ALBERT

Beschreibung: The aim of the present study is to investigate the sensitivity of empirical Bayes estimates of the reliability function with respect to changing of the loss function. In addition to applying some of the basic analytical results on empirical Bayes reliability obtained with the use of the “popular” squared error loss function, we shall derive some expressions corresponding to empirical Bayes reliability estimates obtained with the Higgins–Tsokos, the Harris and our proposed logarithmic loss functions. The concept of efficiency, along with the notion of integrated mean square error, will be used as a criterion to numerically compare our results.It is shown that empirical Bayes reliability functions are in general sensitive to the choice of the loss function, and that the squared error loss does not always yield the best empirical Bayes reliability estimate.

Beschreibung: In this paper we develop a test for determining whether the observed sample path comes from a system with hysteresis perturbed by noise, or if it arises from a system governed by an ordinary differential equation with the same noise. A large sample size test is constructed, which is appropriate in many practical situations. Two models are considered as alternatives to the hysteresis model. An asymptotic expression for the cutoff point of the test is found using a version of the central limit theorem.

Beschreibung: We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.

Beschreibung: General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.

Beschreibung: This paper studies the problem of robust control of a class of uncertain bilinear continuous-time systems. The class of uncertain systems is described by a state space model with time-varying norm-bounded parameter uncertainty in the state equation. We address the problem of robustH∞control in which both robust stability and a prescribedH∞performance are required to be achieved irrespective of the uncertainties. Both state feedback and output feedback controllers are designed. It has been shown that the above problems can be recast intoH∞syntheses for related bilinear systems without parameter uncertainty, which can be solved via a Riccati inequality approach. Two examples are given to show the potential of the proposed technique.

Beschreibung: The paper is concerned with the development of a rigorous mathematical model describing the dynamics of criminal population subject to sentencing policies of any penal (legal) system. The model enables evaluation of the impact of preventive measures used in the society and correctional measures used by the penitentiaries. A performance index reflecting the effectiveness of such measures and the cost to the society for providing the same is introduced and the question of optimality discussed.

Beschreibung: A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the exterior of an open arc in a plane. By means of potential theory the problem is reduced to the Cauchy singular integral equation and next to the Fredholm equation of the 2nd kind which is uniquely solvable. The solution of the integral equation can be computed by standard codes by discretization and inversion of the matrix. The uniqueness and existence theorems are formulated.

Beschreibung: Queueing models with controllable service rate play an important role in telecommunication systems. This paper deals with a single-server model with a batch Markovian arrival process (BMAP) and two service modes, where switch-over times are involved when changing the service mode. The embedded stationary queue length distribution and the explicit dependence of operation criteria on switch-over levels and derived.

Beschreibung: The structure of a steady planar Chapman–Jouguet detonation, which is supported by a direct first-order one-step irreversible exothermic unimolecular reaction, subject to Arrhenius kinetics, is examined. Solutions are studied, by means of a limit-process-expansion analysis, valid forΛ, proportional to the ratio of the reaction rate to the flow rate, going to zero, and forβ, proportional to the ratio of the activation temperature to the maximum flow temperature, going to infinity, with the productΛβ1/2going to zero. The results, essentially in agreement with the Zeldovich–von Neumann–Doring model, show that the detonation consists of (1) a three-region upstream shock-like zone, wherein convection and diffusion dominate; (2) an exponentially thicker five-region downstream deflagration-like zone, wherein convection and reaction dominate; and (3) a transition zone, intermediate to the upstream and downstream zones, wherein convection, diffusion, and reaction are of the same order of magnitude. It is in this transition zone that the ideal Neumann state is most closely approached.

