Related papers: Partial regularities and $a^*$-invariants of Borel…

Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of…

We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the…

In this paper we consider some properties of a space B(X) of Borel functions on a set of reals X, with pointwise topology, that are stronger than separability.

The main purpose of this paper is to construct *-representations from unbounded C$^*$-seminorms on partial *-algebras and to investigate their *-representations.

Irreducibility results for parabolic induction of representations of the general linear group over a local non-archimedean field can be formulated in terms of Kazhdan--Lusztig polynomials of type $A$. Spurred by these results and some…

We introduce an invariant of varieties in positive characteristic which generalizes the a-number of an abelian variety. We calculate it in some examples and discuss its meaning for moduli.

Let $\mathfrak a$ be an ideal of holomorphic functions vanishing only at the origin in $\mathbb{C}^n$. The \textit{type} of $\mathfrak a$ is an invariant that measures the order of vanishing of the functions in $\mathfrak a$ along…

We introduced an $\tilde{\mathcal{A}}$-invariant for quasi-ordinary parameterizations and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low…

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…

We first present an intersection theory of partial differential varieties with quasi-generic differential hypersurfaces. Then based on the generic intersection theory, we define the partial differential Chow form for an irreducible partial…

We obtain the $C^{\a}$ regularity for weak solutions of a class of non-homogeneous ultraparabolic equation, with measurable coefficients. The result generalizes our recent $C^{\a}$ regularity results of homogeneous ultraparabolic equation.

It has recently been claimed that the inclusion of a Pauli term in (2+1) dimensions gives rise to a new type of anomalous spin term. The form of that term is shown to contradict the structure relations for the inhomogeneous Lorentz group.

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

We classify Borel-Schur algebras having finite representation type. We also de- termine Auslander-Reiten sequences for a large class of simple modules over Borel- Schur algebras. A partial information on the structure of the socles of…

We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel ideal to be on such a component. Then considering ACM curves…

In an earlier work, the author observed that Boolean inverse semi-groups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of…

When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal polynomials is expected to have different properties…