Jahn-Teller effects on π-stacking and stereoselectivity in the phenylethaniminopyridine tris-chelates Cu(NN')3(2+)

Optically pure phenylethaniminopyridine (S(C)-L) tris-chelates of Fe(II) and other first row transition metal systems have previously been shown to give exclusively the fac structures in the solid state. Here it is shown by powder X-ray diffraction that the complex [CuL(3)][ClO(4)](2) crystallises exclusively as the mer isomer, although--for a given absolute configuration of the ligand--of the same helicity (Δ/Λ) as that displayed by the other metal complexes. The similar ligand R(C)-L(F), which contains a peripheral (19)F spin label, gave [CuL(F)(3)][ClO(4)](2) which also adopts exclusively the mer structure in the crystal, but is shown by NMR spectroscopy to have a fac:mer ratio of 1:6 in solution at low temperature. Molecular mechanics calculations for a number of isomers and conformers are consistent with the presence of such a mixture of isomers in solution for both complexes. The origin of the difference in behaviour between Fe(II) and Cu(II) is the presence of a Jahn-Teller distortion (and the generally longer M-N bonds) in the Cu(II) complexes. This disturbs intra-ligand π-stacking, leading to the poor fac/mer stereoselectivity while leaving enantioselectivity Δ/Λ apparently unaffected.     

Temperature Integration: An efficient procedure for calculation of free energy differences

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ$lnZ$ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ$lnZ$ at high-T$T$, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a “toy model” of hard rods on a 1-dimensional ring.     

Thermal Expansion in TMTSF-Dmtcnq & (TMTSF)2PF6

We have measured the anisotropic thermal expansion of TMTSF-DMTCNQ and (TMTSF)₂PF₆ in the temperature range 10-300 K using an X-ray diffraction technique with a relative accuracy of 3 parts in 10⁴. Between 10 K and 300 K we find expansion in the a*, b* and c* directions to be respectively 2.5%, 0.2% and 1.7% for TMTSF-DMTCNQ and 3.7%, 1.6% and 1.3% for (TMTSF)₂PF₆     

Uniqueness of Rankin–Selberg products

In the present paper, we show the equality of the γ  -factors defined by Jacquet, Piatetski-Shapiro and Shalika with those obtained via the Langlands–Shahidi method. Our results are new in the case of positive characteristic, where we establish a refined version of the local–global principle for _GLn${\mathrm{GL}}_n$ which has independent interest. In characteristic zero, the results are due to Shahidi. The comparison of γ-factors is made via a uniqueness result for Rankin–Selberg γ-factors.     

A mathematical model for weighing investments

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.     

An optimal bound for inverses of triangular matrices with monotone entries

This article provides a new bound for 1-norms of inverses of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality established in Vecchio and Mallik [Bounds on the inverses of non-negative lower triangular Toeplitz matrices with monotonicity properties, Linear Multilinear Alg., 55 (2007), pp. 365–379]. The results are shown to be in a sense best possible under the given constraints.     

Imperative programs as proofs via game semantics

Game semantics extends the Curry–Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. The system is expressive: it contains all of the connectives of Intuitionistic Linear Logic, and first-order quantification. Use of Laird?s sequoid operator allows proofs with imperative behaviour to be expressed. Thus, we can embed first-order Intuitionistic Linear Logic into this system, Polarized Linear Logic, and an imperative total programming language.     

A tabu search heuristic for bandwidth allocation in fixed WiMAX

In this paper, we propose a mathematical model with the aim to give guidelines for the dimensioning of fixed WiMAX bandwidth provisioning service to residential customers. Our proposal relies on the modeling of a CAC policy associated to a priority-based bandwidth sharing strategy. Both mechanisms aim to satisfy Quality of Service constraints while maximizing the gain of the system. But unlike in Khemiri et al. (Optimal call admission control for an IEEE 802.16 wireless metropolitan area network. In: International Conference on Network Control and Optimization, 2007, accepted), we do not necessarily seek here for an optimal CAC policy. We rather consider a coordinate convex CAC policy, whose mathematical modeling leads to a tractable analytical resolution. We chose the Guaranteed Minima (GM) policy, which consists in reserving a specified amount of bandwidth for each traffic class. The remaining bandwidth is shared between all traffic classes. The purpose of the paper is to determine, using an analytical model and a heuristic approach, the nearly-optimal sizes of the GM reservation thresholds associated to each type of connection. The main concern here is to propose simple and robust computational methods, which can be easily and efficiently used to dimension a realistic WiMAX network.     

Organotrifluoroborate hydrolysis: boronic acid release mechanism and an acid-base paradox in cross-coupling

The hydrolysis of potassium organotrifluoroborate (RBF(3)K) reagents to the corresponding boronic acids (RB(OH)(2)) has been studied in the context of their application in Suzuki-Miyaura coupling. The "slow release" strategy in such SM couplings is only viable if there is an appropriate gearing of the hydrolysis rate of the RBF(3)K reagent with the rate of catalytic turnover. In such cases, the boronic acid RB(OH)(2) does not substantially accumulate, thereby minimizing side reactions such as oxidative homocoupling and protodeboronation. The study reveals that the hydrolysis rates (THF, H(2)O, Cs(2)CO(3), 55 °C) depend on a number of variables, resulting in complex solvolytic profiles with some RBF(3)K reagents. For example, those based on p-F-phenyl, naphthyl, furyl, and benzyl moieties are found to require acid catalysis for efficient hydrolysis. This acid-base paradox assures their slow hydrolysis under basic Suzuki-Miyaura coupling conditions. However, partial phase-splitting of the THF/H(2)O induced by the Cs(2)CO(3), resulting in a lower pH in the bulk medium, causes the reaction vessel shape, material, size, and stirring rate to have a profound impact on the hydrolysis profile. In contrast, reagents bearing, for example, isopropyl, β-styryl, and anisyl moieties undergo efficient "direct" hydrolysis, resulting in fast release of the boronic acid while reagents bearing, for example, alkynyl or nitrophenyl moieties, hydrolyze extremely slowly. Analysis of B-F bond lengths (DFT) in the intermediate difluoroborane, or the Swain-Lupton resonance parameter (?) of the R group in RBF(3)K, allows an a priori evaluation of whether an RBF(3)K reagent will likely engender "fast", "slow", or "very slow" hydrolysis. An exception to this correlation was found with vinyl-BF(3)K, this reagent being sufficiently hydrophilic to partition substantially into the predominantly aqueous minor biphase, where it is rapidly hydrolyzed.