Beschreibung: Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

Beschreibung: The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

Beschreibung: A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

Beschreibung: Design optimization of a gas turbine blade geometry for effective film cooling toreduce the blade temperature has been done using a multiobjective optimization formulation. Three optimization formulations have been used. In the first, the average blade temperature is chosen as the objective function to be minimized. An upper bound constraint has been imposed on the maximum blade temperature. In the second, the maximum blade temperature is chosen as the objective function to be minimized with an upper bound constraint on the average blade temperature. In the third formulation, the blade average and maximum temperatures are chosen as objective functions. Shape optimization is performed using geometric parameters associated with film cooling and blade external shape. A quasi-three-dimensional Navier–Stokes solver for turbomachinery flows is used to solve for the flow field external to the blade with appropriate modifications to incorporate the effect of film cooling. The heat transfer analysis for temperature distribution within the blade is performed by solving the heat diffusion equation using the finite element method. The multiobjective Kreisselmeier–Steinhauser function approach has been used in conjunction with an approximate analysis technique for optimization. The results obtained using both formulations are compared with reference geometry. All three formulations yield significant reductions in blade temperature with the multiobjective formulation yielding largest reduction in blade temperature.

Beschreibung: In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

Beschreibung: The color filters that are used to attenuate noise are usually optimized to perform extremely well when dealing with certain noise distributions. Unfortunately it is often the case that the noise corrupting the image is not known. It is thus beneficial to knowa priorithe type of noise corrupting the image in order to select the optimal filter. A method of extracting and characterizing the noise within a digital color image using the generalized Gaussian probability density function (pdf) (B.D. Jeffs and W.H. Pun,IEEE Transactions on Image Processing,4(10), 1451–1456, 1995 andProceedings of the Int. Conference on Image Processing,465–468, 1996), is presented. In this paper simulation results are included to demonstrate the effectiveness of the proposed methodology.

Beschreibung: We consider a model for biochemical oxygen demand (BOD) in a semi-infinite river where the BOD is prescribed by a time varying function at the left endpoint. That is, we study the problem with a time varying boundary loading. We obtain the well-posedness for the model when the boundary loading is smooth in time. We also obtain various qualitative results such as ordering, positivity, and boundedness. Of greatest interest, we show that a periodic loading function admits a unique asymptotically attracting periodic solution. For non-smooth loading functions, we obtain weak solutions. Finally, for certain special cases, we show how to obtain explicit solutions in the form of infinite series.

Beschreibung: We model the error control of the partial buffer sharing of ATM by a queueing systemM1,M2/G/1/K+1with threshold and instantaneous Bernoulli feedback. We first derive the system equations and develop a recursive method to compute the loss probabilities at an arbitrary time epoch. We then build an approximation scheme to compute the mean waiting time of each class of cells. An algorithm is developed for finding the optimal threshold and queue capacity for a given quality of service.

Beschreibung: Benney's theory of evolution of disturbances in shear flows over smooth and flat boundary is extended to study for shear flows over combined spatially and temporally corrugated walls. Perturbation and multiple-scales analyses are employed for the case where both amplitude of the corrugations and the amplitude of wave motion are small. Analyses for instability of modulated mean shear flows with respect to spanwise-periodic disturbance rolls and for the subsequent vortex formation and vortex stability are presented, and the effects of the corrugated walls on the resulting flow and vortices are determined. It is found that particular corrugated walls can originate and control the longitudinal vortices, while some other types of corrugated walls can enhance instability of such vortices.

Beschreibung: In this paper a simple introduction to the problem of the regularization of ill-posed problems (IPP) is presented. We describe three regularization methods with simple examples which illustrate the principle that for “bad” equations it is unprofitable to carry out exact computations.

Beschreibung: Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. In the simplest case of free-radical polymerization, a mixture of monomer and initiator is placed in a test tube. A reaction is then initiated at one end of the tube. Over time, a self-sustained thermal wave, in which chemical conversion occurs, is produced. This phenomenon is possible because of the highly exothermic nature of the polymerization reactions.Though there are certain advantages to this polymerization process over the more traditional methods, one of the drawbacks is that conversion tends to be incomplete. One way to increase conversion is by using greater amounts of initiator. The disadvantage to using this method is that more initiator results in the production of more free radicals, leading to large numbers of undesirably short polymer chains. A second method is to use a mixture of unstable and stable initiators. In this paper we develop and study a mathematical model of the propagation of free-radical polymerization fronts using such a complex initiation. We compare the propagation velocity, maximum temperature and degree of conversion of fronts with a stable initiator, an unstable initiator and a mixture of the two. In addition, we examine how altering the stability of the stable initiator affects these quantities. We show that it is indeed the case that a mixture of unstable and stable initiators does have many advantages over using either type of initiator individually, in agreement with the existing experimental data.

