Aggregation bounds in stochastic linear programming

Stochastic linear programs become extremely large and complex as additional uncertainties and possible future outcomes are included in their formulation. Row and column aggregation can significantly reduce this complexity, but the solutions of the aggregated problem only provide an approximation of the true solution. In this paper, error bounds on the value of the optimal solution of the original problem are obtained from the solution of the aggregated problem. These bounds apply for aggregation of both random variables and time periods.     

Femtosecond time-resolved transient absorption spectroscopy of xanthophylls

Xanthophylls are a major class of photosynthetic pigments that participate in an adaptation mechanism by which higher plants protect themselves from high light stress. In the present work, an ultrafast time-resolved spectroscopic investigation of all the major xanthophyll pigments from spinach has been performed. The molecules are zeaxanthin, lutein, violaxanthin, and neoxanthin. beta-Carotene was also studied. The experimental data reveal the inherent spectral properties and ultrafast dynamics including the S(1) state lifetimes of each of the pigments. In conjunction with quantum mechanical computations the results address the molecular features of xanthophylls that control the formation and decay of the S* state in solution. The findings provide compelling evidence that S* is an excited state with a conformational geometry twisted relative to the ground state. The data indicate that S* is formed via a branched pathway from higher excited singlet states and that its yield depends critically on the presence of beta-ionylidene rings in the polyene system of pi-electron conjugated double bonds. The data are expected to be beneficial to researchers employing ultrafast time-resolved spectroscopic methods to investigate the mechanisms of both energy transfer and nonphotochemical quenching in higher plant preparations.     

Torsion Modules, Lattices and P-Points

Answering a long-standing question in the theory of torsionmodules, we show that weakly productively bounded domains arenecessarily productively bounded. (See the Introduction fordefinitions.) Moreover, we prove a twin result for the ideallattice L of a domain equating weak and strong global intersectionconditions for families (X_i)_iI of subsets of L with the propertythat _iI A_i 0 whenever A_iX_i. Finally, we show that for domainswith Krull dimension (and countably generated extensions thereof),these lattice-theoretic conditions are equivalent to productiveboundedness. 1991 Mathematics Subject Classification 03E05,06A23, 13C12, 16U20, 16P60.     

Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function

In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function . Instead of the original objective function f, we employ a convex approximation f _{k + 1} at the kth iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate even it the iteration points are calculated approximately, where are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.     

The charge-transfer properties of the S2 state of fucoxanthin in solution and in fucoxanthin chlorophyll-a/c2 protein (FCP) based on stark spectroscopy and molecular-orbital theory

Fucoxanthin chlorophyll-a/c 2 protein (FCP), the membrane-intrinsic light harvesting complex from the diatom Cyclotella meneghiniana, is characterized by Stark spectroscopy to obtain a quantitative measure of the excited-state dipolar properties of the constituent pigments. The electro-optical properties of the carotenoid fucoxanthin (Fx), the primary light harvester in FCP, were determined from the Stark spectrum measured in a MeTHF glass (77 K) and compared to the results from electronic-structure calculations. On photon absorption by Fx, a 17 D change in the static dipole moment (|Delta mu|exp), and a somewhat larger |Delta mu|exp at the red edge, are measured for the S 0 --> S 2 (1 (1)A g (-)-like -->1 (1)B u *+-like) transition. The large change in dipole moment indicates that Fx undergoes photoinduced charge transfer (CT), and underscores the influence of the S 2 state on the polarity-dependent excited-state dynamics of Fx that has so far been attributed to, and discussed in terms of, the S 0 and the S 1/ICT states. MNDO-PSDCI and SACCI-CISD calculations indicate that the 1 (1)B u (*+)-like state intrinsically possesses a dipole moment much smaller than the 2 (1)A g (*-)-like state, suggesting that solvent fields promote the mixing of these two states and could account for the large dipole moments measured here for the S 0 --> S 2 transition. These CT properties of the 1 (1)B u (*+)-like state of Fx are further enhanced in the protein and underpin its photosynthetic capabilities for light harvesting and energy transfer (ET). In FCP, the CT properties of the Fx's vary according to the energetic position: between 450 and 500 nm there appear to be two sets of Fx's that exhibit |Delta mu| exp values on the order of 5 and 15 D, whereas the red-most Fx's, that are very efficient in ET to chlorophyll-a (Chl-a), exhibit strikingly large |Delta mu| exp values on the order of 40 D. Such magnitudes of |Delta mu| exp suggest a mechanism that enhances Coulombic coupling to promote ET from the S 2 state of Fx to Chl-a. These three sets of Fx's, including a fourth red Fx, are identified by fitting the Stark spectrum of FCP with the Stark spectrum of Fx in MeTHF. In contrast to the Fx's in the protein, the electrostatic properties of the Chl's in FCP are comparatively much smaller. Notably, for the Q y band of Chl-a, a |Delta mu| exp of 0.92 D and a change in polarizability ( Delta alpha exp) of 20 A (3), indicate that the Chl-a's are monomeric in nature and decoupled from each other.     

Representation-Tame Algebras Need not be Homologically Tame

We show that even within the class of special biserial algebras, one of the most thoroughly studied classes of representation-tame finite dimensional algebras, the (left) big finitistic dimension may be strictly larger than the little. In fact, we find that the discrepancies Fin dim Λ – fin dim Λ fail to be bounded as Λ traces the special biserial algebras. More precisely: For every positive integer r, we exhibit a special biserial algebra Λ with the property that fin dim Λ = r+1, while Fin dim Λ=2r+1.     

Two-dimensional spectral shearing interferometry for few-cycle pulse characterization

We present a new method for measuring the spectral phase of ultrashort pulses that utilizes spectral shearing interferometry with zero delay. Unlike conventional spectral phase interferometry for direct electric-field reconstruction, which encodes phase as a sensitively calibrated fringe in the spectral domain, two-dimensional spectral shearing interferometry robustly encodes phase along a second dimension. This greatly reduces demands on the spectrometer and allows for complex phase spectra to be measured over extremely large bandwidths, potentially exceeding 1.5 octaves.