A theorem of H. Hopf and the Cauchy-Riemann inequality II

This is a sequel to “A theorem of H. Hopf and the Cauchy-Riemann inequality” [AdCT]. Here the result of the previous paper is extended (see the precise statement in Section 1 of the present paper) to surfaces in three-dimensional homogeneous Riemannian manifolds whose group of isometries has dimension four and the bundle curvature is nonzero, whereas in the previous paper only the case of vanishing bundle curvature was treated. * Partially supported by MEC-FEDER Grant No. MTM 2004-00160.     

Kinetic model for the relationship between mean diameter shortening and age reduction in glass samples

Fission tracks in glass samples are shortened when they experience thermal treatment. Consequently, the observable dimensions associated with track length also diminish. The dimension normally used to characterize track size is the mean diameter of the etched track at the surface, D. Another consequence of length shortening is the reduction of surface density, ρ, implying a reduction of the fission-track age. In this work, a kinetic model is developed to describe the relationship between fission-track mean diameter shortening and surface fission-track density reduction in glass samples, based on geometrical and etching hypotheses. The result is a two-parameter equation given by

(1)

in which h is the thickness of the layer removed during etching and n is a parameter related to the latent track geometry and etching reaction rate. The equation was compared with experimental data on Australite glass found in the literature and with fresh data on Macusanite glass presented in this work. The model fits the experimental curves quite well, showing that it describes the etching effects correctly (within its limitations). In addition, the model equation derived in this work can be very useful in age correction of partially annealed glass samples.     

An Unusual Intramolecular Halogen Bond Guides Conformational Selection

PIK‐75 is a phosphoinositide‐3‐kinase (PI3K) α‐isoform‐selective inhibitor with high potency. Although published structure–activity relationship data show the importance of the NO₂ and the Br substituents in PIK‐75, none of the published studies could correctly determine the underlying reason for their importance. In this publication, we report the first X‐ray crystal structure of PIK‐75 in complex with the kinase GSK‐3β. The structure shows an unusual U‐shaped conformation of PIK‐75 within the active site of GSK‐3β that is likely stabilized by an atypical intramolecular Br???NO₂ halogen bond. NMR and MD simulations show that this conformation presumably also exists in solution and leads to a binding‐competent preorganization of the PIK‐75 molecule, thus explaining its high potency. We therefore suggest that the site‐specific incorporation of halogen bonds could be generally used to design conformationally restricted bioactive substances with increased potencies.     

Dynamics of snoring sounds and its connection with obstructive sleep apnea

Snoring is extremely common in the general population and when irregular may indicate the presence of obstructive sleep apnea. We analyze the overnight sequence of wave packets — the snore sound — recorded during full polysomnography in patients referred to the Sleep Laboratory due to suspected obstructive sleep apnea. We hypothesize that irregular snore, with duration in the range between 10 and 100 s, correlates with respiratory obstructive events. We find that the number of irregular snores — easily accessible, and quantified by what we call the snore time interval index (STII) — is in good agreement with the well-known apnea–hypopnea index, which expresses the severity of obstructive sleep apnea and is extracted only from polysomnography. In addition, the Hurst analysis of the snore sound itself, which calculates the fluctuations in the signal as a function of time interval, is used to build a classifier that is able to distinguish between patients with no or mild apnea and patients with moderate or severe apnea.     

Ultrastructure and morphometry of the egg of Psorophora albigenu Lutz, 1908 (Diptera: Culicidae)

Eggs of Psorophora albigenu were analyzed by light and scanning electron microscopy. Eggs were laid singly and were black and elliptical in outline. A length of approximately 586.4 ± 10.83 μm, a width of 172.3 ± 8.09 μm (n=30), and an egg index (length/width ratio) of 3.33 were observed. The anterior extremity tapered abruptly from a width of 64.9 μm, while such tapering was more gradual at the posterior extremity from a width of 77.4 μm. The ventral surface of the chorionic coating presented cells with tubular aspect containing tubercles in rows with a density of 9-16 tubercles per cell. These tubercles presented two different sizes, with the largest measuring 7.87 ± 01.58 μm and the smallest measuring 0.71 ± 0.53 μm (n=30) in longitudinal diameter. The micropyle orifice was very evident, with a diameter of 3.36 μm. The morphometric characteristics of Ps. albigenu obtained in this study were distinct from those of other species of the Psorophora genus, including Psorophora varipes which has been considered for a long time to be synonymous with Ps. albigenu.     

Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons

In this paper, we study stability properties of hypersurfaces with constant weighted mean curvature (CWMC) in gradient Ricci solitons. The CWMC hypersurfaces generalize the f-minimal hypersurfaces and appear naturally in the isoperimetric problems in smooth metric measure spaces. We obtain a result about the relationship between the properness and extrinsic volume growth under the assumption of a limitation for the weighted mean curvature of the immersion. Moreover, we estimate Morse index for CWMC hypersurfaces in terms of the dimension of the space of parallel vector fields restricted to hypersurface.     

