Abstract: In this article, we deal with a variant of the classical
course timetabling problem that has a practical application in many
areas of education. In particular, in this paper we are interested in
high schools remedial courses. The purpose of such courses is to
provide under-prepared students with the skills necessary to succeed
in their studies. In particular, a student might be under prepared in
an entire course, or only in a part of it. The limited availability
of funds, as well as the limited amount of time and teachers at
disposal, often requires schools to choose which courses and/or which
teaching units to activate. Thus, schools need to model the training
offer and the related timetabling, with the goal of ensuring the
highest possible teaching quality, by meeting the above-mentioned
financial, time and resources constraints. Moreover, there are some
prerequisites between the teaching units that must be satisfied. We
first present a Mixed-Integer Programming (MIP) model to solve
this problem to optimality. However, the presence of many peculiar
constraints contributes inevitably in increasing the complexity of
the mathematical model. Thus, solving it through a general-purpose
solver may be performed for small instances only, while solving
real-life-sized instances of such model requires specific techniques
or heuristic approaches. For this purpose, we also propose a heuristic
approach, in which we make use of a fast constructive procedure
to obtain a feasible solution. To assess our exact and heuristic
approaches we perform extensive computational results on both
real-life instances (obtained from a high school in Lecce, Italy) and
randomly generated instances. Our tests show that the MIP model is
never solved to optimality, with an average optimality gap of 57%.
On the other hand, the heuristic algorithm is much faster (in about the
50% of the considered instances it converges in approximately half of
the time limit) and in many cases allows achieving an improvement
on the objective function value obtained by the MIP model. Such an
improvement ranges between 18% and 66%.
Abstract: The output error of the globoidal cam mechanism can
be considered as a relevant indicator of mechanism performance,
because it determines kinematic and dynamical behavior of
mechanical transmission. Based on the differential geometry and the
rigid body transformations, the mathematical model of surface
geometry of the globoidal cam is established. Then we present the
analytical expression of the output error (including the transmission
error and the displacement error along the output axis) by considering
different manufacture and assembly errors. The effects of the center
distance error, the perpendicular error between input and output axes
and the rotational angle error of the globoidal cam on the output error
are systematically analyzed. A globoidal cam mechanism which is
widely used in automatic tool changer of CNC machines is applied for
illustration. Our results show that the perpendicular error and the
rotational angle error have little effects on the transmission error but
have great effects on the displacement error along the output axis. This
study plays an important role in the design, manufacture and assembly
of the globoidal cam mechanism.
Abstract: In this paper, we present a four-step ortho-rectification
procedure for real-time geo-referencing of video data from a low-cost
UAV equipped with a multi-sensor system. The basic procedures for
the real-time ortho-rectification are: (1) decompilation of the video
stream into individual frames; (2) establishing the interior camera
orientation parameters; (3) determining the relative orientation
parameters for each video frame with respect to each other; (4)
finding the absolute orientation parameters, using a self-calibration
bundle and adjustment with the aid of a mathematical model. Each
ortho-rectified video frame is then mosaicked together to produce a
mosaic image of the test area, which is then merged with a well
referenced existing digital map for the purpose of geo-referencing
and aerial surveillance. A test field located in Abuja, Nigeria was
used to evaluate our method. Video and telemetry data were collected
for about fifteen minutes, and they were processed using the four-step
ortho-rectification procedure. The results demonstrated that the
geometric measurement of the control field from ortho-images is
more accurate when compared with those from original perspective
images when used to pin point the exact location of targets on the
video imagery acquired by the UAV. The 2-D planimetric accuracy
when compared with the 6 control points measured by a GPS receiver
is between 3 to 5 metres.
Abstract: An Acoustic Micro-Energy Harvester (AMEH) is
developed to convert wasted acoustical energy into useful electrical
energy. AMEH is mathematically modeled using Lumped Element
Modelling (LEM) and Euler-Bernoulli beam (EBB) modelling. An
experiment is designed to validate the mathematical model and assess
the feasibility of AMEH. Comparison of theoretical and experimental
data on critical parameter value such as Mm, Cms, dm and Ceb showed
the variances are within 1% to 6%, which is reasonably acceptable.
Then, AMEH undergoes bandwidth tuning for performance
optimization. The AMEH successfully produces 0.9V/(m/s^2) and
1.79μW/(m^2/s^4) at 60Hz and 400kΩ resistive load which only
show variances about 7% compared to theoretical data. At 1g and
60Hz resonance frequency, the averaged power output is about
2.2mW which fulfilled a range of wireless sensors and
communication peripherals power requirements. Finally, the design
for AMEH is assessed, validated and deemed as a feasible design.
