bluuebunny/crossref_metadata_2025 huggingface dataset:
Measurements of the Flow in Backshroud/CasingClearance of Precessing Centrifugal Impeller
Authors: Yoshida Yoshiki , Tsujimoto Yoshinobu , Ohashi Hideo , Saito Akira , Ishizaki Shin
Published: March 2007

Detailed flow measurements have been made to clarify the unsteady flow in the backshroud/
casing clearance of a precessing centrifugal impeller. The unsteady pressure was integrated
to obtain the fluid force moment on the precessing impeller shroud for various precessing
frequencies. It was shown that the fluid force moment can become rotordynamically
destabilizing for small forward precessing motion as originally found by Ohashi et al. The
effects of leakage flow in the backshroud/casing clearance and a gap between impeller side
plate and casing at the impeller outlet are clearly shown, and the discussions are also made
based on the unsteady velocity and pressure measurements.
A Film‐Cooling CFD Bibliography: 1971–1996
Authors: Kercher D. M.
Published: March 2007

After more than 25 years of three‐dimensional film cooling experimental investigations, analytical correlations and modeling, film cooling utilizing computational fluid dynamics has emerged from a similar development‐applications growth process into a near‐attainable heat transfer engineering tool. Analytical applications include high temperature subsonic to hypersonic flow with complex wall‐geometry coolant injection film performance analysis techniques spanning usage from gas turbines to rocket engines to scramjets. In recent years there has been significant development in increased computer power and modeling capacity, increasingly more complex and successful Navier‐Stokes turbulence modeling techniques, innovative labor‐saving meshing techniques, and more successful validation of experimental results. These combined innovations have continued to transition computational film cooling technology from the academic, government and commercial research and development environment to the industrial design‐analysis environment. This bibliography is an openliterature reference resource whose papers collectively describe the continual emerging of numerical film cooling as a viable design tool for high temperature components.
Effect of Film Injection Location on Local Heat Transfer Coefficient on a Gas Turbine Blade
Authors: Mehendale Anant B. , Jiang H. Wanda , Ekkad Srinath V. , Han Je-Chin
Published: March 2007

Experiments were performed to study the effect of film hole location on local heat transfer coefficient distribution of a turbine blade model with air or CO2 film injection to simulate coolant density effect. Tests were performed on a five blade linear cascade at the chord Reynolds number of 3 × 105 at cascade inlet. The test blade had three rows of film holes in
the leading edge region and two rows each on the pressure and suction surfaces. Film hole
locations were varied by leaving the desired ones open and plugging the rest. A combination
of turbulence grid and unsteady wake was used to generate upstream high turbulence
condition. Results indicate that film injection by itself causes a substantial increase in
Nusselt numbers over a blade model without film holes. An increase in mainstream
turbulence intensity causes an increase in Nusselt numbers over most of the blade surface,
for both coolants, and at all blowing ratios. Film injection promotes an earlier boundary
layer transition on the suction surface and the onset of transition depends on the film
injection location; but at high turbulence levels, transition location is almost independent of
film injection location.
Heat Transfer on a Film‐Cooled Rotating Blade Using aTwo‐Equation Turbulence Model
Authors: Garg Vijay K.
Published: March 2007

A three‐dimensional Navier–Stokes code has been used to compare the heat transfer coefficient on a film‐cooled, rotating turbine blade. The blade chosen is the ACE rotor with five rows containing 93 film cooling holes covering the entire span. This is the only filmcooled rotating blade over which experimental data is available for comparison. Over 2.278 million grid points are used to compute the flow over the blade including the tip clearance region, using Coakley′s q − ω turbulence model. Results are also compared with those obtained by Garg and Abhari (1997) using the zero‐equation Baldwin‐Lomax (B‐L)
model. A reasonably good comparison with the experimental data is obtained on the suction
surface for both the turbulence models. At the leading edge, the B‐L model yields a better
comparison than the q − ω model. On the pressure surface, however, the comparison between
the experimental data and the prediction from either turbulence model is poor. A potential
reason for the discrepancy on the pressure surface could be the presence of unsteady effects due to stator‐rotor interaction in the experiments which are not modeled in the present computations. Prediction using the two‐equation model is in general poorer than that using the zero‐equation model, while the former requires at least 40% more computational resources.
Blade Deterioration in a Gas Turbine Engine
Authors: Tabakoff W. , Hamed A. , Shanov V.
Published: March 2007

