Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Equidistribution estimates for Fekete points on complex manifolds

We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.

Evidence for the complex relationship between free amino acid and sugar concentrations and acrylamide-forming potential in potato

Free amino acids and reducing sugars participate in the Maillard reaction during high-temperature cooking and processing. This results not only in the formation of colour, aroma and flavour compounds, but also undesirable contaminants, including acrylamide, which forms when the amino acid that participates in the reaction is asparagine. In this study, tubers of 13 varieties of potato (Solanum tuberosum), which had been produced in a field trial in 2010 and sampled immediately after harvest or after storage for 6 months, were analysed to show the relationship between the concentrations of free asparagine, other free amino acids, sugars and acrylamide-forming potential. The varieties comprised five that are normally used for crisping, seven that are used for French fry production and one that is used for boiling. Acrylamide formation was measured in heated flour, and correlated with glucose and fructose concentration. In French fry varieties, which contain higher concentrations of sugars, acrylamide formation also correlated with free asparagine concentration, demonstrating the complex relationship between precursor concentration and acrylamide-forming potential in potato. Storage of the potatoes for 6 months at 9°C had a significant, variety-dependent impact on sugar and amino acid concentrations and acrylamide-forming potential.

Synthesis and thermal characterization of luminescent powers of terbium(III) with mixed ligands

This work deals with the synthesis and thermal decomposition of complexes of general formula: Ln(beta-dik)(3)L (where Ln=Tb(+3), beta-dik=4,4,4-trifluoro-1-phenyl-1,3butanedione(btfa) and L=1,10-fenantroline(phen) or 2,2-bipiridine(bipy). The powders were characterized by melting point, FTIR spectroscopy, LTV-visible, elemental analysis, scanning differential calorimeter(DSC) and thermogravimetry(TG). The TG/DSC curves were obtained simultaneously in a system DSC-TGA, under nitrogen atmosphere. The experimental conditions were: 0.83 ml.s(-1) carrier gas flow, 2.0 +/- 0.5 mg samples and 10 degrees C.min(-1) heating rate. The CHN elemental analysis of the Tb(btfa)(3)bipy and Tb(btfa)(3)phen complexes, are in good agreement with the expected values. The IR spectra evinced that the metal ion is coordinated to the ligands via C=O and C-N groups. The TG/DTG/DSC curves of the complexes show that they decompose before melting. The profiles of the thermal decomposition of the Tb(btfa)3phen and Tb(btfa)3bipy showed six and five decomposition stages, respectively. Our data suggests that the thermal stability of the complexes under investigation followed the order: Tb(btfa)(3)phen < Tb(btfa)(3)bipy.

New concepts of the power received by ideal energy storage elements: the instantaneous complex power approach

This paper presents some definitions and concepts of the Instantaneous Complex Power Theory [1] which is a new approach for the Akagi's Instantaneous Reactive Power Theory [2].The powers received by an ideal inductor are interpreted and the knowledge of the actual nature of these powers may lead to changes of the conventional electrical power concepts.

Power analysis applying the instantaneous complex power analytical expressions on a RL symmetrical three-phase system

This paper enhances some concepts of the Instantaneous Complex Power Theory by analyzing the analytical expressions for voltages, currents and powers developed on a symmetrical RL three-phase system, during the transient caused by a sinusoidal voltage excitation. The powers delivered to an ideal inductor will be interpreted, allowing a deep insight in the power phenomenon by analyzing the voltages in each element of the circuit. The results can be applied to the understanding of non-linear systems subject to sinusoidal voltage excitation and distorted currents.

Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.

Albumin Is Synthesized In Epididymis And Aggregates In A High Molecular Mass Glycoprotein Complex Involved In Sperm-egg Fertilization.

The epididymis has an important role in the maturation of sperm for fertilization, but little is known about the epididymal molecules involved in sperm modifications during this process. We have previously described the expression pattern for an antigen in epididymal epithelial cells that reacts with the monoclonal antibody (mAb) TRA 54. Immunohistochemical and immunoblotting analyses suggest that the epitope of the epididymal antigen probably involves a sugar moiety that is released into the epididymal lumen in an androgen-dependent manner and subsequently binds to luminal sperm. Using column chromatography, SDS-PAGE with in situ digestion and mass spectrometry, we have identified the protein recognized by mAb TRA 54 in mouse epididymal epithelial cells. The ∼65 kDa protein is part of a high molecular mass complex (∼260 kDa) that is also present in the sperm acrosomal vesicle and is completely released after the acrosomal reaction. The amino acid sequence of the protein corresponded to that of albumin. Immunoprecipitates with anti-albumin antibody contained the antigen recognized by mAb TRA 54, indicating that the epididymal molecule recognized by mAb TRA 54 is albumin. RT-PCR detected albumin mRNA in the epididymis and fertilization assays in vitro showed that the glycoprotein complex containing albumin was involved in the ability of sperm to recognize and penetrate the egg zona pellucida. Together, these results indicate that epididymal-derived albumin participates in the formation of a high molecular mass glycoprotein complex that has an important role in egg fertilization.