Abstract: Tuberculosis (TB) remains a leading cause of
infectious mortality. It is primarily transmitted by the respiratory
route, individuals with active disease may infect others through
airborne particles which releases when they cough, talk, or sing and
subsequently inhale by others. In order to study the effect of the
Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB
patient, a Vaccinated Susceptible Infected and Recovered (VSIR)
mathematical model is being developed to achieve the desired
objectives. The mathematical model, so developed, shall be used to
quantify the effect of BCG Vaccine to protect the immigrant young
adult person. Moreover, equations are to be established for the
disease endemic and free equilibrium states and subsequently utilized
in disease stability analysis. The stability analysis will give a
complete picture of disease annihilation from the total population if
the total removal rate from the infectious group should be greater
than total number of dormant infections produced throughout
infectious period.
Abstract: Aim of this research study is to investigate and
establish the characteristics of brain dominances (BD) and multiple
intelligences (MI). This experimentation has been conducted for the
sample size of 552 undergraduate computer-engineering students. In
addition, mathematical formulation has been established to exhibit
the relation between thinking and intelligence, and its correlation has
been analyzed. Correlation analysis has been statistically measured
using Pearson’s coefficient. Analysis of the results proves that there
is a strong relational existence between thinking and intelligence.
This research is carried to improve the didactic methods in
engineering learning and also to improve e-learning strategies.
Abstract: This paper reports the development and application of a 2D1 depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. κ − ε and 2D LES turbulence models were consider in this article. 2D CFD2 simulations for one hill was done to check the depth-averaged model in practise.
Abstract: In dynamic system theory a mathematical model is
often used to describe their properties. In order to find a transfer
matrix of a dynamic system we need to calculate an inverse matrix.
The paper contains the fusion of the classical theory and the
procedures used in the theory of automated control for calculating the
inverse matrix. The final part of the paper models the given problem
by the Matlab.
Abstract: Knowledge of bone mechanical properties is important
for bone substitutes design and fabrication, and more efficient
prostheses development. The aim of this study is to characterize the
viscoelastic behavior of bone specimens, through stress relaxation
and fatigue tests performed to trabecular bone samples from bovine
femoral heads. Relaxation tests consisted on preloading the samples
at five different magnitudes and evaluate them for 1020 seconds,
adjusting the results to a KWW mathematical model. Fatigue tests
consisted of 700 load cycles and analyze their status at the end of the
tests. As a conclusion we have that between relaxation stress and
each preload there is linear relation and for samples with initial
Young´s modulus greater than 1.5 GPa showed no effects due fatigue
test loading cycles.
Abstract: Nowadays, the rapid development of CAD systems’
programming environments results in the creation of multiple
downstream applications, which are developed and becoming
increasingly available. CAD based manufacturing simulations is
gradually following the same trend. Drilling is the most popular holemaking
process used in a variety of industries. A specially built piece
of software that deals with the drilling kinematics is presented. The
cutting forces are calculated based on the tool geometry, the cutting
conditions and the tool/work-piece materials. The results are verified
by experimental work. Finally, the response surface methodology
(RSM) is applied and mathematical models of the total thrust force
and the thrust force developed because of the main cutting edges are
proposed.
Abstract: The Economic Lot Scheduling Problem (ELSP) is a
valuable mathematical model that can support decision-makers to
make scheduling decisions. The basic period approach is effective for
solving the ELSP. The assumption for applying the basic period
approach is that a product must use its maximum production rate to be
produced. However, a product can lower its production rate to reduce
the average total cost when a facility has extra idle time. The past
researches discussed how a product adjusts its production rate under
the common cycle approach. To the best of our knowledge, no studies
have addressed how a product lowers its production rate under the
basic period approach. This research is the first paper to discuss this
topic. The research develops a simple fixed rate approach that adjusts
the production rate of a product under the basic period approach to
solve the ELSP. Our numerical example shows our approach can find a
better solution than the traditional basic period approach. Our
mathematical model that applies the fixed rate approach under the
basic period approach can serve as a reference for other related
researches.
Abstract: This paper deals with the study of reflection and
transmission characteristics of acoustic waves at the interface of a
semiconductor half-space and elastic solid. The amplitude ratios
(reflection and transmission coefficients) of reflected and transmitted
waves to that of incident wave varying with the incident angles have
been examined for the case of quasi-longitudinal wave. The special
cases of normal and grazing incidence have also been derived with
the help of Gauss elimination method. The mathematical model
consisting of governing partial differential equations of motion and
charge carriers’ diffusion of n-type semiconductors and elastic solid
has been solved both analytically and numerically in the study. The
numerical computations of reflection and transmission coefficients
has been carried out by using MATLAB programming software for
silicon (Si) semiconductor and copper elastic solid. The computer
simulated results have been plotted graphically for Si
semiconductors. The study may be useful in semiconductors,
geology, and seismology in addition to surface acoustic wave (SAW)
devices.
Abstract: A mathematical model of the additional effects of the
liquid in the hydrodynamic gap is presented in the paper. An
incompressible viscous fluid is considered. Based on computational
modeling are determined the matrices of mass, stiffness and damping.
The mathematical model is experimentally verified.
