Methodological Issues in Studying Effects of Networks in Organizations

Three methodological issues are discussed that are important for the analysis of data on networks in organizations. The first is the two-level nature of the data: individuals are nested in organizations. This can be dealt with by using multilevel statistical methods. The second is the complicated nature of statistical methods for network analysis. The third issue is the potential of mathematical modeling for the study of network effects and network evolution in organizations. Two examples are given of mathematical models for gossip in organizations. The first example is a model for cross-sectional data, the second is a model for longitudinal data that reflect the joint development of network structure and individual behavior tendencies.     

On identification in fuzzy systems and its applications in control problems

The problem of identification in fuzzy systems described by the use of fuzzy equation is considered. The identification method and its performance index is also presented. The formal procedure of the identification algorithm is illustrated by means of a numerical example. The possibility of using the proposed algorithm for the solution of a control problem is given as well.     

Layerwise sensing in X-ray tomography in the polychromatic case

An X-ray tomography problem that is an inverse problem for the transport differential equation is studied. The absorption and single scattering of particles are taken into account. The suggested statement of the problem corresponds to stepwise and layerwise sensing of an unknown medium with initial data specified as the integrals of the outgoing flux density with respect to energy. The sought object is a set on which the coefficients of the equations suffer a discontinuity, which corresponds to searching for the boundaries between the different substances composing the sensed medium. A uniqueness theorem is proven under rather general assumptions and a condition guaranteeing the existence of the sought lines. The proof is constructive and can be used for developing a numerical algorithm.     

Theoretical model of laminar flow in tubes in rolling motion

The theoretical model of laminar flow in tubes in rolling motion is established. The velocity and temperature correlations are derived, and the frictional resistance coefficient and Nusselt number are also obtained. The oscillation of parameters is induced by the tangential force due to rolling motion. The effect of centrifugal and Coriolis forces on the flow is negligible. The tangential force does not effect on the average parameters. The oscillating amplitude of Nusselt number increase with the Prandtl number increasing. Both the oscillating amplitudes of frictional resistance coefficient and Nusselt number increase with the rolling frequency increasing.     

ON ASPIRATION SOLUTIONS IN PREDICTING COALITION FORMATION IN COOPERATIVE GAMES

This paper consists of two parts. The first part introduces the strict aspiration as a new aspiration solution concept, which is proved to be existent for any cooperative game. The second part deals with the unsolved problem put forward by Bennett [1] by showing that there is at least one payoff which is balanced, partnered and equal gains aspiration. The proof is algebraic and constructive, thus providing an algorithm for finding such aspirations.     

Modelling torsion in an elastic cable in space

When an imperfectly flexible, elastic cable is suspended in a vertical plane under the sole influence of gravity and boundary conditions involving axial twist are then applied to the endpoints of the cable, its shape extends from the original vertical plane to a three-dimensional configuration in space. The aim of this paper is to develop a mathematical model (consisting of differential equations) for the configuration of and tension in such a twisted cable. The model is solved numerically for different boundary conditions. Although the final model delivers satisfactory results for small amounts of twist (inside the elastic deformation domain of the cable), realistic bounds for the amount of twist that may be applied (before plastic deformation of the cable causes model inaccuracies) are yet unknown. However, the effect of an increase in the amount of torsion applied at the endpoints of the cable is investigated numerically. The model seems capable of capturing first points of twisting bifurcation, when so much twist is applied at the endpoints that the cable jumps from un unstable equilibrium configuration to a more stable one.     

Numerical ranges in physics

Some examples of the incidence of Numerical Ranges in Physics are discussed. The Thermodynamical Inequality is deduced using the theory of Numerical Ranges. The Peierls-Bogoliubov inequality is obtained from the Thermodynamical Inequality. The formalism of Thermo Field Dynamics is summarized in the same framework.     

Improved vehicle scheduling in public transport through systematic changes in the time-table

Vehicle scheduling for a fixed time-table is easy to formulate and solve as a minimal-cost-flow problem. Normally, however, there is considerable flexibility in the time-table. We propose here a method for exploiting this flexibility in order to improve the vehicle scheduling.A given set of trips must be assigned to a fleet of identical vehicles, starting from a common garage. Each trip is characterized by initial stop, final stop, duration, earliest departure time, and latest departure time.The problem is to decide which vehicle should be assigned to each individual trip and when the trip should start, so that a generalized cost is minimized.The minimum-cost-flow problem is first solved for the ‘kernels’ of every trip in order to make clear when the critical time-periods occur and obtain a lower bound for the solution. The kernel is defined as a trip that starts at the latest possible departure time and finishes at the earliest possible arriving time.The departure time for each trip is then chosen, thereby increasing the chances of obtaining a good schedule. The minimum-cost-flow problem is then solved for this fixed time-table.Finally, the departure times for each vehicle are adjusted (blocked) so that each vehicle (and driver) is efficiently used. This method is used as an integral part of the Volvo Traffic Planning Package.     

Symmetric random walk in random environment in one dimension

We give a new proof of the central limit theorem for one dimensional symmetric random walk in random environment. The proof is quite elementary and natural. We show the convergence of the generators and from this we conclude the convergence of the process. We also investigate the hydrodynamic limit (HDL) of one dimensional symmetric simple exclusion in random environment and prove stochastic convergence of the scaled density field. The macroscopic behaviour of this field is given by a linear heat equation. The diffusion coefficient is the same as that of the corresponding random walk. This revised version was published online in June 2006 with corrections to the Cover Date.     

