Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

Science China Mathematics - Liouville first passage percolation (LFPP) with the parameter ξ > 0 is the family of random distance functions $${\left\{ {D_h^\epsilon} \right\}_{\,...     

Intramolecular motion of polystyrene in a theta solvent

Photon correlation spectroscopy has been used to study intramolecular motion in five polystyrene samples (M_w = 2.88 × 10⁶ to 9.35 × 10⁶) in a theta solvent (cyclohexane at 34.5° C). The relaxation times of the first normal mode are greater than those reported elsewhere, but agree well with the values calculated by Zimm for the bead-and-spring model, and modified for the light-scattering case.     

Comparison of δ81Br and δ37Cl composition of volatiles,salt precipitates,and associated water in terrestrial evaporative saline lake systems

This study provides the first characterization of the variability of bromine and chlorine stable isotopic composition in evaporites, associated residual brines, and shoreline gases in terrestrial evaporative saline lakes. The lakes investigated here are groundwater discharge locations, and include both potash-rich alkaline lakes and sodic-dominated neutral pH lakes at a variety of salinities and evaporative stages. The chlorine and bromine isotope systems behave consistently different during evaporative salt precipitation, with ³⁷Cl more enriched in the salt than in the fluid, but ⁸¹Br more enriched in the fluid compared with the precipitated salt. The ⁸¹Br concentration of shore off-gassing was even smaller than mineral precipitate compositions. The trends observed for bromine isotopes are surprising compared with published laboratory studies, indicating that a process besides inorganic mineral precipitation is affecting δ⁸¹Br. Additional processes explored include diffusion, salt deflation, microbial and photolytic conversion to the gas phase, and oxidative bromination of organic matter.

Dedicated to Professor Peter Fritz on the occasion of his 80th birthday     

Spectral element method for viscoelastic flows in a planar contraction channel

A new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic fluid flows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four‐to‐one contraction channel for a fluid governed by an Oldroyd‐B constitutive equation. The behaviour of the Oldroyd‐B fluids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions. Copyright © 2003 John Wiley & Sons, Ltd.     

Intramolecular relaxation of polystyrene in a theta solvent by photon-correlation spectroscopy

Photon-correlation spectroscopy has been used to measure the diffusion coefficient D and first-mode intramolecular relaxation time τ₁ of polystyrene in a theta solvent, cyclohexane at 34.5°C. Measurements were made on five narrow fractions ($\text{M}$_w = 2.88 × 10⁶ to 9.35 × 10⁶) as a function of concentration c, in the dilute regime. D varied linearly with c, D = D_o (I + k_Dc), with D_o = (1.4 ± 0.2) × 10^?4$\text{M}{}_{\mathrm{w}}{}^{\mathrm{?(0.508\pm 0.007)}}$ cm² s^?1. Although the values obtained for τ₁ were reproducible to within 5%, no systematic variation with c was detected. The results are fitted by the relation τ₁ = (7.7 ? 0.3) × 10^?8$\text{M}{}_{\mathrm{w}}{}^{\mathrm{(1.42\pm 0.05)}}$ μs, which agrees well with the theoretical expression of Zimm for the non-draining bead-and-spring model, modified for the light-scattering case.     

The Role of Serotonin in Breast Cancer Stem Cells

Breast tumors were the first tumors of epithelial origin shown to follow the cancer stem cell model. The model proposes that cancer stem cells are uniquely endowed with tumorigenic capacity and that their aberrant differentiation yields non-tumorigenic progeny, which constitute the bulk of the tumor cell population. Breast cancer stem cells resist therapies and seed metastases; thus, they account for breast cancer recurrence. Hence, targeting these cells is essential to achieve durable breast cancer remissions. We identified compounds including selective antagonists of multiple serotonergic system pathway components required for serotonin biosynthesis, transport, activity via multiple 5-HT receptors (5-HTRs), and catabolism that reduce the viability of breast cancer stem cells of both mouse and human origin using multiple orthologous assays. The molecular targets of the selective antagonists are expressed in breast tumors and breast cancer cell lines, which also produce serotonin, implying that it plays a required functional role in these cells. The selective antagonists act synergistically with chemotherapy to shrink mouse mammary tumors and human breast tumor xenografts primarily by inducing programmed tumor cell death. We hypothesize those serotonergic proteins of diverse activity function by common signaling pathways to maintain cancer stem cell viability. Here, we summarize our recent findings and the relevant literature regarding the role of serotonin in breast cancer.     

Reaction of Hydantoin with Boronic Acids

We have examined the reaction of hydantoin (=imidazolidine‐2,4‐dione) with (formylphenyl)boronic acids, where the addition of a boronic acid group is hoped to increase bioactivities. Addition of (2‐formylphenyl)boronic acid to hydantoin gave an unexpected azaborine compound, which presumably arises by initial formation of the (phenylmethylidene)hydantoin, with subsequent loss of H₂O to give the cyclized product. Reactions of (3‐formylphenyl)‐ and (4‐formylphenyl)boronic acids with hydantoin gave the corresponding [(Z)‐phenylmethylidene]hydantoins in good‐to‐excellent yields. Attempts to use (3‐formylthiophen‐2‐yl)boronic acid gave a product where the boronic acid group has been cleaved.     

The use of slater orbitals in variational calculations involving one-electron green's functions

In this paper an application of a minimum principle proposed for electronic systems by Hall, Hyslop and Rees, [1] and [2], is considered. It is shown that the evaluation of the required two-centre molecular integrals involving one-electron Green's functions may be facilitated by the introduction of a particular class of trial functions. These functions incorporate the potential energy of the system as a weighting factor and Slater-type orbitals are then used as a basis set. The evaluation of the resulting integrals is discussed and illustrative calculations for the H ₂ ⁺ ion are presented.