Maximum Lebesgue extension of monotone convex functions

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit construction, where the maximum domain of extension is obtained as a (possibly proper) subspace of a natural Orlicz-type space, characterized by a certain uniform integrability property. As an application, we provide a characterization of the Lebesgue property of monotone convex function on arbitrary solid spaces of random variables in terms of uniform integrability and a “nice” dual representation of the function.     

Defining equations¶of certain rational cuspidal curves. I

In this paper, we describe the defining equations of rational cuspidal plane curves having exactly one cusp such that the tangent line at the cusp intersects only at the cusp. Received: 5 January 2000     

Investigation of the influence of cell density of human fibroblasts cryopreserved inside collagen sponges at various cooling rates

The influence of cell density of cells cryopreserved inside a collagen matrix at various cooling rates was investigated. Human fibroblasts were three-dimensionally cultured for 2 days in a collagen sponge (20 mm in diameter and 1 mm in thickness) as an extracellular matrix to imitate biological tissue (artificial tissue). Different cell densities for the artificial tissue were used, from 10(5) to 10(7) cells/cm(3). Four artificial tissues were first stacked in a test chamber, frozen at a cooling rate of 0.3 to 50 degrees C/min in a solution of Dulbecco's Modified Eagle Medium, 20% fetal bovine serum and 10% dimethylsulfoxide, kept frozen below -185 degrees C for 2 hours, and then finally thawed. Membrane integrity of fibroblasts using a trypan blue exclusion assay was evaluated as an index for post-thaw cellular viability. Results show that with increasing cell density, the post-thaw membrane integrity decreased. Therefore, in the cryopreservation of biological tissue, it seems high cell density is one factor which causes a decline in viability.     

A free-energy perturbation method based on Monte Carlo simulations using quantum mechanical calculations (QM/MC/FEP method): application to highly solvent-dependent reactions

This study describes the framework of the quantum mechanical (QM)/Monte Carlo (MC)/free‐energy perturbation (FEP) method, a FEP method based on MC simulations using quantum chemical calculations. Because a series of structures generated by interpolating internal coordinates between transition state and reactant did not produce smooth free‐energy profiles, we used structures from the intrinsic reaction coordinate calculations. This method was first applied to the Diels–Alder reaction between methyl vinyl ketone and cyclopentadiene and produced ΔG values of 20.1 and 21.4 kcal mol^?1 in aqueous and methanol solutions, respectively. They are very consistent with the experimentally observed values. The other two applications were the free‐energy surfaces for the Cope elimination of N,N‐dimethyl‐3‐phenylbutan‐2‐amine oxide in aqueous, dimethyl sulfoxide, and tetrahydrofuran solutions, and the Kemp decarboxylation of 6‐hydroxybenzo‐isoxazole‐3‐carboxylic acid in aqueous, dimethyl sulfoxide, and CH₃CN solutions. The calculated activation free energies differed by less than 1.8 kcal mol^?1 from the experimental values for these reactions. Although we used droplet models for the QM/MC/FEP simulations, the calculated results for three reactions are very close to the experimental data. It was confirmed that most of the interactions between the solute and solvents can be described using small numbers of solvent molecules. This is because a few solvent molecules can produce large portions of the solute–solvent interaction energies at the reaction centers. When we confirmed the dependency on the droplet sizes of solvents, the QM/MC/FEP for a large droplet with 106 water molecules produced a ΔG value similar to the experimental values, as well as that for a small droplet with 34 molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

New determination methods of halides and cyanide ions by electrospray ionization mass spectrometry based on ternary complex formation

Determination methods of halide ions (X(-) = F(-), Cl(-), Br(-) and I(-)) by electrospray ionization mass spectrometry (ESIMS) were developed, where negative ions of the ternary complexes of group-13 elements, nitrilotriacetic acid (NTA), and halides were measured. In particular, these halides were simultaneously determined by measuring [InX(nta)](-), and the limits of detection (LODs) were 1.1 μmol dm(-3) for F(-), 0.32 μmol dm(-3) for Cl(-), 3.8 nmol dm(-3) for Br(-), and 1.6 nmol dm(-3) for I(-), respectively. This approach was extended to the determination of CN(-), where the ternary complex of Cu(II), CN(-) and 4-(2-pyridylazo)resorcinol (PAR), i.e., [(63)Cu(II)(CN)(par)](-) (m/z 302) was measured. The LOD for CN(-) was 20 nmol dm(-3).     

Anion conductive block poly(arylene ether)s: synthesis, properties, and application in alkaline fuel cells

Anion conductive aromatic multiblock copolymers, poly(arylene ether)s containing quaternized ammonio-substituted fluorene groups, were synthesized via block copolycondensation of fluorene-containing (later hydrophilic) oligomers and linear hydrophobic oligomers, chloromethylation, quaternization, and ion-exchange reactions. The ammonio groups were selectively introduced onto the fluorene-containing units. The quaternized multiblock copolymers (QPEs) produced ductile, transparent membranes. A well-controlled multiblock structure was responsible for the developed hydrophobic/hydrophilic phase separation and interconnected ion transporting pathway, as confirmed by scanning transmission electron microscopic (STEM) observation. The ionomer membranes showed considerably higher hydroxide ion conductivities, up to 144 mS/cm at 80 °C, than those of existing anion conductive ionomer membranes. The durabilities of the QPE membranes were evaluated under severe, accelerated-aging conditions, and minor degradation was recognized by (1)H NMR spectra. The QPE membrane retained high conductivity in hot water at 80 °C for 5000 h. A noble metal-free direct hydrazine fuel cell was operated with the QPE membrane at 80 °C. The maximum power density, 297 mW/cm(2), was achieved at a current density of 826 mA/cm(2).     

Catalytic asymmetric allylation of 3,4-dihydroisoquinolines and its application to the synthesis of isoquinoline alkaloids

A catalytic asymmetric allylation of 3,4-dihydroisoquinoline was carried out with allyltrimethoxylsilane-Cu as the nucleophile in the presence of DTBM-SEGPHOS as the chiral ligand to afford corresponding chiral 1-allyltetrahydroisoquinoline derivatives in good yield and stereoselectivity. The allyl adduct thus obtained was applied to the synthesis of several isoquinoline alkaloids such as crispine A and homolaudanosine. The reaction was further used for the synthesis of the isoquinoline moiety of schulzeine A.     

Conditions for Choquet integral representation of the comonotonically additive and monotone functional

If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed.