Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions

We study the relationship between the Dirichlet problem and the Cauchy problem with inhomogeneous boundary conditions for local operators. Our results are applied to non-autonomous parabolic problems on non-cylindrical domains. Received January 10, 2001; accepted April 5, 2001.     

Overview and critical survey of polyamide6 structural habits: Misconceptions and controversies

Various aspects of the structural habits and associated thermodynamic properties of polyamide6 are critically examined with regard to controversies that appeared in literature mainly due to misconceptions or erroneous/ambiguous interpretations of experimental findings. The structural habits under concern are the crystallization capabilities and chain topology, hydrogen bonds and sheet-like structure, crystalline polymorphism together with thermodynamic stability. Thermo-mechanical properties are also discussed for the sake of complementary argumentation. Comparisons are made with polycaprolactone, that is, the polyester homolog of polyamide6 regarding chain structure, in order to evaluate the actual role of the H-bonds on the structural habits. Additional comparisons with polyethylene and polypropylene are also made at several occasions for the sake of supporting argumentation on the structural behavior of polyamide6. A temperature–time–transformation diagram of polyamide6 is finally proposed from the gathering of plentiful literature data.     

Multi-criteria supplier segmentation using a fuzzy preference relations based AHP

One of the strategic activities of a firm is supplier segmentation, whereby a firm creates groups of suppliers to handle them differently. Existing literature provides several typologies of suppliers, each of which uses different dimensions/variables. In this paper, different typologies are combined by distinguishing two overarching dimensions, the capabilities and the willingness of suppliers to cooperate with a particular firm. These dimensions cover almost all the existing supplier segmentation criteria mentioned in existing literature. For each particular situation, these dimensions can be specified using a multi-criteria decision-making method. A methodology is proposed that includes a fuzzy Analytic Hierarchy Process (AHP) which uses fuzzy preference relations to incorporate the ambiguities and uncertainties that usually exist in human judgment. The proposed methodology is used to segment the suppliers of a broiler company. The result is a segmentation of suppliers based on two aggregated dimensions. Finally some strategies to handle different segments are discussed and concluding remarks and suggestions for future research are provided.     

A robustification approach in unconstrained quadratic optimization

Unconstrained convex quadratic optimization problems subject to parameter perturbations are considered. A robustification approach is proposed and analyzed which reduces the sensitivity of the optimal function value with respect to the parameter. Since reducing the sensitivity and maintaining a small objective value are competing goals, strategies for balancing these two objectives are discussed. Numerical examples illustrate the approach.     

Synthese und strukturelle Charakterisierung von Borsubphthalocyaninaten

Synthesis and Structural Characterization of Boron Subphthalocyaninates Halosubphthalocyaninatoboron, [B(X)_spc] (X = F, Cl, Br) is obtained by heating phthalonitrile with boron trihalide in quinoline (X = F) or the corresponding halobenzene, resp. [B(C₆H₅)_spc] is prepared from phthalonitrile and tetraphenylborate or tetraphenyloboron oxide, resp. [B(OR)_spc] (R = H, CH(CH₃)₂, C(CH₃)₃, C₆H₅) is synthesized by bromide substitution of [B(Br)_spc] in pyridine/HOR. Substitution of [B(Br)_spc] in carboxylic acids yields [B(OOCR)_spc] (R = H, CX₃ (X = H, Cl, F), CH₂X (X = Cl, C₆H₅), C₆H₅). All subphthalocyaninates are characterized electrochemically and by UV‐VIS, IR/FIR, resonance Raman, and ¹H/¹⁰B‐NMR spectroscopy. Typical B–X stretching vibrations are at 622 (X = Br), 950 (Cl), 1063 (F), 1096 cm^–1 (OH) as well as between 1119 and 1052 cm^–1 (OR) resp. 985 and 1028 cm^–1 (OOCR). The difference ν(C=O)–ν(C–O) > 400 cm^–1 confirms the unidentate coordination of the carboxylato ligands. According to the crystal structure analysis of [B(OH)_spc], [B(OH)_spc] · 2 H₂O, [B(C₆H₅)_spc], [B(OC(CH₃)₃)_spc], [B(OOCCH₃)_spc] · 0.5 H₂O · C₂H₅OH and [B(OOCCH₃)_spc] · 0.4 H₂O · 1.1 C₅H₅N the _spc ligand is concavely distorted. This saucer shaped conformation is independent of the acido ligands and the presence of solvate. The outermost C atomes are vertically displaced in part by more than 2 Å from the N_i plane. The B atom is in a distorted tetrahedral coordination geometry. It is displaced by ca 0.64 Å out of the N_i plane towards the acido ligand. The average B–N distance is 1.500 Å, and the B–O distances range from 1.418(5) to 1.473(2) Å.     

Reactive halogen chemistry in the troposphere

Halogen chemistry is well known for ozone destruction in the stratosphere, however reactive halogens also play an important role in the chemistry of the troposphere. In the last two decades, an increasing number of reactive halogen species have been detected in a wide range of environmental conditions from the polar to the tropical troposphere. Growing observational evidence suggests a regional to global relevance of reactive halogens for the oxidising capacity of the troposphere. This critical review summarises our current understanding and uncertainties of the main halogen photochemistry processes, including the current knowledge of the atmospheric impact of halogen chemistry as well as open questions and future research needs.