Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions

The aim of this paper is to establish the oscillation theorems, Rayleigh principle, and coercivity results for linear Hamiltonian and symplectic systems with general boundary conditions, i.e., for the case of separated and jointly varying endpoints, and with no controllability (normality) and strong observability assumptions. Our method is to consider the time interval as a time scale and apply suitable time scales techniques to reduce the problem with separated endpoints into a problem with Dirichlet boundary conditions, and the problem with jointly varying endpoints into a problem with separated endpoints. These more general results on time scales then provide new results for the continuous time linear Hamiltonian systems as well as for the discrete symplectic systems. This paper also solves an open problem of deriving the oscillation theorem for problems with periodic boundary conditions. Furthermore, the present work demonstrates the utility and power of the analysis on time scales in obtaining new results especially in the classical continuous and discrete time theories.     

On the Computations of Gas-Solid Mixture Two-Phase Flow

This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model. The HLL Riemann solver is applied to solve the Riemann problem for the model equations. This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture. Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results. To demonstrate the robustness, effectiveness and capability of these methods, the model results are compared with reference solutions. In addition to that, these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature. The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.     

Pd(0)‐Catalyzed Dearomative Diarylation of Indoles

We have developed a protocol for a Pd(0)‐catalyzed dearomative syn 1,2‐diarylation of indoles using readily available boroxines (dehydrated boronic acids) as coupling partners. This reaction proceeds efficiently using PtBu₃ as the ligand to divergently access to fused indolines while minimizing the extent of direct Suzuki coupling. The scope of the reaction is remarkably broad and all products are obtained as single diastereomers in moderate to excellent yields. We have also compiled data which parallels the steric and electronic properties of both substrate and boroxine with the propensity to undergo the desired dearomative process over direct Suzuki coupling.     

Triplet acetylenes as synthetic equivalents of 1,2-bicarbenes: phantom n,pi state controls reactivity in triplet photocycloaddition

Diaryl acetylenes, in which one of the aryl groups is either a pyridine or a pyrazine, undergo efficient triplet state photocycloaddition to 1,4-cyclohexadiene with formation of 1,5-diaryl substituted tetracyclo[3.3.0.0(2,8).0(4,6)]octanes (homoquadricyclanes). In the case of pyrazinyl acetylenes, the primary homoquadricyclane products undergo a secondary photochemical rearangement leading to diaryl substituted tricyclo[3.2.1.0(4,6)]oct-2-enes. Mechanistic and photophysical studies suggest that photocycloaddition proceeds through an electrophilic triplet excited state whereas the subsequent rearrangement to the tricyclooctenes proceeds through a singlet excited state. Chemical and quantum yields for the cycloaddition, in general, correlate with the electron acceptor character of aryl substituents but are attenuated by photophysical factors, such as the competition between the conversion of acetylene singlet excited state into the reactive triplet excited states (intersystem crossing: ISC) and/or to the radical-anion (photoelectron transfer from the diene to the excited acetylene: PET). Dramatically enhanced ISC between pi-pi S(1) state and "phantom" n,pi triplet excited state is likely to be important in directing reactivity to the triplet pathway. The role of PET can be minimized by the judicious choice of reaction conditions (solvent, concentration, etc.). From a practical perspective, such reactions are interesting because "capping" of the triple bond with the polycyclic framework orients the terminal aryl (4-pyridyl, 4-tetrafluoropyridyl, phenyl, etc.) groups in an almost perfect 60 degrees angle and renders such molecules promising supramolecular building blocks, especially in the design of metal coordination polymers.     

Charge-transfer and spin dynamics in DNA hairpin conjugates with perylenediimide as a base-pair surrogate

