Abstract: Tamil handwritten document is taken as a key source of data to identify the writer. Tamil is a classical language which has 247 characters include compound characters, consonants, vowels and special character. Most characters of Tamil are multifaceted in nature. Handwriting is a unique feature of an individual. Writer may change their handwritings according to their frame of mind and this place a risky challenge in identifying the writer. A new discriminative model with pooled features of handwriting is proposed and implemented using support vector machine. It has been reported on 100% of prediction accuracy by RBF and polynomial kernel based classification model.
Abstract: The present paper attempts to investigate the
prediction of air entrainment rate and aeration efficiency of a free
overfall jets issuing from a triangular sharp crested weir by using
regression based modelling. The empirical equations, Support vector
machine (polynomial and radial basis function) models and the linear
regression techniques were applied on the triangular sharp crested
weirs relating the air entrainment rate and the aeration efficiency to
the input parameters namely drop height, discharge, and vertex angle.
It was observed that there exists a good agreement between the
measured values and the values obtained using empirical equations,
Support vector machine (Polynomial and rbf) models and the linear
regression techniques. The test results demonstrated that the SVM
based (Poly & rbf) model also provided acceptable prediction of the
measured values with reasonable accuracy along with empirical
equations and linear regression techniques in modelling the air
entrainment rate and the aeration efficiency of a free overfall jets
issuing from triangular sharp crested weir. Further sensitivity analysis
has also been performed to study the impact of input parameter on the
output in terms of air entrainment rate and aeration efficiency.
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: The composite flour blend consisting of corn, pearl
millet, black gram and wheat bran in the ratio of 80:5:10:5 was taken
to prepare the extruded product and their effect on physical properties
of extrudate was studied. The extrusion process was conducted in
laboratory by using twin screw extruder. The physical characteristics
evaluated include lateral expansion, bulk density, water absorption
index, water solubility index, and rehydration ratio and moisture
retention. The Central Composite Rotatable Design (CCRD) was
used to decide the level of processing variables i.e. feed moisture
content (%), screw speed (rpm), and barrel temperature (oC) for the
experiment. The data obtained after extrusion process were analyzed
by using response surface methodology. A second order polynomial
model for the dependent variables was established to fit the
experimental data. The numerical optimization studies resulted in
127°C of barrel temperature, 246 rpm of screw speed, and 14.5% of
feed moisture as optimum variables to produce acceptable extruded
product. The responses predicted by the software for the optimum
process condition resulted in lateral expansion 126%, bulk density
0.28 g/cm3, water absorption index 4.10 g/g, water solubility index
39.90%, rehydration ratio 544% and moisture retention 11.90% with
75% desirability.
Abstract: A solution methodology without using integral
transformation is proposed to develop analytical solutions for
transient heat conduction in nonuniform hollow cylinders with
time-dependent boundary condition at the outer surface. It is shown
that if the thermal conductivity and the specific heat of the medium
are in arbitrary polynomial function forms, the closed solutions of the
system can be developed. The influence of physical properties on the
temperature distribution of the system is studied. A numerical
example is given to illustrate the efficiency and the accuracy of the
solution methodology.
Abstract: The article describes the effect of the replacement of
the used reference coordinate system in the georeferencing of an old
map of Europe. The map was georeferenced into three types of
projection – the equal-area conic (original cartographic projection),
cylindrical Plate Carrée and cylindrical Mercator map projection. The
map was georeferenced by means of the affine and the second-order
polynomial transformation. The resulting georeferenced raster
datasets from the Plate Carrée and Mercator projection were
projected into the equal-area conic projection by means of projection
equations. The output is the comparison of drawn graphics, the
magnitude of standard deviations for individual projections and types
of transformation.
Abstract: The purpose of the paper is to estimate the US small
wind turbines market potential and forecast the small wind turbines
sales in the US. The forecasting method is based on the application of
the Bass model and the generalized Bass model of innovations
diffusion under replacement purchases. In the work an exponential
distribution is used for modeling of replacement purchases. Only one
parameter of such distribution is determined by average lifetime of
small wind turbines. The identification of the model parameters is
based on nonlinear regression analysis on the basis of the annual
sales statistics which has been published by the American Wind
Energy Association (AWEA) since 2001 up to 2012. The estimation
of the US average market potential of small wind turbines (for
adoption purchases) without account of price changes is 57080
(confidence interval from 49294 to 64866 at P = 0.95) under average
lifetime of wind turbines 15 years, and 62402 (confidence interval
from 54154 to 70648 at P = 0.95) under average lifetime of wind
turbines 20 years. In the first case the explained variance is 90,7%,
while in the second - 91,8%. The effect of the wind turbines price
changes on their sales was estimated using generalized Bass model.
This required a price forecast. To do this, the polynomial regression
function, which is based on the Berkeley Lab statistics, was used. The
estimation of the US average market potential of small wind turbines
(for adoption purchases) in that case is 42542 (confidence interval
from 32863 to 52221 at P = 0.95) under average lifetime of wind
turbines 15 years, and 47426 (confidence interval from 36092 to
58760 at P = 0.95) under average lifetime of wind turbines 20 years.
In the first case the explained variance is 95,3%, while in the second
– 95,3%.
Abstract: In this paper, we will give a cryptographic application
over the integral closure O_Lof sextic extension L, namely L is an
extension of Q of degree 6 in the form Q(a,b), which is a rational
quadratic and monogenic extension over a pure monogenic cubic
subfield K generated by a who is a root of monic irreducible
polynomial of degree 2 andb is a root of irreducible polynomial of
degree 3.
Abstract: In this paper, an explicit homotopic function is
constructed to compute the Hochschild homology of a finite
dimensional free k-module V. Because the polynomial algebra is of
course fundamental in the computation of the Hochschild homology
HH and the cyclic homology CH of commutative algebras, we
concentrate our work to compute HH of the polynomial algebra, by
providing certain homotopic function.
Abstract: The edges of low contrast images are not clearly
distinguishable to human eye. It is difficult to find the edges and
boundaries in it. The present work encompasses a new approach for
low contrast images. The Chebyshev polynomial based fractional
order filter has been used for filtering operation on an image. The
preprocessing has been performed by this filter on the input image.
Laplacian of Gaussian method has been applied on preprocessed
image for edge detection. The algorithm has been tested on two test
images.
Abstract: The object of the present paper is to investigate several
general families of bilinear and bilateral generating functions with
different argument for the Gauss’ hypergeometric polynomials.
Abstract: Based on the experimental data, the impact of
resistance and reactance of the winding, as well as the magnetic
permeability of the magnetic circuit steel material on the value of the
electromotive force of the induction converter is investigated. The
obtained results allow estimating the main technological spreads and
determining the maximum level of the electromotive force change.
By the method of experiment planning, the expression of a
polynomial for the electromotive force which can be used to estimate
the adequacy of mathematical models to be used at the investigation
and design of induction converters is obtained.
Abstract: In this paper, a new trend for improvement in semianalytical
method based on scale boundaries in order to solve the 2D
elastodynamic problems is provided. In this regard, only the
boundaries of the problem domain discretization are by specific subparametric
elements. Mapping functions are uses as a class of higherorder
Lagrange polynomials, special shape functions, Gauss-Lobatto-
Legendre numerical integration, and the integral form of the weighted
residual method, the matrix is diagonal coefficients in the equations
of elastodynamic issues. Differences between study conducted and
prior research in this paper is in geometry production procedure of
the interpolation function and integration of the different is selected.
Validity and accuracy of the present method are fully demonstrated
through two benchmark problems which are successfully modeled
using a few numbers of DOFs. The numerical results agree very well
with the analytical solutions and the results from other numerical
methods.
Abstract: A mixed method by combining modified pole
clustering technique and modified cauer continued fraction is
proposed for reducing the order of the large-scale dynamic systems.
