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approximation technique for Fractional Evolution Equations with Nonlocal Integral Conditions

MEDITERRANEAN JOURNAL OF MATHEMATICS 2017年第6期14卷 1-16页

作者： Chen, Pengyu Zhang, Xuping Li, Yongxiang Northwest Normal Univ Dept Math Lanzhou 730070 Gansu Peoples R China

We consider a class of fractional evolution equations with nonlocal integral conditions in Banach spaces. New existence of mild solutions to such a problem are established using Schauder fixed-point theorem, diagonal argument and approximation techniques under the hypotheses that the nonlinear term is Caratheodory continuous and satisfies some weak growth condition, the nonlocal term depends on all the value of independent variable on the whole interval and satisfies some weak growth condition. This work may be viewed as an attempt to develop a general existence theory for fractional evolution equations with general nonlocal integral conditions. Finally, as a sample of application, the results are applied to a fractional parabolic partial differential equation with nonlocal integral condition. The results obtained in this paper essentially extend some existing results in this area.

关键词： Fractional evolution equations Nonlocal integral condition approximation technique Compact semigroup

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A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2014年第7期99卷 487-521页

作者： Ling, Daosheng Bu, Lingfang Tu, Fubin Yang, Qingda Chen, Yunmin Zhejiang Univ MOE Key Lab Soft Soils & Geoenvironm Engn Hangzhou 310058 Zhejiang Peoples R China Univ Miami Dept Mech & Aerosp Engn Coral Gables FL 33124 USA

This paper presents a FEM with mesh-separation-based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution-dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi-analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack-tip adaptive mesh refinement strategy to improve the accuracy of crack-tip fields. Both the discontinuities due to intra-element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems. Copyright (C) 2014 John Wiley & Sons, Ltd.

关键词： FEM approximation technique discontinuity hanging node adaptive mesh refinement

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Faster Antenna Noise Temperature Calculations using a Novel approximation technique

Faster Antenna Noise Temperature Calculations using a Novel ...

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2010 IEEE International Symposium Antennas and Propagation/CNC-USNC/URSI Radio Science Meeting

作者： Imbriale, William A. CALTECH Jet Prop Lab Pasadena CA 91109 USA

This paper describes an approximation technique that can accomplish this improvement with extremely small errors in noise temperature calculation of a few tenths of Kelvin.

ISBN: (纸本)9781424449682

This paper describes an approximation technique that can accomplish this improvement with extremely small errors in noise temperature calculation of a few tenths of Kelvin.

关键词： antenna feed antenna feeds approximation technique faster antenna noise temperature calculations noise temperature measurement

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An efficient multiobjective optimizer based on genetic algorithm and approximation techniques for electromagnetic design

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IEEE TRANSACTIONS ON MAGNETICS 2007年第4期43卷 1605-1608页

作者： Ho, S. L. Yang, S. Y. Ni, G. Z. Wong, K. F. Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China

To provide an efficient multiobjective optimizer, an approximation technique based on the moving least squares approximation is integrated into an improved genetic algorithm. In order to use fully, both the a posteriori information gathered from the latest searched nondominated solutions and the a priori knowledge about the search space and individuals, in guiding the search towards more and better Pareto solutions, a gradient direction based perturbation search strategy and a preference function based fitness penalization scheme are proposed. Numerical results are reported to validate the proposed work.

关键词： approximation technique evolutionary computation genetic algorithm (GA) multiobjective optimization

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Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model

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STOCHASTIC HYDROLOGY AND HYDRAULICS 1998年第6期12卷 359-375页

作者： Wu, FC Wang, CK Natl Taiwan Univ Dept Agr Engn Taipei 10617 Taiwan Natl Taiwan Univ Hydrotech Res Inst Taipei 10617 Taiwan

Higher-order approximation techniques for estimating stochastic parameter of the non-homogeneous Poisson (NHP) model are presented. The NHP model is characterized by a two-parameter cumulative probability distribution function (CDF) of sediment displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of the average rest period and step length of sediment particles, respectively. Difficulty of estimating the parameters has, however, restricted the applications of the NHP model. The approximation techniques are proposed to address such problem. The basic idea of the method is to approximate a model involving stochastic parameters by Taylor series expansion. The expansion preserves certain higher-order terms of interest. Using the experimental (laboratory or field) data, one can determine the model parameters through a system of equations that are simplified by the approximation technique. The parameters so determined are used to predict the cumulative distribution of sediment displacement. The second-order approximation leads to a significant reduction of the CDF error (of the order of 47%) compared to the first-order approximation. Error analysis is performed to evaluate the accuracy of the first- and second-order approximations with respect to the experimental data. The higher-order approximations provide better estimations of the sediment transport and deposition that are critical factors for such environment as spawning gravel-bed.

关键词： non-homogeneous Poisson model parameter estimation approximation technique Taylor series cumulative probability distribution function intensity function error analysis

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Making fast buffer insertion even faster via approximation techniques 05

Making fast buffer insertion even faster via approximation t...

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10th Asia and South Pacific Design Automation Conference

作者： Li, Zhuo Sze, C. N. Alpert, Charles J. Hu, Jiang Shi, Weiping Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA

ISBN: (纸本)0780387368

As technology scales to 0.13 micron and below, designs are requiring buffers to be inserted on interconnects of even moderate length for both critical paths and fixing electrical violations. Consequently, buffer insertion is needed on tens of thousands of nets during physical synthesis optimization. Even the fast implementation of van Ginneken's algorithm requires several hours to perform this task. This work seeks to speed up the van Ginneken style algorithms by an order of magnitude while achieving similar results. To this end, we present three approximation techniques in order to speed up the algorithm: (1) aggressive pre-buffer slack pruning, (2) squeeze pruning, and (3) library lookup. Experimental results from industrial designs show that using these techniques together yields solutions in 9 to 25 times faster than van Ginneken style algorithms, while only sacrificing less than 3% delay penalty.

