bluuebunny/crossref_metadata_2025 huggingface dataset:
Computation of Q3D Viscous Flows in Various AnnularTurbine Stages with Heat Transfer
Authors: Ng E. Y. K. , Yi Miao
Published: March 2007

A better understanding of the flow inside the multi‐stage turbomachines will be very useful to both the designer and operator. The numerical calculation for single blade row has been well established with the time marching computation of the Navier‐Stokes equations. But there will exist much more difficulties for the multi‐blade rows due to the rotor‐stator interaction. The major problems are related to the unsteady flow which will inevitably exist in the blade passages due to the different rotating speed and possible the different in blade number. A method is presented for simulating various turbine blade rows in single‐stage environment. A solver has been developed for studying the complex flow analysis of ‘proposed high pressure turbine’ (HPT) using quasi‐3‐D Reynolds‐averaged Navier‐Stokes (Q3D RNS) equations. The code achieves good quality solutions quickly even with relatively coarse mesh sizes. The work is first validated both with UTRC′s and Zeschky and Gallus′ subsonic turbine test cases covering inlet boundary conditions and Reynolds‐averaged values. A H‐type grid is adopted as it is easy to generate and can readily extend to 3D application. When rows are closely spaced, there can be a strong interaction which will impact the aerodynamic, thermal and structural performance of the blade.
Turbulent Flow and Heat Transfer in Circular CouetteFlows in Concentric Annulus
Authors: Torii Shuichi , Yang Wen-Jei
Published: March 2007

A numerical study is performed to investigate heat transfer and fluid flow in the hydrodynamically and thermally fully‐developed region of an annulus, consisting of a heated
rotating inner cylinder and a stationary insulated outer cylinder. Emphasis is placed on the
effect of rotation of an inner core on the flow structure and the thermal field. A Reynolds
stress turbulence model is employed to determine three normal components of the Reynolds stress and its off‐diagonal one. The turbulent heat flux is expressed by Boussinesq approximation in which the eddy diffusivity.for heat is given as functions of the temperature variance and the dissipation rate of temperate fluctuations εt. The governing boundarylayer equations are discretized by means of a control volume finite‐difference technique and numerically solved using the marching procedure. An inner core rotation causes an amplification of the three normal components of the Reynolds stress over the whole cross section, resulting in a substantial enhancement in the Nusselt number.
Fault Diagnostic Method for Pump Running ConditionsBased on Process Modeling and Neural Network
Authors: Uchiyama T. , Kallweit S. , Siekmann H.
Published: March 2007

This paper proposes a fault diagnostic method for pump running conditions. The method is a combination of a process modeling and a classification procedure. The pump head and hydraulic losses in the pipe system are modeled by two equations. The values of the coefficients in the equations are determined from measurable output variables of the pump. Since the pump running conditions affect the coefficient values, they are detected by
classifying those values. A multi‐layer neural network is employed for the classification.
Three running conditions of a drainage pump are clearly detected by this method. The
accuracy of detection is improved by increasing the hidden layers and their units in the
neural network.
Effects of System Rotation on Turbulence Structure:A Review Relevant to Turbomachinery Flows
Authors: Johnston James P.
Published: March 2007

Turbomachine rotor flows may be affected by system rotation in various ways. Coriolis and
centrifugal forces are responsible for (i) modification of the structure of turbulence in
boundary layers and free shear layers, (ii) the generation of secondary flows, and (iii)
“buoyancy” currents in cases where density gradients occur. Turbulence modification involves reduction (stabilization) or increase (destabilization) of turbulent Reynolds stresses by Coriolis forces; effects which areof special importance for the understanding and prediction of flows in radial and mixed flow pump and compressor rotors. Stabilization/destabilization effects are discussed by a selective review of the basic research literature on flows in straight, radial, rotating channels and diffusers.
Appropriate Dynamic‐Stall Models for PerformancePredictions of VAWTs with NLF Blades
Authors: Masson Christian , Leclerc Christophe , Paraschivoiu Ion
Published: March 2007

This paper illustrates the relative merits of using Natural Laminar Flow (NLF) airfoils in the design of Vertical Axis Wind Turbines (VAWT). This is achieved by the application of the double‐multiple‐streamtube model of Paraschivoiu to the performance predictions of VAWTs equipped with conventional and NLF blades. Furthermore, in order to clearly illustrate the potential benefit of reducing the drag, the individual contributions of lift and drag to power are presented. The dynamic‐stall phenomena are modelled using the method of Gormont as modified by several researchers. Among the various implementations of this dynamic‐stall model available in the literature, the most appropriate and general for NLF applications has been identified through detailed comparisons between predicted performances and experimental data. This selection process is presented in the paper. It has been demonstrated that the use ofNLF airfoils in VAWT applications can lead to significant improvements with respect to conventional design only in a very low wind speed range, the extent of which is negligible with respect to the VAWT operational wind speeds.
Wind Turbine Aerodynamic Performanceby Lifting Line Method
Authors: Dumitrescu Horia , Cardos Vladimir
Published: March 2007

