On Extracting Maximum Stable Sets in Perfect Graphs Using Lovász's Theta Function

We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality. This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA.     

Nuclear-Electron Overhauser Effect in MC800 Liquid Asphalt Solutions

Experimental results on the extrapolated ultimate enhancement factors of o-, m-, and p-xylene protons at 1.53 mT are obtained for MC800 asphalt solutions. The ultimate enhancement factors are found such as ?26.9, ?25.7, and ?11.7 for o-, m-, and p-xylene, respectively. These results show that the solvent proton Overhauser effect cannot reach the extrapolated enhancement of ?330 in the extreme narrowing case because of occurrence of small scalar interactions in addition to the dipole–dipole interactions between solvent protons and asphalt electrons. The ortho, meta, and para positions of the –CH₃ group change the nature of the interactions. The nuclear magnetic resonance (NMR) signal enhancements exhibit a sensitive behavior depending on the chemical environment differing from isomer to isomer. The solvation or association of asphalt in xylene isomers at room temperature is revealed. Quantum chemical calculations for the xylene isomers with the electronic and optical properties; absorption wavelengths, excitation energy, atomic charges, dipole moment and frontier molecular orbital energies, molecular electrostatic potential; are carried out using the density functional theory (DFT) method (B3LYP) with the 6-311G(d,p) basis set by the standard Gaussian 09 software package program. The relative importance of scalar and translational dipolar interaction parameters determined in dynamic nuclear polarization experiments is explained by the electronic structure of HOMO–LUMO of the xylene isomers.     

Expanded Organic Building Units for the Construction of Highly Porous Metal–Organic Frameworks

Two new organic building units that contain dicarboxylate sites for their self‐assembly with paddlewheel [Cu₂(CO₂)₄] units have been successfully developed to construct two isoreticular porous metal–organic frameworks (MOFs), ZJU‐35 and ZJU‐36, which have the same tbo topologies (Reticular Chemistry Structure Resource (RCSR) symbol) as HKUST‐1. Because the organic linkers in ZJU‐35 and ZJU‐36 are systematically enlarged, the pores in these two new porous MOFs vary from 10.8 Å in HKUST‐1 to 14.4 Å in ZJU‐35 and 16.5 Å in ZJU‐36, thus leading to their higher porosities with Brunauer–Emmett–Teller (BET) surface areas of 2899 and 4014 m² g^?1 for ZJU‐35 and ZJU‐36, respectively. High‐pressure gas‐sorption isotherms indicate that both ZJU‐35 and ZJU‐36 can take up large amounts of CH₄ and CO₂, and are among the few porous MOFs with the highest volumetric storage of CH₄ under 60 bar and CO₂ under 30 bar at room temperature. Their potential for high‐pressure swing adsorption (PSA) hydrogen purification was also preliminarily examined and compared with several reported MOFs, thus indicating the potential of ZJU‐35 and ZJU‐36 for this important application. Studies show that most of the highly porous MOFs that can volumetrically take up the greatest amount of CH₄ under 60 bar and CO₂ under 30 bar at room temperature are those self‐assembled from organic tetra‐ and hexacarboxylates that contain m‐benzenedicarboxylate units with the [Cu₂(CO₂)₄] units, because this series of MOFs can have balanced porosities, suitable pores, and framework densities to optimize their volumetric gas storage. The realization of the two new organic building units for their construction of highly porous MOFs through their self‐assembly with [Cu₂(CO₂)₄] units has provided great promise for the exploration of a large number of new tetra‐ and hexacarboxylate organic linkers based on these new organic building units in which different aromatic backbones can be readily incorporated into the frameworks to tune their porosities, pore structures, and framework densities, thus targeting some even better performing MOFs for very high gas storage and efficient gas separation under high pressure and at room temperature in the near future.     

New glyoxime derivatives and their transition metal complexes

Two new vic-dioxime ligands and their complexes with Co⁺², Ni⁺², Cu⁺², Cd⁺², and Zn⁺² ions were synthesized. Primer amines (3,4-methylenedioxaaniline and 4-methylbenzylamine) reacted with antichloroglyoxime to give 3,4-methylenedioxaphenylaminoglyoxime (H₂L¹) and N-(4-methylbenzyl)aminoglyoxime (H₂L²) ligands. Structures of the ligands and their complexes are proposed based on elemental analyses, IR, UV-Vis, and ¹H NMR spectra, magnetic susceptibility measurements, and thermogravimetric analyses (TGA). The article was submitted by the authors in English.     

