A skein action of the symmetric group on noncrossing partitions

We introduce and study a new action of the symmetric group \({\mathfrak {S}}_n\) on the vector space spanned by noncrossing partitions of \(\{1, 2,\ldots , n\}\) in which the adjacent transpositions \((i, i+1) \in {\mathfrak {S}}_n\) act on noncrossing partitions by means of skein relations. We characterize the isomorphism type of the resulting module and use it to obtain new representation-theoretic proofs of cyclic sieving results due to Reiner–Stanton–White and Pechenik for the action of rotation on various classes of noncrossing partitions and the action of K-promotion on two-row rectangular increasing tableaux. Our skein relations generalize the Kauffman bracket (or Ptolemy relation) and can be used to resolve any set partition as a linear combination of noncrossing partitions in a \({\mathfrak {S}}_n\)-equivariant way.     

Electrochemistry in ionic liquids: Case study of a manganese corrole

Voltammetry of [5,10,15-tris(pentafluorophenylcorrole)]Mn(III) was investigated in four different ionic liquids (ILs): 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm-TFSI); 1-ethyl-3-methylimidazolium ethylsulfate (EMIm-EtOSO3); 1-ethyl-3-methylimidazolium triflate (EMIm-OTf); and 1-ethyl-3-methylimidazolium tetracyanoborate (EMIm-TCB). We found that MnIV/III E _1/2 values depend on IL counter anion: OTf–< EtOSO₃ ^? < TFSI^? < TCB^?. In EMIm-TCB and BMIm- TFSI, reversible, diffusion-controlled Mn^IV/III reactions occurred, as evidenced in each case by the ratio of anodic to cathodic diffusion coefficients over a range of scan rates. Axial coordination was evidenced by a cathodic to anodic diffusion coefficient ratio greater than one, an increasing cathodic to anodic peak current ratio with increasing scan rate, and a split Soret band in the UV-vis spectrum of the complex.     

Lyapunov inequalities for the periodic boundary value problem at higher eigenvalues

This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the study of some special minimization problems. This allows to obtain the optimal constants. Our applications include the Hill's equation where we give some new conditions on its stability properties and also the study of periodic and nonlinear problems at resonance where we show some new conditions which allow to prove the existence and uniqueness of solutions.     

Analysis of 5'-mononucleotides in infant formula and adult/pediatric nutritional formula by liquid chromatography: First Action 2011.20

A method for the routine determination of 5'-mononucleotides (uridine 5'-monophosphate, inosine 5'-monophosphate, adenosine 5'-monophosphate, guanosine 5'-monophosphate, and cytidine 5'-monophosphate) in infant formula and adult nutritionals is described. After sample dissolution and addition of internal standard, potential interferences were removed by anion-exchange SPE followed by HPLC-UV analysis. Single-laboratory validation performance parameters include recovery (92-101%) and repeatability (1.0-2.3% RSD). The method was approved for Official First Action status by an AOAC expert review panel.     

A matheuristic for the truck and trailer routing problem

In the truck and trailer routing problems (TTRPs) a fleet of trucks and trailers serves a set of customers. Some customers with accessibility constraints must be served just by truck, while others can be served either by truck or by a complete vehicle (a truck pulling a trailer). We propose a simple, yet effective, two-phase matheuristic that uses the routes of the local optima of a hybrid GRASP × ILS as columns in a set-partitioning formulation of the TTRP. Using this matheuristic we solved both the classical TTRP with fixed fleet and the new variant with unlimited fleet. This matheuristic outperforms state-of-the-art methods both in terms of solution quality and computing time. While the best variant of the matheuristic found new best-known solutions for several test instances from the literature, the fastest variant of the matheuristic achieved results of comparable quality to those of all previous method from the literature with an average speed-up of at least 2.5.     

