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Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
Aleksandra Lj. Erić,
Zoran S. Pucanović
Issue:
Volume 2, Issue 2, April 2013
Pages:
51-55
Abstract: Let be a commutative ring with identity and its total graph. The subject of this article is the investigation of the properties of the corresponding line graph In particular, we determine the girth and clique number of In addition to that, we find the condition for to be Eulerian.
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Partial Derivatives of Some Types of Two-Variables Functions
Issue:
Volume 2, Issue 2, April 2013
Pages:
56-61
Abstract: This paper mainly studies the evaluation of partial derivatives of four types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these four types of functions by using differentiation term by term theorem, and hence reducing the difficulty of calculating their higher order partial derivative values greatly. On the other hand, we propose four functions of two-variables to evaluate their any order partial derivatives, and some of their higher order partial derivative values practically. At the same time, we employ Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms for verifying our answers.
Abstract: This paper mainly studies the evaluation of partial derivatives of four types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these four types of functions by using differentiation term by term theorem, and hence reducing the difficulty of calculating their higher order partial derivative valu...
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Generating Functions for Generalized Mock Theta Functions
Issue:
Volume 2, Issue 2, April 2013
Pages:
62-70
Abstract: We consider generalized mock theta functions and give generating functions for the partial generalized mock theta functions.
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Time-Frequency Analysis and Harmonic Gaussian Functions
Tokiniaina Ranaivoson,
Raoelina Andriambololona,
Rakotoson Hanitriarivo
Issue:
Volume 2, Issue 2, April 2013
Pages:
71-78
Abstract: A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted T_n, which associate to a function ψ, of the time variable t, a set of functions Ψ_n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations T_n and the functions Ψ_n are given. It is proved in particular that the square of the modulus of each function Ψ_n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ_n.
Abstract: A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted T_n, which associate to a func...
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Geometric Series of Numbers Approximating Positive Integers
Issue:
Volume 2, Issue 2, April 2013
Pages:
79-93
Abstract: The predictability of cycles in the series of Pythagorean triples led to an investigation that yielded numbers (x) that are associated with irrational square roots (√n). The cycles recur with geometric factors (cycle factors y) that are comprised of a positive integer x where y = x + √(x^2±1). On raising the cycle factors to the positive integer powers (ym), a series is generated where each consecutive member comes closer and closer to positive integers as the series progresses. A formula associates the square root (√n) with these series. Prime factorising the positive integers in the power series (xm) produces predictable patterns among the prime factors in the series. In general, power series that have each consecutive member in the series come closer to positive integers are limited to (x + √(x^2±r))m where x and r are positive integers and r < (x + 1)2 – x2 for the + r condition and r < x2 – (x – 1)2 for the – r condition.
Abstract: The predictability of cycles in the series of Pythagorean triples led to an investigation that yielded numbers (x) that are associated with irrational square roots (√n). The cycles recur with geometric factors (cycle factors y) that are comprised of a positive integer x where y = x + √(x^2±1). On raising the cycle factors to the positive integer po...
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Analysis of M/G/1 Queue Model with Priority
Issue:
Volume 2, Issue 2, April 2013
Pages:
94-97
Abstract: Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.
Abstract: Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the gener...
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Sub Hilbert Spaces in a Bi-Disk
Niteesh Sahni,
Niteesh Sahni
Issue:
Volume 2, Issue 2, April 2013
Pages:
98-100
Abstract: Recently, Sahni and Singh [7] have solved an open problem posed by Yousefi and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables.
Abstract: Recently, Sahni and Singh [7] have solved an open problem posed by Yousefi and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two va...
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Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems
Issue:
Volume 2, Issue 2, April 2013
Pages:
101-105
Received:
2 May 2013
Published:
20 May 2013
Abstract: Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.
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Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
Issue:
Volume 2, Issue 2, April 2013
Pages:
106-109
Received:
21 April 2013
Published:
30 May 2013
Abstract: In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained
