Abstract: The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.
Abstract: This paper covers the present situation and problem of experimental teaching of mathematics specialty in recent years, puts
forward and demonstrates experimental teaching methods for different
education. From the aspects of content and experimental teaching
approach, uses as an example the course “Experiment for Program
Designing & Algorithmic Language" and discusses teaching practice
and laboratory course work. In addition a series of successful methods
and measures are introduced in experimental teaching.
Abstract: This paper presents an application of the improved
QFD method for determining the specifications of kitchen utensils
rack. By using the improved method, the subjective nature in original
QFD was reduced; particularly in defining the relationship between
customer requirement and engineering characteristics. The regression
analysis that was used for obtaining the relationship functions
between customer requirement and engineering characteristics also
accommodated the inaccurateness of the competitive assessment
results. The improved method which is represented in the form of a
mathematical model had become a formal guidance to allocate the
resource for improving the specifications of kitchen utensils rack.
The specifications obtained had led to the achievement of the highest
feasible customer satisfaction.
Abstract: This paper is the tomographic images reconstruction
simulation for defects detection in specimen. The specimen is the
thin cylindrical steel contained with low density materials. The
defects in material are simulated in three shapes.The specimen image
function will be transformed to projection data. Radon transform and
its inverse provide the mathematical for reconstructing tomographic
images from projection data. The result of the simulation show that
the reconstruction images is complete for defect detection.
Abstract: In the present era of aviation technology, autonomous navigation and control have emerged as a prime area of active research. Owing to the tremendous developments in the field, autonomous controls have led today’s engineers to claim that future of aerospace vehicle is unmanned. Development of guidance and navigation algorithms for an unmanned aerial vehicle (UAV) is an extremely challenging task, which requires efforts to meet strict, and at times, conflicting goals of guidance and control. In this paper, aircraft altitude and heading controllers and an efficient algorithm for self-governing navigation using MATLAB® mapping toolbox is presented which also enables loitering of a fixed wing UAV over a specified area. For this purpose, a nonlinear mathematical model of a UAV is used. The nonlinear model is linearized around a stable trim point and decoupled for controller design. The linear controllers are tested on the nonlinear aircraft model and navigation algorithm is subsequently developed for for autonomous flight of the UAV. The results are presented for trajectory controllers and waypoint based navigation. Our investigation reveals that MATLAB® mapping toolbox can be exploited to successfully deliver an efficient algorithm for autonomous aerial navigation for a UAV.
Abstract: Multi-energy systems will enhance the system
reliability and power quality. This paper presents an integrated
approach for the design and operation of distributed energy resources
(DER) systems, based on energy hub modeling. A multi-objective
optimization model is developed by considering an integrated view of
electricity and natural gas network to analyze the optimal design and
operating condition of DER systems, by considering two conflicting
objectives, namely, minimization of total cost and the minimization
of environmental impact which is assessed in terms of CO2
emissions. The mathematical model considers energy demands of the
site, local climate data, and utility tariff structure, as well as technical
and financial characteristics of the candidate DER technologies. To
provide energy demands, energy systems including photovoltaic, and
co-generation systems, boiler, central power grid are considered. As
an illustrative example, a hotel in Iran demonstrates potential
applications of the proposed method. The results prove that
increasing the satisfaction degree of environmental objective leads to
increased total cost.
Abstract: In this paper, a mathematical model of human immunodeficiency
virus (HIV) is utilized and an optimization problem is
proposed, with the final goal of implementing an optimal 900-day
structured treatment interruption (STI) protocol. Two type of commonly
used drugs in highly active antiretroviral therapy (HAART),
reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are
considered. In order to solving the proposed optimization problem an
adaptive memetic algorithm with population management (AMAPM)
is proposed. The AMAPM uses a distance measure to control the
diversity of population in genotype space and thus preventing the
stagnation and premature convergence. Moreover, the AMAPM uses
diversity parameter in phenotype space to dynamically set the population
size and the number of crossovers during the search process.
Three crossover operators diversify the population, simultaneously.
The progresses of crossover operators are utilized to set the number
of each crossover per generation. In order to escaping the local optima
and introducing the new search directions toward the global optima,
two local searchers assist the evolutionary process. In contrast to
traditional memetic algorithms, the activation of these local searchers
is not random and depends on both the diversity parameters in
genotype space and phenotype space. The capability of AMAPM in
finding optimal solutions compared with three popular metaheurestics
is introduced.
Abstract: The paper presents a one-dimensional transient
mathematical model of compressible thermal multi-component gas
mixture flows in pipes. The set of the mass, momentum and enthalpy
conservation equations for gas phase is solved. Thermo-physical
properties of multi-component gas mixture are calculated by solving
the Equation of State (EOS) model. The Soave-Redlich-Kwong
(SRK-EOS) model is chosen. Gas mixture viscosity is calculated on
the basis of the Lee-Gonzales-Eakin (LGE) correlation. Numerical
analysis on rapid decompression in conventional dry gases is
performed by using the proposed mathematical model. The model is
validated on measured values of the decompression wave speed in
dry natural gas mixtures. All predictions show excellent agreement
with the experimental data at high and low pressure. The presented
model predicts the decompression in dry natural gas mixtures much
better than GASDECOM and OLGA codes, which are the most
frequently-used codes in oil and gas pipeline transport service.
Abstract: In this paper, the influencing parameters of a novel
purely mechanical wireless in-mould injection moulding sensor
were investigated. The sensor is capable of detecting the melt
front at predefined locations inside the mould. The sensor comprises
a movable pin which acts as the sensor element generating
structure-borne sound triggered by the passing melt front. Due to
the sensor design, melt pressure is the driving force. For pressure
level measurement during pin movement a pressure transducer
located at the same position as the movable pin. By deriving
a mathematical model for the mechanical movement, dominant
process parameters could be investigated towards their impact
on the melt front detection characteristic. It was found that the
sensor is not affected by the investigated parameters enabling it
for reliable melt front detection. In addition, it could be proved
that the novel sensor is in comparable range to conventional melt
front detection sensors.
