Enols of substituted cyanomalonamides

Twenty open-chain mono-, di-, and trialkyl and aryl-N-substituted cyanomalonamides R2R1NCOCH(CN)CONHR3 were prepared. In solution, signals for both amide and a single enol are mostly observed, despite the potential for E and Z isomeric enols. The equilibrium (KEnol) values between the amides and the enols were determined in different solvents by NMR spectra. They decrease on increasing the polarity of the solvent in the order CDCl3 approximately C6D6>THF-d8>(CD3)2CO>CD3CN>DMF-d7>DMSO-d6. For the R1R2NCOCH(CN)CONHR3 system when R1=R2=H, Me or R1=H, R2=Me, KEnol for R3 follows the order: C6F5>Ph>or=An>or= i-Pr>or= t-Bu, and for R1, R2:H, H>Me, H>Me, Me in all solvents. A unique feature is the appreciable % enol in DMSO-d6 when R1=R2=H, in contrast with enol systems with other electron-withdrawing groups (EWGs). Calculations (B3LYP/6-31G**) corroborate the higher KEnol values for less alkyl-substituted systems, showing that in the most stable conformer when R1=H, R2=R3=Me the N-hydrogens are closer to the CN group. The order of promoting substituents for enol of amide formation is CONH2>CO2CH2CF3>CO2Me>CONHMe. The solid-state structures of the isolated species, determined by X-ray crystallography, were either amides or enols, and a higher KEnol(CDCl3) value does not ensure a solid enol structure. In no system were both solid species isolated. The X-ray structures of the enols were temperature-dependent. In most cases, the difference between the O-H and O...H bond lengths at low temperature were appreciable, but they become closer at the higher temperature. Similar tendency for either the C=C/C-C or the C-O/C=O bonds was observed. This is ascribed to a hydrogen shift between two regioisomeric enols in an asymmetric double-well potential, which becomes faster at a higher temperature. Calculations show that the enol structures are nonsymmetrical, resembling the lower temperature structures, even when they are chemically symmetrical, but the energy differences between the two regioisomers are <1 kcal. The hydrogen bonds in the enol moiety are strong, with O...O distances <2.45 A, and are resonance-assisted hydrogen bonds. IR spectra in solution and the solid state qualitatively corroborate the NMR and X-ray structure determination.     

Single facility location and relocation problem with time dependent weights and discrete planning horizon

In this paper a single facility location problem with multiple relocation opportunities is investigated. The weight associated with each demand point is a known function of time. We consider either rectilinear, or squared Euclidean, or Euclidean distances. Relocations can take place at pre-determined times. The objective function is to minimize the total location and relocation costs. An algorithm which finds the optimal locations, relocation times and the total cost, for all three types of distance measurements and various weight functions, is developed. Locations are found using constant weights, and relocations times are the solution to a Dynamic Programming or Binary Integer Programming (BIP) model. The time horizon can be finite or infinite.     

Optimal location with equitable loads

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn ³) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented.     

Separation and detection of VX and its methylphosphonic acid degradation products on a microchip using indirect laser-induced fluorescence

The application of indirect LIF (IDLIF) technique for on-chip electrophoretic separation and detection of the nerve agent O-ethyl S-[2-(diisopropylamino)ethyl] methylphosphonothiolate (VX) and its major phosphonic degradation products, ethyl methylphosphonic acid (EMPA) and methylphosphonic acid (MPA) was demonstrated. Separation and detection of MPA degradation products of VX and the nerve agent isopropyl methylphosphonofluoridate (GB) are presented. The negatively charged dye eosin was found to be a good fluorescent marker for both the negatively charged phosphonic acids and the positively charged VX, and was chosen as the IDLIF visualization fluorescent dye. Separation and detection of VX, EMPA, and MPA in a simple-cross microchip were completed within less than a minute, and consumed only a 50 pL sample volume. A characteristic system peak that appeared in all IDLIF electropherograms served as an internal standard that increased the reliability of peak identification. The negative peak of both VX and the MPAs is in agreement with indirect detection theory and with previous reports in the literature. The LOD of VX and EMPA by IDLIF was 30 and 37 microM, respectively. Despite the fact that the detection sensitivity is relatively low, the rapid simultaneous on-chip analysis of both VX and its degradation products as well as the separation and detection of the MPA degradation products of both VX and GB, increases detection reliability and may present a choice when sensitivity is not critical compared with speed and simplicity of the assay.     

Experimental Measurements of Stress and Chemical Controls on the Evolution of Fracture Permeability

We explore how fracture permeability in confined tight carbonates evolves due to flow of reactive fluids. Core plugs of the Capitan Massive Limestone are saw-cut to form a smooth axial fracture that is subsequently roughened to control the fracture surface topography. Either distilled water or distilled water–ammonium chloride solutions are circulated through these plugs, where fracture roughness, inlet fluid pH, and confining stresses are controlled. Throughout the experiment we measure the fluid flow rate and chemical composition of the effluent fluid. Mass balance, conducted on the effluent fluid mass and on dissolved mineral components, independently constrains the mineral mass removal. We use an idealized lumped parameter model of asperity supported fractures undergoing simultaneous stress corrosion cracking-induced diffusion and free-face dissolution to infer theoretical rates of aperture loss or gain. This model incorporates the roles of confining stress, fracture contact area, and composition and reactivity of the permeating fluid while identifying zones of diffusion-dominated mass transfer within the fracture. These theoretical rates of aperture strain are compared to those inferred from the experimentally determined permeability evolution and permeating fluid mineral mass balance. By measuring in regimes of both increasing and decreasing permeability we quantitatively constrain the transition between fracture-gaping and fracture-closing modes of behavior. We parameterize this transition in permeability evolution by the ratio of mechanically to chemically controlled dissolved mass fluxes. The transition from regimes of closing to regimes of gaping occurs at unity ( $\chi \approx 1$ ) when stress and chemically driven mass fluxes are theoretically equal.     

Compact convergence of σ-fields and relaxed conditional expectation

The collection of sub-σ-fields of a Borel measure space when endowed with the topology of strong convergence is in general not a compact space. The paper offers a completion of this space which makes it compact. The elements which are added to the space are called relaxed σ-fields. A notion of relaxed conditional expectation with respect to a relaxed σ-field is identified. The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional expectation operator is continuous on the completion of the space. Other properties of conditional expectation are lifted to and interpreted in the relaxed framework. Received: 22 February 1999 / Revised version: 23 October 2000 / Published online: 8 May 2001     

Convergence to convex compact sets in infinite dimensions

We provide a simple test for the convergence of a sequence of subsets in an infinite-dimensional space to a compact convex one. The test reduces, roughly, the convergence problem to finite dimensions. Applications are portrayed demonstrating how convexification phenomena established in finite dimensions are easily generalized to infinite dimensions.     

Approximating the integral of a multifunction

Given a weakly converging sequence of measures, we study the convergence of the corresponding integrals of a continuous unbounded multifunction. We also study the implication of these results to variational problems, and provide further approximating results for the integral of a multifunction, involving both truncation of the multifunction and measure approximation.