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在复变函数中,有时应用教材中的定理和方法判断解析函数孤立奇点的类型比较麻烦,本文给出了判断某些解析函数孤立奇点类型的一种较简单的方法. 相似文献
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复变函数理论是解决实际复杂问题的有利数学计算工具,开拓复变函数理论研究领域,具有一定现实指导意义。文中将一种新的复变函数作为研究对象,对该函数中高阶极点留数计算方法进行改进。在复变函数中,计算留数前提需对极点阶数实行判断,分别对可去奇点和极点等孤立奇点进行定义,采用复变函数零点和极点间存在的关系对函数极点实现阶数确定,再运用等价无穷小代替思想判定函数极点阶数,从而得到极点性质。分析留数定理与复变函数积分间存在的内在关系,获知柯西定理及柯西公式分别为被积函数在积分范围内解析函数和一阶极点的留数定理;高阶导数公式为积分范围内存在n+1阶极点的留数定理,基于上述定理提出引理对复变函数高阶极点留数计算方法实现改进,从而简化计复杂算过程。 相似文献
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对求争最优化问题的极大熵方法中的关键函数－K－S函数的一致不变凸性作了讨论得出“K－S函数是一致不变凸的，则一定是不变凸的”结论，其于K－S函数的特殊熵参数，在证明K－S函数的一致不变凸性中，引入了一个很小的正数ε，以说明只要熵足够大，K－S函数就是一致不变凸的。 相似文献
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本文从cauchy积分定理和cauchy积分公式入手,归纳出它们与复变函数积分之间的内在联系,研究cauchy积分定理和Cauchy积分公式的推广及积分路径上有有限个奇点的解析函数的积分问题,建立了类似于cauchy积分定理和caucby积分公式的结果.并给出了若干应用实例. 相似文献
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奇异积分在基础理论、天体物理以及工程上具有重要作用,如何求解奇点在区域内的奇异积分也因此具有重要意义。本文中介绍了广义的奇点定义,和数形结合理解曲线奇点、曲面奇点,并给出二者的定义。最后我们通过使用区域分割法,划分奇点处区域,使用Green公式来求解奇点在区域内的二维高整数阶奇异积分的解析解,并延伸到n维高整数阶奇异积分的解析解。 相似文献
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在现代物理学中,至少有两个大问题都涉及奇点。这两个大问题,其一是宇宙的标准模型认为宇宙从奇点爆炸形成的;其二是黑洞的结局是组成黑洞的物质挤压到一个尺度为零的奇点。在奇点处,现有的物理理论将全部失效。 宇宙的暴胀模型认为宇宙的膨胀起因于宇宙起源时的超密物质或能量从奇点处开始的大爆炸。如果宇宙当真是从奇点开 相似文献
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米凡 《大科技．科学之谜》2006,(8):55-55
量子理论的先锋人物霍金认为,宇宙中也许并不存在一个最初点——奇点,宇宙应该是无始无终,一直存在着的。这就是“无边界设想”。这无疑更符合逻辑和事实。人们普遍认为宇宙是在一次大爆炸中,由奇点诞生的。但量子论说明,相对论在奇点处失效,也就是说,相对论证明不了奇点的存在,也说明不了奇点的性质。那么,人类所猜测的宇宙的由来正体现出相对论的重大缺陷。我们知道,黑洞会“蒸发”,并在一次大爆炸中消亡。在这场大爆炸中,所谓的中心——奇点神奇地消失了。难道这样一个质量、密度都无限大的物质会突然消失吗?所以,最可能的原因就是该“奇… 相似文献
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In this work a procedure for obtaining polytopic λ-contractive sets for Takagi–Sugeno fuzzy systems is presented, adapting well-known algorithms from literature on discrete-time linear difference inclusions (LDI) to multi-dimensional summations. As a complexity parameter increases, these sets tend to the maximal invariant set of the system when no information on the shape of the membership functions is available. λ-contractive sets are naturally associated to level sets of polyhedral Lyapunov functions proving a decay-rate of λ. The paper proves that the proposed algorithm obtains better results than a class of Lyapunov methods for the same complexity degree: if such a Lyapunov function exists, the proposed algorithm converges in a finite number of steps and proves a larger λ-contractive set. 相似文献
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Mohammad Maqusi 《Journal of The Franklin Institute》1980,310(1):65-75
This paper discusses the identification problem for a class of nonlinear systems. A member of this class may be represented by a single-valued power-law type nonlinearity preceded and succeeded by linear dyadic invariant systems. Such an arrangement allows for a Voltera functional series representation. The identification problem is then concerned with the specification of the associated Voltera kernels.Two approaches are presented for dealing with this problem. Both approaches are, however, based on Walsh function techniques. The first approach relies on direct output measurements when the input is a Walsh function. This approach is suitable for a deterministic case. The second approach assumes ergodic processes for the input. Based on measurements drawn from an input-output dyadic correlation function, determination of the Voltera kernels is made. 相似文献
