Related papers: Algebraic dependences and uniqueness problem of me…

We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.

We classify noninvertible, holomorphic selfmaps of the projective plane that preserve an algebraic web. In doing so, we obtain interesting examples of critically finite maps.

We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed hyperplane and have bounded height. This work constitutes a direct extension of the results obtained…

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for…

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f.

In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on…

In this paper we construct an entire function of two variables having the property that its values and its partial derivatives of any order at any distinct algebraic points are algebraically independent. Such an entire function is generated…

We study the (in)dependence of additivity and homogeneity conditions in the definition of linear mappings between vector spaces over the same scalar field. Unlike other works on the subject, dealing with particular fields like real or…

A number of results are proved concerning the existence of non-real zeros of derivatives of strictly non-real meromorphic functions in the plane.

Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…

Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it…

In this paper which is the completion of [1], we construct the $A_0(q)$-algebra of $Q$-meromorphic functions on the quantum plane. This is the largest non-commutative, associative, $A_0(q)$-algebra of functions constructed on the quantum…

We study meromorphic jacobian pairs, i.e., pairs of polynomials in one variable, with coefficients meromorphic series in a second variable, whose jacobian relative to the two variables depends only on the second variable. We pose two…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

In this paper, we investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…

We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify…