The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type

The solutions to the Riemann problem for a nonsymmetric system of Keyfitz-Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.     

Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one‐dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the δ‐shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one‐dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx ε tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright © 2009 John Wiley & Sons, Ltd.     

The Suitability and Usage of 18O and Chloride as Natural Tracers for Bank Filtrate at the Middle River Elbe

Abstract

Flow times and infiltration behaviour are very important for water extraction from riverbank filtration. Both the chloride content and the isotopic composition of oxygen (δ¹⁸O) were found to be suitable indicators for the conditions encountered in the middle course of the River Elbe near Torgau. The ranges for Elbe water were measured to be 20–43 mg Cl/l (1995-97) and -11 to -8.5‰ δ¹⁸O (1993-97). Both methods permitted flow-time spectra at two adjacent sampling profiles incorporating river and production wells to be obtained, indicating the preferred flow paths and the vertical extension of the riverbank filtrate plume in the aquifer. However, since the differences between the mean values for river water and regional groundwater were too small the percentage of river water abstracted from production wells could not be calculated.     

Book Reviews

Nuclear Chemistry: O. Navratil, J. Hala, R. Kopunec, F. Macasek, V. Mikulaj, L. Leseticky, Translated from Czech to English by J. Hala and P. Huth, Ellis Horwood PTR Prentice Hall, New York (Physical Chemistry Series) and Academia Publishing House, Prague 1992, 389 pp.

Limitation of Exposure to Ionizing Radiation: Recommendations of the National Council on Radiation Protection and Measurements. NCRP Report No. 116, Bethesda, Maryland, 1993,88 pp.     

An Itô Formula of Generalized Functionals and Local Time for Fractional Brownian Sheet

Abstract

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameters H ₁, H ₂ ∈ (0,1). As an application, we give the integral representations for two versions of local times of a fractional Brownian sheet, respectively.     

Human Health Risk Surveillance Through the Determination of Organochlorine Pesticides by High-Performance Liquid Chromatography in Water,Sediments, and Fish from the Chenab River,Pakistan

The current study assessed the spatiotemporal variations and human health surveillance associated with organochlorine pesticide (OCP) contamination in water, sediments, and fish from Chenab River, Pakistan. The OCP determinations were performed using high-performance liquid chromatography with a reverse-phase C18 column. The total OCP levels ranged from 13.33 to 274.59?ng/L in water, 4.63 to 239.11?ng/g in sediments, and 23.79 to 387.12?ng/g in fish species. The overall pattern of mean OCP concentrations followed the order as ΣDDTs?>?Σendosulfan?>?aldrin and OCP pollution pattern among the headworks were Khanki Barrage?>?Qadirabad Barrage?>?Trimmu Barrage?>?Marala Barrage in all three environmental matrixes during both seasons. The estimated daily intake (EDI) for ∑OCPs was found to be 22.44?ng/kg/day. The hazard ratios calculated to assess the carcinogenic risk indicated that the values for ∑DDT and aldrin at the 95th percentile concentrations were greater than one, indicating the probability of carcinogenic risk occurrence of one in million populations due to fish consumption. Therefore, these high levels of OCPs and carcinogenic risk through fish consumption highlight the needs of immediate elimination of OCPs from riverine environment of Chenab River and we recommend long-term monitoring-based freshwater ecological studies to be conducted in the study area.     

Ferric nitrate-promoted oxidative esterification of toluene with N-hydroxyphthalimide: Synthesis of N-hydroxyimide esters

A ferric nitrate-promoted cross-dehydrogenative coupling reaction of N-hydroxyphthalimide (NHPI) with toluene derivatives is reported. The reaction proceeded smoothly using molecular oxygen as an oxidant, providing an efficient method for the synthesis of N-hydroxyimide esters. Furthermore, a plausible mechanism was proposed.     

Incomplete Delta Functions

By applying projection operators to state vectors of coordinates, we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call incomplete delta functions. We show that this class of functions satisfy identities similar to those satisfied by the Dirac delta function. The incomplete delta functions may be employed advantageously in projected subspaces and in the link between functions defined on the whole space and the projected subspace. We apply a similar procedure to finite-dimensional vector spaces for which we define incomplete Kronecker deltas. Dispersion relations for the momenta are obtained and sums over poles are defined and obtained with the aid of differences of incomplete delta functions.