Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups

The partition algebra \(\mathsf {P}_k(n)\) and the symmetric group \(\mathsf {S}_n\) are in Schur–Weyl duality on the k-fold tensor power \(\mathsf {M}_n^{\otimes k}\) of the permutation module \(\mathsf {M}_n\) of \(\mathsf {S}_n\), so there is a surjection \(\mathsf {P}_k(n) \rightarrow \mathsf {Z}_k(n) := \mathsf {End}_{\mathsf {S}_n}(\mathsf {M}_n^{\otimes k})\), which is an isomorphism when \(n \ge 2k\). We prove a dimension formula for the irreducible modules of the centralizer algebra \(\mathsf {Z}_k(n)\) in terms of Stirling numbers of the second kind. Via Schur–Weyl duality, these dimensions equal the multiplicities of the irreducible \(\mathsf {S}_n\)-modules in \(\mathsf {M}_n^{\otimes k}\). Our dimension expressions hold for any \(n \ge 1\) and \(k\ge 0\). Our methods are based on an analog of Frobenius reciprocity that we show holds for the centralizer algebras of arbitrary finite groups and their subgroups acting on a finite-dimensional module. This enables us to generalize the above result to various analogs of the partition algebra including the centralizer algebra for the alternating group acting on \(\mathsf {M}_n^{\otimes k}\) and the quasi-partition algebra corresponding to tensor powers of the reflection representation of \(\mathsf {S}_n\).     

Stability, thermal homolysis and intermediate phases of solid hydroazafullerene C59HN

Density functional (DFT) calculations, high-temperature electron paramagnetic resonance (EPR) and transmission electron microscopy (TEM) results suggest that thermal homolysis of C59HN involves a remarkably stable intermediate C59N-C59HN* structure characterised by charge redistribution from a C59N* radical to a bonded C59HN.     

Coordination Complexes of a Neutral 1,2,4‐Benzotriazinyl Radical Ligand: Synthesis,Molecular and Electronic Structures,and Magnetic Properties

A series of d‐block metal complexes of the recently reported coordinating neutral radical ligand 1‐phenyl‐3‐(pyrid‐2‐yl)‐1,4‐dihydro‐1,2,4‐benzotriazin‐4‐yl ( 1 ) was synthesized. The investigated systems contain the benzotriazinyl radical 1 coordinated to a divalent metal cation, Mn^II, Fe^II, Co^II, or Ni^II, with 1,1,1,5,5,5‐hexafluoroacetylacetonato (hfac) as the auxiliary ligand of choice. The synthesized complexes were fully characterized by single‐crystal X‐ray diffraction, magnetic susceptibility measurements, and electronic structure calculations. The complexes [Mn( 1 )(hfac)₂] and [Fe( 1 )(hfac)₂] displayed antiferromagnetic coupling between the unpaired electrons of the ligand and the metal cation, whereas the interaction was found to be ferromagnetic in the analogous Ni^II complex [Ni( 1 )(hfac)₂]. The magnetic properties of the complex [Co( 1 )(hfac)₂] were difficult to interpret owing to significant spin–orbit coupling inherent to octahedral high‐spin Co^II metal ion. As a whole, the reported data clearly demonstrated the favorable coordinating properties of the radical 1 , which, together with its stability and structural tunability, make it an excellent new building block for establishing more complex metal–radical architectures with interesting magnetic properties.     

Theoretical study of nonlinear optical properties of cobalt bis (dicarbollide) derivatives: the effect of substituents

In the present work, molecular first-order hyperpolarizability (\(\beta _{\mathrm{tot}}\)) and dipole moment (d) are obtained at B3LYP/6–31G(d,p) level of theory by coupled perturbed Hartree–Fock method within the static approach. The investigated molecules are a series of substituted cobalt bis (dicarbollide) derivatives: Hydrogens bonded to the two carbon atoms are replaced by acceptor and donor electron substituents. Correlations between the Hammett electronic parameters of the substituents and the molecular properties are tested. Among them, the named push–pull compounds produced the largest calculated values of \(\beta _{\mathrm{tot}}\) and d. The UV–Vis spectra are reported for all studied compounds.     

An agent-based model for the bibliometric h-index

We model a virtual scientific community in which authors publish and cite articles. Citations are attributed according to a preferential attachment mechanism. From the numerical simulations, the h-index can be computed. This bottom-up approach reproduces well real bibliometric data. We consider two versions of our model. (1) The single-scientist is controlled by two parameters which can be tuned to reproduce the value of the h-index of many real scientists. Moreover, this model shows how the h-index grows with the number of citations, for a fixed number of articles. We also define an average h-index that can be used to compare the scientific productivity of institutions of different sizes. (2) The multi-scientist model considers a population of scientists and allows us to study the impact of removing citations from the low h-index researchers on the community. Simulations on real bibilometric data, as well as the predictions of the model, show that the h-index eco-system can be strongly affected by such a filtering.     

On the efficiency of price competition

We study the efficiency of price competition among multi-product firms in differentiated oligopolies. Under a general affine demand model, we show that total surplus (sum of industry profit and consumers’ surplus) under competition is at least 75% of the maximum total surplus achievable by a centralized planner. We also show, in contrast to more stylized oligopoly models, that price collusion can increase total surplus and that competition does not, in general, yield a Pareto efficient trade-off between industry profit and consumers’ surplus. However, the maximum deviation of total surplus from Pareto optimality is less than 10%. These results have implications regarding the effectiveness of current anti-trust regulations.     