Abstract: An efficient remanufacturing network lead to an
efficient design of sustainable manufacturing enterprise. In
remanufacturing network, products are collected from the customer
zone, disassembled and remanufactured at a suitable remanufacturing
facility. In this respect, another issue to consider is how the returned
product to be remanufactured, in other words, what is the best layout
for such facility. In order to achieve a sustainable manufacturing
system, Cellular Manufacturing System (CMS) designs are highly
recommended, CMSs combine high throughput rates of line layouts
with the flexibility offered by functional layouts (job shop).
Introducing the CMS while designing a remanufacturing network will
benefit the utilization of such a network. This paper presents and
analyzes a comprehensive mathematical model for the design of
Dynamic Cellular Remanufacturing Systems (DCRSs). In this paper,
the proposed model is the first one to date that considers CMS and
remanufacturing system simultaneously. The proposed DCRS model
considers several manufacturing attributes such as multi period
production planning, dynamic system reconfiguration, duplicate
machines, machine capacity, available time for workers, worker
assignments, and machine procurement, where the demand is totally
satisfied from a returned product. A numerical example is presented
to illustrate the proposed model.
Abstract: The article presents two mathematical models of the
interaction between a rotating shaft and an incompressible fluid. The
mathematical model includes both the journal bearings and the
axially traversed hydrodynamic sealing gaps of hydraulic machines.
A method is shown for the identification of additional effects of the
fluid acting on the rotor of the machine, both for a linear and a nonlinear
model. The interaction is expressed by matrices of mass,
stiffness and damping.
Abstract: This paper shows in detail the mathematical model of
direct and inverse kinematics for a robot manipulator (welding type)
with four degrees of freedom. Using the D-H parameters, screw
theory, numerical, geometric and interpolation methods, the
theoretical and practical values of the position of robot were
determined using an optimized algorithm for inverse kinematics
obtaining the values of the particular joints in order to determine the
virtual paths in a relatively short time.
Abstract: The paper deals with possibilities of interpretation of
iron ore reducibility tests. It presents a mathematical model
developed at Centre ENET, VŠB – Technical University of Ostrava,
Czech Republic for an evaluation of metallurgical material of blast
furnace feedstock such as iron ore, sinter or pellets. According to the
data from the test, the model predicts its usage in blast furnace
technology and its effects on production parameters of shaft
aggregate. At the beginning, the paper sums up the general concept
and experience in mathematical modelling of iron ore reduction. It
presents basic equation for the calculation and the main parts of the
developed model. In the experimental part, there is an example of
usage of the mathematical model. The paper describes the usage of
data for some predictive calculation. There are presented material,
method of carried test of iron ore reducibility. Then there are
graphically interpreted effects of used material on carbon
consumption, rate of direct reduction and the whole reduction
process.
Abstract: An artificial neural network is a mathematical model
inspired by biological neural networks. There are several kinds of
neural networks and they are widely used in many areas, such as:
prediction, detection, and classification. Meanwhile, in day to day life,
people always have to make many difficult decisions. For example,
the coach of a soccer club has to decide which offensive player
to be selected to play in a certain game. This work describes a
novel Neural Network using a combination of the General Regression
Neural Network and the Probabilistic Neural Networks to help a
soccer coach make an informed decision.
Abstract: Today’s VLSI networks demands for high speed. And
in this work the compact form mathematical model for current mode
signalling in VLSI interconnects is presented.RLC interconnect line
is modelled using characteristic impedance of transmission line and
inductive effect. The on-chip inductance effect is dominant at lower
technology node is emulated into an equivalent resistance. First order
transfer function is designed using finite difference equation, Laplace
transform and by applying the boundary conditions at the source and
load termination. It has been observed that the dominant pole
determines system response and delay in the proposed model. The
novel proposed current mode model shows superior performance as
compared to voltage mode signalling. Analysis shows that current
mode signalling in VLSI interconnects provides 2.8 times better
delay performance than voltage mode. Secondly the damping factor
of a lumped RLC circuit is shown to be a useful figure of merit.
Abstract: The formulated problem of optimization of the
technological process of water treatment for thermal power plants is
considered in this article. The problem is of multiparametric nature.
To optimize the process, namely, reduce the amount of waste water, a
new technology was developed to reuse such water. A mathematical
model of the technology of wastewater reuse was developed.
Optimization parameters were determined. The model consists of a
material balance equation, an equation describing the kinetics of ion
exchange for the non-equilibrium case and an equation for the ion
exchange isotherm. The material balance equation includes a
nonlinear term that depends on the kinetics of ion exchange. A direct
problem of calculating the impurity concentration at the outlet of the
water treatment plant was numerically solved. The direct problem
was approximated by an implicit point-to-point computation
difference scheme. The inverse problem was formulated as relates to
determination of the parameters of the mathematical model of the
water treatment plant operating in non-equilibrium conditions. The
formulated inverse problem was solved. Following the results of
calculation the time of start of the filter regeneration process was
determined, as well as the period of regeneration process and the
amount of regeneration and wash water. Multi-parameter
optimization of water treatment process for thermal power plants
allowed decreasing the amount of wastewater by 15%.