Vektorfelder und Integralformeln für Strahlensysteme

In this paper we study some vectorfields arising in the theory of rectilinear congruences in the real Euclidean space E³. We also derive some integral formulae concerning the vectorfields above.     

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.     

On Surfaces of Finite Chen — Type

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E³ and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.     

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.     

Eine Charakterisierung Der W-Flächen

Let ℱ: x=x(u¹, u²) be a C³-surface in the euclidean space E³, n the unit normal vector of ℱ and let . We consider the vector of ℝ⁶ and we denote with μ the rank of the matrix (a, a₁, a₂, a_{1, 1}, a_{1, 2}, a_{2, 2}). We then prove the Theorem: ℱ is a W-surface if and only if μ≦5. Further, μ is 4 resp. 3 if and only if the surface ℱ is part of a cylinder of revolution resp. part of a sphere or a plane.      

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.