New restriction estimates for the 3-d paraboloid over finite fields

We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain–Katz–Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.     

Trace formulas for additive and non-additive perturbations

Trace formulas for pairs of self-adjoint, maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained. In particular, the existence of a complex-valued spectral shift function for a pair {H^′,H}$\{H^{\prime },H\}$ of maximal accumulative operators has been proved. We investigate also the existence of a real-valued spectral shift function. Moreover, we treat in detail the case of additive trace class perturbations. Assuming that H   and H^′=H+V$H^{\prime }=H+V$ are maximal accumulative and V is trace class, we prove the existence of a summable   complex-valued spectral shift function. We also obtain trace formulas for pairs {H,H^?}$\{H,H^{?}\}$assuming only that H and  H^?$H^{?}$are resolvent comparable. In this case the determinant of the characteristic function of H is involved in trace formulas.     

Revisit of a series of ICT fluorophores: skeletal characterization,structural modification,and spectroscopic behavior

We have revisited the synthesis of a series of ICT fluorophores, which were reported to have a core structure of 8-oxo-8H-acenaphtho[1,2-b]pyrrol-9-carbonitrile. However, based on the 2D NMR and X-ray diffraction analysis, their core structure was corrected as 1-oxo-1H-phenalene-2,3-dicarbonitrile (1). Compound 1 shows a highly electron-deficient nature and can easily undergo oxidative S_NAr^H reaction on the naphthyl ring to produce a series of novel ICT fluorophores. The regioselectivity of this substitution reaction was studied by introduction of representative nucleophiles. Moreover, due to the strong rigidity and efficient ICT nature, the obtained fluorescent dyes display very good spectroscopic properties even in an aqueous environment.     

Synthesis,structure and reactivity of a macrocyclic imine: aza-[13]-macrodiolides

The in situ synthesis and subsequent reactions of macrocylic imine 2 are reported. The imine was trapped with cyanotrimethylsilane to give α-amino nitrile aza-[13]-macrodiolides in a 1:1 ratio of diastereomers. A crystal structure of the syn α-cyano nitrile diastereomer, 7a, provided insights into the lack of selectivity in reactions of 2 relative to macrocyclic alkene 1. Reactions to functionalize the syn diastereomer 7a are also reported.     

Infrared and NMR Spectroscopic Fingerprints of the Asymmetric H7+O3 Complex in Solution

Infrared (IR) absorption in the 1000–3700 cm⁻¹ range and ¹H NMR spectroscopy reveal the existence of an asymmetric protonated water trimer, H₇⁺O_3, in acetonitrile. The core H₇⁺O₃ motif persists in larger protonated water clusters in acetonitrile up to at least 8 water molecules. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations reveal irreversible proton transport promoted by propagating the asymmetric H₇⁺O₃ structure in solution. The QM/MM calculations allow for the successful simulation of the measured IR absorption spectra of H₇⁺O₃ in the OH stretch region, which reaffirms the assignment of the H₇⁺O₃ spectra to a hybrid-complex structure: a protonated water dimer strongly hydrogen-bonded to a third water molecule with the proton exchanging between the two possible shared-proton Zundel-like centers. The H₇⁺O₃ structure lends itself to promoting irreversible proton transport in presence of even one additional water molecule. We demonstrate how continuously evolving H₇⁺O₃ structures may support proton transport within larger water solvates.     

Electron-spin-dependent terahertz light transport in spintronic-plasmonic media

In this Letter, we demonstrate that electron spin can influence near-field mediated light propagation through a dense ensemble of subwavelength bimetallic ferromagnetic/nonmagnetic microparticles. In particular, we show that ferromagnetic particles coated with nonmagnetic metal nanolayers exhibit an enhanced magnetic field controlled attenuation of the electromagnetic field propagated through the sample. The mechanism is related to dynamic, electromagnetically induced electron spin accumulation in the nonmagnet. The discovery of an electron spin phenomenon in the light interaction with metallic particles opens the door to the marriage of spintronic and plasmonic technologies and could pave the way for the development of light-based devices that exploit the electron spin state.     

Two-photon fluorescence measurements of reversible photodegradation in a dye-doped polymer

We report on the dynamics of photodegradation and subsequent recovery of two-photon fluorescence in a dye-doped polymer. The energy dependence suggests that photodegradation is a linear process, while recovery is entropic. Such recovery could be useful to high-intensity devices such as two-photon absorbers, which can be used in many applications.     

Palladium‐Catalyzed Stereoselective Intramolecular Oxidative Amidation of Alkenes in the Synthesis of 1,3‐ and 1,4‐Amino Alcohols and 1,3‐Diamines

An efficient and practical Pd‐catalyzed intramolecular oxidative allylic amidation provides facile access to derivatives of 1,3‐ and 1,4‐amino alcohols and 1,3‐diamines. The method operates under mild reaction conditions (RT) with molecular oxygen (1 atm) as the sole reoxidant of Pd. Excellent diastereoselectivities were attained with substrates bearing a secondary stereogenic center     

PET Imaging of Bacterial Infections with Fluorine‐18‐Labeled Maltohexaose

A positron emission tomography (PET) tracer composed of ¹⁸F‐labeled maltohexaose (MH¹⁸F) can image bacteria in vivo with a sensitivity and specificity that are orders of magnitude higher than those of fluorodeoxyglucose (¹⁸FDG). MH¹⁸F can detect early‐stage infections composed of as few as 10⁵ E. coli colony‐forming units (CFUs), and can identify drug resistance in bacteria in vivo. MH¹⁸F has the potential to improve the diagnosis of bacterial infections given its unique combination of high specificity and sensitivity for bacteria.