THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.     

A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.     

Equilibrium theory for the hard-core systems

It is found that the density expansion in the argument of the exponential function gives a fine convergence on the equation of state of the hard-sphere system. The pair distribution function and the equation of state is constructed by an intuitive kinetic theoretical method. The equation of state of the hard-core system with attractive potential is constructed semiempirically with the aid of this simple analytical result, and Kamerling-Onnes' constant of the critical point is obtained analytically.     

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated. Finally, numerical results are reported and we discuss possible extensions of these results.     

基于机器视觉的刀具轮廓在线检测方法的研究

超精密单点金刚石车削过程中需要对刀具参数进行检测。基于机器视觉原理,采用新型的机械结构设计了新型刀具在线检测系统。通过垂直放置的两组由同轴远心镜头和CMOS相机组成的光学系统来获取车刀刀尖正面及侧面的图像,再经图像处理系统来获取刀具的轮廓及位置信息,完成对刀具轮廓及位置的在线检测,实验验证可实现测量的重复性定位精度达1μm。在线检测的方式借助了超精密车床自身的高精度和运动机构,可以保证相机焦点和机床主轴之间的相对位置关系,弥补了目前刀具检测系统稳定性差和重复性精度低的不足,提高了加工的整体效率。     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

A study on anomalous yield drop behaviour in modified beta titanium alloys

ABSTRACT

The yield drop phenomenon observed in the Ti–15V-3Al–3Sn-3Cr (Ti–15–3) beta-titanium alloy and its anomalous behaviour in the boron and carbon added Ti–15–3 alloys have been studied. While the base and the carbon containing alloys exhibit yield drop, the boron containing alloy with smaller grain size than base alloy does not appear to show this phenomenon. Tensile tests were interrupted at different stress levels followed by analyses of slip lines and sub-structural characteristics using scanning and transmission electron microscopes to understand this anomalous yield point phenomenon. Infrared thermal imaging technique was used to map the strain localisation and the spatiotemporal evolution of deformation along the gauge length of the specimens during the tensile tests. Deformation in these alloys initiates only in a few grains. Pile-up of dislocations in these grains subsequently triggers the formation of dislocations in other grains and their rapid multiplications. The spreading of deformation by the generation of dislocations from pile up dislocations in one grain to neighbouring un-deformed grains and their rapid multiplication to new regions influence the yield drop phenomenon and its characteristics. It is shown in this study that microscopic instability in the grain level is a necessary, but not the sufficient condition for the manifestation of macroscopic instability during tensile deformation in polycrystalline materials. The presence of boride particles at grain boundaries restricts the slip transfer across the grains as well as the spreading of deformation to new regions, which causes the suppression of yield drop in the boron containing alloy.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.