Beschreibung: A major problem facing battery-powered electric vehicles is in their batteries: weight and charge capacity. Thus, a battery-powered electric vehicle only has a short driving range. To travel for a longer distance, the batteries are required to be recharged frequently. In this paper, we construct a model for a battery-powered electric vehicle, in which driving strategy is to be obtained such that the total travelling time between two locations is minimized. The problem is formulated as an optimization problem with switching times and speed as decision variables. This is an unconventional optimization problem. However, by using the control parametrization enhancing technique (CPET), it is shown that this unconventional optimization is equivalent to a conventional optimal parameter selection problem. Numerical examples are solved using the proposed method.

Beschreibung: This work is motivated by the need forr tools for the analysis of disturbance model uncertainty in feedback control systems. Such tools are developed in this paper for the case where the disturbance is modeled as the output of a first-order filter which is driven by white noise and whose bandwidth,ωd, and gain,K, are uncertain. An analytical expression for the steady-state output variance as a function ofωdis derived: This function is referred to as aV-transform, and is denoted byV(G)(ωd), whereG(s)is the closed-loop transfer function from disturbance to output. Properties ofV-transforms are investigated and the notions ofdisturbance gain marginanddisturbance bandwidth margin, both measures of robustness with respect to disturbance model uncertainty, are introduced. Using these new tools, it is shown that there is a fundamental robustness performance limitation if the plant has nonminimum-phase zeros, but no such limitation in the minimum-phase case.

Beschreibung: In this paper we consider a few dynamic models of suspension bridge described by partial differential equations with linear and nonlinear couplings. We study analytically the stability properties of these models and the relative effectiveness of aerodynamic and structural damping. Increasing aerodynamic or structural damping indefinitely does not necessarily increase the decay rate indefinitely. In view of possible disastrous effects of high wind, structural damping is preferable to aerodynamic (viscous) damping. These results are illustrated by numerical simulation.

Beschreibung: In Ref. [6] the authors constructed analytical solutions including one arbitrary function for the problem of nonlinear, unsteady, supersonic flow analysis concerning slender bodies of revolution due to small amplitude oscillations. An application describing a flow past a right circular cone was presented and the constructed solutions were given in the form of infinite series through a set of convenient boundary and initial conditions in accordance with the physical problem. In the present paper we develop an appropriate convergence analysis concerning the before mentioned series solutions for the specific geometry of a rigid right circular cone. We succeed in estimating the limiting values of the series producing velocity and acceleration resultants of the problem under consideration. Several graphics for the velocity and acceleration flow fields are presented. We must underline here that the proposed convergence technique is unique and can be applied to any other geometry of the considered body of revolution.

Beschreibung: The paper presents a novel approach to predict the response of earthquake-excited structures. The earthquake excitation is expanded in terms of series of deterministic functions. The coefficients of the series are represented as a point inN-dimensional space. Each available ccelerogram at a certain site is then represented as a point in the above space, modeling the available fragmentary historical data. The minimum volume ellipsoid, containing all points, is constructed. The ellipsoidal models of uncertainty, pertinent to earthquake excitation, are developed. The maximum response of a structure, subjected to the earthquake excitation, within ellipsoidal modeling of the latter, is determined. This procedure of determining least favorable response was termed in the literature (Elishakoff, 1991) as an antioptimization. It appears that under inherent uncertainty of earthquake excitation, antioptimization analysis is a viable alternative to stochastic approach.

Beschreibung: In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls,B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.

Beschreibung: In this paper we consider a dynamic model of suspension bridge governed by a pair of coupled partial differential equations which describe both torsional and longitudinal vibration of the road bed. The vertical and torsional motions are coupled through a nonlinear operation with the nonlinearity arising from loss of tension in the vertical cables supporting the decks. We study the impact of wind forces on the stability of motion of this system both in the absence and presence of viscous and structural damping. The results are illustrated by numerical simulation.