The vortex model of propellers is modified and applied to the high‐speed horizontal axis turbines. The turbine blades are replaced by lifting lines and trailing vortices which shed along the blade span. The model is not a free wake model, but it is still a nonlinear one which should be solved iteratively. In addition to the regular case where the trailing vortices are constrained to distribute along a helical surface, another version, where each trailing vortex sheding from the blade grows as a free helical vortex line, is also included. Performance parameters are calculated by application of the Biot‐Savart law along with the Kutta‐Joukowski theorem. Predictions are, shown to compare favorably with existing numerical data from more involved free wake methods, but require less computational effort. Thereby, the present method may be a very useful tool for calculating the aerodynamic loads on horizontal‐axis wind turbine blades.
Heat/Mass Transfer Distribution in a Rotating Two‐Pass Square Channel Part I: Regional Heat Transfer, Smooth Channel
Authors: Park C. W. , Kandis M. , Lau S. C.
Published: March 2007

Naphthalene sublimation experiments have been conducted to examine the effect of rotation on the regional heat]mass transfer distribution for turbulent air flow in a rotating smooth two‐pass square channel that has a 180 turn with sharp corners. The Reynolds number ranges from 5,500 to 14,500 and the rotation number goes up to 0.24. The test channel models the first two passes of serpentine internal cooling passages of gas turbine blades. Flow around a sharp turn causes larger heat]mass transfer increase in the turn and in the second pass than flow around a smooth turn. In the first pass with radially outward flow, rotation increases the heat]mass transfer on the trailing wall and decreases the heat/mass transfer on the leading wall. The reversed trend in the second pass with radially inward flow is evident only after four hydraulic diameters downstream of the turn exit. With rotation, there is an abrupt increase of the regional heat]mass transfer in the upstream portion of the turn on the leading wall. The regional heat]mass transfer on the trailing wall, however, increases along the streamwise direction in the turn, as in the stationary channel case. In the turn and immediately downstream of the turn, the shape of the heat/mass transfer distribution in a rotating channel is invariant over the range of rotation number studied. In a rotating channel, decreasing the Reynolds number increases the heat]mass transfer on the trailing wall and decreases that on the leading wall in the first pass, and increases the heat/mass transfer on both walls in the turn and immediately downstream of the turn.
Small Radial Compressors: Aerodynamic Design and Analysis
Authors: Ismail K. A. R. , Rosolen C. V. A. G. , Benevenuto F. J. , Lucato D.
Published: March 2007

This paper presents a computational procedure for the analysis of steady one‐dimensional centrifugal compressor. The numerical model is based on the conservation principles of mass, momentum and energy, and has been utilized to predict the operational and aerodynamic characteristics of a small centrifugal compressor as well as determining the performance and geometry of compressor blades, both straight and curved.
Modeling of Compressor Performance DeteriorationDue to Erosion
Authors: Hamed A. , Tabakoff W. , Singh D.
Published: March 2007

This paper presents the results of a simulation of compressor performance deterioration due to blade erosion. The simulation at both design and off‐design conditions is based on a mean line row by row model, which incorporates the effects of blade roughness and tip clearance. The results indicate a pronounced effect of blade erosion on the compressor adiabatic efficiency and a lesser effect on the pressure ratio. The loss in performance is mainly caused by the increased blade surface roughness and was highest at 100% speed.
Analytic Creep Durability of Rotating Uniform Disks
Authors: Nyashin Yuriy , Shishlyaev Victor
Published: March 2007

Turbine disks of aircraft engines in operation are subjected to alternating thermocyclic deformation under high temperatures. Operation gives rise to sufficiently high stresses and subsequent creep damaging effects.

In this paper we suggest an approach for describing creep rupture of a simple rotating disk due to the accumulation of creep induced microdefects. The dissipated energy of the creep deformation is considered as the measure of material damage.

The lifetime of the disk can be predicted on the basis of this approach. Both crack initiation and damage propagation to complete rupture of a disk are calculated. The analytic
results can be compared to known experimental data. The derived algorithm can be
applied to estimate the lifetime of real machinery components when creep deformations are
dominant.
Thermal‐Fluid Transport Phenomena of aStrongly‐Heated Gas Flow in Parallel Tube Rotation
Authors: Torii Shuichi , Yang Wen-Jei
Published: March 2007

A numerical analysis is performed to study thermal transport phenomena in gas flow through a strongly heated tube whose axis is in parallel with the rotational axis. The velocity and temperature fields prevail when fluid flows in a rotating tube with uniform heat flux on the tube wall. The two‐equation k − ω turbulence and heat transfer models are employed to determine turbulent viscosity and eddy diffusivity for heat, respectively. The governing boundary‐layer equations are discritized by means of a control volume finitedifference techniques. It is found that the Coriolis and centrifugal (or centripetal) forces cause fluid flow and heat transfer performance in the parallel‐rotation system to be drastically different from those in the stationary case. Consequently, even if a tube rotating around a parallel axis is heated with high heat flux whose level causes a laminarizing flow in the stationary tube case, both the turbulent kinetic energy and the temperature variance remain over the pipe cross section, resulting in the suppression of an attenuation in heat transfer performance. In other words, an increase in tube rotation suppresses laminarization of gas flow.
Heat (Mass) Transfer Distributions in a RotatingTwo‐Pass Channel with Angled Ribs
Authors: Park C. W. , Lau S. C. , Kukreja R. T.
Published: March 2007