A perylenediimide chromophore (P) was incorporated into DNA hairpins as a base-pair surrogate to prevent the self-aggregation of P that is typical when it is used as the hairpin linker. The photoinduced charge-transfer and spin dynamics of these hairpins were studied using femtosecond transient absorption spectroscopy and time-resolved EPR spectroscopy (TREPR). P is a photooxidant that is sufficiently powerful to quantitatively inject holes into adjacent adenine (A) and guanine (G) nucleobases. The charge-transfer dynamics observed following hole injection from P into the A-tract of the DNA hairpins is consistent with formation of a polaron involving an estimated 3-4 A bases. Trapping of the (A 3-4) (+*) polaron by a G base at the opposite end of the A-tract from P is competitive with charge recombination of the polaron and P (-*) only at short P-G distances. In a hairpin having 3 A-T base pairs between P and G ( 4G), the radical ion pair that results from trapping of the hole by G is spin-correlated and displays TREPR spectra at 295 and 85 K that are consistent with its formation from (1*)P by the radical-pair intersystem crossing mechanism. Charge recombination is spin-selective and produces (3*)P, which at 85 K exhibits a spin-polarized TREPR spectrum that is diagnostic of its origin from the spin-correlated radical ion pair. Interestingly, in a hairpin having no G bases ( 0G), TREPR spectra at 85 K revealed a spin-correlated radical pair with a dipolar interaction identical to that of 4G, implying that the A-base in the fourth A-T base pair away from the P chromophore serves as a hole trap. Our data suggest that hole injection and transport in these hairpins is completely dominated by polaron generation and movement to a trap site rather than by superexchange. On the other hand, the barrier for charge injection from G (+*) back onto the A-T base pairs is strongly activated, so charge recombination from G (or even A trap sites at 85 K) most likely proceeds by a superexchange mechanism.     

Study of the tensile constrained recovery behavior of a Fe-Mn-Si shape memory alloy

Free- and constrained recovery behaviors of a Fe-23.3 Mn-2.8 Si (wt.%) Shape Memory Alloy (SMA) were revealed by uncoiling experiments and tensile tests, respectively. With the enhancement of plastic deformation degree, including by additionally elongating the hot rolled specimens, the increase of the amount of ε stress induced martensite (SIM) plates in the detriment if γ austenite, was emphasized by means of optical microscopy and XRD. The tensile-stress variation was analyzed during complex cycling by constrained recovery of the alloy under study, with a tensile strength of 670 MPa and an ultimate strain of 8%. The cycles were composed of: (i) room temperature (RT) loading; (ii) RT partial unloading; (iii) constant strain heating and (iv) constant strain cooling to RT. During the cycles, characterized by average maximum stresses above 500 MPa and recovery stresses above 260 MPa, the observed stress-temperature evolution confirmed the four stage stress variation reported in literature [Z.Z. Dong et al., Acta Mater. 53, 4009 (2005)]. In order to maintain the above stress levels, constrained-recovery strain had to be increased with an average of 1.1% per cycle, between 1 and 3%.     

Applications of time scale symplectic systems without normality

Recently, the authors obtained new characterizations of the positivity and nonnegativity of a time scale quadratic functional F with separable endpoints related to a time scale symplectic system (S). In these results, the assumption of normality is absent. In this paper we present applications of such results. Namely, without assuming normality we derive Sturmian comparison theorems, results for general jointly varying endpoints, and characterizations of the positivity of F via the corresponding time scale Riccati equation, a certain perturbed quadratic functional, and a time scale Riccati inequality. These results generalize and unify many recent as well as classical ones.     

Riccati equations for abnormal time scale quadratic functionals

This paper focuses on developing new Riccati type conditions for an abnormal time scale symplectic system (S). These conditions provide characterizations of the nonnegativity (with and without a certain “image condition”) and positivity of the quadratic functionals associated with such a system. The novelty of these conditions rely on the natural conjoined basis (Xa,Ua) of (S) in which Xa(t) is not necessarily invertible, and thus the system (S) could be abnormal. These results are new even in the special case of continuous time, as are some of them in the discrete time setting.     

Ortho effect in the Bergman cyclization: interception of p-benzyne intermediate by intramolecular hydrogen abstraction

Intramolecular hydrogen atom (H-atom) abstraction from the o-OCH3 group effectively intercepts the p-benzyne intermediate in the Bergman cycloaromatization of 2,3-diethynyl-1-methoxybenzene (1) before this intermediate undergoes either retro-Bergman ring opening or external H-atom abstraction. This process leads to the formation of a new diradical and renders the cyclization step essentially irreversible. Chemical and kinetic consequences of this phenomenon were investigated through the combination of computational and experimental studies.     

First- and second-order optimality conditions for a strong local minimum in control problems with pure state constraints

In this paper first- and second-order optimality conditions for a strong local minimum are presented for optimal control problems with pure state set-inclusion constraints. The first-order condition is of Pontryagin type, while the second-order condition is of the form of an accessory problem associated with the strong local minimality. This latter condition contains an extra term reflecting the presence of the pure state constraints.