The remainder in Weyl's law for random two-dimensional

We prove that the average order of the remainder in counting the number of points of a random lattice inside a disc of radius . Our proof is spectral in nature. Submitted: July 2001, Revised: August 2001, Revised: March 2002.     

Shape fabrication of millimeter-sized metal-containing carboxymethyl cellulose hollow capsules

Dropwise addition of an aqueous carboxymethyl cellulose solution to a solution of a copper or iron salt in n-butanol, leads to self-assembled, permeable millimeter sized metal-ion derivatized carboxymethyl cellulose hollow capsules of uniform dimensions and different morphologies.     

Morphological changes in the cellulose and lignin components of biomass occur at different stages during steam pretreatment

Morphological changes to the different components of lignocellulosic biomass were observed as they occurred during steam pretreatment by placing a pressure reaction cell in a neutron beam and collecting time-resolved neutron scattering data. Changes to cellulose morphology occurred mainly in the heating phase, whereas changes in lignin morphology occurred mainly in the holding and cooling phases. During the heating stage, water is irreversibly expelled from cellulose microfibrils as the elementary fibrils coalesce. During the holding phase lignin aggregates begin to appear and they increase in size most noticeably during the cooling phase. This experiment demonstrates the unique information that in situ small angle neutron scattering studies of pretreatment can provide. This approach could be useful in optimizing the heating, holding and cooling stages of pretreatments to allow the exact size and nature of lignin aggregates to be controlled in order to enhance enzyme accessibility to cellulose and therefore the efficiency of biomass conversion.     

Abnormal photonic energy — a signal of Quark matter possibly seen in exotic cosmic ray events

A phenomenological method is proposed to select possible Quark matter forming events in ultra-relativistic nucleus-nucleus interactions. We compare the released photonic and hadronic energies from a Quark matter forming event and from a normal Hadronic event and derive a relation, which may be used in an event-by-event analysis to differentiate the two phases. We determine thus two regions of QCD deconfinement. We also discuss the hadronic, photonic energy and multiplicity contents and the 〈P_T〉 of several exotic cosmic ray events at ultra high energies. On the basis of the phenomenological model, we suggest that the “Centauro” type are Quark matter events near the projectile fragmentation region with very large baryochemical potential,μ _b. The “Anti-Centauro” type events are created by vacuum excitation in the central region with near zeroμ _b.

     

On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

Towards experiments with highly charged ions at HESR

The atomic physics collaboration SPARC is a part of the APPA pillar at the future Facility for Antiproton and Ion Research. It aims at atomic-physics research across virtually the full range of atomic matter. An emphasis of this contribution are the atomic physics experiments addressing the collision dynamics in strong electro-magnetic fields as well as the fundamental interactions between electrons and heavy nuclei at the HESR. Here we give a short overview about the central instruments for SPARC experiments at this storage ring.     

Magnetically modified single and turbostratic stacked graphenes from tris(2,2'-bipyridyl) iron(II) ion-exchanged graphite oxide

Loading of graphite oxide (GO) with tris(2,2'-bipyridyl) iron(II) ions and subsequent calcination affords a novel graphene-based composite with magnetic and electrically conductive properties. The pH of the starting aqueous suspension and the washing procedure play a crucial role in the successful immobilization of the iron precursor, which is mainly governed by ion exchange. The complex is intercalated between the graphene oxide layers, where it adopts a distorted conformation. Rapid heating of this solid results in the deflagration of GO and the formation of ultrafine ( d = 2-14 nm) Fe2O3 particles with maghemite as the dominant phase. The superparamagnetic maghemite crystals are dispersed uniformly in the high-surface-area diamagnetic matrix built up from single or turbostratic stacked graphenes.     

Graphene‐Based Inverted Planar Perovskite Solar Cells: Advancements,Fundamental Challenges,and Prospects

Metal halide based perovskite solar cells (PSCs) are considered among the most promising photovoltaic technologies, and already present certified efficiencies that surpass 22 %. The high performance and low fabrication cost make this technology competitive with that of state‐of‐the‐art thin‐film photovoltaics. However, PSCs present some striking disadvantages that hinder their commercialization, including short operational lifetimes, high toxicity, and hysteresis effects, which lower both the performance and long‐term stability of the devices. Herein, work conducted within the last two years is summarized with regard to addressing the challenges of low‐temperature‐processed planar inverted PSCs composed of graphene‐based materials. In addition, critical challenges and the prospects of this field are discussed and some prospects for future research directions are proposed.