An Eberhard-Like Theorem for Pentagons and Heptagons

Eberhard proved that for every sequence (p _k ), 3≤k≤r, k≠6, of nonnegative integers satisfying Euler’s formula ∑ _k≥3(6−k)p _k =12, there are infinitely many values p ₆ such that there exists a simple convex polyhedron having precisely p _k faces of size k for every k≥3, where p _k =0 if k>r. In this paper we prove a similar statement when nonnegative integers p _k are given for 3≤k≤r, except for k=5 and k=7 (but including p ₆). We prove that there are infinitely many values p ₅,p ₇ such that there exists a simple convex polyhedron having precisely p _k faces of size k for every k≥3. We derive an extension to arbitrary closed surfaces, yielding maps of arbitrarily high face-width. Our proof suggests a general method for obtaining results of this kind.     

A Hierarchical Optimization Approach to Optimal Production Scheduling in an Industrial Continuous Olefin Polymerization Reactor

The time‐optimal grade‐transition policies, as well as the selection of the optimal grade production sequence, are calculated for a gas‐phase ethylene/but‐1‐ene copolymerization FBR. The tuning parameters (i.e., proportional gain and integral time) of the feedback PI process controllers, as well as the time‐optimal trajectories of the feedforward controllers, are treated as decision variables. A two‐level decomposition approach is applied for solving the optimal‐grade transition‐scheduling problem, taking into account the impact of both transient operation and the sequence of grade transitions on the overall amount of off‐spec polymer and overall transition time.

     

Comparison of sulfo‐conjugated and gluco‐conjugated urinary metabolites for detection of methenolone misuse in doping control by LC‐HRMS,GC‐MS and GC‐HRMS

Methenolone (17β‐hydroxy‐1‐methyl‐5α‐androst‐1‐en‐3‐one) misuse in doping control is commonly detected by monitoring the parent molecule and its metabolite (1‐methylene‐5α‐androstan‐3α‐ol‐17‐one) excreted conjugated with glucuronic acid using gas chromatography‐mass spectrometry (GC‐MS) and liquid chromatography mass spectrometry (LC‐MS) for the parent molecule, after hydrolysis with β‐glucuronidase. The aim of the present study was the evaluation of the sulfate fraction of methenolone metabolism by LC‐high resolution (HR)MS and the estimation of the long‐term detectability of its sulfate metabolites analyzed by liquid chromatography tandem mass spectrometry (LC‐HRMSMS) compared with the current practice for the detection of methenolone misuse used by the anti‐doping laboratories. Methenolone was administered to two healthy male volunteers, and urine samples were collected up to 12 and 26 days, respectively. Ethyl acetate extraction at weak alkaline pH was performed and then the sulfate conjugates were analyzed by LC‐HRMS using electrospray ionization in negative mode searching for [M‐H]^? ions corresponding to potential sulfate structures (comprising structure alterations such as hydroxylations, oxidations, reductions and combinations of them). Eight sulfate metabolites were finally detected, but four of them were considered important as the most abundant and long term detectable. LC clean up followed by solvolysis and GC/MS analysis of trimethylsilylated (TMS) derivatives reveal that the sulfate analogs of methenolone as well as of 1‐methylene‐5α‐androstan‐3α‐ol‐17‐one, 3z‐hydroxy‐1β‐methyl‐5α‐androstan‐17‐one and 16β‐hydroxy‐1‐methyl‐5α‐androst‐1‐ene‐3,17‐dione were the major metabolites in the sulfate fraction. The results of the present study also document for the first time the methenolone sulfate as well as the 3z‐hydroxy‐1β‐methyl‐5α‐androstan‐17‐one sulfate as metabolites of methenolone in human urine. The time window for the detectability of methenolone sulfate metabolites by LC‐HRMS is comparable with that of their hydrolyzed glucuronide analogs analyzed by GC‐MS. The results of the study demonstrate the importance of sulfation as a phase II metabolic pathway for methenolone metabolism, proposing four metabolites as significant components of the sulfate fraction. Copyright © 2015 John Wiley & Sons, Ltd.     

On fixing boundary points of transitive hyperbolic graphs

We show that there is no one-ended, locally finite, planar, hyperbolic graph such that the stabilizer of one of its hyperbolic boundary points acts transitively on the vertices of the graph. This gives a partial answer to a question by Kaimanovich and Woess.     

