Abstract: This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.
Abstract: In this paper, the construction of a detailed spine
model is presented using the LifeMOD Biomechanics Modeler. The
detailed spine model is obtained by refining spine segments in
cervical, thoracic and lumbar regions into individual vertebra
segments, using bushing elements representing the intervertebral
discs, and building various ligamentous soft tissues between
vertebrae. In the sagittal plane of the spine, constant force will be
applied from the posterior to anterior during simulation to determine
dynamic characteristics of the spine. The force magnitude is
gradually increased in subsequent simulations. Based on these
recorded dynamic properties, graphs of displacement-force
relationships will be established in terms of polynomial functions by
using the least-squares method and imported into a haptic integrated
graphic environment. A thoracolumbar spine model with complex
geometry of vertebrae, which is digitized from a resin spine
prototype, will be utilized in this environment. By using the haptic
technique, surgeons can touch as well as apply forces to the spine
model through haptic devices to observe the locomotion of the spine
which is computed from the displacement-force relationship graphs.
This current study provides a preliminary picture of our ongoing
work towards building and simulating bio-fidelity scoliotic spine
models in a haptic integrated graphic environment whose dynamic
properties are obtained from LifeMOD. These models can be helpful
for surgeons to examine kinematic behaviors of scoliotic spines and
to propose possible surgical plans before spine correction operations.
Abstract: Maximal Ratio Combining (MRC) is considered the most complex combining technique as it requires channel coefficients estimation. It results in the lowest bit error rate (BER) compared to all other combining techniques. However the BER starts to deteriorate as errors are introduced in the channel coefficients estimation. A novel combining technique, termed Generalized Maximal Ratio Combining (GMRC) with a polynomial kernel, yields an identical BER as MRC with perfect channel estimation and a lower BER in the presence of channel estimation errors. We show that GMRC outperforms the optimal MRC scheme in general and we hereinafter introduce it to the scientific community as a new “supraoptimal" algorithm. Since diversity combining is especially effective in small femto- and pico-cells, internet-associated wireless peripheral systems are to benefit most from GMRC. As a result, many spinoff applications can be made to IP-based 4th generation networks.
Abstract: This work examines thermal convection in two porous
layers. Flow in the upper layer is governed by Brinkman-s equations
model and in the lower layer is governed by Darcy-s model.
Legendre polynomials are used to obtain numerical solution when the
lower layer is heated from below.
Abstract: Fundamental sensor-motor couplings form the backbone
of most mobile robot control tasks, and often need to be implemented
fast, efficiently and nevertheless reliably. Machine learning
techniques are therefore often used to obtain the desired sensor-motor
competences.
In this paper we present an alternative to established machine
learning methods such as artificial neural networks, that is very fast,
easy to implement, and has the distinct advantage that it generates
transparent, analysable sensor-motor couplings: system identification
through nonlinear polynomial mapping.
This work, which is part of the RobotMODIC project at the
universities of Essex and Sheffield, aims to develop a theoretical understanding
of the interaction between the robot and its environment.
One of the purposes of this research is to enable the principled design
of robot control programs.
As a first step towards this aim we model the behaviour of the
robot, as this emerges from its interaction with the environment, with
the NARMAX modelling method (Nonlinear, Auto-Regressive, Moving
Average models with eXogenous inputs). This method produces
explicit polynomial functions that can be subsequently analysed using
established mathematical methods.
In this paper we demonstrate the fidelity of the obtained NARMAX
models in the challenging task of robot route learning; we present a
set of experiments in which a Magellan Pro mobile robot was taught
to follow four different routes, always using the same mechanism to
obtain the required control law.
Abstract: A given polynomial, possibly with multiple roots, is
factored into several lower-degree distinct-root polynomials with
natural-order-integer powers. All the roots, including multiplicities,
of the original polynomial may be obtained by solving these lowerdegree
distinct-root polynomials, instead of the original high-degree
multiple-root polynomial directly.
The approach requires polynomial Greatest Common Divisor
(GCD) computation. The very simple and effective process, “Monic
polynomial subtractions" converted trickily from “Longhand
polynomial divisions" of Euclidean algorithm is employed. It
requires only simple elementary arithmetic operations without any
advanced mathematics.
