Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Comparison Between Micro- and Macrosurgical Techniques for the Treatment of Localized Gingival Recessions Using Coronally Positioned Flaps and Enamel Matrix Derivative

Background: The aim of this study is to compare the macro- and microsurgery techniques for root coverage using a coronally positioned flap (CPF) associated with enamel matrix derivative (EMD). Methods: Thirty patients were selected for the treatment of localized gingival recessions (GRs) using CPF associated to EMD. Fifteen patients were randomly assigned to the test group (TG), and 15 patients were randomly assigned to the control group (CG). The microsurgical approach was performed in the TG, and the conventional macrosurgical technique was performed in the CG. The clinical parameters evaluated before surgery and after 6 months were GR, probing depth, relative clinical attachment level, width of keratinized tissue (WKT), and thickness of keratinized tissue (TKT). The discomfort evaluation was performed 1 week postoperative. Results: There were no statistically significant differences between groups for all parameters at baseline. At 6 months, there was no statistically significant difference between the techniques in achieving root coverage. The percentage of root coverage was 92% and 83% for TG and CG, respectively. After 6 months, there was a statistically significant increase of WKT and TKT in TG only. Both procedures were well tolerated by all patients. Conclusions: The macro- and microsurgery techniques provided a statistically significant reduction in GR height. After 6 months, there was no statistically significant difference between the techniques regarding root coverage, and the microsurgical technique demonstrated a statistically significant increase in WKT and TKT. J Periodontol 2010;81:1572-1579.

Laser locking to the Hg-199 S-1(0)-P-3(0) clock transition with 5.4x10(-15)/root tau fractional frequency instability

With Hg-199 atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is similar to 15 Hz. Here we lock an ultrastable laser to this ultranarrow S-1(0) - P-3(0) clock transition and achieve a fractional frequency instability of 5.4 x 10(-15) / root tau for tau <= 400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0 x 10(-17) s-(1) (-16.9 mHzs(-1) at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4 x 10(-16) per cavity. (c) 2012 Optical Society of America

Employing perichromism for probing the properties of carboxymethyl cellulose films: an expedient, accurate method for the determination of the degree of substitution of the biopolymer derivative

The properties of films of carboxymethyl cellulose, CMC, of different degree of substitution, DS, have been examined by the use of perichromic indicators (probes). The film properties that have been determined are: empirical polarity, E-T(33); "acidity", alpha; "basicity", beta; and dipolarity/polarizability, pi*. This has been achieved by employing the following perichromic probes: 4-nitroaniline, 4-nitroanisole, 4-nitro-N,N-dimethylaniline, and 2,6-dichloro-4-(2,4,6-triphenyl-pyridinium-1-yl)phenolate, WB. The correlations between both E-T(33)- or pi* and DS were found to be linear; that between beta and DS is a second order polynomial; no obvious correlation was found between alpha and DS. The polarities of CMC films are in the range of those of butyl alcohols. As models for CMC, we have employed cellulose plus CMC of high DS; oxidized cellulose with degree of oxidation = 0.5; sodium glucuronate. The former model behaved akin to CMC, but the plots of the perichromic properties versus DS showed different slopes/intercepts. FTIR data and molecular dynamics simulations on the solvation of WB have shown that this difference can be traced to more efficient hydrogen bonding between the film of the model and the probe. This affects the intra-molecular charge-transfer energy of the latter, leading to different responses to the variation of DS. Based on the excellent linear correlation between E-T(33) and DS, for CMC from different origins, we suggest that perichromism is a simple, accurate, and expedient alternative for the determination of DS of the biopolymer derivative.

