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.     

Über das Anwachsen der Lösungen linearer Differentialgleichungen mit rationalen Koeffizienten in Winkelräumen

Let z=∞ be the only irregular singular point of the linear differential equation $$(D)w^{(n)} + P_{n - 1} (z)w^{(n - 1)} + \cdots + P_o (z)w = 0$$ with rational coefficients p_j(z). If w is a multivalent and irregular solution of (D), we define the index I(τr,W), τ ∈ (0,1), of a branch W of w in the plane cut along a half ray. If r→∞, I(τr,W) possesses a finite number of aymptotic directions being exactly the asymptotic directions of the points z with maximal possible modulus of W(z). It follows that each branch W is of mean type σ(W)=|d|/λ in each sector containing an asymptotic direction of I. The possible values of the order of growth λ=λ(W)<∞ and the constant d are given by the PUISEUX-diagram of (D).     

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.     

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.     

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.     

Fiber-assisted detection with photon number resolution

We report the development of a photon-number-resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers and operates on the well-known principle by which a single-mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.     

The synthesis and crystal structure of 2,6,9‐trimethyl‐4,8‐dinitro‐2,6,9‐triazabicyclo[3.3.1]nona‐3,7‐diene

The first preparation of title compound 1 is accomplished. Its heterocyclic structure was characterized spectroscopically and by X‐ray structure analysis.