About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets

LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let . The numbers and as well as all partially ordered sets for which these maxima are attained are determined.     

Molecular structure of the boron(III) oxide molecule in the SCF approximation

The potential surface for the boron(III) oxide (B₂O₃) ground state has been calculated in restricted HF approximation with a minimal STO—3G basis set. The equilibrium geometry has C_2v symmetry; the corresponding structural parameters are as follows: r(O_i—B₁)= 1.241 Å; r(B_i—O)= 1.341 Å ; ∠B₁QB₂ = 142° and ǒO₁B₁O = 177°. Calculations were also carried out using the SCF-Xα approach for two configurations of B₂O₃ with C_2v and D_∞h symmetry.     

A Concise Total Synthesis of the Fungal Isoquinoline Alkaloid TMC-120B

Recent reports of antiepileptic activity of the fungal alkaloid TMC-120B have renewed the interest in this natural product. Previous total syntheses of TMC-120B comprise many steps and have low overall yields (11–17 steps, 1.5–2.9% yield). Thus, to access this compound more efficiently, we herein present a concise and significantly improved total synthesis of the natural product. Our short synthesis relies on two key cyclization steps to assemble the central scaffold: isoquinoline formation via an ethynyl-imino cyclization and an intramolecular Friedel-Crafts reaction to form the furanone.     

Nitration of 2-substituted pyrimidine-4,6-diones,structure and reactivity of 5,5-gem-dinitropyrimidine-4,6-diones

Nitration of some 2-substituted pyrimidine-4,6-diones in sulfuric acid was studied, which afforded previously unknown 5,5-gem-dinitropyrimidine-4,6-diones in high yields. The gem-dinitro products were easily attacked by nucleophiles with concomitant formation of gem-dinitroacetyl derivatives, which in turn could be further hydrolyzed to salts of dinitromethane and triureas.     

Evaluating the influence of deposition conditions on solvation of reactive conducting polymers with neutron reflectivity

We describe in situ neutron reflectivity (NR) and RAIRS studies of the chemical modification of films of a polypyrrole-based conducting polymer derived from the pentafluorophenyl ester of poly(pyrrole-N-propanoic acid) (PFP) electrodeposited on electrode surfaces. We explore the role of the solvent in controlling the rate of reaction with solution-based nucleophiles (amines, which react with the ester to form amides). By varying the identity of the solvent (water vs acetonitrile) and the neutron contrast (deuteration), we find that both the identity of the solvent and its population within the film are paramount in determining chemical reactivity and electroactivity. IR signatures allow monitoring of the reaction of solution-based amine-tagged species such as amino-terminated poly(propylene glycol), ferrocene ethylamine, and lysine with film-based ester functionalities: the carbonyl bands show ester/amide interconversion and some hydrolysis to acid. Time-dependent spectral analysis shows marked variations in reaction rate with (i) (co-)polymer composition (replacement of some fluorinated ester-functionalized pyrrole with unfunctionalized pyrrole), (ii) the solvent to which the polymer film is exposed, and (iii) the rate of polymer deposition. NR data provide solvent profiles as a function of distance perpendicular to the interface, the variations of which provide an explanation for film reactivity patterns. Homopolymer films are relatively hydrophobic, thus hindering reaction with species present in water solutions. Incorporating pyrrole groups raises the solvent population-dramatically for water-thereby facilitating entry and reaction of aqueous-based lysine. Changing film deposition rate yields films with different absolute levels of solvent and reactivity patterns that are dependent on the size of the reactant molecules: more rapid deposition of polymer gives films with a more open structure leading to a higher solvent content and thence increased reactivity. These results, supported by XPS and AFM data, allow assembly of composition-structure-reactivity correlations, in which the controlling feature is film solvation.     

Folding and unfolding of an elastinlike oligopeptide: "inverse temperature transition," reentrance, and hydrogen-bond dynamics

The temperature-dependent behavior of a solvated oligopeptide, GVG(VPGVG), is investigated. Spectroscopic measurements, thermodynamic measurements, and molecular dynamics simulations find that this elastinlike octapeptide behaves as a two-state system that undergoes an "inverse temperature" folding transition and reentrant unfolding close to the boiling point of water. A molecular picture of these processes is presented, emphasizing changes in the dynamics of hydrogen bonding at the protein/water interface and peptide backbone librational entropy.     

The Existence of the Thermodynamic Limit for the System of Interacting Quantum Particles in Random Media

The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns out to be proportional to the number of particles and/or volume of the system in the thermodynamic limit. The obtained results require very general assumptions on the random one-particle model. The methods are mainly based on subadditive type of inequalities.     

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.