Upon reflection [computational geometry]

The author looks at the geometry of the classic law of mirror reflection. This law tells us that the angle of incidence equals the angle of reflection. It turns out that this little geometric truth can help solve another set of interesting problems called billiard problems, which describe the shortest path a billiard ball can take on a polygonal table. The author starts by looking at two different derivations of the law of reflection, one geometric and one analytic. He then looks at the problem of finding the shortest circuit of a billiard ball around a triangular table     

On a problem of analytic design of an optimal controller

This article is devoted to the further development of the technique of analytic design of an optimal controller for the case of functionals with an integrand of the form x′Qx+x′Pu+ u′ Ru. In this case the problems of analytic design are considered both without disturbances and at constantly acting disturbances. The statement of the problem for optimal control of a vibration-protective system (VPS) is given, for the solution of which the technique outlined in the article can be used for the solution of the problem of analytic design of the optimal controller.     

Optimization of advertising activity of an insurance company and an algorithm for its solution

The problem of optimization of advertising activity of an insurance company consisting of n divisions (branches) is considered. For each branch, an optimal control is found in a closed form (an analytic solution) under constraints on advertising expenses. The quality of behavior of optimal controls and phase coordinates is illustrated by a numerical experiment. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 159–165, March–April 2009.     

Analytic description of discrete dynamics of a robot-manipulator in an indefinite exterior medium by methods of idempotent mathematics

The analytic model of the dynamics of a robot-manipulator is obtained in the infinitely indefinite dynamic and completely observable exterior medium. The unboundedness property of indefiniteness most exactly accounts for the unpredictability of the real world, in which most of the moving objects of the technical nature have to function, and considerably complicates the problem of modeling because in this case the results of the classical theory of control are inapplicable in full measure. In this work an alternative approach to the modeling is developed on the basis of idempotent mathematics, which differs from the known approaches by the possibility of representing a model in the explicit analytic form.     

Decision making in equipment selection: an integrated approach with AHP and PROMETHEE

Multi-attribute equipment selection is a very important issue for an effective manufacturing system, since the improper equipment selection might cause many problems affecting productivity, precision, flexibility and quality of the products negatively. On the other hand, selecting the best equipment among many alternatives is a multi-criteria decision making (MCDM) problem. In this study, an integrated approach which employs analytic hierarchy process (AHP) and preference ranking organization method for enrichment evaluations (PROMETHEE) together, is proposed for the equipment selection problem. The AHP is used to analyze the structure of the equipment selection problem and to determine weights of the criteria, and PROMETHEE method is used to obtain final ranking, and to make a sensitivity analysis by changing the weights. Proposed approach is applied to a problem of selecting milling machines to be purchased in an international company. Company management found the application and results satisfactory and implementable in their equipment selection decisions.     

Development of a Mirror System with Controlled Wave Characteristics for an Adaptive Telescope

The problem of creation of high-accuracy anti-interference devices for astronomical observations is considered. The principle of construction of the mirror system of an adaptive telescope capable of correcting phase distortions of waves perceived by its mirror owing to the use of active reflecting coatings is developed. The processes in a parametrically activated nonlinear medium are mathematically modeled and the possibility of operation in a mode close to the total reflection is shown.     

未标定摄像机P5P问题的一种解析解

经典PnP问题是以摄像机内参已知为前提条件的,然而对未标定摄像机PnP问题的研究更具有实际意义.文中对未标定四参数针孔摄像机P5P问题的解析解进行了研究,不仅可以求出摄像机相对于世界坐标系的位姿,而且还能得到摄像机的内参.首先根据投影方程和旋转矩阵的性质,利用16个变量构造出了16个约束方程,然后通过消元推导出只含一个未知数的4次多项式方程,分析证实一般情况下未标定摄像机P5P问题最多有4组解.大量的仿真实验表明该算法在确定摄像机位姿上精度很高,且鲁棒性很强.该算法在物体定位、手眼定标、路标导航等领域具有比较重要的实际应用价值.     

