一个关于肿瘤治疗的自由边界问题的数学分析

§1Introduction Avarietyofpartialdifferentialequationmodelsfortumorgrowthortherapyhave beendevelopedinthelastthreedecades[see2,3,16-18,21-26].Mostofthosemodelsare informoffreeboundaryproblems,andareverydiversified.Rigorousmathematical analysisofsuchfreeboundaryproblemshasdrawngreatinterest,andmanyinteresting resultshavebeenestablished[4-15].Inthispaperwedealwithamathematicalmodeldescribingtumorchemotherapy.In thismodelthetumorisviewedasdenselypacked,radially-symmetricsphereofradiusR(t)contain…     

Synthesis of functional polymers bearing pendant mono-and oligo-saccharide residues

The present paper focuses on (i) a new synthetic methodology to prepare vinyl ether-based synthetic glycoconjugates (glycopolymers) with well-controlled structure, and on (ii) the application of glycopolymers bearing modified disaccharide residue as thermotropic liquid crystalline (LC) materials. Two vinyl ethers (VEs) having pendant glucose residues with their hydroxyl functions protected by acetyl and isopropylidene groups, respectively, were found to undergo living cationic polymerization initiated by a HI/ZnI2-initiating system. Deprotection of the resultant monodisperse polymers led to water-soluble polymers bearing a pendant glucose residue. Sequential living block copolymerization of glucose-containing VE and alkyl VE, and subsequent deprotection afforded an amphiphilic block copolymer of well-controlled structure. Transmission electron microscopic observation of its cast thin film revealed microphase-separated surface morphologies that varied with varying segment composition ratio. A VE substituted with a heptadecanoated cellobiose pendant was independently prepared, and was cationically polymerized to give a thermotropic LC polymer. From X-ray analysis, the mesophase was assigned to a discotic columnar in type, in which each main chain, extended due to the steric repulsion between the neighboring bulky pendants, was surrounded by three discotic columns.     

Spin dynamics in conducting polymers

It is demonstrated that spin dynamics study is useful for what kinds of systems, on what theoretical basis of analysis, with what kinds of techniques and to get what kinds of information, showing a nice example of polyacetylene. Usefulness of electron spin resonance (ESR) study is stressed especially in a wide frequency range from 5 to 24000 MHz.     

Biomimetic oxidation of thiol and application to odor-removing fiber

The oxidation of HO-CH₂-CH₂-SH (RSH) by molecular oxygen and Fe(III)- as well as Co(II)-multicarboxyphthalocyanine and the mechanism in homogeneous aqueous system were investigated. As application to enzyme-like heterogeneous catalysts, Fe(III)-as well as Co(II)-octacarboxyphthalocyanine were supported on amorphous enriched rayon staple fiber and their enzyme-like activities were estimated. These fibers were applicated to new odor-removers acting as artificial enzyme systems.     

Energy Storage by Poly(<Emphasis Type="Italic">o</Emphasis>-anisidine) Matrix During Oxidative Hydrolysis

The chromaticity of poly(o-anisidine) (POAN) doped with different acids (HA), HA-doped POAN, has been studied by the spectrophotometric technique and the results were substantiated by molecular mechanics (MM+) calculations. The observed absorbance decrease (λ around 720 nm, dark green coloration) with increasing concentration of the inorganic oxidizing agent (KMnO₄) can be attributed to the oxidative hydrolysis mechanism. The oxidative hydrolysis constant (K _h) is highly dependent on the strength of the acid used. The HClO₄-doped POAN matrix has the ability to store about 128.878 kJ⋅g⁻¹ chromogenic energy (CE) at the wavelength 720 nm in a condensed lightweight form. MM+ calculations suggest that the potential energy (PE) in kJ⋅mol⁻¹ of the optimum molecular geometric (OMG) structure of the HClO₄-doped POAN matrix is at least two (2.052) times more stable than the OMG of the base form (POAN-EB) of the POAN matrix. Kinetic parameters of the oxidative hydrolysis reaction of the HA-doped POAN matrix were deduced from absorbance variations with time. The results of computer-oriented kinetic analysis indicate that the rate-controlling step for HA-doped POAN oxidative hydrolysis is governed by the Ginstling-Bronshein equation that represents three-dimensional diffusion (D4). Activation parameters for the oxidative hydrolysis of the HClO₄-doped POAN matrix were computed and discussed.     

M@B<Subscript>9</Subscript> and M@B<Subscript>10</Subscript> molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12, and 13 metals (M=Ag,Au, Cd,Hg, In,Tl)

A density functional and ab initio theory investigation on M@B₉ and M@B₁₀ molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12 and 13 metals (M=Ag, Au, Cd, Hg, In, Ti) has been performed. These unusual clusters all prove to be true minima on the potential energy surfaces of the systems and σ+π double aromatic in nature. The first two vertical one-electron detachment energies of M@B₁₀⁻ (M=Ag, Au) anions and first two ionization potentials of M@B₉ (M=Ag, Au) and M@B₁₀ (M=Cd, Hg) neutrals were calculated to aid future experiments. The cluster complexes designed in this work may expend the domain of planar hyper-coordinate elements to include heavy group 11, 12, and 13 metals and serve as interesting candidates to be targeted in experiments. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by the National Natural Science Foundation of China (Grant No. 20873117)     

Analysis of viscosity abnormalities of polyelectrolytes in dilute solutions

It was found that the interface effects in viscous capillary flow influenced the process of viscosity measurement greatly,and the abnormal viscosity behaviors of polyelectrolytes as well as neutral polymers in dilute solution region were ascribed to interface effect.According to this theory,we have reviewed the previous viscosity data of derivatives of poly-2- vinylpyridine reported by Maclay and Fuoss first.Then,the abnormal viscosity behaviors of a series of sodium polystyrene sulfonate samples with various molecular weights in dilute aqueous solutions were studied further.The solute adsorption behaviors and structural information of polymers have been discussed carefully.