We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic der...

The aim in a constraint satisfaction problem (CSP) is to find an assignment of values to a given set of variables, subject to constraints on the values which can be assigned simultaneously to certain specified subsets of variables. CSPs are used to model a wide variety of computational problems in computer science, discrete mathematics, artificial intelligence, and elsewhere, and they have foun...

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in maximal group. classify groups, and their subgroups rational points, up to conjugacy by birational map.

Abstract The modular operator approach of Tomita–Takesaki to von Neumann algebras is elucidated in the algebraic structure certain supersymmetric (SUSY) quantum mechanical systems. A algebra constructed from operators system. An explicit characterizing dual infinite degeneracy a SUSY two dimensional system given by conjugation operator. Furthermore, entanglement formation for these systems usin...

An algebraic approach is developed to define and study infinite dimensional grassmannians. Using this approach a quantum deformation is obtained for both the ind-variety union of all finite dimensional grassmannians G∞, and the Sato grassmannian ̃ UGM introduced by Sato in [Sa1], [Sa2]. They are both quantized as homogeneous spaces, that is together with a coaction of a quantum infinite dimensi...

An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic combinatorial properties are investigated. They turn out be balanced, some recurrence formulas among them derived.

It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary duals. In this paper we illustrate the new theory by exhibiting its implications for the cycle and bond matroids of infinite graphs. We also describe their algebr...

In this paper we discuss about algebraic calculus from the tensors. Some of basic problems are lying to basics nature that underlying space with geometry. We made survey certain instance finite dimensional spaces also covers infinite vector spaces.

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...