Related papers: The Bertini involution
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…
In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These…
In this paper we generalize the approximation theorem for L^2-Betti numbers to an approximation theorem for center-valued Betti-numbers.
A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where…
The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein polynomials by the $r$th Ditzian-Totik modulus of smoothness $\omega_\phi^{r}(f,t)_w$ where $\phi$ is…
In a recent paper the authors studied the denominators of polynomials that represent power sums by Bernoulli's formula. Here we extend our results to power sums of arithmetic progressions. In particular, we obtain a simple explicit…
Recently we have extended our the "unified" model of evolutionary ecology to incorporate the {\it spatial inhomogeneities} of the eco-system and the {\it migration} of individual organisms from one patch to another within the same…
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
In the current note we extend results by Marmi, Moussa and Yoccoz about cohomological equations for interval exchange transformations to irreducible linear involutions.
In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.
We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…
We give an explicit expression for the invariant measure, absolutely continuous with respect to the Lebesgue measure, of the greedy beta-transformation with three deleted digits. We define a version of the natural extension of the…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural…
In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.
Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative B\"acklund chart, generalizing results in [Fuchssteiner B., Carillo S.,…
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…