Related papers: On the Dimension Theory of Polynomial Rings over P…
In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.
In this paper, we define and study a notion of Ding projective dimension for complexes of left modules over associative rings. In particular, we consider the class of homologically bounded below complexes of left R-modules, and show that…
The ring of integer-valued polynomials on an arbitrary integral domain is well-studied. In this paper we initiate and provide motivation for the study of integer-valued polynomials on commutative rings and modules. Several examples are…
We review the status of low-scale string theories and large extra-dimensions. After an overview on different string realizations, we discuss some of the main important problems and we summarize present bounds on the size of possible…
This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers…
We consider orthogonal polynomials on the surface of a double cone or a hyperboloid of revolution, either finite or infinite in axis direction, and on the solid domain bounded by such a surface and, when the surface is finite, by…
The physical motivations and the basic construction rules for Type I strings and M-theory compactifications are reviewed in light of the recent developments. The first part contains the basic theoretical ingredients needed for building…
In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every $i\geq 0$, $\Ppoly$ has $i$th order scaled $\pthree$-strong dimension 0. We also show that $\Ppoly^\io$ has…
Recently, P. Yuan presented a local method to find permutation polynomials and their compositional inverses over finite fields. The work of P. Yuan inspires us to compute the compositional inverses of three classes of the permutation…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
We develop a new technique for studying monomial ideals in the standard polynomial rings $A[X_1,\ldots,X_d]$ where $A$ is a commutative ring with identity. The main idea is to consider induced ideals in the semigroup ring…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We study the behaviour of principal bundles under pullback along proper surjective morphisms of either schemes over an algebraically closed field of characteristic 0 or complex analytic spaces.
In this lecture moduli dependent charges for p-extended objects are analyzed for generic N-extended supergravities in dimensions 4 \leq D <10. Differential relations and sum rules among the charges are derived.
We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce…
Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.