Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints

We propose an efficient approach to the problem of multi-degree reduction of rectangular Bézier patches, with prescribed boundary control points. We observe that the solution can be given in terms of constrained bivariate dual Bernstein polynomials. The complexity of the method is O(mn₁n₂) with m ? min(m₁, m₂), where (n₁, n₂) and (m₁, m₂) is the degree of the input and output Bézier surface, respectively. If the approximation—with appropriate boundary constraints—is performed for each patch of several smoothly joined rectangular Bézier surfaces, the result is a composite surface of global C^r continuity with a prescribed r ? 0. In the detailed discussion, we restrict ourselves to r ∈ {0, 1}, which is the most important case in practical application. Some illustrative examples are given.     

A new element for analyzing large deformation of thin Naghdi shell model. Part II: Plastic

In this paper a new element is developed that is based on Cosserat theory. In the finite element implementation of Cosserat theory shear locking can occur, especially for very thin shells. In the present investigation the director vector is constrained to remain perpendicular to the mid surface during deformation. It will be shown that this constraint yields accurate results in very large deformation of thin shells also the rate of convergency is very good. For plastic formulation, the model introduced by Simo is used and it has been reduced for constrained director vector and the consistent elasto-plastic tangent moduli is extracted for finite element solution. This model includes both kinematic and isotropic hardening. For numerical investigations an isoparametric nine node element is employed then by linearization of the principle of virtual work, material and geometric stiffness matrices are extracted. The validity and the accuracy of the proposed element is illustrated by the numerical examples and the results are compared with those available in the literature.     

Recent developments in Dual Resource Constrained (DRC) system research

Real world manufacturing systems are usually constrained by both machine and human resources. Human operators are often the constraining resource and transfer between workstations to process jobs when required. This kind of system is known as a Dual Resource Constrained (DRC) system and presents additional technical challenges which must be considered during planning and scheduling. These technical challenges can be categorised into the five main dimensions of job release mechanisms, job dispatching, worker flexibility, worker assignment and transfer costs. This paper aims to provide an overview of recent developments in DRC research concerned with each of these areas and also discusses some possible approaches to solving the resource scheduling problem in a DRC system. The focus is on materials published after 1995 and up to 2009. Previous reviews on DRC systems are commented on and followed by a review of recent works associated with each of the five dimensions of DRC system research. Advancements made and new methodologies proposed are discussed and future research directions are identified.     

Finding the best separation in situations of extremely low chromatographic resolution

Samples with a large number of compounds or similarities in their structure and polarity may yield insufficient chromatographic resolution. In such cases, however, finding conditions where the largest number of compounds appears sufficiently resolved can be still worthwhile. A strategy is here reported that optimises the resolution level of chromatograms in cases where conventional global criteria, such as the worst resolved peak pair or the product of elementary resolutions, are not able to detect any separation, even when most peaks are baseline resolved. The strategy applies a function based on the number of "well resolved" peaks, which are those that exceed a given threshold of peak purity. It is, therefore, oriented to quantify the success in the separation, and not the failure, as the conventional criteria do. The conditions that resolve the same amount of peaks are discriminated by either quantifying the partial resolution of those peaks that exceed the established threshold, or by improving the separation of peaks below it. The proposed approach is illustrated by the reversed-phase liquid chromatographic separation of a mixture of 30 ionisable and neutral compounds, using the acetonitrile content and pH as factors.     

Switching systems with dwell time: Computing the maximal Lyapunov exponent

We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete–continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions. Each discrete action has its own positive weight which accounts for its time-duration. We develop a theory of stability for the mixed systems; in particular, we prove the existence of an invariant Lyapunov norm for mixed systems on graphs and study its structure in various cases, including discrete-time systems for which discrete actions have inhomogeneous time durations. This allows us to adapt recent methods for the joint spectral radius computation (Gripenberg’s algorithm and the Invariant Polytope Algorithm) to compute the Lyapunov exponent of mixed systems on graphs.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.     

Graph splicing systems

In this paper, extended graph splicing systems are defined. It is shown that when strings are represented as linear graphs, any recursively enumerable set can be generated by an extended graph splicing system. It is also shown that the computational completeness of extended graph splicing systems can be proved under some constraints too.     

Another greedy heuristic for the constrained forest problem

The constrained forest problem seeks a minimum-weight spanning forest in an undirected edge-weighted graph such that each tree spans at least a specified number of vertices. We present a greedy heuristic for this NP-hard problem, whose solutions are at least as good as, and often better than, those produced by the best-known 2-approximate heuristic.     

Multidimensional bisection: The performance and the context

Two aspects of the multidimensional bisection algorithms for the global optimisation of Lipschitz continuous functions are investigated. Firstly, for several test functions we examine the numerical performance of the deepest point algorithm and two acceleration procedures. Secondly, we phrase the branch and bound framework of Horst and Tuy in terms of covers, and show the algorithms to be included in this framework. A result of Basso on the convergence of localisations is extended to higher dimensions.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Necessary conditions for constrained optimization problems with semicontinuous and continuous data

We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.