关于BL-代数的模糊滤子与模糊理想

在BL-代数中引入模糊超滤子和模糊固执滤子的概念,证明了如下条件对于BL-代数的非常数模糊滤子f来说是等价的:(1)f是布尔的和素的,(2)f是蕴涵的和素的,(3)f是超的,(4)f是固执的。应用模糊正蕴涵滤子给出G-代数的若干特征性质。提出BL-代数模糊理想的概念,给出一些重要例子,并通过例子说明在BL-代数中模糊理想一般不能由模糊滤子导出。同时,从模糊理想出发构造了商BL-代数,并建立了相应的同态基本定理。最后,研究了BL-代数的几类模糊理想及其相互关系,给出模糊布尔理想、模糊素理想、模糊超理想的特征性质。     

Classification of explicit three-stage symplectic difference schemes for the numerical solution of natural Hamiltonian systems: A comparative study of the accuracy of high-order schemes on molecular dynamics problems

The natural Hamiltonian systems (systems with separable Hamiltonians) are considered. The variety of explicit three-stage symplectic schemes is described. A classification of the third-order accurate schemes is given. All fourth-order schemes are found (there are seven of them). It is proved that there are no fifth-order schemes. The schemes with improved properties, such as invertibility and optimality with respect to the phase error, are listed. Numerical results that demonstrate the properties of these schemes are presented, and their comparative analysis with respect to the accuracy–efficiency criterion is given. The disbalance of total energy is used as the accuracy criterion.     

Batch scheduling of deteriorating reworkables

The problem of scheduling the production of new and recoverable defective items of the same product manufactured on the same facility is studied. Items are processed in batches. Each batch comprises two sub-batches processed consecutively. In the first sub-batch, all the items are newly manufactured. Some of them are of the required good quality and some are defective. The defective items are remanufactured in the second sub-batch. They deteriorate while waiting for rework. This results in increased time and cost for their remanufacturing. All the items in the same sub-batch complete at the same time, which is the completion time of the last item in the sub-batch. Each remanufactured defective item is of the required good quality. It is assumed that the percentage of defective items in each batch is the same. A setup time is required to start batch processing and to switch from manufacturing to remanufacturing. The demands for good quality items over time are given. The objective is to find batch sizes such that the total setup and inventory holding cost is minimized and all the demands are satisfied. Dynamic programming algorithms are presented for the general problem and some important special cases.     

Assignment problems with changeover cost

We consider some variant models, having changeover cost, of the assignment problem. In these models, multiple assignments to an operator are allowed. In addition to assignment costs, a changeover cost is incurred if an operator does one job after another is completed. Two different types of changeover costs and related two models are considered. Mathematical programming formulations are given for the models. When changeover costs are dependent on the operator but independent of the jobs and are non-negative, a linear programming model is obtained. For the case when changeover costs are dependent on the jobs, a linear integer programming formulation is obtained. We also show that, this problem is strongly NP-hard. A heuristic solution method is suggested for it. Numerical findings on the performance of the method are given.     

Logical regularities in pattern recognition (Parametric Approach)

The search for logical regularities of classes in the recognition by precedents problems and the use of logical regularities for solving recognition and prediction problems are considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of a value of a feature in a certain interval of the real axis. The conjunctions are true on the subsets of reference objects of a certain class and are optimal. Various optimality criteria are considered and the problem of finding logical regularities is formulated as an integer programming problem. A qualitative analysis of these problems is performed. Models for evaluating estimates on the basis of systems of logical regularities are considered. Modifications of linear decision rules for finding estimates of how close the reference objects are to classes are proposed that are based on the search for the maximum gap. Approximations of logical regularities of classes by smooth functions is proposed. The concept of the dynamic logical regularity of classes is introduced, an algorithm for finding dynamic logical regularities is proposed, and a prediction method is developed.     

Economic design of screening procedures when the rejected items are reprocessed

In a screening inspection, all of the items are subject to acceptance inspection. If an item fails to meet the predetermined specifications, it is rejected. In this paper, economic screening procedures are considered when the rejected items are reprocessed. It is assumed that the reprocessed and nonreprocessed items are produced by the same manufacturing process and therefore their quality characteristics are identically and independently distributed. Screening procedures based on the performance variable of interest and a variable which is correlated with the performance variable are considered. Cost models are constructed which involve the cost incurred by imperfect quality, reprocessing cost, and inspection cost. Methods of finding the optimal screening procedures are presented and an example is given.     

含瞬时态、具有突变率的广义生-灭Q-矩阵(Ⅱ)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。     

Splitting and conjoining objects in monotopological categories

Power-sets are defined for any concrete category (over Set) with finite concrete products, and their structure described for monotopological categories. These sets are used to define the notions of splitting object and of conjoining object. Characterizations of the existence of these objects in monotopological categories are given. It is proved that no proper monotopological category can be concretely cartesian closed. Most well-known monotopological categories with splitting objects are topological or are c-categories, but it is shown that there are many proper monotopological categories which are not c-categories, and yet have splitting objects, and may even be cartesian closed. One of the characterizations of the existence of splitting objects is used to prove that a monotopological category with splitting objects is cartesian closed iff the largest initial completion in which it is epireflective is cartesian closed iff its MacNeille completion is cartesian closed.     

