On a class of second order Fuchsian hyperbolic equations

Summary We study a class of second order Fuchsian hyperbolic operators. The well-posedness of the Cauchy problem in a space of regular distributions is proved, together with results on the propagation of singularities of the solution. Moreover we give a representation formula for the distribution solutions of the homogeneous equation.     

Significato proiettivo di alcuni tipi di equazioni differenziali del secondo ordine

Sunto. Ogni elemento di 2^o ordine di curva di una superficie (ad asintotiche distinte e non rettilinee) determina duequadriche asintotiche osculatrici. Gli elementi di 2^o ordine tali che queste quadriche abbiano, in ogni punto della superficie, un contatto assegnato con una retta, conica o cubica sghemba associata al punto appartengono alle curve integrali di equazioni differenziali del tipov″P _i (v′)=P _i+3(v′) (i=1, 2) oveP _k (v′) è un polinomio di gradok inv′=dv/du a coefficienti funzioni diu ev. Determinazione della configurazione geometrica a partire dall'equazione.     

Trajectory surface hopping within linear response time-dependent density-functional theory

A fewest switches trajectory surface hopping algorithm based on linear response time-dependent density-functional theory is developed and implemented into the plane wave ab initio molecular dynamics package CPMD. A scheme to calculate nonadiabatic couplings using a multi determinantal approximation of the excited state wave function is introduced. The method is applied to the study of the photorelaxation of protonated formaldimine, a minimal model of the rhodopsin chromophore retinal. A good agreement of the structural and dynamic behavior is found with respect to state averaged multiconfiguration self consistent field based trajectory surface hopping.     

Effect of the π Bridge and Acceptor on Intramolecular Charge Transfer in Push–Pull Cationic Chromophores: An Ultrafast Spectroscopic and TD‐DFT Computational Study

Three (donor–π–acceptor)⁺ systems with a methyl pyridinium or quinolinium as the electron‐deficient group, a dimethyl amino as the electron‐donor group, and an ethylene or butadiene group as the spacer have been investigated in a joint spectroscopic and TD‐DFT computational study. A negative solvatochromism has been revealed in the absorption spectra, which implies a solution color change, and interpreted by considering the variation in the permanent dipole moment modulus and orientation upon photoexcitation. The fluorescence efficiency decreases upon increasing solvent polarity, in agreement with the excited‐state optimized geometries (planar in low‐polarity media and twisted in high‐polarity media). Femtosecond transient absorption has revealed the occurrence of a fast photoinduced intramolecular charge transfer (ICT) and the molecular factors that determine an efficient ICT. Considering the crucial role of the ICT in tuning the nonlinear optical (NLO) properties, these compounds can be considered promising NLO materials.     

Synthesis of (diarylmethyl)amines using Ni-catalyzed arylation of C(sp3)–H bonds

The first nickel catalyzed deprotonative cross coupling between C(sp³)–H bonds and aryl chlorides is reported, allowing the challenging arylation of benzylimines in the absence of directing group or stoichiometric metal activation. This methodology represents a convenient access to the (diarylmethyl)amine moiety, which is widespread in pharmaceutically relevant compounds.     

Automatic Dantzig–Wolfe reformulation of mixed integer programs

Mathematical Programming - Dantzig–Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the...     

Thermodynamic study of heptane + secondary, tertiary and cyclic amines mixtures. Part IV. Excess and solvation enthalpies at 298.15 K

Partial molar enthalpies and excess enthalpies H^E of binary mixtures of heptane + secondary and tertiary n-alkyl, primary cycloalkyl, and secondary (hetero)cyclic amines have been determined at 298.15 K by isothermal titration calorimetry in the whole composition range. All mixtures showed positive H^E values which decrease with increasing amine size in each category, and decrease in the order cyclic primary > cyclic secondary > linear primary [1] > secondary > tertiary when comparing amines of similar size in different categories. From partial molar enthalpies at infinite dilution and known enthalpies of vaporization, the solvation enthalpies have been calculated either for heptane in amines and for amines in heptane. These quantities, together with their cavitational and interactional terms obtained applying the scaled particle theory, are discussed to get insight into the types and relative strength of solute-solvent interactions and into their effects on molecular structure features such as branching and cyclization.     

Looped structure of flowerlike micelles revealed by 1H NMR relaxometry and light scattering

We present experimental proof that so-called "flowerlike micelles" exist and that they have some distinctly different properties compared to their "starlike" counterparts. Amphiphilic AB diblock and BAB triblock copolymers consisting of poly(ethylene glycol) (PEG) as hydrophilic A block and thermosensitive poly(N-isopropylacrylamide) (pNIPAm) B block(s) were synthesized via atom transfer radical polymerization (ATRP). In aqueous solutions, both block copolymer types form micelles above the cloud point of pNIPAm. Static and dynamic light scattering measurements in combination with NMR relaxation experiments proved the existence of flowerlike micelles based on pNIPAm(16kDa)-PEG(4kDa)-pNIPAm(16kDa) which had a smaller radius and lower mass and aggregation number than starlike micelles based on mPEG(2kDa)-pNIPAm(16kDa). Furthermore, the PEG surface density was much lower for the flowerlike micelles, which we attribute to the looped configuration of the hydrophilic PEG block. (1)H NMR relaxation measurements showed biphasic T(2) relaxation for PEG, indicating rigid PEG segments close to the micelle core and more flexible distal segments. Even the flexible distal segments were shown to have a lower mobility in the flowerlike micelles compared to the starlike micelles, indicating strain due to loop formation. Taken together, it is demonstrated that self-assemblies of BAB triblock copolymers have their hydrophilic block in a looped conformation and thus indeed adopt a flowerlike conformation.