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- P-ISSN1226-0657
- E-ISSN2287-6081
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ISSN : 1226-0657
Vol.11 No.1
Abstract
Due to the development of computer network and mobile communications, the security in image data and other related source are very important as in saving or transferring the commercial documents, medical data, and every private picture. Nonetheless, the conventional encryption algorithms are usually focusing on the word message. These methods are too complicated or complex in the respect of image data because they have much more amounts of information to represent. In this sense, we proposed an efficient secret symmetric stream type encryption algorithm which is based on Boolean matrix operation and the characteristic of image data.
Abstract
In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX> where <TEX>${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;<TEX>$\mid$</TEX>p<TEX>$\mid$</TEX>\;{\geq}\;1$</TEX>, and the initial conditions <TEX>$x_{-1}\;and\;x_0$</TEX> are arbitrary positive real numbers.
Abstract
We calculate dim <TEX>$\hat{A}$</TEX> which is a completion of a Noetherian ring A with respect to I-adic topology. We do not use localization but power series techniques.
Abstract
Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let <TEX>$\cal{L}$</TEX> be a subspace lattice on a Hilbert space <TEX>$\cal{H}$</TEX>. Let x and ｙ be vectors in <TEX>$\cal{H}$</TEX> and let <TEX>$P_x$</TEX>, be the projection onto sp(x). If <TEX>$P_xE=EP_x$</TEX> for each <TEX>$ E \in \cal{L}$</TEX> then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in (<TEX>$sp(x)^\perp$</TEX>) and <TEX>$A=-A^\ast$</TEX>. (2) (equation omitted)
Abstract
We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.
Abstract
We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.
Abstract
It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, <TEX>$\cal{l}\geq2$</TEX>, of repetitions. It is shown that the <TEX>$(\cal{l}+1)$</TEX>-adic expansion is the only such representation possible.
Abstract
A punctured torus <TEX>$\Sigma(1,1)$</TEX> is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let <TEX>$\cal{C}$</TEX> be a matrix presentation of the boundary component of <TEX>$\Sigma(1,1)$</TEX>.In the level of the matrix group <TEX>$\mathbb{SL}$</TEX>(<TEX>$\mathbb2,R$</TEX>) we shall show that the trace of <TEX>$\cal{C}$</TEX> is always negative.
Abstract
We prove de Leeuw's restriction theorem result Jodeit, Jr. [4] for multipliers on <TEX>$H^{p}$</TEX> spaces, p＜1.
Abstract
In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛<TEX>$X_n,n\qeq1$</TEX>｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F(<TEX>$chi$</TEX>) and probability density function(pdf) f(<TEX>$chi$</TEX>). Let <TEX>$Y_n\;=\;mas{X_1,X_2,...,X_n}$</TEX> for <TEX>$ngeq1$</TEX>. We say <TEX>$X_{j}$</TEX> is an upper record value of {<TEX>$X_{n},n\geq1$</TEX>}, if <TEX>$Y_{j}$</TEX>＞<TEX>$Y_{j-1}$</TEX>,j＞1. The indices at which the upper record values occur are given by the record times <TEX>${u( n)}n,\geq1$</TEX>, where u(n) = min{j｜j ＞u(n-l), <TEX>$X_{j}$</TEX>＞<TEX>$X_{u(n-1)}$</TEX>,n\qeq2$</TEX> and u(l) = 1. Suppose <TEX>$X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$</TEX> then E<TEX>$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$</TEX> E<TEX>$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$</TEX> - <TEX>$\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$</TEX> and E<TEX>$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$</TEX> = <TEX>$\frac{1}{(r+1)\beta}$</TEX> [E<TEX>$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$</TEX> - E<TEX>$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$</TEX> - (r+1)E<TEX>$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$</TEX>]