On Bounded Solutions of the Emden-Fowler Equation in a Semi-cylinder

Bounded solutions of the Emden-Fowler equation in a semi-cylinder are considered. For small solutions the asymptotic representations at infinity are derived. It is shown that there are large solutions whose behavior at infinity is different. These solutions are constructed when some inequalities between the dimension of the cylinder and the homogeneity of the nonlinear term are fulfilled. If these inequalities are not satisfied then it is proved, for the Dirichlet problem, that all bounded solutions tend to zero and have the same asymptotics as small solutions.     

Dynamic and static loss in stability of flexible spherical shells made out of a composite material

The dynamic and static stability of shallow spherical shells which are rectangular in a plane are investigated. It is assumed that the shell is made out of a composite material which is weakly shear resistant and hence the refined theories which allow for transverse shear deformations and rotational inertia are applied. The solutions which were obtained are compared with solutions founded on the basis of the Kirchhoff-Love theory. It is shown that the results which are obtained on the basis of the classical theory are high for both the static and dynamic loss in stability, and are qualitatively different from the results obtained using the refined theory. The solutions were obtained using the Bubnov-Galerkin method in the higher approximations.     

On fuzzy cliques in fuzzy networks

A definition of fuzzy clique in social networks is suggested which overcomes five limitations of current definitions. This definition is based on the networks in which the 0–1 strengths, the weighted strengths, and fuzzy strengths are all allowed. The fuzzy distance in such a network is defined. The node‐clique and clique‐clique coefficients are suggested. The core and the periphery of fuzzy cliques are discussed formally. A “cone like” property of the cores is discovered. The network structures are discussed using the new definition. A “no circle” property of networks is found. Basic fuzzy tools and the related algorithms are also discussed. Some examples are analyzed to demonstrate the theory.     

Performance evaluation of shared and separate inverted files

In this paper, two different structures for inverted files are analyzed and compared, when the relational join operation is taken into account. The structures are called shared and separate inverted files. The results are given of some experiments which show that the shared inverted organization is always advantageous when the inverted files are not sorted and is almost always advantageous when the files are sorted.     

油田注水系统拓扑布局优化的混合遗传算法

以投资最小为目标函数,建立了注水系统拓扑布局优化数学模型.根据模型特点,将优化问题分为两层,分别采用遗传算法和非线性优化方法进行求解.并对遗传算法的操作过程进行了改进,调整了适应函数,改进了交叉和变异操作,结合了模拟退火算法,在操作过程中使约束条件得到满足,减少了不可行解的产生,使遗传算法的优化性能得到了提高.优化算例说明了该方法的有效性.     

相关系数的传递性

主要研究了相关系数的传递性.首先在区间[-1,1]上引入两个运算和⊕,并讨论了它们的性质.接着利用运算和⊕给出了相关系数的传递性:当Xi与Xk完全相关,Xk与Xj完全相关时,Xi与Xj也完全相关.     

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

Constrained control for uncertain linear systems

The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments.     

小波分析方法在金融股票数据预测中的应用

利用小波分析预测方法对金融数据—股票收盘价这一典型的非平稳时间序列进行预测.使用M a llat小波分解算法对数据进行分解,对分解后的数据进行平滑处理,然后再进行重构,而重构之后的数据就成为近似意义的平稳时间序列,这样就得到了原始数据的近似信号,再应用传统时间序列预测方法对重构后的数据进行预测,将预测结果与实际值,以及和传统预测方法预测结果比较,小波分析方法预测效果更为理想.     

Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm

Multi-item inventory models with stock dependent demand and two storage facilities are developed in a fuzzy environment where processing time of each unit is fuzzy and the processing time of a lot is correlated with its size. These are order-quantity reorder-point models with back-ordering if required. Here possibility and crisp constraints on investment and capacity of the small storehouse respectively are considered. The models are formulated as fuzzy chance constrained programming problem and is solved via generalized reduced gradient (GRG) technique when crisp equivalent of the constraints are available. A genetic algorithm (GA) is developed based on fuzzy simulation and entropy where region of search space gradually decreases to a small neighborhood of the optima and it is used to solve the models whenever the equivalent crisp form of the constraint is not available. The models are illustrated with some numerical examples and some sensitivity analyses have been done. For some particular cases results observed via GRG and GA are compared.     

Non-stationary nonlinear analysis of a composite rotating shaft passing through critical speed

In this paper, nonlinear non-stationary dynamics of a nonlinear composite shaft passing through critical speed is studied. The nonlinearity is due to the large amplitude of shaft vibration. The equations of motion are obtained by three-dimensional constitutive relationships of composite materials. The gyroscopic effect, rotary inertia and coupling caused by material anisotropy are considered but shear deformation is neglected. Without any simplification, axial-flexural-flexural-torsional equations of motion (EOM) for the elastic composite shaft with variable rotational speed are obtained. The approximate analytical method namely asymptotic method is applied to analyze the nonstationary behavior of the composite shaft with constant acceleration. First, the EOMs are discretized using one and two-term Galerkin method. Then, the resulted equations are transformed to normal coordinates. Finally, the asymptotic method is applied to equations described in normal coordinates. Analytical expressions governing the amplitude and phase of motion during passage through critical speeds are obtained. By comparing the results obtained from analytical solutions, it is shown that discretization by one mode is not enough due to the existence of coupling in the equations and at least two modes are necessary for this purpose. Effects of damping, eccentricity, initial angular velocity and fiber angle on response amplitude are investigated. For verification, the results of perturbation theory are compared with numerical simulations and it is shown that there is good agreement between both methods.