Global $$L^q$$-Gevrey Functions and Their Applications

The goal of this paper is to introduce a class of \(C^\infty \) functions derivatives of which satisfy quantitative size estimates. The estimates, called global \(L^q\) Gevrey estimates, first arose in the work of Boggess and Raich ( J. Fourier Anal. Appl. 19:180–224, 2013) when they investigated how to capture a particular type of exponential decay through estimates on the Fourier transform. In the present work, we refine the notion of global \(L^q\)-Gevrey functions and include a discussion of the function theory as well as the relationship to Gevrey classes and known function spaces. In addition, we present explicit examples of global \(L^q\)-Gevrey functions and ways to generate new global \(L^q\)-Gevrey functions from old ones. We conclude with three applications: The first is solving a Carleman-type problem for constructing functions derivatives of which are a given sequence of global \(L^q\)-Gevrey functions. The other two applications concern extensions of a given global \(L^q\)-Gevrey function: the first is constructing an almost analytic extension, and the second is building an approximate solution to a first-order complex vector field coefficients of which are global \(L^q\)-Gevrey functions.     

The intramolecular Morita-Baylis-Hillman-type alkylation reaction

From the initial development of a homologous Morita-Baylis-Hillman reaction utilizing epoxides as electrophiles, the method was expanded to enable the exclusively organocatalyzed intramolecular allylation of enones and to develop the intramolecular MBH-type alkylation of activated alkenes. We successfully utilized both enones and unsaturated thioesters as the activated alkene component. This work, carried out using stoichiometric amounts of the trialkylphosphine, gave an array of functionalized five- and six-membered carbocycles in high yields. With the cycloalkylation of enones and thioesters, conditions that allowed the use of substoichometric amounts of the phosphine catalyst were developed. As a result both five- and six-membered rings can be formed efficiently with little to no loss in yield upon comparison to yields obtained when stoichiometric amounts of trialkylphosphines were employed. We isolated, for the first time, an MBH-type intermediate exhibiting unprecedented trans geometry of the phosphonium salt and acyl group.     

Self-assembly approach toward chiral bimetallic catalysts: bis-urea-functionalized (salen)cobalt complexes for the hydrolytic kinetic resolution of epoxides

A series of novel bis-urea-functionalized (salen)Co complexes has been developed. The complexes were designed to form self-assembled structures in solution through intermolecular urea-urea hydrogen-bonding interactions. These bis-urea (salen)Co catalysts resulted in rate acceleration (up to 13 times) in the hydrolytic kinetic resolution (HKR) of rac-epichlorohydrin in THF by facilitating cooperative activation, compared to the monomeric catalyst. In addition, one of the bis-urea (salen)Co(III) catalyst efficiently resolves various terminal epoxides even under solvent-free conditions by requiring much shorter reaction time at low catalyst loading (0.03-0.05 mol %). A series of kinetic/mechanistic studies demonstrated that the self-association of two (salen)Co units through urea-urea hydrogen bonds was responsible for the observed rate acceleration. The self-assembly study with the bis-urea (salen)Co by FTIR spectroscopy and with the corresponding (salen)Ni complex by (1)H NMR spectroscopy showed that intermolecular hydrogen-bonding interactions exist between the bis-urea scaffolds in THF. This result demonstrates that self-assembly approach by using non-covalent interactions can be an alternative and useful strategy toward the efficient HKR catalysis.     

Existence results for some partial functional differential equations with state-dependent delay

In this paper, we establish sufficient conditions for the existence of solutions for some partial functional differential equations with state-dependent delay; we assume that the linear part is not necessarily densely defined and satisfies the well-known Hille–Yosida conditions. Our approach is based on a nonlinear alternative of Leray–Schauder type and integrated semigroup theory. An application is provided to a reaction–diffusion equation with state-dependent delay.     

Probing the photoinduced metal-nitrosyl linkage isomerism of sodium nitroprusside in solution using transient infrared spectroscopy

We study photoinduced metal-nitrosyl linkage isomerism in sodium nitroprusside (Na(2)[Fe(II)(CN)(5)NO]·2H(2)O, SNP) dissolved in methanol using picosecond transient infrared (IR) spectroscopy. The high sensitivity of this technique allows the simultaneous observation of two known metastable (MS) iron-nitrosyl linkage isomers of SNP, [Fe(II)(CN)(5)(η(1)-ON)](2-) (MS1) and [Fe(II)(CN)(5)(η(2)-NO)](2-) (MS2), at room temperature. The transient population of free nitrosyl radicals (NO·) is also measured in the sample solution. These three transient species are detected using their distinct nitrosyl stretching frequencies at 1794 cm(-1) (MS1), 1652 cm(-1) (MS2), and 1851 cm(-1) (NO·). The metastable isomers and NO· are formed on a subpicosecond time scale and have lifetimes greater than 100 ns. A UV (400 nm)-pump power dependence study reveals that MS1 can be formed with one photon, while MS2 requires two photons to be populated at room temperature in solution. Other photodissociation products including cyanide ion, Prussian blue, and [Fe(III)(CN)(5)(CH(3)OH)](2-) are observed. We develop a photochemical kinetic scheme to model our data, and the analysis reveals that photoisomerization and photodissociation of the metal-NO moiety are competing photochemical pathways in SNP dissolved in methanol at room temperature. Based on the analysis, the solvent-associated Fe(III) species and Prussian blue form on a 130 and 320 ps time scale, respectively. The simultaneous detection and characterization of photoinduced linkage isomerism (MS1 and MS2) and photodissociation of the metal-NO bond in SNP highlights the importance of understanding the role played by metastable metal-nitrosyl linkage isomers in the photochemistry of metal-nitrosyl compounds in chemistry and biology.     

Entanglement and sudden death of two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier

In the presence of degenerate two-photon transitions the problem of the interaction between two two-level atoms and a single-mode is considered. Near resonance case, a closed form of the analytic solution for the wave function is obtained. The entanglement between an atom and field in the interacting system is studied by using the change in atomic and field entropies. The relationship between entropy changes and concurrence entanglement is discussed. Our results show that the behavior of the entropy change in agreement with the behavior of the concurrence to measure the entanglement between two subsystem structures.     

Synthesis and Characterization of Pressure and Temperature Dual‐Responsive Polystyrene Microbeads

A facile approach to the synthesis of pressure and temperature dual‐responsive polystyrene (PS) microbeads with controlled sizes via dispersion polymerization is described. Three different luminophors are selected and directly introduced into the reaction system and thus incorporated into the resultant PS microbeads during polymerization. By manipulating the reaction conditions, including concentrations of the initiator and monomer, polarity of the reaction medium, and injection rate for the monomer, uniform PS microbeads with sizes ranging from 1 to 5 μm are obtained. When a light source centered at 365 nm is used to excite all the luminophors in the PS beads, three distinct and resolvable emission peaks corresponding well with the luminophors are observed. By taking advantage of their sensitive responses to both pressure and temperature, the PS beads can be utilized for quantitative measurements of these two stimulations simultaneously. The PS beads loaded with multiple luminophors have the ability to serve as building blocks for the fabrication of novel sensing and imaging devices and therefore provide a promising strategy for the study of aerodynamics.