bluuebunny/crossref_metadata_2025 huggingface dataset:
Performance and Exit Flow Characteristics ofMixed‐Flow Turbines
Authors: Arcoumanis C. , Martinez-Botas R. F. , Nouri J. M. , Su C. C.
Published: March 2007

The performance and exit flow characteristics of two mixed‐flow turbines have been
investigated under steady‐state conditions. The two rotors differ mainly in their inlet angle
geometry, one has a nominal constant incidence (rotor B) and the other has a constant blade
angle (rotor C), but also in the number of blades. The results showed that the overall peak
efficiency of rotor C is higher than that of rotor B. Two different volutes were also used for
the tests, differing in their cross‐sectional area, which confirm that the new larger area
volute turbine has a higher efficiency than the old one, particularly at lower speeds, and a
fairly uniform variation with velocity ratio.

The flow exiting the blades has been quantified by laser Doppler velocimetry. A difference
in the exit flow velocity for rotors B and C with the new volute was observed which is
expected given their variation in geometry and performance. The tangential velocities near
the shroud resemble a forced vortex flow structure, while a uniform tangential velocity
component was measured near the hub. The exit flow angles for both rotor cases decreased
rapidly from the shroud to a minimum value in the annular core region before increasing
gradually towards the hub. In addition, the exit flow angles with both rotors were reduced
with increasing rotational speeds. The magnitude of the absolute flow angle was reduced in
the case of rotor C, which may explain the improved steady state performance with this
rotor. The results also revealed a correlation between the exit flow angle and the
performance of the turbines; a reduction in flow angle resulted in an increase in the overall
turbine efficiency.
Hysteresis on Wells Turbine Characteristics in Reciprocating Flow
Authors: Setoguchi T. , Takao M. , Kaneko K.
Published: March 2007

The Wells turbine for a wave power generator has hysteretic characteristics in a
reciprocating flow, which results in the inaccurate prediction of performance in a quasisteady
analysis. In order to clarify the hysteretic characteristics, an experimental investigation
has been made by use of a newly devised turbine equipment in which a sinusoidal flow
condition is simulated. The results have shown that hysteresis becomes more pronounced as solidity and blade thickness become larger, but it is insensitive to the Reynolds number and blade surface roughness. By means of pressure measurements on the blade surface, it is found that the hysteresis occurs due to different behavior of wakes between an accelerating flow and a decelerating flow.
Two‐Dimensional Convection Induced by Gravity andCentrifugal Forces in a Rotating Porous Layer Far Awayfrom the Axis of Rotation
Authors: Vadasz Peter , Govender Saneshan
Published: March 2007

The stability and onset of two‐dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.
A Brush Seals Program Modeling and Developments
Authors: Hendricks Robert C. , Flower Ralph , Howe Harold
Published: March 2007

Some events of a US Army/NASA Lewis Research Center brush seals program are
reviewed, and the development of ceramic brush seals is described. Some preliminary roomtemperature flow data are modeled and compare favorably to the results of Ergun.
Flow and Mass Transfer Performance in Short Pin‐FinChannels with Different Fin Shapes
Authors: Goldstein R. J. , Chen S. B.
Published: March 2007

The mass transfer (analogous to heat transfer) and pressure loss characteristics of staggered short pin‐fin arrays are investigated experimentally in the range of Reynolds number 3000 to 18,000 based on fin diameter and mean approach‐flow velocity. Three different shapes of fins with aspect ratio of 2 are examined: one uniform‐diameter circular fin (UDCF) and two stepped‐diameter circular fins (SDCF1 and SDCF2). Flow visualization using oil‐lampblack reveals complex flow characteristics associated with the repeated production of horseshoe vortices and fin wakes, and the interactions among these. The SDCF1 and SDCF2 arrays show flow characteristics different from the UDCF array due to downflow from the steps. For all arrays tested, the near‐endwall flow varies row by row in the initial rows until it reaches a stable pattern after the third row. The row‐averaged Sherwood numbers obtained from the naphthalene sublimation experiment also show a row‐by‐row variation pattern similar to the flow results. While the SDCF2 array has the highest mass transfer rate, the SDCF1 array has the smallest pressure loss at the same approach‐flow velocity. The fin surfaces have higher array‐averaged Sherwood number than the endwall and the ratio between these changes with fin shape and Reynolds number. The performance of the pin‐fin arrays is analyzed under two different constraints: the mass[heat transfer rate at fixed pumping power, and the mass/heat transfer area and pressure loss to fulfill fixed heat load at a fixed mass flow rate. In both cases, the SDCF2 array shows the best performance.
Numerical Study for Optimizing Heat Transfer in HighSpeed Rotating Components
Authors: Wittig S. , Kim S. , Scherer Th. , Weissert I.
Published: March 2007

