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Alternate Cooling Model vs Newton’s Cooling
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作者 Haiduke Sarafian 《American Journal of Computational Mathematics》 2021年第1期64-69,共6页
It is customary to apply Newton’s cooling as the standard model investigating the temperature profile of a hot substance exposed to a cool ambient. The rate of change of temperature in Newton’s model is simplistical... It is customary to apply Newton’s cooling as the standard model investigating the temperature profile of a hot substance exposed to a cool ambient. The rate of change of temperature in Newton’s model is simplistically related to linear-temperature difference of the two e.g. [1]. In our research flavored investigation, we consider a fresh model, cooling that depends to the difference of temperature-squared conducive to similar results. Utilizing a Computer Algebra System (CAS), especially <em>Mathematica</em> [2] we show the equivalency of the two. 展开更多
关键词 newton’s cooling Thermo-Physics Computer Algebra system (CAs) Mathematica
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Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question
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作者 Jerzy K. Filus 《Journal of Applied Mathematics and Physics》 2024年第7期2421-2451,共31页
Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The ... Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared. 展开更多
关键词 special Relativity’s Hyperbolic Versus Circular Versions Galilean Kinematics Partial Equivalence of sR and newton’s Theories Algebra of Relativistic and the Corresponding Galilean Velocities
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基于T-S模糊故障树的驱动电机冷却系统可靠性分析
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作者 柳炽伟 郭美华 《客车技术与研究》 2024年第2期19-25,共7页
车用驱动电机液压冷却系统存在故障机理不确定等问题。本文应用模糊数描述其故障概率和故障程度,建立驱动电机冷却系统的T-S模糊故障树模型,计算系统模糊可能性,分析各部件的概率重要度和关键重要度,找出影响系统可靠性的关键部件。
关键词 电动汽车 驱动电机 冷却系统 T-s模糊故障树 可靠性分析
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Not Relying on the Newton Gravitational Constant Gives More Accurate Gravitational Predictions
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作者 Espen Gaarder Haug 《Journal of Applied Mathematics and Physics》 2023年第10期3124-3158,共35页
The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the k... The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions. 展开更多
关键词 Gravity Predictions Reduction of Errors newton’s Gravitational Constant Collision space-Time Cavendish Apparatus Planck Length Planck Time
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Adapted Metrics for a Modified Coulomb/Newton’s Potential
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作者 Lucian M. Ionescu Cristina-Liliana Pripoae Gabriel Pripoae 《Journal of High Energy Physics, Gravitation and Cosmology》 2023年第4期1311-1355,共45页
Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the eff... Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns. 展开更多
关键词 Modified Gravity Theory sPIN Coulomb’s Law newton’s Law Modified Coulomb’s Law Nuclear Force Adapted Connection Adapted Metric
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Reciprocity Relation between Alternative Gravity Formulas
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作者 Hans Hermann Otto 《Journal of Applied Mathematics and Physics》 2024年第4期1432-1440,共9页
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw... We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter. 展开更多
