Abstract: Batch production plants provide a wide range of
scheduling problems. In pharmaceutical industries a batch process
is usually described by a recipe, consisting of an ordering of tasks
to produce the desired product. In this research work we focused
on pharmaceutical production processes requiring the culture of
a microorganism population (i.e. bacteria, yeasts or antibiotics).
Several sources of uncertainty may influence the yield of the culture
processes, including (i) low performance and quality of the cultured
microorganism population or (ii) microbial contamination. For
these reasons, robustness is a valuable property for the considered
application context. In particular, a robust schedule will not collapse
immediately when a cell of microorganisms has to be thrown away
due to a microbial contamination. Indeed, a robust schedule should
change locally in small proportions and the overall performance
measure (i.e. makespan, lateness) should change a little if at all.
In this research work we formulated a constraint programming
optimization (COP) model for the robust planning of antibiotics
production. We developed a discrete-time model with a multi-criteria
objective, ordering the different criteria and performing a
lexicographic optimization. A feasible solution of the proposed
COP model is a schedule of a given set of tasks onto available
resources. The schedule has to satisfy tasks precedence constraints,
resource capacity constraints and time constraints. In particular
time constraints model tasks duedates and resource availability
time windows constraints. To improve the schedule robustness, we
modeled the concept of (a, b) super-solutions, where (a, b) are input
parameters of the COP model. An (a, b) super-solution is one in
which if a variables (i.e. the completion times of a culture tasks)
lose their values (i.e. cultures are contaminated), the solution can be
repaired by assigning these variables values with a new values (i.e.
the completion times of a backup culture tasks) and at most b other
variables (i.e. delaying the completion of at most b other tasks).
The efficiency and applicability of the proposed model is
demonstrated by solving instances taken from a real-life
pharmaceutical company. Computational results showed that
the determined super-solutions are near-optimal.
Abstract: In this paper, the notion of rank−k numerical range
of rectangular complex matrix polynomials are introduced. Some
algebraic and geometrical properties are investigated. Moreover, for
Є > 0, the notion of Birkhoff-James approximate orthogonality
sets for Є−higher rank numerical ranges of rectangular matrix
polynomials is also introduced and studied. The proposed definitions
yield a natural generalization of the standard higher rank numerical
ranges.
Abstract: Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.
Abstract: Two normal populations with different means and same
variance are considered, where the variance is known. The population
with the smaller sample mean is selected. Various estimators are
constructed for the mean of the selected normal population. Finally,
they are compared with respect to the bias and MSE risks by
the mehod of Monte-Carlo simulation and their performances are
analysed with the help of graphs.
Abstract: We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.
Abstract: In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested.
Abstract: Cholera is a disease that is predominately common in
developing countries due to poor sanitation and overcrowding
population. In this paper, a deterministic model for the dynamics of
cholera is developed and control measures such as health educational
message, therapeutic treatment, and vaccination are incorporated in
the model. The effective reproduction number is computed in terms
of the model parameters. The existence and stability of the
equilibrium states, disease free and endemic equilibrium states are
established and showed to be locally and globally asymptotically
stable when R0 < 1 and R0 > 1 respectively. The existence of
backward bifurcation of the model is investigated. Furthermore,
numerical simulation of the model developed is carried out to show
the impact of the control measures and the result indicates that
combined control measures will help to reduce the spread of cholera
in the population.
Abstract: In this paper, a asymptotically periodic predator-prey
model with Modified Leslie-Gower and Holling-Type II schemes
is investigated. Some sufficient conditions for the uniformly strong
persistence of the system are established. Our result is an important
complementarity to the earlier results.
Abstract: In this study, we examine some spectral properties
of non-selfadjoint matrix-valued difference equations consisting of
a polynomial-type Jost solution. The aim of this study is to
investigate the eigenvalues and spectral singularities of the difference
operator L which is expressed by the above-mentioned difference
equation. Firstly, thanks to the representation of polynomial type Jost
solution of this equation, we obtain asymptotics and some analytical
properties. Then, using the uniqueness theorems of analytic functions,
we guarantee that the operator L has a finite number of eigenvalues
and spectral singularities.
Abstract: It is well-known that, using principal weak flatness
property, some important monoids are characterized, such as regular
monoids, left almost regular monoids, and so on. In this article, we
define a generalization of principal weak flatness called GP-Flatness,
and will characterize monoids by this property of their right (Rees
factor) acts. Also we investigate new classes of monoids called
generally regular monoids and generally left almost regular monoids.
