Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Chalcogen Stabilized bis-Hydridoborate Complexes of Cobalt: Analogues of Tetracyclo[4.3.0.02,4.03,5]nonane

Treatment of Li[BH₃ER] (E=Se or Te, R=Ph; E=S, R=CH₂Ph) with [Cp*CoCl]₂ led to the formation of hydridoborate complexes, [{CoCp*Ph}{Cp*Co}{μ-EPh}{μ-κ²-E,H-EBH₃}], 1a and 1 b ( 1 a : E=Se; 1 b : E=Te) and a bis-hydridoborate species [Cp*Co{μ-κ²-Se,H-SeBH₃}]₂, 2 . All the complexes, 1 a , 1 b and 2 are stabilized by β-agostic type interaction in which 1 b represents a novel bimetallic borate complex with a rare B−Te bond. QTAIM analysis furnished direct proof for the existence of a shared and dative B-chalcogen and Co-chalcogen interactions, respectively. In parallel to the formation of the hydridoborate complexes, the reactions also yielded tetracyclic species, [Cp*Co{κ³-E,H,H-E(BH₂)₂-C₅Me₅H₃}], 3 a and 3 b ( 3 a : E=Se and 3 b : E=S), wherein the bridgehead boron atoms are surrounded by one chalcogen, one cobalt and two carbon atoms of a cyclopentane ring. Molecules 3 a and 3 b are best described as the structural mimic of tetracyclo[4.3.0.0^2,4.0^3,5]nonane having identical structure and similar valence electron counts.     

Extending N-heterocyclic carbene ligands into the third dimension: a new type of hybrid phosphazane/NHC system

A simple, “click” synthetic approach to a new type of hybrid phosph(III)azane/NHC system is described. The presence of the phosphazane P₂N₂ ring unit, with P atoms flanking the NCN fragment and with this ring perpendicular to the binding site of the NHC, provides unique opportunities for modifying the electronic and steric character of these carbenes.     

Application of <Emphasis Type="Italic">k</Emphasis><Subscript>0</Subscript>-INAA for the determination of essential and toxic elements in medicinal plants from West Pokot County,Kenya

Rapid determination of gross alpha and beta emitters in urine by liquid scintillation counting is discussed. This method is based on direct addition of urine into scintillation cocktail. ²⁴¹Am, ²³⁹Pu and ⁹⁰Sr were selected as model radionuclides. The LSA Hidex 300 SL equipped with Triple-Double-Coincidence-Ratio technique was used for sample measurement. The work focused on optimizing the LSC cocktail to urine volume ratio with respect to the model radionuclides. The overall efficiencies for ²⁴¹Am, ²³⁹Pu and ⁹⁰Sr were greater than 92 %; therefore, this method would be suitable for rapid determination of gross alpha/beta activity.     

Rings containing a field of characteristic zero

Let K be a field of characteristic zero, and let R be a ring containing K. Then either \(R^\times = K^\times \) or \(K^\times \) is a subgroup of infinite index in \(R^\times \).     

Development and Molecular Understanding of a Pd-Catalyzed Cyanation of Aryl Boronic Acids Enabled by High-Throughput Experimentation and Data Analysis

A synthetic method for the palladium-catalyzed cyanation of aryl boronic acids using bench stable and non-toxic N-cyanosuccinimide has been developed. High-throughput experimentation facilitated the screen of 90 different ligands and the resultant statistical data analysis identified that ligand σ-donation, π-acidity and sterics are key drivers that govern yield. Categorization into three ligand groups – monophosphines, bisphosphines and miscellaneous – was performed before the analysis. For the monophosphines, the yield of the reaction increases for strong σ-donating, weak π-accepting ligands, with flexible pendant substituents. For the bisphosphines, the yield predominantly correlates with ligand lability. The applicability of the designed reaction to a wider substrate scope was investigated, showing good functional group tolerance in particular with boronic acids bearing electron-withdrawing substituents. This work outlines the development of a novel reaction, coupled with a fast and efficient workflow to gain understanding of the optimal ligand properties for the design of improved palladium cross-coupling catalysts.     

η4‐HBCC‐σ,π‐Borataallyl Complexes of Ruthenium Comprising an Agostic Interaction

Thermolysis of [Cp*Ru(PPh₂(CH₂)PPh₂)BH₂(L₂)] 1 (Cp*=η⁵‐C₅Me₅; L=C₇H₄NS₂), with terminal alkynes led to the formation of η⁴‐σ,π‐borataallyl complexes [Cp*Ru(μ‐H)B{R‐C=CH₂}(L)₂] ( 2 a – c ) and η²‐vinylborane complexes [Cp*Ru(R‐C=CH₂)BH(L)₂] ( 3 a – c ) ( 2 a , 3 a : R=Ph; 2 b , 3 b : R=COOCH₃; 2 c , 3 c : R=p‐CH₃‐C₆H₄; L=C₇H₄NS₂) through hydroboration reaction. Ruthenium and the HBCC unit of the vinylborane moiety in 2 a – c are linked by a unique η⁴‐interaction. Conversions of 1 into 3 a – c proceed through the formation of intermediates 2 a – c . Furthermore, in an attempt to expand the library of these novel complexes, chemistry of σ‐borane complex [Cp*RuCO(μ‐H)BH₂L] 4 (L=C₇H₄NS₂) was investigated with both internal and terminal alkynes. Interestingly, under photolytic conditions, 4 reacts with methyl propiolate to generate the η⁴‐σ,π‐borataallyl complexes [Cp*Ru(μ‐H)BH{R‐C=CH₂}(L)] 5 and [Cp*Ru(μ‐H)BH{HC=CH‐R}(L)] 6 (R=COOCH₃; L=C₇H₄NS₂) by Markovnikov and anti‐Markovnikov hydroboration. In an extension, photolysis of 4 in the presence of dimethyl acetylenedicarboxylate yielded η⁴‐σ,π‐borataallyl complex [Cp*Ru(μ‐H)BH{R‐C=CH‐R}(L)] 7 (R=COOCH₃; L=C₇H₄NS₂). An agostic interaction was also found to be present in 2 a – c and 5 – 7 , which is rare among the borataallyl complexes. All the new compounds have been characterized in solution by IR, ¹H, ¹¹B, ¹³C NMR spectroscopy, mass spectrometry and the structural types were unequivocally established by crystallographic analysis of 2 b , 3 a – c and 5 – 7 . DFT calculations were performed to evaluate possible bonding and electronic structures of the new compounds.