A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum Fields

Let H ₀ and H _I be a self-adjoint and a symmetric operator on a complex Hilbert space, respectively, and suppose that H ₀ is bounded below and the infimum E ₀ of the spectrum of H ₀ is a simple eigenvalue of H ₀ which is not necessarily isolated. In this paper, we present a new asymptotic perturbation theory for an eigenvalue E(λ) of the operator ${H(\lambda)\,:=\,H_0 + \lambda H_{I}\,(\lambda \in \mathbb{R} \setminus \{0\})}$ satisfying lim _{λ → 0} E(λ) = E ₀. The point of the theory is in that it covers also the case where E ₀ is a non-isolated eigenvalue of H ₀. Under a suitable set of assumptions, we derive an asymptotic expansion of E(λ) up to an arbitrary finite order of λ as λ → 0. We apply the abstract results to a model of massless quantum fields, called the generalized spin-boson model (Arai and Hirokawa in J Funct Anal 151:455–503, 1997) and show that the ground-state energy of the model has asymptotic expansions in the coupling constant λ as λ → 0.     

Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

Reaction optimization using solid-phase catalysis-CD HTS: Nb-imidazoline-Cu(I)-catalyzed asymmetric benzoylation of 1,2-diols

Catalytic asymmetric benzoylation of 1,2-diols has been developed using a solid-phase asymmetric catalyst. The reaction conditions were optimized by the screening of different metal salts, solvents, bases, and temperatures. High-throughput screening was performed using circular dichroism detection, and the results revealed that Nb-imidazoline-copper(I) in combination with diisopropylethylamine was able to catalyze with high enantioselectivity, giving the monobenzoylated products in high yields and excellent enantiomeric excesses of up to 95% ee. [reaction: see text]     

Chiral Bis(imidazolidine)‐Derived NCN Pincer Rh Complex for Catalytic Asymmetric Mannich Reaction of Malononitrile with N‐Boc Imines

Chiral bis(imidazolidine)‐derived NCN–rhodium complexes ([PhBidine‐RhX₂] and [tBu‐PhBidine‐RhX₂]) were prepared by a C?H insertion method, and the structures were unequivocally determined by X‐ray crystallographic analysis. The [tBu‐PhBidine‐Rh(OAc)₂] complex smoothly catalyzed an asymmetric Mannich reaction of malononitrile with N‐Boc imines to give products in up to 94 % ee, which are useful for the synthesis of chiral α‐amino acids.     

To-and-fro motion of W5Si3 on a beta-Si3N4 substrate at elevated temperatures.

Behavior of fine crystalline particles of W5Si3 on a beta-Si3N4 substrate at high temperatures was observed by an in situ heating experiment in a transmission electron microscope. Some of the fine particles of W5Si3 moved in a to-and-fro manner.     

The photochemical characteristics of aromatic enediyne compounds substituted with electron donating and electron withdrawing groups

trans- and cis-1-(4-Dimethylaminophenyl)-6-(4-nitrophenyl)hex-3-ene-1,5-diynes (trans- and cis-DANE) were synthesized and their photochemical properties were studied. The absorption spectra of trans-DANE red-shifted compared with the parent compound bisphenylethynylethene (BEE) due to intramolecular charge transfer. The fluorescence spectra, Stokes shift, fluorescence lifetime, fluorescence quantum yield, and quantum yield of trans-to-cis photoisomerization of trans-DANE showed strong dependence upon the solvent polarity in the less-polar region. No fluorescence emission from trans-DANE was observed in medium-polar and polar solvents. The quantum yield of cis-to-trans isomerization was almost solvent independent. The donor-acceptor substituents shifted the equilibrium between the trans perpendicular triplet state and the trans planar triplet state to the trans triplet state, and resulted in an increase in the triplet lifetime. Comparison of the photochemical properties of trans-DANE with trans-4-dimethylamino-4'-nitrostilbene (DANS) suggests that trans-DANE is a possible fluorescent probe in the non-polar region.     

Sensitive determination of anandamide in rat brain utilizing a coupled-column HPLC with fluorimetric detection

A fluorimetric determination method for N-arachidonoylethanolamine (anandamide) was developed using a precolumn fluorescence derivatization followed by coupled-column high-performance liquid chromatography (HPLC). Anandamide extracted from the rat brain tissue was derivatized with 4-N-chloroformylmethyl-N-methylamino-7-N, N-dimethylaminosulfonyl-2,1,3-benzoxadiazole (DBD-COCl), purified by a solid-phase extraction (Emporetrade mark), and assayed by the coupled-column HPLC. The HPLC consisted of phenyl (100 x 4.6 mm i.d. ) and octadecylsilica columns (250 x 4.6 mm i.d.), both connected by a six-port valve. The concentration of anandamide in rat brain was 3. 37 +/- 0.73 pmol/g with 6.47 and 3.57% of intra- and inter-day precisions, respectively. Using this method, we investigated the alteration of anandamide concentration in rat brain 30 min after administration of anandamide (2 mg/kg, i.p.) to rats pretreated with or without phenylmethylsulfonyl fluoride (PMSF; 30 mg/kg, i.p.), an inhibitor of amidohydrolase. In rats pretreated with PMSF, the brain concentration of anandamide was approx. 16-fold higher than that of rats without PMSF (p < 0.01).     

Fluorescence immunological determination of immunoglobulin G in human serum by high-performance liquid gel-permeation chromatography

Summary A high-performance liquid gel-permeation chromatographic method is described for the determination of human serum immunoglobulin G (IgG) by separating the fluorescent immuno complex from the free fluorescence-labeled antibody. Fluorescence-labeled antibody used in this study was fluorescein isothiocyanate (FITC)-labeled Fab fragment goat anti-human IgG (anti-IgG Fab). Immuno complexes and antibody of different molecular sizes can be separated. FITC-labeled anti-IgG Fab was added to the serum and the mixture is passed through the column. An immuno complex separates as well-delineated peak in the column void volume, and was measured by the fluorescence of the column eluate (Ex=490nm, Em=520nm). The total analysis time for a serum sample was approximately 15min. The minimum detection limit was 25 mg/dl. The relative standard deviation was below 2% (peak area). The results of the HPL-GPC analysis correlate well with those obtained by laser nephelometric assay (r=0.992).     

Synthesis and photoinduced memory effect of poly[2-N-carbazolylethyl acrylate-co-2-(3,5-dinitrobenzoyloxy) ethyl methacrylate]

Copolymers containing an intramolecular electron donor-acceptor (EDA) complex were synthesized by free radical copolymerization of 2-N-carbazolylethyl acrylate and 2-(3,5-dinitrobenzoyloxy)ethyl methacrylate. Glass transition temperatures show a positive deviation from the weight-average values of copolymers, indicating the presence of the specific EDA interaction in copolymers in the solid state. Photoinduced “memory effect,” which is defined as the percentage of the difference of the surface potential given by corona charging before and after irradiation of light on polymer films, was 30% for the copolymer with 5 mol% of acceptor content. Memory effect increased to 70% for a 8 μm film by doping with 2 wt% of trichloroacetic acid (TCAA), and leveled off at 5 wt% of TCAA content. Memory effect was also enhanced by increasing the thickness of polymer films and irradiation time. The largest value of memory effect (85%) was obtained from the film of the copolymer with 5 mol% acceptor content doped with 1 wt% TCAA and with thickness larger than 14 μm.