A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation

In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.     

A refined fuzzy time series model for stock market forecasting

Time series models have been used to make predictions of stock prices, academic enrollments, weather, road accident casualties, etc. In this paper we present a simple time-variant fuzzy time series forecasting method. The proposed method uses heuristic approach to define frequency-density-based partitions of the universe of discourse. We have proposed a fuzzy metric to use the frequency-density-based partitioning. The proposed fuzzy metric also uses a trend predictor to calculate the forecast. The new method is applied for forecasting TAIEX and enrollments’ forecasting of the University of Alabama. It is shown that the proposed method work with higher accuracy as compared to other fuzzy time series methods developed for forecasting TAIEX and enrollments of the University of Alabama.     

On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes

We consider certain vacua of four‐dimensional SU(N) gauge theory with the same field content as the 𝒩 = 4 supersymmetric Yang‐Mills theory, resulting from potentials which break the 𝒩 = 4 supersymmetry as well as its global SO(6) symmetry down to SO(3) × SO(3). We show that the theory behaves at intermediate scales as Yang‐Mills theory on M⁴ × S_L² × S_R², where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low‐energy mirror models.     

Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters

This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.     

参数微扰激光超混沌系统模糊模型

研究了存在参数微扰的激光超混沌系统的Takagi-Sugeno (T-S) 模糊模型的逼近性及建立问题。分析了存在参数微扰的激光超混沌系统的动力学特性。基于典型T-S模糊系统的建模原理,研究了激光超混沌T-S模糊系统的通用逼近性,通过确定非线性关键变量、模糊隶属度函数及模糊规则,建立了激光超混沌系统的T-S模糊模型。仿真结果表明,所建立的模糊模型能够有效逼近存在参数微扰的激光超混沌系统。     

参数微扰激光超混沌系统模糊模型

研究了存在参数微扰的激光超混沌系统的Takagi-Sugeno (T-S) 模糊模型的逼近性及建立问题。分析了存在参数微扰的激光超混沌系统的动力学特性。基于典型T-S模糊系统的建模原理,研究了激光超混沌T-S模糊系统的通用逼近性,通过确定非线性关键变量、模糊隶属度函数及模糊规则,建立了激光超混沌系统的T-S模糊模型。仿真结果表明,所建立的模糊模型能够有效逼近存在参数微扰的激光超混沌系统。     

模型参数对奇异星性质的影响

用有效质量口袋模型描述奇异夸克物质,研究了耦合常数和口袋常数的选取对奇异夸克物质的状态方程及奇异星性质的影响.结果表明,随着耦合常数和口袋常数的增大,奇异夸克物质的状态方程变软,相应的奇异星的引力质量和对应的半径均变小.当耦合常数从0.5增大到2.0时,奇异星的质量从1.43M_⊙(M_⊙=1.99×10³⁰ kg)减小到1.25M_⊙,相应的半径由8.3 km减小到7.7 km;当口袋常数B^1/4由160 MeV增大到175 MeV时,奇异星的质量和半径分别由1.47M_⊙和8.6 km减小到1.22M_⊙和7.4 km.这说明奇异夸克物质及奇异星的性质明显依赖于模型参数的取值. 关键词： 模型参数 奇异星 状态方程 质量-半径关系     

An improved model to predict energy-based acoustic parameters in Apulian-Romanesque churches

In this paper an improved model to predict energy relations in churches is proposed. A detailed acoustic survey was carried out of nine Romanesque churches having volumes ranging from 33 000 to 1500 m³. The measured sound level and early/late ratio showed significant correlation with the source-receiver distance, but the comparison with values predicted using theoretical models initially gave unsatisfactory results. The main difference was due to the early energy which was underestimated at points near the source and overestimated at distant points. Barron's revised theory proved to be the most reliable among the analysed models, so, in order to improve its prediction accuracy, a modified early reflected energy component was added to the direct and reverberant sound. The improved model was finally validated and the comparison between predicted and measured values gave good results.     

声发射辅以模糊神经网络的质量检测

利用铸铁工件在加载与卸载时所产生的声发射信号作为神经网络模式识别的输入特征，并对网络输入量与输出量进行模糊化隶属度计算，用最陡下降的BP学习法对连接权重系数进行优化，成功地实现了对铸铁工件样本组的训练和分类。     

On classical mechanical systems with non-linear constraints

In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d’Alembert–Chetaev trajectories of a constrained mechanical system satisfy both Gauss’ principle of least constraint and Hölder’s principle. In the case of a free mechanics, they also satisfy Hertz’s principle of least curvature if the constraint manifold is a cone. We show that the Gibbs–Maggi–Appell (GMA) vector field (i.e. the second-order vector field which defines the d’Alembert–Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi–Carathéodory metric tensor and prove Jacobi–Carathéodory’s theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville’s theorem on the conservation of volume for the flow of the GMA vector field.     

