On dimensional rigidity of bar-and-joint frameworks

Let V={1,2,…,n}. A mapping p:V→R^r, where p¹,…,pⁿ are not contained in a proper hyper-plane is called an r-configuration. Let G=(V,E) be a simple connected graph on n vertices. Then an r-configuration p together with graph G, where adjacent vertices of G are constrained to stay the same distance apart, is called a bar-and-joint framework (or a framework) in R^r, and is denoted by G(p). In this paper we introduce the notion of dimensional rigidity of frameworks, and we study the problem of determining whether or not a given G(p) is dimensionally rigid. A given framework G(p) in R^r is said to be dimensionally rigid iff there does not exist a framework G(q) in R^s for s?r+1, such that ∥qⁱ-q^j∥²=∥pⁱ-p^j∥² for all (i,j)∈E. We present necessary and sufficient conditions for G(p) to be dimensionally rigid, and we formulate the problem of checking the validity of these conditions as a semidefinite programming (SDP) problem. The case where the points p¹,…,pⁿ of the given r-configuration are in general position, is also investigated.     

Lithiation of 2-Alkyl-3-amino- and 2-Alkyl-3-(methylamino)-4(3H)-quinazolinones(1)

3-Amino-2-methyl-4(3H)-quinazolinone has been doubly lithiated, on nitrogen and in the 2-methyl group, with n-butyllithium. The lithium reagent thus obtained reacts with a variety of electrophiles (D(2)O, benzophenone, cyclohexanone, cyclopentanone, acetophenone, benzaldehyde, tetraisopropylthiuram disulfide (TITD)) to give the corresponding 2-substituted derivatives in very good yields. Reactions of the dilithio reagent with 2 molar equiv of methyl iodide or phenyl isocyanate give disubstituted derivatives. Double lithiation of the 2-ethyl and 2-propyl analogues have been achieved using LDA, and subsequent reactions with most electophiles are then similar. In the reaction of the dianion of the 2-ethyl compound with TITD, deamination from position 3 takes place with the formation of the 2-substituted derivative. In reactions with prochiral ketones, the dianion of the 2-ethyl compound gives very high diastereoselectivity. Lithiation and subsequent reactions of 3-(methylamino) analogues take place in a similar manner, thus providing access to a range of substituted 3-(methylamino)-2-alkyl-4(3H)-quinazolinones by a general procedure. Lithiation of 3-(dimethylamino)-2-ethyl-4(3H)-quinazolinone did not take place under similar conditions. Lithiation of 3-amino-2-unsubstituted-4(3H)-quinazolinone was also unsuccessful.     

Catalytic activity and stability of anionic and cationic water soluble cobalt(II) tetraarylporphyrin complexes in the oxidation of 2-mercaptoethanol by molecular oxygen

The catalytic activity and stability of anionic cobalt(II) porphyrin complexes: 5,10,15,20-tetrakis(2,6-dichloro-3-sulfonatophenyl)porphyrinatocobalt(II), 5,10,15,20-tetrakis(2,4,6-trimethyl-3,5disulfonatophenyl)porphyrinatocobalt(II) and the cationic cobalt(II) porphyrin: 5,10,15,20-tetrakis[4-(diethylmethylammonio)phenyl]porphyrinatocobalt(II) tertraiodide have been investigated in the oxidation of 2-mercaptoethanol by dioxygen. All complexes were efficient catalysts for the auto-oxidation of 2-mercaptoethanol. The cationic cobalt(II) porphyrin has been found to be the most reactive catalyst. The rate of auto-oxidation of 2-mercaptoethanol catalysed by 5,10,15,20-tetrakis(2,4,6-trimethyl-3,5disulfonatophenyl)porphyrinatocobalt(II) has been found to increase with increasing the pH from 7 to 9 then decreased at higher pH. The rate constants of auto-oxidation reaction showed linear dependence on catalyst concentration and saturation kinetics in both 2-mercaptoethanol concentrations and dioxygen pressure. Anionic cobalt(II) porphyrin complexes showed higher stability than the cationic catalyst in repeat oxidation reactions. Immobilizing the anionic catalysts on ion exchange resin and supporting the cationic catalyst on clay mineral montmorillonite improved their stabilities towards oxidation.     

Poly(Urethane)-Crosslinked Poly(HEMA) Hydrogels

Abstract

Hydrogels have been prepared from 2-hydroxyethyl methacrylate polymerized in the presence of isocyanate-terminated poly(ethylene glycol) (PEG) crosslinking agents. PEGS of molecular weights 200, 400, and 1000 were investigated. The crosslinked nature of the hydrogels was demonstrated by their insolubility in solvents which normally dissolve poly(HEMA). Hexamethylene diisocyanate (HDI) was mainly used as the isocyanate. The molecular weight of the PEG and the crosslinker content significantly influenced the equilibrium water sorption and mechanical properties of the saturated networks. It was observed that as the molecular weight of the PEG increased, the water sorption increased and the nominal modulus decreased. However, for higher levels of cross-linker, water sorption decreased and modulus increased at low molecular weight PEG; for PEG 1000, water absorption increased as crosslinker content increased. These results are explained by the competing effects of flexibility, crosslink density, and hydrophobicity contributed by the various constituents of the hydrogels.     

