Power series with radius of convergence zero — Overconvergence,elongations, summability

We deal with overconvergence phenomena of power series with radius of convergence zero. Among others it is shown that the partial sums of such a series can be elongated to become Cesàro summable on a set S ⊂ {z: |z| > 0} if and only if the considered power series is overconvergent.     

Lagrangian relaxation based algorithm for trigeneration planning with storages

Trigeneration is a booming power production technology where three energy commodities are simultaneously produced in a single integrated process. Electric power, heat (e.g. hot water) and cooling (e.g. chilled water) are three typical energy commodities in the trigeneration system. The production of three energy commodities follows a joint characteristic. This paper presents a Lagrangian relaxation (LR) based algorithm for trigeneration planning with storages based on deflected subgradient optimization method. The trigeneration planning problem is modeled as a linear programming (LP) problem. The linear cost function poses the convergence challenge to the LR algorithm and the joint characteristic of trigeneration plants makes the operating region of trigeneration system more complicated than that of power-only generation system and that of combined heat and power (CHP) system. We develop an effective method for the long-term planning problem based on the proper strategy to form Lagrangian subproblems and solve the Lagrangian dual (LD) problem based on deflected subgradient optimization method. We also develop a heuristic for restoring feasibility from the LD solution. Numerical results based on realistic production models show that the algorithm is efficient and near-optimal solutions are obtained.     

A linear cyclic oximate-bridged ­tetracopper(II) complex

The crystal structure of the title complex, tetrakis­[μ-6-amino-3-methyl-4-aza­hex-3-en-2-one oximato(1–)-κ⁴N,N′,N′′:O]tetracopper(II) tetraperchlorate 0.6-hydrate, [Cu₄(C₆H₁₂N₃O)₄](ClO₄)₄·0.6H₂O, shows the cation to be an oximate-bridged tetramer composed of four 6-amino-3-methyl-4-aza­hex-3-en-2-one oxime ligands and four copper(II) ions and to have crystallographically imposed symmetry. Each Cu^II atom is four-coordinated by the three N atoms of one oxime ligand and by the O atom of another oxime ligand in a distorted square-planar geometry.     

Suboptimal security solution of a linear-quadratic pursuit-evasion game with mixed noises

The discrete-time, linear-quadratic pursuit-evasion game is considered in this paper. The difference system contains the state-dependent, control-dependent, and additive noises. In addition, each player has additive noises in his own measurement vector, and he is restricted to implement a linear estimator based on his measurements. Each player's philosophy is not to run a risk but to adopt a security control policy. Because of the linear estimation restriction, the security solution is suboptimal, which is found to be the closed-loop controls which are linear in the best estimate of the state. Equations for calculating the state estimation are derived. An algorithm for off-line computing the filter gain is also given.     

Fluorescence of Na2 and K2 excited by a gold vapor laser

The gold vapor laser has been used to irradiate the alkali dimers Li₂, Na₂, K₂, and Rb₂. Significant fluorescence was found only from Na₂ and K₂. Six fluorescent series in the A¹Σ_u⁺-X¹Σ_g⁺ system of Na₂ and three in the B¹Π_u-X¹Σ_g⁺ system of K₂ were assigned, respectively. New spectroscopic constants for the X¹Σ_g⁺ state of ³⁹K₂ are derived, and new RKR potential energy curves for the X¹Σ_g⁺ and B¹Π_u states of ³⁹K₂ are given.     

Controlling conformations in alternating dialkylsilylene-spaced donor-acceptor copolymers by a cooperative Thorpe-Ingold effect and polymer folding

A series of dialkylsilylene-spaced copolymers 6 and 7, which contain Me(2)Si and iPr(2)Si spacer groups, respectively, and have alternating donor and acceptor chromophores, have been designed and regioselectively synthesized by hydrosilylation. The ratio of the donor and acceptor chromophores for each repeat unit is 2:1, and the two donor chromophores are linked by a trimethylene bridge. A 4-aminostyrene moiety is used as the donor and a series of acceptor chromophores with different reduction potentials are employed. Both steady-state and kinetic measurements reveal that the photoinduced electron transfer (PET) in 6 obeyed the Marcus theory in which normal and inverted regions are observed. On the other hand, the iPr(2)Si-spaced copolymers 7 exhibit absorption and emission from the charge-transfer complexes exclusively due to ground-state interactions between the donor and acceptor chromophores. The discrepancy in photophysical behavior may have arisen from the difference in distance between the adjacent donor and acceptor chromophores. The bulkiness of the substituents on the silicon atom (i.e., Me versus iPr) may exert the Thorpe-Ingold effect on the local conformation around the silicon atom. The differences in the small energetic barriers for each of the conformational states may be amplified by extending the distance of the folding structure, which results in perturbing the conformation of the polymers. These results suggest that the electronic interactions between adjacent donor-acceptor pairs in these copolymers are controlled by the synchronization of the substitution effect and corresponding polymeric structures.     

Tri‐ and Bicyclic Taxoids from the Taiwanese Yew Taxus sumatrana

Five new taxoids, including a new 2(3→20)‐abeo‐taxane with a 6/10/6‐membered ring system and four 3,8‐seco‐taxanes having a 6/12‐membered ring system, were isolated from an acetone extract of the leaves and twigs of the Taiwanese yew (Taxus sumatrana, Taxaceae). The structures were established as 2α,7β,10α‐triacetoxy‐5α‐hydroxy‐2(3→20)‐abeo‐taxa‐4(20),11‐dien‐9,13‐dione ( 1 ), (3E,8E)‐2α,9,10β, 13α,20‐pentaacetoxy‐7β‐hydroxy‐3,8‐secotaxa‐3,8,11‐trien‐5‐one ( 2 ), (3E,8E)‐2α,9,10β,13α,20‐pentaacetoxy‐5α,7β‐dihydroxy‐3,8‐secotaxa‐3,8,11‐triene ( 3 ), (3E,8E)‐9,10β,13α‐triacetoxy‐2α,7β,20‐trihydroxy‐5α‐[(2E)‐cinnamoyloxy]‐3,8‐secotaxa‐3,8,11‐triene ( 4 ), and (3E,8E)‐2α,5α,7β,9,10β,13α‐hexaacetoxy‐20‐hydroxy‐3,8‐secotaxa‐3,8,11‐triene ( 5 ), respectively, on the basis 1D‐ and 2D‐NMR spectral analyses. The in vitro cytotoxic activity of compounds 1 – 5 against four human tumor cell lines, including HeLa (cervical epitheloid), WiDr (colon), Daoy (medulloblastoma), and Hep2 (liver carcinoma) tumor cells was evaluated. Whereas compounds 1 – 3 were inactive, the novel taxanes 4 and 5 showed significant cytotoxicity.