A study has been conducted to predict blade erosion of gas turbine engines. The blade material erosion model is based on three dimensional particle trajectory simulation in the three‐dimensional turbine flow field. The trajectories provide the special distribution of the particle impact parameters over the blade surface. A semi‐empirical erosion model, derived from erosion tests of material samples at different particulate flow conditions, is used in the prediction of blade surface erosion based on the trajectory impact data. To improve the blade erosion resistance and to decrease the blade deterioration, the blades must be coated. For this purpose, an experimental study was conducted to investigate the behavior of rhodium platinum aluminide coating exposed to erosion by fly ash particles. New protective coatings are developed for erosion and thermal barrier. Chemical vapor deposition technique (CVD) was used to apply the ceramic TiC coatings on INCO 718 and stainless steel 410. The erosive wear of the coated samples was investigated experimentally by exposing them to particle laden flow at velocities from 180 to 305m/s and temperatures from ambient to 538°C in a specially designed erosion wind tunnel. Both materials (INCO 718 and stainless steel 410) coated with CVD TiC showed one order of magnitude less erosion rate compared to some commercial coatings on the same substrates.
Calculation of Rotor Dynamic Coefficients for Labyrinth Seals
Authors: Williams B. P. , Flack R. D.
Published: March 2007

A single control volume, Iwatsubo based bulk flow method for the calculation of these coefficients is developed and implemented. The method herein uses a unique iterative
technique to first identify the mass flow rate based on pressure drops across the individual
teeth, which is then used in the governing sets of continuity and momentum equations. The
method is applicable to different teeth geometries and arrangements. A parametric analysis
of the effect of mass flow rate on rotor dynamic coefficients is performed and suggests that a
small variation in mass flow rate does not significantly detract from the accuracy of the
predicted dynamic coefficients; the mass flow rate calculation implemented in this paper is
sufficiently accurate. Furthermore, the inclusion of some tangential momentum parameters
has been previously proposed to improve the accuracy of the Iwatsubo method. However,
from the current analysis the inclusion of such parameters is also shown to have little effect
on the rotor dynamic coefficients and does not lead to improved correlation with
experimental data. Comparisons to experimental data suggest that the method herein is
reasonable for use as a design tool to predict the trends and actual values of cross‐coupled
stiffness, the most important seal parameter in rotor dynamic analyses. The method is also
shown to be useful in predicting the order of magnitude of principal stiffness and damping
coefficients.
Heat Transfer and Friction in a Low‐Aspect‐RatioRectangular Channel with Staggered Slit‐Ribbed Walls
Authors: Hwang Jenn-Jiang , Liou Tong-Miin
Published: March 2007

Fully developed heat transfer and friction in a rectangular channel with slit‐ribbed walls are examined experimentally. The slit ribs are transversely arranged on the bottom and top
channel walls in a staggered manner. Effects of rib open‐area ratio (β= 24%, 37%, and 46%), rib pitch‐to‐height ratio (Pi/H = 10, 15and20), and Reynolds number (10, 000 ≤ Re≤50, 000) are examined. The rib height‐to‐channel hydraulic diameter ratio is fixed at
H/De = 0.081. It is disclosed that the heat transfer coefficient for the slit‐ribbed channel is
higher than that for the solid‐ribbed channel, and increases with rib open‐area ratio. Results
also show that the friction factor for the slit‐ribbed channel is significantly lower than that
for the solid‐ribbed one. Moreover, the ribs with larger open‐area ratios in a higher flow
Reynolds number condition could give the better thermal performance under the constant
friction power constraint. Roughness functions for friction and heat transfer are further
developed in terms of rib and flow parameters.
Modelling of Shaft Orbiting with 3‐D Solid Finite Elements
Authors: Yu J. , Craggs A. , Mioduchowski A.
Published: March 2007

A 3‐D solid finite element model which can include bending, torsional, axial and other motions is proposed to analyse dynamic responses of shafts. For uniform shafts, this model shows consistency with beam theories when bending vibration is examined. For non‐uniform shafts such as tapered ones, however, this model gives much more reliable and accurate results than beam theories which use an assumption that plane sections remain plane. Reduction procedures can be applied which involve only small matrix operations for such a system with a large number of degrees of freedom. The equations of motion have been consistently derived in a rotating frame. Shaft orbiting motion is then defined in this frame, giving a clear view of its trajectories. Forced responses due to excitation in the rotating frame have been examined to find some characteristics of the orbiting shaft. Resonant orbiting frequencies, i.e., natural frequencies of rotating shafts, can be determined in terms of the rotating or fixed frame. Trajectories of transverse displacements have been found to be varying with the forcing frequencies. At resonance, a uniform shaft will only have forward or backward orbiting motion with circular orbits. For other forcing frequencies, however, even a uniform shaft could present both forward and backward orbiting motions with non‐circular orbits at different locations along its length. It is anticipated that modelling of shaft orbiting in the rotating frame with the proposed 3‐D solid finite elements will lead to accurate dynamic stress evaluation.
Axial Compressor Stall and Surge Prediction by Measurements
Authors: Hönen H.
Published: March 2007

The paper deals with experimental investigations and analyses of unsteady pressure distributions in different axial compressors. Based on measurements in a single stage research compressor the influence of increasing aerodynamic load onto the pressure and velocity fluctuations is demonstrated. Detailed measurements in a 14‐stage and a 17‐stage gas turbine compressor are reported. For both compressors parameters could be found which are clearly influenced by the aerodynamic load.

