The stable forking conjecture and generic structures

 We prove that for any simple theory which is constructed via Fr?issé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds. Received: 22 January 2001 / Published online: 19 December 2002 This article is part of the author's D-Phil thesis, written at the University of Oxford and supported by the Ministry of Higher Education of Iran. The author would like to thank the Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran, for its financial support whilst working on this article. Mathematics Subject Classification (2000): 03C45 Key words or phrases: Generic structures – Fr?issé-Hrushovski method – Predimension – Simple theories – Stable theories – Stable forking conjecture     

Large area single-mode parity-time-symmetric laser amplifiers

By exploiting recent developments associated with parity-time (PT) symmetry in optics, we here propose a new avenue in realizing single-mode large area laser amplifiers. This can be accomplished by utilizing the abrupt symmetry breaking transition that allows the fundamental mode to experience gain while keeping all the higher order modes neutral. Such PT-symmetric structures can be realized by judiciously coupling two multimode waveguides, one exhibiting gain while the other exhibits an equal amount of loss. Pertinent examples are provided for both semiconductor and fiber laser amplifiers.     

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.     

Effects of Magnetic Nanofluid Fuel Combustion on the Performance and Emission Characteristics

Although the compression ignition engines are a significant source of power, their detrimental emissions create considerable problems to the environment as well as to humans. The objective of the present experimental investigation is to examine the effects of the magnetic nanofluid fuels on combustion performance characteristics and exhaust emissions. In this regard, the Fe₃O₄ nanoparticles dispersed in the diesel fuel with the nanoparticle concentrations of 0.4 and 0.8 vol% were employed for combustion in a single-cylinder, direct-injection diesel engine. After a series of experiments, it was demonstrated that the nanoparticle additives, even at very low concentrations, have considerable influence in diesel engine characteristics. Furthermore, the results indicated that the nanofluid fuel with nanoparticle concentration of 0.4 vol% shows better combustion characteristics in comparison with that of 0.8 vol%. Based on the experimental results, NO _x and SO₂ emissions dramatically reduce, while CO emissions and smoke opacity noticeably increase with increasing the dosing level of nanoparticles.     

Sequentially Cohen-Macaulay Modules Under Base Change

ABSTRACT

Assume that ?:(R, ± 𝔪) → (S, ± 𝔫) is a local flat homomorphism between commutative Noetherian local rings R and S. Let M be a finitely generated R-module. We investigate the ascent and descent of sequentially Cohen-Macaulay properties between the R-module M and the S-module M ? _R  S.     

Liquid-liquid extraction and spectrophotometric determination of palladium with 2-mercaptobenz-amide

2-Mercaptobenzamide (MBA) was investigated as a reagent for the extraction of palladium. The palladium complex of MBA was extracted into tributyl phosphate (TBP). The pK_a of the ligand was 5.45 with the stability constant of the palladium complex β₂=10^7.1. The composition of the complex in TBP was Pd:MBA:TBP=1:2:2. Addition of sodium chloride accelerated the rate of extraction. Various interfering ions could be masked with EDTA; Ag(I), Au(III), Os(VIII), Se(IV), Te(IV) etc. interfered. The molar absorptivity was 1.59×10⁴ l mol^?1 cm^?1; 1–35 μg Pd could be determined at pH 6.0.     

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13C-13C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³C-¹³C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³C-¹³C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.     

Phytotherapeutic inhibition of supragingival dental plaque

Antimicrobial activities and biofilm-formation preventive properties of Mentha piperita and Cuminum cyminum essential oils and chlorhexidine were assessed against Streptococcus mutans and Streptococcus pyogenes. Gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) analysis led to the identification of 26 and 32 compounds in the essential oils of M. piperita and C. cyminum, respectively. Minimal bactericidal concentrations (MBC) of the oils and chlorhexidine and microbial decimal reduction time (D value) were determined. Antibacterial and in vivo biofilm preventive efficacies of all the concentrations of M. piperita oil were significantly (p<0.001) higher. The biofilm inhibitory properties in planktonic cultures were in M. piperita > chlorhexidine > C. cyminum order. In vivo experiments conducted on male and female volunteers who brushed with essential oil blended toothpastes indicated that lower concentrations of the oils, in particular the M. piperita oil, were significantly higher (p<0.001) and effective during the course of the study as compared to chlorhexidine. In conclusion, there may be a potential role for essential oils in the development of novel anticaries treatments.     

Theoretical and experimental investigation of morphology and temperature effects on adsorption of organic vapors in single-walled carbon nanotubes

Hexane adsorption on single-walled carbon nanotube (SWNT) bundles is studied by both simulation and experimentally using a previously developed computer-aided methodology, which employed a smaller physisorbed probe molecule, nitrogen, to explore the porosity of nanotube samples. Configurational-bias grand canonical Monte Carlo simulation of hexane adsorption on localized sites of the bundles is carried out to predict adsorption on their external surface and in their internal sites. These localized isotherms are then combined into a global isotherm for a given sample by using knowledge of its tube-diameter distribution and structural parameters, such as the fraction of open-ended nanotubes and the external surface area of bundles in samples, which have been independently determined from the standard nitrogen adsorption isotherm. The near-perfect replication of experimental isotherms demonstrates the validity of our method for structural characterization of SWNT samples. The effect of temperature on adsorption is also studied and the simulation results are extrapolated to predict the limiting hexane adsorption capacity of the samples. The similarity between the hexane adsorption isotherms and those of other organic molecules demonstrates that the adsorption mechanisms explored here are not specific to hexane, and that the proposed methodology can be potentially applicable to other sorbates with equal success.     

