Abstract: This paper evaluates the performance of a novel
algorithm for tracking of a mobile node, interms of execution time
and root mean square error (RMSE). Particle Filter algorithm is used
to track the mobile node, however a new technique in particle filter
algorithm is also proposed to reduce the execution time. The
stationary points were calculated through trilateration and finally by
averaging the number of points collected for a specific time, whereas
tracking is done through trilateration as well as particle filter
algorithm. Wi-Fi signal is used to get initial guess of the position of
mobile node in x-y coordinates system. Commercially available
software “Wireless Mon" was used to read the WiFi signal strength
from the WiFi card. Visual Cµ version 6 was used to interact with
this software to read only the required data from the log-file
generated by “Wireless Mon" software. Results are evaluated through
mathematical modeling and MATLAB simulation.
Abstract: This study aims to specify to what extent students
understand topology during the lesson and to determine possible
misconceptions. 14 teacher trainees registered at Secondary School
Mathematics education department were observed in the topology
lessons throughout a semester and data collected at the first topology
lesson is presented here. Students- knowledge was evaluated using a
written test right before and after the topology lesson. Thus, what the
students learnt in terms of the definition and examples of topologic
space were specified as well as possible misconceptions. The
findings indicated that students did not fully comprehend the topic
and misunderstandings were due to insufficient pre-requisite
knowledge of abstract mathematical topics and mathematical
notation.
Abstract: This paper describes a combined mathematicalgraphical
approach for optimum tool path planning in order to
improve machining efficiency. A methodology has been used that
stabilizes machining operations by adjusting material removal rate in
pocket milling operations while keeping cutting forces within limits.
This increases the life of cutting tool and reduces the risk of tool
breakage, machining vibration, and chatter. Case studies reveal the
fact that application of this approach could result in a slight increase
of machining time, however, a considerable reduction of tooling cost,
machining vibration, noise and chatter can be achieved in addition to
producing a better surface finish.
Abstract: As there has been a recognizable transition in
automotive industry from mass production to mass customization,
automobile manufacturers and their suppliers have been seeking ways
for more flexible and efficient processes. Eventually, modular
production is currently being applied to manage the changing orders of
the industry. In this paper, two different modular assembly line
concepts were studied: conveyor line and box assembly line.
Mathematical model for two assembly line concepts were developed
and their production line efficiency were compared as a performance
measure to improve their assembly line balancing.
Abstract: Worldwide conventional resources of fossil fuel are depleting very fast due to large scale increase in use of transport vehicles every year, therefore consumption rate of oil in transport sector alone has gone very high. In view of this, the major thrust has now been laid upon the search of alternative energy source and also for cost effective energy conversion system. The air converted into compressed form by non conventional or conventional methods can be utilized as potential working fluid for producing shaft work in the air turbine and thus offering the capability of being a zero pollution energy source. This paper deals with the mathematical modeling and performance evaluation of a small capacity compressed air driven vaned type novel air turbine. Effect of expansion action and steady flow work in the air turbine at high admission air pressure of 6 bar, for varying injection to vane angles ratios 0.2-1.6, at the interval of 0.2 and at different vane angles such as 30o, 45o, 51.4o, 60o, 72o, 90o, and 120o for 12, 8, 7, 6, 5, 4 and 3 vanes respectively at speed of rotation 2500 rpm, has been quantified and analyzed here. Study shows that the expansion power has major contribution to total power, whereas the contribution of flow work output has been found varying only up to 19.4%. It is also concluded that for variation of injection to vane angle ratios from 0.2 to 1.2, the optimal power output is seen at vane angle 90o (4 vanes) and for 1.4 to 1.6 ratios, the optimal total power is observed at vane angle 72o (5 vanes). Thus in the vaned type novel air turbine the optimum shaft power output is developed when rotor contains 4-5 vanes for almost all situations of injection to vane angle ratios from 0.2 to 1.6.
Abstract: In the forming of ceramic materials the plasticity
concept is commonly used. This term is related to a particular
mechanical behavior when clay is mixed with water. A plastic
ceramic material shows a permanent strain without rupture
when a compressive load produces a shear stress that exceeds
the material-s yield strength. For a plastic ceramic body it
observes a measurable elastic behavior before the yield
strength and when the applied load is removed. In this work, a
mathematical model was developed from applied concepts of
the plasticity theory by using the stress/strain diagram under
compression.
Abstract: Calcium [Ca2+] dynamics is studied as a potential form
of neuron excitability that can control many irregular processes like
metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and
increases the synaptic strength and thus triggers the neurotransmitter
release. The modeling and analysis of calcium dynamics in neuron
cell becomes necessary for deeper understanding of the processes
involved. A mathematical model has been developed for cylindrical
shaped neuron cell by incorporating physiological parameters like
buffer, diffusion coefficient, and association rate. Appropriate initial
and boundary conditions have been framed. The closed form solution
has been developed in terms of modified Bessel function. A computer
program has been developed in MATLAB 7.11 for the whole
approach.
Abstract: In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.
Abstract: In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.
Abstract: The study of piezoelectric material in the past was in
T-Domain form; however, no one has studied piezoelectric material in the S-Domain form. This paper will present the piezoelectric material in the transfer function or S-Domain model. S-Domain is a
well known mathematical model, used for analyzing the stability of the material and determining the stability limits. By using S-Domain
in testing stability of piezoelectric material, it will provide a new tool for the scientific world to study this material in various forms.