Experiments have been conducted to study the local heat (mass) transfer distributions in a two‐pass test model of internal turbine blade cooling passages, with 60 ribs on the leading and trailing walls. For radial outward flow in the first pass, rotation did not significantly increase the local nor the overall heat (mass) transfer between consecutive ribs on the trailing wall. Rotation‐induced Coriolis force lowered the relative overall heat (mass) transfer on the leading wall less in the rib‐roughened channel than in a smooth channel. When the rotation number was high, there were twin peaks in the local heat (mass) transfer distribution between ribs on the leading wall. For radial inward flow in the second pass, the sharp turn reduced the difference between the heat (mass) transfer.on the leading wall and that on the trailing wall.
Detection of Mechanical Abnormalities inInduction Motors by Electric Measurements
Authors: Trzynadlowski Andrzej M.
Published: March 2007

The paper gives an overview of the issues and means of detection of mechanical abnormalities in induction motors by electric measurements. If undetected and untreated, the worn or damaged bearings, rotor imbalance and eccentricity, broken bars of the rotor cage, and torsional and lateral vibration lead to roughly a half of all failures of induction motor drives. The detection of abnormalities is based on the fact that they cause periodic disturbance of motor variables, such as the speed, torque, current, and magnetic flux. Thus, spectral analysis of those or related quantities may yield a warning about an incipient failure of the drive system. Although the traditional non‐invasive diagnostics has mostly been based on the signature analysis of the stator current, other media can also be employed. In particular, the partial instantaneous input power is shown, theoretically and experimentally, to offer distinct advantages under noisy operating conditions. Use of torque and flux estimates is also discussed.
Turbulence Amplification with Incidence at the Leading Edge of a Compressor Cascade
Authors: Hobson Garth V. , Wakefield Bryce E. , Roberts William B.
Published: March 2007

Detailed measurements, with a two‐component laser‐Doppler velocimeter and a thermal anemometer were made near the suction surface leading edge of controlled‐diffusion airfoils in cascade. The Reynolds number was near 700,000, Mach number equal to 0.25, and freestream turbulence was at 1.5% ahead of the cascade.

It was found that there was a localized region of high turbulence near the suction surface leading edge at high incidence. This turbulence amplification is thought to be due to the interaction of the free‐shear layer with the freestream inlet turbulence. The presence of the local high turbulence affects the development of the short laminar separation bubble that forms very near the suction side leading edge of these blades. Calculations indicate that the local high levels of turbulence can cause rapid transition in the laminar bubble allowing it to reattach as a short “non‐burst” type.

The high turbulence, which can reach point values greater than 25% at high incidence, is the reason that leading edge laminar separation bubbles can reattach in the high pressure gradient regions near the leading edge. Two variations for inlet turbulence intensity were measured for this cascade. The first is the variation ofmaximum inlet turbulence with respect to inlet‐flow angle; and the second is the variation of leading edge turbulence with respect to upstream distance from the leading edge of the blades.
Experimental Investigation of Steady and UnsteadyFlow Field Upstream and Downstream of anAutomotive Torque Converter Pump
Authors: Marathe B. V. , Lakshminarayana B.
Published: March 2007

The objective of this investigation is to understand the steady and the unsteady flow field at the exit of an automotive torque converter pump with a view towards improving its performance. The measurements were conducted in a stationary frame of reference using a high frequency response five‐hole probe and the data were processed to derive the flow properties in the relative (pump) frame of reference. The experimental data were processed at three different operating conditions: maximum efficiency point, design point and near‐stall point. The unsteady values of flow properties (pressure, velocity and flow angles) were divided into five components: mean, periodic, blade aperiodic, revolution aperiodic and unresolved components.

The velocity profiles indicate zones of separation near the core region at speed ratio (SR) 0.8. This zone is transported to the shell region at SR 0.065 due to the presence of a strong secondary vortex. The secondary vortex (weak) for the SR 0.8 rotates anti‐clockwise, and is located only near core‐wake region. The secondary vortex (strong) at SR 0.065 rotates clockwise, and encompasses the entire passage. The unsteady flow data show that unresolved and periodic components dominate the unsteadiness at the pump exit. The overall aperiodicity is negligible and is dominated by the blade aperiodic component.
Transition to Fluid‐Induced Limit CycleSelf‐Excited Vibrations of a Rotor andInstability Threshold “Hysteresis”
Authors: Muszynska Agnes
Published: March 2007

The transient process which starts at the instability threshold of a rotor rotating in a fluid environment, and ends up in the limit cycle of self‐excited vibrations known as fluid whirl or fluid whip, is discussed in this paper. A one‐lateral‐mode, isotropic, nonlinear model of the rotor with fluid interaction allows for exact particular solutions and an estimation of the transient process. The fluid interacting with the rotor is contained in a small radial clearance area, such as in bearings, seals, or rotor‐to‐stator clearances, and its effects are represented by fluid film radial stiffness, damping, and fluid inertia rotating at a different angular velocities.

