Boronic Acid Catalysis for Mild and Selective [3+2] Dipolar Cycloadditions to Unsaturated Carboxylic Acids

Herein, the concept of boronic acid catalysis (BAC) for the activation of unsaturated carboxylic acids is applied in several classic dipolar [3+2] cycloadditions involving azides, nitrile oxides, and nitrones as partners. These cycloadditions can be used to produce pharmaceutically interesting, small heterocyclic products, such as triazoles, isoxazoles, and isoxazolidines. These cycloadducts are formed directly and include a free carboxylic acid functionality that can be employed for further transformations, thereby avoiding prior masking or functionalization. In all cases, BAC provides faster reactions, under milder conditions, with much improved product yields and regioselectivities. In some instances, such as triazole formation from the reaction of azides with 2‐alkynoic acids, catalysis with ortho‐nitrophenylboronic acid circumvents the undesirable product decarboxylation observed when using thermal activation. By using NMR spectroscopic studies, the boronic acid catalyst was shown to provide activation by a LUMO‐lowering effect in the unsaturated carboxylic acid, likely via a monoacylated hemiboronic ester intermediate.     

Mild and efficient boronic acid catalysis of Diels-Alder cycloadditions to 2-alkynoic acids

The concept of boronic acid catalysis (BAC) for the activation of unsaturated carboxylic acids is applied to the Diels-Alder cycloaddition between 2-alkynoic acids as dienophiles and various dienes. These [4+2] cycloadditions produce cyclohexadienyl carboxylic acids, which can be oxidized in situ to produce polysubstituted aromatic carboxylic acids. The boronic acid catalyst is suspected to provide activation by a LUMO-lowering effect of the unsaturated carboxylic acid likely via a covalent, monoacylated hemiboronic ester intermediate.     

Optimal switching control of a fed-batch fermentation process

Considering the hybrid nature in fed-batch culture of glycerol biconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, we propose a state-based switching dynamical system to describe the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to our proposed switching system and constraints of continuous state inequality and control function is presented. Because the number of the switchings is not known a priori, we reformulate the above optimal control problem as a two-level optimization problem. An optimization algorithm is developed to seek the optimal solution on the basis of a heuristic approach and control parametrization technique. Numerical results show that, by employing the obtained optimal control strategy, 1,3-PD concentration at the terminal time can be increased considerably.     

A nonlinear Lagrangian for constrained optimization problems

A novel nonlinear Lagrangian is presented for constrained optimization problems with both inequality and equality constraints, which is nonlinear with respect to both functions in problem and Lagrange multipliers. The nonlinear Lagrangian inherits the smoothness of the objective and constraint functions and has positive properties. The algorithm on the nonlinear Lagrangian is demonstrated to possess local and linear convergence when the penalty parameter is less than a threshold (the penalty parameter in the penalty method has to approximate zero) under a set of suitable conditions, and be super-linearly convergent when the penalty parameter is decreased following Lagrange multiplier update. Furthermore, the dual problem based on the nonlinear Lagrangian is discussed and some important properties are proposed, which fail to hold for the dual problem based on the classical Lagrangian. At last, the preliminary and comparing numerical results for several typical test problems by using the new nonlinear Lagrangian algorithm and the other two related nonlinear Lagrangian algorithms, are reported, which show that the given nonlinear Lagrangian is promising.     

Unified design of wavelength-independent deep-etched fused-silica gratings

We present a unified design of wavelength-independent deep-etched fused-silica gratings as polarizing beam splitters and polarization-independent two-port beam splitters by using the simplified modal method. By defining unified grating parameters as the ratio of incident wavelength to grating period and the ratio of groove depth to grating period, unified grating structures are found to be approximately wavelength-independent, which is based on the modal view of the accumulated phase difference of two excited propagating grating modes. Diffraction efficiencies given by the rigorous coupled-wave analysis (RCWA) verified this unified design at the wavelength of 1064 nm. It should be noted that this unified design of wavelength-independent gratings is an analytic result, which is impossible to be derived with the well-known numerical RCWA. Modal method is powerful and presents a clear physical picture for us to obtain this unified design. Therefore, this unified design can be used as a general guideline for designing deep-etched fused-silica gratings as beam splitters for practical applications from ultraviolet to near infrared.     

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500-1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.     

Electron-rich tetrathiafulvalene-triarylamine conjugates: synthesis and redox properties

By combining tetrathiafulvalenes (TTFs) and triarylamines, four TTF-triarylamine conjugates bridged by an annulated pyrrole ring were designed and synthesized by an N-arylation reaction. Electrochemical and photophysical investigations suggest that these novel conjugates possess very strong electron-donating ability with very high HOMO energy levels of around -4.70 eV; the HOMOs are mainly located on the TTF moiety. We observed significant electronic coupling between the TTF moieties and the triarylamine groups. However, no evidence for such electronic communication between end-capping TTF units (conjugates 5 and 7) or between two terminal triarylamine groups (conjugate 9) could be found. Differential scanning calorimetry (DSC) measurements together with PM3-optimized geometries suggest that conjugates 5 and 7, which adopt three-dimensional propeller-shaped structures, may easily pack and crystallize in the solid state because of the large rigid planar blades consisting of TTF and one of the phenyl rings of the triarylamine moiety. However, conjugate 9, with two bulky end-capping triarylamine groups, forms an amorphous material with a glass transition at 74.5 degrees C.     

Thermal [3+2] cycloaddition reaction of azomethine imines with allenoates for dinitrogen-fused heterocycles

The thermal [3+2] cycloaddition reactions of two classes of azomethine imines with allenoates have been investigated. The reactions are operationally simple and proceed smoothly under mild reaction conditions to provide a variety of dinitrogen-fused heterocycles in moderate to excellent yields.