Transform-limited spectral compression by self-phase modulation of amplitude-shaped pulses with negative chirp

Spectral compression by self-phase modulation of amplitude- and phase-shaped pulses is demonstrated as superior compared to pulses that have only been phase shaped. We synthesize linearly negatively chirped parabolic pulses, which we send through a nonlinear photonic crystal fiber, in which self-phase modulation compresses the spectrum of the pulses to within 20% of the Fourier transform limit.     

Invariance principles for sums of Banach space valued random elements and empirical processes

Summary Almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable Banach space. It is then shown that empirical processes readily fit into this general framework. Thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes.Both authors were partially supported by NSF grants. This work was done while the second author was visiting the M.I.T. Mathematics Department     

A Unified Treatment of the Relationship Between Ligand Substituents and Spin State in a Family of Iron(II) Complexes

The influence of ligands on the spin state of a metal ion is of central importance for bioinorganic chemistry, and the production of base‐metal catalysts for synthesis applications. Complexes derived from [Fe(bpp)₂]²⁺ (bpp=2,6‐di{pyrazol‐1‐yl}pyridine) can be high‐spin, low‐spin, or spin‐crossover (SCO) active depending on the ligand substituents. Plots of the SCO midpoint temperature (T ) in solution vs. the relevant Hammett parameter show that the low‐spin state of the complex is stabilized by electron‐withdrawing pyridyl (“X”) substituents, but also by electron‐donating pyrazolyl (“Y”) substituents. Moreover, when a subset of complexes with halogeno X or Y substituents is considered, the two sets of compounds instead show identical trends of a small reduction in T for increasing substituent electronegativity. DFT calculations reproduce these disparate trends, which arise from competing influences of pyridyl and pyrazolyl ligand substituents on Fe‐L σ and π bonding.     

Cooperative AND ion-pair recognition by heteroditopic calix[4]diquinone receptors

A new family of heteroditopic calix[4]diquinone receptors capable of the cooperative recognition of ion-pair species through a contact binding mechanism has been developed. The receptors bind contact ion pairs cooperatively, with an unprecedented AND recognition phenomenon being observed to operate in certain cases, in which receptors display no affinity for either of the individual "free" cation or anion, but bind the cation and anion ion-pair strongly. X-ray crystallographic, solution-state, and computational methods rationalize the observed recognition behavior of the receptors. It is shown that the contact ion-pair interaction occurs through a pi-stacking-mediated folding of the receptors such that the anion and cation binding sites are arranged in close proximity, while in the solid state an unusual ion-mediated receptor dimerization is observed. Molecular dynamics simulations are further used to explain the observed trends in the association constants of different ion-pair species and the mechanism of interaction.     

Meinardus' theorem on weighted partitions: Extensions and a probabilistic proof

The number c_n of weighted partitions of an integer n, with parameters (weights) b_k, k1, is given by the generating function relationship . Meinardus (1954) established his famous asymptotic formula for c_n, as n→∞, under three conditions on power and Dirichlet generating functions for the sequence b_k. We give a probabilistic proof of Meinardus' theorem with weakened third condition and extend the resulting version of the theorem from weighted partitions to other two classic types of decomposable combinatorial structures, which are called assemblies and selections.     

Theoretical evidence for the nucleophilic addition of sulfur dioxide to 1,2-bridged chloronium and bromonium ions

