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.     

Untersuchung der tribologischen Eigenschaften von Nutzfahrzeugmotoren unter besonderer Berücksichtigung der Luftfiltration

Es wurde eine unter Betriebsverhältnissen anwendbare Prüfmethode für die Bestimmung der Verschleβeigenschaften von Verbrennungsmotoren mit Hilfe der Gammaspektrometrie der neutronenaktivierten Verschleiβprodukte ausgearbeitet und die die Lebensdauer begrenzende Wirkung des abrasiven Verschleiβes festgestellt. Durch Verbesserung der Luftfilterung konnte die potentielle Lebensdauer der Motoren gut angenähert, und es konnten die Verunreinigung des Schmieröls vermindert und die Dauer der Ölwechselperiode verdoppelt werden.     

Stress-induced textures in polymers

The effect of an applied stress on the annealing texture of polyethylene is demonstrated by means of stress annealing experiments. Cold-drawn polyethylene specimens were annealed for various times at 126°C with and without a compression stress of 0.4 kg/mm² normal to the drawing direction. The observed change in the annealing texture resulting from the compression stress indicates that stress-induced alignment of the crystalline regions in the polyethylene occurs (stress-induced texture). The alignment may be understood in terms of the elastic energy stored in the material during annealing. The stored elastic energy is minimized by aligning the crystallites such that the crystallographic direction of lowest modulus is parallel to the direction of the applied stress. The importance of this observation for the interpretation of the high-temperature deformation textures of polymers is discussed.     

Critical curves for fast diffusive polytropic filtration equations coupled through boundary

This article deals with the critical curve of a fast diffusive polytropic filtration system coupled at the boundary condition. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results.     

Finite-dimensional simple modular Lie superalgebra ℳ

A new family of finite-dimensional simple modular Lie superalgebra ? is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601–3619]. The simplicity and generators of ? are discussed and the derivation superalgebra of ? is characterized. Furthermore, the invariance of the nonnatural filtration of ? is determined by the method of minimal dimension of image spaces.     

Discrete-Time BSDEs with Random Terminal Horizon

This article studies the theory of discrete-time backward stochastic differential equations (also called BSDEs) with a random terminal time, which is not a stopping time. We follow Cohen and Elliott [2 Cohen , S.N. , and Elliott , R.J. 2010 . A general theory of finite state backward stochastic difference equations . Stochastic Processes and Their Applications 120 ( 4 ): 442 – 466 .[Crossref], [Web of Science ®] , [Google Scholar]] and consider a reference filtration generated by a general discrete-time finite-state process. The martingale representation theorem for essentially bounded martingales under progressively enlarged filtration is established. Then we prove the existence and uniqueness theorem of BSDEs under enlarged filtration using some weak assumptions of the driver. We also present conditions for a comparison theorem. Applications to nonlinear expectations and optimal design of dynamic default risk are explored.     

Critical extinction exponents for a polytropic filtration equation with absorption and source

In this paper, instead of energy methods, we apply the supersolution and subsolution methods to investigate the critical extinction exponents for a polytropic filtration equation with absorption and source, and improve the results of Mu et al. (J. Math. Anal. Appl. 2012; 391 :429–440). Copyright © 2012 John Wiley & Sons, Ltd.     

Varieties of strange plane curves

Abstract

Let A be a commutative ring with identity, let X, Y be indeterminates and let F(X,Y), G(X, Y) ∈ A[X, Y] be homogeneous. Then the pair F(X, Y), G(X, Y) is said to be radical preserving with respect to A if Rad((F(x, y), G(x, y))R) = Rad((x,y)R) for each A-algebra R and each pair of elements x, y in R. It is shown that infinite sequences of pairwise radical preserving polynomials can be obtained by homogenizing cyclotomic polynomials, and that under suitable conditions on a ?-graded ring A these can be used to produce an infinite set of homogeneous prime ideals between two given homogeneous prime ideals P ? Q of A such that ht(Q/P) = 2.     

Valuation Extensions of Filtered and Graded Algebras

In this note we relate the valuations of the algebras appearing in the noncommutative geometry of quantized algebras to properties of sublattices in some vector spaces. We consider the case of algebras with PBW-bases and prove that under some mild assumptions, the valuations of the ground field extend to a noncommutative valuation. Later we introduce the notion of F-reductor and graded reductor and reduce the problem of finding an extending noncommutative valuation to finding a reductor in an associated graded ring having a domain for its reduction.