On the Collision between two PNG Droplets

In this article we study the interface generated by the collision between two crystals growing layer by layer on a one-dimensional substrate through random decomposition of particles. We relate this interface with the notion of β-path in an equivalent directed polymer model and, by using asymptotics results from J. Baik and E. Rains, J. Stat. Phys., 100:523–541 (2000). and some hydrodynamic tools introduced by E. Cator and P. Groeneboom, Ann. Probab., 33:879–903 (2005), we derive a law of large numbers for such a path and obtain some bounds for its fluctuations. 2000 Mathematics Subject Classification: 60C05, 60K35     

The Voice Handicap Index: Correlation Between Subjective Patient Response and Quantitative Assessment of Voice

The aim of this prospective study is to elucidate the relationship between the Voice Handicap Index (VHI) and several voice laboratory measurements in the network of the multidimensional voice assessment. Fifty-eight patients were included. Each patient replies to the questionnaire and performs a voice assessment during the same time. The following parameters were measured: minimum frequency, maximum frequency, range, minimum intensity, subglottic pressure, mean flow, maximum phonation time, jitter, and dysphonia severity index. Regarding the relationship with the scores of the VHI, poor correlations with the minimal frequency for all the scores except the emotional one (total and subscales) and with the range for only the physical one are found. Seventeen questions correlate with the voice laboratory measurements we performed, with a decreased distribution between physical, functional, and emotional subscales. We observe that acoustic parameter is correlated with the emotional subscale, the parameters of the profile range are more often involved in the emotional subscale, as is the minimal frequency, but never with the physical subscale, and all the subscales are interesting despite the smaller number of differences with the emotional one. The VHI and the laboratory measurements give independent informations in practice.     

Gras-Type Conjectures Fattitle for Function Fields

Based on results obtained in [15], we construct groups of special S-units for function fields of characteristic p>0, and show that they satisfy Gras-type Conjectures. We use these results in order to give a new proof of Chinburg's ₃-Conjecture on the Galois module structure of the group of S-units, for cyclic extensions of prime degree of function fields.     

Orbitrap mass spectrometry for monitoring the ganglioside pattern in human cerebellum development and aging

We have developed here a superior approach based on high‐resolution (HR) mass spectrometry (MS) for monitoring the changes occurring with development and aging in the composition and structure of cerebellar gangliosidome. The experiments were focused on the comparative screening and structural analysis of gangliosides expressed in fetal and aged cerebellum by Orbitrap MS with nanoelectrospray ionization (nanoESI) in the negative ion mode. The employed ultrahigh‐resolution MS platform allowed the discrimination, without the need of previous separation, of 159 ions corresponding to 120 distinct species in the native ganglioside mixtures from fetal and aged cerebellar biopsies, many more than detected before, when MS platforms of lower resolution were employed. A number of gangliosides, in particular polysialylated belonging to GT, GQ, GP, and GS classes, modified by O‐fucosylation, O‐acetylation, or CH₃COO^? were discovered here, for the first time in human cerebellum. These components, found differently expressed in fetal and aged tissues, indicated that the ganglioside profile in cerebellum is development stage‐ and age‐specific. Following the fragmentation analysis by high‐energy collision‐induced dissociation (HCD) tandem MS (MS/MS), we have also observed that the intimate structure of certain compounds has not changed during the development and aging of the brain, an aspect which could open new directions in the investigation of ganglioside biomarkers in cerebellar tissue.     

Rare-Earth Metal Complexes of the Antibacterial Drug Oxolinic Acid: Synthesis,Characterization, DNA/Protein Binding and Cytotoxicity Studies

“Drug repositioning” is a current trend which proved useful in the search for new applications for existing, failed, no longer in use or abandoned drugs, particularly when addressing issues such as bacterial or cancer cells resistance to current therapeutic approaches. In this context, six new complexes of the first-generation quinolone oxolinic acid with rare-earth metal cations (Y³⁺, La³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺) have been synthesized and characterized. The experimental data suggest that the quinolone acts as a bidentate ligand, binding to the metal ion via the keto and carboxylate oxygen atoms; these findings are supported by DFT (density functional theory) calculations for the Sm³⁺ complex. The cytotoxic activity of the complexes, as well as the ligand, has been studied on MDA-MB 231 (human breast adenocarcinoma), LoVo (human colon adenocarcinoma) and HUVEC (normal human umbilical vein endothelial cells) cell lines. UV-Vis spectroscopy and competitive binding studies show that the complexes display binding affinities (K_b) towards double stranded DNA in the range of 9.33 × 10⁴ − 10.72 × 10⁵. Major and minor groove-binding most likely play a significant role in the interactions of the complexes with DNA. Moreover, the complexes bind human serum albumin more avidly than apo-transferrin.     