Abstract: This paper presents a controller design technique for
Synchronous Reluctance Motor to improve its dynamic performance
with fast response and high accuracy. The sliding mode control is the
most attractive and suitable method to use for this purpose, since it is
simple in design and for its insensitivity to parameter variations or
external disturbances. When this method implemented it yields fast
dynamic response without overshoot and a zero steady-state error.
The current loop control with decentralized sliding mode is presented
in this paper. The mathematical model for the synchronous machine,
the inverter and the controller is developed. The stability of the
sliding mode controller is analyzed. Simulation of synchronous
reluctance motor and the controller with PWM-inverter has been
curried out, using the SIMULINK software package of MATLAB.
Simulation results are presented to show the effectiveness of the
approach.
Abstract: In communication networks where communication nodes are connected with finite capacity transmission links, the packet inter-arrival times are strongly correlated with the packet length and the link capacity (or the packet service time). Such correlation affects the system performance significantly, but little attention has been paid to this issue. In this paper, we propose a mathematical framework to study the impact of the correlation between the packet service times and the packet inter-arrival times on system performance. With our mathematical model, we analyze the system performance, e.g., the unfinished work of the system, and show that the correlation affects the system performance significantly. Some numerical examples are also provided.
Abstract: In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.
Abstract: This paper is concerned with an investigation into the
localized non-stability of a thin elastic orthotropic semi-infinite plate.
In this study, a semi-infinite plate, simply supported on two edges
and different boundary conditions, clamped, hinged, sliding contact
and free on the other edge, are considered. The mathematical model
is used and a general solution is presented the conditions under which
localized solutions exist are investigated.
Abstract: Mathematical and computational modeling of calcium
signalling in nerve cells has produced considerable insights into how
the cells contracts with other cells under the variation of biophysical
and physiological parameters. The modeling of calcium signaling in
astrocytes has become more sophisticated. The modeling effort has
provided insight to understand the cell contraction. Main objective
of this work is to study the effect of voltage gated (Operated)
calcium channel (VOC) on calcium profile in the form of advection
diffusion equation. A mathematical model is developed in the form
of advection diffusion equation for the calcium profile. The model
incorporates the important physiological parameter like diffusion
coefficient etc. Appropriate boundary conditions have been framed.
Finite volume method is employed to solve the problem. A program
has been developed using in MATLAB 7.5 for the entire problem
and simulated on an AMD-Turion 32-bite machine to compute the
numerical results.
Abstract: In this paper, a set of experimental data has been used to assess the influence of abrasive water jet (AWJ) process parameters in cutting 6063-T6 aluminum alloy. The process variables considered here include nozzle diameter, jet traverse rate, jet pressure and abrasive flow rate. The effects of these input parameters are studied on depth of cut (h); one of most important characteristics of AWJ. The Taguchi method and regression modeling are used in order to establish the relationships between input and output parameters. The adequacy of the model is evaluated using analysis of variance (ANOVA) technique. In the next stage, the proposed model is embedded into a Simulated Annealing (SA) algorithm to optimize the AWJ process parameters. The objective is to determine a suitable set of process parameters that can produce a desired depth of cut, considering the ranges of the process parameters. Computational results prove the effectiveness of the proposed model and optimization procedure.
Abstract: Among many different methods that are used for
optimizing different engineering problems mathematical (numerical)
optimization techniques are very important because they can easily
be used and are consistent with most of engineering problems. Many
studies and researches are done on stability analysis of three
dimensional (3D) slopes and the relating probable slip surfaces and
determination of factors of safety, but in most of them force
equilibrium equations, as in simplified 2D methods, are considered
only in two directions. In other words for decreasing mathematical
calculations and also for simplifying purposes the force equilibrium
equation in 3rd direction is omitted. This point is considered in just a
few numbers of previous studies and most of them have only given a
factor of safety and they haven-t made enough effort to find the most
probable slip surface. In this study shapes of the slip surfaces are
modeled, and safety factors are calculated considering the force
equilibrium equations in all three directions, and also the moment
equilibrium equation is satisfied in the slip direction, and using
nonlinear programming techniques the shape of the most probable
slip surface is determined. The model which is used in this study is a
3D model that is composed of three upper surfaces which can cover
all defined and probable slip surfaces. In this research the meshing
process is done in a way that all elements are prismatic with
quadrilateral cross sections, and the safety factor is defined on this
quadrilateral surface in the base of the element which is a part of the
whole slip surface. The method that is used in this study to find the
most probable slip surface is the non-linear programming method in
which the objective function that must get optimized is the factor of
safety that is a function of the soil properties and the coordinates of
the nodes on the probable slip surface. The main reason for using
non-linear programming method in this research is its quick
convergence to the desired responses. The final results show a good
compatibility with the previously used classical and 2D methods and
also show a reasonable convergence speed.
Abstract: The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.
Abstract: Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space
is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft closed mapping, soft open mappings, soft connected spaces and soft paracompact spaces. We also redefine the concept of soft points such that it is reasonable in soft topological spaces. Moreover, some basic properties of these concepts are explored.
Abstract: Multi criteria decision making (MCDM) methods like analytic hierarchy process, ELECTRE and multi-attribute utility theory are critically studied. They have irregularities in terms of the reliability of ranking of the best alternatives. The Routing Decision Support (RDS) algorithm is trying to improve some of their deficiencies. This paper gives a mathematical verification that the RDS algorithm conforms to the test criteria for an effective MCDM method when a linear preference function is considered.