The Numerical Solution of Laplace's Equation on a Wedge

Laplace's equation is considered on regions in the plane, withthe boundary having corners; and the double-layer potentialis used to derive a solution. The essential difficulties, boththeoretically and numerically, are reduced to the case in whichthe boundary is a simple open wedge. The theoretical behaviourof the double layer integral equation is studied explicitly,and then piecewise linear and piecewise quadratic collocationmethods are applied to the numerical solution of the equation.The major question of interest is the stability of the inversesof the approximating equations. The behaviour of the numericalmethods is somewhat surprising, and it is much better than pastanalyses would have led one to expect.     

拟桶式空间的强对偶空间值的向量测度

证明了在某种紧性条件下拟桶式空间的强对偶空间值的向量测度的唯一存在性。     

On a Class of Similarity Solutions of the Equation ut(|u|m-1ux)x with m -1

Self similar solutions of the one-dimensional porous-medium equation are studied in thispaper. These solutions emerge from initial values that consistof two onstant states: one non-positive for x < 0 and onenon–negative for x > 0. With a diffusivity of the form we consider, for m > 0 sign-change solutions, and for m m (–1,0] non-negativesolutions.The method we use is based on a transformation whichmaps the ordinary differential equation for f into a singularelliptic boundary-value problem with Dirichlet conditions. Specialattention is given to the behaviour of f near zero. We alsopresent a number of numerical results.     

COLLECTIVE DECISION MAKING IN AN INTERNATIONAL RIVER POLLUTION MODEL

In this paper, we study international river pollution problems. We introduce a model in which countries located along a river from upstream to downstream derive benefits from causing pollution, but also incur environmental costs from experiencing its own pollution and the pollution of all its upstream countries. The total welfare, being the sum of all benefits minus the sum of all costs, is maximized when all countries cooperate. Several principles from international water law are applied to find reasonable and fair distributions of the total welfare that can be obtained under full cooperation. Such a distribution of the welfare at efficient pollution levels can be implemented by monetary compensations.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES—VIII. CELLULAR DISTRIBUTION INV–79 CHINESE HAMSTER CELLS AND PHOTOTOXICITY OF SELECTIVELY SULFONATED ALUMINUM PHTHALOCYANINES

Abstract— Water soluble chloro aluminum phthalocyanines sulfonated to different degrees are studied for phototoxicity and cellular distribution inV–79 Chinese hamster cells. The more hydrophobic disulfonated dyes, with sulfonate substituents on adjacent benzyl groups of the phthalocyanine ring structure, exhibited the best cell penetrating properties and the highest phototoxicity. Fluorescence microscopy revealed that the dye was uniformly distributed in the cytoplasm but absent in the nucleus. The greater cell membrane penetrating properties of the lower as compared to the higher sulfonated dyes are attributed to the amphiphilic nature of the former.     

对四-2,3-吡啶并紫菜嗪铬的薄膜电极的光电化学研究

Photocurrent spectra and photoluminescence measurements of the electrode covered by a thin film of chromium tetra-2,3-pyridinoporphyrazine by conventional 3-electrode system method have been performed. The cathodic photocurrent has been measured. The shape of the photocurrent spectrum is similar to that of photoluminescence spectrum. Their intensities change as a function of the applied potential. Two photoluminescence peaks are located at about 470 nm and 520 nm. The results indicate that the thin film behaves like a p-type semiconductor with a band gap width of about 2 eV.     

EXCITATION OF CHLOROPLASTS IN Euglena gracilis IN THE ABSENCE OF LIGHT

Abstract— Challenging Euglena gracilis —a unicellular microorganism that contains chloroplasts—with phenylacetaldehyde induces malondialdehyde formation, sustained red emission and Hill activity. In chloroplasts, phenylacetaldehyde appears to undergo peroxidase catalyzed oxidation to formic acid and triplet benzaldehyde; the latter or, less likely, a precursor thereof promotes lipid peroxidation. Triplet benzaldehyde and/or the excited species formed in lipid peroxidation transfer energy to the chlorophylls. This explanation also applies to spinach chloroplasts preparations, thus accounting for the previous unexplained observation that phenylacetaldehyde induced sustained red emission and Hill activity. A homogeneous picture is now available regarding the intracellular generation of excited states and concomitant excitation of built-in structures.     

CHEMIEXCITATION IN THE PEROXIDATIVE METABOLISM OF N- METHYLCARBAZOLE: MECHANISTIC IMPLICATIONS

Abstract –The peroxidative metabolism of TV-methylcarbazole emits light independently of the presence of oxygen. It is likely that two chemiexcited transients are formed by electron transfer to the activated peroxidase, the cation radical by one electron transfer and a cation biradical by two electron transfer consistent with the failure to observe horseradish peroxidase-II in the steady state of the reaction. In the spectral range investigated (390–700 nm) the observed emission (570–700 nm) is ascribed to the biradical, as the latter is equivalent to an excited state of the postulated iminium cation.
While lipoxygenase has no effect upon JV-methylcarbazole, it markedly enhances the emission if peroxidase is present. This effect requires oxygen and is ascribed to an excited product formed by lipoxygenase acting upon an intermediate hydroperoxide of the aerobic process promoted by peroxidase.     

The onset of thermal runaway in partially insulated or cooled reactors

The conditions for the onset of thermal runaway in partiallyinsulated or cooled reactors are investigated. The temperaturein the reactor is taken to satisfy a nonlinear elliptic equationand the reaction is modelled by an Arrhenius heat generationterm with finite activation energy. To determine the onset ofthermal runaway, the method of matched asymptotic expansionsis used to derive expressions for the critical Frank-Kamenetskiiparameter _c() for reactors containing either a small coolingrod or having a small cooling patch on their boundary. The theoryused to determine _c() is an extension of the results of Wardand Keller (1991). These previous results of Ward and Kellerare also extended to the case of finite activation energiesby using a numerical scheme to evaluate the coefficients inthe asymptotic results for _c(). In some special cases, the asymptoticexpansions for _c() are compared with numerical results for _c(),and clear agreement is found.