The denominator polynomial of the reduced order model is obtained
by using modified pole clustering technique while the coefficients of
the numerator are obtained by modified cauer continued fraction.
This method generated 'k' number of reduced order models for kth
order reduction. The superiority of the proposed method has been
elaborated through numerical example taken from the literature and
compared with few existing order reduction methods.
Abstract: In this paper, we introduce a generalized Chebyshev
collocation method (GCCM) based on the generalized Chebyshev
polynomials for solving stiff systems. For employing a technique
of the embedded Runge-Kutta method used in explicit schemes, the
property of the generalized Chebyshev polynomials is used, in which
the nodes for the higher degree polynomial are overlapped with those
for the lower degree polynomial. The constructed algorithm controls
both the error and the time step size simultaneously and further
the errors at each integration step are embedded in the algorithm
itself, which provides the efficiency of the computational cost. For
the assessment of the effectiveness, numerical results obtained by the
proposed method and the Radau IIA are presented and compared.
Abstract: The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wavebeam both in elevation and azimuth. In this paper a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.
Abstract: The relationship between eigenstructure (eigenvalues
and eigenvectors) and latent structure (latent roots and latent vectors)
is established. In control theory eigenstructure is associated with
the state space description of a dynamic multi-variable system and
a latent structure is associated with its matrix fraction description.
Beginning with block controller and block observer state space forms
and moving on to any general state space form, we develop the
identities that relate eigenvectors and latent vectors in either direction.
Numerical examples illustrate this result. A brief discussion of the
potential of these identities in linear control system design follows.
Additionally, we present a consequent result: a quick and easy
method to solve the polynomial eigenvalue problem for regular matrix
polynomials.
Abstract: It is well known, that any interpolating polynomial
p (x, y) on the vector space Pn,m of two-variable polynomials with
degree less than n in terms of x and less than m in terms of y, has
various representations that depends on the basis of Pn,m that we
select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of
this short note is twofold : a) to present transformations between the
coordinates of the polynomial p (x, y) in the aforementioned basis
and b) to present transformations between these bases.
Abstract: In this paper the issue of dimensionality reduction is
investigated in finger vein recognition systems using kernel Principal
Component Analysis (KPCA). One aspect of KPCA is to find the
most appropriate kernel function on finger vein recognition as there
are several kernel functions which can be used within PCA-based
algorithms. In this paper, however, another side of PCA-based
algorithms -particularly KPCA- is investigated. The aspect of
dimension of feature vector in PCA-based algorithms is of
importance especially when it comes to the real-world applications
and usage of such algorithms. It means that a fixed dimension of
feature vector has to be set to reduce the dimension of the input and
output data and extract the features from them. Then a classifier is
performed to classify the data and make the final decision. We
analyze KPCA (Polynomial, Gaussian, and Laplacian) in details in
this paper and investigate the optimal feature extraction dimension in
finger vein recognition using KPCA.
Abstract: There is an essential need for obtaining the mathematical representation of fish body undulations, which can be used for designing and building new innovative types of marine propulsion systems with less environmental impact. This research work presents a case study to derive the mathematical model for fish body movement. Observation and capturing image methods were used in this study in order to obtain a mathematical representation of Clariasbatrachus fish (catfish). An experiment was conducted by using an aquarium with dimension 0.609 m x 0.304 m x 0.304 m, and a 0.5 m ruler was attached at the base of the aquarium. Progressive Scan Monochrome Camera was positioned at 1.8 m above the base of the aquarium to provide swimming sequences. Seven points were marked on the fish body using white marker to indicate the fish movement and measuring the amplitude of undulation. Images from video recordings (20 frames/s) were analyzed frame by frame using local coordinate system, with time interval 0.05 s. The amplitudes of undulations were obtained for image analysis from each point that has been marked on fish body. A graph of amplitude of undulations versus time was plotted by using computer to derive a mathematical fit. The function for the graph is polynomial with nine orders.