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

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

Stability of quasi-linear hyperbolic dissipative systems

In this work we want to explore the relationship between certain eigenvalue condition for the symbols of first order partial differential operators describing evolution processes and the linear and nonlinear stability of their stationary solutions.Comment: 16 pages, Te

A priori estimates in terms of the maximum norm for the solutions of the Navier–Stokes equations

AbstractIn this paper, we consider the Cauchy problem for the incompressible Navier–Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first derive corresponding a priori estimates for certain parabolic systems. Because of the pressure term, the case of the Navier–Stokes equations is more difficult, however

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

Liver segments: an anatomical rationale for explaining inconsistencies with Couinaud's eight-segment concept

Background and purpose: An increasing number of surgical and radiological observations call Couinaud's concept of eight liver segments into question and such inconsistencies are commonly explained with anatomical variations. This paper was intended to demonstrate that, beyond variability, another anatomical principle may allow to understand supposedly differing concepts on liver segmentation. Materials and methods: The study was performed on 25 portal vein casts scanned by helical CT. The branches of the right and left portal vein and their corresponding territories were determined both anatomically and mathematically (MEVIS LiverAnalyzer, MEVISLab). Results: The number of branches coming-off the right and left portal vein was never 8, but many more (mean number 20, range 9-44). Different combinations of these branches and their respective territories, carried out in this study, yielded larger entities and supposedly contradictory subdivisions (including Couinaud's eight segments), without calling upon anatomical variability. Conclusions: We suggest the human liver to be considered as corresponding to 1 portal venous territory at the level of the portal vein, to 2 territories at the level of the right and left branch of the portal vein, and to 20 at the level of the rami of the right and left branch. This "1-2-20-concept” is a rationale for reconciling apparent discrepancies with the eight-segment concept. On a pragmatic level, in cases in which imaging or surgical observations do not fit with Couinaud's scheme, we propose clinicians not to autonomically conclude to the presence of an anatomical variation, but to become aware of the presence of an average of 20 (and not 8) second-order portal venous territories within the human live

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

INTRODUCTION

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70110/2/PFLDAS-12-5-iii-1.pd