Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Neutrosophic logic (4)
- Algebraic structures (1)
- Burkholder (1)
- Finite complex modulo numbers (1)
- Groupoid (1)
-
- Lattice theory (1)
- Martingale transform (1)
- Matrices (1)
- Matrix algebra (1)
- Natural class of intervals (1)
- Neutrosophic theory (1)
- Non associative algebraic structures (1)
- Non associative linear algebra (1)
- Non associative vector spaces (1)
- Number theory (1)
- Riesz transforms (1)
- Sharp constant (1)
- Special quasi dual number (1)
- Supermodular lattices (1)
Articles 1 - 7 of 7
Full-Text Articles in Other Mathematics
Innovative Uses Of Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, Indra Venkatbabu
Innovative Uses Of Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, Indra Venkatbabu
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors bring out the innovative applications of matrices defined, described and developed by them. Here they do not include the natural product on matrices newly described and defined by them in the book on ‘natural product ×n on matrices’.
This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. We construct three types of matrices called Average Time Dependent data matrix (ATD matrix), Refined Time Dependent Data matrix (RTD matrix) and Combined Effective Time …
Perturbation Of Burkholder's Martingale Transform And Monge-Ampère Equation, Nicholas Boros, Prabhu Janakiraman, Alexander Volberg
Perturbation Of Burkholder's Martingale Transform And Monge-Ampère Equation, Nicholas Boros, Prabhu Janakiraman, Alexander Volberg
Faculty Scholarship – Mathematics
Given a sequence of martingale differences, Burkholder found the
sharp constant for the Lp-norm of the corresponding martingale transform. We
are able to determine the sharp Lp-norm of a small "quadratic perturbations"
of the martingale transform in Lp. By "quadratic perturbation" of the martin-
gale transform we mean the Lp norm of the square root of the squares of the
martingale transform and the original martingale (with small constant). The
problem of perturbation of martingale transform appears naturally if one wants
to estimate the linear combination of Riesz transforms (as, for example, in the
case of Ahlfors{Beurling operator).
Supermodular Lattices, Florentin Smarandache, Iqbal Unnisa, W.B. Vasantha Kandasamy
Supermodular Lattices, Florentin Smarandache, Iqbal Unnisa, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In lattice theory the two well known equational class of lattices are the distributive lattices and the modular lattices. All distributive lattices are modular however a modular lattice in general is not distributive.
In this book, new classes of lattices called supermodular lattices and semi-supermodular lattices are introduced and characterized as follows: A subdirectly irreducible supermodular lattice is isomorphic to the two element chain lattice C2 or the five element modular lattice M3. A lattice L is supermodular if and only if L is a subdirect union of a two element chain C2 and the five element modular lattice M3.
Special Quasi Dual Numbers And Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy
Special Quasi Dual Numbers And Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce a new notion called special quasi dual number, x = a + bg.
Among the reals – 1 behaves in this way, for (– 1)2 = 1 = – (– 1). Likewise –I behaves in such a way (– I)2 = – (– I). These special quasi dual numbers can be generated from matrices with entries from 1 or I using only the natural product ×n. Another rich source of these special quasi dual numbers or quasi special dual numbers is Zn, n a composite number. For instance 8 in Z12 is such that …
Non Associative Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy
Non Associative Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of non associative vector spaces and non associative linear algebras over a field. We construct non associative space using loops and groupoids over fields. In general in all situations, which we come across to find solutions may not be associative; in such cases we can without any difficulty adopt these non associative vector spaces/linear algebras. Thus this research is a significant one.
This book has six chapters. First chapter is introductory in nature. The new concept of non associative semilinear algebras is introduced in chapter two. This structure is …
Non Associative Algebraic Structures Using Finite Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy
Non Associative Algebraic Structures Using Finite Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Authors in this book for the first time have constructed nonassociative structures like groupoids, quasi loops, non associative semirings and rings using finite complex modulo integers. The Smarandache analogue is also carried out. We see the nonassociative complex modulo integers groupoids satisfy several special identities like Moufang identity, Bol identity, right alternative and left alternative identities. P-complex modulo integer groupoids and idempotent complex modulo integer groupoids are introduced and characterized. This book has six chapters. The first one is introductory in nature. Second chapter introduces complex modulo integer groupoids and complex modulo integer loops.
Exploring The Extension Of Natural Operations On Intervals, Matrices And Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy
Exploring The Extension Of Natural Operations On Intervals, Matrices And Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
This book extends the natural operations defined on intervals, finite complex numbers and matrices. The intervals [a, b] are such that a ≤ b. But the natural class of intervals [a, b] introduced by the authors are such that a ≥ b or a need not be comparable with b. This way of defining natural class of intervals enables the authors to extend all the natural operations defined on reals to these natural class of intervals without any difficulty. Thus with these natural class of intervals working with interval matrices like stiffness matrices finding eigenvalues takes the same time as …