Nonhomogeneous Dirichlet Problems for Degenerate Parabolic-Hyperbolic Equations

The aim of the paper is to give a formulation for the initial boundary value problem of parabolic-hyperbolic type in the case of nonhomogeneous boundary data a ₀. Here u=u(x,t)∈?, with (x,t)∈Q=Ω× (0,T), where Ω is a bounded domain in ? ^N with smooth boundary and T>0. The function b is assumed to be nondecreasing (allowing degeneration zones where b is constant), Φ is locally Lipschitz continuous and g∈L ^∞(Ω× (0,b)). After introducing the definition of an entropy solution to the above problem (in the spirit of Otto [14]), we prove uniqueness of the solution in the proposed setting. Moreover we prove that the entropy solution previously defined can be obtained as the limit of solutions of regularized equations of nondegenerate parabolic type (specifically the diffusion function b is approximated by functions b ^? that are strictly increasing). The approach proposed for the hyperbolic-parabolic problem can be used to prove similar results for the class of hyperbolic-elliptic boundary value problems of the form again in the case of nonconstant boundary data a ₀.     

Synthesis,crystal structure and fluorescence properties of two dinuclear zinc(II) complexes incorporating tridentate (NNO) Schiff bases

Reactions of hydrated zinc(II) trifluoroacetate and sodium azide with two tridentate Schiff bases HL¹ (2-((E)-(2-(dimethylamino)ethylimino)methyl)-4-chlorophenol) and HL² (2-((E)-(2-(dimethylamino)ethylimino)methyl)-4-bromophenol) under the same reaction conditions yielded two dinuclear isostructural zinc(II) complexes, [Zn(L¹)(N₃)]₂ (1) and [Zn(L²)(N₃)]₂ (2), respectively. The complexes were characterized systematically by elemental analysis, UV–Vis, FT-IR, and ¹H NMR spectroscopic methods. Single-crystal X-ray diffraction studies reveal that each of the dinuclear complexes consists of two crystallographically independent zinc(II) ions connected by double bridging phenoxides. All zinc(II) ions in 1 and 2 are surrounded by similar donor sets and display distorted square–pyramidal coordination geometries. The ligands and complexes reveal intraligand ¹(π → π*) flourescence. The enhancement of the fluorescence intensities for the complexes compared to the ligands indicates their potential to serve as photoactive materials.     

Linear sets in the projective line over the endomorphism ring of a finite field

Let \({{\mathrm{{PG}}}}(1,E)\) be the projective line over the endomorphism ring \( E={{\mathrm{End}}}_q({\mathbb F}_{q^t})\) of the \({\mathbb F}_q\)-vector space \({\mathbb F}_{q^t}\). As is well known, there is a bijection \(\varPsi :{{\mathrm{{PG}}}}(1,E)\rightarrow {\mathcal G}_{2t,t,q}\) with the Grassmannian of the \((t-1)\)-subspaces in \({{\mathrm{{PG}}}}(2t-1,q)\). In this paper along with any \({\mathbb F}_q\)-linear set L of rank t in \({{\mathrm{{PG}}}}(1,q^t)\), determined by a \((t-1)\)-dimensional subspace \(T^\varPsi \) of \({{\mathrm{{PG}}}}(2t-1,q)\), a subset \(L_T\) of \({{\mathrm{{PG}}}}(1,E)\) is investigated. Some properties of linear sets are expressed in terms of the projective line over the ring E. In particular, the attention is focused on the relationship between \(L_T\) and the set \(L'_T\), corresponding via \(\varPsi \) to a collection of pairwise skew \((t-1)\)-dimensional subspaces, with \(T\in L'_T\), each of which determine L. This leads among other things to a characterization of the linear sets of pseudoregulus type. It is proved that a scattered linear set L related to \(T\in {{\mathrm{{PG}}}}(1,E)\) is of pseudoregulus type if and only if there exists a projectivity \(\varphi \) of \({{\mathrm{{PG}}}}(1,E)\) such that \(L_T^\varphi =L'_T\).     

Pointwise Green Function Bounds for Shock Profiles of Systems with Real Viscosity

Following the pointwise semigroup approach of [ZH,MZ.1], we establish sharp pointwise Green function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic-parabolic systems of conservation laws of dissipative type, under the necessary assumptions ([Z.1,Z.3,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave; transversality of the connecting profile; and hyperbolic stability of the corresponding ideal shock of the associated inviscid system, with no additional assumptions on the structure or strength of the shock. These bounds are used in a companion paper [MZ.2] to establish nonlinear stability of small-amplitude Lax shocks of symmetrizable hyperbolic-parabolic systems.     

Liquid chromatography: a tool for the analysis of metal species

An overview is presented of classic and more recent applications of liquid chromatography for the analysis of metal species. The different approaches involving ion-exchange, ion-pair, and chelation separation mechanisms are discussed as well as the new philosophy of simply removing interferents before specific detections of metal ions (alkali and alakaline earths, rare earths, heavy and transition metals). New more selective materials enabling difficult separations and studies on multimodal or hyphenated techniques for metal speciation (e.g. arsenic and chromium) are considered.     

Analytical techniques for the separation and determination of transuranium element ultratraces in depleted uranium ammunitions

It is well known that ammunition containing depleted uranium (DU) was used by NATO during the Balkan conflict. To evaluate the DU origin (natural uranium enrichment or spent nuclear fuel reprocessing) it is necessary to check the presence of activation products (²³⁶U, ^239+240Pu, ²⁴¹Am, ²³⁷Np, etc.) in the ammunition.

Every transuranium element (TRU) was separated from the uranium matrix by extraction chromatography with microporous polyethylene (Icorene) supporting suitable stationary phases. Plutonium was separated by tri-n-octylamine (TNOA). ²⁴¹Am was separated by TNOA and di(2ethylhexylphosphoric) acid (HDEHP). Neptunium also was separated by tri-n-octylamine using different conditions. After elution, the TRU elements were electroplated and counted by alpha spectrometry. The TRU decontamination factors from uranium were higher than 10⁶.

The final chemical yields ranged from 50 to 70%. The detection limit was 1?Bq?kg^?1 for 0.10?g ammunition; ^{239 + 240}Pu and ²⁴¹Am concentrations in two penetrators were 26 and 70?Bq?kg^?1 and <1 and 3.4?Bq?kg^?1, respectively; the ²³⁷Np concentration in one penetrator was 30.1?Bq?kg^?1.

The presence of these anthropogenic radionuclides in the penetrators indicates that at least part of the uranium originated from the reprocessing of nuclear fuel, although because of their very low concentrations, the radiotoxicological effect is negligible.