Related papers: n-Linear Algebra of type II
In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to…
We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…
Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was…
This book has seven chapters. In Chapter one, an elaborate recollection of Smarandache structures like S-semigroups, S-loops, and S-groupoids is given. It also gives notions about N-ary algebraic stuctures and their Smarandache analogue,…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial…
This thesis is divided into two parts. The first one is composed of recollections on operad theory, model categories, simplicial homotopy theory, rational homotopy theory, Maurer-Cartan spaces, and deformation theory. The second part deals…
Over the years, integer linear programs have been employed to model inference in many natural language processing problems. This survey is meant to guide the reader through the process of framing a new inference problem as an instance of an…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…
In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…