Amazingly, the derived routine gives the expected results for the
test polynomials of very high degree, such as p( x) =(x+1)1000.
Abstract: Graph coloring is an important problem in computer
science and many algorithms are known for obtaining reasonably
good solutions in polynomial time. One method of comparing
different algorithms is to test them on a set of standard graphs where
the optimal solution is already known. This investigation analyzes a
set of 50 well known graph coloring instances according to a set of
complexity measures. These instances come from a variety of
sources some representing actual applications of graph coloring
(register allocation) and others (mycieleski and leighton graphs) that
are theoretically designed to be difficult to solve. The size of the
graphs ranged from ranged from a low of 11 variables to a high of
864 variables. The method used to solve the coloring problem was
the square of the adjacency (i.e., correlation) matrix. The results
show that the most difficult graphs to solve were the leighton and the
queen graphs. Complexity measures such as density, mobility,
deviation from uniform color class size and number of block
diagonal zeros are calculated for each graph. The results showed that
the most difficult problems have low mobility (in the range of .2-.5)
and relatively little deviation from uniform color class size.
Abstract: In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.
Abstract: According to Hermite there exists only a finite
number of number fields having a given degree, and a given value of
the discriminant, nevertheless this number is not known generally.
The determination of a maximum number of number fields of degree
10 having a given discriminant that contain a subfield of degree 5
having a fixed class number, narrow class number and Galois group
is the purpose of this work. The constructed lists of the first
coincidences of 52 (resp. 50, 40, 48, 22, 6) nonisomorphic number
fields with same discriminant of degree 10 of signature (6,2) (resp.
(4,3), (8,1), (2,4), (0,5), (10,0)) containing a quintic field. For each
field in the lists, we indicate its discriminant, the discriminant of its
subfield, a relative polynomial generating the field over its quintic
field and its relative discriminant, the corresponding polynomial over
Q and its Galois closure are presented with concluding remarks.
Abstract: This paper presents the application of a signal intensity independent registration criterion for non-rigid body registration of medical images. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the ratios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation. The geometric transformation model adopted is a local cubic B-splines based model.
Abstract: As the Computed Tomography(CT) requires normally
hundreds of projections to reconstruct the image, patients are exposed
to more X-ray energy, which may cause side effects such as cancer.
Even when the variability of the particles in the object is very less,
Computed Tomography requires many projections for good quality
reconstruction. In this paper, less variability of the particles in an
object has been exploited to obtain good quality reconstruction.
Though the reconstructed image and the original image have same
projections, in general, they need not be the same. In addition
to projections, if a priori information about the image is known,
it is possible to obtain good quality reconstructed image. In this
paper, it has been shown by experimental results why conventional
algorithms fail to reconstruct from a few projections, and an efficient
polynomial time algorithm has been given to reconstruct a bi-level
image from its projections along row and column, and a known sub
image of unknown image with smoothness constraints by reducing the
reconstruction problem to integral max flow problem. This paper also
discusses the necessary and sufficient conditions for uniqueness and
extension of 2D-bi-level image reconstruction to 3D-bi-level image
reconstruction.
Abstract: In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.
Abstract: The incorporation of computational fluid dynamics in the design of modern hydraulic turbines appears to be necessary in order to improve their efficiency and cost-effectiveness beyond the traditional design practices. A numerical optimization methodology is developed and applied in the present work to a Turgo water turbine. The fluid is simulated by a Lagrangian mesh-free approach that can provide detailed information on the energy transfer and enhance the understanding of the complex, unsteady flow field, at very small computing cost. The runner blades are initially shaped according to hydrodynamics theory, and parameterized using Bezier polynomials and interpolation techniques. The use of a limited number of free design variables allows for various modifications of the standard blade shape, while stochastic optimization using evolutionary algorithms is implemented to find the best blade that maximizes the attainable hydraulic efficiency of the runner. The obtained optimal runner design achieves considerably higher efficiency than the standard one, and its numerically predicted performance is comparable to a real Turgo turbine, verifying the reliability and the prospects of the new methodology.
