The Markovian Two-echelon Repairable Item Provisioning Problem

A repairable-item provisioning system with two levels of repair is presented. Under the assumption that the machine time-to-failure and the repair times are exponentially distributed, a new algorithm is developed to compute the long-run average number of machines operating. Using the new algorithm we determine the optimal number of machines and repair channels at the two repair centres to minimize cost and meet a service-level constraint. The algorithm, which is based on Little's result in queueing theory and the theory of regenerative processes, is extremely efficient in terms of computer storage and execution time.     

Why Does Pivalaldehyde (Trimethylacetaldehyde) Unexpectedly Seem More Basic Than 1‐Adamantanecarbaldehyde in the Gas Phase? FT‐ICR and High‐Level Ab Initio Studies

Fourier transform ion cyclotron resonance spectroscopy (FT ICR) techniques, including collision-induced dissociation (CID) methodology, were applied to the study of the gas-phase protonation of pivalaldehyde (1) and 1-adamantanecarbaldehyde (2). A new synthetic method for 2 was developed. The experiments, together with a thorough computational study involving ab initio and density functional theory (DFT) calculations of high level, conclusively show that upon monoprotonation in the gas phase, compound 1 yields monoprotonated methyl isopropyl ketone 3. The mechanism of this gas-phase acid-catalyzed isomerization is different from that reported by Olah and Suryah Prakash for the reaction in solution. In the latter case, isomerization takes place through the diprotonation of 1.     

Ligand-induced distortion of a tetranuclear manganese butterfly complex

The reaction of the pentadentate Schiff-base ligand 1,3-bis(salicylideneamino)-2-propanol (salproH3) with [Mn3O(O2CR)6(py)3] (R = Me, Et, But) gives the corresponding tetranuclear manganese product [Mn4O2O2CR)5(salpro)] (4Mn(III)). The syntheses, structure and magnetochemical characterization of these complexes are reported. The structure of the [Mn4(mu3-O)2]8+ is butterfly-like much more closed than in previous complexes with this core as a result of the alkoxide oxygen of the salpro ligand bridging the two wingtip Mn atoms. Variable-temperature, solid-state magnetic susceptibility studies reveal that these complexes possess S = 0 ground state spins. Fitting of the magnetic susceptibility data to the theoretical chiMT vs. T expression derived for a C2v symmetry complex, assuming an isotropic Heisenberg spin-Hamiltonian and using the Van Vleck equation, revealed that the various exchange parameters are all antiferromagnetic, and the core thus experiences spin frustration effects.     

On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which <β₁β₁>=<β₂β₂> where β₁ and β₂ are the greatest words in <<β₁>> and <<β₂>> of M(n).     

Influence of Amide Connectivity on the Hydrogen-Bond-Directed Self-Assembly of [n.n]Paracyclophanes

Reported here is the synthesis and self-assembly characterization of [n.n]paracyclophanes ( [n.n]pCps , n=2, 3) equipped with anilide hydrogen bonding units. These molecules differ from previous self-assembling [n.n]paracyclophanes ( [n.n]pCps ) in the connectivity of their amide hydrogen bonding units (C-centered/carboxamide vs. N-centered/anilide). This subtle change results in a ≈30-fold increase in the elongation constant for the [2.2]pCp -4,7,12,15-tetraanilide ( [2.2]pCpNTA ) compared to previously reported [2.2]pCp -4,7,12,15-tetracarboxamide ( [2.2]pCpTA ), and a ≈300-fold increase in the elongation constant for the [3.3]pCp -5,8,14,17-tetraanilide ( [3.3]pCpNTA ) compared to previously reported [3.3]pCp -5,8,14,17-tetracarboxamide ( [3.3]pCpTA ). The [n.n]pCpNTA monomers also represent the reversal of a previously reported trend in solution-phase assembly strength when comparing [2.2]pCpTA and [3.3]pCpTA monomers. The origins of the assembly differences are geometric changes in the association between [n.n]pCpNTA monomers—revealed by computations and X-ray crystallography—resulting in a more favorable slipped stacking of the intermolecular π-surfaces ( [n.n]pCpNTA vs. [n.n]pCpTA ), and a more complementary H-bonding geometry ( [3.3]pCpNTA vs. [2.2]pCpNTA ).     

Total structure determination of grassypeptolide, a new marine cyanobacterial cytotoxin

A collection of the cyanobacterium Lyngbya confervoides off Grassy Key in Florida yielded grassypeptolide (1), a 31-membered macrocyclic depsipeptide with unusually high D-amino acid content, two thiazolines, and one beta-amino acid. We report the rigorous 3D structure determination and conformational analysis in solution and solid state by NMR, MS, X-ray crystallography, chemical degradation, and molecular modeling involving distance geometry and restrained molecular dynamics. Grassypeptolide (1) inhibited cancer cell growth with IC50 values from 1.0 to 4.2 microM.