Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps

Sections 1–3 contain the material of unpublished preprints [P4 and S]     

Test of the Coherent Tube Model approach to relativistic nucleus-nucleus interactions

Coherent Tube Model predictions concerning secondary pion multiplicities and transverse momenta were compared with the experimental data. It was shown that the discrepancies between the model and our experimental data could not be removed by taking into account fragmentation processes.     

Unboundedness properties of smoothness Morrey spaces of regular distributions on domains

We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R~n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R~n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).     

Interactions of 9.4 GeV/c deuterons in an emulsion: Multiplicity and angular distributions

An analysis of 1650 stars induced by 9.4 GeV/c deuterons in a nuclear emulsion is presented. Multiplicity and angular distributions of secondaries are discussed.     

Wavelet Frames,Sobolev Embeddings and Negative Spectrum of Schrödinger Operators on Manifolds with Bounded Geometry

We consider weighted function spaces of Sobolev-Besov type and Schrödinger type operators on noncompact Riemannian manifolds with bounded geometry. First we give characterization of the spaces in terms of wavelet frames. Then we describe the necessary and sufficient conditions for the compactness of Sobolev embeddings between the spaces. An asymptotic behavior of the corresponding entropy numbers is calculated. At the end we use the asymptotic behavior to estimate the number of negative eigenvalues of the Schrödinger type operators.     

Entropy Numbers of Embeddings of Weighted Besov Spaces

We investigate the asymptotic behavior of the entropy numbers of the compact embedding $$ B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}). $$ Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is given by $w_\alpha (x) = (1+| x |^2)^{\alpha/2}$, and $B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of parameters: $s_2 < s_1$, $0 < p_1,p_2 \le \infty$, and $$ \alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} > d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big). $$ In almost all cases we give a sharp two-sided estimate.     

Spectral theory of some degenerate elliptic operators with local singularities

This paper is based on our previous results (Haroske and Skrzypczak (2008) [23], Haroske and Skrzypczak (in press) [25]) on compact embeddings of Muckenhoupt weighted function spaces of Besov and Triebel-Lizorkin type with example weights of polynomial growth near infinity and near some local singularity. Our approach also extends (Haroske and Triebel (1994) [21]) in various ways. We obtain eigenvalue estimates of degenerate pseudodifferential operators of type b₂○p(x,D)○b₁ where bi∈Lri(Rn,wi), wi∈A_∞, i=1,2, and , ?>0. Finally we deal with the ‘negative spectrum’ of some operator Hγ=A−γV for γ→∞, where the potential V may have singularities (in terms of Muckenhoupt weights), and A is a positive elliptic pseudodifferential operator of order ?>0, self-adjoint in L₂(Rn). This part essentially relies on the Birman-Schwinger principle. We conclude this paper with a number of examples, also comparing our results with preceding ones.     

Entropy numbers of Sobolev embeddings of radial Besov spaces

Let be the radial subspace of the Besov space . We prove the independence of the asymptotic behavior of the entropy numbers

from the difference s₀−s₁ as long as the embedding itself is compact. In fact, we shall show that

This is in a certain contrast to earlier results on entropy numbers in the context of Besov spaces B_p,q^s(Ω) on bounded domains Ω.     

z-Scan characterization of zwitterionic chromophores for optoelectronic switching

Single beam z-scan measurements have been made on films containing amorphous polycarbonate and the zwitterionic chromophore, PYR-3, that has a very high second order nonlinear optical (NLO) figure of merit. The third order NLO figure of merit is ≈1.6 at 1030 nm and is comparable to that found in organic compounds optimized for high n ₂ values. The two-photon absorption coefficient is 2.1×10⁻¹² m/W, which is very low and advantageous for NLO device applications. The third order NLO refractive index is −1.4×10⁻¹⁸ m²/W.