Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

A new route to trinuclear carbocyanines

Amides or vinylogous amides react with tosyl chloride-pyridine to form activated intermediates which condense with Fischer's base or their vinylogs to give carbocyanine structures. Under the same conditions formylated Fischer's base reacts with vinylogous Fischer's bases to give trinuclear carbocyanines in good yields. Their structure and the limitations of this route are discussed.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Design and synthesis of push-pull chromophores for second-order nonlinear optics derived from rigidified thiophene-based pi-conjugating spacers.

Two series of push-pull chromophores built around thiophene-based pi-conjugating spacers rigidified either by covalent bonds or by noncovalent intramolecular interactions have been synthesized and characterized by UV-vis spectroscopy, electric field induced second harmonic generation (EFISH) and differential scanning calorimetry. Comparison of the linear and second-order nonlinear optical properties of chromophores based on a covalently bridged dithienylethylene (DTE) spacer with those of their analogues based on open chain DTE shows that the rigidification of the spacer produces a considerable bathochromic shift of the absorption maximum together with a dramatic enhancement of the molecular quadratic hyperpolarizability (mu beta) which reaches values among the highest reported so far. A second series of NLO-phores has been derived from a 2,2'-bi(3,4-ethylenedioxythiophene) (BEDOT) pi-conjugating spacer. As indicated by X-ray and UV-vis data, rigidification of the spacer originates in that case, from noncovalent intramolecular interactions between sulfur and oxygen atoms. Again, comparison with the parent compounds based on an unsubstituted bithiophene spacer reveals a marked red shift of the absorption maximum and a large enhancement of mu beta. In an attempt to distinguish the contribution of the electronic and geometrical effects of the ethylenedioxy group, a third series of NLO-phores based on 3,4-ethylenedioxythiophene (EDOT) and 3,4-dihexyloxythiophene spacers has been synthesized. Comparison with compounds based on unsubstituted thiophene shows that, despite a red shift of lambda(max), introduction of alkoxy groups leads to a decrease of mu beta. Theoretical calculations indicate that this effect results from a decrease of the dipole moment (mu) caused by the auxiliary electron-donor alkoxy groups on the thiophene ring. In contrast, replacement of BT by BEDOT produces an increase of mu, which associated with the noncovalent rigidification of the BT system accounts for the observed enhancement of mu beta.     

Following the aggregation of amyloid-forming peptides by computer simulations

There is experimental evidence suggesting that the toxicity of neurodegenerative diseases such as Alzheimer's disease may result from the soluble intermediate oligomers. It is therefore important to characterize extensively the early steps of oligomer formation at atomic level. As these structures are metastable and short lived, experimental data are difficult to obtain and they must be complemented with numerical simulations. In this work, we use the activation-relaxation technique coupled with a coarse-grained energy model to study in detail the mechanisms of aggregation of four lys-phe-phe-glu (KFFE) peptides. This is the shortest peptide known to form amyloid fibrils in vitro. Our simulations indicate that four KFFE peptides adopt a variety of oligomeric states (tetramers, trimers, and dimers) with various orientations of the chains in rapid equilibrium. This conformational distribution is consistent with all-atom molecular-dynamics simulations in explicit solvent and is sequence dependent; as seen experimentally, the lys-pro-gly-glu (KPGE) peptides adopt disordered structures in solution. Our unbiased simulations also indicate that the assembly process is much more complex than previously thought and point to intermediate structures which likely are kinetic traps for longer chains.     

Chiral induction in quinoline-derived oligoamide foldamers: assignment of helical handedness and role of steric effects

Chiral groups attached to the end of quinoline-derived oligoamide foldamers give rise to chiral helical induction in solution. Using various chiral groups, diastereomeric excesses ranging from 9% to 83% could be measured by NMR and circular dichroism. Despite these relatively weak values and the fact that diastereomeric helices coexist and interconvert in solution, the right-handed or left-handed helical sense favored by the terminal chiral group could be determined unambiguously using X-ray crystallography. Assignment of chiral induction was performed in an original way using the strong tendency of racemates to cocrystallize, and taking advantage of slow helix inversion rates, which allowed one to establish that the stereomers observed in the crystals do correspond to the major stereomers in solution. The sense of chiral helical induction was rationalized on the basis of sterics. Upon assigning an Rs or Ss chirality to the stereogenic center using a nomenclature where the four substituents are ranked according to decreasing sizes, it is observed that Rs chirality always favors left-handed helicity and Ss chirality favors right-handed helicity (P). X-ray structures shed some light on the role of sterics in the mechanism of chiral induction. The preferred conformation at the stereocenter is apparently one where the bulkiest group should preferentially point away from the helix, the second largest group should be aligned with the helix backbone, and the smallest should point to the helix.     

Comparative dielectric and thermotropic properties of liquid crystalline polyesters as a function of mesogen group and flexible thioether group length

Two polyesters containing rigid biphenyl and hydroquinone bisbenzoate groups and presenting flexible thioether moieties with different lengths (14 elements in the flexible group) have been carried out using a reaction of the Michaël type. The properties of these polyesters have been compared to those of polyesters of the same type presenting shorter flexible groups (11 elements). All these polymers present thermotropic properties: the biphenyl ones are smectic and the bisbenzoate ones are nematic. The biphenyl polyesters present two types of dielectric relaxations: α and β. The bisbenzoate ones show three relaxations, α and two β (β and β^′). The lengthening of the flexible group increases significantly the flexibility of the molecular chains.