相关论文: Series with general exponents
The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.
Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear…
Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and…
A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…
We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…
In recent years, averaging operators on Lie algebras (also called embedding tensors in the physics literature) and associated tensor hierarchies form an efficient tool for constructing supergravity and higher gauge theories. A Lie algebra…
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
Let R be a commutative ring with identity and M be an R- module. The aim of this paper is to introduce and investigate the notions of nil-M-Noetherian and nil-M-Artinian modules as generalizations of Noetherian and Artinian modules. Also,…
Resco and Small gave the first example of an affine Noetherian algebra which is not finitely presented. It is shown that their algebra has no finite-dimensional filtrations whose associated graded algebras are Noetherian, affirming their…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…