Batching in single operation manufacturing systems

We introduce a new decision problem important to the efficient operation of resources in manufacturing systems. This problem of ‘batching’ is considered for single machine activities. It is shown that even for these simple models, lot splitting may occur and that these batching decisions may have a dramatic impact on the manufacturing lead time of items to be processed.     

Bifurcation analysis in an age-structured model of a single species living in two identical patches

In this paper, we consider the age-structured model of a single species living in two identical patches derived in So et al. [J.W.-H. So, J. Wu, X. Zou, Structured population on two patches: modeling dispersal and delay, J. Math. Biol. 43 (2001) 37–51]. We chose a birth function that is frequently used but different from the one used in So et al. which leads to a different structure of the homogeneous equilibria. We investigate the stability of these equilibria and Hopf bifurcations by analyzing the distribution of the roots of associated characteristic equation. By the theory of normal form and center manifold, an explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived. Finally, some numerical simulations are carried out for supporting the analytic results.     

The square root base of polynomials in Clifford analysis

In this paper the problem of taking the square root of bases of special monogenic polynomials is studied, thus leading to a number of results under some additional conditions of associated infinite matrices, related essentially to the so-called algebraicness of these matrices.     

Multi-goal analysis of a short-run reservoir operation

An application of multi-goal mathematical programming to a water resource management problem is described. This paper is concerned with the regulation of a reservoir which releases water to downstream users and has recreational activities located on its sides.The Pareto-optimal alternatives of the problem are found by an efficient search algorithm without applying the standard generating techniques of multi-goal programming. The application of the analysis to a real situation (a lake in Northern Italy) is given in detail.     

The covalidation of dissimilarly structured strategic airlift models

A methodology is presented which allows comparison between models constructed under different modeling paradigms. Consider two models that exist to study different aspects of the same system, specifically Air Mobility Command's strategic airlift system. One model simulates a fleet of aircraft moving a given combination of cargo and passengers from an onload point to an offload point. The second model is a linear program that optimizes aircraft and route selection given cargo and passenger requirements in order to minimize late and nondeliveries. Further, the optimization model represents a more aggregated view of the airlift system than does the simulation. The two models do not have immediately comparable input or output structures, which complicates comparisons between the two models. We develop a methodology that structures this comparison and use it to compare the two large-scale models described above. Further, our technique has the fortunate byproduct of improving the fidelity of the models through a series of iterative refinements of the input to each model based on the output of the other. Models that compare favorably with regard to our methodology are deemed covalid models.     

The dynamics of structures on an elastic base

The problem of the dynamics of structures interacting with an elastic homogeneous half-plane through a rigid unyielding plate is reduced to the construction of the matrix of transmission momentum functions (the Green's matrix), which establishes the dependence between the generalized coordinates of the oscillations of the plate and the force characteristics. The elements obtained for this matrix are represented by graphs as the result of numerical solution of the nonsteady-state dynamic contact problem. We conclude that approximating a Green's matrix of exponential type on an infinite time interval is unjustified.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 60–63.     

The problem of the bending of a beam lying on an elastic base

The plane contact problem of the transmission of a normal force of specified strength onto an elastic anisotropic, wedge-shaped plate by an elastic beam of variable flexural stiffness is considered. The beam is coupled to one of the edges of the plate and its other edge is stress-free. The solution of the problem is obtained in closed form by reducing it to a Karleman boundary-value problem with shear for a strip. A conclusion is reached concerning the nature of the discontinuity of the normal contact stress at the vertex of the wedge.     

Multiscaling analysis of a slowly varying single species population model displaying an Allee effect

We consider the growth of a single species population modelled by a logistic equation modified to accommodate an Allee effect, in which the model parameters are slowly varying functions of time. We apply a multitiming technique to construct general approximate expressions for the evolving population in the case where the population survives to a (slowly varying) finite positive limiting state, and that where the population declines to extinction. We show that these expressions give excellent agreement with the results of numerical calculations for particular instances of the changing model parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

Reducing abstraction: The case of constructing an operation table for a group

This paper describes students' mental processes while constructing an operation table for a group. More specifically, undergraduate students' approaches are analyzed as the students fill in an operation table for four elements—a, b, c, and d—in such a way that it represents a group of order four. The data are analyzed from the perspective of reducing abstraction, which aims to explain students' conceptions of abstract algebra concepts. From this perspective, most students' responses and conceptions can be attributed to their tendency to work on a lower level of abstraction than the level on which concepts are introduced in class.     

