Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems

In this paper we introduce qualification conditions for multivalued functions in Banach spaces involving the A-approximate subdifferential, and we show that these conditions guarantee metric regularity of multivalued functions. The results are then applied for deriving Lagrange multipliers of Fritz—John type and Kuhn—Tucker type for infinite non-smooth vector optimization problems.     

On the correlation of crystal defects and band gap properties of ZnO nanobelts

The energetics and dynamics of electromigration of the oxygen vacancy is investigated with first-principles calculations and kinetic Monte Carlo methods. To simulate the charged oxygen vacancy under external fields within the first-principles approach, we introduce a slab model with electron-accepting dopants in the surface. The analysis of the density of states confirms that the oxygen vacancies are positively charged. When the external field is applied, the total energy of the slab linearly changes with respect to the position of the charged vacancy in the field direction, which allows for probing local permittivity around the vacancy site. The activation energy of vacancy migration is lowered along the field direction in a manner that the charge state of the vacancy is maintained along the migration path. Kinetic Monte Carlo simulations based on the first-principles inputs are also carried out and it is shown that the high-temperature condition is important for the fast redistribution of charged vacancies.     

Rheological,morphological, and interfacial properties of compatibilized PLA/PBAT blends

The focus of this paper was to gain a true understanding of the impact of a multifunctional epoxide (Joncryl®;ADR-4368) on the interfacial properties of biopolymer blends based on poly(lactic acid) (PLA) and poly(butylene adipate-co-terephthalate) (PBAT). The effect of Joncryl on the shear rheological, morphological, and interfacial properties of the blends was systematically investigated. For the deformed drop retraction experiments, different sandwich model systems (droplet/matrix), representing various scenarios of compatibilization, were prepared, aiming to probe the role of the epoxy-functionalized chains on the interface. The decrease of the interfacial tension in the modified/compatibilized PLA_PBAT and the formation of the PLA-Joncryl-PBAT copolymer were highlighted. A new relaxation peak relative to this copolymer was detected by the relaxation spectrum. Transient start-up shear and nonlinear stress relaxation experiments were carried out and confirmed the obtained results. In addition, the interface contribution was demonstrated using the Lee and Park model. The relaxation time increased with the amount of added Joncryl. Hence, the coexistence of chain extension/branching chains coupled to the PLA-Joncryl-PBAT copolymer formation had to be taken into account to explain the improved mechanical properties.     

Straightforward Bienaymé and copper catalyzed N-arylation sequence to access diverse 5H-pyrido[2′,1′:2,3]imidazo[4,5-b]indoles and analogues

A two-step sequence is reported giving access to diverse 5H-pyrido[2′,1′:2,3]imidazo[4,5-b]indoles and analogues via a Bienaymé multicomponent reaction followed by N-arylation. The desired polycylic scaffolds were obtained in high yield using copper iodide in association with TMEDA in aqueous or dioxane media.     

Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations

The focus of this contribution is the examination of the influence of different interpolation orders (especially for the pressure field) by solving the stationary incompressible Navier-Stokes equations with least-squares finite elements. We consider two different div-grad first-order systems which result in a three-field formulation with stresses, velocitites and pressure, see e.g. SCHWARZ & SCHRÖDER [1] and BOCHEV & GUNZBURGER [2]. Additionally, a numerical example is presented to show the performance of the considered formulations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sufficient Conditions for Error Bounds and Applications

Our aim in this paper is to present sufficient conditions for error bounds in terms of Fréchet and limiting Fréchet subdifferentials in general Banach spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (x, y) C × D, g(x, y, u) = 0, where g takes values in an infinite-dimensional space and u plays the role of a parameter. This symmetric structure offers us the choice of imposing conditions either on C or D. We use these results to prove the nonemptiness and weak-star compactness of Fritz–John and Karush–Kuhn–Tucker multiplier sets, to establish the Lipschitz continuity of the value function and to compute its subdifferential and finally to obtain results on local controllability in control problems of nonconvex unbounded differential inclusions.     

On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control

Journal of Optimization Theory and Applications - We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way...     

Evaluation of N‐hydroxymethylphthalimide in alkaline medium: Novel entry to the tricyclic [1,3]oxazepine core via an intramolecular π and O‐cationic cyclization

Fused isoindolo[1,3]benzo(or thieno)oxazepines 8a,b and one of their positional isomers aromatic tricyclic N,O‐acetals 13b are reported to occur efficiently in a three‐step sequence from N‐hydroxy‐methylphthalimide (6) . The key step of this methodology is the intramolecular arylation of an endocyclic and/or exocyclic N‐acyliminium cation. The mechanism leading to these species, in particular to a tricyclic lactam 13b , is discussed.     

Diastereoselective access to chiral non‐racemic [1,3]oxazolo‐[2,3‐a]isoindol‐5‐one ring systems viaO‐cationic cyclization

Dedicated to Professor Jean Morel for his retirement The title compounds 4 have been prepared from suitable β‐amino‐ alcohol 2 and phthalic anhydride ( 5 ) in a three‐step sequence in moderate to good yields (58‐94%). The key step of this methodology is based on an intramolecular O‐cationic cyclization involving N‐acyliminium species. The high levels of the observed chemoselectivity during the intermolecular or intramolecular cyclization were also discussed.