Über das Äquivalenzproblem beschränkter hermitescher Formen

Ohne Zusammenfassung     

Anti-Inflammatory and Antioxidant Properties of Carvacrol and Magnolol,in Periodontal Disease and Diabetes Mellitus

Periodontal disease and diabetes mellitus are two pathologies that are extremely widespread worldwide and share the feature of chronic inflammation. Carvacrol is a phenolic monoterpenoid, produced by a variety of herbs, the most well-known of which is Origanum vulgare. Magnolol is a traditional polyphenolic compound isolated from the stem bark of Magnolia officinalis, mainly used in Chinese medicine. The purpose of this paper is to review the therapeutic properties of these bioactive compounds, in the treatment of periodontitis and diabetes. Based on our search strategy we conducted a literature search in the PubMed and Google Scholar databases to identify studies. A total of one hundred eighty-four papers were included in the current review. The results show that carvacrol and magnolol have anti-inflammatory, antioxidant, antimicrobial, anti-osteoclastic, and anti-diabetic properties that benefit both pathologies. Knowledge of the multiple activities of carvacrol and magnolol can assist with the development of new treatment strategies, and the design of clinical animal and human trials will maximize the potential benefits of these extracts in subjects suffering from periodontitis or diabetes.     

Interaction barriers,nuclear shapes and the optimum choice of a compound nucleus reaction for producing super-heavy elements

Potential barriers and nuclear shapes are calculated for the first time in the fragmentation theory for the various target-projectile combinations. It is shown that the choice of the reaction partners of a cool compound nucleus reaction can be optimized on the basis of this information. Combinations with largest mass- and charge asymmetries, largest interaction radii and smallest interaction barriers are shown to be most favourable. The interaction radius, which is defined to be the radius of the compound nucleus at the top of the barrier, is shown to be related with both mass- and charge asymmetries of the reaction. The calculations are illustrated for the compound nuclei ²⁵⁸104 and ²⁶⁰106.     

An extension to Norton's equivalent

The aggregation method for queueing networks known as the Norton's equivalent is interpreted as a conditional estimate of the intensities of associated point processes. For multi-class Markovian queueing networks, it is shown that a first-order equivalent system of an isolated station can be obtained via the conditional estimates of intensities of the arrival and departure processes to and from that station. Based on these conditional estimates, separation results for optimal flow control problems in queueing networks can be obtained. Several examples which illustrate these concepts are given. The results obtained here generalize those which require the product form networks.     

Real hypersurfaces of with non-negative Ricci curvature

We prove the non-existence of Levi flat compact real hypersurfaces without boundary in , with non-negative totally real Ricci curvature.

     

Vrănceanu connections and foliations with bundle-like metrics

We show that the Vrănceanu connection which was initially introduced on non-holonomic manifolds can be used to study the geometry of foliated manifolds. We prove that a foliation is totally geodesic with bundle-like metric if and only if this connection is a metric one. We introduce the notion of a foliated Riemannian manifold of constant transversal Vrănceanu curvature and the notion of a transversal Einstein foliated Riemannian manifold. The geometry of these two classes of manifolds is studied and the relationship between them is determined.     

On the solution of the diophantine equation A3 + B3 + C3 + D3 = 0

This paper presents a complete and symmetric solution of the diophantine equation of the title in terms of four parameters α, β, γ, δ, subject to α + β + γ + δ = 0.