Effect of Cactus (Opuntia ficus-indica) and Acacia (Acacia seyal) Gums on the Pasting,Thermal, Textural,and Rheological Properties of Corn,Sweet Potato,and Turkish Bean Starches

This study was planned to explore the locally available natural sources of gum hydrocolloids as a natural modifier of different starch properties. Corn (CS), sweet potato (SPS), and Turkish bean (TBS) starches were mixed with locally extracted native or acetylated cactus (CG) and acacia (AG) gums at 2 and 5% replacement levels. The binary mixtures (starch–gums) were prepared in water, freeze dried, ground to powder, and stored airtight. A rapid viscoanalyzer (RVA), differential scanning calorimeter (DSC), texture analyzer, and dynamic rheometer were used to explore their pasting, thermal, textural, and rheological properties. The presence of acetylated AG or CG increased the final viscosity (FV) in all three starches when compared to starch pastes containing native gums. Plain SPS dispersion had a higher pasting temperature (PT) than CS and TBS. The addition of AG or CG increased the PT of CS, SPS, and TBS. The thermograms revealed the overall enthalpy change of the starch and gum blends: TBS > SPS > CS. The peak temperature (T_p) of starches increased with increasing gum concentration from 2 to 5% for both AG and CG native and modified gums. When compared to the control gels, the addition of 2% CG, either native or modified, reduced the syneresis of starch gels. However, further addition (5% CG) increased the gels’ syneresis. Furthermore, the syneresis for the first cycle on the fourth day was higher than the second cycle on the eighth day for all starches. The addition of native and acetylated CG reduced the hardness of starch gels at all concentrations tested. All of the starch dispersions had higher G′ than G″ values, indicating that they were more elastic and less viscous with or without the gums. The apparent viscosity of all starch gels decreased as shear was increased, with profiles indicating time-dependent thixotropic behavior. All of the starch gels, with or without gums, showed a non-Newtonian shear thinning trend in the shear stress vs. shear rate graphs. The addition of acetylated CG gum to CS resulted in a higher activation energy (Ea) than the native counterparts and the control. More specifically, starch gels with a higher gum concentration (5%) provided greater Ea than their native counterparts.     

Probing the Brønsted Acidity of the External Surface of Faujasite-Type Zeolites

We outline two methodologies to selectively characterize the Brønsted acidity of the external surface of FAU-type zeolites by IR and NMR spectroscopy of adsorbed basic probe molecules. The challenge and goal are to develop reliable and quantitative IR and NMR methodologies to investigate the accessibility of acidic sites in the large pore FAU-type zeolite Y and its mesoporous derivatives often referred to as ultra-stable Y (USY). The accessibility of their Brønsted acid sites to probe molecules (n-alkylamines, n-alkylpyridines, n-alkylphosphine- and phenylphosphine-oxides) of different molecular sizes is quantitatively monitored either by IR or ³¹P NMR spectroscopy. It is now possible, for the first time to quantitatively discriminate between the Brønsted acidity located in the microporosity and on the external surface of large pore zeolites. For instance, the number of external acid sites on a Y (LZY-64) zeolite represents 2 % of its total acid sites while that of a USY (CBV760) represents 4 % while the latter has a much lower framework Si/Al ratio.     

Litter on the beaches of the Red Sea of Yemen

Distribution of litter: ropes, netting, lamb bulbs, foot wear, plastic bags, bottles, aluminum cans, cardboard, wood loges, rubber, polystyrene blocks and plastic sheets accumulating on Red Sea beaches of Yemen were examined. The results of the study reflected these wastes to be varied from a region to region but they were similar in almost all-coastal areas. Most of the litter were plastics including food bags, oil and water bottles, bait bags, and also vehicles tires. Most of pollution occurred from the sea, due to the heavy traffic and to the fishing vessels, which fish in the area.     

Silver nanoclusters doped in zeolite to decontaminate water resources from the quinalphos pesticide

Ag (I) nanoclusters doped in mordenite zeolite were prepared and spectroscopically analyzed. Strong luminescence emission that is dependent on the excitation wavelength was observed. These variations in the emission modes are due to the site selective luminescence where various luminophores might be excited upon selecting the proper excitation wavelength. The selected material was found to have strong affinity to remove the quinalphos pesticide, which is widely used for the protection of several vegetable and fruit crops, from water bodies. HPLC and GC–MS techniques were used to follow the kinetic data and to identify the photodecomposition products, respectively. The photodecomposition of quinalphos in the presence of the silver doped mordenite catalyst gives different products compared to the irradiation of quinalphos without catalyst. The presence of the Ag-mordenite catalyst not only adsorbs the quinalphos from the solution but it also reduces its toxic effect as tested on the fruit fly (Drosophila melanogaster).     

Elastic-plastic contact model for rough surfaces based on plastic asperity concept

A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elastic-plastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to-shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior.