β-Lactam Derivatives as Enzyme Inhibitors: Peptidic Derivatives of ( RS )-2-Oxo-4-phenylazetidine-1-alkanoic Acids

4-Phenylazetidine-2-one was transformed into 4-phenylazetidine-1-alkanoic acids, which were reacted in the presence of diphenylphosphoroazidate with amino acid esters and dipeptide esters yielding β-lactam peptides with different spacers between the lactam ring and the peptide moiety. All structures were established by elementary analyses, HPLC, optical rotation, and spectroscopic data and all new compounds were tested as inhibitors of PPE using standard procedures. Four compounds exhibited a weak activity compared with the standard inhibitor trifluoroacetyl-l-val-l-tyr-l-val.     

A simple and efficient one step synthesis of 1,3,4-oxadiazoles utilizing polymer-supported reagents and microwave heating

1,3,4-Oxadiazoles can be rapidly and efficiently synthesized from a variety of carboxylic acids and acid hydrazides in one simple step. The use of commercially available PS-PPh₃ resin combined with microwave heating delivered the product 1,3,4-oxadiazoles in high yields and purities.     

A simple and efficient one step synthesis of benzoxazoles and benzimidazoles from carboxylic acids

Benzoxazoles or benzimidazoles can be rapidly and efficiently synthesized from a variety of carboxylic acids with 2-aminophenols or 1,2-phenylenediamines in one simple step, respectively. The use of commercially available PS-PPh₃ resin combined with microwave heating delivered a variety of benzoxazoles and benzimidazoles in high yields and purities.     

A characterization of nonreflexive banach spaces

D. P. Mil'man and V. D. Mil'man considered sequences of decreasing nonempty closed bounded convex sets with empty intersection to obtain characteristics of non-reflexivity. They showed that in every nonreflexive space there is such a sequence which is ω-separated. We show that in every nonreflexive space there is also always such a sequence which is not ω-separated     

A Novel Dual Drug Approach That Combines Ivermectin and Dihydromyricetin (DHM) to Reduce Alcohol Drinking and Preference in Mice

Alcohol use disorder (AUD) affects over 18 million people in the US. Unfortunately, pharmacotherapies available for AUD have limited clinical success and are under prescribed. Previously, we established that avermectin compounds (ivermectin [IVM] and moxidectin) reduce alcohol (ethanol/EtOH) consumption in mice, but these effects are limited by P-glycoprotein (Pgp/ABCB1) efflux. The current study tested the hypothesis that dihydromyricetin (DHM), a natural product suggested to inhibit Pgp, will enhance IVM potency as measured by changes in EtOH consumption. Using a within-subjects study design and two-bottle choice study, we tested the combination of DHM (10 mg/kg; i.p.) and IVM (0.5–2.5 mg/kg; i.p.) on EtOH intake and preference in male and female C57BL/6J mice. We also conducted molecular modeling studies of DHM with the nucleotide-binding domain of human Pgp that identified key binding residues associated with Pgp inhibition. We found that DHM increased the potency of IVM in reducing EtOH consumption, resulting in significant effects at the 1.0 mg/kg dose. This combination supports our hypothesis that inhibiting Pgp improves the potency of IVM in reducing EtOH consumption. Collectively, we demonstrate the feasibility of this novel combinatorial approach in reducing EtOH consumption and illustrate the utility of DHM in a novel combinatorial approach.     

Enhanced weak-signal sensitivity in two-photon microscopy by adaptive illumination

We describe a technique to enhance both the weak-signal relative sensitivity and the dynamic range of a laser scanning optical microscope. The technique is based on maintaining a fixed detection power by fast feedback control of the illumination power, thereby transferring high measurement resolution to weak signals while virtually eliminating the possibility of image saturation. We analyze and demonstrate the benefits of adaptive illumination in two-photon fluorescence microscopy.     

The Role of Methoxy Group in the Nazarov Cyclization of 1,5-bis-(2-Methoxyphenyl)-1,4-Pentadien-3-one in the Gas Phase and Condensed Phase

ESI-protonated 1,5-bis-(2-methoxyphenyl)-1,4-pentadien-3-one (1) undergoes a gas-phase Nazarov cyclization and dissociates via expulsions of ketene and anisole. The dissociations of the [M + D]⁺ ions are accompanied by limited HD scrambling that supports the proposed cyclization. Solution cyclization of 1 was effected to yield the cyclic ketone, 2,3-bis-(2-methoxyphenyl)-cyclopent-2-ene-1-one, (2) on a time scale that is significantly shorter than the time for cyclization of dibenzalacetone. The dissociation characteristics of the ESI-generated [M + H]⁺ ion of the synthetic cyclic ketone closely resemble those of 1, suggesting that gas-phase and solution cyclization products are the same. Additional mechanistic studies by density functional theory (DFT) methods of the gas-phase reaction reveals that the initial cyclization is followed by two sequential 1,2-aryl migrations that account for the observed structure of the cyclic product in the gas phase and solution. Furthermore, the DFT calculations show that the methoxy group serves as a catalyst for the proton migrations necessary for both cyclization and fragmentation after aryl migration. An isomer formed by moving the 2-methoxy to the 4-position requires relatively higher collision energy for the elimination of anisole, as is consistent with DFT calculations. Replacement of the 2-methoxy group with an OH shows that the cyclization followed by aryl migration and elimination of phenol occurs from the [M + H]⁺ ion at low energy similar to that for 1.

Fourier analysis on the Heisenberg group. I. Schwartz space

We derive a usable characterization of the group FT (Fourier Transform) of Schwartz space on the Heisenberg group $\text{H}$ⁿ, in terms of certain asymptotic series. To accomplish this we study in detail the FT of multiplication and differentiation operators on $\text{H}$ⁿ, the relation of multiple Fourier series to the FT, and the process of group contraction on $\text{H}$ⁿ. We use our characterization to solve a form of the division problem for convolution of $\text{H}$ⁿ, which has application to Hardy space theory.