Cooling of high speed rotating components is a typical situation found in turbomachinery as well as in automobile engines. Accurate knowledge of discharge coefficients and heat transfer of related components is essential for the high performance of the whole engine. This can be achieved by minimized cooling air flows and avoidance of hot spots. In high speed rotating clutches for example aerodynamic investigations improving heat transfer have not been considered in the past. Advanced concepts of modern plate design try to reduce thermal loads by convective cooling methods. Therefore, secondary cooling air flows have to be enhanced by an appropriate design of the rotor stator system with orifices. CFD modelling is used to improve the basic understanding of the flow field in typical geometries used in these systems.

The computational results are obtained by a 3‐D‐finite‐volume‐code based on body fitted structured grids. The Navier Stokes equations are solved by a pressure‐correction method combined with the standard k‐e‐turbulence model. Considering the rotation of orifices in disks or shafts, the frame of reference has to be changed to the rotating system. The flow through orifices in high speed rotating disks can be calculated with a high level of accuracy in comparison with experiments as shown in Wittig et al. [1994].

Numerical results of the flow in a high speed rotating system are presented with emphasis on geometrical variations. Calculations are carried out in order to find an optimum design in terms of position and size of the orifices in the housing. These variations induce different physical phenomena. Special consideration is directed towards the basic problems of the flow through orifices in high speed rotating disks and shafts and the flow inside rotor‐stator systems. As expected, the very complex flow fields are dominated by rotational effects. In addition it is shown that differences occur between the configuration of optimized mass flow rate and the geometry with a maximum of total heat transfer. Obviously, optimization procedures are dependent on the knowledge of the local flow field and cannot be performed without advanced CFD‐methods. It is demonstrated that the approach presented here is suitable for these tasks.
Experimental Investigation of Rotor‐Stator Interactionin Axial‐Flow Turbines and Compressors
Authors: Gallus Heinz E.
Published: March 2007

Detailed results of unsteady flow measurements in a stator‐rotor‐stator assembly of an axial‐flow turbine as well as an inlet guide vane‐rotor‐stator formation of an axial‐flow
compressor are presented in this paper.

The measurements include the time‐dependent 3‐D velocity vector fields in the axial gaps between the blade rows by means of triple‐hot wire‐technique, furthermore the total pressure field downstream of the blade rows by means of semiconductor total pressure probes and the unsteady flow field determination in the rotor passages by LDV‐technique. Special semiconductor pressure measurements along the casing all over the rotor tip clearance permit detailed discussion of the rotor tip clearance flows.

The conclusion of the measured data provides a new and very instructive view of the
physics of the unsteady blade‐row interaction in axial‐flow turbines and compressors.
Application of Through‐Flow Calculation to Designand Performance Prediction of Centrifugal Compressor
Authors: Choi Y. S. , Kang S. H.
Published: March 2007

A computer code predicting the flows through the centrifugal compressor with the radial vaneless diffuser was developed and applied to investigate the detailed flowfields, i.e.,
secondary flows and jet‐wake type flow pattern in design and off‐design conditions. Various
parameters such as slip factors, aerodynamic blockages, entropy generation and two‐zone
modeling which are widely used in design and performance prediction, were discussed.

A control volume method based on a general curvilinear coordinate system was used to
solve the time‐averaged Navier–Stokes equations and SIMPLER algorithm was used
to solve the pressure linked continuity equation. The standard k − ε turbulence model was used to obtain the eddy viscosity. Performance of the code was verified using the measured data for the Eckardt impeller.
Integrated Diagnostics and Prognostics of Rotating Machinery
Authors: Ng Kam W.
Published: March 2007

This paper provides an overview of current research efforts in integrated diagnostics and prognostics of rotating machinery. Specifically, the following topics are discussed: sensing techniques and sensors; signal detection, identification and extraction; classification of faults; predictive failure models; data/model fusion; information management; and man–machine interface. Technical issues, recommendations, and future research directions are also addressed.
Theoretical Rotordynamic Coefficients of Labyrinth GasSeals: a Parametric Study on a Bulk Model
Authors: Forte Paola , Latini Fabio
Published: March 2007

To date, available mathematical bulk models for the determination of linearized
rotordynamic coefficients of labyrinth gas seals yield results which are not always in good
agreement with the experimental ones. The object of this work is to discuss the limits of these models and to point out possible improvements and aspects that need further investigation.

After a study of the steady flow characteristics with an FEM code, a parametric computer
program, based on a known two‐volume model, has been developed. A perturbation approach has been applied to the governing equations of the bulk model to calculate the stiffness and damping coefficients. Predicted coefficients are compared to the results of an earlier one‐volume model.