For the 14‐stage compressor the principles for the monitoring of aerodynamic load and stall are reported. Results derived from a monitoring system for multi stage compressors based on these principles are demonstrated. For the 17‐stage compressor the data enhancement of the measuring signals is shown. The parameters derived from these results provide a good base for the development of another prediction method for the compressor stability limit. In order design an on‐line system the classification of the operating and load conditions is provided by a neural net. The training results of the net show a good agreement with different experiments.
Secondary Flow Phenomena in an Axially Rotating FlowPassage with Sudden Expansion or Contraction
Authors: Torii Shuichi , Yang Wen-Jei
Published: March 2007

This paper investigates rotational effects on secondary flow in rotating flow passages with sudden expansion or contraction. Consideration is given to laminar flow. The governing boundary‐layer equations are discretized by means of a finite‐difference technique and numerically solved to determine the distributions of velocity vector under the appropriate boundary conditions. The Reynolds number (Re) and rotation rate are varied to determine their effects on the formation ofsecondary flows. It is disclosed from the study that: (i) when laminar flow is introduced into an axially rotating pipe with expansion, the stretch ofthe secondary flow zone is amplified with an increase in the rotation rate and Re, and (ii) in contrast, for axially rotating pipe flows with contraction, the secondary flow region is somewhat suppressed due to pipe rotation, and the change is slightly affected by the rotation rate and Re. Results may find applications in automotive and rotating hydraulic transmission lines.
A New Approach to Assess the Quality of Small High‐Speed Centrifugal Fans Using Noise Measurement
Authors: Cui Dingjun , Craighead Ian A.
Published: March 2007

The requirements for a special approach for the quality assessment of small high‐speed centrifugal fans are outlined and a new parameter designating the noise levels from the product in comprehensive form will be discussed and described as a criterion for such quality assessment.

By applying techniques of signal processing and condition monitoring, the sources of the vibration and noise in different sections of the product can be identified, then the noise from each source from different components can be determined. Using this criterion, more aspects of the quality of the products can be assessed and suggestions to improve the quality of the products can be made. Finally, the assessment of a number ofvacuum cleaner motor/fan units available in the commercial market will be presented and compared with conventional specifications. It will be shown that the new parameter provides a more useful indication of appliance quality.
Rotating Flows Driven by Axisymmetric Bladesin a Cylinder
Authors: Kim Jae Won
Published: March 2007

A study is made of steady state flow of a viscous fluid, driven by a rotating endwall disk having radial blades in a finite geometry. Numerical solutions to the Navier‐Stokes equations are obtained for the flows in the cylindrical cavity. The bottom endwall disk of the vessel is impulsively rotating at a constant rotating speed ft with respect to the longitudinal axis of it. Details of the three components velocity field are examined at high Reynolds number for its engineering application. The main parameter for this study is the number of the radial blades of a rotating pulsator. The numerical results for the fluid flows and pressure distribution, for both an odd and an even number of the blades are procured. The present output offers an optimal number of the blades for rotating machinery such as agitator. The grid‐net for the numerical computation is constructed on a body‐fitted coordinate system transformed from physical coordinates. It is also flexible to suit any number of blades attached on the rotating bottom disk. The algorithm for the numerical computation is based on the SIMPLE release by Patankar, and the results are validated with prior published data. In addition, a characteristic model is prepared for the pressure measurement. The pressure measurements performed for the present model are consistent with this computational work. The explicit effect of the blade on the overall flow character is scrutinized. The numerical data are processed to describe the behavior of the meridional velocities under different blade conditions. Also, the traces of particles are plotted to assess the effects. Pronounced differences are noted and these results supply comprehensive data for practical application.
The Dynamics of Rotor with Rubbing
Authors: Sawicki Jerzy T. , Padovan Joe , Al-Khatib Rabih
Published: March 2007

