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p^k元域及其单超越扩域上的二项方程三项方程和因式方程 被引量:1
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作者 孙宗明 《内蒙古师范大学学报(自然科学汉文版)》 CAS 2011年第6期541-546,共6页
设F是pk元域,E是F的单超越扩域.综述了F与E上的二项方程、三项方程和因式方程,给出了方程在F与E中有根或没有根的条件,若方程有根,则给出根的个数与根的求法.
关键词 P^K元域 单超越扩域 二项方程 三项方程 因式方程 方程的根 根的个数
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2D/3D起伏地表多震相地震波走时的因式分解程函方程算法 被引量:1
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作者 张云 李夕海 +3 位作者 白超英 牛超 王艺婷 曾小牛 《石油地球物理勘探》 EI CSCD 北大核心 2023年第4期857-871,共15页
起伏地表条件的地震波走时计算方法是研究该类地表区地下结构的基础工具。快速行进法和快速扫描法均是基于有限差分求解程函方程而发展起来的地震波走时计算方法,由于震源附近波前曲率较大,这两种算法均存在震源奇异性问题。研究成果表... 起伏地表条件的地震波走时计算方法是研究该类地表区地下结构的基础工具。快速行进法和快速扫描法均是基于有限差分求解程函方程而发展起来的地震波走时计算方法,由于震源附近波前曲率较大,这两种算法均存在震源奇异性问题。研究成果表明,对于复杂模型快速行进法的计算效率高于快速扫描法。为此,借鉴快速扫描法解决震源奇异性的思路,采用快速行进法求解因式分解程函方程,从而规避了震源奇异性问题。具体而言,将地震波走时分解为一个距离函数T0与一个走时扰动值T1乘积的形式,通过快速行进法求解T1,并与T0相乘,得到地震波走时;同时,为弥补规则网格迎风差分格式不适用于地表/界面起伏的缺陷,构建了适用于不规则网格的不等距迎风差分格式,进而结合分区多步技术形成了全局多震相地震波走时计算方法。2D和3D数值模拟实例表明,所提算法从根本上解决了快速行进法的震源奇异性问题,显著提高了原算法的计算精度与效率,可精确计算多震相地震波走时。 展开更多
关键词 因式分解程函方程 走时扰动因子 不等距迎风差分格式 多震相地震波走时计算
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A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space 被引量:1
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作者 ZHANG Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期851-854,共4页
For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the paramet... For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results. 展开更多
关键词 event space Birkhoffian system integrating factor conservation theorem Killing equation
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Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid
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作者 韩光泽 王小燕 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2015年第6期897-904,共8页
Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantl... Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores. 展开更多
关键词 Stokes-Einstein equation Eyring's equation Slit nanopore Self-diffusion coellicient Simple quasicrystal model of liquid
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Settlement modeling in central core rockfill dams by new approaches 被引量:2
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作者 Behnia D. Ahangari K. +2 位作者 Goshtasbi K. Moeinossadat S.R. Behnia M. 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2016年第4期703-710,共8页
One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study... One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study aims to apply intelligent methods to predict settlement after constructing central core rockfill dams.Attempts were made in this research to prepare models for predicting settlement of these dams using the information of 35 different central core rockfill dams all over the world and Adaptive Neuro-Fuzzy Interface System(ANFIS) and Gene Expression Programming(GEP) methods.Parameters such as height of dam(H) and compressibility index(Ci) were considered as the input parameters.Finally,a form was designed using visual basic software for predicting dam settlement.With respect to the accuracy of the results obtained from the intelligent methods,they can be recommended for predicting settlement after constructing central core rockfill dams for the future plans. 展开更多
关键词 Settlement Adaptive Neuro-Fuzzy Interface System(ANFIS)Gene Expression Programming (GEP)Visual Basic (VB)
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Modeling of shear wave velocity in limestone by soft computing methods 被引量:2
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作者 Behnia Danial Ahangari Kaveh Moeinossadat Sayed Rahim 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2017年第3期423-430,共8页
The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have... The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system (ANFIS), and gene expression programming (GEP) methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity (Vp), density (7) and porosity (.n), were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future. 展开更多
关键词 Shear wave velocity Limestone Neuro-genetic Adaptive neuro-fuzzy inference system Gene expression programming
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Exact Vacuum Solutions to the Einstein Equation 被引量:1
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作者 Yingqiu GU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2007年第5期499-506,共8页
In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this proced... In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution. 展开更多
关键词 Einstein equation Exact vacuum solution Canonical metric Black hole
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IMPLICITIZATION USING UNIVARIATE RESULTANTS 被引量:2
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作者 Liyong SHEN Chunming YUAN 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2010年第4期804-814,共11页
Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational... Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces. 展开更多
关键词 IMPLICITIZATION rational space curves rational surfaces resultants.
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Predicting crest settlement in concrete face rockfill dams using adaptive neuro-fuzzy inference system and gene expression programming intelligent methods 被引量:6
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作者 Danial BEHNIA Kaveh AHANGARI +1 位作者 Ali NOORZAD Sayed Rahim MOEINOSSADAT 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2013年第8期589-602,共14页
This paper deals with the estimation of crest settlement in a concrete face rockfill dam (CFRD), utilizing intelligent methods. Following completion of dam construction, considerable movements of the crest and the b... This paper deals with the estimation of crest settlement in a concrete face rockfill dam (CFRD), utilizing intelligent methods. Following completion of dam construction, considerable movements of the crest and the body of the dam can develop during the first impoundment of the reservoir. Although there is vast experience worldwide in CFRD design and construction, few accurate experimental relationships are available to predict the settlement in CFRD. The goal is to advance the development of intelligent methods to estimate the subsidence of dams at the design stage. Due to dam zonifieation and uncertainties in material properties, these methods appear to be the appropriate choice. In this study, the crest settlement behavior of CFRDs is analyzed based on compiled data of 24 CFRDs constructed during recent years around the world, along with the utilization of gene ex- pression programming (GEP) and adaptive neuro-fuzzy inference system (ANFIS) methods. In addition, dam height (H), shape factor (St), and time (t, time after first operation) are also assessed, being considered major factors in predicting the settlement behavior. From the relationships proposed, the values ofR2 for both equations of GEP (with and without constant) were 0.9603 and 0.9734, and for the three approaches of ANFIS (grid partitioning (GP), subtractive clustering method (SCM), and fuzzy c-means clustering (FCM)) were 0.9693, 0.8657, and 0.8848, respectively. The obtained results indicate that the overall behavior evaluated by this approach is consistent with the measured data of other CFRDs. 展开更多
关键词 Concrete face rockfill dam (CFRD) Crest settlement Adaptive neuro-fuzzy inference system (ANFIS) Geneexpression programming (GEP)
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Beyond the Friedmann-Lema tre-Robertson-Walker Big Bang Singularity
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作者 Cristi Stoica 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第10期613-616,共4页
Einstein's equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein's whenever the latter is defined,but applicable in wider situations,is proposed.The new equation ... Einstein's equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein's whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein's equation and the metric tensor. 展开更多
关键词 SINGULARITIES Friedmann-Lemaatre-Robertson-Walker big bang singular general relativity
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