The model has also been tested with different expressions of the axial velocities in the two volumes and different laws for leakage and shear stress. The theoretical results are compared to the published experimental ones, pointing out the small effect of the various parameters in improving the correlation and the need of more complex models.
Effect of Rotor–Stator Interaction on ImpellerPerformance in Centrifugal Compressors
Authors: Sato K. , He L.
Published: March 2007

A 3‐D unsteady thin‐layer Navier‐Stokes code has been used to calculate the flow through a centrifugal compressor stage. The validation of the code for steady flows in centrifugal compressors was conducted for the Krain’s impeller with a vaneless diffuser as a test case and the numerical results were compared with the experimental results. The predicted flow field and performance agreed well with the experimental data. An unsteady stage solution was then conducted with this impeller followed by a generic low‐solidity vaned‐diffuser to examine the unsteady effects on the impeller performance. The computational results showed a stabilising effect of the blade row interaction.
Bidirectional Brush Seals – Post‐Test Analysis
Authors: Hendricks Robert C. , Wilson Jack , Wu Tom Y. , Flower Ralph , Mullen Robert L.
Published: March 2007

A post‐test analysis of a set of inside‐diameter/outside‐diameter (ID/OD) bidirectional brush seals used in three‐port wave rotor tests was undertaken to determine brush bristle and configuration wear, pullout, and rotor coating wear. The results suggest that sharp changes in the pressure profiles were not well reflected in bristle tip configuration patterns or wear. Also, positive‐to‐negative changes in axial pressure gradients appeared to have little effect on the backing plates. Although the brushes had similar porosities, they had very different unpacked arrays. This difference could explain the departure of experimental data from computational fluid dynamics flow predictions for well‐packed arrays at higher pressure drops. The rotor wear led to “car track” scars (upper and lower wear bands) with a whipped surface between the bands. Those bands may have resulted from bristle stiffening at the fence and gap plates during alternate portions of the rotor cycle. Within the bristle response range the wear surface reflected the pressure distribution effect on bristle motion. No sacrificial metallurgical data were taken. The bristles did wear, with correspondingly more wear on the
ID brush configurations than on the OD configurations; the complexity in constructing the
ID brush was a factor.
Experimental Investigations on Tilting PadJournal Bearings
Authors: Brancati Renato , Pagano Stefano , Rocca Ernesto , Russo Michele , Russo Riccardo
Published: March 2007

The results of a survey conducted on an experimental system consisting of a rigid rotor supported on two radial bearings each with five tilting pads is presented. In particular, the system was set up in order to assess the dynamic behaviour of the bearing in unusual
operating conditions. The response of the bearing to different unbalance values was
determined after acquiring and analysing the orbits described by the journal axis for assigned unbalance values in different operating conditions. Analysis of the results shows some particular operating features that were not entirely predicted by the theoretical model and which may give rise to malfunctions in the rotor‐tilting pad bearings system. The tests were carried out in the rotor dynamics laboratory of the Dipartimento di Ingegneria Meccanica per l′Energetica at the University of Naples.
Revisiting Rotor Rigid Body Modes: Parametric Study of Stability
Authors: Littrell Nathan B. , Muszynska Agnes , Goldman Paul
Published: March 2007

This paper presents an analytical model of a rigid rotor supported in two fluid film bearings with an emphasis on predicting the instability threshold speed. The factors contributing to the stability of the rotor are discussed and presented graphically using root locus plots. The parametric study of the stability starts from the discussion of the rotor/bearing system with “mirror symmetry”. Three basic cases are considered:

(i) Rotor with relatively small gyroscopic effect (small polar moment of inertia) and
relatively high transverse moment of inertia. It is found that the pivotal mode
instability exists, but the lateral mode controls stability.
(ii) Highly gyroscopic rotor (relatively large polar moment of inertia) with also relatively
low transverse moment of inertia. It is found that the pivotal mode is infinitely
stable and the lateral mode controls stability.
(iii) Highly gyroscopic rotor with relatively high transverse moment of inertia. It is
found that the pivotal mode exists and controls stability. The lateral mode always
exists.