关键词 Gravity Formulas Reciprocity Distance Relation newton EINsTEIN Bhandari Higgs Field Dirac’s Large Number
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Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations
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作者 Zaki Harari 《Advances in Aerospace Science and Technology》 2024年第1期10-27,共18页
Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision mod... Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering. 展开更多
关键词 Tsiolkovsky Rocket Equation Ideal Rocket Equation Rocket Propulsion newton’s Third Law Combustion Oscillations Combustion Instability
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The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe
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作者 Joel Almeida 《Natural Science》 2024年第6期65-101,共37页
This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This per... This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves. 展开更多
关键词 Dead Universe Theory Heat Death of the Universe Big Bang Theory Universe’s Ultimate Fate Universe Expansion Big Freeze Universe Cosmological Models End of Universe Theories Natural Galaxy Drift Future of the Universe Universe cooling Down Cosmology and Entropy
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减少大型低温乙烯球罐预冷过程中VOC_(S)排放
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作者 李翠芳 《石油化工安全环保技术》 CAS 2024年第4期59-62,I0004,共5页
对某石化企业乙烯罐区3000m^(3)低温乙烯球罐预冷过程的工艺操作进行了简要介绍,针对乙烯球罐需要预冷至-30℃以下才能接料投用的苛刻工艺条件及预冷操作的技术难题和安全环保风险,在理论分析可行的基础上,提出将预冷方式由“插底管进... 对某石化企业乙烯罐区3000m^(3)低温乙烯球罐预冷过程的工艺操作进行了简要介绍,针对乙烯球罐需要预冷至-30℃以下才能接料投用的苛刻工艺条件及预冷操作的技术难题和安全环保风险,在理论分析可行的基础上,提出将预冷方式由“插底管进液”改为“顶部喷洒液滴”。实践证明,顶部喷洒液滴的预冷方式将球罐预冷时间由56h缩短至12h,减少了乙烯等挥发性有机物(VOC_(S))向火炬排放约30t,实现了碳减排和清洁生产目的。同时,也消除了因罐顶与罐底温差大导致球罐材质发生脆裂泄漏而引发的安全环保风险。 展开更多
关键词 低温乙烯球罐 预冷 温差 脆裂泄漏 VOC_(s)
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基于层次分析法与改进D-S理论的阀水冷系统状态评估
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作者 杨群 齐鹏洋 +1 位作者 李昊 刘钊 《宁夏电力》 2024年第1期55-61,共7页
为了及时评估保障换流阀可靠运行的阀水冷系统运行状态,首先,分析了换流站阀水冷系统整体构成,选取主要历史数据和实时数据构建了评估指标体系,通过三角形函数和半梯形函数以及专家调查法确定各个指标的隶属度;其次,基于层次分析法确定... 为了及时评估保障换流阀可靠运行的阀水冷系统运行状态,首先,分析了换流站阀水冷系统整体构成,选取主要历史数据和实时数据构建了评估指标体系,通过三角形函数和半梯形函数以及专家调查法确定各个指标的隶属度;其次,基于层次分析法确定各个评估指标权重,改进D-S理论建立阀水冷系统运行状态评估模型;最后,通过采集实际工程阀水冷系统主要指标数据对模型进行了验证,并以阀水冷系统滤芯清洗前后数据为例对评估结果进行了对比。结果表明,所建模型能够对阀水冷系统运行状态做出准确识别和评估,有利于运维人员及时掌控阀水冷系统运行状态,保障其可靠运行。 展开更多
关键词 换流阀 状态评估 阀水冷系统 层次分析法 改进D-s证据理论
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Gauss-Newton法的半局部收敛性
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作者 张文红 李冲 《东南大学学报(自然科学版)》 EI CAS CSCD 北大核心 2001年第5期135-139,共5页
设f:Rn→Rm 是Frechet可微的 ,m≥n .则非线性最小二乘问题可描述为下面的极小化问题 :minF(x) :=12 f(x) Tf(x) .Gauss Newton法是求解非线性最小二乘问题的最基本的方法之一 ,其n + 1步迭代定义为 :xn + 1=xn - f′(xn) Tf′(x) -1f′... 设f:Rn→Rm 是Frechet可微的 ,m≥n .则非线性最小二乘问题可描述为下面的极小化问题 :minF(x) :=12 f(x) Tf(x) .Gauss Newton法是求解非线性最小二乘问题的最基本的方法之一 ,其n + 1步迭代定义为 :xn + 1=xn - f′(xn) Tf′(x) -1f′(xn) Tf(xn) .本文主要研究解非线性最小二乘问题的Gauss Newton法的半局部收敛性 .假设f(x)在B(x0 ,r)内连续可导且f′(x0 )满秩 ,若f的导数满足Lipschitz连续F′(x) -f′(x′)≤γx -x′ , x ,x′∈B(x0 ,r) .在一个关于初始点x0 的判断准则c =f(x0 ) ,β =f′T(x0 )f′(x0 ) -1f′(x0 ) T ,β2 cγ <1 1 0下 ,Gauss Newton法产生的序列 {xn}收敛到一个驻点x ,从而给出了Gauss Newton法的半局部收敛性 . 展开更多
关键词 非线性最小二乘问题 Garuss-newton 半局部收敛性 最优化方法
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关于Newton-Cote's数值积分公式的修正
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作者 郭瑞 阿布都热西提.阿布都外力 《新疆大学学报(自然科学版)》 CAS 2010年第2期186-190,共5页
对Newton-Cote's数值积分公式进行了研究,证明了当n=9时的Newton-Cote's数值积分公式是可行,积分误差是可以控制.最后通过数值例子验证了Newton-Cote's积分当8≤n≤200时,除n=9以外理论上是不可行.
