Related papers: On generalized series fields and exponential-logar…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…
We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…
Some exact solutions for the Einstein field equations corresponding to inhomogeneous $G_2$ cosmologies with an exponential-potential scalar field which generalize solutions obtained previously are considered. Several particular cases are…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
An integral basis of the simplest number fields of degree 3,4 and 6 over $\mathbb{Q}$ are well-known, and widely investigated. We generalize the simplest number fields to any degree, and show that an integral basis of these fields is…
We discuss certain special cases of algebraic approximants that are given as zeroes of so-called "effective characteristic polynomials" and their generalization to a multiseries setting. These approximants are useful for the convergence…
We study a class of tame $\mathcal{L}$-theories $T$ of topological fields and their $\mathcal{L}_\delta$-extension $T_{\delta}^*$ by a generic derivation $\delta$. The topological fields under consideration include henselian valued fields…
In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…
Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection del) which uses the…
The coeffective differential complex on a symplectic manifold is extended both in length and in scope, unifying the constructions of various other authors.
We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…