Abstract: This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding a jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.
Abstract: This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide high fidelity signal reconstruction for speech signals; these strategies circumvent the problem of exponentially increasing number of samples as the bit-depth is increased and hence are highly efficient. Specifically, the results indicate that the distribution of the intervals between samples is one of the key factors in the quality of signal reconstruction; including samples with short intervals does not improve the accuracy of the signal reconstruction, whilst samples with large intervals lead to numerical instability. The proposed sampling method, termed reduced conventional level crossing (RCLC) sampling, exploits redundancy between samples to improve the efficiency of the sampling without compromising performance. A reconstruction technique is also proposed that enhances the numerical stability through linear interpolation of samples separated by large intervals. Interpolation is demonstrated to improve the accuracy of the signal reconstruction in addition to the numerical stability. We further demonstrate that the RCLC and interpolation methods can give useful levels of signal recovery even if the average sampling rate is less than the Nyquist rate.
Abstract: A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.
Abstract: Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.
Abstract: Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.
Abstract: In this paper, we presented not only development technology of an explosion proof type and portable combustible gas leak detector but also algorithm to improve accuracy for measuring gas concentrations. The presented techniques are to apply the flame-proof enclosure and intrinsic safe explosion proof to an infrared gas leak detector at first in Korea and to improve accuracy using linearization recursion equation and Lagrange interpolation polynomial. Together, we tested sensor characteristics and calibrated suitable input gases and output voltages. Then, we advanced the performances of combustible gaseous detectors through reflecting demands of gas safety management fields. To check performances of two company's detectors, we achieved the measurement tests with eight standard gases made by Korea Gas Safety Corporation. We demonstrated our instruments better in detecting accuracy other than detectors through experimental results.
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: In this paper, a new model order reduction
phenomenon is introduced at the design stage of linear phase digital
IIR filter. The complexity of a system can be reduced by adopting the
model order reduction method in their design. In this paper a mixed
method of model order reduction is proposed for linear IIR filter. The
proposed method employs the advantages of factor division technique
to derive the reduced order denominator polynomial and the reduced
order numerator is obtained based on the resultant denominator
polynomial. The order reduction technique is used to reduce the delay
units at the design stage of IIR filter. The validity of the proposed
method is illustrated with design example in frequency domain and
stability is also examined with help of nyquist plot.
Abstract: Given a bivariate normal sample of correlated variables,
(Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation
coefficient is obtained in terms of the ranges, |Xi − Yi|.
An approximate confidence interval for ρX,Y is then derived, and
a simulation study reveals that the resulting coverage probabilities
are in close agreement with the set confidence levels. As well, a
new approximant is provided for the density function of R, the
sample correlation coefficient. A mixture involving the proposed
approximate density of R, denoted by hR(r), and a density function
determined from a known approximation due to R. A. Fisher is shown
to accurately approximate the distribution of R. Finally, nearly exact
density approximants are obtained on adjusting hR(r) by a 7th degree
polynomial.
Abstract: Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.
Abstract: Let the vertices of a graph such that every two
adjacent vertices have different color is a very common problem in
the graph theory. This is known as proper coloring of graphs. The
possible number of different proper colorings on a graph with a given
number of colors can be represented by a function called the
chromatic polynomial. Two graphs G and H are said to be
chromatically equivalent, if they share the same chromatic
polynomial. A Graph G is chromatically unique, if G is isomorphic to
H for any graph H such that G is chromatically equivalent to H. The
study of chromatically equivalent and chromatically unique problems
is called chromaticity. This paper shows that a wheel W12 is
chromatically unique.
Abstract: Recently, a lot of attention has been devoted to
advanced techniques of system modeling. PNN(polynomial neural
network) is a GMDH-type algorithm (Group Method of Data
Handling) which is one of the useful method for modeling nonlinear
systems but PNN performance depends strongly on the number of
input variables and the order of polynomial which are determined by
trial and error. In this paper, we introduce GPNN (genetic
polynomial neural network) to improve the performance of PNN.
GPNN determines the number of input variables and the order of all
neurons with GA (genetic algorithm). We use GA to search between
all possible values for the number of input variables and the order of
polynomial. GPNN performance is obtained by two nonlinear
systems. the quadratic equation and the time series Dow Jones stock
index are two case studies for obtaining the GPNN performance.
Abstract: New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Abstract: In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.