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采用Gröbner基方法,可以把一个在有限群作用下不变的多项式写成不变环的生成元的多项式.核心问题是如何有效地计算这个正维不变理想的Gröbner基.本文引入一个有效提升算法来计算这组Gröbner基.当用straight line program模型对整个计算过程进行复杂度分析时,可以把计算开销控制在多项式时间内. 相似文献
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采用Gr(o)bner基方法,可以把一个在有限群作用下不变的多项式写成不变环的生成元的多项式.核心问题是如何有效地计算这个正维不变理想的Gr(o)bner基.本文引入一个有效提升算法来计算这组Gr(o)bner基.当用straight line program模型对整个计算过程进行复杂度分析时,可以把计算开销控制在多项式时间内. 相似文献
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《Journal of The Franklin Institute》2019,356(8):4622-4647
The Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues. 相似文献
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量子不变量理论是研究几何相因子问题的有效方法。利用Ｌｅｗｉｓ－Ｒｉｅｓｅｎｆｅｌｄ不变量理论研究了谐振磁场中的自旋系统,给出了两种不同循环演化周期的精确解,并进而分别计算了此系统两种不同的几何相因子。研究表明,不同循环演化周期的几何相因子与初始态的选择有关。 相似文献
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《Journal of The Franklin Institute》2021,358(17):9263-9287
For constrained linear parameter varying systems subject to bounded disturbances and noises, this article investigates an off-line output feedback robust model predictive control approach. The sub-observer gains with robust positively invariant sets, and sub-controller gains with robust control invariant sets are simultaneously off-line optimized and stored in a look-up table. According to real-time estimation error bounds and estimated states, the time-varying sub-observer gains and sub-controller gains are on-line searched. The proposed off-line output feedback robust model predictive control approach with the guarantee of nested robust positively invariant sets and robust control invariant sets in theory reduces the on-line computational burden. 相似文献
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It is well known that sliding mode control is based on the definition of an invariant manifold, where the system dynamics are forced to in a finite time. Such a manifold is somewhat arbitrarily defined, as long as the system dynamics are stable on it. Computational and control effort may vary depending on selected manifold. Obviously, if a system has naturally acceptable stable dynamics around a desired equilibrium point, no control is needed unless uncertainties or disturbances are present. It would be desirable that if such a system had uncertainties or disturbances, the control effort be designed only to overcome the effect of such factors. For a system with first order dynamics and affine control input, designing a sliding mode control overcoming only such uncertainties or disturbances is a trivial task. When a higher order dynamics system is involved, unit control may be used, where the input control signals are not discontinuous, but when only discontinuous control inputs are available, a design approach is not readily available. In this paper, taking advantage of the natural stable dynamics of a system, a sliding mode control approach is introduced for designing multiple discontinuous control inputs, where the control effort overcomes only uncertainties, disturbances or unstable dynamics. Two illustrative examples are given in order to show the feasibility of the method. 相似文献
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K.B. Datta 《Journal of The Franklin Institute》1980,309(2):103-123