A delta white noise functional

The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Comparison of the Kerr effect and X-ray pole figure methods for determining crystallographic texture in PrFeB magnets

In this study, magnetic domains in Pr₁₆Fe₇₆B₈ sintered magnets have been observed by Kerr effect and a histogram of the angular distribution of domain orientations has been used to determine the magnetic texture (cos Φ). The degree of easy-axis alignment of Pr₂Fe₁₄B matrix grains in these magnets has been also determined by X-ray pole figure analysis using the (0 0 4) reflection. The (0 0 4) pole figure measurements were carried out by the Schultz's reflection method. The (0 0 4) normalized intensity data has been fitted for a Gaussian distribution and the degree of crystal alignment, cos Θ, has been calculated using the Stoner–Wohlfarth model. Comparison of these methods has been carried out. It has been shown that in magnets with medium and high degrees of crystallographic alignment, the pole figure values are higher than that obtained by the Kerr effect method. Conversely, in magnets with low degrees of alignment, cos Θ is lower than cos Φ.     

High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

Production of recombinant bleaching enzymes from thermophilic microorganisms in fungal hosts

Cost-effective production of enzymes for industrial processes makes the appropriate selection of the host-vector expression system critical. We have developed two systems for the bulk production of bleaching enzymes from thermophiles. Kluyveromyces lactis has been developed as a secretion host employing expression vectors based on the 2μ-like plasmid pKD1 of Kluyveromyces drosophilarium. Our second system involves the filamentous fungus Trichoderma reesei. Fusion and nonfusion vectors have been constructed using the strong cellobiohydrolase 1 (cbh1) promoter. The KEX2 protease cleavage site and a 6 × HIS-tag have been incorporated to facilitate both cleavage and purification of the mature foreign proteins.     

Spectroscopic Studies on the Interaction of Tetramethylpyridylporphyrins and Cationic Clays

In the present work, the interaction between5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21H,23H-porphine (TMPyP) and its metallated form(CoTMPyP) with three cationic clays was investigatedby X-ray diffraction (XRD), UV-VIS and resonance Ramanspectroscopies. Sodium montmorillonites K10 and KSFand a synthetic fluorohectorite (FHT) containingdifferent macrocycle loadings, were prepared by an ionexchange reaction. In nonsaturated KSF and FHT, theCoTMPyP molecule assumes a flat orientation, relativeto the host layers, giving rise to at least twoabsorption bands in the Soret region (ca. 445 and 465 nm)assigned to adsorbed and intercalated CoTMPyP,respectively. For the delaminated K10 sample, a broadband centered around 456 nm, indicates a majorcontribution from the metalloporphyrin on the clayexternal surfaces. The electronic spectra of FHTsamples containing increasing amounts of CoTMPyPshow bands red shifted even when a small amount ofporphyrin is used, suggesting that the electroniclevels of the macrocycle are more affected by theinteraction with the clay than by the metalloporphyrindistortion inside the galleries. The resonance Ramanspectra obtained for all CoTMPyP samples presentedonly minor shifts in peak positions and band width,with the exception of the FHT saturated sample, wherethe bands are clearly broader when compared to otherloadings, suggesting that porphyrin aggregation isoccurring. In the case of TMPyP, the bands at ca. 430and 468 nm were assigned to nonprotonated andprotonated molecules, respectively. This assignment issupported by resonance Raman spectroscopy, which alsoshowed the ₂ mode (ca. 1550 cm^-1) to bethe most sensitive peak to protonation.     

Enzymatic bleaching of organosolv sugarcane bagasse pulps with recombinant xylanase of the fungus Humicola grisea and with commercial cartazyme HS xylanase

Organosolv (ethanol/water and acetosolv) pulps were treated with Humicola grisea var. thermoidea and compared with Cartazyme HS xylanase-treated pulp. The ethanol/water pulps treated with H. grisea had the same viscosity as unbleached pulps (8 cP). Ethanol/water pulps treated with Cartazyme had higher viscosity than H. grisea-treated pulps (12 cP). Acetosolv pulps treated with H. grisea and Cartazyme presented a reduction in viscosity; however, the pulps treated with H. grisea had a lower reduction in viscosity than Cartazyme-treated pulps. Ethanol/water pulps treated with H. grisea had a 23% reduction in kappa number in 4 and 8 h of treatment, compared with the unbleached pulps. Cartazyme-treated pulps had a kappa number similar to that of the control pulps for 4 h of treatment. Extending the treatment time to 12 h resulted in a reduction of 33%. The acetosolv pulp treated with H. grisea had a kappa number reduced to 23% in 4 h. Cartazyme treatment resulted in a reduction of 55 and 44% in kappa number for 4 and 8 h of treatment, respectively, when compared with control pulp. Extending the treatment time to 12 h decreased the kappa number 72%. Fourier transform infrared spectra and principal component analysis showed differences among unbleached, H. grisea-treated, and Cartazyme-treated pulps.     

A New ent‐Kaurane Diterpene from Stems of Alibertia macrophylla K. Schum. (Rubiaceae)

Phytochemical investigations of the stems of a specimen of Alibertia macrophylla led to the isolation and characterization of the new diterpene ent‐kaurane‐2β,3α,16α‐triol ( 1 ), along with triterpenes 2 – 8 , iridoids 9 – 12 , and phenolic acids 13 – 15 . The structure of 1 was established based on spectroscopic studies (¹H‐ and ¹³C‐NMR, IR, and HR‐ESI‐MS). This is the first report of the isolation of a diterpene from the Alibertia genus in Rubiaceae.     

Interaction and lipid-induced conformation of two cecropin-melittin hybrid peptides depend on peptide and membrane composition

The interaction of two hybrid peptides of cecropin A and melittin [CA(1-8)M(1-18) and CA(1-7)M(2-9)] with liposomes was studied by differential scanning calorimetry (DSC), circular dichroism (CD), and quasi-elastic light scattering (QELS). The study was carried out with large unilamellar vesicles (LUVs) of three different lipid compositions: 1,2-dimyristoil-sn-glycero-3-phosphocholine (DMPC), 1,2-dimyristoyl-sn-glycero-3-phospho-rac-(1-glycerol) (DMPG) and a binary mixture of DMPC/DMPG, in a wide range of peptide-to-lipid (P:L) molar ratios (0 to 1:7). DSC results indicate that, for both peptides, the interaction depends on membrane composition, with very different behavior for zwitterionic and anionic membranes. CD data show that, although the two peptides have different secondary structures in buffer (random coil for CA(1-7)M(2-9) and predominantly beta-sheet for CA(1-8)M(1-18)), they both adopt an alpha-helical structure in the presence of the membranes. Overall, results are compatible with a model involving a strong electrostatic surface interaction between the peptides and the negatively charged liposomes, which gives place to aggregation in the gel phase and precipitation after a threshold peptide concentration. In the case of zwitterionic membranes, a progressive surface coverage with peptide molecules destabilizes the membrane, eventually leading to membrane disruption. Moreover, delicate modulations in behavior were observed depending on the peptide.