Abstract: The paper compares the treatment of fractions in a
typical undergraduate college curriculum and in abstract algebra
textbooks. It stresses that the main difference is that the
undergraduate curriculum treats equivalent fractions as equal, and
this treatment eventually leads to paradoxes and impairs the students-
ability to perceive ratios, proportions, radicals and rational exponents
adequately. The paper suggests a simplified version of rigorous
theory of fractions suitable for regular college curriculum.
Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.
Abstract: The aim of this paper is to determine the stress levels
at the end of a long slender shaft such as a drilling assembly used in
the oil or gas industry using a mathematical model in real-time. The
torsional deflection experienced by this type of drilling shaft (about 4
KM length and 20 cm diameter hollow shaft with a thickness of 1
cm) can only be determined using a distributed modeling technique.
The main objective of this project is to calculate angular velocity and
torque at the end of the shaft by TLM method and also analyzing of
the behavior of the system by transient response. The obtained result
is compared with lumped modeling technique the importance of these
results will be evident only after the mentioned comparison. Two
systems have different transient responses and in this project because
of the length of the shaft transient response is very important.
Abstract: Levenberg-Marquardt method (LM) was proposed to
be applied as a non-linear least-square fitting in the analysis of a
natural gamma-ray spectrum that was taken by the Hp (Ge) detector.
The Gaussian function that composed of three components, main
Gaussian, a step background function and tailing function in the lowenergy
side, has been suggested to describe each of the y-ray lines
mathematically in the spectrum. The whole spectrum has been
analyzed by determining the energy and relative intensity for the
strong y-ray lines.
Abstract: In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.
Abstract: Cryptographic algorithms play a crucial role in the
information society by providing protection from unauthorized
access to sensitive data. It is clear that information technology will
become increasingly pervasive, Hence we can expect the emergence
of ubiquitous or pervasive computing, ambient intelligence. These
new environments and applications will present new security
challenges, and there is no doubt that cryptographic algorithms and
protocols will form a part of the solution. The efficiency of a public
key cryptosystem is mainly measured in computational overheads,
key size and bandwidth. In particular the RSA algorithm is used in
many applications for providing the security. Although the security
of RSA is beyond doubt, the evolution in computing power has
caused a growth in the necessary key length. The fact that most chips
on smart cards can-t process key extending 1024 bit shows that there
is need for alternative. NTRU is such an alternative and it is a
collection of mathematical algorithm based on manipulating lists of
very small integers and polynomials. This allows NTRU to high
speeds with the use of minimal computing power. NTRU (Nth degree
Truncated Polynomial Ring Unit) is the first secure public key
cryptosystem not based on factorization or discrete logarithm
problem. This means that given sufficient computational resources
and time, an adversary, should not be able to break the key. The
multi-party communication and requirement of optimal resource
utilization necessitated the need for the present day demand of
applications that need security enforcement technique .and can be
enhanced with high-end computing. This has promoted us to develop
high-performance NTRU schemes using approaches such as the use
of high-end computing hardware. Peer-to-peer (P2P) or enterprise
grids are proven as one of the approaches for developing high-end
computing systems. By utilizing them one can improve the
performance of NTRU through parallel execution. In this paper we
propose and develop an application for NTRU using enterprise grid
middleware called Alchemi. An analysis and comparison of its
performance for various text files is presented.
Abstract: The computer modeling is carried out for parameter of
sensitivity of optoelectronic chemical and biosensors, using
phenomena of surface plasmon resonance (SPR). The physical model
of SPR-sensor-s is described with (or without) of modifications of
sensitive gold film surface by a dielectric layer. The variants of
increasing of sensitivity for SPR-biosensors, constructed on the
principle gold – dielectric – biomolecular layer are considered. Two
methods of mathematical treatment of SPR-curve are compared –
traditional, with estimation of sensor-s response as shift of the SPRcurve
minimum and proposed, for system with dielectric layer, using
calculating of the derivative in the point of SPR-curve half-width.
Abstract: A mathematical model for the hydrodynamic
lubrication of parabolic slider bearings with couple stress lubricants
is presented. A numerical solution for the mathematical model using
finite element scheme is obtained using three nodes isoparametric
quadratic elements. Stiffness integrals obtained from the weak form
of the governing equations were solved using Gauss Quadrature to
obtain a finite number of stiffness matrices. The global system of
equations was obtained for the bearing and solved using Gauss Seidel
iterative scheme. The converged pressure solution was used to obtain
the load capacity of the bearing. Parametric studies were carried out
and it was shown that the effect of couple stresses and profile
parameter are to increase the load carrying capacity of the parabolic
slider bearing. Numerical experiments reveal that the magnitude of
the profile parameter at which maximum load is obtained increases
with decrease in couple stress parameter. The results are presented in
graphical form.
Abstract: The Swine flu outbreak in humans is due to a new
strain of influenza A virus subtype H1N1 that derives in part from
human influenza, avian influenza, and two separated strains of swine
influenza. It can be transmitted from human to human. A
mathematical model for the transmission of Swine flu is developed in
which the human populations are divided into two classes, the risk
and non-risk human classes. Each class is separated into susceptible,
exposed, infectious, quarantine and recovered sub-classes. In this
paper, we formulate the dynamical model of Swine flu transmission
and the repetitive contacts between the people are also considered.
We analyze the behavior for the transmission of this disease. The
Threshold condition of this disease is found and numerical results are
shown to confirm our theoretical predictions.
Abstract: This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.
Abstract: Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.