Sputtered magnesium diboride thin films: Growth conditions and surface morphology

Magnesium diboride (MgB₂) thin films were deposited on C-plane sapphire substrates by sputtering pure B and Mg targets at different substrate temperatures, and were followed by in situ annealing. A systematic study about the effects of the various growth and annealing parameters on the physical properties of MgB₂ thin films showed that the substrate temperature is the most critical factor that determines the superconducting transition temperature (T_c), while annealing plays a minor role. There was no superconducting transition in the thin films grown at room temperature without post-annealing. The highest T_c of the samples grown at room temperature after the optimized annealing was 22 K. As the temperature of the substrate (T_s) increased, T_c rose. However, the maximum T_s was limited due to the low magnesium sticking coefficient and thus the T_c value was limited as well. The highest T_c, 29 K, was obtained for the sample deposited at 180 °C, annealed at 620 °C, and was subsequently annealed a second time at 800 °C. Three-dimensional (3D) AFM images clearly demonstrated that the thin films with no transition, or very low T_c, did not have the well-developed MgB₂ grains while the films with higher T_c displayed the well-developed grains and smooth surface. Although the T_c of sputtered MgB₂ films in the current work is lower than that for the bulk and ex situ annealed thin films, this work presents an important step towards the fabrication of MgB₂ heterostructures using rather simple physical vapor deposition method such as sputtering.     

Adaptive disturbance transmission decoupling in active vehicle suspensions

With active vehicle suspension, one can tailor a vehicles response to load and inertial without affecting the vehicle response to road disturbances. This decoupling is achieved in [1] and [2] using a filtered combination of measured signals. These filters require exact knowledge of certain vehicle parameters including vehicle mass to achieve the desired decoupling. Here we propose a parameter adaptive version of these filters which does not require knowledge of vehicle parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Superconducting vortex pinning with artificial magnetic nanostructures

This review is dedicated to summarizing the recent research on vortex dynamics and pinning effects in superconducting films with artificial magnetic structures. The fabrication of hybrid superconducting/magnetic systems is presented together with the wide variety of properties that arise from the interaction between the superconducting vortex lattice and the artificial magnetic nanostructures. Specifically, we review the role that the most important parameters in the vortex dynamics of films with regular array of dots play. In particular, we discuss the phenomena that appear when the symmetry of a regular dot array is distorted from regularity towards complete disorder including rectangular, asymmetric, and aperiodic arrays. The interesting phenomena that appear include vortex-lattice reconfigurations, anisotropic dynamics, channeling, and guided motion as well as ratchet effects. The different regimes are summarized in a phase diagram indicating the transitions that take place as the characteristic distances of the array are modified respect to the superconducting coherence length. Future directions are sketched out indicating the vast open area of research in this field.     

Ionization probability of sputtered particles as a function of their energy: Part II. Positive Si ions

In this paper we represent the experimental ionization probability of sputtered silicon atoms as a function of their energy, which has been obtained for positive Si⁺ ions sputtered from silicon by O₂⁺ ion beam. To explain the experimental data, we have considered ionization of an outgoing atom at a critical distance from the surface, which occurs due to the electron transition between this atom and the surface, and suggested the formation of a local surface charge with the polarity opposite to that of the outgoing ion that has just been formed. Then we have considered the interaction between those two charges, outgoing ion, and surface charge as a process of the particle passage through a spherical potential barrier; as a result, we have obtained the theoretical energy distribution of secondary ions. Together with the well-known Sigmund-Thompson energy distribution of sputtered atoms, the obtained ion energy distribution allowed us to derive the equation for the secondary ion yield versus the sputtered particle energy. Both equations derived have exhibited a quite good correlation with our experimental results and also with a large number of published experimental data.     

Computational Design of Single-Peptide Nanocages with Nanoparticle Templating

Protein complexes perform a diversity of functions in natural biological systems. While computational protein design has enabled the development of symmetric protein complexes with spherical shapes and hollow interiors, the individual subunits often comprise large proteins. Peptides have also been applied to self-assembly, and it is of interest to explore such short sequences as building blocks of large, designed complexes. Coiled-coil peptides are promising subunits as they have a symmetric structure that can undergo further assembly. Here, an α-helical 29-residue peptide that forms a tetrameric coiled coil was computationally designed to assemble into a spherical cage that is approximately 9 nm in diameter and presents an interior cavity. The assembly comprises 48 copies of the designed peptide sequence. The design strategy allowed breaking the side chain conformational symmetry within the peptide dimer that formed the building block (asymmetric unit) of the cage. Dynamic light scattering (DLS) and transmission electron microscopy (TEM) techniques showed that one of the seven designed peptide candidates assembled into individual nanocages of the size and shape. The stability of assembled nanocages was found to be sensitive to the assembly pathway and final solution conditions (pH and ionic strength). The nanocages templated the growth of size-specific Au nanoparticles. The computational design serves to illustrate the possibility of designing target assemblies with pre-determined specific dimensions using short, modular coiled-coil forming peptide sequences.