Both asymmetry in rotor geometry (location of center of mass with respect to the
bearings) and fluid bearing parameters (stiffness, damping) are considered. It is shown
that, for a given bearing asymmetry parameter, the maximum stability is achieved when
the geometric asymmetry parameter is of equal value. The recommendations on the
optimal design from the stability standpoint are given.
Mechanical Behavior of an Industrial Gas Turbine underFault Conditions, a Case History
Authors: Florjancic Stefan S. , Lively Noel , Thomas Richard
Published: March 2007

The resolve of journal bearing field problems and the full vibrational assessment of an industrial gas turbine, simple cycle rotor train, ABB’s GTllN2 is presented. Three units
experienced several times damage of the journal bearings on the compressor end. The
analysis of the damage, including tests, indicated that insufficient jacking oil flow was the
cause. The jacking concept was corrected and starting history has proven reliable operation,
resulting in not one additional failure.

During the same period, two last stage blades failed in one of the units damaging
neighboring blades additionally. The machine tripped under the unbalance. Some auxiliary
piping and the babbitt of the journal bearing was damaged. However, the rotor came to a safe stop with only some rubbing, and the turbine casing fulfilled its containment function
perfectly.

In order to better understand the dynamic behavior of the train, an extensive vibration
measurement program was decided between Kentucky Utilities and ABB, and executed
by Bently Nevada. The results proved excellent rotor balance, verified original design
parameters, and no fluid induced instabilities were found. This joint effort allowed to fully
assess and prove the rotor dynamic integrity of the gas turbine.
Numerical and Experimental Investigations of CouplingEffects in Anisotropic Elastic Rotors
Authors: Irretier Horst , Jacquet-Richardet Georges , Reuter Frank
Published: March 2007

It is known that in elastic disc‐shaft systems in particular, the one‐nodal‐diameter mode of the discs can be highly coupled with the bending modes of the shaft. Consequently, when the system rotates, the elastic modes of the flexible discs are coupled with the gyroscopic modes of the flexible shaft equipped with rigid discs. In the paper this coupling effect is investigated numerically and experimentally.

A numerical model, based on a finite element cyclic symmetry approach, is presented. This model has been developed for studying the wheel‐shaft coupling effects on the global behavior of turbomachinery rotors. In order to better illustrate the phenomenon involved and to validate the model, the method is applied here to a thin tuned and detuned circular disc mounted on an elastic shaft. Related frequency and mode shapes of the rotating assembly are discussed. Additional experimental results, based on an experimental modal analysis technique for rotating structures, are presented. Both numerical and experimental results are compared.
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals
Authors: Chandrawansa Kumari , Ruymgaart Frits H. , Van Rooij Arnoud C. M.
Published: March 2007

An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be
blurred by motion. Mathematically, this means that we actually observe
the convolution of the irregular function representing the picture with a
spread function. Since these observations will contain measurement errors,
statistical aspects will be pertinent. Traditional recovery is corrupted by
the Gibbs phenomenon (i.e., overshooting) near the edges, just as in the
case of direct approximations. In order to eliminate these undesirable
effects, we introduce an integral Cesàro mean in the inversion procedure,
leading to multivariable Fejér kernels. Integral metrics are not sufficiently
sensitive to properly assess the quality of the resulting estimators. Therefore, the performance of the estimators is studied in the Hausdorff metric,
and a speed of convergence of the Hausdorff distance between the graph of
the input signal and its estimator is obtained.
Quasi‐Feller Markov chains
Authors: Lasserre Jean B.
Published: March 2007

We consider the class of Markov kernels for which the weak or strong
Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster‐Lyapunov sufficient condition. We also
characterize a subclass, the quasi (weak or strong) Feller kernels, for which
the sequences of expected occupation measures share the same asymptotic
properties as for (weak or strong) Feller kernels. In particular, it is shown
that the sequences of expected occupation measures of strong and quasi
strong‐Feller kernels with an invariant probability measure converge setwise to an invariant measure.
Stability investigation of quadratic systems with delay
Authors: Davydov Vladimir , Khusainov Denis
Published: March 2007

Systems of differential equations with quadratic right‐hand sides with
delay are considered in the paper. Compact matrix notation form is
proposed for the systems of such type. Stability investigations are
performed by Lyapunov′s second method with functions of quadratic form.
Stability conditions of quadratic systems with delay, uniformly by
argument deviation, and with delay depending on the system′s parameters
are derived. A guaranteed radius of the ball of asymptotic stability region
for zero solution is obtained.
A note on controllability of semilinear integrodifferentialsystems in Banach spaces
Authors: Balachandran K. , Sakthivel R.
Published: March 2007

Sufficient conditions for controllability of semilinear integrodifferential systems in a Banach space are established. The results are obtained by using
the Schaefer fixed‐point theorem.
Existence and uniqueness of solutions of a semilinearfunctional‐differential evolution nonlocal Cauchy problem
Authors: Kolodziej Katarzyna
Published: March 2007

