Related papers: Proofs for Folklore Theorems on the Radon-Nikodym …
Recently, Voros has found the sums involving certain powers of z-1/2, which, when taken over Riemann xi-function zeroes /rho, must be positive for the Riemann hypothesis holds true and vice versa. Here we analyze these sums, write them as…
In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of…
We show that the use of Brylinski's Radon transform elucidates some points of the Green-Griffiths approach to the Hodge conjecture.
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
Traces $\Phi$ on von Neumann algebras with values in complex order complete vector lattices are considered. The full description of these traces is given for the case when $\Phi$ is the Maharam trace. The version of Radon-Nikodym-type…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using…
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
Riddles based on simple puns can be classified according to the patterns of word, syllable or phrase similarity they depend upon. We have devised a formal model of the semantic and syntactic regularities underlying some of the simpler types…
Urban legends are a genre of modern folklore, consisting of stories about rare and exceptional events, just plausible enough to be believed, which tend to propagate inexorably across communities. In our view, while urban legends represent a…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
This article presents a pedagogical probabilistic exploration of the Newton-Girard identities. We show that the coefficients in these classical relations between power sums and elementary symmetric polynomials can be interpreted as the…
There is a lot of statistical researches of Russian elections 04.12.2011. The purpose of this activity is to give a mathematical proof of large falsifications and to estimate possible 'real results of elections'. My purpose is to show that…
We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for…
Consistency conditions for nonminimally coupled $f(R)$ theories have been derived by requiring the absence of tachyons and instabilities in the scalar fluctuations. This note confirms these results and clarifies a subtlety regarding…
In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the…
A characterization is presented of barycenters of the Radon probability measures supported on a closed convex subset of a given space. A case of particular interest is studied, where the underlying space is itself the space of finite signed…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].