Temperature dependence of S.C.L.C. in anthracene crystals

Zusammenfassung Aus der Temperaturabhängigkeit des Löcherstroms in Anthrazen-Einkristallen wird die Aktivierungsenergie bei verschiedenen Dunkelstromwerten gemessen. Die Aktivierungsenergien liegen zwischen 0,65 eV und 0,95 eV für Ströme von 10^–10 bzw. 10^–12 Ampère bei Zimmertemperatur.Ferner wird für mehrere Temperaturwerte die Aktivierung der in Haftstellen sitzenden Ladungsträger mit Hilfe von Licht verschiedener Intensität untersucht.     

On a problem of C. C. Chen and D. E. Daykin

Let α(k, p, h) be the maximum number of vertices a complete edge-colored graph may have with no color appearing more than k times at any vertex and not containing a complete subgraph on p vertices with no color appearing more than h times at any vertex. We prove that $\text{α(k, p, h) ≤ h + 1 + (k ? 1){(p ? h ? 1) × (h}{}^{\mathrm{p}}\text{+ 1)}}{}^{\mathrm{<mtext>1</mtext><mtext>h</mtext>}}$ and obtain a stronger upper bound for α(k, 3, 1). Further, we prove that a complete edge-colored graph with n vertices contains a complete subgraph on p vertices in which no two edges have the same color if

$\text{(}\text{n}\text{3}\text{)>(}\text{p}\text{3}\text{)}\text{Σ}\text{i=1}\text{t}\text{(}\text{e}{}_{\mathrm{i}}\text{2}\text{)}$

where e_i is the number of edges of color i, 1 ≤ i ≤ t.     

I—ring which Satisfies A.D.C.C on Principal Left Ideals

Derndtl0n1AringRiscalledI-ring,ifasasemigroupRisgeneratedbyitsidemPOtentelements.Defhotl0n2AringRissaidtosatisfyalm0stdescending(0rascending)chaincondi-tionsonleftideals,ifforeverydescending(ascending)chainofleftideals0fR,I,nI2n...nI.Xi..-(I,GI2G...GI'g..-),thereexistsaPOsitiveintegerpsuchthatRPI=Ii(IiGR-'I,)foralli,whereR-'I,={ueRlR'u=IP}.By[5JitisknownthatAringRsatisfiesA.D.C.C(OTA.A.C,C)onleftidealsifandonlyifforeverydescending(0rascending)chalnOfleftidealsofR,I,nI2n-..n…     

关于I. Laine和杨重骏的一个问题

本文主要研究线性差分方程 $A_n(z)f(z+n)+\cdots+A_1(z)f(z+1)+A_0(z)f(z)=0$亚纯解的增长级.当上述方程的系数中没有起控制作用的系数时,我们给出了一些约束条件,得到了一些结果,所得结果部分回答了I. Laine和杨重骏的一个问题.     

On J. C. C. Nitsche type inequality for annuli on Riemann surfaces

Assume that (N, ?) and (M, S) are two Riemann surfaces with conformal metrics ? and S. We prove that if there is a harmonic homeomorphism between an annulus A ? N with a conformal modulus Mod(A) and a geodesic annulus A _S (p, ρ₁, ρ₂)?M, then we have ρ₂/ρ₁ ≥ Ψ _S Mod(A)²+ 1, where Ψ _S is a certain positive constant depending on the upper bound of Gaussian curvature of the metric S. An application for the minimal surfaces is given.     

Univalent harmonic mappings of annuli and a conjecture of J. C. C. Nitsche

Letw=f(z) be a univalent harmonic mapping of the annulus {ρ≤|z|≤1} onto the annulus {σ≤|w|≤1}. It is shown thatσ≤1/(1+(ρ ²/2)(logρ)²).     

ON THE CONJECTURE OF A.LINS, W.DE MELO AND C.C.PUGH

We have proved that Lienard equation with F(x) = -F(-x) has at most n limit cycles. Under the condition, an affirmative answer to A.Lins, W.de Melo and C.C.Pugh's conjecture is given.     

On C2.L-Geometries

A C₂.L-geometry is a geometry of rank 3 with elements called points, lines and quads, where residues of points are linear spaces, residues of lines are generalized digons and residues of quads are generalized quadrangles. Some sufficient conditions can be found in the literature for a C₂.L-geometry to be a quotient of a truncated C_n-building. We shall weaken those conditions in this paper.     

On a theorem of A. and C. Rényi and a conjecture of C. C. Yang concerning periodicity of entire functions

Analysis Mathematica - A theorem of A. and C. Rényi on periodic entire functions states that an entire function f(z) must be periodic if P(f(z)) is periodic, where P(z) is a nonconstant...