Delayed nonlinear cournot and bertrand dynamics with product differentiation

Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.     

Possible Involvement of a Tetrahydrobiopterin in Photoreception for UV‐B‐induced Anthocyanin Synthesis in Carrot

Our previous studies of action spectra for UV‐B‐induced anthocyanin accumulation in cultured carrot cells indicated that a reduced form of pterin, possibly tetrahydrobiopterin, contributes to UV‐B photoreception. In this report, we provide additional evidence for the involvement of pterin in UV‐B light sensing. UV‐B‐induced phenylalanine ammonia‐lyase (PAL) activity was considerably suppressed by N‐acetylserotonin (an inhibitor of tetrahydrobiopterin biosynthesis), and this suppression was partially recovered by adding biopterin or tetrahydrobiobiopterin. In addition, protein(s) specifically bound to biopterin were detected by radiolabeling experiments in N‐acetylserotonin‐treated cells. Furthermore, diphenyleneiodonium, a potent inhibitor of electron transfer, completely suppressed UV‐B‐induced PAL activity. These results suggest the occurrence of an unidentified UV‐B photoreceptor (other than UVR8, the tryptophan‐based UV‐B sensor originally identified in Arabidopsis) with reduced pterin in carrot cells. After reexamining published action spectra, we suggest that anthocyanin synthesis is coordinately regulated by these two UV‐B sensors.     

Pd-catalyzed cycloisomerization-allylation of 4-alkynones: synthesis of 5-homoallylfuran derivatives

In the presence of Pd₂(dba)₃-tBu₃P catalyst and Cs₂CO₃, cycloisomerization-allylation reactions of 4-alkynone derivatives with allyl carbonates in MeCN proceed in 5-exo mode to give highly-substituted furans having homoallyl groups at 5-position.     

PIFA-mediated oxidative cycloisomerization of 2-propargyl-1,3-dicarbonyl compounds: divergent synthesis of furfuryl alcohols and furfurals

PhI(OCOCF₃)₂ (PIFA) in the presence of trifluoroacetic acid (TFA) in CH₂Cl₂ efficiently promotes the oxidative cycloisomerization of 2-propargyl 1,3-dicarbonyl compounds to give 4,5-disubstituted furfuryl alcohols. PIFA in hexafluoroisopropanol (HFIP) or PIFA-BF₃·OEt₂ in CH₂Cl₂ bring about the direct formation of furfurals from 2-propargyl 1,3-dicarbonyl compounds. In a few cases, PhIO is suitable for the direct formation of furfurals.     

Cage-shaped borate esters with tris(2-oxyphenyl)methane or -silane system frameworks bearing multiple tuning factors: geometric and substituent effects on their Lewis acid properties

Boron complexes that contain new tridentate ligands, tris(o‐oxyaryl)methanes and ‐silanes, were prepared. These complexes had a cage‐shaped structure around a boron center and showed higher Lewis acidity and catalytic activity than open‐shaped boron compounds. The cage‐shaped ligands determined the properties of the borates by altering the geometry and were consistently bound to the metal center by chelation. The synthesized compounds were L?B(OC₆H₄)₃CH, L?B(OC₆H₄)₃SiMe, and its derivatives (L=THF or pyridine as an external ligand). Theoretical calculations suggested that the cage‐shaped borates had a large dihedral angle (C_ipso‐O‐B‐O) compared with open‐shaped borates. The geometric effect due to the dihedral angle means that compared with open‐shaped, the cage‐shaped borates have a greater Lewis acidity. The introduction of electron‐withdrawing groups on the aryl moieties in the cage‐shaped framework increased the Lewis acidity. Substitution of a bridgehead Si for a bridgehead C decreased the Lewis acidity of the boron complexes because the large silicon atom reduces the dihedral angle of C_ipso‐O‐B‐O. The ligand‐exchange rates of the para‐fluoro‐substituted compound B(OC₆H₃F)₃CH and the ortho‐phenyl‐substituted compound B(OC₆H₃Ph)₃CH were less than that of the unsubstituted borate B(OC₆H₄)₃CH. The ligand‐exchange rate of B(OC₆H₄)₃SiMe was much faster than that of B(OC₆H₄)₃CH. A hetero Diels–Alder reaction and Mukaiyama‐type aldol reactions were more effectively catalyzed by cage‐shaped borates than by the open‐shaped borate B(OPh)₃ or by the strong Lewis acid BF₃?OEt₂. The cage‐shaped borates with the bulky substituents at the ortho‐positions selectively catalyzed the reaction with less sterically hindered substrates, while the unsubstituted borate showed no selectivity.     

