Robust dynamical recurrences based on Floquet spectrum

Robust recurrence behavior of wave packets in periodically driven systems and coupled higher dimensional systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to nonlinear resonances developed in the systems and provide the analytical understanding of recurrence times. We apply these analytical results to investigate the recurrence times of matter waves in optical lattice in the presence of external periodic forcing. The obtained analytical results can experimentally be observed using currently available experimental setups.     

Controlled acceleration of a modulated quantum bouncer

Cold atoms bouncing on a modulated atomic mirror exhibit dynamic localization and acceleration subject to modulated strength. We explain the characteristics of acceleration using accelerated mapping and define control parameters. We show that the effective Planck’s constant plays a vital role in limiting overall linear growth of accelerated atoms with time. For large values of the effective Planck’s constant, the atomic quantum accelerated is seized if the localization window overlaps the accelerated window.     

Deterministic and random coincidence point results for f-nonexpansive maps

Some deterministic and random coincidence theorems for f-nonexpansive maps are obtained. As applications, invariant approximation theorems are derived. Our results unify, extend and complement various known results existing in the literature.     

An extension of Levi-Civita's theorem to nonholonomic dynamical systems

This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic systems admitting certain invariant relations whose equations of motion involve constraint multipliers. Sufficient conditions allowing such extension are obtained and, as an application of the theory a generalization of Routh's motion is presented.     

混合配体席夫碱稀土茂配合物催化合成聚甲基丙烯酸甲酯

The synthesis of high molecular mass (Mr＞5×105) polymers with a narrow molecular mass distribution (Mr,max/Mr,min＜1.05) is a challenging theme in modem polymer chemistry.     

Best proximity pairs and equilibrium pairs for Kakutani multimaps

New existence theorems of best proximity pairs for a finite family of Kakutani multimaps are proved in a normed space setting. As applications, new existence theorems of equilibrium pairs for free n$n$-person and 1-person games are obtained. Our results generalize and improve several well-known results.     

Fixed point theorems for generalized metrically inward maps

We prove fixed point results for multimaps satisfying a generalized metric (or an α-metric) inwardness condition. Our results extend, generalize or improve several known results.     

Easy Access to Crystalline Indolines via Hydrogen Bond Transfer

Several indoline derivatives with specific geometries are biologically active and have inhibitor properties. Many indolines are a key part of natural products. Much attention has been focused on the development of synthetic routes for their easy access. Current synthesis depends largely on metal catalysis, iodine reagents, and Oxone. To date, no synthetic route has been established that is metal‐free, reagent‐free, and environmentally friendly and provides a base for green chemistry. Here, we report the first facile metal‐free and reagent‐free synthesis of indoline derivatives, which could potentially be influential in the design of new biologically active compounds. The synthesis proceeds through intramolecular amination between a urea nucleophile and unactivated alkene. The ring closure occurs in a few hours in the presence of pre‐dried silica gel and gives good yields of indolines products, but in the absence of silica gel, the ring closure occurred overnight with stirring in dry solvent. An electron withdrawing group at the substituted aryl moiety of ureas increases the hydrogen bond donor ability of substrates that mediate the internal proton transfer at the terminal alkene and results in facile amination to give the indoline product with an “in plane” orientation of the carbonyl group and aromatic part of indoline framework. Such orientation in indolines is important for potent biological activities.