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SEQUENCES OF MATRIX INVERSES FROM PASCAL, CATALAN, AND RELATED CONVOLUTION ARRAYS
"... A sequence of sequences 5 / arising from the first column of matrix inverses of matrices containing certain columns of Pascal's triangle provided a fruitful study in [1]. Here, we use convolution arrays of the sequences S / to form a sequence of matrix inverses, leading to interrelationships b ..."
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iPoj, of / every/^column of the convolution array for the sequence So =  1,1,1, J, which is Pascal's triangle. As a second example, the matrix Pii3 would contain every third column of the convolution array for the Catalan sequence Sx written in triangular form. We call the inverse ofPfj the matrix Pj
On Generalizations of the Stirling Number Triangles
, 2000
"... Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinitedimensional lower triangular matrices) of numbers will be denoted by S2(k; n, m) and S1(k; n, m) with k ∈ Z. The original Stirling number triangles of the second and first kind arise w ..."
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Pascal’s triangle, and s2(−1, n, m) turns out to be Catalan’s triangle. Generating functions are given for the columns of these triangles. Each S2(k) and S1(k) matrix is an example of a Jabotinsky matrix. The generating functions for the rows of these triangular arrays therefore constitute exponential
PROSPER K. DOH
"... Abstract: This work is devoted to a systematic investigation of triangular matrix forms of the Pascal Triangle. To start, the twelve matrix forms (collectively referred to as Gmatrices) are presented. To highlight one way in which the Gmatrices relate to each other, a set of four operators named c ..."
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Abstract: This work is devoted to a systematic investigation of triangular matrix forms of the Pascal Triangle. To start, the twelve matrix forms (collectively referred to as Gmatrices) are presented. To highlight one way in which the Gmatrices relate to each other, a set of four operators named
Article 00.2.4 On Generalizations of the Stirling Number Triangles 1
"... Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinitedimensional lower triangular matrices) of numbers will be denoted by S2(k;n,m) and S1(k;n,m) with k ∈ Z. The original Stirling number triangles of the second and first kind arise when ..."
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, and s2(−1,n,m) turns out to be Catalan’s triangle. Generating functions are given for the columns of these triangles. Each S2(k) and S1(k) matrix is an example of a Jabotinsky matrix. The generating functions for the rows of these triangular arrays therefore constitute exponential convolution
INSTITUT DE ROB `OTICA I INFORM `ATICA INDUSTRIAL PREPRINT 1 A BranchandPrune Solver for Distance Constraints
"... Abstract — Given some geometric elements such as points and lines in , subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position ..."
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. The experimental results qualify this approach as a promising one. Index Terms — Kinematic and geometric constraint solving, distance constraint, CayleyMenger determinant, branchandprune, interval method, direct and inverse kinematics, octahedral manipulator. I.
Theoretical Foundations of Equitability and the Maximal Information Coefficient
, 2014
"... The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables [1]. MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important for analyzing ..."
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The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables [1]. MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important for analyzing
Status of StrangenessFlavor Signature of QGP ∗
"... Is the new state of matter formed in relativistic heavy ion collisions the deconfined quark–gluon plasma? We survey the status of several strange hadron observables and discuss how these measurement help understand the dense hadronic matter. PACS numbers: 12.38.Mh,24.10.Pa,25.75.q 1. ..."
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Is the new state of matter formed in relativistic heavy ion collisions the deconfined quark–gluon plasma? We survey the status of several strange hadron observables and discuss how these measurement help understand the dense hadronic matter. PACS numbers: 12.38.Mh,24.10.Pa,25.75.q 1.
Results 1  10
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42