On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales

In a previous paper we introduced a new concept, the notion of ℰ-martingales and we extended the well-known Doob inequality (for 1 < p < + ∞) and the Burkholder–Davis–Gundy inequalities (for p = 2) to ℰ-martingales. After showing new Fefferman-type inequalities that involve sharp brackets as well as the space bmo _q , we extend the Burkholder–Davis–Gundy inequalities (for 1 < p < + ∞) to ℰ-martingales. By means of these inequalities we give sufficient conditions for the closedness in L ^p of a space of stochastic integrals with respect to a fixed ℝ^d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. Finally we investigate the relation between uniform convergence in probability and semimartingale topology. Received: 22 July 1997 / Revised version: 3 July 1998     

Interactions of porphyrinyl-nucleosides with DNA using the example of porphyrinyl-thymidine

meso-Tri(N-memyl-4-pyridinium)porphyrinyl-p-phenylene-5′-O-thymidine, interacting with plasmid ds DNA showed an 8 nm red-shift of the Soret band. The observed Soret band shift was 4 run less than the shift of the respective meso-tetra(N-methyl-4-pyridinium)porphyrin, which is usually assumed to indicate intercalation. Experimental spectra and the MMX- and AM-1 calculations of a series of model structures further suggest that the investigated porphyrinyl-thymidine also interacts with adenine due to its nucleobase. The possibility of intercalation was also viewed based on interaction of immobilized porphyrin with ds DNA. Theoretical considerations suggested that there are no steric limitations to the formation of a system in which the porphyrinyl-thymidine in question interacts with a molecule of porphyrinyl-adenosine, via A-T base pairing, to join two ds DNA molecules.     

The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Positive solutions for nonlinear singular superlinear elliptic equations

Positivity - We consider a nonlinear nonparametric elliptic Dirichlet problem driven by the p-Laplacian and reaction containing a singular term and a $$(p-1)$$ -superlinear perturbation. Using...     

UV‐induced transformations of matrix‐isolated 1,3,4‐thiadiazole‐2‐thiones

Monomers of 5‐mercapto‐1,3,4‐thiadiazole‐2‐thione (bismuthiol) were studied using an experimental matrix‐isolation technique as well as by carrying out theoretical quantum chemical calculations. The calculations, performed using the quadratic configuration interaction method with single and double excitations (QCISD)/6‐31++G(d,p)//DFT(B3LYP)/6‐311++G(2d,p), predict that the thione–thiol tautomer of bismuthiol should be significantly (by more than 19 kJ mol^?1) more stable than other tautomeric forms. Accordingly, only the signatures of the thione–thiol tautomer were observed in the FT‐IR spectrum of bismuthiol, recorded directly after deposition of an Ar matrix. UV (λ > 320 nm) irradiation induced the conversion of the thione–thiol tautomer into the dithiol form. Analogous investigations were carried out for two related compounds: 5‐methyl‐1,3,4‐thiadiazole‐2‐thione and 5‐methylthio‐1,3,4‐thiadiazole‐2‐thione. For these two species, only the thione tautomeric forms were observed after deposition of Ar matrices. These tautomers were predicted (by QCISD calculations) to be more stable (by at least 19 kJ mol^?1) than other tautomeric forms. Upon UV irradiation, the most stable thione forms of these compounds were transformed into the corresponding thiol tautomers. Direct observation of the thione → thiol phototautomeric processes provides a clear proof that intramolecular proton transfer reaction can occur in molecules, such as bismuthiol, in spite of the increased NH···S distance, in comparison to other phototautomerizing species studied so far. All the isomers of the studied compounds (substrates and products of the photoreactions) were identified by comparison of their IR spectra with the spectra calculated at the DFT(B3LYP)/6‐311++G(2d,p) level of theory for possible isomeric structures. Copyright © 2009 John Wiley & Sons, Ltd.     

BaHfO3:Ce sintered ceramic scintillators

Raw powders of BaHfO₃:Ce were prepared with modified Pechini process and were calcined in the 650–1700 °C range of temperatures, at different atmospheres – air, vacuum and nitrogen–hydrogen mixture. The powders were converted into sintered ceramics by vacuum sintering. The materials were characterized by XRD, TEM, photoluminescence and radioluminescence spectroscopy. UV-VUV excitation spectra were recorded using synchrotron radiation. Excitation spectra proved that atmosphere of preparation significantly influences the host-to-activator energy transfer, which is the most efficient for materials made in reducing conditions. Also radioluminescence efficacy was found to be superior for materials prepared in such conditions.     

Morrey Spaces on Domains: Different Approaches and Growth Envelopes

We deal with Morrey spaces on bounded domains \(\Omega \) obtained by different approaches. In particular, we consider three settings \(\mathcal {M}_{u,p}(\Omega )\), \(\mathbb {M}_{u,p}(\Omega )\) and \(\mathfrak {M}_{u,p}(\Omega )\), where \(0<p\le u<\infty \), commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes \(\mathfrak {E}_{\mathsf {G}}(\mathcal {M}_{u,p}(\Omega ))\) as well as \(\mathfrak {E}_{\mathsf {G}}(\mathfrak {M}_{u,p}(\Omega ))\), and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether \(\frac{n}{u}\ge \frac{1}{p}\) or \(\frac{n}{u} < \frac{1}{p}\) plays a decisive role when it comes to the behaviour of these spaces.     

A note on the Σ1 collection scheme and fragments of bounded arithmetic

We show that for each n ≥ 1, if T₂ⁿ does not prove the weak pigeonhole principle for Σ^b_n functions, then the collection scheme B Σ₁ is not finitely axiomatizable over T₂ⁿ. The same result holds with Sⁿ₂ in place of T 2ⁿ (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Noncommutative closed Friedman universe

Heller et al. (J Math Phys 46:122501, 2005; Int J Theor Phys 46:2494, 2007) proposed a model unifying general relativity and quantum mechanics based on a noncommutative algebra defined on a groupoid having the frame bundle over space–time as its base space. The generalized Einstein equation is assumed in the form of the eigenvalue equation of the Einstein operator on a module of derivations of the algebra . No matter sources are assumed. The closed Friedman world model, when computed in this formalism, exhibits two interesting properties. First, generalized eigenvalues of the Einstein operator reproduce components of the perfect fluid energy-momentum tensor for the usual Friedman model together with the corresponding equation of state. One could say that, in this case, matter is produced out of pure (noncommutative) geometry. Second, owing to probabilistic properties of the model, in the noncommutative regime (on the Planck level) singularities are irrelevant. They emerge in the process of transition to the usual space–time geometry. These results are briefly discussed.