The effects of fluid damping and fluid inertia circumferential velocity ratios on the rotor startup and shutdown instability threshold differences are also discussed.
Two‐Phase Air/Oil Flow in Aero‐Engine Bearing Chambers – Assessment of an Analytical Prediction Method for the Internal Wall Heat Transfer
Authors: Glahn A. , Wittig S.
Published: March 2007

The present paper gives a theoretical outline on liquid film flows driven by superimposed effects of interfacial shear and gravity forces and discusses related heat transfer processes which are relevant for lubrication oil systems of aero engines. It is shown that a simple analytical approach is able to predict measured heat transfer data fairly well. Therefore, it offers scope for improvements within the analysis of bearing chamber heat transfer characteristics as well as for appropriate studies with respect to other components of the lubrication oil system such as vent pipeline elements.
Transformation of Gear Inter‐Teeth Forces into Acceleration and Velocity
Authors: Bartelmus Walter
Published: March 2007

The paper deals with mathematical modelling and computer simulation of a gearbox system. Results of computer simulation show new possibilities of extended interpretation of a diagnostic acceleration signal if signal is obtained by synchronous summation. Four groups of factors: design, production technology, operation, change of gear condition are discussed. Results of computer simulations give the relation between inter‐teeth forces and vibration (acceleration, velocity). Some results of computer simulations are referred to the results obtained in rig measurements and in field practice. The paper shows a way of increasing the expert′s knowledge on the diagnostic signal, which is generated by a gearbox system, on a base of mathematical modelling and computer simulation.
Performance Evaluation of an Air‐ConditioningCompressor Part I: Measurement and Design Modeling
Authors: Bein Thomas W. , Lee Yu-Tai
Published: March 2007

In order to comply with legislation to eliminate the use of refrigerants that damage the ozone layer, it is necessary to redesign centrifugal compressors, used by the US Navy for shipboard air‐conditioning systems, to use an environmentally acceptable refrigerant. This paper describes an evaluation of a 125‐ton compressor designed to use HCFC‐124 as the refrigerant. The objectives are not only conducting the performance evaluation, but also
pinpointing the design problems for achieving a high‐performance compressor. The design
method used to design the 125‐ton compressor is first reviewed and some related performance curves are predicted based on a quasi‐3D method. In addition to an overall performance measurement, a series of instruments were installed on the compressor to identify where the measured performance differs from the predicted performance. The measurement techniques for providing the diagnostic flow parameters are also described briefly. Part II of this paper provides predictions of flow details in the areas of the compressor where there were differences between the measured and predicted performance.
Performance Evaluation of an Air‐ConditioningCompressor Part II: Volute Flow Predictions
Authors: Lee Yu-Tai , Bein Thomas W.
Published: March 2007

A numerical method that solves the Reynolds‐averaged Navier‐Stokes equations is used to study an inefficient component of a shipboard air‐conditioning HCFC‐124 compressor system. This high‐loss component of the centrifugal compressor was identified as the volute through a series of measurements given in Part I of the paper. The predictions were made using three grid topologies. The first grid closes the connection between the cutwater and the discharge diffuser. The other two grids connect the cutwater area with the discharge diffuser. Experiments were performed to simulate both the cutwater conditions used in the predictions. Surface pressures along the outer wall and near the inlet of the volute were surveyed for comparisons with the predictions. Good agreements between the predicted results and the measurements validate the calculations. Total pressure distributions and flow stream traces from the prediction results support the loss distribution through the volute. A modified volute configuration is examined numerically for further loss comparison.
On the Development of Viscous Solvers for Computationof Transient Flows in Turbomachines
Authors: Wiedermann Alexander , Miyagawa Kazuyoshi , Eguchi Tsuyoshi
Published: March 2007

This paper focuses on development and validation of a viscous solver for the computation of unsteady flows in turbomachinery blade rows and stages consisting of rotors and stators. The code has been evolved from steady‐state single flow solvers developed by Wiedermann based on time‐marching finite difference schemes. A two‐equation eddy viscosity model is applied, and the wall boundary conditions are determined by the y+‐distance of the first grid line away from the wall. For the solution of transient flow fields the original time‐stepping algorithm is replaced by a time‐accurate scheme.

