Resonance for Singular Perturbation Problems

Consider the resonance for a second-order equation εy"-xpy’+ qy = 0. Another proof is given for the necessity of the Matkowsky condition and the connection with a regular eigenvalue problem is established. Also, if p, q are analytic, necessary and sufficient conditions are derived

Numerical Methods for Singular Perturbation Problems

Consider the two-point boundary value problem for a stiff system of ordinary differential equations. An adaptive method to solve these problems even when turning points are present is discussed

Ein weiterer Fundort von Cicindela germanica L. 1758 (Coleoptera: Cicindelidae) aus Ostwestfalen

Autoren älterer Arbeiten melden die Art des öfteren als zahlreich, sehr häufig oder auch massenhaft auftretend (WESTHOFF 1881 , VERHOEFF 1890, ROETTGEN 1911, HORION 1941 u.a.). Gleichzeitig wird aber auch betont, daß so häufiges Auftreten lokal beschränkt ist und die Art auch in weiten Gebieten fehlt. In jüngeren Arbeiten wird von einem Rückgang oder gar vom Aussterben in den ehemaligen Vorkommensgebieten berichtet (BARNER 1937, HORION 1941). Wegen der Seltenheit der Nachweise in der zweiten Hälfte dieses Jahrhunderts und des allgemeinen Rückgangs der Art, soll hier ein jüngerer Nachweis bekannt gemacht werden: Am 7.6.1981 sah ich ein Exemplar im Naturschutzgebiet "Stockberg" bei Höxter-Ottbergen

On the well posedness of Robinson Trautman Maxwell solutions

We show that the so called Robinson-Trautman-Maxwell equations do not constitute a well posed initial value problem. That is, the dependence of the solution on the initial data is not continuous in any norm built out from the initial data and a finite number of its derivatives. Thus, they can not be used to solve for solutions outside the analytic domain.Comment: 9 page

Metallic phase of disordered graphene superlattices with long-range correlations

Using the transfer matrix method, we study the conductance of the chiral particles through a monolayer graphene superlattice with long-range correlated disorder distributed on the potential of the barriers. Even though the transmission of the particles through graphene superlattice with white noise potentials is suppressed, the transmission is revived in a wide range of angles when the potential heights are long-range correlated with a power spectrum $S(k)\sim1/k^{\beta}$. As a result, the conductance increases with increasing the correlation exponent values gives rise a metallic phase. We obtain a phase transition diagram in which a critical correlation exponent depends strongly on disorder strength and slightly on the energy of the incident particles. The phase transition, on the other hand, appears in all ranges of the energy from propagating to evanescent mode regimes.Comment: 8 pages, 11 figure