Young-Measure Quasi-Static Damage Evolution

An existence result for the quasi-static evolution of incomplete damage in elastic materials is presented. The absence of gradient terms in the damage variable causes a critical lack of compactness. Therefore, the analysis is developed in the framework of Young measures, where a notion of solution is defined, presenting some improvements with respect to previous contributions. The main new feature in the proof of the existence result regards a delicate construction of the joint-recovery sequence.     

On global spatial regularity in elasto-plasticity with linear hardening

We study the global spatial regularity of solutions of elasto-plastic models with linear hardening. In order to point out the main idea, we consider a model problem on a cube, where we prescribe Dirichlet and Neumann boundary conditions on the top and the bottom, respectively, and periodic boundary conditions on the remaining faces. Under natural smoothness assumptions on the data we obtain \({u \in {\rm L}^\infty((0, T); {\rm H}^{\frac{3}{2}-\delta}(\Omega))}\) for the displacements and \({z \in {\rm} L^\infty((0,T); {\rm H}^{\frac{1}{2}-\delta}(\Omega))}\) for the internal variables. The proof is based on a difference quotient technique and a reflection argument.     

On inaudible curvature properties of closed Riemannian manifolds

Following Mark Kac, it is said that a geometric property of a compact Riemannian manifold can be heard if it can be determined from the eigenvalue spectrum of the associated Laplace operator on functions. On the contrary, D’Atri spaces, manifolds of type A{\mathcal{A}}, probabilistic commutative spaces, \mathfrakC{\mathfrak{C}}-spaces, \mathfrakTC{\mathfrak{TC}}-spaces, and \mathfrakGC{\mathfrak{GC}}-spaces have been studied by many authors as symmetric-like Riemannian manifolds. In this article, we prove that for closed Riemannian manifolds, none of the properties just mentioned can be heard. Another class of interest is the class of weakly symmetric manifolds. We consider the local version of this property and show that weak local symmetry is another inaudible property of Riemannian manifolds.     

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.     

Spontaneous low-frequency blood oxygenation level-dependent fluctuations and functional connectivity analysis of the 'resting' brain

Functional magnetic resonance imaging techniques using the blood oxygenation level-dependent (BOLD) contrast are widely used to map human brain function by relating local hemodynamic responses to neuronal stimuli compared to control conditions. There is increasing interest in spontaneous cerebral BOLD fluctuations that are prominent in the low-frequency range (<0.1 Hz) and show intriguing spatio-temporal correlations in functional networks. The nature of these signal fluctuations remains unclear, but there is accumulating evidence for a neural basis opening exciting new avenues to study human brain function and its connectivity at rest. Moreover, an increasing number of patient studies report disease-dependent variation in the amplitude and spatial coherence of low-frequency BOLD fluctuations (LFBF) that may afford greater diagnostic sensitivity and easier clinical applicability than standard fMRI. The main disadvantage of this emerging tool relates to physiological (respiratory, cardiac and vasomotion) and motion confounds that are challenging to disentangle requiring thorough preprocessing. Technical aspects of functional connectivity fMRI analysis and the neuroscientific potential of spontaneous LFBF in the default mode and other resting-state networks have been recently reviewed. This review will give an update on the current knowledge of the nature of LFBF, their relation to physiological confounds and potential for clinical diagnostic and pharmacological studies.     

Mössbaueruntersuchungen an195Pt und201Hg

Using the Mössbauer technique the magnetic hyperfine splitting of the 130 keV transition in¹⁹⁵Pt has been observed in a Pt-Fe alloy. The derived magnetic moment is μ₁₃₀=(0.81 _?0.25 ^+0.13 μ _k . Isomershift measurements with the 130 keV and the 99 keV transitions in alloys yielded Δ〈r ²〉₁₃₀/Δ〈r ²〉₉₉=1.5±0.2 for the ratio of the changes in the mean square charge radius of the two excited states. From isomershifts of the 99 keV transition in compounds an estimate of Δ〈r ²〉₉₉/〈r ²〉=?(1.6 _?0.9 ^+4.4 ) · 10^?4 is made for the change in radius of the first excited state. The linewidth of the Mössbauer spectrum of the 32.2 keV transition in²⁰¹Hg gives a lower limit of 0.1 ns for the half-life of the second excited state. The results are compared with values for other nuclides in this mass region.     

Isospectral potentials and conformally equivalent isospectral metrics on spheres,balls and Lie groups

We construct pairs of conformally equivalent isospectral Riemannian metrics ?1g and ?2g on spheres Sⁿ and balls Bⁿ⁺¹ for certain dimensions n, the smallest of which is n=7, and on certain compact simple Lie groups. In the case of Lie groups, the metric g is left-invariant. In the case of spheres and balls, the metric g not the standard metric but may be chosen arbitrarily close to the standard one. For the same manifolds (M, g) we also show that the functions ?₁ and ?₂ are isospectral potentials for the Schrödinger operator ?₂\gD + \gf. To our knowledge, these are the first examples of isospectral potentials and of isospectral conformally equivalent metrics on simply connected closed manifolds.     

Über Reaktionen oxygenierter Kobalt(II)-Chelate. VII. Zur Stabilität einfach und doppelt verbrückter μ-Peroxo-dikobalt(III)-Komplexe

On reactions of oxygenated Cobalt(II) Chelates. VII. Stability of mono and doubly bridged μ-Peroxo-dicobalt(III) Complexes. The oxygen carrier properties of the cobalt(II) chelates of symmetrical diethylenetriamine-4-acetic acid (dtma) and unsymmetrical ethylenediamine-1,1-diacetic acid (edda) have been investigated by O₂ equilibrium measurements in alkaline solution. Maximum O₂ uptake is at pH = pK_H (4), indicating that μ-peroxo-μ-hydroxodicobalt(III) ion is the only oxygenated species formed in aqueous solution. Relationships between stability and structural factors are discussed.     

Structure-Activity Relationship for Di- up to Tetranuclear Macrocyclic Ruthenium Catalysts in Homogeneous Water Oxidation

Two di- and tetranuclear Ru(bda) (bda: 2,2′-bipyridine-6,6′-dicarboxylate) macrocyclic complexes were synthesized and their catalytic activities in chemical and photochemical water oxidation investigated in a comparative manner to our previously reported trinuclear congener. Our studies have shown that the catalytic activities of this homologous series of multinuclear Ru(bda) macrocycles in homogeneous water oxidation are dependent on their size, exhibiting highest efficiencies for the largest tetranuclear catalyst. The turnover frequencies (TOFs) have increased from di- to tetranuclear macrocycles not only per catalyst molecule but more importantly also per Ru unit with TOF of 6 s⁻¹ to 8.7 s⁻¹ and 10.5 s⁻¹ in chemical and 0.6 s⁻¹ to 3.3 s⁻¹ and 5.8 s⁻¹ in photochemical water oxidation per Ru unit, respectively. Thus, for the first time, a clear structure–activity relationship could be established for this novel class of macrocyclic water oxidation catalysts.