Edge quantisation of elliptic operators

The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy , where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol which includes the (in general not explicitly known) number of additional conditions of trace and potential type on the edge. We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet–Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich–Dynin formula for edge boundary value problems. Nicoleta Dines and Bert-Wolfgang Schulze were supported by Chinese-German Cooperation Program “Partial Differential Equations”, NNSF of China and DFG of Germany. Xiaochun Liu was supported by NNSF of China through Grant No. 10501034, and Chinese-German Cooperation Program “Partial Differential Equations”, NNSF of China and DFG of Germany.     

Qualitative analysis of a diffusive prey–predator model

In this work we examine a Lotka–Volterra model with diffusion describing the dynamics of multiple interacting prey and predator species. We show that the solution exists, and is unique, bounded, nonnegative, and globally defined. We also prove the non-existence of nonconstant steady state solutions if certain conditions are satisfied. For the particular case of two prey (e.g., engineered and native, respectively) and one common predator species, by performing a linear stability analysis about the initial native-dominant steady state, we determine under which conditions the engineered species invasion succeeds.     

Antioxidant potential and authenticity of some commercial fruit juices studied by EPR and IRMS

Antioxidant status of foods, plant, or fruit products is generally characterized by means of spectroscopic methods. Methods like HPLC, UV-VIS, or MS spectroscopy are used to understand the chemical and physical properties of different samples, and also EPR spectroscopy seems to be a valuable tool to characterize antioxidant activity of juice beverages. In this technique, certain antioxidants present in fruit juices interact with free radicals interrupting the chain reaction that can possibly damage essential molecules. Recording the EPR signal decay caused by the reaction with a natural or artificial reducing agent, it is possible to draw conclusions about the antioxidant capability of materials. IRMS is a powerful tool to distinguish between an authentic fruit juice and a juice obtained by concentrate dilution. This technique allows also the detection of commercial C₄ cane or corn derived sugar syrups in C₃ fruit juices. In the present study, four commercial fruit juices were investigated using stable isotope measurements (oxygen, hydrogen, and carbon) and EPR measurements in order to check the correct labeling in the Romanian markets and to compare antioxidant activity of the studied juices and the reference. It was proven that the number of paramagnetic species decreases in time with different reaction rates and this was correlated with the antioxidant activity of the studied juices. Stable isotope ratio measurements have demonstrated that the fruit juices studied were reconstructed from concentrates with tap water, according to their label.     

Linking supply chain processes’ performance to a company’s financial strategic objectives

The main aim of this paper is to develop a performance measurement method which links supply chain (SC) processes’ performance to a company’s financial strategy through demonstrating and utilising the relationship between SC processes’ performance and a company’s financial performance.     

Micro- and nano-mechanical characterization of polyamide 11 and its composites containing cellulose nanofibers

Nanocomposites from polyamide 11 and dried cellulose nanofibers (CNs), 16–30 nm in thickness and 50–400 nm in length, were prepared via direct melt mixing and their micro- and nano-mechanical properties were studied. (PF) QNM (Quantitative Nanomechanical Mapping) method was used to map nanomechanical properties at the surface of polyamide 11 and nanocomposites. This new AFM method emphasized both the increased modulus in nanocomposites as compared to the matrix and the microstructure on different levels in polyamide 11 and its nanocomposites. PF QNM showed that their crystalline structure consists of bundles of lamellar stacks, 200–350 nm in width and 20–40 nm wide lamellar stacks. Moreover, PF QNM study emphasized higher structural order in nanocomposites with 3 and 5 wt.% CNs and lower in the nanocomposite with 8 wt.% CNs as compared to the reference. These observations were verified and are consistent with both crystallinity values determined by DSC and micro-mechanical test results. The oriented bundles of lamellar stacks, observed by PF QNM, could be considered as the main blocks determining high mechanical properties for the studied nanomaterials.     

Bulk titanium for structural and biomedical applications obtaining by spark plasma sintering (SPS) from titanium hydride powder

Titanium is a low density element with excellent mechanical properties, and is an attractive material for structural and biomedical applications. In recent years, a new process technology is emerging by which titanium and titanium alloys can be obtained by using titanium hydride (TiH₂) as a precursor for Ti and its mixture with alloying elements. The feasibility of this manufacturing approach has been fully demonstrated from powder to sintering and from microstructure to mechanical properties. In this paper, a study concerning powder metallurgy processing of Ti by spark plasma sintering (SPS) route is presented. The influence of the technological parameters on the hardness and microstructures change during SPS has been studied. The experimental results are related to microscopic, thermal, and mechanical analysis.     

On the compatibility of the IPP/PA6/EPDM blends with and without functionalized IPP I. Thermo-oxidative behaviour

Binary isotactic polypropylene (IPP)/polyamide 6 (PA6) and ternary IPP/PA6/ethylene–propylene diene terpolymer (EPDM) blends in various ratios were obtained in a Haake Rheocord mixer. Processing behaviour was changed in the presence of IPP functionalized with bismaleimide (BMI), maleic anhydride (MA) and acrylic acid (AA) as reactive compatibilizing agents. The thermal and thermo-oxidative behaviour of blends was studied by differential scanning calorimetry and thermogravimetry. The functionalized IPPs modify the crystallinity degree and the decomposition behaviour of both IPP and PA6 as a result of chemical reactions of functional groups with those of the PA6. The changes depend on the IPP/PA6 or IPP/PA6/EPDM ratio, the chemical nature and amount of the functionalized IPP. On the basis of the processing and thermal data one can conclude that the compatibilizing agent effect increases in the following order: IPP-AA 相似文献   

Thermo-oxidative degradation of some elastomers with a high content of 3,4 isoprene units

New elastomers with high content of 3,4 isoprene units have been developed during the last decades in an attempt to ensure superior performances of the final products and the present study is devoted to the investigation of some peculiarities of their ageing behaviour. On thermo-oxidative degradation, 3,4 isoprene units are less affected in comparison to cis-1, 4 and trans-1, 4 isoprene units. The degradation process consists mainly in splitting of the main chains at temperatures of 80–100 °C while at higher temperatures (120–130 °C) branching becomes a significant modification and this reaction is enhanced for the polymers containing preponderantly 3,4 units. Such behaviour leads to the fact that the processability of polymers containing high amounts of 1,2 and 1,3 isoprene units is less affected by thermo-oxidative degradation in comparison with cis-1, 4-polyisoprene, which could be explained by the fact that large amounts of double bonds are not present in the backbone of macromolecules but in the pendent groups.     

GRAFTED STYRENE-DIVINYLBENZENE COPOLYMERS CONTAINING BENZALDEHYDES AND THEIR WITTIG REACTIONS WITH VARIOUS PHOSPHONIUM SALTS

A chloromethylated styrene-divinylbenzene copolymer support system functionalized with 4-benzaldehyde and 2-benzaldehyde was prepared.The degree of functionalization with aldehyde groups is well suited for the subsequent use of the products as Wittig reagents.The polymer bound aldehyde was reacted with Wittig reagents to give olefin groups grafted on styrene-divinylbenzene copolymers.The reactions were carried out in phase transfer catalysis conditions.A simple procedure for the calculation of the degree of functionalization and the statistical modeling of the structural repetitive unit of the copolymer are reported.