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Acellular dermal matrix graft with or without enamel matrix derivative for root coverage in smokers: a randomized clinical study

Aim: The aim of this randomized controlled clinical study was to compare the use of an acellular dermal matrix graft (ADMG) with or without the enamel matrix derivative (EMD) in smokers to evaluate which procedure would provide better root coverage. Material and Methods: Nineteen smokers with bilateral Miller Class I or II gingival recessions >= 3 mm were selected. The test group was treated with an association of ADMG and EMD, and the control group with ADMG alone. Probing depth, relative clinical attachment level, gingival recession height, gingival recession width, keratinized tissue width and keratinized tissue thickness were evaluated before the surgeries and after 6 months. Wilcoxon test was used for the statistical analysis at significance level of 5%. Results: No significant differences were found between groups in all parameters at baseline. The mean gain recession height between baseline and 6 months and the complete root coverage favored the test group (p = 0.042, p = 0.019 respectively). Conclusion: Smoking may negatively affect the results achieved through periodontal plastic procedures; however, the association of ADMG and EMD is beneficial in the root coverage of gingival recessions in smokers, 6 months after the surgery.

DERIVATIVE SPECTROPHOTOMETRIC METHOD FOR DEYERMINATION OF ACYCLOVIR IN POLYMERIC NANOPARTICLES

A derivative spectrophotometric method was validated for quzintification of acyclovir in poly (n-butylcyanoacrylate) (PBCA) nanoparticles. Specificity, linearity. precision, accuracy, recovery. detection (LOD) and quantification (LOQ) Inuits were established for method validation. First-derivative it 295.2 nm eliminated interferences from nanoparticle ingredients and presented linearity for acyclovir concentrations ranging front 1.25 to 40.0 mu g/mL. (r = 0.9999). Precision and accuracy data demonstrated good reproducibility. Recovery ranged from 99.3 to 101.2. LOD) was 0.08 mu g/mL and LOQ. 0.25 mu g/mL. Thus. the proposed method proved to be easy. low cost. and accurate, and therefore, an useful alternative to quantify acyclovir in nanoparticles.

Toward the Optimization of an e-Tongue System Using Information Visualization: A Case Study with Perylene Tetracarboxylic Derivative Films in the Sensing Units

The wide variety of molecular architectures used in sensors and biosensors and the large amount of data generated with some principles of detection have motivated the use of computational methods, such as information visualization techniques, not only to handle the data but also to optimize sensing performance. In this study, we combine projection techniques with micro-Raman scattering and atomic force microscopy (AFM) to address critical issues related to practical applications of electronic tongues (e-tongues) based on impedance spectroscopy. Experimentally, we used sensing units made with thin films of a perylene derivative (AzoPTCD acronym), coating Pt interdigitated electrodes, to detect CuCl(2) (Cu(2+)), methylene blue (MB), and saccharose in aqueous solutions, which were selected due to their distinct molecular sizes and ionic character in solution. The AzoPTCD films were deposited from monolayers to 120 nm via Langmuir-Blodgett (LB) and physical vapor deposition (PVD) techniques. Because the main aspects investigated were how the interdigitated electrodes are coated by thin films (architecture on e-tongue) and the film thickness, we decided to employ the same material for all sensing units. The capacitance data were projected into a 2D plot using the force scheme method, from which we could infer that at low analyte concentrations the electrical response of the units was determined by the film thickness. Concentrations at 10 mu M or higher could be distinguished with thinner films tens of nanometers at most-which could withstand the impedance measurements, and without causing significant changes in the Raman signal for the AzoPTCD film-forming molecules. The sensitivity to the analytes appears to be related to adsorption on the film surface, as inferred from Raman spectroscopy data using MB as analyte and from the multidimensional projections. The analysis of the results presented may serve as a new route to select materials and molecular architectures for novel sensors and biosensors, in addition to suggesting ways to unravel the mechanisms behind the high sensitivity obtained in various sensors.

