Related papers: The Multiplicative Kowalski-Slodkowski Theorem for…

There has been a recent interest in hierarchical generalisations of classic incompleteness results. This paper provides evidence that such generalisations are readibly obtainable from suitably hierarchical versions of the principles used in…

The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory that algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes…

Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.

In this paper, we prove that every iterative differential embedding problem over an algebraic function field in positive characteristic with an algebraically closed field of constants has a proper solution.

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…

A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form $\omega$, for which the bilinear form $\omega(I\cdot,\cdot)$ is positive definite. In this work we prove $dd^c$-lemma for 1- and (1,1)-forms for compact…

Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems,…

Subregular W-algebras are an interesting and increasingly important class of quantum hamiltonian reductions of affine vertex algebras. Here, we show that the $\mathfrak{sl}_{n+1}$ subregular W-algebra can be realised in terms of the…

In this paper, we prove that every continuous $h$-mid-convex with suitable conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem, Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.

In this work we study three topologies defined over the same set: the hedgehog. As the name suggests, the hedgehog can be described as a set of spines identified at a single point. Among others, we give a proof of the Kowalsky hedgehog…

A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We…

Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$, $\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of $\omega_0$. We prove that for a complex polarization of $\omega$ there exists a commutative…

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in…

We prove that no separable Banach algebra is universal for homomorphic embeddings of all separable Banach algebras, whether embeddings are merely bounded or required to be contractive. The same holds in the commutative category. The proof…

We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term…

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime…

This paper proves a commutative algebraic extension of a generalized Skolem-Mahler-Lech theorem due to the first author. Let $A$ be a finitely generated commutative $K$-algebra over a field of characteristic $0$, and let $\sigma$ be a…

Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on a Banach ideal space E and three…

Consider a finite dimensional complex Hilbert space $\cH$, with $dim(\cH) \geq 3$, define $\bS(\cH):= \{x\in \cH \:|\: ||x||=1\}$, and let $\nu_\cH$ be the unique regular Borel positive measure invariant under the action of the unitary…