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Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1812.00597

In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.

We study the composition operators of the Hardy space on D $\infty$ $\cap$ {\ell} 1 , the {\ell} 1 part of the infinite polydisk, and the behavior of their approximation numbers.

In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered., Comment: 21 pages

We focus on measurability and integrability for set valued functions in non-necessarily separable Fr\'echet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm., Comment: 15 pages

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 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 ND.

The transition between different states in manganites can be driven by various external stimuli. Controlling these transitions with light opens the possibility to investigate the microscopic path through which they evolve. We performed femtosecond (fs) transmission electron microscopy on a bi-layered manganite to study its response to ultrafast photoexcitation. We show that a photoinduced temperature jump launches a pressure wave that provokes coherent oscillations of the lattice parameters, detected via ultrafast electron diffraction. Their impact on the electronic structure are monitored via ultrafast electron energy loss spectroscopy (EELS), revealing the dynamics of the different orbitals in response to specific structural distortions.

DAE$\delta$ALUS (Decay-At-rest Experiment for $\delta_{CP}$ studies At the Laboratory for Underground Science) provides a new approach to the search for CP violation in the neutrino sector. High-power continuous-wave proton cyclotrons efficiently provide the necessary proton beams with an energy of up to 800 MeV to create neutrinos from pion and muon decay-at-rest. The experiment searches for $\bar{\nu}_{\mu} \rightarrow \bar{\nu}_e$ at short baselines corresponding to the atmospheric $\Delta m^2$ region. The $\bar{\nu}_e$ will be detected via inverse beta decay. Thus, the cyclotrons will be employed at a future ultra-large gadolinium-doped water or scintillator detector. In this paper we address the most challenging questions regarding a cyclotron-based high-power proton driver in the megawatt range with a kinetic energy of 800 MeV. Aspects of important subsystems like the ion source and injection chain, the magnet design and radio frequency system will be addressed. Precise beam dynamics simulations, including space charge and the $\text{H}_2^+$ stripping process, are the base for the characterization and quantification of the beam halo -- one of the most limiting processes in high-power particle accelerators.

This report provides a first design for H2+ accelerators as the DAEdALUS neutrino sources. A description of all aspects of the system, from the ion source to the extracted beam, is provided. The analysis provides a first proof of principle of a full cyclotron system which can provide the necessary beam power for the CP violation search proposed by the DAEdALUS Collaboration.

A new approach to search for CP violation in the neutrino sector [1,2] is proposed by the experiment called DAE{\delta}ALUS (Decay At rest Experiment for {\delta}cp At Laboratory for Underground Science). DAE{\delta}ALUS needs three sources of neutrino fluxes, each one located at 1.5, 8 and 20 km from the underground detector. Here we present the study for a Superconducting Ring Cyclotron able to accelerate the H2+ molecules and to deliver proton beam with maximum energy of 800 MeV and the required high power. The magnetic field produced by the proposed superconducting magnetic sector, simulated by the code TOSCA, the isochronous magnetic field, some preliminary feature on the beam dynamic and the magnetic forces acting on the coils are here presented., Comment: 3 pages, 6 figures, PAC11

A Multi Megawatt Cyclotron complex able to accelerate H2+ to 800 MeV/amu is under study. It consists of an injector cyclotron able to accelerate the injected beam up to 50 MeV/n and of a booster ring made of 8 magnetic sectors and 8 RF cavities. The magnetic field and the forces on the superconducting coils are evaluated using the 3-D code OPERA. The injection and extraction trajectories are evaluated using the well tested codes developed by the MSU group in the '80s. The advantages to accelerate H2+ are described and preliminary evaluations on the feasibility and expected problems to build the injector cyclotron and the ring booster are here presented., Comment: Presentation at Cyclotron'10 conference, Lanzhou, China, Sept 7, 2010