Abstract: We consider the problem of stabilization of an unstable
heat equation in a 2-D, 3-D and generally n-D domain by deriving a
generalized backstepping boundary control design methodology. To
stabilize the systems, we design boundary backstepping controllers
inspired by the 1-D unstable heat equation stabilization procedure.
We assume that one side of the boundary is hinged and the other
side is controlled for each direction of the domain. Thus, controllers
act on two boundaries for 2-D domain, three boundaries for 3-D
domain and ”n” boundaries for n-D domain. The main idea of the
design is to derive ”n” controllers for each of the dimensions by
using ”n” kernel functions. Thus, we obtain ”n” controllers for the
”n” dimensional case. We use a transformation to change the system
into an exponentially stable ”n” dimensional heat equation. The
transformation used in this paper is a generalized Volterra/Fredholm
type with ”n” kernel functions for n-D domain instead of the one
kernel function of 1-D design.
Abstract: In this paper, the results of Kano from one dimensional
cosine and sine series are extended to two dimensional cosine and sine
series. To extend these results, some classes of coefficient sequences
such as class of semi convexity and class R are extended from
one dimension to two dimensions. Further, the function f(x, y) is
two dimensional Fourier Cosine and Sine series or equivalently it
represents an integrable function or not, has been studied. Moreover,
some results are obtained which are generalization of Moricz’s
results.
Abstract: Round addition differential fault analysis using
operation skipping for lightweight block ciphers with on-the-fly key
scheduling is presented. For 64-bit KLEIN, it is shown that only a pair
of correct and faulty ciphertexts can be used to derive the secret master
key. For PRESENT, one correct ciphertext and two faulty ciphertexts
are required to reconstruct the secret key. Furthermore, secret key
extraction is demonstrated for the LBlock Feistel-type lightweight
block cipher.
Abstract: The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
Abstract: The agenda of showing the scheduled time for
performing certain tasks is known as timetabling. It is widely used in
many departments such as transportation, education, and production.
Some difficulties arise to ensure all tasks happen in the time and
place allocated. Therefore, many researchers invented various
programming models to solve the scheduling problems from several
fields. However, the studies in developing the general integer
programming model for many timetabling problems are still
questionable. Meanwhile, this thesis describes about creating a
general model which solves different types of timetabling problems
by considering the basic constraints. Initially, the common basic
constraints from five different fields are selected and analyzed. A
general basic integer programming model was created and then
verified by using the medium set of data obtained randomly which is
much similar to realistic data. The mathematical software, AIMMS
with CPLEX as a solver has been used to solve the model. The model
obtained is significant in solving many timetabling problems easily
since it is modifiable to all types of scheduling problems which have
same basic constraints.
Abstract: The Com-Poisson (CMP) model is one of the most
popular discrete generalized linear models (GLMS) that handles
both equi-, over- and under-dispersed data. In longitudinal context,
an integer-valued autoregressive (INAR(1)) process that incorporates
covariate specification has been developed to model longitudinal
CMP counts. However, the joint likelihood CMP function is
difficult to specify and thus restricts the likelihood-based estimating
methodology. The joint generalized quasi-likelihood approach
(GQL-I) was instead considered but is rather computationally
intensive and may not even estimate the regression effects due
to a complex and frequently ill-conditioned covariance structure.
This paper proposes a new GQL approach for estimating the
regression parameters (GQL-III) that is based on a single score vector
representation. The performance of GQL-III is compared with GQL-I
and separate marginal GQLs (GQL-II) through some simulation
experiments and is proved to yield equally efficient estimates as
GQL-I and is far more computationally stable.
Abstract: The modelling of physical phenomena, such as the
earth’s free oscillations, the vibration of strings, the interaction of
atomic particles, or the steady state flow in a bar give rise to Sturm-
Liouville (SL) eigenvalue problems. The boundary applications of
some systems like the convection-diffusion equation, electromagnetic
and heat transfer problems requires the combination of Dirichlet and
Neumann boundary conditions. Hence, the incorporation of Robin
boundary condition in the analyses of Sturm-Liouville problem. This
paper deals with the computation of the eigenvalues and
eigenfunction of generalized Sturm-Liouville problems with Robin
boundary condition using the finite element method. Numerical
solution of classical Sturm–Liouville problem is presented. The
results show an agreement with the exact solution. High results
precision is achieved with higher number of elements.
Abstract: In this paper, for an arbitrary multiplicative functional
f from the set of all upper triangular fuzzy matrices to the fuzzy
algebra, we prove that there exist a multiplicative functional F and a
functional G from the fuzzy algebra to the fuzzy algebra such that the
image of an upper triangular fuzzy matrix under f can be represented
as the product of all the images of its main diagonal elements under
F and other elements under G.
Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
Abstract: Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.