Abstract: Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Abstract: In this paper we study the boundedness properties of
certain oscillatory integrals with polynomial phase. We obtain sharp
estimates for these oscillatory integrals. By the virtue of these
estimates and extrapolation we obtain Lp boundedness for these
oscillatory integrals under rather weak size conditions on the kernel
function.
Abstract: In this research, Response Surface Methodology (RSM) is used to investigate the effect of four controllable input variables namely: discharge current, pulse duration, pulse off time and applied voltage Surface Roughness (SR) of on Electrical Discharge Machined surface. To study the proposed second-order polynomial model for SR, a Central Composite Design (CCD) is used to estimation the model coefficients of the four input factors, which are alleged to influence the SR in Electrical Discharge Machining (EDM) process. Experiments were conducted on AISI D2 tool steel with copper electrode. The response is modeled using RSM on experimental data. The significant coefficients are obtained by performing Analysis of Variance (ANOVA) at 5% level of significance. It is found that discharge current, pulse duration, and pulse off time and few of their interactions have significant effect on the SR. The model sufficiency is very satisfactory as the Coefficient of Determination (R2) is found to be 91.7% and adjusted R2-statistic (R2 adj ) 89.6%.
Abstract: We study the problem of reconstructing a three dimensional binary matrices whose interiors are only accessible through few projections. Such question is prominently motivated by the demand in material science for developing tool for reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested to reconstruct 3D-object (crystalline structure) by reconstructing slice of the 3D-object. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. Formally, 3Dobject (crystalline structure) having a priory information is modeled by a class of 3D-binary matrices satisfying a priori information. We consider 3D-binary matrices with periodicity constraints, and we propose a polynomial time algorithm to reconstruct 3D-binary matrices with periodicity constraints from two orthogonal projections.
Abstract: In this paper, Novel method, Particle Swarm Optimization (PSO) algorithm, based technique is proposed to estimate and analyze the steady state performance of self-excited induction generator (SEIG). In this novel method the tedious job of deriving the complex coefficients of a polynomial equation and solving it, as in previous methods, is not required. By comparing the simulation results obtained by the proposed method with those obtained by the well known mathematical methods, a good agreement between these results is obtained. The comparison validates the effectiveness of the proposed technique.
Abstract: This paper considers the control of the longitudinal
flight dynamics of an F-16 aircraft. The primary design objective
is model-following of the pitch rate q, which is the preferred
system for aircraft approach and landing. Regulation of the aircraft
velocity V (or the Mach-hold autopilot) is also considered, but
as a secondary objective. The problem is challenging because the
system is nonlinear, and also non-affine in the input. A sliding
mode controller is designed for the pitch rate, that exploits the
modal decomposition of the linearized dynamics into its short-period
and phugoid approximations. The inherent robustness of the SMC
design provides a convenient way to design controllers without gain
scheduling, with a steady-state response that is comparable to that
of a conventional polynomial based gain-scheduled approach with
integral control, but with improved transient performance. Integral
action is introduced in the sliding mode design using the recently
developed technique of “conditional integrators", and it is shown that
robust regulation is achieved with asymptotically constant exogenous
signals, without degrading the transient response. Through extensive
simulation on the nonlinear multiple-input multiple-output (MIMO)
longitudinal model of the F-16 aircraft, it is shown that the conditional
integrator design outperforms the one based on the conventional linear
control, without requiring any scheduling.
Abstract: In this study, the density dependent nonlinear reactiondiffusion
equation, which arises in the insect dispersal models, is
solved using the combined application of differential quadrature
method(DQM) and implicit Euler method. The polynomial based
DQM is used to discretize the spatial derivatives of the problem. The
resulting time-dependent nonlinear system of ordinary differential
equations(ODE-s) is solved by using implicit Euler method. The
computations are carried out for a Cauchy problem defined by a onedimensional
density dependent nonlinear reaction-diffusion equation
which has an exact solution. The DQM solution is found to be in a
very good agreement with the exact solution in terms of maximum
absolute error. The DQM solution exhibits superior accuracy at large
time levels tending to steady-state. Furthermore, using an implicit
method in the solution procedure leads to stable solutions and larger
time steps could be used.