Given an integer m ≥ 1, let ‖·‖ be a norm in R and let S+ denote the set of points d = (d0, . . . , dm) in R with nonnegative coordinates and such that ‖d‖ = 1. Consider for each 1 ≤ j ≤ m a function fj(z) that is analytic in an open neighborhood of the point z = 0 in the complex plane and with possibly negative Taylor coefficients. Given n = (n0, . . . , nm) in Z with nonnegative coordinates, ...

Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete latt...

By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demjanenko [L3] states that, for a quasiminimal model of E over K, this number is bounded by a constant depending only on the rank of E over K and on K (see also [HSi], [Zi4]). This conjecture was proved by Silverman [Si1] for elliptic curv...

BACKGROUND The morphology and polarity of the P wave on 12-lead ECG are of limited clinical value in localizing ectopic atrial rhythms. It was the aim of this study to assess the spatial resolution of body surface P-wave integral mapping in identifying the site of origin of ectopic right atrial (RA) impulse formation in patients without structural atrial disease. METHODS AND RESULTS Sixty-two...

The so-called Bercovici-Pata bijection maps the set of classical infinitely divisible laws to the set of free infinitely divisible laws. The purpose of this work is to study the free infinitely divisible laws corresponding to the classical Generalized Gamma Convolutions (GGC). Characterizations of their free cumulant transforms are derived as well as free integral representations with respect t...

We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generi...

Sugeno integral is one of the basic aggregation operations on a qualitative scale where only minimum and maximum, as well as order-reversing maps are allowed. Recently some variants of this aggregation operation, named soft and drastic integrals, have been introduced in a previous work by three of the authors. In these operations, importance weights play the role of tolerance thresholds enablin...

Let μ be a non-negative Radon measure on R which only satisfies the polynomial growth condition. Let Y be a Banach space and H(μ) the Hardy space of Tolsa. In this paper, the authors prove that a linear operator T is bounded from H(μ) to Y if and only if T maps all (p, γ)-atomic blocks into uniformly bounded elements of Y; moreover, the authors prove that for a sublinear operator T bounded from...

We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with four-point integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps. Full text

We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact expression for the differential operator with respect to the commuting variables which results from Berezin integration over all Grassmann variables. Also, we der...