Effects Of Partial Inhibition Of Respiratory Complex I On H2o 2 Production By Isolated Brain Mitochondria In Different Respiratory States.

The aim of this work was to characterize the effects of partial inhibition of respiratory complex I by rotenone on H2O2 production by isolated rat brain mitochondria in different respiratory states. Flow cytometric analysis of membrane potential in isolated mitochondria indicated that rotenone leads to uniform respiratory inhibition when added to a suspension of mitochondria. When mitochondria were incubated in the presence of a low concentration of rotenone (10 nm) and NADH-linked substrates, oxygen consumption was reduced from 45.9 ± 1.0 to 26.4 ± 2.6 nmol O2 mg(-1) min(-1) and from 7.8 ± 0.3 to 6.3 ± 0.3 nmol O2 mg(-1) min(-1) in respiratory states 3 (ADP-stimulated respiration) and 4 (resting respiration), respectively. Under these conditions, mitochondrial H2O2 production was stimulated from 12.2 ± 1.1 to 21.0 ± 1.2 pmol H2O2 mg(-1) min(-1) and 56.5 ± 4.7 to 95.0 ± 11.1 pmol H2O2 mg(-1) min(-1) in respiratory states 3 and 4, respectively. Similar results were observed when comparing mitochondrial preparations enriched with synaptic or nonsynaptic mitochondria or when 1-methyl-4-phenylpyridinium ion (MPP(+)) was used as a respiratory complex I inhibitor. Rotenone-stimulated H2O2 production in respiratory states 3 and 4 was associated with a high reduction state of endogenous nicotinamide nucleotides. In succinate-supported mitochondrial respiration, where most of the mitochondrial H2O2 production relies on electron backflow from complex II to complex I, low rotenone concentrations inhibited H2O2 production. Rotenone had no effect on mitochondrial elimination of micromolar concentrations of H2O2. The present results support the conclusion that partial complex I inhibition may result in mitochondrial energy crisis and oxidative stress, the former being predominant under oxidative phosphorylation and the latter under resting respiration conditions.

A New Platinum Complex With Tryptophan: Synthesis, Structural Characterization, Dft Studies And Biological Assays In Vitro Over Human Tumorigenic Cells.

A new platinum(II) complex with the amino acid L-tryptophan (trp), named Pt-trp, was synthesized and characterized. Elemental, thermogravimetric and ESI-QTOF mass spectrometric analyses led to the composition [Pt(C11H11N2O2)2]⋅6H2O. Infrared spectroscopic data indicate the coordination of trp to Pt(II) through the oxygen of the carboxylate group and also through the nitrogen atom of the amino group. The (13)C CP/MAS NMR spectroscopic data confirm coordination through the oxygen atom of the carboxylate group, while the (15)N CP/MAS NMR data confirm coordination of the nitrogen of the NH2 group to the metal. Density functional theory (DFT) studies were applied to evaluate the cis and trans coordination modes of trp to platinum(II). The trans isomer was shown to be energetically more stable than the cis one. The Pt-trp complex was evaluated as a cytotoxic agent against SK-Mel 103 (human melanoma) and Panc-1 (human pancreatic carcinoma) cell lines. The complex was shown to be cytotoxic over the considered cells.

Synthesis, characterization, DFT and Td-dfT study of the [Fe(mnt)(L)(t-BuNC) 2] octahedral complex (L = phen, bipy)

FeBr2 has reacted with an equivalent of mnt2- (mnt = cis-1,2-dicyanoethylene-1,2-dithiolate) and the α-diimine L (L = 1,10'-phenantroline, 2,2'-bipyridine) in THF solution, and followed by adding of t-butyl-isocyanide to give [Fe(mnt)(L)(t-BuNC)2] neutral compound. The products were characterized by infrared, UV-visible and Mössbauer spectroscopy, besides thermogravimetric and conductivity data. The geometry in the equilibrium was calculated by the density functional theory and the electronic spectrum by the time-dependent. The experimental and theoretical results in good agreement have defined an octahedral geometry with two isocyanide neighbours. The π→π* intraligand electronic transition was not observed for cis-isomers in the near-IR spectral region.

Management of a complex dentoalveolar trauma: a case report

This paper describes the case of a 12-year-old male patient who presented a severe lateral luxation of the maxillary central incisors due to a bicycle fall. Treatment involved suture of the soft tissues lacerations, and repositioning and splinting of the injured teeth, followed by endodontic treatment and periodontal surgery. After a 2-year follow-up, clinical and radiographic evaluation revealed that the incisors presented satisfactory esthetic and functional demands.