Beschreibung: Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. This new approach to polymer production requires both theoretical and experimental study. Agreement between the existing theoretical and experimental work done on this subject has generally been fairly good. However, experimental results tend to show a higher degree of conversion than theoretical results. The reason for this discrepancy may be attributed to an autoacceleration of the polymerization rate which occurs when conversion has reached a certain point. This autoacceleration is due to a decrease in the termination rate caused by a phenomenon known as the gel effect. In this paper, we develop a mathematical model of the frontal polymerization process, taking the gel effect into consideration. Specifically, we determine how it will affect the degree of conversion, maximum temperature, and propagation velocity of the system.

Beschreibung: A class of nonlinear systems with norm-bounded uncertainties and state-delay is considered. Two criteria are developed for the robust stability analysis: one is delay-independent and the other is delay-dependent. Methods for robust feedback synthesis are then examined. It is established that linear memoryless controllers are capable of guaranteeing the delay-dependent and delay-independent stabilizability of the closed-loop systems. All the results are expressed in the form of linear matrix inequalities which can be solved by efficient and numerically-stable routines. The developed theory is applied to the stability robustness problem of an industrial jacketed continuous stirred tank reactor.

Beschreibung: This paper deals with a numerical model for the kinetics of some diffusion-limited phase transformations. For the growth and dissolution processes in 3D we consider a single spherical precipitate at a constant and uniform concentration, centered in afinitespherical cell of a matrix, at the boundary of which there is no mass transfer, see also Asthana and Pabi [1] and Caers [2].The governing equations are the diffusion equation (2nd Fick's law) for the concentration of dissolved element in the matrix, with a known value at the precipitate-matrix interface, and the flux balans (1st Fick's law) at this interface. The numerical method, outlined for this free boundary value problem (FBP), is based upon a fixed domain transformation and a suitably adapted nonconforming finite element technique for the space discretization. The algorithm can be implemented on a PC. By numerous experiments the method is shown to give accurate numerical results.

Beschreibung: For a class of Markov processes on the integer multidimensional lattice, it is shown that the evolution of the mean values of some random variables can be approximated by ordinary differential equations. To illustrate the approach, a Markov model of a chemical reaction is considered

Beschreibung: We consider a bulk arrival, bulk service queueing system. Customers are served in batches ofrunits if the queue length is not less thanr. Otherwise, the server delays the service until the number of units in the queue reaches or exceeds levelr. We assume that unserved customers may get impatient and leave the system. An ergodicity condition and steady-state probabilities are derived. Various system characteristics are also computed.

Beschreibung: Model reduction has become an important issue in the analysis of electric power systems, due to their constantly increasing size and complexity. In this paper we present a decomposition algorithm which is capable of reducing the number of equations in the model, while preserving the potential for parallel computation. A variety of experimental results are provided to illustrate the performance of the algorithm.

Beschreibung: This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.

Beschreibung: The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

Beschreibung: This paper presents the emergency control approach intended to urgently return to the stability basin the system states affected by abrupt changes in certain system coefficients on a short time interval. Because of its short duration, the modeling of both the fault and controller involvesδ-functions significantly simplifying analysis and control of fault phenomena. The design of an mergency controller is based on the technique for computing fault-induced jumps of the system states, which is described in the paper. An emergency controller instantaneously returning states of a sample nonlinear system to its stability basin is designed.

Beschreibung: A numerical method for solving linear quadratic optimal control problems with control inequality constraints is presented in this paper. The method is based upon hybrid function approximations. The properties of hybrid functions which are the combinations of block-pulse functions and Legendre polynomials are first presented. The operational matrix of integration is then utilized to reduce the optimal control problem to a set of simultaneous nonlinear equations. The inequality constraints are first converted to a system of algebraic equalities, these equalities are then collocated at Legendre–Gauss–Lobatto nodes. An illustrative example is included to demonstrate the validity and applicability of the technique.

Beschreibung: Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.

