);不同NYHA分级HFpEF血清sST2表达水平高于对照组,且心功能分级较高的HFpEF患者sST2水平明显增高,差异有统计学意义(P<0.05)。相关性分析结果显示,RT-3DE相关参数LVEDV、LVESV、Tmsv6-SD%、Tmsv12-SD%、Tmsv16-SD%、Tmsv 6-Dif%、Tmsv 12-Dif%、Tmsv 16-Dif%均与NYHA心功能分级存在显著正相关性(r=0.687,0.752,0.501,0.565,0.581,0.522,0.596,0.603;P<0.05),LVEF与NYHA心功能分级存在负相关性(r=-0.731,P<0.05)。LVEDV、LVESV与血清sST2表达存在显著正相关性(r=0.335,0.356;P均<0.05),LVEF与血清sST2、心功能分级存在负相关性(r=-0.313,P<0.05)。结论RT-3DE能够有效监测HFpEF患者左心房容积功能和左心室舒张功能变化情况,RT-3DE相关参数与心功能分级密切相关,对于心衰患者程度评估具有重要价值。 展开更多
关键词 实时三维超声心动图 射血分数保留心衰 可溶性致癌抑制因子2 心功能分级 超声检查
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基于2D-STI获得左心房功能诊断老年尿毒症血透患者射血分数保留性心力衰竭的价值
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作者 岳岚 姜鹏涛 +1 位作者 洪丽杰 叶萌 《浙江临床医学》 2024年第8期1233-1234,1237,共3页
目的探讨超声心动图二维斑点追踪技术(2D-STI)在早期诊断老年尿毒症血液透析患者射血分数保留性心力衰竭(HFpEF)中的应用价值。方法选取2022年12月至2023年12月本院HFpEF患者30例(HFpEF组)以及无心力衰竭症状且射血分数>50%血透患者3... 目的探讨超声心动图二维斑点追踪技术(2D-STI)在早期诊断老年尿毒症血液透析患者射血分数保留性心力衰竭(HFpEF)中的应用价值。方法选取2022年12月至2023年12月本院HFpEF患者30例(HFpEF组)以及无心力衰竭症状且射血分数>50%血透患者30例(对照组),比较两组常规心脏超声下心功能相关指标、2D-STI下整体左心房储器功能、管道功能和收缩功能,并分析其相关性。结果两组患者左心房容积指数、左心房管道功能、储备功能水平、E/A及E/Em值比较,差异有统计学意义(P<0.05)。结论2D-STI技术可以作为老年尿毒症血液透析患者射血分数保留性心力衰竭早期诊断的依据,为临床早期的诊疗提供有效信息。 展开更多
关键词 超声心动图 二维斑点追踪 射血分数保留行心力衰竭 左房功能
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(3+1)-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的精确解
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作者 陈进华 字德荣 《红河学院学报》 2024年第5期136-140,共5页
借助Jumarie’s modified Riemann-Liouville导数的性质,将(3+1)-维时空分数阶Yu-Toda-Sasa-Fukuyama方程简化为常微分方程.通过构造一元三次多项式,运用完全判别法得到了(3+1)-维时空分数阶Yu-Toda-Sasa-Fukuyama方程的7组精确解.
关键词 (3+1)-维时空分数阶Yu-Toda-Sasa-Fukuyama方程 Jumarie’s modified Riemann-Liouville导数 精确解 多项式完全判别法 JACOBI椭圆函数
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Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter H∈(1/4,1/2) 被引量:2
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作者 李劲 黄建华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第2期189-208,共20页
A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameter ∈ (1/4,1/2) under the Dirichlet bounda... A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameter ∈ (1/4,1/2) under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the and the identity of the infinite double series spectrum of the spatial differential operator in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with ∈ (1/2,1) without any additional restriction on the parameter H. 展开更多
关键词 infinite-dimensional fractional Brownian motion (FBM) stochastic convolution stochastic nomNewtonian fluid random attractor
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Singular and non-topological soliton solutions for nonlinear fractional differential equations 被引量:4
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作者 Ozkan Guner 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第10期10-15,共6页
In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations(FDEs) based on a f... In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations(FDEs) based on a fractional complex transform and apply it to solve nonlinear space-time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics. 展开更多
关键词 SOLITONS ansatz method the space-time fractional Boussinesq equation the space-time fractional(2+l)-dimensional breaking soliton equations
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The Generalized Pythagorean Comma Harmonic Powers of a Fundamental Frequency Are Equivalent the Standing Wave Harmonic Fraction System
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作者 Donald Chakeres 《Advances in Pure Mathematics》 2018年第7期652-665,共14页
Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A C... Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system. 展开更多
关键词 Power LAWS HARMONIC Systems STANDING Wave HARMONIC fractionS dimensional Analysis Buckingham Pi Theorem PYTHAGOREAN COMMA
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The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion
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作者 Yirang Yuan Hongxing Rui +1 位作者 Dong Liang Changfeng Li 《International Journal of Geosciences》 2012年第5期972-991,共20页
Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations ... Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects. 展开更多
关键词 Seawater INTRUSION Three-dimensional Region UPWIND fractionAL STEPS NORM ESTIMATE Numerical Simulation
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FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE 被引量:4
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作者 袁益让 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期427-438,共12页
Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are t... Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred. 展开更多
关键词 General region semiconductor device 3-dimensional heat conduction characteristic finite difference parallel fractional steps l^2 error estimate.
