Zeros of Stieltjes and Van Vleck polynomials and applications

Stieltjes and Van Vleck polynomials arise in the study of the polynomial solutions of the generalized Lame's differential equations. In this paper, the location of the zeros of these polynomials, relative to a prescribed location of the complex constants occurring in the differential equation is determined. Various results to this effect have been put forward from time to time by Marden, Stieltjes, Van Vleck, Bôcher, Klein, and Pólya, but all (except the one due to Marden) were obtained under very restrictive conditions on these constants. Some of these results are shown to be corollaries of our main theorem here. Moreover, applications to certain problems arising in physics and fluid mechanics are discussed.     

Multiple ionization in fast ion-atom collisions: simultaneous measurement of recoil momentum and projectile energy loss

The stability of nonlinear laser light filaments in a homogeneous isothermal plasma with respect to coupled electromagnetic and density perturbations is examined. In addition to the previously known modulational instability of a trapped electromagnetic mode, a new fast growing resonant instability is found. It corresponds to the growth of an excited eigenmode in the waveguide formed by the filament density depletion, the associated density response being supersonic and transversally localized. The evolution of the instability is illustrated by numerical simulations in two and three spatial dimensions.     

Ziziphus nummularia Attenuates the Malignant Phenotype of Human Pancreatic Cancer Cells: Role of ROS

Pancreatic cancer (PC) is the fourth leading cause of all cancer-related deaths. Despite major improvements in treating PC, low survival rate remains a major challenge, indicating the need for alternative approaches, including herbal medicine. Among medicinal plants is Ziziphus nummularia (family Rhamnaceae), which is a thorny shrub rich in bioactive molecules. Leaves of Ziziphus nummularia have been used to treat many pathological conditions, including cancer. However, their effects on human PC are still unknown. Here, we show that the treatment of human pancreatic ductal adenocarcinoma cells (Capan-2) with Ziziphus nummularia ethanolic extract (ZNE) (100–300 μg/mL) attenuated cell proliferation in a time- and concentration-dependent manner. Pretreatment with N-acetylcysteine, an ROS scavenger, attenuated the anti-proliferative effect of ZNE. In addition, ZNE significantly decreased the migratory and invasive capacity of Capan-2 with a concomitant downregulation of integrin α₂ and increased cell–cell aggregation. In addition, ZNE inhibited in ovo angiogenesis as well as reduced VEGF and nitric oxide levels. Furthermore, ZNE downregulated the ERK1/2 and NF-κB signaling pathways, which are known to drive tumorigenic and metastatic events. Taken together, our results suggest that ZNE can attenuate the malignant phenotype of Capan-2 by inhibiting hallmarks of PC. Our data also provide evidence for the potential anticancer effect of Ziziphus nummularia, which may represent a new resource of novel anticancer compounds, especially ones that can be utilized for the management of PC.     

Method development and optimization for the determination of selenium in bean and soil samples using hydride generation electrothermal atomic absorption spectrometry

The present investigation is the first part of an initiative to prepare a regional map of the natural abundance of selenium in various areas of Brazil, based on the analysis of bean and soil samples. Continuous-flow hydride generation electrothermal atomic absorption spectrometry (HG-ET AAS) with in situ trapping on an iridium-coated graphite tube has been chosen because of the high sensitivity and relative simplicity. The microwave-assisted acid digestion for bean and soil samples was tested for complete recovery of inorganic and organic selenium compounds (selenomethionine). The reduction of Se(VI) to Se(IV) was optimized in order to guarantee that there is no back-oxidation, which is of importance when digested samples are not analyzed immediately after the reduction step. The limits of detection and quantification of the method were 30 ng L⁻¹ Se and 101 ng L⁻¹ Se, respectively, corresponding to about 3 ng g⁻¹ and 10 ng g⁻¹, respectively, in the solid samples, considering a typical dilution factor of 100 for the digestion process. The results obtained for two certified food reference materials (CRM), soybean and rice, and for a soil and sediment CRM confirmed the validity of the investigated method. The selenium content found in a number of selected bean samples varied between 5.5 ± 0.4 ng g⁻¹ and 1726 ± 55 ng g⁻¹, and that in soil samples varied between 113 ± 6.5 ng g⁻¹ and 1692 ± 21 ng g⁻¹.     

A closer look at "social" boundary genes reveals knowledge to gene expression profiles

As social network analysis is gaining popularity in modeling real world problems, the task of applying the social network model concepts and notions to biological data is still one of the most attractive research problems to be addressed. According, our work described in this paper focuses on a particular set of genes that reside on the community boundaries in gene co-expression networks. Stemmed from community mining problem in social networks, peripheries of communities (i.e., boundaries) can be used to aid certain biological analysis. The proposed method consists of three parts: 1) Finding communities of gene co-expression networks through clustering. 2) Analyzing stability of community structures by Monte Carlo method. 3) Designing of dynamic adoption of boundaries using geometric convexity. We validated our findings using breast cancer gene expression data from various studies. Our approach contributes to the new branch of applying social network mechanisms in biological data analysis, leading to new data mining strategies implied by witnessing social behaviors in gene expression analysis.     

