Hamiltonicity, independence number, and pancyclicity

A graph on n vertices is called pancyclic if it contains a cycle of length ? for all 3≤?≤n. In 1972, Erd?s proved that if G is a Hamiltonian graph on n>4k⁴ vertices with independence number k, then G is pancyclic. He then suggested that n=Ω(k²) should already be enough to guarantee pancyclicity. Improving on his and some other later results, we prove that there exists a constant c such that n>ck^7/3 suffices.     

Some New Results on Circulant Weighing Matrices

We obtain a few structural theorems for circulant weighing matrices whose weight is the square of a prime number. Our results provide new schemes to search for these objects. We also establish the existence status of several previously open cases of circulant weighing matrices. More specifically we show their nonexistence for the parameter pairs (n, k) (here n is the order of the matrix and k its weight) = (147, 49), (125, 25), (200, 25), (55, 25), (95, 25), (133, 49), (195, 25), (11 w, 121) for w < 62.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

Flexible Hierarchical TiO2/Fe2O3 Composite Membrane with High Separation Efficiency for Surfactant‐Stabilized Oil‐Water Emulsions

Globally, efficient oil‐water separation for surfactant‐stabilized oil‐water emulsions has been in urgent demand. The current options available for separation are neither sustainable nor resistant to fouling. Herein, we introduce a hierarchically nanostructured TiO₂/Fe₂O₃ composite membrane, which is capable of separating surfactant‐stabilized oil‐water emulsions with high separation efficiency. The high oil rejection rate is contributed by the acquisition of an interconnected delicate network and underwater superoleophobic interface. Meanwhile, its self‐cleaning function promote the facile recovery of the contaminated membrane. Furthermore, the mechanical flexible characteristic of the TiO₂/Fe₂O₃ composite membrane widens its applicability in industrial employment. Thanks to these properties, this novel membrane can be considered as a practical option for treating surfactant‐stabilized oil‐water emulsions.     

Electrons Mediate the Gas‐Phase Oxidation of Formic Acid with Ozone

Gas‐phase reactions of CO₃^.? with formic acid are studied using Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometry. Signal loss indicates the release of a free electron, with the formation of neutral reaction products. This is corroborated by adding traces of SF₆ to the reaction gas, which scavenges 38 % of the electrons. Quantum chemical calculations of the reaction potential energy surface provide a reaction path for the formation of neutral carbon dioxide and water as the thermochemically favored products. From the literature, it is known that free electrons in the troposphere attach to O₂, which in turn transfer the electron to O₃. O₃^.? reacts with CO₂ to form CO₃^.?. The reaction reported here formally closes the catalytic cycle for the oxidation of formic acid with ozone, catalyzed by free electrons.     

Dynamic Coupling at the Ångström Scale

While momentum transfer from active particles to their immediate surroundings has been studied for both synthetic and biological micron‐scale systems, a similar phenomenon was presumed unlikely to exist at smaller length scales due to the dominance of viscosity in the ultralow Reynolds number regime. Using diffusion NMR spectroscopy, we studied the motion of two passive tracers—tetramethylsilane and benzene—dissolved in an organic solution of active Grubbs catalyst. Significant enhancements in diffusion were observed for both the tracers and the catalyst as a function of reaction rate. A similar behavior was also observed for the enzyme urease in aqueous solution. Surprisingly, momentum transfer at the molecular scale closely resembles that reported for microscale systems and appears to be independent of swimming mechanism. Our work provides new insight into the role of active particles on advection and mixing at the Ångström scale.     

Resonant electron transfer and luminescent enhancement in a toluene suspension of Si nanocrystals

Efficient resonant electron transfer from the surface bonding structure to the conduction band of quantum confined Si nanocrystals is observed by Si nanocrystals in a toluene suspension. Based on the electron transfer mechanism, the enhancement of photoluminescence originates from the band-to-band recombination in the p-type Si nanocrystals suspended in a toluene solution. The energy levels of the electrons in the Si nanocrystals chemisorbed with toluene molecules are calculated using the method of linear combination of atomic orbitals, and the characteristics of the obtained density of states is in good agreement with the observed photoluminescence properties.     

Anharmonic vibrational calculations modeling the raman spectra of intermediates in the photoactive yellow protein (PYP) photocycle

The role of anharmonic effects in the vibrational spectroscopy of the dark state and two major chromophore intermediates of the photoactive yellow protein (PYP) photocycle is examined via ab initio vibrational self-consistent field (VSCF) calculations and time-resolved resonance Raman spectroscopy. For the first time, anharmonicity is considered explicitly in calculating the vibrational spectra of an ensemble consisting of the PYP chromophore surrounded by model compounds used as mimics of the important active-site residues. Predictions of vibrational frequencies on an ab initio corrected semiempirical potential energy surface show remarkable agreement with experimental frequencies for all three states, thus shedding light on the potential along the reaction path. For example, calculated frequencies for vibrational modes of the red-shifted intermediate, PYPL, exhibit an overall average error of 0.82% from experiment. Upon analysis of anharmonicity patterns in the PYP modes we observe a decrease in anharmonicity in the C8-C9 stretching mode nu29 (trans-cis isomerization marker mode) with the onset of the cis configuration in PYPL. This can be attributed to the loss of the hydrogen-bonding character of the adjacent C9-O2 to the methylamine (Cys69 backbone). For several of the modes, the anharmonicity is mostly due to mode-mode coupling, while for others it is mostly intrinsic. This study shows the importance of the inclusion of anharmonicity in theoretical spectroscopic calculations, and the sensitivity of experiments to anharmonicity. The characterization of protein active-site residues by small molecular mimics provides an acceptable chemical structural representation for biomolecular spectroscopy calculations.     

Vibrational spectroscopy of the G...C base pair: experiment, harmonic and anharmonic calculations, and the nature of the anharmonic couplings

The results of harmonic and anharmonic frequency calculations on a guanine-cytosine complex with an enolic structure (a tautomeric form with cytosine in the enol form and with a hydrogen at the 7-position on guanine) are presented and compared to gas-phase IR-UV double resonance spectral data. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces; the improved PM3 potential surfaces are obtained from standard PM3 theory by coordinate scaling such that the improved PM3 harmonic frequencies are the same as those computed at the RI-MP2/cc-pVDZ level. Comparison of the data with experimental results indicates that the average absolute percentage deviation for the methods is 2.6% for harmonic RI-MP2/cc-pVDZ (3.0% with the inclusion of a 0.956 scaling factor that compensates for anharmonicity), 2.5% for harmonic RI-MP2/TZVPP (2.9% with a 0.956 anharmonicity factor included), and 2.3% for adapted PM3 CC-VSCF; the empirical scaling factor for the ab initio harmonic calculations improves the stretching frequencies but decreases the accuracy of the other mode frequencies. The agreement with experiment supports the adequacy of the improved PM3 potentials for describing the anharmonic force field of the G...C base pair in the spectroscopically probed region. These results may be useful for the prediction of the pathways of vibrational energy flow upon excitation of this system. The anharmonic calculations indicate that anharmonicity along single mode coordinates can be significant for simple stretching modes. For several other cases, coupling between different vibrational modes provides the main contribution to anharmonicity. Examples of strongly anharmonically coupled modes are the symmetric stretch and group torsion of the hydrogen-bonded NH2 group on guanine, the OH stretch and torsion of the enol group on cytosine, and the NH stretch and NH out-of-plane bend of the non-hydrogen-bonded NH group on guanine.