Beschreibung: A multidisciplinary optimization procedure, with the integration of aerodynamic and heat transfer criteria, has been developed for the design of gas turbine blades. Two different optimization formulations have been used. In the first formulation, the maximum temperature in the blade section is chosen as the objective function to be minimized. An upper bound constraint is imposed on the blade average temperature and a lower bound constraint is imposed on the blade tangential force coefficient. In the second formulation, the blade average and maximum temperatures are chosen as objective functions. In both formulations, bounds are imposed on the velocity gradients at several points along the surface of the airfoil to eliminate leading edge velocity spikes which deteriorate aerodynamic performance. Shape optimization is performed using the blade external and coolant path geometric parameters as design variables. Aerodynamic analysis is performed using a panel code. Heat transfer analysis is performed using the finite element method. A gradient based procedure in conjunction with an approximate analysis technique is used for optimization. The results obtained using both optimization techniques are compared with a reference geometry. Both techniques yield significant improvements with the multiobjective formulation resulting in slightly superior design.

Beschreibung: The problems of robust performance and feedback control synthesis for a class of linear discrete-time systems with time-varying parametric uncertainties are addressed in this paper. The uncertainties are bound and have a linear matrix fractional form. Based on the concept of strongly robust H∞-performance criterion, results of robust stability and performance are developed and expressed in easily computable linear matrix inequalities. Synthesis of robust feedback controllers is carried out for several system models of interest.

Beschreibung: The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output mapHthat can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.

Beschreibung: Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentiallyΘ(N!). We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants.We illustrate this approach using threshhold graphs, and show that any computation of reliability using Gilbert's formula will be polynomial-time if and only if the number of invariants considered is polynomial; we then show families of graphs with polynomial-time, and non-polynomial reliability computation, and show that these encompass most previously known results.We then codify our approach to indicate how it can be used for other classes of graphs, and suggest several classes to which the technique can be applied.

Beschreibung: Proportional navigation is one of the most popular and one of the most used of the guidance laws. But the way it is studied is always the same: the acceleration needed to reach a known target is derived or analyzed. This way of studying guidance laws is called “the direct problem” by the authors. On the contrary, the problem considered here is to find, from the knowledge of a part of the trajectory of a maneuvering object, the target of this object. The authors call this way of studying guidance laws “the inverse problem”.

Beschreibung: Nonlinear evolution equations based upon moments of the aerosol size distribution function are solved asymptotically for constant-rate aerosol reactors (i.e., where condensible monomer is added at a constant rate) operating in the free-molecular limit. The governing equations are nondimensionalized and a large parameter that controls nucleation behavior is identified. Asymptotic analyses are developed in terms of this parameter. Comparison of the asymptotic results with direct numerical integration of the governing equations is favorable. The asymptotic results provide a simplified analytical approach to estimating average particle sizes, particle number densities, and peak supersaturation values for constant-rate aerosol reactors.

Beschreibung: An approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Werners' maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner's maximizing set is defined using the results obtained by first conducting an optimization through anti-optimization modeling of the uncertain loads. An example of a ten-bar truss is used to illustrate the present optimization process. The results are compared with those yielded by other optimization methods.

Beschreibung: Endothelial cells, lining the entire vascular system, respond to change in concentration of specific agonist like adenosine triphosphate (ATP) by increasing cytosolicCa2+concentration, producing prostacyclin, endothelium derived relaxing factor and ecto-enzymes. Three different ecto-enzymes metabolize ATP in three steps (ATP→ADP→AMP→adenosine ) . Normally experiments with endothelium are carried out in a rectangular flow chamber provided with a cell surface at one of its walls and feed stream containing ATP. The ATP concentration near the cell surface depends upon two factors, rate of its degradation and the rate at which it reaches from upstream. Closed form solutions for the concentration profile of ATP in such a flow chamber indicates that concentration near the cell surface is lower than the bulk concentration depending on the activity of ecto-enzymes and it increases with increase in tangential flow rate (shear stress). This indicates that shear induced response of endothelial cell (at least for low shear rate) may be due to change in ATP concentration near the cell surface which is sensed by purinoreceptors instead of a mechanoreceptor. Several workers have tried to investigate this problem analytically. Unfortunately, solutions obtained by these workers have limited success. In the present work, exact solution of the problem has been obtained in terms of a confluent hypergeometric function. Solution of the transformed equation gives accurate results even in the entrance region of the flow chamber which eliminates the need of solutions based on approximate methods like perturbation or finite difference techniques.