Electronic structure and optical properties of Sb2S3 crystal

The electronic and optical properties of Sb₂S₃ are studied using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in Wien2k. In this approach, the alternative form of the generalized gradient approximation (GGA) proposed by Engel and Vosko (EV-GGA) was used for the exchange correlation potential. The calculated band structure shows a direct band gap. The contribution of different bands was analyzed from total and partial density of states curves. Moreover, the optical properties, including the dielectric function, absorption spectrum, refractive index, extinction coefficient, reflectivity and energy-loss spectrum are all obtained and analyzed in detail.     

500 GHz mode-hop-free idler tuning range with a frequency-stabilized singly resonant optical parametric oscillator

A 1064 nm pumped continuous-wave, mid-IR (3-4 μm), signal-wave resonant optical parametric oscillator is frequency stabilized at the kilohertz jitter level to the transmission peak of an external high-finesse Fabry-Perot cavity. Owing to the high stability of the resonator length against acoustical perturbation, fine pump tuning of the idler wave around 3.3 μm results in an unprecedented mode-hop-free continuous scan over 500 GHz (17 cm?1).     

Structural characterization and activation energy of NiTiO3 nanopowders prepared by the co-precipitation and impregnation with calcinations

In this paper, we report on the formation of novel hexagonal NiTiO₃ nanopowders synthesized by the impregnation or co-precipitation methods through the thermal decomposition reaction of the precursors. The decomposition course was followed using differential thermal analysis (DTA) and thermogravimetric analysis (TGA) techniques. The intermediate decomposition products as well as the formed titanate were characterized using X-ray diffraction (XRD) and Fourier transform infrared (FT-IR) spectroscopy. XRD patterns of the precursors calcined at 1000 °C showed the formation of the single ilmenite-type rhombohedral structure only with the impregnated precursor, while with the precipitated NiTiO₃ powders one it indicates the presence of some NiO and TiO₂ impurities. Transmission electron microscopy (TEM) exhibited loosely agglomerated hexagonal particles with uniform morphology having a size around 61 nm. The Brunauer-Emmett-Teller (BET) surface area measurements showed a type III isotherm with calculated surface area of 152 m²/g. The plot of ln σ_ac vs. temperature as a function of frequency indicates a semiconducting behavior with ferroelectric phase transition at 605 K. The calculated activation in the ferroelectric region is 0.93 eV suggests the predominance of hopping conduction mechanism. Kinetic analysis of TG data according to different integral methods showed that in the NiC₂O₄·2H₂O–TiO₂ precursor, the water molecules are coordinately bounded and the presence of TiO₂ reduces the activation energy needed to the oxalate decomposition reaction.     

Synthese Originale de 5-Aryl (ou 5-benzyl)-2[(1-Diethoxyphosphonyl)methyl]-1,3,4-oxadiazoles par Action du Phosphonomethylhydrazide sur les Imidates N-Acyles

The phosphonomethylhydrazide 2a reacts with N-acylated imidates 3a–d to give the corresponding 5-aryl (or 5-benzyl)-2-[(1-diethoxyphosphonyl)methyl]-1,3,4-oxadiazoles 4a–d after the elimination of ethanamide 5. Compounds 2a–e are prepared by the action of triethyl phosphonoacetate 1 with hydrazine and its derivatives. The structures of 1,3,4-oxadiazoles 4a–d and hydrazides 2a–e have been unequivocally confirmed by means of IR, ¹ H, ¹³ C, ³¹ P NMR and mass spectrometry.     

The Stereoselective Synthesis of Conjugated Allylsilanes

2-trimethylsilylethylidenetriphenylphosphorane (5) (Seyferth–Wittig reagent) reacts stereoselectively with the carbonyl compounds 6a–f to give the conjugated allylsilanes 7a–f, each as a mixture of E-and Z-isomers. The stereoselectivity of reactions of E-cinnamaldehyde (6c) with 5 has been investigated at different temperatures. A successful E-stereoselective synthesis of 7c was achieved by reacting 5 with E-cinnamaldehyde (6c) under the conditions of a Wittig–Schlosser modification reaction. Structures of the allylsilanes 7a–f were deduced by compatible analytical and spectroscopic (IR, ¹H NMR, ¹³C NMR, and GC/MS) measurements. An assignment of the E:Z ratios of 7a–f is based on their ¹H NMR spectral data.