Search results for " Integra"

Integration of functions ranging in complex Riesz space and some applications in harmonic analysis

2015

The theory of Henstock—Kurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.

Generalized Henstock integrals in the theory of series in multiplicative systems

2004

Properties of a Henstock type integral defined by means of a differential basis generated by P-adic paths ae studied. It is proved that this integral solves the problem of coefficients reconstruction by using generalized Fourier formulas for a series over multiplivative systems.

MR2886259 Naralenkov, Kirill Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions. Czechoslovak Math. J. 61(136…

2012

In this paper the author essentially discusses the difference between the Henstock-Kurzweil and McShane integrals of vector-valued functions from the descriptive point of view. He first considers three notions of absolute continuity for vector-valued functions AC, AC*, AC_{\delta}) and studies the relationships between the corresponding classes of functions. Then he uses such notions to give descriptive characterizations of the Henstock-Kurzweil and McShane integrable functions.

Exact mechanical models of fractional hereditary materials

2012

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β R such that 0 β 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 β 1 / 2 and 1 / 2 β 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to th…

Hermitian natural differential operators

1986

Regional Mobility Spaces? Visa Waiver Policies and Regional Integration

2016

Visa policies today are a central instrument for filtering wanted and unwanted types of travellers, leading to a hierarchy of mobility rights. While there is evidence of a “global mobility divide”, we still know little about the role of regional integration when it comes to the distribution of mobility rights and the (re)structuring of mobility spaces. Against this background, the paper examines the structure of visa relations in different bodies of regional integration (EU, MERCOSUR, ASEAN, ECOWAS, EAC, NAFTA, SADC and SICA). In this article, we compare visa policies in the member states of these institutions in 1969 and 2010 from a social network perspective. While one would generally exp…

Study of single top production at high energy electron positron colliders

2014

The effect of single top production on the study of top quark pair production in future high energy electron--positron colliders is evaluated. The rate of the single top quark production process is sizeable throughout a large range of center-of-mass energies and cannot easily be distinguished from the dominant pair production process. We discuss the impact on the top quark mass extraction from a scan through the pair production threshold and the determination of top quark form factors in the continuum. These results advocate for the exploration of the inclusive $e^+e^-\rightarrow W^+bW^-\bar{b}$ process, that includes both top quark pair and single top quark production.

Simple differential equations for Feynman integrals associated to elliptic curves

2019

The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is therefore of current interest, if these methods extend beyond the case of multiple polylogarithms. In this talk I discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.

The sunrise integral and elliptic polylogarithms

2016

We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated integral structure of our functions allows us to furthermore compute the equal mass case to arbitrary order.

The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory

1998

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local B\"acklund transformation. These calculations prepare the theory for an exact canonical quantization.