Redox-controlled, reversible rearrangement of a tris(2-pyridylthio)methyl ligand on nickel to an isomer with an “N,S-confused” 2-pyridylthiolate arm

Interchange between the nickel +2 and +3 oxidation states precisely controls the reversible rearrangement of the tris(2-pyridylthio)methanide (tptm) ligand in the organometallic nickel(II) complex [{Ni(μ-Br)-(tptm)}(2)] (2). Oxidation of 2 first gives the corresponding Ni(III) complex [{Ni(μ-Br)(tptm)}(2)][PF(6)](2) (4). However, in solution the tptm ligand in 4 slowly undergoes a rearrangement, in which the N and S atoms of one of the pyridylthiolate arms exchange Ni and C bonding partners, thereby resulting in an "N,S-confused" isomer of tptm in the product, [NiBr(bpttpm)]PF(6) (5; bpttpm= bis(2-pyridylthio)(2-thiopyridinium)-methyl). Reduction of 5 reverses this ligand rearrangement and 2 is reformed quantitatively. The individual steps involved in these unusual ligand rearrangements were investigated by a number of methods, including voltammetric analysis, and a mechanism for this process is proposed. X-ray crystal structure determinations of the key compounds 2, 4 and 5 have been obtained.     

Efficient direct electron transfer with enzyme on a nanostructured carbon film fabricated with a maskless top-down UV/ozone process

We have developed a new carbon film electrode material with thornlike surface nanostructures to realize efficient direct electron transfer (DET) with enzymes, which is very important for various enzyme biosensors and for anodes or cathodes used in biofuel cells. The nanostructures were fabricated using UV/ozone treatment without a mask, and the obtained nanostructures were typically 2-3.5 nm high as confirmed by atomic force microscopy measurements. X-ray photoelectron spectroscopy and transmission electron microscopy revealed that these nanostructures could be formed by employing significantly different etching rates depending on nanometer-order differences in the local sp(3) content of the nanocarbon film, which we fabricated with the electron cyclotron resonance sputtering method. These structures could not be realized using other carbon films such as boron-doped diamond, glassy carbon, pyrolyzed polymers based on spin-coated polyimide or vacuum-deposited phthalocyanine films, or diamond-like carbon films because those carbon films have relatively homogeneous structures or micrometer-order crystalline structures. With physically adsorbed bilirubin oxidase on the nanostructured carbon surface, the DET catalytic current amplification was 30 times greater than that obtained with the original carbon film with a flat surface. This efficient DET of an enzyme could not be achieved by changing the hydrophilicity of the flat carbon surface, suggesting that DET was accelerated by the formation of nanostructures with a hydrophilic surface. Efficient DET was also observed using cytochrome c.     

Hydrodynamic interpretation on the rotational diffusion of peroxylamine disulfonate solute dissolved in room temperature ionic liquids as studied by electron paramagnetic resonance spectroscopy

Rotational motion of a nitroxide radical, peroxylamine disulfonate (PADS), dissolved in room temperature ionic liquids (RTILs) was studied by analyzing electron paramagnetic resonance spectra of PADS in various RTILs. We determined physical properties of PADS such as the hyperfine coupling constant (A), the temperature dependence of anisotropic rotational correlation times (τ(∥) and τ(⊥)), and rotational anisotropy (N). We observed that the A values remain unchanged for various RTILs, which indicates negligible interaction between the N-O PADS group and the cation of RTIL. Large N values suggest strong interaction of the negative sulfonyl parts of PADS with the cations of RTILs. Most of the τ(∥), τ(⊥), and (τ(∥)τ(⊥))(1/2) values are within the range calculated on the basis of a hydrodynamic theory with stick and slip boundary conditions. It was deduced that this theory could not adequately explain the measured results in some RTILs with smaller BF(4) and PF(6) anions.