A bayesian approach to binary response curve estimation

Summary The purpose of the present paper is to propose a practical procedure for the estimation of the binary response curve. The procedure is based on a model which approximates the response curve by a finely segmented piecewise constant function. To obtain a stable estimate we assume a prior distribution of the parameters of the model. The prior distribution has several parameters (hyper-parameters) which are chosen to minimize an information criterion ABIC. The procedure is applicable to data consisting of observations of a binary response variable and a single explanatory variable. The practical utility of the procedure is demonstrated by examples of applications to the dose response curve estimation, to the intensity function estimation of a point process and to the analysis of social survey data. The application of the procedure to the discriminant analysis is also briefly discussed. The Institute of statistical mathematics     

An estimate of the attraction domain with a specified exponential stability index in a wheeled robot control problem

The problem of synthesizing a law for the control of the plane motion of a wheeled robot is investigated. The rear wheels are the drive wheels and the front wheels are responsible for the turning of the platform. The aim of the control is to steer a target point to a specified trajectory and to stabilize the motion along it. The trajectory is assumed to be specified by a smooth curve. The actual curvature of the trajectory of the target point, which is related to the angle of rotation of the front wheels by a simple algebraic relation, is considered as the control. The control is subjected to bilateral constraints by virtue of the fact that the angle of rotation of the front wheels is limited. The attraction domain in the distance to trajectory - orientation space, is investigated for the proposed control law. Arrival at a trajectory with a specified exponential stability index is guaranteed in the case of initial conditions belonging to the given domain. An estimate of the attraction domain in the form of an ellipse is given.     

Diffusion-controlled smoulder propagation in a semi-infinite solid: The asymptotic temperature distribution

The authors consider the steady propagation of a two-dimensionaldiffusioncontrolled smouldering reaction front parallel to theplane boundary of a semi-infinite nonporous reactant. The reactionfront is assumed to be a sheet of line heat sources of variablestrength. The distribution of oxidizer concentration and temperaturein the porous burnt char and of the temperature in the reactantis determined in the form of an asymptotic expansion involvinga similarity variable. The temperature on the reaction frontin the asymptotic region is found to be constant to high order.The dependence of this temperature on the Lewis numbers associatedwith the reactant and the char is found to be in general agreementwith observations.     

A Model of the joint motion of agents with a three-level hierarchy based on a cellular automaton

The collective interaction of agents for jointly overcoming (negotiating) obstacles is simulated. The simulation uses a cellular automaton. The automaton’s cells are filled with agents and obstacles of various complexity. The agents' task is to negotiate the obstacles while moving to a prescribed target point. Each agent is assigned to one of three levels, which specifies a hierarchy of subordination between the agents. The complexity of an obstacle is determined by the amount of time needed to overcome it. The proposed model is based on the probabilities of going from one cell to another.     

Uniqueness of finding the coefficient of the derivative in a first order nonlinear equation

The problem of using an additional boundary condition to find a coefficient that depends on the spatial variable is considered. The existence and uniqueness of the solution to the direct problem is studied. The solution to the direct problem is proved to be stable with respect to the sought coefficient. Uniqueness conditions for the solution to the coefficient inverse problem are described.     

From the main equation to the Klein-Gordon equation

The purpose of this paper is to bring out some connections between the work of Isaacs and physics. The first five sections are devoted to classical dynamics. The theories of Hamilton and Jacobi are revisited via the geometrical approach to optimal control and de Broglie's ideas. The other sections contain a stochastic-type generalization, leading to the Klein-Gordon equation of relativistic wave mechanics.     

A parametric method of constructing Poincaré mappings in hydrodynamic systems

The plane-parallel motion of the particles of an incompressible medium reduces to an investigation of a Hamilton system. The stream function is a Hamilton function. A Hamilton function, which depends periodically on time and corresponds to the agitation of an incompressible medium in a domain which varies periodically with time, is considered. This agitation of the medium is due to dynamic chaos. The transition to dynamic chaos is described by investigating the location of the Lagrangian particles over time intervals which are multiples of the period (Poincaré points (PP)). The set of PP can be obtained using a Poincaré mapping in the phase flow. The method which has been developed is used to investigate the plane-parallel motion of the particles in an incompressible fluid in a thin layer, bounded by a flat bottom, rectilinear side walls and an upper boundary which is deformed according to a specified periodic law. The motion of the particles is determined from Hamilton's system of equations. The Hamiltonian (the stream function) is found in the thin-layer approximation and depends on two dimensionless parameters: the amplitude of deformation and the tangential velocity in the deforming boundary. The characteristic boundary, which separates the domain of the chaotic motion of the PP from the domain of ordered motion, is determined numerically in the domain of the two parameters. The topological structure of the phase trajectories up to the transition to chaotic conditions is analysed using the Poincaré mapping, found with an accuracy up to the third order with respect to the amplitude. The phase trajectories of the PP, found analytically, turn out to be close to the trajectories of the initial Hamilton system, determined numerically. The mapping found in the domain of the two dimensionless parameters enables one to determine, qualitatively, the boundary of the transition to chaos.     

Nonaxisymmetric Free Convection Flow over a Rotating Disk in a Viscoelastic fluid with Magnetic Field

The non axisymmetric motion produced by a buoyancy-induced secondary flow of a viscoelastic fluid over an infinite rotating disk in a verticalplane with a magnetic field applied normal to the disk has been studied.The governing Navier Stokes equations and the energy equation admit a self similar solution. The system of ordinary differential equations has been solved numerically using Runge-Kutta Gill subroutine.The turning moment for the viscoelastic fluid is found to be less than that of the Newtonian fluid but the turning moment is increased due to the magnetic parameter. The resultant force due to the buoyancy-induced secondary flow increases with the magnetic parameter but reduces as the viscoelastic parameter increases. The quantity of fluid, which is pumped outwards due to the centrifuging action of the disk, for the viscoelastic fluid is more than that of the Newtonian fluid. The buoyancy-induced secondary flow boundary layer is much thicker than the primary boundary layer thickness. The thermal boundary layer due to the primary flow increases with the magnetic parameter decreases as the viscoelastic parameter increases. The heat transfer increases with the viscoelastic parameter but decreases as the magnetic parameter increases. The effect of the viscoelastic parameter is more pronounced on the secondary flow than on the primary flow.     

Hierarchic control of a linear heat equation with missing data

The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial condition. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel–Legendre transform and appropriate Carleman inequalities.     

Generalized Latin squares on the torus

The notion of a Latin square is generalized. The natural object on which to define this extension is the torus. A theorem is proved which shows that the existence of a Latin square implies the existence of a linear Latin square, a Latin square with special form. The theorems in the paper are used to provide alternate proofs of results due to Pólya and Chandra (in relation to a problem of Moser). The inability to extend the results to orthogonal Latin squares is noted.     

On the space-filling enneahedra

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling polyhedra of four to eight faces have been previously reported. The search is here extended to the convex space-fillers of nine faces. The number of types is found to be at least 40.     

Optimization of expedition to Phobos using the impulse control and solution to Lambert problems taking into account attraction of the earth and mars

The trajectory of expedition to Mars and its satellite Phobos with return to the Earth is optimized. The attraction of the Sun, or the Earth, or Mars is considered at each part of the trajectory. The Earth and Mars positions correspond to ephemerides DE424, and the position of Phobos corresponds to ephemerides MAR097. Not more than 6 impulses are assumed on the trajectory. The spacecraft must start from the Earth in the period of 2020–2030 and stay at Phobos at least for 30 days. The total time of the expedition is limited to 1500 days. The characteristic velocity is minimized.     

两自由度非线性振动系统主参数激励下的分岔分析

本文给出了参数激励作用下两自由度非线性振动系统,在1:2内共振条件下主参数激励低阶模态的非线性响应.采用多尺度法得到其振幅和相位的调制方程,分析发现平凡解通过树枝分岔产生耦合模态解,采用Melnikov方法研究全局分岔行为,确定了产生Smale马蹄型混沌的参数值.     