The emphasis of the code validation will be on blade‐row interaction in a complete
turbomachinery stage. A 3‐D example will be discussed and those parameters evaluated
which are important for actual blading design.
Dynamic Analysis of Engine Bearings
Authors: Hirani H. , Athre K. , Biswas S.
Published: March 2007

This paper presents a simple methodology to evaluate the stiffness and damping coefficients of an engine bearing over a load cycle. A rapid technique is used to determine the shaft ‘limit cycle’ under engine dynamic loads. The proposed theoretical model is based on short and long bearing approximations. The results obtained by present approximation are compared with those obtained by numerical method. The influence of thermal effects on the stiffness and damping coefficients is predicted by using a simplified thermal analysis. In order to illustrate the application of the proposed scheme, one engine main bearing and a connecting rod bearing are analysed.
Smoothness of invariant density for expanding transformations in higher dimensions
Authors: Adl-Zarabi Kourosh , Proppe Harald
Published: March 2007

Let Ω be a bounded region in ℝn and let be a partition of Ω
into a finite number of closed subsets having piecewise C2 boundaries of
finite (n − 1)‐dimensional measure. Let τ : Ω → Ω be an expanding transformation on 𝒫 where, , and τi ∈ CM, m ≥ 2. We show that the
τ‐invariant density h ∈ CM−2.
On the structure of the solution set of evolution inclusions with Fréchet subdifferentials
Authors: Cardinali Tiziana
Published: March 2007

In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o ∂−f of a function
f : Ω → R ∪ {+∞} (Ω is an open subset of a real separable Hilbert space)
having a φ‐monotone . subdifferential of order two and a perturbation
F : I × Ω → Pfc(H) with nonempty, closed and convex values.

First we show that the Cauchy problem has a nonempty solution set
which is an Rδ‐set in C(I, H), in particular, compact and acyclic. Moreover, we obtain a Kneser‐type theorem. In addition, we establish a continuity result about the solution‐multifunction x → S(x). We also produce a
continuous selector for the multifunction x → S(x). As an application of
this result, we obtain the existence of solutions for a periodic problem.
A class of nonlinear variational inequalities involvingpseudomonotone operators
Authors: Verma Ram U.
Published: March 2007

We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topological vector spaces setting. The obtained result generalizes similar variational inequality problems on monotone operators.
Stability and attractivity of solutions of differential equations with impulses at fixed times
Authors: Sivasundaram S. , Vassilyev S.
Published: March 2007

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of
comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.
The moments of the area under reflected Brownian bridgeconditional on its local time at zero
Authors: Knight Frank B.
Published: March 2007

This paper develops a recursion formula for the conditional moments of
the area under the absolute value of Brownian bridge given the local time
at 0. The method of power series leads to a Hermite equation for the generating function of the coefficients which is solved in terms of the parabolic
cylinder functions. By integrating out the local time variable, this leads to
an integral expression for the joint moments of the areas under the positive and negative parts of the Brownian bridge.
On the local time density of the reflecting Brownian bridge
Authors: Gittenberger Bernhard , Louchard Guy
Published: March 2007

Expressions for the multi‐dimensional densities of Brownian bridge local
time are derived by two different methods: A direct method based on
Kac′s formula for Brownian functionals and an indirect one based on a
limit theorem for strata of random mappings.
Fatou′s Lemma and Lebesgue′s convergence theorem for measures
Authors: Hernández-Lerma Onésimo , Lasserre Jean B.
Published: March 2007

Analogues of Fatou′s Lemma and Lebesgue′s convergence theorems are
established for ∫fdμn when {μn} is a sequence of measures. A “generalized” Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more
general result established in vector lattices and related to the Dunford‐Pettis property in Banach spaces.
Rigorous solution of a mean field spin glass model
Authors: Dorlas T. C. , Wedagedera J. R.
Published: March 2007

A separable spin glass model whose exchange integral takes the form
Jij = J(ξi1ξj2 + ξi2ξj1) which was solved by van Hemmen et al. [12]
using large deviation theory [14] is rigorously treated. The almost sure
convergence criteria associated with the cumulant generating function C(t)
with respect to the quenched random variables ξ is carefully investigated,
and it is proved that the related excluded null set 𝒩 is independent of t.
The free energy and hence the other thermodynamic quantities are rederived using Varadhan′s Large Deviation Theorem. A simulation is also
presented for the entropy when ξ assumes a Gaussian distribution.
On a third order parabolic equation with a nonlocal boundary condition
Authors: Bouziani Abdelfatah
Published: March 2007

In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which
combine classical boundary conditions and an integral condition, such as
the total mass, flux or energy, for a third order parabolic equation. We
present a functional analysis method based on an a priori estimate and on
the density of the range of the operator generated by the studied problem.
Analyzing the dynamics of the forced Burgers equation
Authors: Smaoui Nejib
Published: March 2007

We study numerically the long‐time dynamics of a system of reaction‐diffusion equations that arise from the viscous forced Burgers equation (ut + uux − vuxx = F). A nonlinear transformation introduced by Kwak is used
to embed the scalar Burgers equation into a system of reaction diffusion
equations. The Kwak transformation is used to determine the existence of
an inertial manifold for the 2‐D Navier‐Stokes equation. We show
analytically as well as numerically that the two systems have a similar,
long‐time dynamical, behavior for large viscosity v.
Extinction in a generalized Lotka‐Volterra predator‐prey model
Authors: Ackleh Azmy S. , Marshall David F. , Heatherly Henry E.
Published: March 2007