The phenomenon of conglomerate crystallization. Part 40: The crystallization behavior oftrans- Co(III) amines (+)546-trans-[Co(3,2,3-tet)(NO2)2]Cl·3H2O (I), (−)589 -trans-[Co(3,2,3-tet)Cl2]NO3 (II), and of (+)546-trans-[Co(3,2,3-tet)(NO2)2]NO3 (III)

A racemic solution of (I) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₄₆-trans-[Co(3,2,3-tet)(NO₂)₂]Cl·3H₂O (I), CoClO₇N₆C₈H₂₈. It crystallizes in the enantiomorphic space groupP2_l2_l2_l, with lattice constantsa=18.501(15) å,b=14.433(2) å, andc=6.441(3) å;V=1720.07 å³ andd(calc. M.W.=414.73,Z=4)=1.601 g cm^?3. A total of 2305 data were collected over the range of 4?≤2θ ≤55?; of these, 1724 (independent and withI > 3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.920 cm^?1), and the relative transmission coefficients ranged from 0.8258 to 0.9565. Refinement was carried out for both lattice enantiomorphs, and at this stage theR(F) andR _w (F) residuals were, respectively, 0.0381 and 0.0479 for (+ + +) and 0.0448 and 0.0532 for (? ? ?). Thus, the former was selected as correct for our specimen, and the final cycle of refinement with the (+ + +) model converged toR(F) andR _w (F) of 0.0315 and 0.0365. A racemic solution of (II) crystallizes as a conglomerate from which a crystal we selected was found to be (?)₅₈₉-trans-[Co(3,2,3-tet)Cl₂]NO₃ (II), CoCl₂O₃N₅C₈H₂₂. It crystallizes in the enantiomorphic space groujp,P2_l with lattice constantsa=6.395(2) å,b=8.886(2) å,c=13.185(2) å, andΒ=99.24(2)?;V=739.59 å³ andd(calc. M.W.=366.14,Z=2)=1.646 g cm ^?3. A total of 2912 data were collected over the range of 4?<2θ<64?; of these, 2147 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ =15.424 cm^?1), and the relative transmission coefficients ranged from 0.9632 to 0.9985. Refinement was carried out for both lattice enantiomorphs, and the finalR(F) andR _w (F) residuals were, respectively, 0.0326 and 0.0328 for (+ + +) and 0.0347 and 0.0348 for (? ? ?). Thus, the (+ + +) was selected as correct for our specimen. A racemic solution of (III) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₈₉-trans-[Co(3,2,3-tet)(NO₂)₂]NO₃ (III), CoO₇N₇C₈H₂₂. It crystallizes in the enantiomorphic space group,P2_l with lattice constantsa=6.295(1) å, b=15.108(3) å,c=8.029(1) å, andΒ=100.28(2)?;V=751.35 å³ andd(calc. M.W.=387.24,Z=2)=1.712 g cm^?3. A total of 2393 data were collected over the range of 4?≤2θ≤60?; of these, 1869 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.859 cm^?1), and the relative transmission coefficients ranged from 0.8814 to 0.9976. Refinement was carried out for both lattice enantiomorphs and the finalR(F) andR _w (F) residuals were, respectively, 0.0463 and 0.0482 for (+ + +) and 0.0441 and 0.0442 for (? ? ?). Thus, the latter was selected as correct for our specimen, and the final cycle of refinement with the (? ? ?) model converged toR(F) andR _w (F) of 0.0436 and 0.0421. For all three compounds, the six-membered rings are chairs; the secondary nitrogens are chiral centers, and the five-membered rings are ordered and conformationally dissymmetric, as expected. Coincidentally, in (I), (II), and (III) the central rings are right-handed helices withδ(+50.0?),δ(+53.3?), andδ(+48.3?), respectively. Thus, the secondary nitrogens of all three cations are (R), rendering the cations chiral. The incidence of conglomerate crystallization intrans coordination compounds is rare, and those known are asymmetrically substituted (see Ref. 4 for the four known cases). Thus, the incidence of such crystallization mode in a new series of [trans- Co(amine ligands)X₂]⁺ cations bearing symmetrical pairs oftrans ligands was an unexpected and welcomed event. In all three cases, the counteranions are bonded to the hydrogens of the terminal -NH₂ moieties, thus forming an overall entity which resembles a macrocycle. In fact, parallels between the crystallization behavior of our compounds and that of macrocycles bearing related fragments is discussed. Finally, in the three compounds, homochiral cations are linked into infinite strings by hydrogen bonds between the axial ligands and amino hydrogens on adjacent cations of the string. In turn, strings are stitched together by the counteranions which form bonds with amino hydrogens on cations of adjacent strings.