This paper presents the description of some phenomena associated with dynamic behavior of rotors interacting with stationary components. Numerical simulations show rotor vibration spectrum rich in subharmonic, quasi‐periodic, and chaotic vibrations. The nonlinear
calculation techniques are applied to demonstrate the changes of the vibration patterns for
different operating conditions. Some conclusions are discussed with regard to unique
characteristics of rub‐induced rotor response, initial conditions, as well as appropriate ranges of system parameters. Of special interest are the changes in the apparent nonlinearity of the system dynamics as rubs are induced at different rotor speeds. In particular, starting with 2nd order sub/superharmonics, which are symptomatic of quadratic nonlinearity, progressively higher order polynomial behavior is excited, i.e., cubic, giving rise to 3rd order sub/superharmonics. As the speed is transitioned between such apparent nonlinearities, chaotic like behavior is induced because of the lack of whole or rational tone tuning between the apparent system frequency and the external source noise. The cause of such behavior will be discussed in detail along with the results of several parametric studies.
On the stabilization of the energy of a harmonic oscillator disturbed by random processes of the “white and shot noises” types
Authors: Kulinich Grigori L. , Kushnirenko Svitlana V.
Published: March 2007

In this paper the behavior of the instantaneous energy of a harmonic oscillator is investigated in the case when at a certain angle to the vector of the
phase velocity of the oscillator, random disturbances of the “white and
shot noises” types are acting.
Periodic solutions of systems with asymptotically evennonlinearities
Authors: Kloeden Peter E. , Krasnosel′skii Alexander M.
Published: March 2007

New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal
linear part as well as degenerate “next order” terms are obtained for the
2π‐periodic problem for the scalar equation x″ + n2x = g(|x|) + f(t, x) + b(t) with bounded g(u) and f(t, x) → 0 as |x| → 0. The result is also applied to the solvability of a two‐point boundary value problem and to resonant problems for equations arising in control theory.
BSDEs with polynomial growth generators
Authors: Briand Philippe , Carmona René
Published: March 2007

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in
the state variable. We deal with the case of a fixed terminal time, as well
as the case of random terminal time. The need for this type of extension
of the classical existence and uniqueness results comes from the desire to
provide a probabilistic representation of the solutions of semilinear partial
differential equations in the spirit of a nonlinear Feynman‐Kac formula.
Indeed, in many applications of interest, the nonlinearity is polynomial,
e.g, the Allen‐Cahn equation or the standard nonlinear heat and Schrödinger equations.
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.
Parallelization algorithms for modeling ARM processes
Authors: Melamed Benjamin , Singh Santokh
Published: March 2007

AutoRegressive Modular (ARM) processes are a new class of nonlinear
stochastic processes, which can accurately model a large class of stochastic
processes, by capturing the empirical distribution and autocorrelation function simultaneously. Given an empirical sample path, the ARM modeling
procedure consists of two steps: a global search for locating the minima of
a nonlinear objective function over a large parametric space, and a local
optimization of optimal or near optimal models found in the first step. In
particular, since the first task calls for the evaluation of the objective function at each vector of the search space, the global search is a time consuming procedure. To speed up the computations, parallelization of the global
search can be effectively used by partitioning the search space among
multiple processors, since the requisite communication overhead is negligible.

This paper describes two space‐partitioning methods, called Interleaving and Segmentation, respectively. The speedups resulting from these
methods are compared for their performance in modeling real‐life data.
On finite capacity queueing systems with a general vacation policy
Authors: Loris-Teghem Jacqueline
Published: March 2007

We consider a Poisson arrival queueing system with finite capacity and a
general vacation policy as described in Loris‐Teghem [Queueing Systems 3
(1988), 41‐52]. From our previous results regarding the stationary queue
length distributions immediately after a departure and at an arbitrary
epoch, we derive a relation between both distributions which extends a
result given in Frey and Takahashi [Operations Research Letters 21
(1997), 95‐100] for the particular case of an exhaustive service multiple
vacation policy.
Complex‐analytic and matrix‐analytic solutions for a queueing system with group service controlled by arrivals
Authors: Abolnikov Lev , Dukhovny Alexander
Published: March 2007

A bulk M/G/1 system is considered that responds to large increases (decreases) of the queue during the service act by alternating between two service modes. The switching rule is based on two “up” and “down” thresholds for total arrivals over the service act. A necessary and sufficient
condition for the ergodicity of a Markov chain embedded into the main
queueing process is found. Both complex‐analytic and matrix‐analytic
solutions are obtained for the steady‐state distribution. Under the assumption of the same service time distribution in both modes, a combined complex‐matrix‐analytic method is introduced. The technique of “matrix unfolding” is used, which reduces the problem to a matrix iteration process
with the block size much smaller than in the direct application of the matrix‐analytic method.
Single server queueing networks with varying service times and renewal input
Authors: Gall Pierre Le
Published: March 2007

