Search results for "Integrable system"
showing 10 items of 354 documents
Lineability of non-differentiable Pettis primitives
2014
Let \(X\) be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an \(X\)-valued Pettis integrable function on \([0,1]\) whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that \(\mathbf{ND}\), the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to \(\mathbf{ND}\).
On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
2009
Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an absolutely summing operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.
Decomposability in the space ofHKP-integrable functions
2014
In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.
A Decomposition Theorem for the Fuzzy Henstock Integral
2012
We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.
A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions
2009
We proved in our earlier paper [9] that in case of separable Banach space-valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selectors and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Applying the representation theorem we describe the multipliers of the Henstock-Kurzweil-Pettis integrable multifunctions. Then we use this description to obtain a characterization of the Henstock-Kurzweil-Pettis integrability in terms of subadditive operators.
Probabilities to Accept Languages by Quantum Finite Automata
1999
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.
Mappings of finite distortion and asymmetry of domains
2013
We establish an anisotropic Bonnesen inequality for images of balls under homeomorphisms with exponentially integrable distortion. Mathematics Subject Classification (2000): 30C65, 46E35.
Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method
1999
A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.
"Table 17" of "Search for supersymmetry in final states with jets, missing transverse momentum and one isolated lepton in sqrt{s} = 7 TeV pp collisio…
2016
Number of b-tagged jets in the combined electron plus three jets W+jets and top control region.
"Table 3" of "Search for lepton flavour violation in the emu continuum with the ATLAS detector in sqrt(s) = 7 TeV pp collisions at the LHC"
2012
The ratios of the observed and expected upper cross section limits to the theoretical cross sections as a function of the scalar top mass.