Novel palladium nanoparticles supported on β‐cyclodextrin@graphene oxide as magnetically recyclable catalyst for Suzuki–Miyaura cross‐coupling reaction with two different approaches in bio‐based solvents

A novel nanocatalyst was designed and prepared. Initially, the surface of magnetic graphene oxide (M‐GO) was modified using thionyl chloride, tris(hydroxymethyl)aminomethane and acryloyl chloride as linkers which provide reactive C═C bonds for the polymerization of vinylic monomers. Separately, β‐cyclodextrin (β‐CD) was treated with acryloyl chloride to provide a modified β‐CD. Then, in the presence methylenebisacrylamide as a cross‐linker, monomers of modified β‐CD and acrylamide were polymerized on the surface of the pre‐prepared M‐GO. Finally, palladium acetate and sodium borohydride were added to this composite to afford supported palladium nanoparticles. This fabricated nanocomposite was fully characterized using various techniques. The efficiency of this easily separable and reusable heterogeneous catalyst was successfully examined in Suzuki–Miyaura cross‐coupling reactions of aryl halides and boronic acid as well as in modified Suzuki–Miyaura cross‐coupling reactions of N‐acylsuccinimides and boronic acid in green media. The results showed that the nanocatalyst was efficient in coupling reactions for direct formation of the corresponding biphenyl as well as benzophenone derivatives in green media based on bio‐based solvents. In addition, the nanocatalyst was easily separable, using an external magnet, and could be reused several times without significant loss of activity under the optimum reaction conditions.     

Intransitive Permutation Group with Bounded Movement

Let G be a intransitive permutation group on a set with no fixed point in ; let m, n be a positive integer and let |^g – | m, for every and g G. When G has t orbits and degree n close to [2mp/(p – 1)] + t – 1, this paper constructs such a group with m close to [n(p – 1)/2p].AMS Subject Classification: 20BXX.     

Coupled fixed point theorems for contractions in fuzzy metric spaces

In the present work, we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces.     

Some results on the annihilators and attached primes of local cohomology modules

Let \((R, \mathfrak {m})\) be a local ring and M a finitely generated R-module. It is shown that if M is relative Cohen–Macaulay with respect to an ideal \(\mathfrak {a}\) of R, then \({\text {Ann}}_R(H_{\mathfrak {a}}^{{\text {cd}}(\mathfrak {a}, M)}(M))={\text {Ann}}_RM/L={\text {Ann}}_RM\) and \({\text {Ass}}_R (R/{\text {Ann}}_RM)\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M|\,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})={\text {cd}}(\mathfrak {a}, M)\},\) where L is the largest submodule of M such that \(\mathrm{cd}(\mathfrak {a}, L)< \mathrm{cd}(\mathfrak {a}, M)\). We also show that if \(H^{\dim M}_{\mathfrak {a}}(M)=0\), then \({\text {Att}}_R(H^{\dim M-1}_{\mathfrak {a}}(M))= \{\mathfrak {p}\in {\text {Supp}}(M)|\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M-1\},\) and so the attached primes of \(H^{\dim M-1}_{\mathfrak {a}}(M)\) depend only on \({\text {Supp}}(M)\). Finally, we prove that if M is an arbitrary module (not necessarily finitely generated) over a Noetherian ring R with \(\mathrm{cd}(\mathfrak {a}, M)=\mathrm{cd}(\mathfrak {a}, R/{\text {Ann}}_RM)\), then \({\text {Att}}_R(H^{\mathrm{cd}(\mathfrak {a}, M)}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {V}}({\text {Ann}}_RM)|\,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\mathrm{cd}(\mathfrak {a}, M)\}.\) As a consequence of this, it is shown that if \(\dim M=\dim R\), then \({\text {Att}}_R(H^{\dim M}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M|\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M\}\).     

Acetone extracted propolis as a novel membrane and its application in phenol biosensors: the case of catechol

A novel biosensor for catechol has been constructed by immobilizing polyphenol oxidase (PPO) into acetone-extracted propolis (AEP) composite modified with gold nanoparticles (GNPs) and attached to multiwalled carbon nanotube (MWCNTs) on a gold electrode surface. The propolis for AEP was obtained from honeybee colonies. Under the optimum conditions, this method could be successfully used for the amperometric determination of catechol within a concentration range of 1 × 10^?6 to 5 × 10^?4?M, with a detection limit of 8 × 10^?7?M (S/N = 3). The effects of pH and operating potential are also explored to optimize the measurement conditions. The best response was obtained at pH?5, while an optimum ratio of signal-to-noise (S/N) was obtained at ?20?mV (versus Ag/AgCl), which was selected as the applied potential for the amperometric measurements. All subsequent experiments were performed at pH?5. Cyclic voltammetry and electrochemical impedance spectroscopy was used to characterize the PPO/CNTs/GNPs/AEP/Au biosensor. The biosensor also exhibited good selectivity, stability, and reproducibility.     

Faltings’ local–global principle for finiteness dimension of cofinite modules

Archiv der Mathematik - Let R denote a commutative Noetherian ring, $$\mathfrak {a}$$ an ideal of R, and M an $$\mathfrak {a}$$ -cofinite R-module. The purpose of this article is to show that for a...     

Weakly associated primes and primary decomposition of modules over commutative rings

Summary We characterize finitely generated Laskerian modules over a commutative ring in terms of weakly associated prime ideals.     

Dynamic Pore-Scale Modeling of Residual Trapping Following Imbibition in a Rough-walled Fracture

Transport in Porous Media - We present a new, fully dynamic pore-network modeling platform that is employed to conduct a systematic pore-scale study of capillary trapping under various two-phase...     

Analysis of Adsorbate–Adsorbate and Adsorbate–Adsorbent Interactions to Decode Isosteric Heats of Gas Adsorption

A qualitative interpretation is proposed to interpret isosteric heats of adsorption by considering contributions from three general classes of interaction energy: fluid–fluid heat, fluid–solid heat, and fluid—high‐energy site (HES) heat. Multiple temperature adsorption isotherms are defined for nitrogen, T=(75, 77, 79) K, argon at T=(85, 87, 89) K, and for water and methanol at T=(278, 288, 298) K on a well‐characterized polymer‐based, activated carbon. Nitrogen and argon are subjected to isosteric heat analyses; their zero filling isosteric heats of adsorption are consistent with slit‐pore, adsorption energy enhancement modelling. Water adsorbs entirely via specific interactions, offering decreasing isosteric heat at low pore filling followed by a constant heat slightly in excess of water condensation enthalpy, demonstrating the effects of micropores. Methanol offers both specific adsorption via the alcohol group and non‐specific interactions via its methyl group; the isosteric heat increases at low pore filling, indicating the predominance of non‐specific interactions.