The nucleophilic addition of SO2, SO2ClF, and SO2F2 to carbenium ions and the nucleophilic addition of SO2 to 1,2-bridged halonium ions are theoretically investigated by using B3LYP/6-311+G(d,p). On the basis of geometric changes in ion-solvent complexes compared to isolated molecules, the theoretical data for the addition of solvent to carbenium ions uniformly agree with experiments by Olah and Donovan. The relative reactivity of carbenium ions (methyl > ethyl > iso-propyl > tert-butyl) follows the familiar trend based on electron demand at the carbenium center. The theoretical data for the addition of SO2 to 1,2-bridged halonium ions with use of similar methods indicate that this addition exhibits a reversed trend on the basis of the electron demand; SO2 adds to 2,2-dimethylethylene chloronium and bromonium ions but does not add to the fluoronium analogue. Furthermore, the addition depends on the stereochemistry of the approaching SO2. When SO2 approaches syn to the halogen atom on the halonium ion, addition is observed. When SO2 is anti, addition is not observed. The reversed reactivity and stereochemistry of the addition of SO2 to halonium ions can be explained by electron donation from the halogen atom to the sulfur atom of the approaching SO2. This sulfur-halogen interaction activates the nucleophilicity of the approaching SO2 and makes a normally unreactive tertiary carbenium carbon susceptible to addition. The theoretical evidence for covalently bound halonium ion-SO2 complexes is discussed in the context of previously reported experimental evidence for the existence of equilibria involving beta-halocarbenium ions.     

Investigation of the effects of the local environment on the surface-enhanced Raman spectra of striped gold/silver nanorod arrays

The effects of the local environment on surface-enhanced Raman scattering (SERS) spectra utilizing gold, silver, and gold/silver striped nanorod array substrates was investigated. The arrays were fabricated using an electrochemical metal deposition into an anodic aluminum oxide template. The analyte chosen for this study was p-nitroso-N,N-dimethylaniline (p-NDMA), which has an electronic structure that is highly sensitive to its surrounding environment. Changes in the peak positions and peak ratios were used to probe the influence of water and the striping pattern on the SERS signal of p-NDMA. We present the results of the fabrication and characterization of the nanorod array substrates, as well as SERS spectra of p-NDMA in both polar and nonpolar environments and SERS spectra on a variety of striped nanorod arrays. The Raman data suggests that the p-NDMA molecule exists in a more polarized state when bound to the gold as compared to the silver rods. We have attempted to use these differences to determine whether the SERS signal predominantly arises from the tips of the rods or from the interior of the array.     

The Anti-Inflammatory Effect of a γ-Lactone Isolated from Ostrich Oil of Struthio camelus (Ratite) and Its Formulated Nano-Emulsion in Formalin-Induced Paw Edema

The ostrich oil of Struthio camelus (Ratite) found uses in folk medicine as an anti-inflammatory in eczema and contact dermatitis. The anti-inflammatory effect of a γ-lactone (5-hexyl-3H-furan-2-one) isolated from ostrich oil and its formulated nano-emulsion in formalin-induced paw edema was investigated in this study. Ostrich oil was saponified using a standard procedure; the aqueous residue was fractionated, purified, and characterized as γ-lactone (5-hexyl-3H-furan-2-one) through the interpretation of IR, NMR, and MS analyses. The γ-lactone was formulated as nano-emulsion using methylcellulose (MC) for oral solubilized form. The γ-lactone methylcellulose nanoparticles (γ-lactone-MC-NPs) were characterized for their size, shape, and encapsulation efficiency with a uniform size of 300 nm and 59.9% drug content. The γ-lactone was applied topically, while the formulated nanoparticles (NPs) were administered orally to rats. A non-steroidal anti-inflammatory drug (diclofenac gel) was used as a reference drug for topical use and ibuprofen suspension for oral administration. Edema was measured using the plethysmograph method. Both γ-lactone and γ-lactone-MC-NPs showed reduction of formalin-induced paw edema in rats and proved to be better than the reference drugs; diclofenac gel and ibuprofen emulsion. Histological examination of the skin tissue revealed increased skin thickness with subepidermal edema and mixed inflammatory cellular infiltration, which were significantly reduced by the γ-lactone compared to the positive control (p-value = 0.00013). Diuretic and toxicity studies of oral γ-lactone-MC-NPs were performed. No diuretic activity was observed. However, lethargy, drowsiness, and refusal to feeding observed may limit its oral administration.