Heat transfer process in an elliptical channel

This paper addresses the problem of heat transport in an elliptical channel in the presence of a temperature gradient parallel to its axis. The Williams equation is used as the basic equation describing the kinetics of the process and a model of diffusive reflection is used as the boundary conditions on the channel wall. The deviation of the gas condition from the equilibrium is assumed to be small. In order to find a linear correction to the local equilibrium function of distribution, a boundary problem consisting of a linear homogeneous partial differential equation of the first order with a homogeneous boundary condition has been built. The solution of the built boundary value problem has been found by the method of characteristics. The value of the heat flow through the cross section of the channel is found by using numerical procedures implemented by the computer algebra Maple 17 system. The results were compared with the analogous results found in the open press.     

Discrim: a computer program using an interactive approach to dissect a mixture of normal or lognormal distributions

DISCRIM is an interactive computer graphics program that dissects mixtures of normal or lognormal distributions. The program was written in an effort to obtain a more satisfactory solution to the dissection problem than that offered by a graphical or numerical approach alone. It combines graphic and analytic techniques using a Tektronix¹ terminal in a time-share computing environment. The main program and subroutines were written in the FORTRAN language.     

Multi-criteria analysis for a maintenance management problem in an engine factory: rational choice

The industrial organization needs to develop better methods for evaluating the performance of its projects. We are interested in the problems related to pieces with differing degrees of dirt. In this direction, we propose and evaluate a maintenance decision problem of maintenance in an engine factory that is specialized in the production, sale and maintenance of medium and slow speed four stroke engines. The main purpose of this paper is to study the problem by means of the analytic hierarchy process to obtain the weights of criteria, and the TOPSIS method as multicriteria decision making to obtain the ranking of alternatives, when the information was given in linguistic terms.     

Analytic solution for planar indeterminate impact problems using an energy constraint

This work proposes an analytic method for resolving planar multi-point indeterminate impact problems for rigid-body systems. An event-based approach is used to detect impact events, and constraints consistent with the rigid-body assumption are used to resolve the indeterminacy associated with multi-point impact analysis. The work-energy relation is utilized to determine post-impact velocities based on an energetic coefficient of restitution to model energy dissipation, thereby yielding an energetically consistent set of post-impact velocities based on Stronge’s energetic coefficient of restitution for the treatment of rigid impacts. The effect of stick–slip transition is analyzed based on Coulomb friction. This paper also discusses the transition from impact to contact. This analysis is essential for considering the rocking block problem that is used as an example herein. The predictions of the model for the rocking block problem are compared to experimental results published in the literature. An example of a planar ball undergoing two-point impact is also presented.     

FUZZY SYSTEMS: BASIS FOR A MODELING METHODOLOGY?

Modeling becomes a key methodological issue when we have to deal with large, complex and ill-structured problems. The traditional analytic approach to modeling aims at capturing the aggregate logic of a problematic situation, which is taken to represent the essence of the problem. The aggregate logic does not, and should not, describe the full complexity of the modeling situation, but should give a sufficient basis for finding an optimal solution to the problem. In recent criticism, however, it is pointed out that the analytic approach does not give an adequate basis for solving complex and ill-structured problems, and a systems approach is recommended. Checkland finds that the so-called hard systems thinking is no better than the analytic approach and introduces a soft systems methodology. In this paper a fuzzy systems approach is found to be more flexible than the analytic and the hard systems methods, but more precise and easier to validate than the soft systems approach.     

Analytic Flow Design Method for an Automated Distribution Center with Multiple Shipping Areas

An analytic flow design algorithm for an automated distribution center with multiple shipping areas is presented. The main elements of the analytic flow design are the number of devices and the volumes of product flow between the devices. In the design of an automated distribution center, it is necessary to satisfy the demand throughput while minimizing construction costs. In the conventional design process, system engineers utilize experimental and intuitional approaches. However, conventional approaches are time-consuming and the design outcome is dependent on the skill of the designer. Therefore, a theoretical design algorithm is needed. We propose an analytic flow design algorithm using a dynamic network flow model and considering time-variable flow volumes according to shipment and storage schedules. To verify the feasibility of the proposed method, we perform analytic flow design using real data and confirm that the proposed method can yield a feasible analytic flow design in several minutes.     

