On an alternative functional equation

Aequationes mathematicae -     

On the boundedness and continuity of convex functions and additive functions

Aequationes mathematicae -     

State preparation and excited electronic and vibrational behavior in hemes

The temporally overlapping, ultrafast electronic and vibrational dynamics of a model five-coordinate, high-spin heme in a nominally isotropic solvent environment has been studied for the first time with three complementary ultrafast techniques: transient absorption, time-resolved resonance Raman Stokes, and time-resolved resonance Raman anti-Stokes spectroscopies. Vibrational dynamics associated with an evolving ground-state species dominate the observations. Excitation into the blue side of the Soret band led to very rapid S2 --> S1 decay (sub-100 fs), followed by somewhat slower (800 fs) S1 --> S0 nonradiative decay. The initial vibrationally excited, non-Boltzmann S0 state was modeled as shifted to lower energy by 300 cm(-1) and broadened by 20%. On a approximately 10 ps time scale, the S0 state evolved into its room-temperature, thermal distribution S0 profile largely through VER. Anti-Stokes signals disappear very rapidly, indicating that the vibrational energy redistributes internally in about 1-3 ps from the initial accepting modes associated with S1 --> S0 internal conversion to the rest of the macrocycle. Comparisons of anti-Stokes mode intensities and lifetimes from TRARRS studies in which the initial excited state was prepared by ligand photolysis [Mizutani, T.; Kitagawa, T. Science 1997, 278, 443, and Chem. Rec. 2001, 1, 258] suggest that, while transient absorption studies appear to be relatively insensitive to initial preparation of the electronic excited state, the subsequent vibrational dynamics are not. Direct, time-resolved evaluation of vibrational lifetimes provides insight into fast internal conversion in hemes and the pathways of subsequent vibrational energy flow in the ground state. The overall similarity of the model heme electronic dynamics to those of biological systems may be a sign that the protein's influence upon the dynamics of the heme active site is rather subtle.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

La2O3 promotional effect to Co3O4/γ-Al2O3 catalyst in the oxidative dehydrogenation of ethylbenzene with CO2 as soft oxidant

Co₃O₄/γ-Al₂O₃ catalysts with variable Co₃O₄ loadings (5–20 wt%) and deposition of 15% Co₃O₄ on La₂O₃/γ-Al₂O₃ were prepared by wet impregnation method. La₂O₃-γ-Al₂O₃ support with variable composition of La₂O₃ (2–6 wt%) were prepared by co-precipitation method. All the catalysts were tested for oxidative dehydrogenation of ethylbenzene with CO₂ as soft oxidant. Among the Co₃O₄/γ-Al₂O₃ catalysts, 15% Co₃O₄/γ-Al₂O₃ has shown good performance and hence this catalyst has been chosen to investigate the effect of La₂O₃ species. CO₂ pulse chemisorption data indicate more amount of CO₂ uptake over 15% Co₃O₄/4%La₂O₃/γ-Al₂O₃ catalyst which clearly indicates that this catalyst exhibits good performance in ethylbenzene dehydrogenation with CO₂ as soft oxidant because of reverse water gas shift reaction. Temperature programmed reduction studies indicate that the Co₃O₄ catalysts follow two step reduction mechanism from Co₃O₄ to CoO and then to Co and La₂O₃ promotional effect is visible through facile reduction of Co₃O₄ species. La₂O₃ doping has a vital influence in getting enhanced ethylbenzene conversion, styrene yield and alleviates catalyst deactivation compared to that of unpromoted Co₃O₄/γ-Al₂O₃ catalyst. TGA studies indicate the presence low amount coke deposition during time-on-stream over 15% Co₃O₄/4%La₂O₃/γ-Al₂O₃ catalyst compared to 15% Co₃O₄/γ-Al₂O₃ catalyst.     

Chiral protein scissors activated by light: recognition and protein photocleavage by a new pyrenyl probe

Strong chiral discrimination and site-selective photocleavage of two model proteins, lysozyme and bovine serum albumin (BSA), by new pyrenyl probes are reported here. The enantiomeric pyrenyl probes D-phenylalanine-1(1-pyrene)methylamide (PMA- D-Phe) and L-phenylalanine-1(1-pyrene)methylamide (PMA- l-Phe) were synthesized by coupling the carboxyl function of D-phenylalanine or L-phenylalanine with the amino group of 1(1-pyrene)methylamine. Binding affinities of the two enantiomers with the proteins were quantitated in absorption titrations. BSA indicated 10-fold selectivity for PMA- D-Phe, and the binding constants for the L- and D-enantiomers were 3.8 x 10(5) and 4.0 x 10(6) M(-1), respectively. Lysozyme, similarly, indicated a 6-fold preference for PMA- D-Phe with binding constants of 3.3 x 10 (5) and 2.0 x 10(6) M(-1) for the L- and D-isomers, respectively. Such strong chiral discrimination illustrates the key role of the chiral center of the probe (Phe) in the binding interactions. The enantiomers were tested to examine how the chiral discrimination for their binding influences reactivity toward protein photocleavage. Irradiation of the probe-protein complexes, at 342 nm in the presence of hexammine cobalt(III) chloride, resulted in the cleavage of the protein backbone. Photocleavage did not proceed in the dark or in the absence of the pyrenyl probes. Both enantiomers indicated low reactivity with BSA (<5% yield), while large photocleavage yields ( approximately 57%) have been noted with lysozyme. This lysozyme photocleavage yield is a significant improvement over previous reports. However, both enantiomers cleaved lysozyme at the same location between Trp108-Val109, despite the strong chiral selectivity for binding. H-atom abstraction from Trp 108, accessible from the active site cleft, could initiate the observed peptide bond cleavage.