The number of extreme points of tropical polyhedra

The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define it, showing that the maximum is attained by the polar of the cyclic polytope. We show that the same bound is valid in the tropical setting, up to a trivial modification. Then, we study the tropical analogues of the polars of a family of cyclic polytopes equipped with a sign pattern. We construct bijections between the extreme points of these polars and lattice paths depending on the sign pattern, from which we deduce explicit bounds for the number of extreme points, showing in particular that the upper bound is asymptotically tight as the dimension tends to infinity, keeping the number of constraints fixed. When transposed to the classical case, the previous constructions yield some lattice path generalizations of Gale's evenness criterion.     

Sustainable Heck–Matsuda Reaction with Catalytic Amounts of Diazonium Salts: An Experimental and Theoretical Study

The palladium‐catalyzed Heck–Matsuda reaction with a catalytic amount of an in‐situ‐generated diazonium salt proceeded under mild and sustainable conditions. The reaction proceeded at room temperature, under base‐free conditions, and only generated tBuOH, H₂O, and N₂ as by‐products. Ortho‐substituted diazonium salts were more‐efficiently coupled to methyl acrylate than their corresponding para isomers, which required the addition of anisole as an additive. In support of these experimental data, we carried out theoretical studies to gain a deeper understanding of these reaction outcomes.     

Analysis of performance of an anaerobic sequencing batch reactor submitted to increasing organic load with different influent concentrations and cycle lengths

The performance of an anaerobic sequencing batch reactor (ASBR) was assessed when submitted to increasing organic load with different influent concentrations and cycle lengths. The 5-L mechanically stirred (75 rpm) ASBR contained 2 L of granular biomass and treated 2 L of synthetic wastewater per cycle. Volumetric organic loads (VOLs) from 0.66 to 2.88 g of chemical oxygen demand (COD)/(L x d) were applied by using influent concentrations from 550 to 3,600 mg of COD/L in 8- and 12-h cycles. Reactor stability was maintained for VOLs from 0.66 to 2.36 g of COD/(L x d), with organic matter removal efficiencies for filtered samples (epsilonF) between 84 and 88%. For VOLs from 0.78 to 2.36 g of COD/(L x d) at an influent concentration of 2,000 mg of COD/L, when cycle length was reduced from 12 to 8 h, epsilonF did not vary, yet showed a very distinct behavior from the other conditions. In addition, two operation strategies were studied for VOLs with approximately similar values of 2.36 and 2.08 g of COD/(L x d). One involved operation with an influent concentration of 2,000 mg of COD/L and an 8-h cycle, whereas the other involved an influent concentration of 2,600 mg of COD/L and a 12-h cycle. Only the former resulted in system stability and efficiency. These results indicate that besides organic load, influent concentration and cycle length play a significant role in ASBR systems.     

Isomeric distribution and catalyzed isomerization of cobalt(III) complexes with pentadentate macrocyclic ligands. importance of hydrogen bonding

We have investigated the isomeric distribution and rearrangement of complexes of the type [CoXLn]2+,3+ (where X = Cl-, OH-, H2O, and Ln represents a pentadentate 13-, 14-, and 15-membered tetra-aza or diaza-dithia (N4 or N2S2) macrocycle bearing a pendant primary amine). The preparative procedures for chloro complexes produced almost exclusively kinetically preferred cis isomers (where the pendant primary amine is cis to the chloro ligand) that can be separated by careful cation-exchange chromatography. For L13 and L14 the so-called cis-V isomer is isolated as the kinetic product, and for L15 the cis-VI form (an N-based diastereomer) is the preferred, while for the L14(S) complex both cis-V and trans-I forms are obtained. All these complexes rearrange to form stable trans isomers in which the pendent primary amine is trans to the monodentate aqua or hydroxo ligand, depending on pH and the workup procedure. In total 11 different complexes have been studied. From these, two different trans isomers of [CoClL14(S)]2+ have been characterized crystallographically for the first time in addition to a new structure of cis-V-[CoClL14(S)]2+; all were isolated as their chloride perchlorate salts. Two additional isomers have been identified and characterized by NMR as reaction intermediates. The remaining seven forms correspond to the complexes already known, produced in preparative procedures. The kinetic, thermal, and baric activation parameters for all the isomerization reactions have been determined and involve large activation enthalpies and positive volumes of activation. Activation entropies indicate a very important degree of hydrogen bonding in the reactivity of the complexes, confirmed by density functional theory studies on the stability of the different isomeric forms. The isomerization processes are not simple and even some unstable intermediates have been detected and characterized as part of the above-mentioned 11 forms of the complexes. A common reaction mechanism for the isomerization reactions has been proposed for all the complexes derived from the observed kinetic and solution behavior.     