Finding all solutions of nonlinearly constrained systems of equations

A new approach is proposed for finding all-feasible solutions for certain classes of nonlinearly constrained systems of equations. By introducing slack variables, the initial problem is transformed into a global optimization problem (P) whose multiple global minimum solutions with a zero objective value (if any) correspond to all solutions of the initial constrained system of equalities. All-globally optimal points of (P) are then localized within a set of arbitrarily small disjoint rectangles. This is based on a branch and bound type global optimization algorithm which attains finite-convergence to each of the multiple global minima of (P) through the successive refinement of a convex relaxation of the feasible region and the subsequent solution of a series of nonlinear convex optimization problems. Based on the form of the participating functions, a number of techniques for constructing this convex relaxation are proposed. By taking advantage of the properties of products of univariate functions, customized convex lower bounding functions are introduced for a large number of expressions that are or can be transformed into products of univariate functions. Alternative convex relaxation procedures involve either the difference of two convex functions employed in BB [23] or the exponential variable transformation based underestimators employed for generalized geometric programming problems [24]. The proposed approach is illustrated with several test problems. For some of these problems additional solutions are identified that existing methods failed to locate.     

Behavior of mixtures of symmetric and asymmetric electrolytes near discretely charged planar surfaces: a Monte Carlo study

Canonical Monte Carlo (CMC) simulations are employed in this work in order to study the structure of the electrical double layer (EDL) near discretely charged planar surfaces in the presence of symmetric and asymmetric indifferent electrolytes within the framework of a primitive model. The effects of discreteness and strength of surface charge, charge asymmetry, and size asymmetry are specific focuses of this work. The CMC simulation protocol is initially tested against the classical theory, the modified Gouy-Chapman (GC) theory, in order to assess the reliability of the simulation results. The CMC simulation results and the predictions of the classical theory show good agreement for 1:1 electrolytes and low surface charge, at which conditions the GC theory is valid. Simulations with symmetric and asymmetric electrolytes and mixtures of the two demonstrate that size plays an important role in determining the species present in the EDL and how the surface charge is screened. A size-exclusion effect could be consistently detected. Although it is energetically favorable that higher-valence ions screen the surface charge, their larger size prevents them from getting close to the surface. Smaller ions with lower valences perform the screening of the charge, resulting in higher local concentrations of small ions close to the surface. The simulations also showed that the strength of the surface charge enhances the size-exclusion effect. This effect will definitely affect the magnitude of the forces between interacting charged surfaces.     

Thermodynamics of complex formation in chloroform-oxygenated solvent mixtures

Complex formation equilibria in binary mixtures of chloroform with dipropyl ether (PE), diisopropyl ether (IPE), methyl tert-butyl ether (MBE), tetrahydrofuran (THF). 1,4-dioxane (DOX), acetone (AC), and methyl acetate (MA) have been analyzed in detail using several association models. Vapor-liquid equilibria, excess enthalpy and excess heat capacity data for these mixtures have been correlated using a multiproperty global fitting procedure. The thermodynamic properties for chloroform +PE, +IPE, +MBE, +AC, and +MA are best correlated using the ideal association model while for chloroform +THF and +DOX the best model is an athermal solvation model where the Flory-Huggins expression for the species activity coefficients is considered. The model parameters, i.e., the equilibrium constant, enthalpies and heat capacities of complexation, were found to be reliable, well representing the chloroform-oxygenated solvent H-bonded complexes. A detailed discussion is given on the test proposed by McGlashan and Rastogi to decide whether the solution contains only 11 complexes or 21 complexes as well. The complex formation equilibria in chloroform mixtures is compared to those previously examined for halothane (2-bromo-2-chloro-1,1,1-trifluoroethane) mixed with the same oxygenated solvents. It was found that the H-bonds formed by halothane are stronger than those formed by chloroform.     

Polymers with amino acids in their side chain: Conformation of poly(N-methacryloyl-L-methionine)

A homopolymer bearing L-Methionine (PMet) in its side chain was synthesized by free radical polymerization of the corresponding vinyl monomer. Viscosimetric and pHmetric measurements indicate that PMet, in water at low pH, takes a compact conformation, which is destroyed (expanded) with increasing ionization of the carboxyl groups of the side chains. The influence of temperature and of some additives (neutral salt, urea, organic solvent, SDS) on the compact conformation and the pH-induced conformational transition was investigated. It was concluded that hydrogen bonds are the main factors responsible for the existence of the compact conformation. © 1995 John Wiley & Sons, Inc.