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基于分数阶Tikhonov正则化的激光吸收光谱燃烧场二维重建光路优化研究 被引量:1
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作者 庞维煦 李宁 +4 位作者 黄孝龙 康杨 李灿 范旭东 翁春生 《物理学报》 SCIE EI CAS CSCD 北大核心 2023年第3期277-287,共11页
为探究基于激光吸收光谱技术的燃烧场二维测量光路布置方式,实现有限投影下更精确的燃烧场二维重建,根据分数阶微积分理论,提出一种基于分数阶Tikhonov正则化的光路优化方法.将经典的整数阶Tikhonov正则化推广到分数阶模式,建立了基于... 为探究基于激光吸收光谱技术的燃烧场二维测量光路布置方式,实现有限投影下更精确的燃烧场二维重建,根据分数阶微积分理论,提出一种基于分数阶Tikhonov正则化的光路优化方法.将经典的整数阶Tikhonov正则化推广到分数阶模式,建立了基于分数阶Tikhonov正则化的光路设计目标函数.利用遗传算法分析(0,1)范围内不同阶数的计算结果,得到最佳光路布置方式.采用近红外波段7185.6 cm^(-1)的H_(2)O特征吸收谱线结合20条测试光路对10×10离散化网格区域进行计算,对比分析五种光路布置方式对多种分布模型的重建结果,结果表明,基于分数阶Tikhonov正则化的光路布置方式具有最佳重建效果.研究结果对有限投影条件下激光吸收光谱二维测量光路的优化设计理论研究具有重要意义,可以促进激光吸收光谱技术在复杂发动机燃烧场二维重建及燃烧效率提升方面的应用. 展开更多
关键词 激光吸收光谱 二维重建 分数阶Tikhonov正则化 光路优化
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Characteristic fractional step finite difference method for nonlinear section coupled system
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作者 袁益让 李长峰 +1 位作者 孙同军 刘允欣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第10期1311-1330,共20页
For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of c... For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources. 展开更多
关键词 three-dimensional section coupled system complete nonlinear equation characteristic fractional step CONVERGENCE numerical simulation
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基于余幂-激活离散超混沌加密的多参数加权分数傅里叶变换安全通信方法 被引量:7
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作者 孟庆微 王西康 +1 位作者 齐子森 张悦 《电子与信息学报》 EI CSCD 北大核心 2023年第5期1688-1696,共9页
为提高物理层安全传输性能,该文提出一种新的基于2维余幂-激活(2D-CPA)离散超混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。首先,将激活函数和余弦函数作为非线性因子引入1维立方(cubic)混沌映射,构造2维混沌映射。非线... 为提高物理层安全传输性能,该文提出一种新的基于2维余幂-激活(2D-CPA)离散超混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。首先,将激活函数和余弦函数作为非线性因子引入1维立方(cubic)混沌映射,构造2维混沌映射。非线性因子可对原始cubic混沌映射的迭代过程进行扰动,从而获得更加饱满的相轨。利用分岔图、相图、Lyapunov指数谱等对提出的2维混沌映射动力学特性进行了验证。结果表明,构造的2维混沌序列随机性良好,可进入超混沌状态。然后,利用余幂-激活离散超混沌序列分别构建幅度变换矩阵、相位旋转矩阵和MP-WFRFT参数池,完成对星座幅相加密,以及MP-WFRFT动态变换加密过程,进一步消除数据统计特征,同时提升MP-WFRFT变换的抗参数扫描性能。数值仿真结果表明,加密数据的星座图呈类高斯分布,且传输系统对密钥的敏感性良好。 展开更多
关键词 2维离散超混沌 星座加密 多参数加权分数傅里叶变换 LYAPUNOV指数
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THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION 被引量:1
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作者 袁益让 程爱杰 +1 位作者 羊丹平 李长峰 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1547-1565,共19页
A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media.... A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory. 展开更多
关键词 enhanced (chemical) oil production three-dimensional porous coupled system second-order implicit characteristic fractional step differences optimal order l^2 estimate application in actual oilfields
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