Using recent results in tandem queues and queueing networks with renewal
input, when successive service times of the same customer are varying (and
when the busy periods are frequently not broken up in large networks), the
local queueing delay of a single server queueing network is evaluated utilizing new concepts of virtual and actual delays (respectively). It appears
that because of an important property, due to the underlying tandem
queue effect, the usual queueing standards (related to long queues) cannot
protect against significant overloads in the buffers due to some possible
“agglutination phenomenon” (related to short queues). Usual network
management methods and traffic simulation methods should be revised,
and should monitor the partial traffic streams loads (and not only the
server load).
The asymptotic behavior of elementary symmetric functions on a probability distribution
Authors: Kozyakin V. S. , Pokrovskii A. V.
Published: March 2007

The problem on asymptotic of the value
π(m, n) = m! σm(p(1, n), p(2, n), ⋯, p(n, n))
is considered, where σm(x1, x2, ⋯, xn) is the mth elementary symmetric
function of n variables. The result is interpreted in the context of nonequiprobable random mappings theory.
Approximating a harmonizable isotropic random field
Authors: Swift Randall J.
Published: March 2007

The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a
harmonizable isotropic random field. This approximation is useful for
numerical simulation of such a field.
On random orthogonal polynomials
Authors: Farahmand K.
Published: March 2007

Let be a sequence of normalized Legendre polynomials orthogonal with respect to the interval (−1, 1). The asymptotic estimate of the expected number of real zeros of the random polynomial
where gj, j = 1, 2, …, n are independent identically and normally distributed random variables is known. In
this paper, we first present the asymptotic value for the above expected
number when coefficients are dependent random variables. Further, for
the case of independent coefficients, we define the expected number of zero
up‐crossings with slope greater than u or zero down‐crossings with slope
less than −u. Promoted by the graphical interpretation, we define these
crossings as u‐sharp. For the above polynomial, we provide the expected
number of such crossings.
On the spectrum of ψ‐contracting operators
Authors: Al-Nayef Anwar A.
Published: March 2007

The spectrum σ(A) of a continuous linear operator A : E → E defined on a
Banach space E, which is contracting with respect to the Hausdorff
measure of noncompactness, is investigated.
Random fixed points for ∗‐nonexpansive random operators
Authors: Khan Abdul Rahim , Hussain Nawab
Published: March 2007

The notion of a ∗‐nonexpansive multivalued map is different from that of
a continuous map. In this paper we prove some fixed point theorems for
∗‐nonexpansive multivalued random operators in the setup of Banach
spaces and Fréchet spaces. Our work generalizes, refines and improves the
earlier results of a number of authors.
The MX/G/1 queue with queue length dependent service times
Authors: Choi Bong Dae , Kim Yeong Cheol , Shin Yang Woo , Pearce Charles E. M.
Published: March 2007

We deal with the MX/G/1 queue where service times depend on the queue
length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the
transient queue length distribution at time t and its limiting distribution
and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.
Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples
Authors: Liang Han-Ying , Jing Bing-Yi
Published: March 2007

In this paper we are concerned with the heteroscedastic regression model yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n under correlated errors ei, where it is assumed that , the design points (xi, ti, ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.
Fractional differential equations driven by Lévy noise
Authors: Anh V. V. , McVinish R.
Published: March 2007

This paper considers a general class of fractional differential equations driven by Lévy noise. The singularity spectrum for these equations is obtained. This result allows to determine the conditions under which the solution is a semimartingale. The prediction
formula and a numerical scheme for approximating the sample paths of these equations
are given. Almost sure, uniform convergence of the scheme and some numerical results
are also provided.
On the time of the maximum of Brownian motion with drift
Authors: Buffet Emannuel
Published: March 2007

The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.
Real zeros of classes of random algebraic polynomials
Authors: Farahmand K. , Sambandham M.
Published: March 2007

There are many known asymptotic estimates for the expected number of real zeros of an algebraic polynomial a0 + a1x + a2x2 + ⋯+an−1xn−1 with identically distributed random coefficients. Under different assumptions for the distribution of the coefficients it is shown that the above expected number is asymptotic to O(logn). This order for the expected number of zeros remains valid for the case when the coefficients are grouped into two, each group with a different variance. However, it was recently shown that if the coefficients are non‐identically distributed such that the variance of the jth term is the expected number of zeros of the polynomial increases to . The present paper provides the value for this asymptotic formula for the polynomials with the latter variances when they are grouped into three with different patterns for their variances.
On an even order neutral differential inequality
Authors: Wang Peiguang , Debnath Lokenath
Published: March 2007

In this paper, we prove new results related to the nonexistence criteria for eventually positive solutions of certain even order neutral differential inequality with distributed deviating arguments.
Cycle times in a starlike network with state‐dependent routing
Authors: Daduna Hans
Published: March 2007

For a star like network (central server system) with state
dependent branching we compute the cycle time distribution. The
Laplace‐Stieltjes transform of this distribution is of product form. This
allows to define a recursive algorithm for evaluation of cycle time
moments of any order.
On a multi‐channel transportation loss system with controlled input and controlled service
Authors: Dshalalow Jewgeni
Published: March 2007