Operator Function Method in the Problem of Normal Waves in an Inhomogeneous Waveguide

The problem of normal waves in a closed (screened) regular waveguiding structure of arbitrary cross-section is considered by reducing it to a boundary value problem for the longitudinal electromagnetic field components in Sobolev spaces. The variational statements of the problem is used to determine the solution. The problem is reduced to studying an operator function. The properties of the operators contained in the operator function necessary to analyze its spectral properties are studied. Theorems on the spectrum discreteness and the distribution of characteristic numbers of the operator function on the complex plane are proved. The problem of completeness of the system of root vectors of the operator function is considered. The theorem on the double completeness of the system of root vectors of the operator function with finite deficiency is proved.     

Numerical Simulation of Anisotropy Directions in Soft Tissues and in Particular in Skin

Orientation of collagen fibers and their spatial distribution predefine macroscopic mechanical properties of the soft tissue and in particular its anisotropy directions. In this contribution, we apply two different procedures to automatically generate these directions for a 3D FE-model. The first procedure is based on an analogy with a heat conduction problem. Accordingly, a thermal flux under certain temperature boundary conditions is calculated by the same FE model and is further utilized for the definition of the anisotropy directions. The numerical result shows good agreement with Langer's lines data in human skin. Within the second procedure, the fiber vector field is calculated by the Laplacian smoothing method based on the user defined fiber direction sketches. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decision-making in Government

The economic assessment of a research and development project is an important factor in planning and carrying out a project but its value depends on the forecasts on which it is based. The reasons why probabilistic methods are considered inappropriate when forecasting for novel projects are discussed and an alternative technique using credibility forecasts is described. Credibility forecasts for stages of a project are transformed into pairs of standardized “focus” forecasts from which are obtained two focus cash flow curves for the complete project. Two derived focus values of any suitable economic criterion are compared with a neutral value of the criterion to evaluate the attractiveness of the project and the degree of risk involved. The use of this technique for the initial assessment of a project and for reassessment at later stages is discussed and the procedure is illustrated by an example.     

Hypersingularities in three-dimensional crack configurations in composite laminates

Three-dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi-analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter-fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three-dimensional crack configurations in composite laminates so-called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The optimum anisotropy in problems of heat conduction in solids

Some problems of optimizing the internal structure of solids, made of a material which is locally orthotropic with respect to the heat-conducting properties, are formulated. The state variable (the inverse temperature) is determined from the solution of the boundary value problem of heat conduction. The orthogonal rotation tensor, which defines the optimum orientation of the orthotropy axes of the material that delivers an extremum to the dissipation functional, is used as the control variable. The necessary conditions for an extremum are derived and some properties of the equations defining the optimal structures are investigated. Examples are given of the solution of problems of the optimum arrangement of the orthotropic material, and the possibility of effectively using the membrane analogy for this purpose is pointed out.     

The linearization method in the inverse problem of determination of low-permeability zones in an oil-bearing layer

The possibility of determination of low-permeability zones in an oil-bearing layer from bore-pressure measurements is studied. The formulation of the problem on the pressure distribution in the layer is considered in the case when the pressure is invariable across the layer. The problem is reduced to an integral equation. The linearization of the inverse problem of determination of low-permeability zones is considered. An iterative technique is proposed for solution of this problem. The technique involves reduction of the inverse problem to an operator equation.     

Scheduling Production in a Heavily Constrained Plant – Anode Manufacture in an Aluminium Smelter

In this paper a mathematical model of an anode manufacturing plant is developed with the objective of assisting in the planning and scheduling of production for up to a month ahead. A model of the overall smelter already exists and is based on a monthly time frame. The anode plant is a part of this model but is a very heavily constrained area and it is necessary to have a daily planning model that will help to achieve the optimal level of operations as dictated by the overall model of the smelter. The anode area is responsible for the production of carbon blocks (called anodes) which are an integral part of the aluminium smelting process. The plant is also responsible for the delivery of all raw materials within the smelter. The model developed is a daily one replicated for up to a month ahead, interconnected by opening and closing stocks.     

The anticipative concept in warehouse optimization using simulation in an uncertain environment

The modern business environment is highly unpredictable. An anticipation approach in a real case study is presented to cope with such instability and minimize the total inventory cost without stock-outs occurring and inventory capacity being exceeded. The anticipation concept is performed using simulation models supported by inventory control algorithms on a selected sample of representative items. The inventory control algorithms include Silver–Meal, Part period balancing, Least-unit cost, and Fuzzy inventory control algorithm based on fuzzy stock-outs, highest inventory level and total cost. Transportation cost is explicitly defined as a discrete function of shipment size. The algorithms are tested on historic data. Simulation results are presented and the risk of accepting them as reliable is discussed. The process of simulation model implementation is briefly discussed to further validate the model and train order managers to use the simulation model in their order placement process.     

Numerical method in wave-body interactions

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.     

Spin-up in Couette Flow

A viscoelastic fluid is contained in the annular region between two infinitely long coaxial circular cylinders. The relation between shearing stress and the history of the rate of shear in the fluid is assumed to be linear. At some instant of time the inner cylinder is given an angular velocity which is subsequently held constant. The resulting angular velocity and stress fields are calculated.     

Estimation of dynamic strains in finite end-constrained pipes in seismic areas

The work presents an analysis of the dynamical response of a buried pipe under seismic excitation. The pipe is assumed to be of finite length and the Winkler model to schematize soil-structure interaction is considered. With reference to the boundary conditions of end-constrained pipe the axial motions are discussed. Careful numerical integrations are performed in order to prevent undesirable oscillations close to the discontinuities. The main result emphasized by the numerical analysis is that end-constrained finite length pipelines are subject to strains greater than infinite length pipes, or free-end finite length pipes.