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576,617
Finite Sequences and Tuples of Elements of a Nonempty Sets
, 1990
"... this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D ..."
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Cited by 330 (7 self)
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this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D
The definition of finite sequences and matrices of . . .
, 2006
"... In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form. ..."
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In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.
Long Finite Sequences
, 1998
"... Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large ..."
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Cited by 10 (3 self)
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Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly
Computing with Hereditarily Finite Sequences
"... Abstract. We use Prolog as a flexible metalanguage to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects (rooted ordered trees representing hereditarily ..."
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finite sequences and rooted ordered binary trees representing Gödel’s System T types). This paper focuses on an application that can be seen as an unexpected “paradigm shift”: we provide recursive definitions showing that the resulting representations are directly usable to perform symbolically
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
Optimal control of autonomous linear systems switched with a preassigned finite sequence
 In Proceedings of the 2001 IEEE International Symposium on Intelligent Control
, 2001
"... finite sequence ..."
The Infinite Hidden Markov Model
 Machine Learning
, 2002
"... We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. Th ..."
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Cited by 638 (41 self)
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. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying statetransition matrix, and the expected number of distinct hidden states in a finite
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 585 (8 self)
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This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures
Shift Equivalence of Pfinite Sequences
"... We present an algorithm which decides the shift equivalence problem for Pfinite sequences. A sequence is called Pfinite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shifting one of the sequences s times makes it ..."
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We present an algorithm which decides the shift equivalence problem for Pfinite sequences. A sequence is called Pfinite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shifting one of the sequences s times makes
Irregularities in the Distributions of Finite Sequences
, 1968
"... Suppose (x1, x1,..., xs+J is a sequence of numbers with xi E [0, 1) which has the property that for each r < s and for each k < r, the subinterval [k/r, (k + l/n)) contains at least one point of the subsequence (xl, xz,..., x7*). For fixed d, we wish to find the maximum s = s(d) for which such ..."
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Cited by 3 (3 self)
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the following finite variant of this problem: For n 3 1,0 < k < n, define k k+l B n,k = I y,. n 1 Fix an integer d 3 0 and suppose (x1, xg,..., x,+,J is a sequence with xi E [0, 1) and with s = s(d) chosen to be maximal such that for each r Q s and each k < r, BrPk contains at least one point
Results 1  10
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576,617