Estimating the Probability of Ruin for Variable Premiums by Simulation

There is a duality between the surplus process of classical risk theory and the single-server queue. It follows that the probability of ruin can be retrieved from a single sample path of the waiting time process of the single-server queue. In this paper, premiums are allowed to vary. It has been shown that the stationary distribution of a corresponding storage process is equal to the survival probability (with variable premiums). Thus by simulation of the corresponding storage process, the probability of ruin can be obtained. The special cases where the surplus earns interest and the premiums are charged by layers are considered and illustrated numericall

Berry phase investigation of spin-S ladders

We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of non-frustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated to a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated to a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as cross-overs between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these cross-overs turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.Comment: 9 pages, 10 figures The second version has been entirely rewritte

Coordination of a bifunctional ligand to a rhodium(III) dimethyl complex : Lewis acidity enhancement by chelation

The addition of the ambiphilic compound (Me2PCH2AlMe2)2 (1) to Cp*RhMe2(DMSO) (DMSO ) dimethylsulfoxide) (2) gives Cp*RhMe2(PMe2CH2AlMe2‚DMSO) (3‚DMSO). The addition of Lewis acids (LA) such as La(dbm)3 (dbm ) dibenzoylmethane) and AlMe3 to a solution of complex 3‚DMSO gives a competition reaction that results in the formation of LA‚DMSO and Cp*RhMe2(PMe2CH2AlMe2) (3). When heated to 40 °C, complex 3 ionizes to a putative zwitterionic species, Cp*Rh+Me(PMe2CH2AlMe3 -) (3′), which is converted to [Cp*Rh(Me)(µ2 -η2 -Me2PCH2)]2 (4) irreversibly. Spin saturation transfer experiments demonstrated that the rate of the methyl abstraction by the alane moiety was 0.76 ( 0.09 s-1 , while the rate of abstraction of the methyl in Cp*RhMe2(PMe3) by AlMe3 was 0.10 ( 0.02 s-1 . The zwitterionic species 3′ could be trapped in solution by addition of PMe3 to afford both Cp*Rh+Me(PMe3)(Me2- PCH2AlMe3 -) (5) and [Cp*Rh+Me(PMe3)(Me2PCH2AlMe2)]AlMe4 - (6). When compound 1 was added to complex 3′, the formation of the zwitterionic complex Cp*Rh+Me(η2 -Me2PCH2Al-Me2CH2PMe2) (7) was observed

Antiferromagnetic spin-S chains with exactly dimerized ground states

We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (S_{i-1}S_{i})(S_{i}S_{i+1})+h.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/(4S(S+1)-2). This result generalizes the Majumdar-Ghosh point of the J_1-J_2 chain, to which the present model reduces for S=1/2. For S=1, we use the density matrix renormalization group method (DMRG) to show that the transition between the Haldane and the dimerized phases is continuous with central charge c=3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.Comment: 8 pages, 8 figure

alpha,omega-Bis(trialkoxysilyl) difunctionalized polycyclooctenes from ruthenium-catalyzed chain-transfer ring-opening metathesis polymerization

International audienceThe ring-opening metathesis polymerization/cross-metathesis (ROMP/CM) of cyclooctene (COE) using bis(trialkoxysilyl)alkenes as chain-transfer agents (CTAs) and Ru catalysts to afford difunctionalized polyolefins is reported. The formation of alpha,omega-bis(trialkoxysilyl) telechelic polycycloolefins (DF) with controlled molar mass values takes place quite selectively (>90 wt%), along with minor amounts of cyclic non-functionalized polymers (CNF), as evidenced by NMR, MALDI-ToF MS, SEC analyses and fractionation experiments. The nature of the CTA and catalyst influenced much the efficiency and selectivity of the reaction. (MeO)(3)SiCH2CH=CHCH2Si(OMe)(3) (2) and (MeO)(3)Si(CH2)(3)NHC(O)OCH2CH=CHCH2OC(O)NH (CH2)(3)Si(OMe)(3) (5) proved to be the most efficient CTAs in terms of reactivity, catalyst productivity and selectivity towards DF. Diurethane CTA 5 is easily prepared, and can also be conveniently generated in situ during the ROMP/CM. Grubbs' 2nd-generation catalyst (G2) and Hoveyda-Grubbs's catalyst (HG2) afforded the best compromise in terms of selectivity and productivity, with turnover numbers of up to 95 000 mol(COE) mol(Ru)(-1) and 5000 mol(CTA) mol(Ru)(-1)

High Performance Pre-Computing: Prototype Application to a Coastal Flooding Decision Tool

International audienceAfter defining the High Performance Pre- Computing --referred as HPPC-- concept, the aim of the present study is to develop a prototype whether to approve or not the benefits of this concept. Our application case tries to answer the geophysical issue of coastal flooding. This is an example of an alert system based on the HPPC architecture, thus on pre-computed scenarios. The prototype provides the scientists with an ergonomic and on-demand tool allowing the run of scenarios of any implemented numerical models. These runs are available through a web application which submits the corresponding jobs on the remote french public cluster of HPC@LR. In this study we simulate the waves propagation over a Mediterranean grid using the wave model WaveWatch III⃝R . A reference simulation using usual conditions is approximated using the k-NN algorithm over 12, 98 and then 980 pre-computed scenarios. This simple experiment demonstrates how useful the pre-computing of scenarios is for alert systems as far as enough and relevant scenarios are pre-computed. This is the reason why searches continue in each critical points of the HPPC architecture such as the design of experiment, the approximation of the results by meta-models and the research of the closest scenarios in this big data context

α,ω-Di(glycerol carbonate) telechelic polyesters and polyolefins as precursors to polyhydroxyurethanes: an isocyanate-free approach

International audienceα,ω-Di(glycerol carbonate) telechelic poly(propylene glycol) (PPG), poly(ethylene glycol) (PEG), poly(ester ether) (PEE), and poly(butadiene) (PBD) have been synthesized through chemical modification of the corresponding α,ω-dihydroxy telechelic polymers (PPG-OH2, PEG-OH2, PEE-OH2 and PBD-OH2, respectively). Tosylation of the polymer diols with 4-tosylmethyl-1,3-dioxolan-2-one (GC-OTs) afforded, in high yields, the desired PPG, PEG, PEE and PBD end-capped at both termini with a five-membered ring cyclic glycerol carbonate (4-hydroxymethyl-1,3-dioxolan-2-one, GC). The GC-functionalization of the polymers at both chain-ends has been confirmed by NMR (1H, 13C, 1D and 2D) and FTIR spectroscopies. Using PPG-GC2 to demonstrate the concept, the corresponding polyhydroxyurethanes (PHUs/non-isocyanate polyurethanes (NIPUs)) have been subsequently prepared following a non-isocyanate method upon ring-opening catalyst-free polyaddition of the PPG-GC2 with JEFFAMINEs (Mn = 230-2000 g mol−1). The effect of various additives introduced during the polyaddition reaction has been studied at different temperatures. In particular, addition of LiBr (5 mol%) to the reaction medium was found to slightly promote the cyclocarbonate/amine reaction. The polymerization process was supported by FTIR and SEC analyses