A multi‐channel loss queueing system is investigated. The input
stream is a controlled point process. The service in each of m parallel
channels depends on the state of the system at certain moments of time
when input and service may be controlled. To obtain explicitly the
limiting distribution of the main process (Zt) (the number of busy
channels) in equilibrium, an auxiliary three dimensional process with
two additional components (one of them is a semi‐Markov process) is
treated as semi‐regenerative process. An optimization problem is
discussed. Simple expressions for an objective function are derived.
The geometrization of Galilei′s principle
Authors: Günther Christian
Published: March 2007

Galilei′s fundamental principle is reformulated in terms of
abstract geometry and it is generalized to nonlinear and relativistic
systems. As a consequence the notion of a general mechanical system is
developed and shown to be a universal frame for particle dynamics.
On some queue length controlled stochastic processes
Authors: Abolnikov Lev , Dshalalow Jewgeni E. , Dukhovny Alexander M.
Published: March 2007

The authors study the input, output and queueing processes in a general controlled single‐server bulk queueing system. It is supposed that inter‐arrival time, service time, batch size of arriving units and the capacity of the server depend on the queue length.

The authors establish an ergodicity criterion for both the queueing process with continuous time parameter and the embedded process, study their
transient and steady state behavior and prove ergodic theorems for some functionals of the input, output and queueing processes. The following results are
obtained: Invariant probability measure of the embedded process, stationary
distribution of the process with continuous time parameter, expected value of
a busy period, rates of input and output processes and the relative speed of convergence of the expected queue length. Various examples (including an optimization problem) illustrate methods developed in the paper.
On the variance of the number of real roots of a random trigonometric polynomial
Authors: Farahmand K.
Published: March 2007

This paper provides an upper estimate for the variance of the number of real
zeros of the random trigonometric polynomial g1cosθ + g2cos2θ + …+gncosnθ. The coefficients gi(i = 1, 2, …, n) are assumed independent and
normally distributed with mean zero and variance one.
Oscillations of a polarizable vacuum
Authors: Gilson James G.
Published: March 2007

A classical basis for one‐dimensional Schrödinger quantum theory is
constructed from simple vacuum polarization harmonic oscillators within
standard stochastic theory. The model is constructed on a two‐dimensional
phase configuration surface with phase velocity vectors that have a speed of
light zitterbewegung behaviour character. The system supplies a natural
Hermitian scalar product describing probability density which is derived from
angular momentum considerations. The generality of the model which is
extensive is discussed.
On network flow equations and splitting formulas for Sojourn times in queueing networks
Authors: Daduna Hans
Published: March 2007

LEMOINE′s network flow equations are generalized to the case of
multiserver networks. These equations provide a basis for recursive evaluation
of residual conditional sojourn time moments.
An abstract inverse problem
Authors: Choulli M.
Published: March 2007

In this paper we consider an inverse problem that corresponds to an
abstract integrodifferential equation. First, we prove a local existence and
uniqueness theorem. We also show that every continuous solution can be
locally extended in a unique way. Finally, we give sufficient conditions for the
existence and a stability of the global solution.
Weighted norms and Volterra integral equations in LP spaces
Authors: Kwapisz Jaroslaw
Published: March 2007

A new simple proof of existence and uniqueness of solutions of the
Volterra integral equation in Lebesque spaces is given. It is shown that the
weighted norm technique and the Banach contraction mapping principle can
be applied (as in the case of continuous functions space).
Markov chains with transition delta‐matrix: ergodicityconditions, invariant probability measures and applications
Authors: Abolnikov Lev , Dukhovny Alexander
Published: March 2007

A large class of Markov chains with so‐called Δm,n‐and
‐transition matrices (“delta‐matrices”) which frequently occur in
applications (queues, inventories, dams) is analyzed.

The authors find some structural properties of both types of
Markov chains and develop a simple test for their irreducibility and aperiodicity. Necessary and sufficient conditions for the ergodicity of both
chains are found in the article in two equivalent versions. According to
one of them, these conditions are expressed in terms of certain
restrictions imposed on the generating functions Ai(z) of the elements of
the ith 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 disc of the complex plane. The invariant
probability measures of Markov chains of both kinds are found in terms
of generating functions. It is shown that the general method in some important special cases can be simplified and yields convenient and, sometimes, explicit results.