关键词 积分误差 代数精度 newton—Cote’s数值积分
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大型石化企业储罐VOC_(S)治理改造与节能应用探究 被引量:1
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作者 王楠 《石油化工安全环保技术》 CAS 2023年第3期59-63,68,I0004,共7页
为减小因丁辛醇罐区储罐排放尾气引起的环境污染和其它安全隐患,通过对不同治理技术进行研究,择优应用冷却回收技术对含100%丁醛组分的醛储罐排放尾气进行回收。采用新型储罐密封技术对80%以上为丁醛的轻组分储罐、含60%左右丁醇的重组... 为减小因丁辛醇罐区储罐排放尾气引起的环境污染和其它安全隐患,通过对不同治理技术进行研究,择优应用冷却回收技术对含100%丁醛组分的醛储罐排放尾气进行回收。采用新型储罐密封技术对80%以上为丁醛的轻组分储罐、含60%左右丁醇的重组分储罐及含20%左右丁醇的杂醇储罐进行处理,以满足降低挥发性有机物量的目标,实现罐区尾气异味治理,有效减少现场异味,保护环境。 展开更多
关键词 冷却回收 储罐密封 挥发性有机物 异味治理
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Novel Newton’s learning algorithm of neural networks 被引量:2
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作者 Long Ning Zhang Fengli 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第2期450-454,共5页
Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the ... Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the gradient method is linearly convergent while Newton's method has second order convergence rate. The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton's learning algorithm. Simulation results show that the convergence rate of Newton's learning algorithm is high and apparently faster than the traditional BP method's, and the robustness of Newton's learning algorithm is also better than BP method' s. 展开更多
关键词 newtons method Hesse matrix fast learning BP method neural network.
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Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration 被引量:1
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作者 SHEN Yu-jing HAN Dan-fu SHAO Xin-ping 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第2期127-140,共14页
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is g... A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem. 展开更多
关键词 Navier-stokes equation Darcy's law interface coupling two-grid algorithm newton iteration
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The Research of the Flow of Bodies with Use of the Vector Form of the Newton’s Law for the Viscous Liquid 被引量:2
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作者 Andrey N. Volobuev Eugene S. Petrov 《Engineering(科研)》 2011年第2期162-167,共6页
On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form... On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out. 展开更多
关键词 newton’s LAW for VIsCOsITY A Body FLOW CIRCULATION of speed Resistance Factor A VIsCOsITY TENsOR
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A Discrete Newton's Method for Gain Based Predistorter 被引量:1
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作者 Xiaochen LIN Minglu JIN Aifei LIU 《International Journal of Communications, Network and System Sciences》 2008年第1期16-21,共6页
Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presen... Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method. 展开更多
关键词 PREDIsTORTION DIsCRETE newton’s METHOD Power Amplifiers (PAs) LOOKUP Table (LUT)
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Q-Theory: A Connection between Newton’s Law and Coulomb’s Law? 被引量:1
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作者 Christopher Pilot 《Journal of High Energy Physics, Gravitation and Cosmology》 2021年第2期632-660,共29页
Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, <i>q<... Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, <i>q<sub>pl</sub></i>, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, <img src="Edit_770c2a48-039c-4cc9-8f66-406c0cfc565c.png" width="90" height="15" alt="" />, where <i>ζ</i>(3) equals Apery’s constant, 1.202 …, and, <i>n</i><sub>+</sub>(0)=<i>n</i>_(0), is the relaxed, <i>i.e.</i>, <img src="Edit_813d5a6f-b79a-49ba-bdf7-5042541b58a0.png" width="25" height="12" alt="" />, number density of the positive and negative mass planckions. In the present epoch, we estimate that, <i>n</i><sub>+</sub>(0) equals, 7.848E54 m<sup>-3</sup>, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, <i>l</i><sub>+</sub>(0)=<i>l</i><sub>_</sub>(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, <img src="Edit_efc8003d-5297-4345-adac-4ac95536934d.png" width="80" height="15" alt="" />, due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, <i>g</i>=9.81m/s<sup>2</sup>, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure. 展开更多
关键词 Extended Gravity Winterberg Model Planckion Mass Theory Modified Quantum Vacuum Planck Charge newton’s Law Coulomb’s Law Dark Energy
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Newton Did Not Invent or Use the So-Called Newton’s Gravitational Constant;G, It Has Mainly Caused Confusion 被引量:1
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作者 Espen Gaarder Haug 《Journal of Modern Physics》 2022年第2期179-205,共27页
Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and... Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass;namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength. 展开更多
关键词 newton Gravity newton’s Gravitational Constant schwarzschild Radius Quantum Gravity Planck Length
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Kantorovich’s theorem for Newton’s method on Lie groups
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作者 WANG Jin-hua LI Chong 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第6期978-986,共9页
The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and ... The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori. 展开更多
关键词 newtons method Lie group Kantorovich's theorem Lipschitz condition
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