Distributional estimates for the bilinear Hilbert transform

We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L^p bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint estimates on L^p1 × L^p2 when either 1/p₁ + 1/p₂ = 3/2 or one of p₁, p₂ is equal to 1. As a consequence of this work we also obtain that the square root of the bilinear Hilbert transform of two characteristic functions is exponentially integrable over any compact set.     

Highly confined hybrid spoof surface plasmons in ultrathin metal-dielectric heterostructures

Highly confined "spoof" surface plasmons (SSPs) are theoretically predicted to exist in a perforated metal film coated with a thin dielectric layer. Strong modes confinement results from the additional waveguiding by the layer. Spectral characteristics, field distribution, and lifetime of these SSPs are tunable by the holes' size and shape. SSPs exist both above and below the light line, offering two classes of applications: "perfect" far-field absorption and efficient emission into guided modes. It is experimentally shown that these plasmonlike modes can turn thin, weakly absorbing semiconductor films into perfect absorbers.     

Decoration of 1,3-oxazole by alkyl substituents via CH activation (microreview)

Chemistry of Heterocyclic Compounds - Microreview describes recent advances in the synthesis of alkyl-substituted 1,3-oxazoles via CH activation reaction. The latest selected examples...     

The reaction of 4-aminocoumarin with β-carbonyl-substituted 4Н-chromenes: synthesis of 5H-chromeno[4,3-b]pyridin-5-one derivatives

Chemistry of Heterocyclic Compounds - Reactions of 4Н-chromene-3-carbaldehydes and 1Н-benzo[f]chromene-3-carbaldehydes with 4-aminocoumarin were used to obtain a series of...     

Pressure-induced suppression of ferromagnetic phase in LaCoO3 nanoparticles

Magnetic and structural properties of nanocrystalline LaCoO₃ with particle size ranging from 25 to 38 nm, prepared by the citrate method, were investigated. All nanoparticles exhibit ferromagnetism below T_C ≈ 85 K. It was found that the unit-cell volume increases monotonically with decreasing particle size and ferromagnetic (FM) moment increases simultaneously with lattice expansion, whereas T_C remains nearly unchanged. It appears that both magnetic and structural properties of LaCoO₃ nanoparticles are size-dependent due to the surface effect. On the other hand, an applied pressure suppresses strongly the FM phase leading to its disappearance at ～11 kbar. Remarkably, the T_C does not change visibly under pressure. Our data reveal that the ferromagnetism in LaCoO₃ nanoparticles, likely related to the intermediate-spin (IS) Co³⁺ state, is simply controlled by the unit-cell volume. Within this scenario, the FM coupled IS states appear/disappear with expanding/compressing the lattice and/or Co–O bonds.     

Barriers to internal rotation and tunnelling splittings of the torsional states in the HO(CH2)OH,DO(CH2)OH and DO(CH2)OD molecules

Torsional states caused by vibrations of hydroxyl groups in the methanediol molecule and its two deuterated analogues – DO(CH₂)OH and DO(CH₂)OD were analysed at MP2/cc-pVTZ and CCSD(T)/cc-pVQZ levels of theory. In the first case, 2D PES and 2D surfaces of kinematic coefficients were calculated with geometry optimisation for all other geometric parameters, and in the second case, only the energy of optimised configurations at the MP2/cc-pVTZ level of theory was determined. Then 2D PES was recounted to the complete basis set (CBS) limit by extrapolating the results of calculations at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory The calculated values were then averaged over four equivalent points on the coordinate plane. Hamiltonian matrices were constructed using DVR and Fourier methods. After their subsequent diagonalization, the energies of the stationary torsional states were computed. Their classification by C_2V(M) and C_S(M) molecular symmetry groups has been performed. The splitting values due to the tunnelling of the thirty most deeply located torsional states in the three studied molecules were also determined. The torsional states, internal rotation barriers, and tunnelling frequencies in the molecules of methanediol and hydrogen trioxide were compared.     

Conservative and Semismooth Derivatives are Equivalent for Semialgebraic Maps

Set-Valued and Variational Analysis - Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity for the...     

1H-1,2,4-Triazolo-5-diazonium salts in the synthesis of novel [1,2,4]triazolo[1,5-c][1,2,4]benzotriazin-6-ols

Chemistry of Heterocyclic Compounds - Condensation of 1H-1,2,4-triazolo-5-diazonium salts with 1,3-cyclohexanedione, accompanied by cascade processes of cyclization and oxidative aromatization,...     

Thin-Layer Chromatography of Metal Cations Modified with Amines and Surfactants and the Sorption-Catalytic Detection of Cobalt(II) and Copper(II)

JPC – Journal of Planar Chromatography – Modern TLC - The thin-layer chromatography (TLC) procedures of metal cations, modified with amines and cationic surfactant micelles, followed by...