Red to blue tunable upconversion in Tm3+-doped ZrO2 nanocrystals

The effect of dopant concentration on the blue upconversion (UPC) emission of Tm(3+) -doped ZrO(2) nanocrystals under different excitation wavelengths in the red region is reported. The UPC emissions are due to the f-f electronic transitions from excited states (1)G(4) and (1)D(2) of Tm(3+). We observed a chromatic change in the UPC with tuning the excitation wavelength. The UPC emission bands at 475, 488, and 501 nm are observed under excitation at 649 nm, but bands centered at 454 and 460 nm are observed when the excitation wavelength is tuned to 655 nm. The UPC emission could be tuned from 501 to 454 nm ( approximately 47 nm) by changing the excitation wavelength from 649 to 655 nm ( approximately 6 nm). The pump power dependence of the emission bands at 475, 488, and 501 nm were investigated on excitation intensity at 649 nm, and the emission bands at 454 and 460 nm are investigated on excitation intensity at 655 nm, which confirms that all of these UPC emission lines are a two-photon absorption process.     

Arrowroot starch-based films incorporated with a carnauba wax nanoemulsion,cellulose nanocrystals,and essential oils: a new functional material for food packaging applications

Arrowroot starch (AA)-based films incorporated with a carnauba wax nanoemulsion (CWN), cellulose nanocrystals (CNCs), and essential oils (EOs) from Mentha spicata (MEO) and Cymbopogon martinii (CEO) were produced using the casting technique and then characterized in terms of their water barrier, tensile, thermal, optical, and microstructural properties and in vitro antifungal activity against Rhizopus stolonifer and Botrytis cinerea. Whereas the incorporation of CNCs decreased the moisture content and water vapor permeability of the AA/CWN/CNC film, the additional incorporation of either EO decreased the transparency and affected the microstructure of the AA/CWN/CNC/EO nanocomposites. MEO and CEO incorporation improved the thermal stability of the films and provided excellent protection against fruit-spoiling fungi. Because of their excellent barrier properties against fungal growth, water vapor permeability, and ultraviolet and visible light, these AA/CWN/CNC/EO films have promising potential for application as active food packaging or coating materials.

Graphic abstract

     

Microbiological Decontamination of Water: Improving the Solar Disinfection Technique (SODIS) with the Use of Nontoxic Vital Dye Methylene Blue

Rational use of water is a major challenge for governments and global organizations, with easy and inexpensive interventions being sought by communities that are not supplied with drinking water. In this context, solar disinfection (SODIS) has shown great efficiency for water disinfection. To speed up the process and improve inactivation, we studied the effects of methylene blue (MB) as a photodynamic agent because of its ability to absorb visible light (red wavelength) and generate singlet oxygen as a reactive species, thereby inactivating bacteria and viruses present in water. In this study, samples of clean mineral water were artificially contaminated with Gram‐positive (Staphylococcus epidermidis or Deinococcus radiodurans) or with Gram‐negative strains (Escherichia coli or Salmonella typhimurium) and exposed to traditional SODIS or to MB‐SODIS. A lethal synergistic effect was observed when cultures were illuminated in the presence of MB. The obtained results indicate that bacterial inactivation can be achieved in a much shorter time when using MB associated with SODIS treatment. Therefore, this technique was able to provide safe water for consumption through the inactivation of microorganisms in general, including pathogens and some strains resistant to the traditional SODIS procedure, thus allowing its use in areas usually less exposed to sunlight.     

Effect of Diets,Familial History,and Alternative Therapies on Genomic Instability of Breast Cancer Patients

This study evaluates a correlation between family history, micronutrients intake, and alternative therapies with genetic instability, before and during breast cancer treatment. For this study, a total of 150 women were selected. Among those, 50 women were breast cancer patients on chemotherapy, while 50 breast cancer patients were on radiotherapy, and 50 were healthy females. All the participants signed the informed consent form and answered the public health questionnaire. Samples of buccal epithelial and peripheral blood cells were collected and analyzed through micronucleus and comet assays. The cells were evaluated for apoptosis and DNA damage. Results showed the association of patients’ family history with an increase in toxicogenetic damage before and during cancer therapy. On the other hand, patients with late-onset cancer also presented genetic instability before and during therapy, along with those who did not take sufficient vegetables and alternative therapies. A positive correlation was observed between the genetic instability and alternative therapies, while inverse correlation was recorded with the vegetable consumption. Results clearly explain that the nutritional aspects and alternative therapies influence the genetic instability before and during cancer therapies especially in radiotherapy treated patients. Our data could be used for the monitoring therapies and management of breast cancer patients.