Plasma Based Synthesis of Nanomaterials for Development of Plasmon Enhanced Infrared Responsive Optoelectronic Device

Plasma Chemistry and Plasma Processing - We report plasma based fabrication of an optoelectronic device with plasmon enhanced infrared sensitivity realized by integrating plasmonic gold...     

Total Synthesis of Lajollamycin B

The first total synthesis of lajollamycin B, a structurally novel nitro-tetraene spiro-β-lactone/γ-lactone antibiotic, is described. The convergent synthesis involves the construction of the C8′–C11′ nitrodienylstannane and its coupling with the segment prepared from the C1′–C7′ ω-iodoheptadienoic acid and the right-hand heterocyclic fragment, which has been utilized for our previous syntheses of oxazolomycin A. The revision of the geometry of the terminal Δ^{10′, 11′}-double bond from E to Z is also described for the structure of natural lajollamycin B.     

Enhancing the Viscosity-Sensitive Range of a BODIPY Molecular Rotor by Two Orders of Magnitude

Molecular rotors are a class of fluorophores that enable convenient imaging of viscosity inside microscopic samples such as lipid vesicles or live cells. Currently, rotor compounds containing a boron-dipyrromethene (BODIPY) group are among the most promising viscosity probes. In this work, it is reported that by adding heavy-electron-withdrawing −NO₂ groups, the viscosity-sensitive range of a BODIPY probe is drastically expanded from 5–1500 cP to 0.5–50 000 cP. The improved range makes it, to our knowledge, the first hydrophobic molecular rotor applicable not only at moderate viscosities but also for viscosity measurements in highly viscous samples. Furthermore, the photophysical mechanism of the BODIPY molecular rotors under study has been determined by performing quantum chemical calculations and transient absorption experiments. This mechanism demonstrates how BODIPY molecular rotors work in general, why the −NO₂ group causes such an improvement, and why BODIPY molecular rotors suffer from undesirable sensitivity to temperature. Overall, besides reporting a viscosity probe with remarkable properties, the results obtained expand the general understanding of molecular rotors and show a way to use the knowledge of their molecular action mechanism for augmenting their viscosity-sensing properties.     

Alkali Blues: Blue-Emissive Alkali Metal Pyrrolates

2-Iminopyrroles [H^tBuL, 4-tert-butyl phenyl(pyrrol-2-ylmethylene)amine] are non-fluorescent π systems. However, they display blue fluorescence after deprotonation with alkali metal bases in the solid state and in solution at room temperature. In the solid state, the alkali metal 2-imino pyrrolates, M(^tBuL), aggregate to dimers, [M(^tBuL)(NCR)]₂ (M=Li, R=CH₃, CH(CH₃)CNH₂), or polymers, [M(^tBuL)]_n (M=Na, K). In solution (solv=CH₃CN, DMSO, THF, and toluene), solvated, uncharged monomeric species M(^tBuL)(solv)_m with N,N′-chelated alkali metal ions are present. Due to the electron-rich pyrrolate and the electron-poor arylimino moiety, the M(^tBuL) chromophore possesses a low-energy intraligand charge-transfer (ILCT) excited state. The chelated alkali cations rigidify the chromophore, restricting intramolecular motions (RIM) by the chelation-enhanced fluorescence (CHEF) effect in solution and, consequently, switch-on a blue fluorescence emission.     

Exploration of Nano-Saturns: A Spectacular Sphere–Ring Supramolecular System

Saturn-like systems consisting of nanoscale rings and spheres are fascinating motifs in supramolecular chemistry. Several ring molecules are known to include spherical molecules at the center of the cavity via noncovalent attractive interactions. In this Minireview, we generalize the molecular design, the structural features, and the supramolecular chemistry of such “nano-Saturns”, which consist of monocyclic rings and fullerene spheres (mainly C₆₀), on the basis of previous experimental and theoretical studies. Ring molecules are classified into three types (loop, belt, and disk) according to their shapes and possible interactions. Whereas typical belt-shaped rings tend to form tight complexes due to the wide contact area via π–π interactions, flat disk-shaped rings generally form weak complexes due to the narrow contact area mainly via CH–π interactions. In spite of the small association energies, disk-shaped rings are attractive because such rings can mimic the planet Saturn precisely as exemplified by an anthracene cyclic hexamer–C₆₀ complex.     

In Which Cases and Why the Standard Model of Tunneling Two-Level Systems Describes the Low-Temperature Inner Dynamics of Real Glasses Inadequately

Optics and Spectroscopy - Experiments carried out in recent years using single-molecule spectroscopy to study the low-temperature dynamics of some molecular solid-state media with a disordered...     

On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation

It is proved that, for some initial data, the solutions of the Cauchy problem for the cubic Schrödinger evolution equation blow up in finite time whose exact value is estimated from above. In addition, lower bounds for the blow-up rate of the solution in certain norms are obtained.

     

On Equitable Colorings of Hypergraphs

Mathematical Notes - A two-coloring is said to be equitable if, on the one hand, there are no monochromatic edges (the coloring is regular) and, on the other hand, the cardinalities of color...     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).