Beschreibung: By means of a four-region asymptotic analysis, a uniformly valid description of the Sutherland-viscosity-law Navier-Stokes structure of the normal shock wave in the hypersonic approximation is obtained.

Beschreibung: By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.

Beschreibung: In the article entitled “Time-Delay Polynomial Networks and Rates of Approximation,” which appeared in Volume 4, Number 1, pp. 59-72 (1998), please note the following: “inf” should be replaced with “sup” on:Page 64, Theorem 1, Equation (2)Page 67, Theorem 2, Equation (2)Page 70, 2nd paragraph, line 11, Proof of Theorem 1Page 72, line 9, Proof of Theorem 2

Beschreibung: We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small perturbation equation to a nonlinear time independent partial differential equation (P.D.E.) concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first equation are constructed, while solutions including one arbitrary function for the second equation are extracted. As an application the evaluation of the small perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.

Beschreibung: The author studies an M/G/1 queueing system with multiple vacations. The server is turned off in accordance with the K-limited discipline, and is turned on in accordance with the T-N-hybrid policy. This is to say that the server will begin a vacation from the system if either the queue is empty orKcustomers were served during a busy period. The server idles until it finds at leastNwaiting units upon return from a vacation.Formulas for the distribution generating function and some characteristics of the queueing process are derived. An optimization problem is discussed.

Beschreibung: This paper deals with the robustness of the class of nonlinear piecewise deterministic systems with unknown but bounded uncertainties. Under the assumption that all the modes of the markovian jump process (disturbance) communicate, the complete access to the system state and the boundedness of the uncertainties, a sufficient condition for stochastic stability of this class of systems is given. An example is presented to validate the proposed results.

Beschreibung: The main purpose of this paper is to incorporate a refined hysteresis model, viz. a vector Preisach model, in 2D magnetic field computations. To this end the governing Maxwell equations are rewritten in a suitable way, which allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problem is solved numerically by a FE approximation, using a quadratic mesh, followed by the time discretisation based upon a modified Cranck Nicholson algorithm. The latter includes a suitable iteration procedure to deal with the nonlinear hysteresis behaviour. Finally, the effectiveness of the presented mathematical tool has been confirmed by several numerical experiments.

Beschreibung: Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

Beschreibung: The structure of the quasi-isothermal deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis–Semenov number unity, in the limit of the activation-temperature ratio,β=Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of: (1) the heat-addition-temperature ratio,α=(Tb−Tu)/Tu, of orderβ−1/2, less than order unity [whereTa,Tb, andTuare the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively]; and (2) the exponent,a, which characterizes the pre-exponential thermal dependence of the reaction-rate term, unity. The examination indicates that, as in the order-unity heat-addition case, this deflagration has a four-region structure: the upstream diffusion-convection and downstream diffusion-reaction regions, and the far-upstream (or cold-boundary) and the far-downstream (or hot-boundary) regions.

Beschreibung: In order to analyze the relaxation effects in a turbulent boundary layer with zero and nonzero free stream turbulence, the Reynolds-averaged equations of motion and energy are solved. As the closure of the Reynolds-averaged equations, the transport equation for turbulent shear stresses is used. The proposed approach leads to calculation of the relaxation scales in the turbulent boundary layer with zero and nonzero free stream turbulence. Results for friction coefficients, velocity profiles, shear stresses, thickness of the boundary layer and so called “superlayer” in a flat-plate turbulent boundary layer are presented. The results obtained are in agreement with those available from the experimental data.

Beschreibung: This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

Beschreibung: A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived.

Beschreibung: The multisensor estimation problem is considered in this paper. New distributed algorithms, which are able to locally process the information and which deliver identical results to those generated by their centralized counterparts are presented. The algorithms can be used to provide robust and computationally efficient solutions to the multisensor estimation problem. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Beschreibung: The results concern the fundamental problem of Lyapunov analysis of sliding motions. It consist first to estimate the useful part of the sliding surface (the so-called “sliding domain”) and second to estimate the useful part of the state domain that is the domain of all initial conditions for which the corresponding solutions converge to the sliding domain. The application of such results concern the design of a realistic bounded control. Several examples are exposed in order to illustrate the obtained results.

