The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces

The main aim of this paper is to construct explicitly orthogonal bases for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. Actually, we describe even the so-called Gelfand-Tsetlin bases for such spaces in terms of Gegenbauer polynomials. As an application, we obtain an algorithm how to compute an orthogonal basis of the space of homogeneous solutions of a generalized Moisil-Theodoresco system in R^m.Comment: submitte

A Goursat decomposition for polyharmonic functions in Euclidean space

The Goursat representation formula in the complex plane, expressing a real–valued biharmonic function in terms of two holomorphic functions and their anti–holomorphic complex conjugates, is generalized to Euclidean space, expressing a real–valued polyharmonic function of order p in terms of p so–called monogenic functions of Clifford analysis

Contaminants in Unionid Mussels from the Confluence of the Mississippi and Illinois Rivers

Unionid mussels were collected from three mussel beds near the confluence of the Mississippi and Illinois rivers in 2003 to evaluate concentrations of selected elements and organic compounds in three abundant species and to preliminarily investigate the relative contribution of these waterways to observed contaminant burdens. Copper (Cu), selenium (Se), and zinc (Zn) concentrations were higher and lead (Pb) concentrations were lower in Amblema plicata collected downstream of the confluence than in those collected upstream. Mean concentrations of nickel (Ni), total mercury (Hg), methylmercury (MeHg), Pb, and Zn varied by species. Concentrations of cadmium (Cd) decreased with age in A. plicata from two of three sites. Tissue concentrations of some elements, e.g., arsenic (As), Cd, Cu, Pb, Se, and Zn, were similar to or higher than those previously reported for unionid mussels from areas of contaminated sediment. Concentrations of Cd, Cu, and Zn in A. plicata were comparable to those collected from the Mississippi River approximately 450 and 900 km upstream from our study sites (Naimo et al. 1992). Although total Hg concentrations we observed were an order of magnitude lower than in that study, MeHg concentrations were above those associated with reductions in soft tissue mass in a study of Elliptio complanata (Salazar et al. 1995). A number of polychlorinated biphenyl (PCB) congeners were detected in A. plicata tissues, with 85% of detections occurring in mussels from downstream of the confluence. Concentrations of individual PCB congeners were ???33 ng/g ww and the maximum summed PCB congener concentration was 100.2 ng/g ww. Although few persistent pesticides were detected, -hexachlorocyclohexane (HCH) was detected in each of the species collected from below the confluence of the two rivers, and in A. plicata collected above it on both the Mississippi and Illinois rivers, at a maximum concentration of 103.5 ng/g ww. Aldrin, ??-HCH and dichlorodiphenyltrichloroethane (DDT) were detected in few of the specimens collected. The findings of this preliminary investigation suggest that unionid mussels from near the confluence of the Mississippi and Illinois rivers may be at risk of negative health effects of elevated exposure to certain environmental contaminants. Studies examining the health and productivity of unionid mussels from this area appear warranted.published or submitted for publicationis peer reviewe

THE HOWE DUALITY FOR HODGE SYSTEMS

In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces

Nanomechanical testing of Ti/Ni multilayer thin films

The main aim of the present work was to study the dependence of mechanical properties of Ti/Ni multilayer thin films on the thicknesses of constituent Ti and Ni layers. The multilayer thin films were made by depositing Ti and Ni layers alternately on single crystalline silicon substrates using magnetron sputtering method. Thickness of individual Ti and Ni layers varied from 1.7 nm to 100 nm, the total multilayer thickness was around 1 µm. The mechanical properties were characterized by means of nanoindentation experiments using a Hysitron dual head TI950 triboindenter equipped with diamond Berkovich tip in both static and dynamic loading regime in the load range from 50 µN to 11 mN. Moreover, nanoindentation tests were performed at elevated temperatures up to 500 oC using a Hysitron xSol heating stage. The nanoindentation data were evaluated using the recently developed home-made Nanoindentation General Evaluation Tool (NIGET) [1] software for independent analysis of loading and unloading curves which includes among others a basic treatment of uncertainties and systematic errors that are missing in commercial software provided together with instrumented indentation testing devices. The NIGET software has a graphical interface which uses libraries of the open source software Gwyddion [2]. The nanoindentation results were correlated with microstructure studies using XRD (X-ray diffraction technique), a Tescan LYRA 3XMU FEG/SEM×FIB scanning electron microscope (SEM), a Philips CM12 STEM transmission electron microscope (TEM) and a JEOL JEM-2100Fhigh resolution TEM. Thin lamellar cross sections for TEM observations were prepared using a focused ion beam (FIB) in SEM from two locations in each sample: an undisturbed layer and a central region of indentation print made with Berkovich tip with a relatively high load from the range of 0.5 to 1N. Please click Additional Files below to see the full abstract

Substituted tetrahydroisoquinolines: synthesis, characterization, antitumor activity and other biological properties

A novel group of aryl methyl sulfones based on nonsteroidal anti-inflammatory compounds exhibiting a methyl sulfone instead of the acetic or propionic acid group was designed, synthesized and evaluated in vitro for inhibition against the human cyclooxygenase of COX-1 and COX-2 isoenzymes and in vivo for anti-inflammatory activity using the carrageenan induced rat paw edema model in rats. Also, in vitro chemosensitivity and in vivo analgesic and intestinal side effects were determined for defining the therapeutic and safety profile. Molecular modeling assisted the design of compounds and the interpretation of the experimental results. Biological assay results showed that methyl sulfone compounds 2 and 7 were the most potent COX inhibitors (IC50 between 0.04 and 0.71 M). Also, these highly active methyl sulfones displayed greater COX-2 activity than the parent carboxylic NSAIDs, thus indicating that the replacement of the acetic or propionic acids by a methyl sulfone group enables some of these structures to possess higher COX-2 inhibitory activity than that of the corresponding alkyl carboxylic analogues. The improved inhibitory activity is attributed to the higher flexibility of the sulfone-receptor interaction that enables more profound exploration of the binding site compared with that of acidic analogues. This observation is underpinned by molecular modeling studies that indicates a change in the binding mode or mechanism compared to the standard binding mode displayed by ibuprofen. The most promising compounds 2 and 7 possess a therapeutical profile that enables their chemical scaffolds to be utilized for development of new NSAIDs