The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

We define the algebraic fundamental group π ₁(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G? π₁(G) is exact.     

Algorithmic analysis of irrational rotations in a single neuron model

We study computability of real-valued functions and the information needed for simulation of dynamical systems. In particular, we describe application of Kolmogorov complexity theory to computer simulation of irrational rotations in a single neuron model. We deduce the information needed for a parameter in simulating the dynamics by showing a difference in Kolmogorov complexity between a computable parameter and a non-computable parameter. Finally, we show that all trajectories generated by irrational rotations are non-computable iff its parameter is non-computable.     

The Conley index over a base

We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in , and the problem of continuing two periodic orbits which are not homotopic as loops.

     

A fuzzy knowledge base of an expert system for analysis of manual lifting tasks

Development of the fuzzy knowledge base of an expert system for analysis of manual lifting tasks (liftan) is described. The system, written in Maclisp and implemented on a DEC-10 mainframe computer, allows a non-expert in the field to utilize the relevant knowledge and apply it to analyze specific work situations. The knowledge base of liftan consists of 85 rules related to risk analysis and 64 rules used to create explanations and messages to the user. The values of the variables used in the fuzzy knowledge base are represented using the linguistic approach. In order to illustrate the practical implementation of the developed knowledge base, an example is shown.     

Stability analysis of an open cracked rotor with the anisotropic rotational damping in rotating operation

The damping effects with the distinction of stationary damping and the anisotropic rotating damping on the dynamic stability of the rotating rotor with an open crack on the surface of the shaft is studied. The motion equations of the cracked rotor system are formed by Lagranges principal. Different from previous studies, the anisotropic system with the multi periodical varied coefficients is simplified by the moving frame method such that the stability analysis based on the root locus method can be applied. The corresponding Campbell diagram, decay rate plot and roots locus plot are derived to prove the destabilizing influence of both the rotational damping and the varied anisotropy ratio of the rotating damping. The effects of anisotropy of stiffness on the decisions of the critical range are also presented. The result with theoretical precision would not only generally provide practical applicability to crack detection and instability control of the heavy loading turbo-machinery system, but also give the suggestion that, the increased proportion and the aggravated anisotropy of the rotational damping due to the crack of the fatigue rotor should been taken into consideration on the modeling of cracked rotor system.     

The interior operation in aψ-density topology

We prove that for an arbitrary setA ? ? its interior in aψ-density topology equalsA ∩ φ^β(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS.     

Stresses in an elastic plate lying over a base due to strip-loading

The closed-form analytic expressions for the stresses at any point of an elastic plate coupling in different ways to a base as a result of a two-dimensional shear strip-loading are obtained. The contact between the horizontal layer and the base is either smooth-rigid or rough-rigid or welded. The variations of the shear stresses with the horizontal distance have been studied numerically. It is found that the effect of different boundary conditions on the stress field is significant and the stresses for an elastic layer lying over an elastic half-space differ considerably from those of an entire homogeneous elastic half-space.     

An analysis of the joint operation of a CFRP concrete in flexural elements

The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 687–700, September–October, 2007.     

Performance analysis in a re-entrant operation with combinational routing and yield probabilities

Queuing networks arising from multistage processes with probabilistic re-entrant lines are common in manufacturing environments. Probabilistic re-entrant operation is defined as lots entering the operation with different repeated cycle requirements. This paper extends our work [S. Kumar, M.K. Omar, Stochastic re-entrant line modeling for an environmental stress testing in a semiconductor assembly industry, Appl. Math. Comput. 173 (2006) 603–615.] and proposes a modified analytical method based on the mean value analysis (MVA) technique and considering a probabilistic re-entrant line with yield loss probabilities. Introducing probabilities consideration into the MVA approach will substantially increase the complexity of the modeling and results analysis. However, the contribution of this paper is the introduction of a solution methodology that can overcome such complexity and allow operational managers to compute performance measures such as total cycle time and the mean throughput.