Beschreibung: We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.

Beschreibung: The normal to a triangular parametric surface is investigated where the parameters used are barycentric coordinates. Formulae for the normal are obtained for non-rational and rational surfaces.

Beschreibung: A variety of signal processing functions are performed by Underwater Acoustic Systems. These include: 1) detection to determine presence or absence of information signals in the presence of noise, or an attempt to describe which of a predetermined finite set of possible messages{mi,i,...,M}the signal represents; 2) estimation of some parameterθˆassociated with the received signal (i.e. range, depth, bearing angle, etc.); 3) classification and source identification; 4) dynamics tracking; 5) navigation (collision avoidance and terminal guidance); 6) countermeasures; and 7) communications. The focus of this paper is acoustic communications.There is a global current need to develop reliable wireless digital communications for the underwater environment, with sufficient performance and efficiency to substitute for costly wired systems. One possible goal is a wireless system implementation that insures underwater terminal mobility. There is also a vital need to improve the performance of the existing systems in terms of data-rate, noise immunity, operational range, and power consumption, since, in practice, portable high-speed, long range, compact, low-power systems are desired.We concede the difficulties associated with acoustic systems and concentrate on the development of robust data transmission methods anticipating the eventual need for real time or near real time video transmission. An overview of the various detection techniques and the general statistical digital communication problem is given based on a statistical decision theory framework. The theoretical formulation of the underwater acoustic data communications problem includes modeling of the stochastic channel to incorporate a variety of impairments and environmental uncertainties, and proposal of new compensation strategies for an efficient and robust receiver design.

Beschreibung: A self-consistent Boltzmann-Poisson-Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current-voltage characteristics, transconductance, gate capacitance, and unity-gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7μm, and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity-gain frequency of 47.8 GHz.

Beschreibung: Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

Beschreibung: In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Beschreibung: The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less thanrand not greater thanR(≥r). The server takes vacations each time the queue level falls belowr(≥1)in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.

Beschreibung: Several questions concerning the convergence of quantized estimators are considered based upon points of accuracy. Examples are considered in which quantizers converge and in which they fail to converge, and points of accuracy are shown to provide explanations for both types of behavior.

Beschreibung: In this paper, a unified analytical framework for performance analysis of multi-hop wireless packet networks is developed. The effect of coupling between the hops on the degradation of the delay-throughput characteristics and the probability of blocking is investigated. The issue of hop decoupling is addressed.

Beschreibung: In this work, a new definition of production systems bottlenecks is formulated and analyzed. Specifically, a machine is defined as the bottleneck if the sensitivity of the system's performance index to this machine's production rate in isolation is the largest. Although appealing from the systems point of view, this definition suffers a deficiency due to the fact that the sensitivities involved cannot be either measured on-line or efficiently calculated off-line. To avoid this, the paper develops a method based on indirect but real-time data. From this point of view, the main result of the work is as follows: The bottleneck machine in a serial production line can be identified by analyzing relationships between the so-called manufacturing blockage and manufacturing starvation of each machine. This leads to a simple rule for bottleneck identification. The rule requires neither the calculation of the production rate sensitivities nor the production rate itself. When the probabilities of manufacturing blockages and starvations are not available from on-line measurements, the paper presents their analytical estimates which, under certain conditions, can be used for bottleneck identification. Finally, a case study at an automotive component plant is described.

Beschreibung: We shall consider the boundary value problemy(n)+λQ(t,y,y1,⋅⋅⋅,y(n−2))=λP(t,y,y1,⋅⋅⋅,y(n−1)),n≥2,t∈(0,1),y(i)(0)=0,0≤i≤n−3,αy(n−2)(0)−βy(n−1)(0)=0,γy(n−2)(1)+δy(n−1)=0,whereλ〉0,α,β,γandδare constants satisfyingαγ+αδ+βγ〉0,β,δ≥0,β+α〉0andδ+γ〉0to characterize the values ofλso that it has a positive solution. For the special caseλ=1, sufficient conditions are also established for the existence of positive solutions.