In this paper we discuss the asymptotic behavior of a predator‐prey model
with distributed growth and mortality rates. We exhibit simple criteria
on the parameters which guarantee that all subpopulations but one predator‐prey pair are driven to extinction as t → ∞. Finally, we present numerical simulations to illustrate the theoretical results.
Remembering Wim Cohen
Authors: Syski Ryszard
Published: March 2007

This article is a short biographical account on deceased Jacob Willem
Cohen.
Linear‐implicit strong schemes for Itô‐Galkerin approximations of stochastic PDEs
Authors: Kloeden P. E. , Shott S.
Published: March 2007

Linear‐implicit versions of strong Taylor numerical schemes for finite
dimensional Itô stochastic differential equations (SDEs) are shown to have
the same order as the original scheme. The combined truncation and
global discretization error of an γ strong linear‐implicit Taylor scheme
with time‐step Δ applied to the N dimensional Itô‐Galerkin SDE for a
class of parabolic stochastic partial differential equation (SPDE) with a
strongly monotone linear operator with eigenvalues λ1 ≤ λ2 ≤ ⋯ in its
drift term is then estimated by

where the constant K depends on the initial value, bounds on the other
coefficients in the SPDE and the length of the time interval under consideration.
Palm theory for random time changes
Authors: Miyazawa Masakiyo , Nieuwenhuis Gert , Sigman Karl
Published: March 2007

Palm distributions are basic tools when studying stationarity in the context of point processes, queueing systems, fluid queues or random measures. The framework varies with the random phenomenon of interest, but
usually a one‐dimensional group of measure‐preserving shifts is the starting point. In the present paper, by alternatively using a framework involving random time changes (RTCs) and a two‐dimensional family of shifts,
we are able to characterize all of the above systems in a single framework.
Moreover, this leads to what we call the detailed Palm distribution (DPD)
which is stationary with respect to a certain group of shifts. The DPD has
a very natural interpretation as the distribution seen at a randomly chosen
position on the extended graph of the RTC, and satisfies a general duality
criterion: the DPD of the DPD gives the underlying probability P in return.

To illustrate the generality of our approach, we show that classical
Palm theory for random measures is included in our RTC framework. We
also consider the important special case of marked point processes with
batches. We illustrate how our approach naturally allows one to distinguish between the marks within a batch while retaining nice stationarity
properties.
Two‐step procedures in Palm theory
Authors: Nieuwenhuis Gert
Published: March 2007

Random time changes (RTCs) are right‐continuous and non‐decreasing
random functions passing the zero‐level at 0. The behavior of such systems can be studied from a randomly chosen time‐point and from a randomly chosen level. From the first point of view, the probability characteristics are described by the time‐stationary distribution P. From the second point of view, the detailed Palm distribution (DPD) is the ruling probability mechanism. The main topic of the present paper is a relationship
between P and its DPD. Under P, the origin falls in a continuous part of
the graph. Under the DPD, there are two typical situations: the origin
lies in a jump‐part of the extended graph or it lies in a continuous part.
These observations lead to two conditional DPDs. We derive two‐step procedures, which bridge the gaps between the several distributions. One step
concerns the application of a shift, the second is just a change of measure
arranged by a weight‐function. The procedures are used to derive local
characterization results for the distributions of Palm type. We also consider simulation applications. For instance, a procedure is mentioned to
generate a simulation of the RTC as seen from a randomly chosen level in
a jump‐part when starting with simulations from a randomly chosen time‐point. The point process with batch‐arrivals is often used as an application.
Reflected forward‐backward SDEs and obstacle problems with boundary conditions
Authors: Ma Jin , Cvitanić Jakša
Published: March 2007

In this paper we study a class of forward‐backward stochastic differential
equations with reflecting boundary conditions (FBSDER for short). More
precisely, we consider the case in which the forward component of the
FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on
time and is possibly random. The solvability of such FBSDER is studied
in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one‐dimensional, then the adapted
solution of such FBSDER will give the viscosity solution of a quasilinear
variational inequality (obstacle problem) with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
On the stability of stationary solutions of a linear integro‐differential equation
Authors: Dorogovtsev A. Ya. , Trofimchuk O. Yu.
Published: March 2007

In this paper the following two connected problems are discussed. The problem of the existence of a stationary solution for the abstract equation

containing a small parameter ε in Banach space B is considered. Here A ∈ ℒ(B) is a fixed operator, E ∈ C([0, +∞), ℒ(B)) and ξ is a stationary process. The asymptotic expansion of the stationary solution for equation (1)
in the series on degrees of e is given.

