Related papers: On K-semistable domains -- more examples

Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…

We introduce and study a new class of integral domains which we call irreducible divisor pair domains (IDPDs). In particular, we show how IDPDs fit in with other classes of integral domains defined in terms of factorization conditions. For…

We present some results in the analysis of non-compact differential equations on unbounded domains.

We derive a formula for the level spacing probability distribution in quantum graphs. We apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases. Moreover, we derive an…

We study the distribution of integral points on log varieties.

For $m\geq 2$, we study derivations on symbol algebras of degree $m$ over fields with characteristic not dividing $m$. A differential central simple algebra over a field $k$ is split by a finitely generated extension of $k$. For certain…

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is…

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.

Sufficient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-accessible but computable point on a computably compact arc is…

We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…

In this paper we investigate some divisibility properties of Jacobsthal numbers.

Let $k$ be a natural number and $s$ be real. In the 1-dimensional case, the $k$-th order derivatives of the functions $\lvert x\rvert^s$ and $\log \lvert x\rvert$ are multiples of $\lvert x\rvert^{s-k}$ and $\lvert x\rvert^{-k}$,…

Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after…

Let $\clX$ a projective stack over an algebraically closed field $k$ of characteristic 0. Let $\clE$ be a generating sheaf over $\clX$ and $\clO_X(1)$ a polarization of its coarse moduli space $X$. We define a notion of pair which is the…

Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

The logarithmic Chow semistability is a notion of Geometric Invariant Theory for the pair consists of varieties and its divisors. In this paper we introduce a obstruction of semistability for polarized toric manifolds and its toric…

We derive a combinatorial criterion for detecting k-separability of N-partite Dicke states. The criterion is efficiently computable and implementable without full state tomography. We give examples in which the criterion succeeds, where…

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…

The k-satisfiability problem is a well-known task in computational complexity theory. In this paper approach for it's solving is introduced.