Variations of the Catalan numbers from some nonassociative binary operations

We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations.     

Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

Mass-imbalanced Bose-Einstein condensed mixtures in rotating perturbed trap

We consider the mass-imbalanced sensibility for the emergence of vortex patterns in the Bose-Einstein condensed binary mixture of rubidium-cesium (⁸⁵Rb-¹³³Cs), confined in quasi-two-dimensional harmonic traps, with one species linearly perturbed in one direction. Non-dipolar coupled species are chosen to highlight mass symmetry effects. We first analyze the condensed mixture in the unperturbed non-rotating regime, where radial phase separation is verified in the immiscible regime, which occurs for large ratio between inter- and intra-species repulsive interactions. By going to the linear perturbed regime, the radial phase separation that occurs in the immiscible condition splits up with the two densities having their maxima at distinct positions. In the rotating regime of both unperturbed and perturbed cases, the minimum rotation is determined in terms of the inter-species interaction to observe vortex structures. In the immiscible regime a dramatic spatial interchange between the species is verified by increasing the rotation.     

Base-Promoted Glycosylation Allows Protecting Group-Free and Stereoselective O-Glycosylation of Carboxylic Acids**

Here we report a simple and general method to achieve fully unprotected, stereoselective glycosylation of carboxylic acids, employing bench-stable allyl glycosyl sulfones as donors. Running the glycosylation reaction under basic conditions was crucial for the efficiencies and selectivities. Both the donor activation stage and the glycosidic bond forming stage of the process are compatible with free hydroxyl groups, thereby allowing for the use of fully unprotected glycosyl donors. This transformation is stereoconvergent, occurs under mild and metal-free conditions at ambient temperature with visible light (455 nm) irradiation, and displays remarkable scope with respect to both reaction partners. Many natural products and commercial drugs, including an acid derived from the complex anticancer agent taxol, were efficiently glycosylated. Experimental studies provide insights into the origin of the stereochemical outcome.     

Thermally Responsive Selenide-containing Materials Based on Transalkylation of Selenonium Salts

Covalent adaptable networks (CANs) possess unique properties as a result of their internal dynamic bonds, such as self-healing and reprocessing abilities. In this study, we report a thermally responsive C−Se dynamic covalent chemistry (DCC) that relies on the transalkylation exchange between selenonium salts and selenides, which undergo a fast transalkylation reaction in the absence of any catalyst. Additionally, we demonstrate the presence of a dissociative mechanism in the absence of selenide groups. After incorporation of this DCC into selenide-containing polymer materials, it was observed that the cross-linked networks display varying dynamic exchange rates when using different alkylation reagents, suggesting that the reprocessing capacity of selenide-containing materials can be regulated. Also, by incorporating selenonium salts into polymer materials, we observed that the materials exhibited good healing ability at elevated temperatures as well as excellent solvent resistance at ambient temperature. This novel dynamic covalent chemistry thus provides a straightforward method for the healing and reprocessing of selenide-containing materials.     

Boron-Catalyzed α-Functionalizations of Carboxylic Acids

Catalytic, chemoselective, and asymmetric α-functionalizations of carboxylic acids promise up-grading simple feedstock materials to value-added functional molecules, as well as late-stage structural diversifications of multifunctional molecules, such as drugs and their leads. In this personal account, we describe boron-catalyzed α-functionalizations of carboxylic acids developed in our group (five reaction types). The reversible boron carboxylate formation is key to the acidification of the α-protons and enolization using mild organic bases, allowing for chemoselective and asymmetric bond formations of carboxylic acids. The ligand effects on reactivity and stereoselectivity, substrate scopes, and mechanistic insights are summarized.     

Evaluation of an activated carbon from olive stones used as an adsorbent for heavy metal removal from aqueous phases

The performance of a microporous activated carbon prepared chemically from olive stones for removing Cu(II), Cd(II) and Pb(II) from single and binary aqueous solutions was investigated via the batch technique. The activated carbon sample was characterized using N₂ adsorption–desorption isotherms, SEM, XRD, FTIR, and Boehm titration. The effect of initial pH and contact time were studied. Adsorption kinetic rates were found to be fast and kinetic experimental data fitted very well the pseudo-second-order equation. The adsorption isotherms fit the Redlich–Peterson model very well and maximum adsorption amounts of single metal ions solutions follow the trend Pb(II) > Cd(II) > Cu(II). The adsorption behavior of binary solution systems shows a relatively high affinity to Cu(II) at the activated carbon surface of the mixture with Cd(II) or Pb(II). An antagonistic competitive adsorption phenomenon was observed. Desorption experiments indicated that about 59.5% of Cu(II) and 23% of Cd(II) were desorbed using a diluted sulfuric acid solution.     

Chitosan‐Silica Sulfate Nano Hybrid as a Novel and Highly Proficient Heterogeneous Nano Catalyst for Regioselective Ring Opening of Epoxides via Carboxylic Acids

The synthesis and characterization of chitosan‐silica sulfate nano hybrid (CSSNH ) as a novel and efficient heterogeneous nano catalyst involving acid‐base bifunctional activity is described. The catalytic potency and activity of this eco‐friendly catalyst was investigated in regioselective ring opening of epoxides with carboxylic acids to access structurally diverse 1,2‐diol mono‐esters in good to excellent yields. CSSNH catalyst was characterized using different microscopic and spectroscopic techniques encompassing scanning electron microscopy, transmission electron microscopy, X‐ray diffraction, N₂ adsorption isotherm, and Fourier transform infrared spectroscopy. The green nature, cheapness, efficiency, ease of preparation, handling and reusability of this new catalyst makes this catalyst to be useful for green industrial processes.