Gadolinium Photocatalysis: Dearomative [2+2] Cycloaddition/Ring-Expansion Sequence with Indoles

Lanthanide photocatalysts are much less investigated in synthetic chemistry than rare and expensive late transition metals. We herein introduce Gd^III photocatalysis of a highly regioselective, intermolecular [2+2] photocycloaddition/ring-expansion sequence with indoles, which could provide divergent access to cyclopenta[b]indoles and indolines. A simple and commercially available Gd(OTf)₃ salt is sufficient for this visible-violet-light-induced transformation. The reaction proceeds either through a transient or start-to-end dearomatization cascade and shows excellent regioselectivity (usually >95:5 r.r.), broad scope (59 examples), good functional group tolerance and facile scale-up under mild, direct visible-light-excitation conditions. Mechanistic investigations reveal that direct excitation of the Gd(OTf)₃/indole mixture gives an excited state intermediate, which undergoes the subsequent [2+2] cycloaddition and cyclobutane-expansion cascade.     

High-temperature phase transitions in CsH2PO4 under ambient and high-pressure conditions: a synchrotron x-ray diffraction study

To clarify the microscopic origin of the temperature-induced three-order-of-magnitude jump in the proton conductivity of CsH(2)PO(4) (superprotonic behavior), we have investigated its crystal structure modifications within the 25-300 degrees C temperature range under both ambient- and high-pressure conditions using synchrotron x-ray diffraction. Our high-pressure data show no indication of the thermal decomposition/polymerization at the crystal surface recently proposed as the origin of the enhanced proton conductivity [Phys. Rev. B 69, 054104 (2004)]. Instead, we found direct evidence that the superprotonic behavior of the title material is associated with a polymorphic structural transition to a high-temperature cubic phase. Our results are in excellent agreement with previous high-pressure ac impedance measurements.     

Kinetics of N-glutaryl-L-phenylalanine p-nitroanilide hydrolysis catalyzed by alpha-chymotrypsin in aqueous solutions of alkyltrimethylammonium bromides

The rate of N-glutaryl-L-phenylalanine p-nitroanilide hydrolysis catalyzed by alpha-chymotripsin has been measured in aqueous solutions of cetyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and dodecyltrimethylammonium bromide at concentrations below and above their critical micellar concentrations (CMC). For the three surfactants considered superactivity was observed, with maximum catalytic efficiencies taking place near the corresponding CMCs. The effect of the surfactants after the CMCs is mostly due to a decreased thermodynamic activity of the substrate due to its incorporation into the micelles. After addition of the surfactants, the Michaelis constant values (corrected to take into account the free substrate concentration) tend to decrease, passing through an ill defined minimum, afterwards reaching a constant value. The catalytic rate constants show the same profiles that the catalytic efficiency, being maxima near the surfactants CMCs. This maximum is more important for the surfactant having the shorter tail. This result is explained by considering that the hydrophobicity of the surfactant influences more the CMC than its association to the enzyme.     

Maximum principles and isoperimetric inequalities for some Monge–Ampère-type problems

In this note we derive a maximum principle for an appropriate functional combination of u(x)$u(\mathbf{x})$ and |∇u|²${|\mathrm{\nabla }u|}^2$, where u(x)$u(\mathbf{x})$ is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in R^N+1${\mathbb{R}}^{N+1}$.     

Construction of the mutually orthogonal extraordinary supersquares

Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in $\mathbb{F}_d \times \mathbb{F}_d$ . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\mathbb{F}_d \times \mathbb{F}_d$ are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d ? 1 mutually orthogonal Latin squares is only a special case, namely Type I.