Water‐Stable Zirconium‐Based Metal–Organic Framework Material with High‐Surface Area and Gas‐Storage Capacities

We designed, synthesized, and characterized a new Zr‐based metal–organic framework material, NU‐1100 , with a pore volume of 1.53 ccg^?1 and Brunauer–Emmett–Teller (BET) surface area of 4020 m²g^?1; to our knowledge, currently the highest published for Zr‐based MOFs. CH₄/CO₂/H₂ adsorption isotherms were obtained over a broad range of pressures and temperatures and are in excellent agreement with the computational predictions. The total hydrogen adsorption at 65 bar and 77 K is 0.092 g g^?1, which corresponds to 43 g L^?1. The volumetric and gravimetric methane‐storage capacities at 65 bar and 298 K are approximately 180 v_STP/v and 0.27 g g^?1, respectively.     

Bioadhesion to solids: contact angle hysteresis effect

It was recently reported that the ease of removal of sporelings of green seaweed Ulva under shear stress from the polymer surfaces was found to be linearly and positively correlated with contact angle and wetting hysteresis, i.e., the higher the hysteresis, the greater the removal. Motivated by this report, we examined the relationship between the bioadhesion of blood platelets and proteins with contact angle hysteresis of solid substrates using the data of published papers. It was determined that there is a linear and positive relationship between the contact angle hysteresis and bioadhesion of both blood platelets and γ-globulin protein contacting the solid substrates, i.e., the higher the hysteresis, the greater the bioadhesion. The reasons are discussed and it is proposed that testing the effect of CAH on the adhesion strengths of biomaterials on surfaces is useful in order to gain a better insight on the bioadhesion mechanism.     

A practical access to new pyrrolizine carboxylates via KHMDS-catalyzed carbocyclizations

Easy and effective preparation of new 1H-pyrrolizine carboxylates was achieved with high efficiency via KHMDS-induced carbocyclization of N-alkynyl proline carboxylates under substantially mild conditions. Meanwhile, some trans-diiodoallylic N-proline carboxylates were obtained from N-propargyl proline carboxylates using molecular I₂ with or without KHMDS. This method is quite feasible in terms of practical and quick access to the pyrrolizines and their derivatives over the formation of carbanions.     

Radiation induced copolymerization reactivity of different allyl monomers with styrene

Radiation induced copolymerizations of electron donating such as allyl phenol (AP) and electron withdrawing such as allyl isothiocyanate (AITC) monomers with styrene (Sty) as a comonomer were studied in order to correlate the electronic behavior with copolymerization yield and molecular weight. The allyl monomers and comonomer were mixed in the same mol ratios under Ar atmosphere and copolymerized by using gamma radiation in various absorbed doses (55, 110, 165 kGy) obtained from a Co-60 source. Poly(AP-co-Sty), and poly(AITC-co-Sty) could have been prepared at all of the absorbed doses. The maximum copolymerization yields were calculated as a 16.35 and 6.52 percent for poly(AP-co-Sty) and poly(AITC-co-Sty), respectively. The molecular weights of poly(AP-co-Sty) copolymers are found to be higher in comparison to those of poly(AITC-co-Sty). Both results indicate that, under the same irradiation conditions, AP is more reactive on styrene than AITC is. Thus, the monomers having electron withdrawing (EW) substituents attached to allyl group may result in better copolymerization yield and molecular weight than those with electron donating (ED) substituents. Thermal stabilities of the poly(AP-co-Sty) copolymers are also higher than those of poly(AITC-co-Sty).     

A new mathematical model for the enzymatic kinetic resolution of racemates

A mathematical model is presented for the kinetic resolution of racemates. It takes all intermediate binding steps into account and assumes that such steps are reversible. The model describing dynamics of the chiral reaction products consists of two nonlinear differential equations. With this model, the enantioselectivity of enzyme has been studied. Mathematical and numerical simulation of the model show that there are several ways to control the enantiomeric ratio (E) but the affinity and the binding rates of the intermediate enzyme complex to the racemic substrates are the key steps for the enzyme enantioselectivity.