The exact and approximate method in mechanical system's analysis

The main aim of this work is to present results of the mechanical system's analysis based on the exact and approximate Galerkin's methods. The considered system is the flexural vibrating one-dimension bending beam. The exact and approximate method were used to assign the dynamic flexibility of the considered system and results of this work were juxtaposed to verify the approximate method's accuracy. The correction coefficients were introduced into the approximate method to unify results of both methods. The aim of this work was to check accuracy of the approximate method and to verify if this method may be used to mechatronic system's analysis, where it is impossible to use the exact method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Approximation of the Spectra of Phan-Thien Tanner Liquids

The linear stability of the linear Phan-Thien Tanner (PTT) fluid model is investigated for plane Poiseuille flow. The PTT model involves parameters that can be used to fit shear and extensional data, which makes it suitable for describing both polymer solutions and melts. The base flow is determined using a Chebyshev-tau method. The linear stability equations are also discretized using Chebyshev approximations to furnish a generalized eigenvalue problem. The spectrum is shown to comprise a continuous part and a discrete part. The theoretical and numerical results are validated for the UCM and Oldroyd-B models, which are special cases of the PTT model, by comparing with results in the literature. It is demonstrated that the linear PTT fluid is stable to infinitesimal disturbances with respect to the range of shear-thinning, extensional and elasticity parameters considered. The computational efficiency and accuracy of the numerical method are also investigated.     

Stability study and control of helicopter blade flapping vibrations

The response of a two-degree-of-freedom, controlled, autoparametric system to harmonic excitations is studied and solved. The objective of this research is to investigate the effect of linear absorber on the vibrating system and the saturation control of a linear absorber to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The stability of the obtained numerical solution is investigated using both phase plane methods and frequency response equations. Variation of some parameters leads to the bending of the frequency response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work.     

A neural network system for solving an assortment problem in the steel industry

A neural network model for solving an assortment problem found in the iron and steel industry is discussed in this paper. The problem arises in the yard where steel plate is cut into rectangular pieces. The neural network model can be categorized as a Hopfield model, but the model is expanded to handle inequality constraints. The idea of a penalty function is used. A large penalty is applied to the network if a constraint is not satisfied. The weights are updated based on the penalty values. A special term is added to the energy function of the network to guarantee the convergence of the neural network which has this feature. The performance of the neural network was evaluated by comparison with an existing expert system. The results showed that the neural network has the potential to identify in a short time near-optimal solutions to the assortment problem. The neural network is used as the core of a system for dealing with the assortment problem. In building the neural networks system for practical use, there were many implementation issues. Some of them are presented here, and the fundamental ideas are explained. The performance of the neural network system is compared to that of the expert system and evaluated from the practical viewpoint. The results show that the neural network system is useful in handling the assortment problem.     

Using computer software in the teaching of mechanics

The paper looks at ways of using computer software in the teaching of mechanics. The various reasons for using software are discussed to justify the use of software. A number of examples are then considered to show how different types of software can be used. Examples shown are taken from very specific types of software, more general simulation software and mathematical software. The paper discusses using software to explore mechanics, to challenge ‘misconceptions’, to make links between mathematical representations and motion and to solve non-standard problems. The paper also stresses the need for structured approaches to the use of software.     

Contribution to error estimate

The error estimate of an approximate solution to a nonlinear ordinary differential equations of the second order is obtained. The differential equation is subject to either two-point boundary conditions or initial conditions. The independent variable interval may be finite or infinite. The theory is applied to five problems.     

Successive Proportional Additive Numeration Using Fuzzy Linguistic Labels (Fuzzy Linguistic SPAN)

The SPAN (Successive Proportional Additive Numeration or Social Participatory Allocation Network) is a procedure that converts individual judgments into a group decision. The procedure is based on a voting design by which individual experts allocate their votes iteratively between their preferred options and other experts. The process ends when all the votes are allocated to options, and the one with the highest number of votes is selected. The method requires the experts to specify an exact allocation of votes to both options and other experts. The Fuzzy Linguistic SPAN allows experts to allocate their votes using linguistic labels such as “most of” or “a few”, and determine the preferred option. This method is demonstrated using the Max–Min aggregation function used to develop a proportional representation of the option and member voting schemes. The method is also demonstrated using the LOWA aggregation function. The Fuzzy Linguistic SPAN method is beneficial since the linguistic voting process is easier for the experts and significantly reduces the computational process compared to the traditional SPAN. The paper presents the method and two examples with comparisons to the numerical SPAN method.