Design of an analytic constrained predictive controller using neural networks

This paper shows how the solution of the standard predictive control problem can be recast as a continuous function of the state, the reference signal, the noise and the disturbances, and hence can be approximated arbitrarily closely by a feed-forward neural network. The existence of such a continuous mapping eliminates the need for linear independency of the active constraints, and therefore the resulting analytic constrained predictive controller will combine constraint handling with speed while being applicable to fast and complex control systems with many constraints. The effectiveness of the proposed controller design methodology is shown for a simulation example of an elevator model and for a real-time laboratory inverted pendulum system.     

New results in realization theory for linear time-varying analytic systems

The realization of linear time-varying systems specified by an analytic weighting pattern is approached in a novel manner using an algebraic framework defined over the ring of analytic functions. Realizations are given by a state representation consisting of a first-order vector differential equation and an output equation, both with analytic coefficients. Various new criteria for realizability are derived, including conditions given in terms of the finiteness of modules over the ring of analytic functions generated by the elementary rows or columns of a (generalized) Hankel matrix. These results are related to local criteria for realizability specified in terms of the rank of matrix functions, as developed in the work of Silverman and Meadows [5], [8], [9] and Kalman [7]. It is shown that the construction of minimal realizations reduces to the problem of computing a basis for a finite free module defined over the ring of analytic functions. A minimal realization algorithm is then derived using a constructive procedure for computing bases for finite free modules over a Bezout domain. The Silverman-Meadows realization algorithm [5] is a special case of the procedure given here. In the last part of the paper, the realization algorithm is applied to the problem of system reduction.     

On Ground Water Flow to an Imperfect Gallery: Case of Evaporation from a Free Surface

The plane steady-state filtration in a phreatimetric formation to an imperfect gallery in the presence of evaporation from the free surface of groundwater is considered. In order to study the evaporation effect, a multiparameter mixed boundary-value problem of the theory of analytic functions is posed and solved by the Polubarinova-Kochina method. Based on the proposed model, we develop an algorithm to compute the seepage flow characteristics and provide the hydrodynamic analysis of the impact of the dependences of all the physical parameters of the scheme on the flow rate of the gallery and the ordinate of the exit point of the depression curve on an impermeable screen.     

区间犹豫模糊的改进层次TODIM在云制造资源中的应用研究

针对具有递阶层次准则结构的决策问题,考虑到决策者偏好表达的不确定和犹豫性以及认知的参照依赖和损失规避行为,提出一种区间犹豫模糊多层的TODIM多准则决策方法。首先在对传统JACCARD距离修正后提出一种新的区间犹豫模糊距离测度,接着结合层次分析法思想与TODIM方法建立一种能够解决递阶层次准则结构决策问题的区间犹豫模糊决策方法。最后将该方法运用于云制造资源选择问题,并通过对比分析证实了其有效性和可用性。     

直觉模糊层次分析法处理医院用药风险评价

基于直觉模糊集的模糊逼近理论,给出了将直觉模糊互补判断矩阵转换为模糊逼近矩阵的方法,提出了直觉模糊环境下的AHP方法,简称为直觉模糊层次分析法,将其应用于对医疗机构的用药风险的评价问题,给出了各子风险类别的权重。经检验,是一种实用性较强的医疗机构用药风险评价方法。     

Direct synthesis of a layered medium from its seismic transmission response

A surface seismogram is recorded due to an upgoing unit-spike source incident on the lower interface of a horizontally layered system. This observed seismogram represents the seismic transmission response of the system. The following direct (noniterative) method is given for the determination of the reflection coefficients of the interfaces. First the observed seismogram is normalized by its first break, and then the least-squares inverse (i.e. zero-delay spiking filter) is computed from the normalized seismogram. Next this least-squares inverse is decomposed by means of an inverse recursion relation into the reflection coefficients of the interfaces. This method differs from that of Claerbout in that his transformation of this transmission response problem to a reflection response problem is not required.