Two theorems about the existence and uniqueness of mild and classical
solutions of a semilinear functional‐differential evolution nonlocal Cauchy
problem in a general Banach space are proved. Methods of semigroups
and the Banach contraction theorem are applied.
Cooling of a layered plate under mixed conditions
Authors: Zaman F. D. , Al-Khairy R.
Published: March 2007

We consider the temperature distribution in an infinite plate composed of
two dissimilar materials. We suppose that half of the upper surface
(y = h, −∞ < x < 0) satisfies the general boundary condition of the Neumann type, while the other half (y = h, 0 < x < ∞) satisfies the general
boundary condition of the Dirichlet type. Such a plate is allowed to cool
down on the lower surface with the help of a fluid medium which moves
with a uniform speed v and which cools the plate at rate Ω. The resulting
mixed boundary value problem is reduced to a functional equation of the
Wiener‐Hopf type by use of the Fourier transform. We then seek the solution using the analytic continuation and an extended form of the Liouville
theorem. The temperature distribution in the two layers can then be
written in a closed form by use of the inversion integral.
Galerkin approximation and the strong solution of theNavier‐Stokes equation
Authors: Breckner Hannelore
Published: March 2007

We consider a stochastic equation of Navier‐Stokes type containing a noise
part given by a stochastic integral with respect to a Wiener process. The
purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Negatively dependent bounded random variable probabilityinequalities and the strong law of large numbers
Authors: Amini M. , Bozorgnia A.
Published: March 2007

Let X1, …, Xn be negatively dependent uniformly bounded random
variables with d.f. F(x). In this paper we obtain bounds for the probabilities and where is the
sample pth quantile and ξp is the pth quantile of F(x). Moreover, we
show that is a strongly consistent estimator of ξp under mild
restrictions on F(x) in the neighborhood of ξp. We also show that
converges completely to ξp.
G‐H‐KKM selections with applications to minimax theorems
Authors: Verma Ram U.
Published: March 2007

Based on the G‐H‐KKM selections, some nonempty intersection theorems
and their applications to minimax inequalities are presented.
A model for a dynamic preventive maintenance policy
Authors: Cocozza-Thivent Christiane
Published: March 2007

This paper exhibits a stochastic model which describes the evolution of a
material submitted to inspections. When an inspection takes place, a decision depending on the observed state of the material is taken. If the
material is in “not too bad” state, no service is rendered, only the date of
the next inspection is chosen. If the material is in a “bad” working state,
a service takes place. Roughly speaking, the failure rates of the material
are constant, the inspection and repair rates are general. We define the
average cost function corresponding to the utilization of this material and
we show how it can be computed. Then we determine the inspection rates
which give the optimal maintenance policy using a simulated annealing
algorithm. We observe experimentally that the best durations between inspections are deterministic ones.
On filtering over Îto‐Volterra observations
Authors: Basin Michael V.
Published: March 2007

In this paper, the Kalman‐Bucy filter is designed for an Îto‐Volterra process over Ito‐Volterra observations that cannot be reduced to the case of a
differential observation equation. The Kalman‐Bucy filter is then designed
for an Ito‐Volterra process over discontinuous Ito‐Volterra observations.
Based on the obtained results, the filtering problem over discrete observations with delays is solved. Proofs of the theorems substantiating the filtering algorithms are given.
Waiting time analysis for MX/G/1 priority queues with/without vacations under random order of service discipline
Authors: Kawasaki Norikazu , Takagi Hideaki , Takahashi Yutaka , Hong Sung-Jo , Hasegawa Toshiharu
Published: March 2007

We study MX/G/1 nonpreemptive and preemptive‐resume priority queues
with/without vacations under random order of service (ROS) discipline
within each class. By considering the conditional waiting times given the
states of the system, which an arbitrary message observes upon arrival, we
derive the Laplace‐Stieltjes transforms of the waiting time distributions
and explicitly obtain the first two moments. The relationship for the
second moments under ROS and first‐come first‐served disciplines extends
the one found previously by Takacs and Fuhrmann for non‐priority single
arrival queues.
Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations
Authors: Beghin L. , Nieddu L. , Orsingher E.
Published: March 2007

The telegrapher′s process with drift is here examined and its distribution is
obtained by applying the Lorentz transformation. The related characteristic function as well as the distribution are also derived by solving an initial
value problem for the generalized telegraph equation.
Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long‐range dependence
Authors: Leonenko N. N. , Anh V. V.
Published: March 2007

This paper establishes the rate of convergence (in the uniform Kolmogorov
distance) for normalized additive functionals of stochastic processes with
long‐range dependence to a limiting Rosenblatt distribution.
A simple asymptotically optimal filter over an infinite horizon
Authors: Chigansky P. , Liptser R. , Bobrovsky B. Z.
Published: March 2007

