Optimal timing of a sequence of tasks with general completion costs

Scheduling a sequence of tasks––in the acceptation of finding the execution times––is not a trivial problem when the optimization criterion is irregular as for instance in earliness–tardiness problems. This paper presents an efficient dynamic programming algorithm to solve the problem with general cost functions depending on the end time of the tasks, idle time costs and variable durations also depending on the execution time of the tasks. The algorithm is also valid when the precedence graph is a tree and it can be adapted to determine the possible execution windows for each task not exceeding a maximum fixed cost.     

Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.     

The role of intersystem crossing steps in singlet oxygen chemistry and photo-oxidations

Singlet oxygen chemistry and photo-oxidation reactions, in general, often require one or more critical reaction steps that involve an intersystem crossing from a singlet state to a triplet state or vice versa. This paper considers two important intersystem crossing mechanisms, electron spin-electron orbit (spin-orbit) coupling and electron spin-nuclear spin (spin-spin) coupling, and how they may be involved : (1) in the deactivation of ¹O₂ to ³O₂ ; (2) in the thermal catalytic conversion of ³O₂ to ¹O₂; and (3) in the fragmentation of aromatic endoperoxides to yield O₂ and an aromatic substrate.     

Oxaziridinium salts as hydrophobic epoxidation reagents: remarkable hydrophobically-directed selectivity in olefin epoxidation

Selective epoxidation of cinnamates versus crotonate was used to detect hydrophobic binding of the cinnamates in the transition states with hydrophobic oxidizing agents in water solution. With peracids as oxidants, no such effect was seen, in accord with the calculated geometries of epoxidation in which the hydrophobic groups of substrate and oxidant could not stack. However, with oxaziridinium salts carrying fused benzene rings there was significantly high selectivity for the cinnamates in water solution, which could be suppressed with added 2-propanol. The hydrophobically induced selectivity changes were even larger, in free energy terms, than those reported previously for the atom-transfer reactions in hydride reductions. Furthermore, the oxaziridinium ions could be generated with oxone from catalytic amounts of the corresponding iminium salts. These substrate selectivities should also carry over to positional selectivities in polyenes.     

Supramolecular assemblies for light-induced electron-transfer reactions

In this paper, we present a summary of our work on highly photostable supramolecular ruthenium complexes, which may be incorporated into more complex systems for artificial solar energy conversion. We have used supramolecular chemistry and photochemistry to synthesize highly photostable ruthenium bipyridine coronates and a bipyridazine podate complex and to enhance photoelectron-transfer reactions in physical model systems for artificial photosynthesis. The recent progress of covalent and non-covalent sensitizer-relay assemblies for highly efficient photoelectron transfer is described.

A detailed mechanistic investigation of the binding behavior of cationic species to crow-ether-modified bipyridine derivatives is presented as an example of supramolecular binding in systems for photoelectron transfer. The host properties of the free ligands and the derived bis-heteroleptic ruthenium complexes are compared using UV—visible, luminescence quenching and proton nuclear magnetic resonance titrations. The combination of these three methods confirms that supramolecular binding of cations and the electron relay methylviologen (MV²⁺) to the complexes can be observed. The binding constants determined are of the order of (1–6) × 10⁴ 1 mol⁻¹ for the crown-ether ruthenium complexes and 1 × 10²−4 × 10³ 1 mol⁻³ for the crown-ether ligands. Single-photon-counting (SPC) investigations give strong indications for the coexistence of different binding mechanisms. The kinetic scheme of Yekta et al. has been adapted to interpret the binding mechanism.     

Inverse deuterium isotope effect in the intersystem crossing of diphenylcarbene

The singlet-to-triplet intersystem crossing rate (k_st) of diphenylcarbene (DPC) is found to exhibit an inverse isotope effect in various solvents. An off-resonance coupling model between the initial singlet state and a sparse triplet vibronic manifold accounts for k_ST showing both an inverse isotope effect in a given solvent as well as an inverse energy gap effect in a solvent series.     

Loop amplitudes for the fermionic string

We obtain simple formulae for loop amplitudes of the fermionic closed oriented Polyakov string in d= 10, as integrals over moduli and supermoduli space. The integrals over supermoduli may be carried out, leaving an integral over moduli with respect to the Weil-Petersson measure. The integrand consists of Green functions and determinants of laplacians on tensors and spinors.     

What can we learn from hydrodynamic analysis at RHIC?

We can establish a new picture, the perfect fluid sQGP core and the dissipative hadronic corona, of the space-time evolution of produced matter in relativistic heavy-ion collisions at RHIC. It is also shown that the picture works well also in the forward rapidity region through an analysis based on a new class of the hydro-kinetic model and that this is a manifestation of the rapid increase of the entropy density in the vicinity of QCD critical temperature, namely, deconfinement.     

The Aharonov–Bohm effect in graphene rings

This is a review of electronic quantum interference in mesoscopic ring structures based on graphene, with a focus on the interplay between the Aharonov–Bohm effect and the peculiar electronic and transport properties of this material. We first present an overview on recent developments of this topic, both from the experimental as well as the theoretical side. We then review our recent work on signatures of two prominent graphene-specific features in the Aharonov–Bohm conductance oscillations, namely Klein tunneling and specular Andreev reflection. We close with an assessment of experimental and theoretical development in the field and highlight open questions as well as potential directions of the developments in future work.