Palladium‐catalysed room‐temperature Suzuki–Miyaura coupling in water extract of pomegranate ash,a bio‐derived sustainable and renewable medium

An agro waste‐derived, ‘water extract of pomegranate ash’ (WEPA), has been utilized for the first time as a renewable medium for Pd(OAc)₂‐catalysed Suzuki–Miyaura cross‐coupling at room temperature. This method offers a simple and sustainable synthesis of biaryls from aryl halides and arylboronic acids under ligand‐ and external base‐free aerobic and ambient conditions. This method has been found effective for both activated and unactivated aryl halides in the production of biaryls with moderate to nearly quantitative yields. The protocol shows high chemoselectivity over identical/similar reactive sites in aryl halides (i.e. selectivity over identical halogens or different halogens of aryl halides). This method exhibits high regioselectivity, i.e. the selective reactivity of a halogen over other identical halogens at different positions on the aromatic nucleus. Therefore, we disclose here a clean, benign, substantial chemo‐ and regioselective and highly economic alternative method for the palladium‐assisted synthesis of biaryls using an agro waste‐derived medium.     

Gorenstein projective bimodules via monomorphism categories and filtration categories

We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras A and B, we use the special monomorphism category $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ to describe some Gorenstein projective bimodules over the tensor product of A and B. If one of the two algebras is Gorenstein, we give a sufficient and necessary condition for $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ being the category of all Gorenstein projective bimodules. In addition, if both A and B are Gorenstein, we can describe the category of all Gorenstein projective bimodules via filtration categories. Similarly, in this case, we get the same result for infinitely generated Gorenstein projective bimodules.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Enantioselective LC‐ESI‐MS/MS determination of dropropizine enantiomers in rat plasma and application to a pharmacokinetic study

We developed and validated a simple, sensitive, selective and reliable LC–ESI‐MS/MS method for direct quantitation of dropropizine enantiomers namely levodropropizine (LDP) and dextrodropropizine (DDP) in rat plasma without the need for derivatization as per regulatory guidelines. Dropropizine enantiomers and carbamazepine (internal standard) were extracted from 50 μL rat plasma using ethyl acetate. LDP and DDP resolved with good baseline separation (R_s = 4.45) on a Chiralpak IG‐3 column. The mobile phase consisted of methanol with 0.05% diethylamine pumped at a flow rate of 0.5 mL/min. Detection and quantitation were done in multiple reaction monitoring mode following the transitions m/z 237 → 160 and 237 → 194 for dropropizine enantiomers and the internal standard, respectively, in the positive ionization mode. The proposed method provided accurate and reproducible results over the linearity range of 3.23–2022 ng/mL for each enantiomer. The intra‐ and inter‐day precisions were in the ranges of 3.38–13.6 and 5.11–13.8 for LDP and 4.19–11.8 and 8.89–10.1 for DDP. Both LDP and DDP were found to be stable under different stability conditions. The method was successfully used in a stereoselective pharmacokinetic study of dropropizine enantiomers in rats following oral administration of racemate dropropizine at 100 mg/kg. The pharmacokinetic results indicate that the disposition of dropropizine enantiomers is not stereoselective and chiral inversion does not occur in rats.     

Quantitative analysis of enasidenib in dried blood spots of mouse blood using an increased‐sensitivity LC–MS/MS method: Application to a pharmacokinetic study

A simple, sensitive and rapid assay method has been developed and validated as per regulatory guidelines for the estimation of enasidenib on mouse dried blood spots (DBS) using liquid chromatography coupled to tandem mass spectrometry with electrospray ionization in the positive‐ion mode. The method employs liquid extraction of enasidenib from DBS disks of mouse whole blood followed by chromatographic separation using 0.2% formic acid–acetonitrile (25:75, v/v) at a flow rate of 1.0 mL/min on an Atlantis dC₁₈ column with a total run time of 2.0 min. The MS/MS ion transitions monitored were m/z 474.0 → 267.1 for enasidenib and m/z 309.2 → 251.3 for the internal standard (warfarin). The assay was linear in the range of 1.01 – 3044 ng/mL. The within‐run and between‐run precisions were in the range of 3.18 – 9.06 and 4.66 – 8.69%, respectively. Stability studies showed that enasidenib was stable on DBS cards for 1 month. This novel method has been applied to analyze the DBS samples of enasidenib obtained from a pharmacokinetic study in mice.     

Validation of a HPLC/MS method for simultaneous quantification of clonidine,morphine and its metabolites in human plasma

A high‐performance liquid chromatography–tandem mass spectrometry method was developed and validated for the simultaneous quantification of morphine, morphine's major metabolites morphine‐3‐glucuronide and morphine‐6‐glucuronide, and clonidine, to support the pharmacokinetic analysis of an ongoing double‐blinded randomized clinical trial that compares the use of morphine and clonidine in infants diagnosed with neonatal abstinence syndrome. Plasma samples were processed by solid‐phase extraction and separated on an Inertsil ODS‐3 (4 μm) column using an 0.1% formic acid in water–0.1% formic acid in methanol gradient. Detection of the analytes was conducted in the positive multiple reaction monitoring mode. The range of quantitation was 1–1000 ng/mL for morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide, and 0.25–100 ng/mL for clonidine. Intra‐day and inter‐day accuracy and precision were ≤15% for all analytes across the quantitation range. Extraction recovery rates were ≥94% for morphine, ≥90% for M3G, ≥87% for M6G and ≥ 79% for clonidine. Matrix effect ranged from 85–94% for clonidine to 101–106% for M3G. The method fulfilled all predetermined acceptance criteria and required only 100 μL of starting plasma volume. Furthermore, it was successfully applied to 30 clinical trial plasma samples.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

Finely dispersed palladium on silk‐fibroin as an efficient and ligand‐free catalyst for Heck cross‐coupling reaction

A palladium–fibroin complex (Pd/Fib.) was prepared by the addition of sonicated fibroin fiber in water to palladium acetate solution. Pd (OAc)₂ was absorbed by fibroin and reduced with NaBH₄ at room temperature to the Pd(0) nanoparticles. Powder‐X‐ray diffraction, scanning electron microscopy–energy‐dispersive X‐ray spectroscopy, Fourier transform‐infrared, CHN elemental analysis and inductively coupled plasma‐atomic emission spectroscopy were carried out to characterize the Pd/Fib. catalyst. Catalytic activity of this finely dispersed palladium was examined in the Heck coupling reaction. The catalytic coupling of aryl halides (‐Cl, ‐Br, ‐I) and olefins led to the formation of the corresponding coupled products in moderate to high yields under air atmosphere. A variety of substrates, including electron‐rich and electron‐poor aryl halides, were converted smoothly to the targeted products in simple procedure. Heterogeneous supported Pd catalyst can be recycled and reused several times.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.