As examples, several queueing and inventory (dam) models, each
of independent interest, are analyzed with the help of the general
methods developed in the article.
An asymptotic optimal design
Authors: Rekab Kamel
Published: March 2007

The problem of designing an experiment to estimate the product
of the means of two normal populations is considered. A Bayesian
approach is adopted in which the product of the means is estimated by
its posterior mean. A fully sequential design is proposed and shown to be
asymptotically optimal.
On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities
Authors: Heikkilä S. , Kumpulainen M. , Lakshmikantham V.
Published: March 2007

In this paper we shall first study solvability of mixed monotone
systems of operator equations in an ordered normed space by using a
generalized iteration method. The obtained results are then applied to
prove existence of coupled extremal quasisolutions of the systems of first
and second order mixed quasimonotone differential equations with
discontinuous right hand sides. Most of the results deal with systems in
a Banach space ordered by a regular order cone.
General algorithm and sensitivity analysis for variational inequalities
Authors: Noor Muhammad Aslam
Published: March 2007

The fixed point technique is used to prove the existence of a
solution for a class of variational inequalities related to odd order
boundary value problems, and to suggest a general algorithm. We also
study the sensitivity analysis for these variational inequalities and
complementarity problems using the projection technique. Several
special cases are discussed, which can be obtained from our results.
A first passage problem and its applications to the analysis of a class of stochastic models
Authors: Abolnikov Lev , Dshalalow Jewgeni H.
Published: March 2007

A problem of the first passage of a cumulative random process with
generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic
models (bulk queueing systems, inventory control and dam models).

Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a
fixed level, the shortage before the first excess, the levels of the first and pre‐first excesses, the index of the first excess and others. The results obtained are
illustrated by a number of numerical examples and then are applied to a bulk
queueing system with a service delay discipline.
Controllability of nonlinear Volterra integrodifferential systems with prescribed controls
Authors: Balachandran K. , Lalitha D.
Published: March 2007

Sufficient conditions for the global controllability of nonlinear
Volterra integrodifferential systems with prescribed controls are derived.
The method is a transformation of the given control system into a
boundary value problem and then the result is obtained by the
application of the Schaefer fixed point theorem.
A generalized upper and lower solutions method for nonlinear second order ordinary differential equations
Authors: Nieto Juan J. , Cabada Alberto
Published: March 2007

The purpose of this paper is to study a nonlinear boundary value
problem of second order when the nonlinearity is a Carathéodory
function. It is shown that a generalized upper and lower solutions
method is valid, and the monotone iterative technique for finding the
minimal and maximal solutions is developed.
Convergence rates for empirical Bayes two‐action problems: the uniform U(0, θ) distribution
Authors: Tahir Mohamed
Published: March 2007

The purpose of this paper is to study the convergence rates of a
sequence of empirical Bayes decision rules for the two‐action problems in
which the observations are uniformly distributed over the interval (0, θ),
where θ is a value of a random variable having an unknown prior
distribution. It is shown that the proposed empirical Bayes decision rules
are asymptotically optimal and that the order of associated convergence
rates is O(n−α), for some constant α, 0 < α < 1, where n is the number
of accumulated past observations at hand.
On a first passage problem in general queueing systems with multiple vacations
Authors: Dshalalow Jewgeni H.
Published: March 2007

The author studies a generalized single‐server queueing system with
bulk arrivals and batch service, where the server takes vacations each time the
queue level falls below r(≥1) in accordance with the multiple vacation
discipline. The input to the system is assumed to be a compound Poisson
process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment
of new techniques related to the first excess level processes. A preliminary
analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing
process explicitly. Various examples and applications are discussed.
Problem of uniqueness in the renewal process generated by the uniform distribution
Authors: Ugrin-Šparac D.
Published: March 2007

The renewal process generated by the uniform distribution, when
interpreted as a transformation of the uniform distribution into a discrete
distribution, gives rise to the question of uniqueness of the inverse image.
The paper deals with a particular problem from the described domain,
that arose in the construction of a complex stochastic test intended to
evaluate pseudo‐random number generators. The connection of the
treated problem with the question of a unique integral representation of
Gamma‐function is also mentioned.
A note on the convexity of the expected queue length of the M/M/s queue with respect to the arrival rate: a third proof
Authors: Mehrez A. , Brimberg J.
Published: March 2007

The convexity of the expected number in an M/M/s queue with
respect to the arrival rate (or traffic intensity) is well known.
Grassmann [1] proves this result directly by making use of a bound on
the probability that all servers are busy. Independently, Lee and Cohen
[2] derive this result by showing that the Erlang delay formula is a
convex function. In this note, we provide a third method of proof, which
exploits the relationship between the Erlang delay formula and the
Poisson probability distribution. Several interesting intermediate results
are also obtained.
On the virtual waiting time for an M/G/1 retrial queue with two types of calls
Authors: Choi Bong Dae , Han Dong Hwan , Falin Guennadi
Published: March 2007

