We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the "quotient," which was the key assumption in the original proof of (Olkin-Rubin in Ann Math Stat 33:1272-1280, 1962). Inst...
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We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the "quotient," which was the key assumption in the original proof of (Olkin-Rubin in Ann Math Stat 33:1272-1280, 1962). Instead, we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) "quotient" for any division algorithm satisfying some natural conditions. For that purpose, a new proof of the Olkin-Baker functional equation on symmetric cones is given.
In this paper, the definitions of quasi-orthogonal idempotent sequences and Iq-dimensions of a ring R are given. The relations between Iq-dimensions and block decomposition numbers of a ring are discussed. As a genera...
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In this paper, the definitions of quasi-orthogonal idempotent sequences and Iq-dimensions of a ring R are given. The relations between Iq-dimensions and block decomposition numbers of a ring are discussed. As a generalization of monic polynomials, the concept of quasi-monic polynomials over a ring is introduced. It is shown that, for a quasi-monic polynomial over a ring, the division algorithm holds. Suslin Lemma and Horrocks' Theorem are extended to the setting of quasi-monic polynomials. For a commutative ring R, if f(x) is a quasi-monic polynomial in R[x], then GD(R) = GD(R[x]/f(x)) is proved, where GD(R) denotes the global dimension of R.
The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended m...
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The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended matrix-variate beta distributions. Some fundamental properties of these distributions are established. We show that using a linear transformation on the extended matrix-variate beta distributions of the first and second kind, we can generalize these distributions. We also show that the distribution of the sum of two independent inverse Riesz matrices introduced by Tounsi and Zine (J Multivar Anal 111:174-182, 2012) can be written in terms of the generalized extended matrix-variate beta function. Finally, using Fixed point iterative method, we provide a calculable maximum a posteriori (MAP) estimator for the unknown covariance matrix of a multivariate normal distribution based on the class of the extended matrix-variate beta prior distribution. Additionally, we evaluated the Gaussian finite sample performance by calculating such evaluation criteria as Mean Square Error (MSE) and Hilbert-Schmidt distance (DHS). The obtained results confirm the performance of the proposed prior.
In this paper. we introduce the Riesz-Dirichlet distribution on a symmetric cone as an extension of the Dirichlet distribution defined by the Wishart distribution. We also show that some projections of these distribut...
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In this paper. we introduce the Riesz-Dirichlet distribution on a symmetric cone as an extension of the Dirichlet distribution defined by the Wishart distribution. We also show that some projections of these distributions related to the Pierce decomposition are also Dirichlet. (c) 2008 Elsevier Inc. All rights reserved.
In his youth, John Reynolds showed a talent for arithmetic and was destined for a career as a mathematician at the Tower Mint in London. He became skilled in the algorithms needed to determine the correct relationship...
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In his youth, John Reynolds showed a talent for arithmetic and was destined for a career as a mathematician at the Tower Mint in London. He became skilled in the algorithms needed to determine the correct relationship between the weight and purity of coins and their values. This was a matter of national importance, and his work came to the attention of King James I, who reigned from 1603 to 1625, and his chief ministers, including Robert Cecil and Francis Bacon. It seemed that John might attain high office himself, but the murky administration of the early Stuart period cast its shadow over his career. Nevertheless, for the next forty years he continued to play a major part in the nation's affairs. He produced books of tables for the valuation of coins in the commercial world, and for the highly technical work of the assayers. Also, he was actively involved in the production of standard measures and instruments used by the excise officers. His life and works illustrate how mathematical ideas were employed by the English government in the period of the early Stuart kings and the Commonwealth. (C) 2018 Elsevier Inc. All rights reserved.
In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let X and Y be independent, non-degenerate random variables with values in (0, 1), then U = 1 - XY and V = ...
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In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let X and Y be independent, non-degenerate random variables with values in (0, 1), then U = 1 - XY and V = 1-X/U are independent if and only if there exist positive numbers p(i), i = 1, 2, 3, such that X and Y follow beta distributions with parameters (p(1) + p(3), p(2)) and (p(3), p(1)), respectively. (C) 2015 Elsevier Inc. All rights reserved.
Let I subset of K[x(1),..., x(n)] be an ideal and G be the reduced Grobner basis of I with respect to lexicographic monomial order. We introduce the index of an expression of fK[x(1),..., x(n)] with respect to G. A mi...
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Let I subset of K[x(1),..., x(n)] be an ideal and G be the reduced Grobner basis of I with respect to lexicographic monomial order. We introduce the index of an expression of fK[x(1),..., x(n)] with respect to G. A minimal expression is characterized as the one with zero G-index. In case where I is a binomial prime ideal, a new division algorithm with minimal and unique expression is presented. The application of our new method on benchmark polynomial systems cyclic-9 and cyclic-12 shows its superiority in comparison with the existing division algorithm.
In this paper we generalize the fundamental equation of information to the symmetric cone domain and find the general solution under the assumption of continuity of the respective functions.
In this paper we generalize the fundamental equation of information to the symmetric cone domain and find the general solution under the assumption of continuity of the respective functions.
The Riesz distributions on a symmetric cone are used to introduce a class of beta-Riesz distributions. Some fundamental properties of these distributions are established. In particular, we study the effect of a projec...
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The Riesz distributions on a symmetric cone are used to introduce a class of beta-Riesz distributions. Some fundamental properties of these distributions are established. In particular, we study the effect of a projection on a beta-Riesz distribution and we give some properties of independence. We also calculate the expectation of a beta-Riesz random variable. As a corollary, we give the regression on the mean of a Riesz random variable;that is, we determine the conditional expectation E(U broken vertical bar U + V) where U and V are two independent Riesz random variables. (c) 2004 Elsevier B.V. All rights reserved.
Elementary mathematics, for instance, algebraic equations is an important field of study in higher education. In particular, graphical representations of curves of equations make the understanding of mathematical prob...
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ISBN:
(纸本)9780889866508
Elementary mathematics, for instance, algebraic equations is an important field of study in higher education. In particular, graphical representations of curves of equations make the understanding of mathematical problem easy for students. Therefore, we have developed a web-based education system with a graphics database for elementary mathematics, particularly, algebraic equations. In this paper, the analytical properties of quadratic and cubic algebraic equations are discussed on the basis of the Sturm concept because of its educational value and usefulness in analyzing and designing a real system. Some graphical representations utilized for the web-based education system of algebraic equations are shown. An intranet e-learning system constructed in our laboratory on a Linux web-server (Apache HTTP server) is presented.
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