The discrete linear restricted Chebyshev approximation

A numerically stable simplex algorithm for calculating the restricted Chebyshev solution of overdetermined systems of linear equations is described. In this algorithm minimum computer storage is required and no conditions are imposed on the coefficient matrix or on the right hand side of the system of equations. Also a new way of implementing a triangular decomposition method to the basis matrix is used. The ordinary Chebyshev solution, the one-sided Chebyshev solutions and the Chebyshev approximation by non-negative functions are obtained as special cases in this algorithm. Numerical results are given.     

New necessary and sufficient optimality conditions for strong bilevel programming problems

In this paper we are interested in a strong bilevel programming problem (S). For such a problem, we establish necessary and sufficient global optimality conditions. Our investigation is based on the use of a regularization of problem (S) and some well-known global optimization tools. These optimality conditions are new in the literature and are expressed in terms of \(\max \)–\(\min \) conditions with linked constraints.     

Ultrafast UV photon echo peak shift and fluorescence up conversion studies of non-polar solvation dynamics

We present photon echo peak shift and femtosecond fluorescence up-conversion studies of non-polar solvation dynamics of a simple non-polar dye p-terphenyl in ethanol and cyclohexane, using excitation in the UV range at 290 nm. The UV fluorescence up-conversion experiments were combined with a polychromatic detection and the results highlight the high sensitivity of this approach to fully characterize the excited state dynamics of the dye. We also demonstrate the feasibility of UV photon echo and transient grating and its sensitivity for the detection of non-polar solvation dynamics by measuring the frequency correlation function of the dye in the ground state. While solvation dynamics in the picosecond regime is observed in ethanol, electronic coherence dephasing occurs on timescales faster than 100 fs in ethanol as well as in the non-polar solvent cyclohexane.     

Synthesis,X-ray structure and theoretical study of benzazole thioether and its zinc complex as corrosion inhibitors for steel in acidic medium

A ligand, 2-((benzo[d]thiazol-2-ylthio)methyl)-1H-benzo[d]imidazole, and its zinc complex have been synthesized. The structure of these compounds have been determined by spectroscopic techniques and single crystal X-ray diffraction. The corrosion inhibition study of these compounds for steel in 0.5 M H₂SO₄ medium has also been investigated using potentiodynamic polarization and EIS techniques. The quantum calculations were applied to investigate the relationship between the electronic properties and the corrosion inhibition efficiency of the two benzazoles derivatives. Surface analysis (XRF) indicated that the rust layer formed on the Cu-containing steels was enriched with Cu compounds. Polarization curves revealed that both inhibitors acted as a mixed-type inhibitor.     

Mapping of the Photoinduced Electron Traps in TiO2 by Picosecond X‐ray Absorption Spectroscopy

Titanium dioxide (TiO₂) is the most popular material for applications in solar‐energy conversion and photocatalysis, both of which rely on the creation, transport, and trapping of charges (holes and electrons). The nature and lifetime of electron traps at room temperature have so far not been elucidated. Herein, we use picosecond X‐ray absorption spectroscopy at the Ti K‐edge and the Ru L₃‐edge to address this issue for photoexcited bare and N719‐dye‐sensitized anatase and amorphous TiO₂ nanoparticles. Our results show that 100 ps after photoexcitation, the electrons are trapped deep in the defect‐rich surface shell in the case of anatase TiO₂, whereas they are inside the bulk in the case of amorphous TiO₂. In the case of dye‐sensitized anatase or amorphous TiO₂, the electrons are trapped at the outer surface. Only two traps were identified in all cases, with lifetimes in the range of nanoseconds to tens of nanoseconds.     

Ultrafast nonadiabatic dynamics of [Fe(II)(bpy)(3)](2+) in solution

The ultrafast relaxation of aqueous iron(II)-tris(bipyridine) upon excitation into the singlet metal-to-ligand charge-transfer band (1MLCT) has been characterized by femtosecond fluorescence up-conversion and transient absorption (TA) studies. The fluorescence experiment shows a very short-lived broad 1MLCT emission band at approximately 600 nm, which decays in < or =20 fs, and a weak emission at approximately 660 nm, which we attribute to the 3MLCT, populated by intersystem crossing (ISC) from the 1MLCT state. The TA studies show a short-lived (<150 fs) excited-state absorption (ESA) below 400 nm, and a longer-lived one above 550 nm, along with the ground-state bleach (GSB). We identify the short-lived ESA as being due to the 3MLCT state. The long-lived ESA decay and the GSB recovery occur on the time scale of the lowest excited high-spin quintet state 5T2 lifetime. A singular value decomposition and a global analysis of the TA data, based on a sequential relaxation model, reveal three characteristic time scales: 120 fs, 960 fs, and 665 ps. The first is the decay of the 3MLCT, the second is identified as the population time of the 5T2 state, while the third is its decay time to the ground state. The anomalously high ISC rate is identical in [RuII(bpy)3]2+ and is therefore independent of the spin-orbit constant of the metal atom. To reconcile these rates with the regular quasi-harmonic vibrational progression of the 1MLCT absorption, we propose a simple model of avoided crossings between singlet and triplet potential curves, induced by the strong spin-orbit interaction. The subsequent relaxation steps down to the 5T2 state dissipate approximately 2000 cm-1/100 fs. This rate is discussed, and we conclude that it nevertheless can be described by the Fermi golden rule, despite its high value.     

Convergence of Global and Bounded Solutions of Some Nonautonomous Second Order Evolution Equations with Nonlinear Dissipation

In this paper we study the asymptotic behavior of solutions of the following nonautonomous wave equation with nonlinear dissipation.

$\left\{\begin{array}{ll} u_{tt}+\vert u_{t}\vert^{\alpha}u_{t}-\Delta u +f(u)=g(t,x),\quad{\rm in}\,\mathbb{R}_{+}\times\Omega,\\ \qquad\qquad u(t,x)=0,\quad\, {\rm on}\,\mathbb{R}_{+}\times\partial\Omega,\end{array}\right.$

where f is an analytic function, α is a small positive real and g(t, ·) tends to 0 sufficiently fast in L ²(Ω) as t tends to ∞.

We also obtain a general convergence result and the rate of decay of solutions for a class of second order ODE containing as a special case

$\left\{\begin{array}{ll} \ddot{U}(t)+\Vert\dot{U}(t)\Vert^{\alpha}\dot{U}(t)+\nabla F(U(t))=g(t),\quad t \in \mathbb{R}_+,\\ \qquad U(0)=U_{0}\,\in \mathbb{R}^{N},\quad\dot{U}(0)=U_{1}\in \mathbb{R}^{N}. \end{array}\right.$

     

Understanding the origin of the enantioselectivity and the mechanism of the asymmetric reduction of ketimine generated from acetophenone with oxazaborolidine catalyst

Structural Chemistry - The enantioselectivity of the oxazaborolidine-catalysed asymmetric reduction reaction of ketimine generated from acetophenone has been investigated by transition state theory...