关于Zd中离散填充指标的注记

探讨了Z^d中离散填充指标的一些性质，给出了Z^d中离散填充维数的一个等价定义．     

R￣d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题（定理１和定理２），进而寻求Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency

Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fraction0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.     

Analysis of Organic Compounds in Antarctic Snow and Their Origin

Abstract

Organic compounds extractable with n-hexane were identified and quantitatively determined in pack, surface and deep snow samples taken at different depths and collected at several altitudes above sea level from Antarctica during the 1993/94 Italian expedition. The comparison between the composition of organic compounds in snow and the ones in pack and sea-water samples pointed out that the three matrices substantially contain the same biogenic and anthropogenic organic compounds. The contribution of marine aerosol to organic content in the snow is confirmed by the enrichment ratios calculated for the more representative classes of identified compounds (n-alkanes, phthalates and low molecular weight alkylbenzenes). The changes in the composition of organic compounds in snow as the altitude increases seem to depend on the dimensional spectrum of the aerosol. Thus, smallest particles, richest in surfactant material, reach the highest altitudes.     

Comparison of Proton Acceptor and Proton Donor Properties of H2O and H2O2 in Organic Crystals of Drug-like Compounds: Peroxosolvates vs. Crystallohydrates

Two new peroxosolvates of drug-like compounds were synthesized and studied by a combination of X-ray crystallographic, Raman spectroscopic methods, and periodic DFT computations. The enthalpies of H-bonds formed by hydrogen peroxide (H₂O₂) as a donor and an acceptor of protons were compared with the enthalpies of analogous H-bonds formed by water (H₂O) in isomorphic (isostructural) hydrates. The enthalpies of H-bonds formed by H₂O₂ as a proton donor turned out to be higher than the values of the corresponding H-bonds formed by H₂O. In the case of H₂O₂ as a proton acceptor in H-bonds, the ratio appeared reversed. The neutral O∙∙∙H-O/O∙∙∙H-N bonds formed by the lone electron pair of the oxygen atom of water were the strongest H-bonds in the considered crystals. In the paper, it was found out that the low-frequency Raman spectra of isomorphous crystalline hydrate and peroxosolvate of N-(5-Nitro-2-furfurylidene)-1-aminohydantoin are similar. As for the isostructural hydrate and peroxosolvate of the salt of protonated 2-amino-nicotinic acid and maleic acid monoanion, the Raman spectra are different.     

Effect of Natural Deep Eutectic Solvents on trans-Resveratrol Photo-Chemical Induced Isomerization and 2,4,6-Trihydroxyphenanthrene Electro-Cyclic Formation

trans-Resveratrol is a natural bioactive compound with well-recognized health promoting effects. When exposed to UV light, this compound can undergo a photochemically induced trans/cis isomerization and a 6π electrochemical cyclization with the subsequent formation of 2,4,6-trihydroxyphenanthrene (THP). THP is a potentially harmful compound which can exert genotoxic effects. In this work we improved the chromatographic separation and determination of the two resveratrol isomers and of THP by using a non-commercial pentafluorophenyl stationary phase. We assessed the effect of natural deep eutectic solvents (NaDES) as possible photo-protective agents by evaluating cis-resveratrol isomer and THP formation under different UV-light exposure conditions with the aim of enhancing resveratrol photostability and inhibiting THP production. Our results demonstrate a marked photoprotective effect exerted by glycerol-containing NaDES, and in particular by proline/glycerol NaDES, which exerts a strong inhibitory effect on the photochemical isomerization of resveratrol and significantly limits the formation of the toxic derivative THP. Considering the presence of resveratrol in various commercial products, these results are of note in view of the potential genotoxic risk associated with its photochemical degradation products and in view of the need for the development of green, eco-sustainable and biocompatible resveratrol photo-stable formulations.     

Transfer of charge in liquid alloys

Hard sphere diameters of liquid alkali metal alloys (Na-Cs and K-Rb) are calculated at 373 K ensuring the minimum Helmholtz free energy of the system. These diameters are then used to fix the packing density of the alloy. On alloying, the hard sphere diameters of Na in Na-Cs and K in K-Rb alloys expand whereas those of Cs and Rb contract.     

Investigating magnetorheological properties of a mixture of two types of carbonyl iron powders suspended in an ionic liquid

In this work, properties of a magnetorheological (MR) fluid, prepared by dispersing a mixture of two types of carbonyl iron powders (CIPs) of different sizes, in an ionic liquid (N,N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium tetrafluoroborate) that is stable from 9 °C to ca. 300 °C, have been investigated. At first, the random packing density of the mixture was computed as function of mixing ratio of CIP, in order to find out the tendency of the variation. Next, several mixtures, all having the same weight, were prepared at various mixing ratios and dispersed in the ionic liquid, in order to experimentally find the most suitable mixing ratio of CIP. Then, the magnetic clusters of the synthesized MR fluids were observed by using a digital microscope equipped with two permanent magnets, whereas the MR properties were investigated by using a rotation viscometer equipped with a solenoid coil. The experimental results pointed out that the MR fluid with 60 wt% fraction of large particles exhibited the highest MR response.     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.