Elliptic semiplanes and group divisible designs with orthogonal resolutions

In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD _k ((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker.     

On quadratic and sesquilinear functionals

LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX.     

On the periodic points of a two-parameter family of maps of the plane

We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation.     

Comments on the primary and scatter dose-spread kernels used for convolution methods

The basic primary and scatter dose-spread kernels used for convolution methods are usually produced by Monte Carlo simulations with the interaction point forced to the center of a large water phantom. However, it is still not clear whether such Monte Carlo based kernels allow accurate dose calculations with a wide range of field sizes and depths, especially in thorax phantoms. Using the differential primary and scatter concept, this paper proposes another type of basic kernel, with which perfectly accurate primary and scatter absorbed dose calculations can be performed under conditions that the beam is parallel, the incident beam intensity is uniform within and zero outside the field, and the primary beam attenuation coefficient along raylines is not a function of depth and off-axis distance.     

Structure analytical methods for quantitative reference applications

The analytical methods mass spectrometry, UV/Vis, IR, Raman, Fluorometry, XRD, Mössbauer, and NMR used to elucidate chemical structure are evaluated regarding their capabilities to be used as primary analytical techniques in quantitative measurements, considering the criteria in the CCQM definition of primary methods. This includes a review of the respective measurement equations, the evaluation of the measurement uncertainty, and a discussion of evidence for the “highest metrological level”, as obtained from intercomparisons in contest with other methods. It is shown that only few methods fulfill the CCQM criteria. Quantitative NMR spectroscopy is one of them and may be considered as a potential primary method as recommended by CCQM because of being free of empirical factors in the uncertainty budget.     

Xylanolytic enzyme production by anAspergillus niger isolate

Production of xylanolytic enzymes by anAspergillus niger CCMI 850 isolate was investigated in batch cultures. The effect of the composition of a fermentation medium that did not include chemical inducers, on β-xylanase, β-xylosidase, α-l-arabinofuranosidase, and total cellulase activity was studied. With 4% xylan as the carbon source, about 65 U/mL of β-xylanase was obtained, whereas the total cellulase activity was undetectable, under the specified conditions. This β-xylanase activity represents the highest reported for a wild-type strain ofA. niger. The effect of pH and temperature on the activity of β-xylanase was studied. Partial characterization of the β-xylanase showed that with insoluble birchwood as substrate theK _m andV _max were 0.3 mM and 19 μmol/min, respectively. Aspects of using the crude β-xylanase preparation for applications in the pulp and paper industry were discussed.     

Traceability and analytical chemistry

 The basic concepts of traceability as they are defined by the Comité Consultatif pour la Cluantité de Matière are contrasted with the practical exploitation in chemical analysis. The applicability of traceability concepts are tested for their practical applicability on four different analytical methodologies, neutron activation analysis, plasma mass spectrometry, beam microscopical analysis and speciation analysis of organometallic compounds. Received: 31 March 1998 · Accepted: 6 June 1998     

Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space

LetE be a real Banach space andL(E) the family of all nonempty compact starshaped subsets ofE. Under the Hausdorff distance,L(E) is a complete metric space. The elements of the complement of a first Baire category subset ofL(E) are called typical elements ofL(E). ForXL(E) we denote by the metrical projection ontoX, i.e. the mapping which associates to eachaE the set of all points inX closest toa. In this note we prove that, ifE is strictly convex and separable with dimE2, then for a typicalXL(E) the map is not single valued at a dense set of points. Moreover, we show that a typical element ofL(E) has kernel consisting of one point and set of directions dense in the unit sphere ofE.