Strength considerations of optical waveguide fibers

An important aspect of optical waveguide fiber made of glass is whether it will break under a wide variety of service and manufacturing conditions. This paper covers some of the testing in which stress, length, time, and environment were vaned. The use of Weibull statistics with these data indicates that a statistically predictable behavior exists for populations of glass fibers. Extrapolation from short lengths and short times to very long lengths and very long times must be based on an understanding of the “constants” in the prediction equation. That is, these “constants” can be shown to vary when the three basic parameters cover orders of magnitude in range.     

A Deodhar-type stratification on the double flag variety

We describe a partition of the double flag variety G/B⁺ × G/B^- of a complex semisimple algebraic group G analogous to the Deodhar partition on the flag variety G/B⁺. This partition is a refinement of the stratification into orbits both for B⁺ × B^- and for the diagonal action of G, just as Deodhar's partition refines the orbits of B⁺ and B^-. We give a coordinate system on each stratum, and show that all strata are coisotropic subvarieties. Also, we discuss possible connections to the positive and cluster geometry of G/B⁺ × G/B^-, which would generalize results of Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double Schubert cells.     

Error quantification in strain mapping methods.

In this article a method for determining errors of the strain values when applying strain mapping techniques has been devised. This methodology starts with the generation of a thickness/defocus series of simulated high-resolution transmission electron microscopy images of InAsxP1-x/InP heterostructures and the application of geometric phase. To obtain optimal defocusing conditions, a comparison of different defocus values is carried out by the calculation of the strain profile standard deviations among different specimen thicknesses. Finally, based on the analogy of real state strain to a step response, a characterization of strain mapping error near an interface is proposed.     

Laser pulse control of exciton dynamics in a biological chromophore complex

Femtosecond laser pulse control of exciton dynamics in a biological chromophore complex is studied theoretically. The computations use the optimal control theory specified to open quantum systems and formulated in the framework of the rotating wave approximation. Based on the laser pulse induced formation of an excitonic wave packet the possibility to localize excitation energy at a certain chromophore within a photosynthetic antenna system (FMO complex of green bacteria) is investigated. Details of exciton dynamics driven by a polarization shaped pulse are discussed.     

Oxidative Coupling of Methane over W‐Mn/SiO2 Catalyst

W‐Mn/SiO₂ catalyst has been developed in our laboratory (LICP), which is active, selective and stable for oxidative coupling of methane (OCM) in fixed bed and fluidized bed reactors. The research results have been reproduced at different reaction conditions by two groups of J. H. Lunsford (JH‐LL) from Texas A & M University and R. M. Lambert (RMLL) from University of Cambridge respectively. The basic research aspects on this catalyst systems, reaction performances, structure characterization and reaction mechanism were reviewed. A model on two active sites related to W^6+/5+ and Mn^3+/2+ has been suggested for activation of methane and oxygen respectively.     

Idempotency of linear combinations of three idempotent matrices, two of which are commuting

The considerations of the present paper were inspired by Baksalary [O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67-78] who characterized all situations in which a linear combination P=c₁P₁+c₂P₂+c₃P₃, with c_i, i=1,2,3, being nonzero complex scalars and P_i, i=1,2,3, being nonzero complex idempotent matrices such that two of them, P₁ and P₂ say, are disjoint, i.e., satisfy condition P₁P₂=0=P₂P₁, is an idempotent matrix. In the present paper, by utilizing different formalism than the one used by Baksalary, the results given in the above mentioned paper are generalized by weakening the assumption expressing the disjointness of P₁ and P₂ to the commutativity condition P₁P₂=P₂P₁.     

