Minimal average degree aberration and the state polytope for experimental designs

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Gröbner bases provide a systematic way of doing this. The algebraic method does not, in general, produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on “aberration” and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase.     

HFI and DFT study of the bonding in complexes of halogen and interhalogen diatomics with Lewis base

We have analyzed by means of DFT calculations with use of the pseudo-potential the nuclear quadrupole coupling constants of a range of XYB complexes (n aσ type in Mulliken notation) formed between diatomic interhalogen molecules XY and Lewis bases B. The geometrical parameters, rotational and halogen nuclear quadrupole coupling constants obtained by these calculations substantially corresponded to the data of microwave spectroscopy in the gas phase. An analysis of the quality of the calculations that employ the pseudo-potential and the expanded basis set for the halogen compounds was carried out. The ZORA model is shown to be a viable alternative to the computationally demanding BH and HLYP model for the calculation of halogen and nitrogen coupling constants in molecules. In addition, the ZORA model, in contrast to the pseudo-potential model, leads to realistic values of iodine nuclear quadrupole coupling constants. From electron partitioning analyses and Klopman's approach it follows that for the IClB complexes the electrostatic bonding is predominant relative to covalent bonding.     

A theorem on independence

Suppose we are given a family of sets , where S(j) = ∩^k_i=1 H_i(j), and suppose each collection of sets H_i(j₁),…,H_i(j_k+1) has a lower bound under the partial ordering defined by inclusion, then the maximal size of an independent subcollection of is k. For example, for a fixed collection of half-spaces H₁,…,H_k in , we define to be the collection of all sets of the form

where χ_i, I=1,…, k are points in . Then the maximal size of an independent collection of such sets us k. This leads to a proof of the bound of 2d due to Rényi et al. (1951) for the maximum size of an independent family of rectangles in with sides parallel to the coordinate axes, and to a bound of d+1 for the maximum size of an independent family of simplices in with sides parallel to given hyperplanes H₁,…,H_d+1.     

Developing a methodology for carbon isotope analysis of lacustrine diatoms

Stable isotope analysis of sedimentary carbon in lakes can help reveal changes in terrestrial and aquatic carbon cycles. A method based on a single, photosynthetic organism, where host effects are minimised, should offer more precision than carbon isotope studies of bulk lake sediments. Here we report the development of a systematic method for use on fossil lacustrine diatom frustules, adapted from previous studies in marine environments. A step-wise cleaning experiment on diatomaceous lake sediments from Lake Challa, near Mount Kilimanjaro, was made to demonstrate the necessary treatment stages to remove external sedimentary carbon. Changes in soluble carbon compounds during these cleaning experiments were measured using gas chromatography/mass spectrometry (GC/MS). The mass spectrometry methods were refined to measure the small percentage of carbon in these samples and details of these methods are presented. Samples of cleaned diatoms containing <1% carbon yielded robust results. Carbon isotope analyses of diatom samples containing different species mixtures were performed and suggested that differences existed, although the effects lay within current experimental error and require further work. Unlike what was found in work on oxygen and silicon isotopes from diatom frustules, mineral contamination had no discernible impact on the diatom carbon isotope ratios from these sediments. The range of values found in the lakes investigated thus far can be interpreted with reference to the supply and nature of carbon from the catchment as well as to the demand generated from lake primary productivity.     

The fabrication and performance of 1.3μm DFB EMBH lasers with coplanar contacts

The fabrication and performance characteristics of coplanar contact etched mesa-buried heterostructure (EMBH) distributed feedback (DFB) lasers emitting at 1.3μm wavelength are described. The processing was designed such that the lasers could be evaluated as coplanar contact or conventional (top/bottom) contact devices. The threshold current was as low as 14mA and the 3dB small signal response was as high as 9.4 GHz. Both these properties showed negligible differences when the device was biased either coplanarly or conventionally.     

The fabrication and performance of 1.3μm DFB EMBH lasers with coplanar contacts

The fabrication and performance characteristics of coplanar contact etched mesa-buried heterostructure (EMBH) distributed feedback (DFB) lasers emitting at 1.3μm wavelength are described. The processing was designed such that the lasers could be evaluated as coplanar contact or conventional (top/bottom) contact devices. The threshold current was as low as 14mA and the 3dB small signal response was as high as 9.4 GHz. Both these properties showed negligible differences when the device was biased either coplanarly or conventionally.     

Partial differential equations associated with certain non-linear algorithms

Zusammenfassung In der letzten Zeit sind eine Anzahl nicht-linearer Algorithmen untersucht worden, die in der Analysis und numerischen Mathematik von besonderer Wichtigkeit sind.Diese Algorithmen betreffen Grössen, die in einem zweidimensionalen Schema angeordnet werden können, und verknüpfen vier Grössen miteinander, die an den Eckpunkten eines Rhombus in diesem Schema vorkommen. Wenn die Dimensionen dieses Rhombus unendlich klein gemacht werden, dann führen die algorithmischen Beziehungen zu Systemen von zwei simultanen partiellen Differentialgleichungen erster Ordnung.In dieser Arbeit werden einige allgemeinere Ergebnisse hergeleitet, die sich auf solche partielle Differentialgleichungssysteme beziehen; die Ergebnisse werden an Hand spezieller Beispiele erläutert. Der -Algorithmus, derq — d Algorithmus und verschiedene andere Algorithmen werden im Detail untersucht. Diese Algorithmen führen auf die partielle Differentialgleichung der Padéschen Fläche, auf die korrespondierende Kettenbruchkoeffizientenfläche und auf eine Anzahl weiterer partieller Differentialgleichungen.

---

---

Communication MR 65 of the Computation Department of the Mathematical Centre, Amsterdam.     

Zur Theorie der mit gewissen speziellen Funktionen verknüpften Padéschen Tafeln

Ohne Zusammenfassung     

Chemistry of bifunctional photoprobes. 6. Synthesis and characterization of high specific activity metalated photochemical probes: development of novel rhenium photoconjugates of human serum albumin and fab fragments

Functionalization of perfluoro aryl azides by bifunctional chelating agents (BFCAs) capable of forming high specific activity complexes with (99m)Tc (for gamma-imaging) and (188)Re (for radiotherapy) is described. The synthesis of multidonor BFCAs containing N(2)S(2), N(4), and N(3)S donor groups containing imidazole, pyridine, and pyrazine functionalities that may be important for tuning the pharmacokinetic parameters is also described. Functionalization of perfluoro aryl azides at various sites on BFCAs yields novel bifunctional photolabile chelating agents (BFPCAs) that are useful for covalent attachment to biomolecules. A representative Re-BFPCA 8a in a model solvent, diethylamine, proceeded to give a high yield of intermolecular NH insertion product without the decomplexation of the metal ion from 8a. All products originated from the photolysis of 8a in diethylamine are characterized by analytical techniques, and a plausible mechanism of formation of different photolytic products is suggested. The high yield of intermolecular NH insertion of Re-BFPCA 8a is extended to labeling of human serum albumin (HSA) and Fab fragments under aqueous conditions. The photolabeling technology developed here offers a new way to attach diagnostically and therapeutically useful radiotracers (e.g., (99m)Tc, (188)Re) to Fab fragments for potential noninvasive imaging and therapy of cancer.