We have proved also the existence of a stationary with respect to time
solution of the boundary value problem in B for a telegraph equation (6)
containing the small parameter ε. The asymptotic expansion of this solution is also obtained.
Controllability of quasilinear stochastic evolution equations in Hilbert spaces
Authors: Balasubramaniam P.
Published: March 2007

Controllability of the quasilinear stochastic evolution equation is studied
using semigroup theory and a stochastic version of the well known fixed
point theorem. An application to stochastic partial differential equations
is given.
A monotone iterative method for boundary value problems of parametric differential equations
Authors: Liu Xinzhi , McRae Farzana A.
Published: March 2007

This paper studies boundary value problems for parametric differential
equations. By using the method of upper and lower solutions, monotone
sequences are constructed and proved to converge to the extremal solutions
of the boundary value problem.
Existence of periodic solution for first order nonlinear neutral delay equations
Authors: Wang Genqiang , Yan Jurang
Published: March 2007

In this paper by using the coincidence degree theory, sufficient conditions
are given for the existence of periodic solutions of the first order nonlinear
neutral delay differential equation.
The strict stability of dynamic systems on time scales
Authors: Sivasundaram S.
Published: March 2007

The strict stability of dynamic systems on time scales is examined with
sufficient conditions. Results analogous to Lyapunov′s theorems ae proved
and discussed using a comparison principle.
A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm‐Liouville equations I
Authors: Venkatesulu M. , Baruah Pallav Kumar
Published: March 2007

In the studies of acoustic waveguides in ocean, buckling of columns with
variable cross sections in applied elasticity, transverse vibrations in non
homogeneous strings, etc., we encounter a new class of problems of the
type defined on an interval [d1, d2] and
on the adjacent interval [d2, d3] satisfying
certain matching conditions at the interface point x = d2.

Here in Part I, we constructed a fundamental system for (L1, L2) and
derive certain estimates for the same. Later, in Part II, we shall consider
four types of boundary value problems associated with (L1, L2) and study
the corresponding spectra.
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals
Authors: Kleptsyna M. L. , Le Breton A.
Published: March 2007

The optimal filtering problem for multidimensional continuous possibly
non‐Markovian, Gaussian processes, observed through a linear channel
driven by a Brownian motion, is revisited. Explicit Volterra type filtering
equations involving the covariance function of the filtered process are derived both for the conditional mean and for the covariance of the filtering
error. The solution of the filtering problem is applied to obtain a
Cameron‐Martin type formula for Laplace transforms of a quadratic functional of the process. Particular cases for which the results can be further
elaborated are investigated.
Weak laws of large numbers for arrays of rowwise negatively dependent random variables
Authors: Taylor R. L. , Patterson R. F. , Bozorgnia A.
Published: March 2007

Weak laws of large numbers for arrays of rowwise negatively dependent
random variables are obtained in this paper. The more general hypothesis
of negative dependence relaxes the usual assumption of independence. The
moment conditions are similar to previous results, and the stochastic
bounded condition also provides a generalization of the usual distributional assumptions.
Invariant measures for Chebyshev maps
Authors: Boyarsky Abraham , Góra Paweł
Published: March 2007

Let Tλ(x) = cos(λarccosx), −1 ≤ x ≤ 1, where λ > 1 is not an integer.
For a certain set of λ′s which are irrational, the density of the unique absolutely continuous measure invariant under Tλ is determined exactly. This
is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed
as the unique left eigenvector of a matrix.
Vector‐valued fuzzy multifunctions
Authors: Beg Ismat
Published: March 2007

Some of the properties of vector‐valued fuzzy multifunctions are studied.
The notion of sum fuzzy multifunction, convex hull fuzzy multifunction,
close convex hull fuzzy multifunction, and upper demicontinuous are
given, and some of the properties of these fuzzy multifunctions are investigated.
A stochastic inventory model with stock dependent demand items
Authors: Benkherouf Lakdere , Boumenir Amin , Aggoun Lakhdar
Published: March 2007

In this paper, we propose a new continuous time stochastic inventory
model for stock dependent demand items. We then formulate the problem
of finding the optimal replenishment schedule that minimizes the total expected discounted costs over an infinite horizon as a Quasi‐Variational Inequality (QVI) problem. The QVI is shown to have a unique solution under some conditions.
Single server tandem queues and queueing networks with non‐correlated successive service times
Authors: Le Gall Pierre
Published: March 2007

To evaluate the local actual queueing delay in general single server queueing networks with non‐correlated successive service times for the same customer, we start from a recent work using the tandem queue effect, when
two successive local arrivals are not separated by “premature departures”.
In that case, two assumptions were made: busy periods not broken up,
and there are limited variations for successive service times. These assumptions are given up after having crossed two stages. The local arrivals become indistinguishable for the sojourn time inside a given busy period. It
is then proved that the local sojourn time of this tandem queue effect may
be considered as the sum of two components: the first (independent of the
local interarrival time) corresponding to the case where upstream, successive service times are supposed to be identical to the local service time,
and the second (negligible after having crossed 2 or 3 stages) depending on
local interarrival times increasing because of broken up busy periods. The
consequence is the possible occurrence of the agglutination phenomenon of
indistinguishable customers in the buffers (when there are limited “premature departures”), due to a stronger impact of long service times upon the
local actual queueing delay, which is not consistent with the traditional
concept of local traffic source only generating distinguishable customers.
On the probabilistic domain invariance
Authors: Beg Ismat , Gal Sorin
Published: March 2007

Probabilistic version of the invariance of domain for contractive field and
Schauder invertibility theorem are proved. As an application, the stability of
probabilistic open embedding is established.
Convergence estimates and approximation solvability of nonlinear implicit variational inequalities
Authors: Verma Ram U.
Published: March 2007

Approximation‐solvability of a class of nonlinear implicit variational inequalities
involving a class of partially relaxed monotone mappings ‐ a computation‐oriented
class in a Hilbert space setting‐ is presented with some applications.
The H∞‐optimization in locally convex spaces
Authors: Hu Chuan-Gan , Ma Li-Xin
Published: March 2007

In this paper, the ordinary H∞‐control theory is extended to locally convex
spaces through the form of a parameter. The algorithms of computing the infimal
model‐matching error and the infimal controller are presented in a locally convex
space. Two examples with the form of a parameter are enumerated for computing
the infimal model‐matching error and the infimal controller.
Existence of Solutions of a Class of Abstract Second OrderNonlinear Integrodifferential Equations
Authors: Balachandran K. , Park J. Y.
Published: March 2007

In this paper we prove the existence of solutions of nonlinear second order integrodifferential
equations in Banach spaces. The results are obtained by using
the theory of strongly continuous cosine families of operators and the Schaefer
fixed point theorem.
Stability analysis of nonlinear Lyapunov systems associated withan nth order system of matrix differential equations
Authors: Murty K. N. , Shaw Michael D.
Published: March 2007

This paper introduces the notion of Lipschitz stability for nonlinear nth order
matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz
stability. We develop variation of parameters formula for the solution of the
nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We
study observability and controllability of a special system of nth order nonlinear Lyapunov systems.
Operational behavior of the MAP/G/1 queue under N‐policy with asingle vacation and set‐up
Authors: Lee Ho Woo , Ahn Boo Yong
Published: March 2007

This paper considers the MAP/G/1 queue under N‐policy with a single vacation
and set‐up. We derive the vector generating functions of the queue length at an
arbitrary time and at departures in decomposed forms. We also derive the
Laplace‐Stieltjes transform of the waiting time. Computation algorithms for
mean performance measures are provided.
A classical approach to eigenvalue problems associated with apair of mixed regular Sturm‐Liouville equations II
Authors: Venkatesulu M. , Baruah Pallav Kumar
Published: March 2007

In the studies of acoustic waveguides in ocean, buckling of columns with variable
cross sections in applied elasticity, transverse vibrations in nonhomogeneous
strings, etc., we encounter a new class of problems of the type
defined on an interval [d1, d2] and
defined on the interval [d2, d3] satisfying certain
matching conditions at the interface point x = d2.

Earlier, in Part I, we constructed a fundamental system for (L1, L2)
and
derived certain estimates for the same.

Here, in Part II, we consider four types of boundary value problems associated

with (L1, L2) and study the corresponding spectra.
Planar random motions with drift
Authors: Orsingher E. , Ratanov N.
Published: March 2007

In this paper we consider planar random motions with four directions and four
different speeds, switching at Poisson paced times. We are able to obtain, in some cases, the explicit distribution of the position (X(t), Y(t)), t > 0 in all its components (the discrete one, lying on the edge ∂Qt of the probability support Qt, as well as the absolutely continuous one, concentrated inside Qt).
New continuity estimates of geometric sums
Authors: Gordienko Evgueni , de Chávez Juan Ruiz
Published: March 2007

The paper deals with sums of a random number of independent and identically distributed random variables. More specifically, we compare two such sums, which differ from each other in the distributions of their summands. New upper bounds (inequalities) for the uniform distance between distributions of sums are established. The right‐hand sides of these inequalities are expressed in terms of Zolotarev′s and the uniform distances between the distributions of summands. Such a feature makes it possible to consider these inequalities as continuity estimates and to apply them to the study of the stability (continuity) of various applied stochastic models involving geometric sums and their generalizations.
Free area estimation in a partially observed dynamic germ‐grainmodel
Authors: De Giosa Marcello , Mininni Rosa Maria
Published: March 2007

The estimation problem of the expected local fraction of free area function S for a
partially observed dynamic germ‐grain model is presented. Properties of the
estimators are proved by martingale and product integral methods. Confidence
bounds are provided. Furthermore, an estimator of the hazard rate
α(t) = −dS(t)/(S(t)dt)

is obtained by the kernel function method and
asymptotic properties of the estimator are proved and used to find confidence
intervals. By a simulated illustrative example, the qualitative behavior of the
estimators is shown.