关键词： buffer circuits integrated circuit design integrated circuit interconnections buffer insertion approximation technique electrical violation physical synthesis optimization van Ginneken algorithm aggressive prebuffer slack pruning squeeze pruning library lookup

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An efficient multiobjective optimizer based on genetic algorithm and approximation techniques for electromagnetic design

An efficient multiobjective optimizer based on genetic algor...

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12th Biennial IEEE Conference on Electromagnetic Field Computation

作者： Ho, S. L. Yang, S. Y. Ni, G. Z. Wong, K. F. Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China

ISBN: (纸本)1424403200

关键词： approximation technique evolutionary computation genetic algorithm (GA) multiobjective optimization

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Study of Inheritance and approximation techniques for Adaptive Multi-objective Particle Swarm Optimization 12

Study of Inheritance and Approximation Techniques for Adapti...

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12th International Conference on Informatics in Control Automation and Robotics (ICINCO)

作者： Bouoni, Ibtissem Smairi, Nadia Zidi, Kamel Fac Sci Gafsa Gafsa Tunisia ISG Tunis Lab Optimizat Strategy & Intelligent Comp Tunis Tunisia Univ Tabuk Tabuk Saudi Arabia

ISBN: (纸本)9789897581496

In this paper, we propose to introduce inheritance and approximation techniques for the evaluation of the objective function. The main idea of the approaches is to reduce MO-TRIBES complexity. Besides, in our study, we incorporate at the beginning, an inheritance technique then an approximation technique (approximation 1: to consider the whole swarm, approximation 2: to consider the tribe) at the evaluation of the objective function. We conducted in our experiments eleven well-known multi-objective test functions. The results showed a good behavior of our propositions on most tested functions. Moreover, TRIBES-inheritance provided the best compared to MO-TRIBES, we concluded that MO-TRIBES with inheritance give the best time than MO-TRIBES and MO-TRIBES with approximation. It also kept the same performances with MO-TRIBES with a simple improvement for several functions.

关键词： Multi-objective Optimization Particle Swarm Optimization MO-TRIBES Inheritance technique approximation technique Fitness Evaluation Time

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Resource allocation in power domain NOMA-based cooperative multicell networks

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IET COMMUNICATIONS 2020年第7期14卷 1162-1168页

作者： Nazari, Ali Javan, Mohammad Reza Hosseini, Shima Salar Shahrood Univ Technol Dept Elect Engn Shahrood Iran

In this paper, we propose a novel resource allocation scheme for non-orthogonal multiple access (NOMA) based cooperative cellular networks where in each cell, two pairs of transmitter-receiver want to communicate via the base station (BS) which serves as a decode-and-forward (DF) relay. In the first hop, the transmitters simultaneously transmit their information and the BS applies joint decoding method. The BS transmits the received information towards the receivers based on NOMA technique. The receivers apply the successive interference cancellation (SIC) where the SIC ordering of receivers is determined based on the direct channel gain. We formulate the resource allocation problem as an optimization problem which is non-convex. To tackle the non-convexity, we adopt the successive convex approximation (SCA) with difference of two concave functions (D.C.) as the approximation technique. We also study the computational complexity of our proposed scheme. Finally, we study the performance of our scheme by simulations and compare it with existing transmission schemes like the orthogonal frequency multiple access (OFDMA) and the case where both of the first hop and the second hop adopt PD-NOMA as well as the case where a special sort of subcarrier pairing is performed between the first and second hops.

关键词： convex programming cellular radio cooperative communication multi-access systems resource allocation interference suppression decode and forward communication relay networks (telecommunication) radio receivers radio transmitters approximation theory approximation technique orthogonal frequency division multiple access subcarrier pairing power domain NOMA-based cooperative multicell networks resource allocation scheme nonorthogonal multiple access-based wireless cooperative multicell cellular networks transmitter-receiver base station BS transmitters joint decoding received information receivers NOMA technique successive interference cancellation resource allocation problem nonconvex nonconvexity successive convex approximation

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The extrapolated interval global optimization algorithm

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JOURNAL OF GLOBAL OPTIMIZATION 2011年第2期50卷 249-270页

作者： Nataraj, P. S. V. Sondur, Shanta Indian Inst Technol IDP Syst & Control Engn Bombay 400076 Maharashtra India

This paper presents a new approach based on extrapolation to accelerate the linear convergence process of Vectorized Moore-Skelboe (VMS) algorithm. The VMS is a modified version of basic Moore-Skelboe (MS) algorithm, where the vectorization is used as a means to speed up the basic MS algorithm. We propose to further accelerate the converging process of VMS from linear to quadratic by combining the Richardson extrapolation technique with VMS. The effectiveness of the proposed algorithm is tested on various multivariate examples and compared with the unaccelerated conventional method, i.e., MS and well-known optimization software GlobSol. The test results show that the proposed extrapolation-based VMS offer considerable speed improvements over both the existing algorithms.

关键词： Asymptotic expansion Extrapolation methods REP Interval analysis Bernstein polynomial approximation technique

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