元胞自动机交通流模型的相变特性研究

系统地研究 VDR模型和T²模型在不同车流密度时车辆位置的相关性. 通过VDR模型、BJH模型和T²模型的序参量计算，确定在这三个模型中车流从自由流动到阻塞的相变特性，结果发现引入慢启动规则后，在不同的延迟概率和最大速度情况下，将引起交通相变特性的改变. 关键词： 交通流 元胞自动机 相关函数 序参量     

Connecting Jacobi elliptic functions with different modulus parameters

The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear differential equations and remarkable new cyclic identities involving Jacobi elliptic functions.     

优化模式物理参数的扩展四维变分同化方法

数值模拟的一个重要误差来源是模式物理参数,为提高模拟准确率,如何改进模式物理参数是亟需解决的问题.本文对经典四维变分同化技术进行了改进,提出了一种新的利用观测资料来同时优化模式初始场和物理参数的扩展四维变分同化方法,并以Ekman边界层模式和Lorenz模式为例进行了数值试验.结果表明,利用本文提出的新方法,通过对观测资料的变分同化,可以在实现对模式初始场进行优化的同时,纠正了模式物理参数中的误差,从而有效提高了模式的模拟准确率.该方法对于改进数值模式物理参数有着重要的促进意义.     

一类参数未知混沌系统的追踪控制与参数辨识

针对一类参数未知的混沌系统,提出一种追踪控制方法,基于Lyapunov稳定性理论,设计了追踪控制器和参数自适应控制律,实现了混沌系统的追踪控制和未知参数的辨识.以统一混沌系统为例进行了数值模拟,结果表明了该方法的有效性. 关键词： 混沌系统 追踪控制 参数辨识     

On the equivalence of different order parameters for Ising ferromagnets

In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter _{i j k} are the same as those of the magnetization _i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT _c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ _e independent of the way in which the odd interactionsJ _o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.     

Determination of structure parameters in molecular tunnelling ionisation model

We extracted the accurate structure parameters in a molecular tunnelling ionisation model (the so-called MO-ADK model) for 23 selected linear molecules including some inner orbitals. The molecular wave functions with the correct asymptotic behaviour are obtained by solving the time-independent Schrödinger equation with B-spline functions and molecular potentials numerically constructed using the modified Leeuwen–Baerends (LBα) model. We show that the orientation-dependent ionisation rate reflects the shape of the ionising orbitals in general. The influences of the Stark shifts of the energy levels on the orientation-dependent ionisation rates of the polar molecules are studied. We also examine the angle-dependent ionisation rates (or probabilities) based on the MO-ADK model by comparing with the molecular strong-field approximation calculations and with recent experimental measurements.     

双参数奇摄动非线性反应扩散问题

讨论了一类具有双参数的非线性反应扩散方程奇摄动初始边值问题.在适当的假设下,构造了解的渐近展开式并讨论了它的渐近性态.     

Optical design and multi-objective optimization with fuzzy method for miniature zoom optics

In this paper a thinning L-type zoom lens design was proposed to exploit the reflecting and refracting surfaces connected by a prism. However, in the L-type designs, the modulation transfer function (MTF) value is comparatively low compared with that in its coaxial counterparts. If we increase the MTF, that would cause the relative illuminace (RI) degradation. We propose a combination of the Taguchi method and fuzzy approach to improve both the RI and MTF in L-type zoom systems. The resulting experimental values of orthogonal array L9 of the Taguchi method were used as inputs for fuzzy approach to obtain the MPCI value. The MPCI value was then analyzed by variance, revealing that the two most significant factors were (1) the surface 7 to image length and (2) the semi-aperture of the front element. In our proposed method, the appropriate weight of MTF and RI for the inputs of fuzzy controllers increased the MTF by 3.74%, but the RI only reduced by 0.13% in the systematic wide-angle end, respectively.     

Dependence of thermodynamic properties of model systems on some dissipative particle dynamics parameters

The influence of systematic perturbation of input interaction parameters on thermodynamic equilibrium properties is studied employing dissipative particle dynamics (DPD) simulations. The values of both the excess pressure and the surface tension are found to be very sensitive to the values of the soft repulsion parameter between unlike DPD particles for high values of the coarse-graining level (number of water molecules per DPD particle). For the case in which a molecular surfactant is present at the interface we have determined the dependence of these properties on the values of the parameters that characterize the bonding force between polymer beads. No significant differences were found between linear and branched surfactants.