Related papers: A transformal transcendence result for algebraic d…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
This paper presents a derivation of the possible residual symmetries of rational K-matrices which are invertible in the ''classical limit'' (the spectral parameter goes to infinity). This derivation uses only the boundary Yang-Baxter…
We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup…
In this second part, we study the Diophantine properties of values of arithmetic Gevrey series of non-zero order at algebraic points. We rely on the fact, proved in the first part, that the minimal differential operator (with polynomial…
It is shown that if It is shown that if \begin{equation}\label{abstract_eq} f(z+1)^n=R(z,f),\tag{\dag} \end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $\deg_f(R(z,f))=n$, has an admissible meromorphic…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup…
Let $S$ be a semigroup. Our main results is that we describe the complex-valued solutions of the following functional equations \[g(x\sigma (y)) = g(x)g(y)+f(x)f(y),\ x,y\in S,\] \[f(x\sigma (y)) = f(x)g(y)+f(y)g(x),\ x,y\in S,\] and…
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying…
This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of…
We fix a field $\kk$ of characteristic $p$. For a finite group $G$ denote by $\delta(G)$ and $\sigma(G)$ respectively the minimal number $d$, such that for any finite dimensional representation $V$ of $G$ over $\kk$ and any $v\in…
Let $\mathcal{O}_K$ be a complete discrete valuation ring with field of fractions $K$ and algebraically closed residue field $k.$ Let $G$ be a smooth connected commutative algebraic group over $K$ which does not contain a copy of…
Let $\mathfrak g$ be a simple Lie algebra over an algebraically closed field $\bf k$ of characteristic zero and $\bf G$ its adjoint group. Let $\mathfrak q$ be a biparabolic subalgebra of $\mathfrak g$. The algebra $Sy(\mathfrak q)$ of…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
For a proper subfield $K$ of $\QQ$ we show the existence of an algebraic number $\alpha$ such that no power $\alpha^n$, $n\geq 1$, lies in $K$. As an application it is shown that these numbers, multiplied by convenient Gaussian numbers, can…
Several structural results about permutation groups of finite rank definable in differentially closed fields of characteristic zero (and other similar theories) are obtained. In particular, it is shown that every finite rank definably…
We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e.…
For $\nu\in[0,1]$ and a complex parameter $\sigma,$ $Re\, \sigma>0,$ we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane $z\in\mathbb{C}$: \[…
In this paper, we give a new proof and an extension of the following result of B\'ezivin. Let $f:\B{N}\to K$ be a multiplicative function taking values in a field $K$ of characteristic 0 and write $F(z)=\sum_{n\geq 1} f(n)z^n\in K[[z]]$ for…