Synthesis and characterization of the atropisomeric relationships of a substituted N-phenyl-bipyrazole derivative with anti-inflammatory properties

This work describes the atropisomeric relationships of 3-methyl-5-(3-methyl-5-phenyl-1H-pyrazol-1-yl)-1-phenyl-1H-pyrazol-4-amine (2d), which belongs to series 4-aminobipyrazole derivatives designed as anti-inflammatory agents. The 1H nuclear magnetic resonance spectra obtained in the presence of a chiral lanthanide shift salt associated to chiral high-performance liquid chromatography analysis, X-ray diffraction, and molecular modeling tools confirmed that ortho bis-functionalized bipyrazole 2d exists as a mixture of aR,aS-atropisomers. These results provide useful information to understand the pharmacological profile of this derivative and of other 4-aminobipyrazole analogs. Chirality 24:463470, 2012. (c) 2012 Wiley Periodicals, Inc.

Higher spatial derivative field theories

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.

delta-Lactam derivative from thermophilic soil fungus exhibits in vitro anti-allergic activity

From cultures of thermophilic soil fungus Humicola grisea var thermoidea, a delta-lactam derivative (3-(2-(4-hydroxyphenyl)-2-oxoethyl)-5,6-dihydropyridin-2( 1H)-one) that displayed anti-allergic activity was isolated, which was predicted by in silico computational chemistry approaches. The in vitro anti-allergic activity was investigated by beta-hexosaminidase release assay in rat basophilic leukaemia RBL-2H3 cells. The delta-lactam derivative exhibited similar anti-allergic activity (IC50 = 18.7 +/- 6.7 mu M) in comparison with ketotifen fumarate (IC50 = 15.0 +/- 1.3 mu M) and stronger anti-allergic activity than azelastine (IC50 = 32.0 mu M). Also, the MTT cytotoxicity assay with RBL-2H3 cells showed that delta-lactam does not display cytotoxicity at concentrations lower than 50 mu M. This study suggests that the delta-lactam derivative has the potential to be used as a lead compound in the development of anti-allergic drugs for clinical use in humans.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

Effects of enamel matrix derivative and transforming growth factor-β1 on human osteoblastic cells

Abstract Background Extracellular matrix proteins are key factors that influence the regenerative capacity of tissues. The objective of the present study was to evaluate the effects of enamel matrix derivative (EMD), TGF-β1, and the combination of both factors (EMD+TGF-β1) on human osteoblastic cell cultures. Methods Cells were obtained from alveolar bone of three adult patients using enzymatic digestion. Effects of EMD, TGF-β1, or a combination of both were analyzed on cell proliferation, bone sialoprotein (BSP), osteopontin (OPN) and alkaline phosphatase (ALP) immunodetection, total protein synthesis, ALP activity and bone-like nodule formation. Results All treatments significantly increased cell proliferation compared to the control group at 24 h and 4 days. At day 7, EMD group showed higher cell proliferation compared to TGF-β1, EMD + TGF-β1 and the control group. OPN was detected in the majority of the cells for all groups, whereas fluorescence intensities for ALP labeling were greater in the control than in treated groups; BSP was not detected in all groups. All treatments decreased ALP levels at 7 and 14 days and bone-like nodule formation at 21 days compared to the control group. Conclusions The exposure of human osteoblastic cells to EMD, TGF-β1 and the combination of factors in vitro supports the development of a less differentiated phenotype, with enhanced proliferative activity and total cell number, and reduced ALP activity levels and matrix mineralization.

Derivative spectrophotometric method for determination of acyclovir in polymeric nanoparticles

A derivative spectrophotometric method was validated for quantification of acyclovir in poly (n-butylcyanoacrylate) (PBCA) nanoparticles. Specificity, linearity, precision, accuracy, recovery, detection (LOD) and quantification (LOQ) limits were established for method validation. First-derivative at 295.2 nm eliminated interferences from nanoparticle ingredients and presented linearity for acyclovir concentrations ranging from 1.25 to 40.0 µg/mL (r = 0.9999). Precision and accuracy data demonstrated good reproducibility. Recovery ranged from 99.3 to 101.2. LOD was 0.08 µg/mL and LOQ, 0.25 µg/mL. Thus, the proposed method proved to be easy, low cost, and accurate, and therefore, an useful alternative to quantify acyclovir in nanoparticles.