Theoretical investigation of the He-I2(E3Πg) ion-pair state: ab initio intermolecular potential and vibrational levels

We present a theoretical study on the potential energy surface and vibrational bound states of the E electronic excited state of the HeI(2) van der Waals system. The interaction energies are computed using accurate ab initio methods and large basis sets. Relativistic small-core effective core potentials in conjunction with a quintuple-zeta quality basis set are employed for the heavy iodine atoms in multireference configuration interaction calculations for the (3)A' and (3)A" states. For the representation of the potential energy surface we used a general interpolation technique for constructing potential surfaces from ab initio data based on the reproducing kernel Hilbert space method. The surface presents global and local minima for T-shaped configurations with well-depths of 33.2 and 4.6 cm(-1), respectively. Vibrational energies and states are computed through variational quantum mechanical calculations. We found that the binding energy of the HeI(2)(E) T-shaped isomer is 16.85 cm(-1), in excellent agreement with recent experimental measurements. In lieu of more experimental data we also report our predictions on higher vibrational levels and we analyze the influence of the underlying surface on them. This is the first attempt to represent the potential surface of such a highly excited electronic state of a van der Waals complex, and it demonstrates the capability of the ab initio technology to provide accurate results for carrying out reliable studies to model experimental data.     

An ab initio study of the E 3Πg state of the iodine molecule

The E (3)Π(g) state of the iodine molecule is studied by ab initio multireference methods coupled with effective core potentials and large basis sets. Two potential minima are found, a global featuring an ion-pair character, and a local presenting a purely Rydberg nature. Four avoided crossings along the dissociation coordinate attribute an interesting topology to its potential energy curve, and their effect on the vibrational levels of I(2) is discussed.     

Specializations of Multigradings and the Arithmetical Rank of Lattice Ideals

In this article, we study specializations of multigradings and apply them to the problem of the computation of the arithmetical rank of a lattice ideal I _{L 𝒢}  ? K[x ₁,…, x _n ]. The arithmetical rank of I _{L 𝒢} equals the ?-homogeneous arithmetical rank of I _{L 𝒢} , for an appropriate specialization ? of 𝒢. To the lattice ideal I _{L 𝒢} and every specialization ? of 𝒢, we associate a simplicial complex. We prove that combinatorial invariants of the simplicial complex provide lower bounds for the ?-homogeneous arithmetical rank of I _{L 𝒢} .     

Grothendieck groups arising from contravariantly finite subcategories

The subject of the paper is the study of the relative homological properties of a given additive category C in relation to a given contravariantly finite subcategory X in C under the assumption that any X-epic has a kernel in C. We introduce the notion of the Grothendieck group relative to the pair (C, X) and also that of the Cartan map cx relative to (C, X) and we show that the cokernel of cx is isomorphic to the corresponding Grothendieck group of the stable category C/Jx We also show that if the right x-dimension of C is finite, then cx is an isomorphism. In case C is a finite dimensional k-additive Krull-Schmidt category, we introduce the notion of the x-dimension vector of an object of C. We give criteria for when an indecomposable object is determined, up to isomorphism, by its x-dimension vector.     

Dielectric and dynamic mechanical studies on homogeneous PBA/PBMA interpenetrating polymer networks

Broadband dielectric relaxation spectroscopy (DRS, 10⁻²‐10⁹ Hz), thermally stimulated depolarization currents (TSDC) techniques and dynamic mechanical analysis (DMA) were employed to investigate the dynamic glass transition and, thus, phase morphology in sequential IPNs of poly(butyl acrylate) (PBA) and poly(butyl methacrylate) (PBMA) with 10 weight % of ethyleneglycol dimethacrylate (EGDMA) as branching agent. In a parallel investigation, similar IPNs with only 0.1% branching agent showed clearly phase separation. In the highly branched IPNs, forced compatibilization induces miscibility of the two components. The results are discussed in terms of suppression of cooperativity and dynamic heterogeneity in the IPNs.     

On confidence intervals from simulation of finite Markov chains

Consider a finite state irreducible Markov reward chain. It is shown that there exist simulation estimates and confidence intervals for the expected first passage times and rewards as well as the expected average reward, with 100% coverage probability. The length of the confidence intervals converges to zero with probability one as the sample size increases; it also satisfies a large deviations property.     

Dominant three-body decays of a heavy higgs and top quark

We calculate the dominant three body Higgs decays,HW ⁺ W ^–(Z ⁰, ) and , in the Standard Model. We find that the branching ratios of these decays are of the order of few percent for large Higgs masses. We comment on the behaviour of the partial decay width below the threshold. Numerical results of the following three body top decays,tW ⁺ b(,g, Z ⁰) andtW ⁺ bH, are also given. We discuss the feasibility of observing these Higgs and top decays at future high energy colliders.