We consider an M/G/1 retrial queueing system with two types
of calls which models a telephone switching system. In the case that
arriving calls are blocked due to the channel being busy, the outgoing
calls are queued in priority group whereas the incoming calls enter the
retrial group in order to try service again after a random amount of time.
In this paper we find the Laplace‐Stieltjes transform of the distribution of
the virtual waiting time for an incoming call. When the arrival rate of
outgoing calls is zero, it is shown that our result is consistent with the
known result for a retrial queueing system with one type of call.
Quasilinearization for some nonlocal problems
Authors: Yin Yunfeng
Published: March 2007

The method of generalized quasilinearization [4] is applied to
study semilinear parabolic equation ut − Lu = f(t, x, u) with nonlocal
boundary conditions in this paper. The
convexity of f in u is relaxed by requiring f(t, x, u) + Mu2 to be convex
for some M > 0. The quadratic convergence of monotone sequence is
obtained.
Optimal control of nonlinear second order evolution equations
Authors: Ahmed N. U. , Kerbal Sebti
Published: March 2007

In this paper we study the optimal control of systems governed
by second order nonlinear evolution equations. We establish the
existence of optimal solutions for Lagrange problem.
Rothe approach to the existence of solution of anablation‐transpiration cooling control system
Authors: Zhu Guo Bao
Published: March 2007

A one dimensional ablation model with transpiration cooling
control and nonlinear effect is studied, which is a distributed parameter
control system with moving boundary and both governing equation and
boundary conditions involving control variable. A solution is given by a
Rothe approximation scheme.
Mathtype, Version 3.0
Authors: Clay David W.
Published: March 2007

MathType is a mathematical equation editor in the Windows 3.1
environment. It lets you build up any kind of mathematical expression
by using simple point‐and‐click techniques and then insert them into any
Windows 3.1 compatible word processor; for instance, Word Perfect
5.1/5.2 for Windows, Word 2.0 for Windows, and AMI Pro 3.0 for Windows. An expression designed by MathType can be transferred into a
word processor by using standard Cut and Paste commands or by using
Object Linking and Embedding techniques.
First excess levels of vector processes
Authors: Dshalalow Jewgeni H.
Published: March 2007

This paper analyzes the behavior of a point process marked by a two‐dimensional renewal process with dependent components about some fixed (two‐dimensional) level. The compound process evolves until one of its marks hits (i.e.
reaches or exceeds) its associated level for the first time. The author targets a
joint transformation of the first excess level, first passage time, and the index of
the point process which labels the first passage time. The cases when both marks
are either discrete or continuous or mixed are treated. For each of them, an explicit and compact formula is derived. Various applications to stochastic models are
discussed.
Stability and asymptotic stability in impulsive semidynamical systems
Authors: Kaul Saroop K.
Published: March 2007

In this paper we generalize two results of Lasalle′s, the invariance theorem
and asymptotic stability theorem of discrete and continuous semidynamical
systems, to impulsive semidynamical systems.
Existence and relaxation results for nonlinear evolutioninclusions revisited
Authors: Migórski S.
Published: March 2007

In this paper we confirm the validity of some recent results of Hu, Lakshmikantham, Papageorgiou [4] and Papageorgiou [13] concerning the existence and relaxation for nonlinear evolution inclusions. We fill a gap in the proofs of these results due to the use of incorrect Nagy′s compactness embedding theorem.
Bound and periodic solutions of the Riccati equation in Banach space
Authors: Dorogovtsev A. Ya. , Petrova T. A.
Published: March 2007

An abstract, nonlinear, differential equation in Banach space is considered.
Conditions are presented for the existence of bounded solutions of this equation
with a bounded right side, and also for the existence of stationary (periodic)
solutions of this equation with a stationary (periodic) process in the right side.
Identification of linear stochastic systems based on partialinformation
Authors: Ahmed N. U. , Radaideh S. M.
Published: March 2007

In this paper, we consider an identification problem for a system of partially
observed linear stochastic differential equations. We present a result whereby one
can determine all the system parameters including the covariance matrices of the
noise processes. We formulate the original identification problem as a deterministic control problem and prove the equivalence of the two problems. The method
of simulated annealing is used to develop a computational algorithm for identifying the unknown parameters from the available observation. The procedure is
then illustrated by some examples.
On the limiting behavior of a harmonic oscillator with random external disturbance
Authors: Kulinich G. L.
Published: March 2007

This paper deals with the limiting behavior of a harmonic oscillator under
the external random disturbance that is a process of the white noise type.
Influence of noises is investigated in resonance and non‐resonance cases.
Note on strong solutions of a stochastic inclusion
Authors: Motyl Jerzy
Published: March 2007

Two different definitions of strong solutions of a stochastic integral set‐valued
equation are discussed. A selection property of a set‐valued stochastic integral is
given.