Related papers: Linearizing the Word Problem in (some) Free Fields
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form…
We show that if the Sch\"{u}tzenberger graph of every positive word, that contains an $R$-word only once as it's subword, is finite over an Adain presentation $\langle X|u=v\rangle$, then the Sch\"{u}tzenberger graph of every positive word…
We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
Given a finite set of closed rational points of affine space over a field, we give a Gr\"obner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
An explicitly covariant formalism for dealing with Bargmann-Wigner fields is developed. An invariance of the Barmann-Wigner norm can be proved in a unified way for both massive and massless fields. It is shown that there exists some freedom…
For the Alt-Caffarelli problem, we study free boundary regularity of energy minimizers. In six dimensions, we show that free boundaries are analytic for generic boundary data. In general, we improve previous generic Hausdorff dimensions of…
We establish new measures of linear independence of logarithms on commutative algebraic groups in the so-called \emph{rational case}. More precisely, let k be a number field and v_{0} be an arbitrary place of k. Let G be a commutative…
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…
Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be…
A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a…
Over an arbitrary field $\mathbb{F}$, let $p$ and $q$ be monic polynomials with degree $2$ in $\mathbb{F}[t]$. The free Hamilton algebra of the pair $(p,q)$ is the free noncommutative algebra in two generators $a$ and $b$ subject only to…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is…
An optimum solution free from degeneration is found to the system of linear algebraic equations with empirical coefficients and right-hand sides. The quadratic risk of estimators of the unknown solution vector is minimized over a class of…
This paper revisits the solution of the word problem for $\omega$-terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCammond's algorithm, based on normal forms for such…
A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i.e., $L=\{f(n)\mid n\in \mathbb N\}\subset\mathbb N$. We show that the base-$q$ representation of $L$ is a context-free language if…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…