On the optimal control of the Schlögl-model

Optimal control problems for a class of 1D semilinear parabolic equations with cubic nonlinearity are considered. This class is also known as the Schlögl model. Main emphasis is laid on the control of traveling wave fronts that appear as typical solutions to the state equation. The well-posedness of the optimal control problem and the regularity of its solution are proved. First-order necessary optimality conditions are established by standard adjoint calculus. The state equation is solved by the implicit Euler method in time and a finite element technique with respect to the spatial variable. Moreover, model reduction by Proper Orthogonal Decomposition is applied and compared with the numerical solution of the full problem. To solve the optimal control problems numerically, the performance of different versions of the nonlinear conjugate gradient method is studied. Various numerical examples demonstrate the capacities and limits of optimal control methods.     

Facile Synthesis of Mutagen X (MX): 3-Chloro-4-(dichloromethyl)-5-hydroxy-5H-furan-2-one

3-Chloro-4-(dichloromethyl)-5-hydroxy-5H-furan-2-one (Mutagen X, MX) was synthesized in six steps from commercially-available and inexpensive starting materials (27% overall yield). This synthesis enables the preparation of MX analogs and does not require the use of chlorine gas, as do previously reported methods.     

Fixation of carbon dioxide and related small molecules by a bifunctional frustrated pyrazolylborane Lewis pair

The bifunctional frustrated Lewis pair 1-[bis(pentafluorophenyl)boryl]-3,5-di-tert-butyl-1H-pyrazole (1) was employed for small molecule fixation by reaction with carbon dioxide, paraformaldehyde, tert-butyl isocyanate, tert-butyl isothiocyanate, methyl isothiocyanate and benzonitrile, affording the adducts 3-8 as zwitterionic, bicyclic boraheterocycles. Treatment of 1 with tert-butyl isocyanide gave the isocyanide-borane complex 9, whereas the zwitterionic alkynylborate 10 was formed by C-H bond activation of phenylacetylene. The molecular structures of all products 3-10 were established by X-ray diffraction analyses. DFT calculations at the M06-2X/6-311++G(d,p) level of theory revealed that CO(2) fixation by 1 and formation of the adduct 3 is strongly exothermic and proceeds with a low energy barrier of approximately 7.3 kcal mol(-1) via an intermediate van der Waals complex.     

Intramolecular heterolytic dihydrogen cleavage by a bifunctional frustrated pyrazolylborane Lewis pair

The reaction of bis(pentafluorophenyl)borane, HB(C(6)F(5))(2), with 3,5-di-tert-butyl-1H-pyrazole (3) affords the zwitterionic pyrazolium-borate trans-5 and, after dehydrogenation by use of the frustrated carbene-borane Lewis pair 1/B(C(6)F(5))(3), the bifunctional pyrazolylborane 6, which is able to cleave dihydrogen heterolytically with the formation of a mixture of cis-5 and trans-5.     

Stereoselective Diels–Alder reactions of 3-phosphonopropenoyl derivatives of 1,3-oxazolidin-2-ones

Dienophiles of the general structure (EtO)₂P(O)CHCHCOX have been prepared, where X represents an oxazolidinone chiral auxiliary. Use of the (S)-4-isopropyl-5,5-diphenyl-1,3-oxazolidin-2-one auxiliary gave Diels–Alder adducts with several cyclic and acyclic dienes. The crystal structures of the main cyclohexa-1,3-diene and 2,3-dimethylbutadiene adducts formed during reactions in the presence of dialkylaluminium halides are consistent with a reaction, which is stereoselectively endo with respect to the carbonyl group and occurs on the less hindered face of the dienophile when aluminium is chelated between the two carbonyl groups.     

Resonant Voice: Spectral and Nasendoscopic Analysis

Although resonant voice therapy is a widely used therapeutic approach, little is known about what characterizes resonant voice and how it is physiologically produced. The purpose of this study was to test the hypothesis that resonant voice is produced by narrowing the laryngeal vestibule and is characterized by first formant tuning and more ample harmonics. Videonasendoscopic recordings of the laryngeal vestibule were made during nonresonant and resonant productions of /i/ in six subjects. Spectrums of the two voice types were also obtained. Spectral analysis showed that first formant tuning was exhibited during resonant voice productions and that the degree of harmonic enhancement in the range of 2.0 to 3.5 kHz was related to voice quality: nonresonant voice had the least amount of energy in this range, whereas a resonant-relaxed voice had more energy, and a resonant-bright voice had the greatest amount of energy. Visual-perceptual judgments of the videoendoscopic data indicated that laryngeal vestibule constriction was not consistently associated with resonant voice production.