High-resolution infrared study of the 2ν3 (A1, E) and ν1 + ν3 (E) bands of NF3

The 2ν₃ overtone (A₁, E) and the ν₁ + ν₃ (E) combination bands of the oblate symmetric top ¹⁴NF₃ were studied by FTIR spectroscopy with a resolution of 2.5 × 10⁻³ cm⁻¹. Nearly 500 lines up to K_max/J_max = 30/43 were observed for the weak A₁ component reaching the v₃ = 2⁰ substate (1803.1302 cm⁻¹), the majority of which corresponded to reinforced K = 3p-type transitions. For the strong E component reaching the v₃ = 2^±2 substate (1810.4239 cm⁻¹), about 3550 transitions were assigned up to K_max/J_max = 65/69, favoring a clear observation of the ℓ(4, −2) and ℓ(4, 4) splittings within the kℓ = −2 and +4 sublevels, respectively. The two v₃ = 2 substates are linked by the ℓ(2, 2)- and ℓ(2, −1)-type interactions, providing severe crossings, respectively, at K′ = 6 and near K′ = 24 on the v₃ = 2⁺² side. A model working in the D-reduction and including all these ℓ-type interactions could reproduce together 3695 nonzero weighted experimental data (NZW) through 33 free parameters with a standard deviation of σ = 0.357 × 10⁻³  cm⁻¹. As for the ν₁ + ν₃ (E) combination band, about 3690 lines were assigned up to K_max/J_max = 45/55. Its v₁ = v₃ = 1 upper state (1931.577 5 cm⁻¹) was treated using the same model recently applied to the v₃ = 1 (E, 907.5413 cm⁻¹) state. It yielded 21 free parameters through 3282 NZW experimental data, adjusted with σ = 0.344 × 10⁻³  cm⁻¹ in the D-reduction. For the two excited states, the small and unobserved ℓ(0, 6) interaction was tested as useless. To confirm the adequacy of the vibrationally isolated models used, some other reductions of the Hamiltonian were tried. For the v₃ = 2 state, the D-, L-, and LD-reductions led to similar σ’s, while the Q one was not successful. For the v₁ = v₃ = 1 state, the D- and Q-reductions gave comparable σ’s, while the QD-reduction was not as good. The corresponding unitary equivalence relations are generally more nicely fulfilled for the v₃ = 2 state than for the v₁ = v₃ = 1 state. The three derivable anharmonicity constants in cm⁻¹ are x₃₃ = −4.1528, g₃₃ = +1.8235 and x₁₃ = −7.9652.     

Origin of Ferromagnetism and Magnetic Anisotropy in a Family of Copper(II) Triangles

Previously reported ferromagnetic triangles (NnBu₄)₂[Cu₃(μ₃-Cl)₂(μ-4-NO₂-pz)₃Cl₃] ( 1 ), (PPN)₂[Cu₃(μ₃-Cl)₂(μ-pz)₃Cl₃] ( 2 ), (bmim)₂[Cu₃(μ₃-Cl)₂(μ-pz)₃Cl₃] ( 3 ) and newly reported (PPh₄)₂[Cu₃(μ₃-Cl)₂(μ-4-Ph-pz)₃Cl₃] ( 4 ) were studied by magnetic susceptometry, electron paramagnetic resonance (EPR) spectroscopy and ab initio calculations to assess the origins of their ferromagnetism and of the magnetic anisotropy of their ground S=3/2 state (PPN⁺=bis(triphenylphosphine)iminium, bmim⁺=1-butyl-3-methylbenzimidazolium, pz⁻=pyrazolate). Ab initio studies revealed the d character of the magnetic orbitals of the compressed trigonal bipyramidal copper(II) ions. Ferromagnetic interactions were attributed to weak orbital overlap via the pyrazolate bridges. From the wavefunctions expansions, the ratios of the magnetic couplings were determined, which were indeterminate by magnetic susceptometry. Single-crystal EPR studies of 1 were carried out to extend the spin Hamiltonian with terms which induce zero-field splitting (zfs), namely dipolar interactions, anisotropic exchange and Dzyaloshinskii–Moriya interactions (DMI). The data were treated through both a giant-spin model and through a multispin exchange-coupled model. The latter indicated that ≈62 % of the zfs is due to anisotropic and ≈38 % due to dipolar interactions. The powder EPR data of all complexes were fitted to a simplified form of the multispin model and the anisotropic and dipolar contributions to the ground state zfs were estimated.     

Phosphine‐Catalyzed Interrupted Morita–Baylis–Hillman Reaction and Switchable Domino Reactions of α‐Substituted Activated Olefins with Formaldehyde and Mechanism Elucidation

3‐Olefinic oxindoles can undergo interrupted Morita‐Baylis‐Hillman reaction with formaldehyde. Apart from the previous reported dephosphoration to access reductive aldol‐type products, here we uncovered that completely different pathways were followed by tuning the substitutions of 3‐olefinic oxindoles. In combination with formalin, an unexpected domino phosphorus‐ylide formation, aldol‐type addition, hemeacetal formation and O‐substitution process was observed to produce 1,3‐dioxolane derivatives. Moreover, a switchable sequence to produce formate derivatives via a key hydride transfer process was furnished by simply replacing formalin with paraformaldehyde. Density functional theory calculations were conducted to well elucidate the catalytic reaction mechanism.     

A description via second degree character of a family of quasi-symmetric forms

Periodica Mathematica Hungarica - The purpose of this paper is to give, through the second degree character, new characterizations of a part of the family of quasi-symmetric forms. In fact, thanks...