N-H and alpha(C-H) bond dissociation enthalpies of aliphatic amines

Bond dissociation enthalpies (BDEs) of a large series of aliphatic amines (21) were measured by means of photoacoustic calorimetry. Despite the different structures studied in the primary, secondary, and tertiary amine series, the alpha(C-H) BDEs were found to be very similar for unconstrained amines with values very close to 91 kcal/mol. alphaC- and N-alkylation or introduction of an hydroxy group only slightly affect the BDEs, a fact in perfect agreement with calculations performed at different CBS levels. This demonstrates the predominance of the two-orbital-three-electron interaction involving the N and alphaC(*) orbitals. On the other hand, the N-H BDE decreases when going from primary to secondary amines. This result is interpreted in term of a hyperconjugation in sigmaC-C bonds, which leads to a stabilization of the aminyl radical. For cyclized amines, the BDEs depend on the relative geometry of the singly occupied alphaC(*) orbital with respect to that of the N atom, disfavoring the two-orbital-three-electron interaction. However, such structures can exhibit through-bond interaction. For a crowded structure such as triisopropylamine, for which the alphaC(*) orbital is not coplanar with the nitrogen one, the relaxation of a strain energy allows the BDE to be comparable to flexible structures.     

Rate constant and RRKM product study for the reaction between CH3 and C2H3 at T = 298 K

The total rate constant k₁ has been determined at P = 1 Torr nominal pressure (He) and at T = 298 K for the vinyl‐methyl cross‐radical reaction: (1) CH₃ + C₂H₃ → Products. The measurements were performed in a discharge flow system coupled with collision‐free sampling to a mass spectrometer operated at low electron energies. Vinyl and methyl radicals were generated by the reactions of F with C₂H₄ and CH₄, respectively. The kinetic studies were performed by monitoring the decay of C₂H₃ with methyl in excess, 6 < [CH₃]₀/ [C₂H₃]₀ < 21. The overall rate coefficient was determined to be k₁(298 K) = (1.02 ± 0.53) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ with the quoted uncertainty representing total errors. Numerical modeling was required to correct for secondary vinyl consumption by reactions such as C₂H₃ + H and C₂H₃ + C₂H₃. The present result for k₁ at T = 298 K is compared to two previous studies at high pressure (100–300 Torr He) and to a very recent study at low pressure (0.9–3.7 Torr He). Comparison is also made with the rate constant for the similar reaction CH₃ + C₂H₅ and with a value for k₁ estimated by the geometric mean rule employing values for k(CH₃ + CH₃) and k(C₂H₃ + C₂H₃). Qualitative product studies at T = 298 K and 200 K indicated formation of C₃H₆, C₂H₂, and C₃H₅ as products of the combination‐stabilization, disproportionation, and combination‐decomposition channels, respectively, of the CH₃ + C₂H₃ reaction. We also observed the secondary C₄H₈ product of the subsequent reaction of C₃H₅ with excess CH₃; this observation provides convincing evidence for the combination‐decomposition channel yielding C₃H₅ + H. RRKM calculations with helium as the deactivator support the present and very recent experimental observations that allylic C‐H bond rupture is an important path in the combination reaction. The pressure and temperature dependencies of the branching fractions are also predicted. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 304–316, 2000     

Synthesis and characterization of superparamagnetic nanoparticles coated with fluorescent gold nanoclusters

Multifunctional nanoparticles (NPs) combining the superparamagnetism of Mn−Zn ferrite and the fluorescence property of gold nanoclusters (NCs) have been prepared by wet chemistry. Magnetic NPs synthesized by co-precipitation method were coated several times with oppositely charged polyelectrolytes (PEs) using the layer-by-layer technique. Common techniques (Fourier transform infrared spectroscopy, electron microscopy, zeta potential, etc.) indicated the monodispersity and the stability of the coated NPs providing a positive charged surface. Fluorescent gold NCs bound to a standard protein bovine serum albumin were adsorbed on the surface of the magnetic NPs. Structural investigations proved the presence of small gold clusters (~2 nm) in a shell surrounding the magnetic nanomaterial. The stable nanocomposite kept the original fluorescence property of the metal clusters with 211-fold increase of the red emission (λ = 690 nm) compared to the uncoated NPs. These NPs can be moved with a permanent magnet despite a 72-wt% increase of the non-magnetic fraction due to the PE coating and the protein adsorption.     

Dynamics of covering maps of the annulus I: semiconjugacies

It is often the case that a covering map of the open annulus is semiconjugate to a map of the circle of the same degree. We investigate this possibility and its consequences on the dynamics. In particular, we address the problem of the classification up to conjugacy. However, there are examples which are not semiconjugate to a map of the circle, and this opens new questions.