Robust and sensitive high-performance liquid chromatographic-UV detection technique for the determination of tigecycline in rabbit plasma

An isocratic HPLC method with detection at 248 nm was developed and fully validated for the determination of tigecycline in rabbit plasma. Minocycline was used as an internal standard. A Hypersil BDS RP-C18 column (250 x 4.6 mm, 5 microm particle size) was used with the mobile phase phosphate buffer (pH 7.10, 0.070 M)-acetonitrile (76 + 24, v/v) at a flow rate of 1.0 mL/min. The elution time of tigecycline and minocycline was approximately 8.1 and 9.9 min, respectively. Calibration curves of tigecycline were linear in the concentration range of 0.021-3.15 microg/mL in plasma. The LOD and LOQ in plasma were estimated as 7 and 21 ng/mL, respectively. The intraday and interday precision values of the method were in the range of 5.0-7.1 and 5.6-9.1%, while the corresponding accuracy values were in the ranges of 92.8-111.1 and 97.6-102.3%, respectively. At the LOQ, the intraday precision was 18.7%, while intraday and interday accuracy values were 97.3 and 98.0%, respectively. Robustness of the proposed method was studied using a Plackett-Burman experimental design. A pharmacokinetic profile is presented for confirmation of the applicability of the method to pharmacokinetic studies.     

Synthesis of triazafluoranthenones via silver(I)-mediated nonoxidative and oxidative intramolecular palladium-catalyzed cyclizations

Silver(I) fluoride (AgF)-mediated intramolecular nonoxidative and oxidative palladium-catalyzed cyclizations of 1,3-diphenyl- and 8-iodo-1,3-diphenylbenzo[e][1,2,4]triazin-7(1H)-ones 6a (R = H) and 7a (R = I) afford a new 'alkaloid like' ring system 2-phenyl-6H-[1,2,4]triazino[5,6,1-jk]carbazol-6-one 8a (triazafluoranthenone) in 86 and 100% yields, respectively. Furthermore, these cyclization protocols were used to prepare triazafluoranthenone analogues 8b-e bearing dialkylamino, methoxy, and phenylsulfanyl substituents at C-5, which were also independently synthesized from triazafluoranthenone 8a by regioselective nucleophilic addition. Similar AgF-mediated intramolecular nonoxidative and oxidative palladium-catalyzed cyclizations of 8,10-dihydro-1-iodo-10-phenylphenazin-2(7H)-ones 13 gave the new 'alkaloid like' ring system 8H-indolo[1,2,3-mn]phenazin-8-one 14 in 80 and 18% yields, respectively.     

On-line sorptive preconcentration platform incorporating a readily exchangeable Oasis HLB extraction micro-cartridge for trace cadmium and lead determination by flow injection-flame atomic absorption spectrometry

A simple, sensitive and inexpensive flow injection solid phase extraction (SPE) system was developed for automatic determination of trace level concentrations of metals. The potentials of this novel scheme, coupled to flame atomic absorption spectrometry (FAAS), were demonstrated for trace cadmium and lead determination in environmental water samples. The method was based on on-line chelate complex formation of target species with ammonium diethyldithiophosphate (DDTP), retention onto the surface of reversed-phase poly(divinylbenzene-N-vinylpyrrolidone) co-polymeric beads (Oasis HLB) and elution with methanol prior to atomization. A special PVC adapter was designed for easy and rapid replacement of the commercially available SPE cartridge. All main chemical and hydrodynamic parameters affecting the complex formation, sorption and elution of the analyte were optimized thoroughly. Moreover, the effect of potential interfering species occurring in environmental samples was also explored.For 90 s preconcentration time, enhancement factors of 155 and 180, detection limits (3s) of 0.09 μg L^− 1 and 0.9 μg L^− 1 and relative standard deviations (R.S.D.) of 2.9% (at 4.0 μg L^− 1) and 2.6% (at 20.0 μg L^− 1) were obtained for cadmium and lead, respectively, with a sample throughput of 24 h^− 1. The measurement trueness of the developed method was evaluated by analyzing a certified reference material and spiked environmental water samples. The proposed method is well suited to detect the target elements at concentration levels below the maximum allowed concentrations endorsed by the European Framework Directive (2008/105/EC) in inland and coastal waters.     

Nanostructured Heteroarm Star Block Terpolymers via an Extension of the “In–Out” Polymerization Route

In this communication an extended “in–out” polymerization method is presented, which leads to the synthesis of novel heteroarm star block terpolymers of the type A_n(B‐b‐C)_n. A four step/one‐pot synthetic procedure is pursued using anionic polymerization under an inert atmosphere. The resulted star‐shaped terpolymer consists of a divinyl benzene nodule bearing pure polystyrene and poly(hexyl methacrylate)‐block‐poly(methyl methacrylate) diblock copolymer arms. It is shown that this kind of star terpolymers can self‐assemble in the bulk forming lamellae mesophase by arm and block segregation. The mechanical properties of the terpolymer have been examined in detail. Finally, the proposed synthetic procedure can be easily employed in other controlled polymerization methods.