Fractional programming and characterization of some vertices of the feasible region

This paper considers a problem of nonlinear programming in which the objective function is the ratio of two linear functions and the constraints define a bounded and connected feasible region. Using a coordinate transformation, this problem is transformed into a simpler one, whose geometric interpretation is of particular significance. The transformation leads to a characterization of some special vertices of the feasible region from both the theoretical and operational points of view.     

Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

Interactions of dendrimers with selected amino acids and proteins studied by continuous wave EPR and Fourier transform EPR

Interactions of polyamidoamine dendrimers, termed Gn, where n indicates the generation (=number of amidoamine layers), at different protonation levels with selected amino acids and proteins have been investigated by means of continuous wave electron paramagnetic resonance (cw-EPR) and pulsed-EPR (electron spin-echo = ESE) analyses. A low-generation dendrimer (G2) and a high-generation one (G6) were labeled with nitroxides for the EPR measurements. Gly, Glu, Arg, and Leu were selected as representative of neutral(zwitterionic)-polar, acidic, basic, and low-polar amino acids, respectively. The water-soluble proteins alpha-chymotrypsin and albumin were selected on the basis of a basic and an acidic isoelectric point, respectively. The cw-EPR spectra were analyzed by computing the line shapes to extract information about the dendrimer-biomolecule interactions. In general, dendrimers at a high protonation level interact stronger with amino acids than those at a low level of protonation. However, even for highly protonated dendrimers, a synergistic effect between hydrophilic and hydrophobic interactions promoted the formation of stable Gn-amino acid adducts, as demonstrated by the enhanced interactions with Leu. As expected from acid-base interactions, stable adducts were formed between Arg and highly protonated dendrimers and between Glu and low level protonated dendrimers. The relatively strong dendrimer interactions with the protein chymotrypsin and the poor interactions of dendrimers with albumin demonstrated that the protonated amino groups of the dendrimers are predominantly involved in the interactions with these proteins and indicated a significant role in the interactions with the dendrimers of the hydrophobic external residues of chymotrypsin. Computer-aided analysis of the ESE experiments was consistent with the cw-EPR results and supported the conclusion of a partial complexation of the nitroxides of the dendrimer with Leu and alpha-chymotrypsin.     

An optically active vinyl sulfoxide copolymer and the configuration of sulfoxide adjacent to radical or anionic sites

Optically active vinyl p-tolyl sulfoxide was synthesized and copolymerized with styrene to produce an optically active copolymer. The question of the configuration of sulfur in a sulfoxide when adjacent to a radical site is discussed. The configuration of sulfur in a sulfoxide is proven to be nonplanar when adjacent to an anionic site.     

Relaxation processes of the liquid crystal ME6N in the isotropic phase studied by Raman scattering experiments

We have investigated the Raman profiles of the nu(C[Triple Bond]N) and nu(C=O) vibrational modes of the nematic liquid crystal ME6N (4-cyanophenyl-4(')-hexylbenzoate) in the isotropic phase at different temperatures and used them as probes of the dynamics and structural organization of this liquid. The vibrational time correlation functions of the nu(C[Triple Bond]N) mode, rather adequately interpreted within the assumption of exponential modulation function (the Kubo-Rothschild theory), indicate that the system experiences an intermediate dynamical regime that gets only slightly faster with increasing temperature. However, this theory fails in predicting the non-exponential behavior that the time correlation functions manifest in the long time range (t>3 ps). For this reason we have additionally approached the interpretation of vibrational correlation functions in terms of the theory formulated by Rothschild and co-workers for locally structured liquids. The application of this theory reveals that the molecular dynamics in this liquid crystal in the isotropic phase is that deriving from a distribution of differently sized clusters, which narrows as the temperature increases. Even at the highest temperature reached in this study (87 degrees C above the nematic-isotropic transition), the liquid has not yet achieved the structure of the simple liquid and the dynamics has not reached the limit of the single channel process. The vibrational and orientational relaxations occur in very different time scales. The temperature independence of the orientational dynamics in the whole range from 55 degrees C to 135 degrees C has been referred to the nonhydrodynamic behavior of the system, arising when local pseudonematic structures persist for times longer than the orientational relaxation. The occurrence of the process of resonant vibrational energy transfer between the C=O groups of adjacent molecules has been revealed in the isotropic phase by a slightly positive Raman noncoincidence effect in the band associated with the nu(C=O) mode. A qualitative interpretation is tentatively given in terms of partial cancellation of contributions deriving from structures having opposite orientations of their C=O groups.     

Supramolecular steric effects as the means of making reactive carbon radicals persistent. Quantitative characterization of the external surface of MFI zeolites through a persistent radical probe and a langmuir adsorption isotherm

The photochemistry of tetraphenylacetone (1) adsorbed on the external surface of a MFI zeolite (the sodium form of LZ-105) has been investigated in combination with computational chemistry, surface area measurements, EPR analysis, and classical adsorption isotherms. All of the methods are consistent with a supramolecular structural model in which 1 is first adsorbed strongly through intercalation of a single benzene ring into a hole on the LZ-105 external surface (site I) followed by a weaker binding to the external framework between the holes (site II) until a monolayer of 1 is formed. From both computational and surface area measurements, it is estimated that the site I holes on the external surface will be filled at ca. 0.3-0.5 wt %/wt loading of 1/LZ-105, which corresponds to 6.5 x 10(18) (ca. 10(-)(5) mol) of holes or molecules of 1 adsorbed in holes per gram of zeolite. The supramolecular composition of ca. 0.3-0.5% of 1 on LZ-105 characterizes a "break point" for the photochemistry and the EPR measurements, since it represents the value for saturation of the site I holes with 1. These conclusions are supported quantitatively by experimental isotherms of the adsorption of 1 on LZ-105. Photolysis of 1 intercalated in the site I holes causes fragmentation into two isomeric supramolecular diphenylmethyl (DPM) radicals, one (DMP)(in) which is adsorbed into the internal surface and becomes strongly persistent (half-life of many weeks) and the other (DMP)(ex) which diffuses on the external surface and rapidly dimerizes (less than a few minutes) to produce the radical-radical combination product tetraphenylethane (2). Photolysis of 1 adsorbed on the solid external surface produces two supramolecularly equivalent DPM radicals (DMP)(ex) that diffuse on the external surface and rapidly dimerize to produce 2, and do not produce persistent DPM radicals.     

CH...O and CH...F links form the cage structure of dioxane-trifluoromethane

The molecular beam Fourier transform microwave spectrum of 1,4-dioxane-trifluoromethane has been assigned and measured. The two subunits form a cage stabilized by one C-H...O and two C-H...F weak hydrogen bonds. The C-H...O link involves the axial lone pair of one of the two equivalent ring oxygens, while the two C-H...F bridges connect trifluoromethane to the two axial hydrogens in positions 3 and 5. The dissociation energy has been estimated from the D(J) centrifugal distortion parameter to be approximately 6.8 kJ/mol.