A filtering problem over an infinite horizon for a continuous time signal
and discrete time observation in the presence of non‐Gaussian white noise
is considered. Conditions are presented, under which a nonlinear Kalman
type filter with limiter is asymptotically optimal in the mean square sense
for long time intervals given provided the sampling frequency is sufficiently high.
Periodic and boundary value problems for second order differential inclusions
Authors: Palmucci Michela , Papalini Francesca
Published: March 2007

In this paper we study differential inclusions with boundary conditions in
which the vector field F(t, x, y) is a multifunction with Caratheodory type
conditions. We consider, first, the case which F has values in ℝ and we
establish the existence of extremal solutions in the order interval determined by the lower and the upper solution. Then we prove the existence of
solutions for a Dirichlet problem in the case in which F takes their values
in a Hilbert space.
On the “freezing” method for nonlinear nonautonomous systems with delay
Authors: Gil′ Michael I.
Published: March 2007

Nonlinear nonautonomous differential systems with delaying argument are considered. Explicit conditions for absolute stability are derived. The proposed approach is based on the generalization of the “freezing” method for ordinary differential equations.
Nonlinear essential maps of Mönch, 1‐set contractive demicompact and monotone (S)+ type
Authors: Agarwal Ravi P. , O′Regan Donal
Published: March 2007

In this paper the notion of an essential map is extended to a wider class of
maps. Here we show if F is essential and F≅G, then G has a fixed
point.
Nonoscillation of the solutions of impulsive differential equations of third order
Authors: Dimitrova Margarita Boneva
Published: March 2007

Necessary and sufficient conditions are found for existence of at least one
bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions are investigated.
Controllability of semilinear stochastic evolution equations in Hilbert space
Authors: Balasubramaniam P. , Dauer J. P.
Published: March 2007

Controllability of semilinear stochastic evolution equations is studied by
using stochastic versions of the well‐known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation
is given.
Strong result for real zeros of random algebraic polynomials
Authors: Uno T.
Published: March 2007

An estimate is given for the lower bound of real zeros of random algebraic
polynomials whose coefficients are non‐identically distributed dependent
Gaussian random variables. Moreover, our estimated measure of the
exceptional set, which is independent of the degree of the polynomials,
tends to zero as the degree of the polynomial tends to infinity.
A k‐out‐of‐n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy
Authors: Chakravarthy Srinivas R. , Krishnamoorthy A. , Ushakumari P. V.
Published: March 2007

In this paper we study a k‐out‐of‐n reliability system in which a single unreliable server maintains n identical components. The reliability system is
studied under the (N, T) policy. An idle server takes a vacation for a random amount of time T and then attends to any failed component waiting in line upon completion of the vacation. The vacationing server is recalled instantaneously upon the failure of the Nth component. The failure times of the components are assumed to follow an exponential distribution. The server is subject to failure with failure times exponentially distributed. Repair times of the component, fixing times of the server, and vacationing times of the server are assumed to be of phase type. Using matrix‐analytic methods we perform steady state analysis of this model. Time spent by a failed component in service, total time in the repair facility, vacation time of the server, non‐vacation time of the server, and time until failure of the system are all shown to be of phase type. Several performance measures are evaluated. Illustrative numerical examples are presented.
A weak convergence approach to hybrid LQG problems with infinite control weights
Authors: Yin G. George , Yong Jiongmin
Published: March 2007

This work is concerned with a class of hybrid LQG (linear quadratic Gaussian)
regulator problems modulated by continuous‐time Markov chains. In contrast to
the traditional LQG models, the systems have both continuous dynamics and
discrete events. In lieu of a model with constant coefficients, these coefficients
vary with time and exhibit piecewise constant behavior. At any time t, the system
follows a stochastic differential equation in which the coefficients take one of the
m
possible configurations where m
is usually large. The system may jump to any
of the possible configurations at random times. Further, the control weight in the
cost functional is allowed to be indefinite. To reduce the complexity, the Markov
chain is formulated as singularly perturbed with a small parameter. Our effort is
devoted to solving the limit problem when the small parameter tends to zero via
the framework of weak convergence. Although the limit system is still modulated
by a Markov chain, it has a much smaller state space and thus, much reduced
complexity.
Harmonic close‐to‐convex mappings
Authors: Jahangiri Jay M. , Silverman Herb
Published: March 2007

Sufficient coefficient conditions for complex functions to be close‐to‐convex harmonic
or convex harmonic are given. Construction of close‐to‐convex harmonic
functions is also studied by looking at transforms of convex analytic functions.
Finally, a convolution property for harmonic functions is discussed.
On second order impulsive functional differential equations inBanach spaces
Authors: Benchohra M. , Ntouyas S. K.
Published: March 2007

In this paper, a fixed point theorem due to Schaefer is used to investigate the
existence of solutions for second order impulsive functional differential equations
in Banach spaces.
Connections between the convective diffusion equation and theforced Burgers equation
Authors: Smaoui Nejib , Belgacem Fethi
Published: March 2007

The convective diffusion equation with drift b(x) and indefinite weight r(x),

is introduced as a model for population dispersal. Strong connections between
Equation (1) and the forced Burgers equation with positive frequency (m ≥ 0),

are established through the Hopf‐Cole transformation. Equation (2) is a prime
prototype of the large class of quasilinear parabolic equations given by

A compact attractor and an inertial manifold for the forced Burgers equation are
shown to exist via the Kwak transformation. Consequently, existence of an
inertial manifold for the convective diffusion equation is guaranteed. Equation (2)
can be interpreted as the velocity field precursed by Equation (1). Therefore, the
dynamics exhibited by the population density in Equation (1) show their effects on
the velocity expressed in Equation (2). Numerical results illustrating some aspects
of the previous connections are obtained by using a pseudospectral method.
Investigation of interval stability of linear systems of neutraltype of Lyapunov function method
Authors: Khusainov Denis Ya.
Published: March 2007

Systems of differential equations with deviating argument of neutral type [1, 3, 8]
are used. The mathematical model takes into account not only the previous
moments of time, but also the speed of their change. These equations more
adequately describe the dynamics of processes, but their investigation faces
significant difficulties. The qualitative behavior of solutions of neutral type
systems includes the features both, differential and difference equations [2, 9].
Stability investigations require the smallest size of the delay′s speed value [7].
Recently, so‐called interval, or robust stability theory has received intensive
development. It is based on two theorems of V.L. Kharitonov [4, 5] for scalar:
equations. However, difficulties have appeared to obtain similar results for
systems in vector‐matrix form. It is even more complicated to derive conditions
of interval stability for systems of differential‐difference equations, though there
are results for scalar equation in [6, 10].
Algebraic polynomials with random coefficients
Authors: Farahmand K.
Published: March 2007

This paper provides an asymptotic value for the mathematical expected number of
points of inflections of a random polynomial of the form

when n is large. The coefficients , w ∈ Ω are assumed to be a sequence of independent
normally distributed random variables with means zero and variance one, each
defined on a fixed probability space (A, Ω, Pr). A special case of dependent coefficients is also studied.
Periodic solutions of non‐densely defined delay evolutionequations
Authors: Ezzinbi Khalil , Liu James H.
Published: March 2007

We study the finite delay evolution equation

where the linear operator A
is non‐densely defined and satisfies the Hille‐Yosida
condition. First, we obtain some properties of “integral solutions” for this case
and prove the compactness of an operator determined by integral solutions. This
allows us to apply Horn′s fixed point theorem to prove the existence of periodic
integral solutions when integral solutions are bounded and ultimately bounded.
This extends the study of periodic solutions for densely defined operators to the
non‐densely defined operators. An example is given.
On a class of nonclassical hyperbolic equations with nonlocalconditions
Authors: Bouziani Abdelfatah
Published: March 2007

This paper proves the existence, uniqueness and continuous dependence of a
solution of a class of nonclassical hyperbolic equations with nonlocal boundary
and initial conditions. Results are obtained by using a functional analysis method
based on an a priori estimate and on the density of the range of the linear operator
corresponding to the abstract formulation of the considered problem.
Filtering and predicting the cost of hidden perished items in an inventory model
Authors: Aggoun Lakhdar , Benkherouf Lakdere
Published: March 2007

This paper is concerned with a discrete time, discrete state inventory model for items of changing quality. Items are assumed to be in one of a finite number, M, of quality classes that are ordered in such a way that Class 1 contains the best quality and the last class contains the pre‐perishable quality. The changes of items′ quality are dependent on the state of the ambient environment. Furthermore, at each epoch time, items of different classes may be sold or moved to a lower quality class or stay in the same class. These items are priced according to their quality, and costs are incurred as items lose quality. Based on observing the history of the inventory level and prices, we propose recursive estimators as well as predictors for the joint distribution of the accumulated losses and the state of the environment.
Random Fixed Points and Random Approximations in Nonconvex Domains
Authors: Khan Abdul Rahim , Thaheem A. B. , Hussain Nawab
Published: March 2007