Beschreibung: The structure of the deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis-Semenov number unity, in the limit of the activation-temperature ratio,β=Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of (1) the heat-addition-temperature ratio,α=(Tb−Tu)/Tu, of order unity [whereTa,Tb, andTuare the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively]; and (2) the exponent,a, which characterizes the pre-exponential thermal dependence of the reaction-rate term, unity. This examination indicates that the deflagration has a four-region structure. To obtain a uniformly valid solution of the problem, in addition to the (classical) upstream diffusion-convection and downstream diffusion-reaction regions, a far-upstream (or cold-boundary) region and a far-downstream (or hot-boundary) region must be introduced.

Beschreibung: In this paper we offer a general theory of rotorcraft trim. The theory is set in the context of control theory. It allows for completely arbitrary trim controls and trim settings for multi-rotor aircraft with tests to ensure that a system is trimmable. In addition, the theory allows for “optimal trim” in which some variable is minimized or maximized rather than set to a specified value. The theory shows that sequential trim cannot work for free flight. The theory is not tied to any particular trim algorithm; but, in this paper, it is exercised with periodic shooting to show how free-flying rotorcraft can be trimmed in a variety of ways (zero yaw, zero pitch, zero roll, minimum power, etc.) by use of the general theory. The paper also discusses applications to harmonic balance and auto-pilot trim techniques.

Beschreibung: An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.

Beschreibung: A technique is developed for evaluation of eigenvalues in solution of the differential equationd2y/dr2+(1/r)dy/dr+λ2(β−r2)y=0which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow(β〉1). A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case ofβ〉1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values ofβwere obtained.

Beschreibung: LIDAR (Laser Integrated Radar) is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF), which has been the standard nonlinear filter in past engineering applications.

Beschreibung: Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven by the adaptive control law and bounded discontinuous control. The discontinuous control driven by the sliding control law is then obtained so that the output error quickly converges to zero. Finally, the performance improvements obtained by adding the sliding mode control input are shown through computer simulations.

Beschreibung: This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

Beschreibung: We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.

Beschreibung: In this paper we provide sufficient conditions for the existence and uniqueness of the solution of the newly obtained equation of motion for constrained mechanical systems.

Beschreibung: This paper considers the problem of assigning the dynamics of a nonlinear analytic system using nonlinear generalized sampled-data hold function (GSHF) control, in the neighborhood of an equilibrium point. On every sampling interval, the control input consists of a nonlinear time-periodic function applied to the sampled value of the state vector. The nonlinear monodromy map is the state transition map from one sample time to the next. It is shown that this map is arbitrarily assignable by GSHF feedback if and only if the linear part of the system is controllable. Two approaches are proposed to construct a GSHF controller that performs the assignment. The first approach matches the coefficients of the Taylor series expansion of the monodromy map around the equilibrium. The second approach interpolates an optimal control law at several points in the vicinity of the equilibrium. These approaches are illustrated on an example.

Beschreibung: The management of bottlenecks has become a central topic in the planning and control of production systems. In this paper, we critically analyze bottlenecks from an economic perspective. Using a queueing network model, we demonstrate that bottlenecks are inevitable when there are differences in job arrival rates, processing rates, or costs of productive resources. These differences naturally lead to the creation of bottlenecks both for facilities design and demand planning problems. To evaluate bottlenecks from an economic perspective, we develop the notion of an “economic bottleneck,” which defines resources as bottlenecks based on economic, rather than physical, characteristics.

Beschreibung: A finite element based sensitivity analysis procedure is developed for buckling and postbuckling of composite plates. This procedure is based on the direct differentiation approach combined with the reference volume concept. Linear elastic material model and nonlinear geometric relations are used. The sensitivity analysis technique results in a set of linear algebraic equations which are easy to solve. The procedure developed provides the sensitivity derivatives directly from the current load and responses by solving the set of linear equations. Numerical results are presented and are compared with those obtained using finite difference technique. The results show good agreement except at points near critical buckling load where discontinuities occur. The procedure is very efficient computationally.

Beschreibung: In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.