Stochastic generalizations of some fixed point theorems on a class of nonconvex
sets in a locally bounded topological vector space are established. As applications, Brosowski‐Meinardus type theorems about random invariant approximation are obtained. This work extends or provides stochastic versions of several well known results.
Oscillation criteria for a class of partial functional‐differential equations of higher order
Authors: Kiguradze Tariel , Kusano Takaŝi , Yoshida Norio
Published: March 2007

Higher order partial differential equations with functional arguments including hyperbolic equations and beam equations are studied. Sufficient conditions are derived for every solution of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi‐dimensional oscillation problem to a one‐dimensional problem for higher order functional differential inequalities.
A method of upper and lower solutions for functional differential inclusions
Authors: Benchohra Mouffak , Ntouyas Sotiris K.
Published: March 2007

In this paper, a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for first order functional differential inclusions.
Mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator
Authors: Mesloub Said , Bouziani Abdelfatah
Published: March 2007

In this paper, we prove the existence, uniqueness and continuous dependence on the data of a solution of a mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator. The proof uses a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the considered problem.
Principal eigenvalue characterization connected with stochastic particle motion in a finite interval
Authors: Belgacem Fethi Bin Muhammad , Karaballi Ahmed Abdullatif
Published: March 2007

In this paper, we show that despite their distinction, both the Statonovich and Îto s
calculi lead to the same reactive Fokker‐Planck equation:

describing stochastic dynamics of a particle moving under the influence of an
indefinite potential m(x, t), a drift b(x, t), and a constant diffusion D. We treat
the periodic‐parabolic eigenvalue problem (1) for finite domains having
absorbing barriers. We show that under conditions required by the maximum
principle, the positive principal eigenvalue λ* (and the negative principal λ*
eigenvalue) is connected to the probability eigendensity function p(x, t) by a
Raleigh‐Ritz like formulation. In the process, we establish the manner of effect of
the drift and any inducing potential on the size of the principal eigenvalue. We
show that the degree of convexity of the potential plays a major role in this
regard.
On a generalized Jacobi transform
Authors: Sarabia José , Kalla S. L.
Published: March 2007

In this paper, we study a generalized Jacobi transform and obtain images of
certain functions under this transform. Furthermore, we define a Jacobi random
variable and derive its moments, distribution function, and characteristic function.
Existence of solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces
Authors: Kanakaraj M. , Balachandran K.
Published: March 2007

The existence of mild solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.
Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation‐invariant operators on multidimensional integer lattices
Authors: Diamond Phil , Kloeden Peter , Vladimirov Igor
Published: March 2007

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst‐case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white‐noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback‐Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a ≥ 0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces
Authors: Dhage B. C. , O′Regan Donal , Agarwal Ravi P.
Published: March 2007

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.
A note of stability of weakly efficient solution set for optimization with set‐valued maps
Authors: Qun Luo
Published: March 2007

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set‐valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set‐valued maps (in the sense of Baire category) are
stable. Secondly, we obtain some sufficient conditions for the existence of one essential
weakly efficient solution or one essential component of the weakly efficient solution set .
Necessary and sufficient conditions for the ergodicity of Markov chains with transition Δm,n(Δ′m,n)‐matrix
Authors: Abolnikov L. , Dukhovny A.
Published: March 2007

This paper isolates and studies a class of Markov chains with a
special quasi‐triangular form of the transition matrix [so‐called ‐matrix]. Many discrete stochastic processes encountered in
applications (queues, inventories and dams) have transition matrices
which are special cases of a ‐matrix. Necessary and
sufficient conditions for the ergodicity of a Markov chain with
transition ‐matrix are determined in the article in two
equivalent versions. According to the first version, these conditions are
expressed in terms of certain restrictions imposed on the generating
functions Ai(x) of the elements of the i‐th row of the transition matrix,
i = 0, 1, 2, …; in the other version they are connected with the
characterization of the roots of a certain associated function in the unit
circle of the complex plane. Results obtained in the article generalize,
complement, and refine similar results existing in the literature.
Topological structures in computer science
Authors: Khalimsky Efim
Published: March 2007

Topologies of finite spaces and spaces with countably many
points are investigated. It is proven, using the theory of ordered
topological spaces, that any topology in connected ordered spaces, with
finitely many points or in spaces similar to the set of all integers, is an
interval‐alternating topology. Integer and digital lines, arcs, and curves
are considered. Topology of N‐dimensional digital spaces is described. A
digital analog of the intermediate value theorem is proven. The
equivalence of connectedness and pathconnectedness in digital and
integer spaces is also proven. It is shown here how methods of
continuous mathematics, for example, topological methods, can be
applied to objects, that used to be investigated only by methods of
discrete mathematics. The significance of methods and ideas in digital
image and picture processing, robotic vision, computer tomography and
system′s sciences presented here is well known.