A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Functions: a modelling tool in mathematics and science

It is difficult for the students to transfer concepts, ideas and procedures learned in mathematics to a new and unanticipated situation in science. An alternative to this traditional transfer method stresses the importance of modelling activities in an interdisciplinary context between mathematics and science. In the paper we introduce a modelling approach to the concept of function in upper secondary school is introduced. We discuss pedagogical and didactical issues concerning the interplay between mathematics and science. The discussion is crystallized into a didactical model for interdisciplinary instruction in mathematics and science. The model is considered as an iterative movement with two phases: (1) the horizontal linking of the subjects: Situations from science are embedded in contexts which are mathematized by the students, (2) the vertical structuring in the subjects: The conceptual anchoring of the students' constructs from the horizontal linking in the systematic and framework of mathematics and science respectively.     

Unsymmetrically Substituted Benzonaphthoporphyrazines: A New Class of Cationic Photosensitizers for the Photodynamic Therapy of Cancer*

Abstract— Unsymmetrical zinc(II) complexes of benzonaphthoporphyrazines 5 a-12a bearing between one and eight pyri-dyloxy substituents are synthesized by statistical tetra-merization of 6-(l,l-dimethylethyl)-2,3-naphthalenedi-carbonitrile (1) with 4-(3-pyridyloxy)- or 4,5-bis-(3-pyri-dyloxy)-1,2-benzenedicarbonitrile (2, 3). Methylation of 5a-12a leads to the cationic pyridyloxybenzonaphtho-porphyrazines 5b- 12b having between one to eight positive charges. The Q-band transition in the visible spectra exhibits a bathochromic shift from 680 to 760 nm dependent upon the number of annelated naphthalene rings. The singlet oxygen quantum yields of the benzonaphthoporphyrazines determined by the dye-sensitized photoox-idation of 1,3-diphenylisobenzofurane is surprisingly high (in the range of zinc phthalocyanine). The photoox-idative stabilities of the photosensitizers described quantitatively by first-order kinetics decrease with the number of annelated naphtho groups. A linear correlation between the logarithm of the decomposition rate constant and the position of the highest occupied molecular orbital (HOMO)-level of the photosensitizers is found. Destabi-lization of the HOMO leads to a decrease of the pho-tostability. Due to their adjustable long wavelength absorption, their intramolecular polarity axis and their different hydrophilic/hydrophobic character, these novel compounds may be suitable photosensitizers for the photodynamic therapy of cancer.     

Increased oxygen transfer in a yeast fermentation using a microbubble dispersion

A microbubble dispersion (MBD) was used to supply oxygen for aerobic fermentations in a standard 2 L stirred tank fermenter. The microbubble dispersion was formed using only surfactants produced naturally. Growth rates ofSaccharomyces cerevisiae cultures were found to be equal or greater with MBD sparging than with gas sparging. The oxygen transfer coefficent with MBD sparging was found to be 190/h and independent of impeller speed from 100–580 rpm. The oxygen transfer coefficient with air sparging rose from 55 to 132/h over the same range of impeller speeds. Power requirements for the fermenter systems were estimated.     

Self-assembly of oligomeric porphyrin rings

A cobalt porphyrin equipped with two different but geometrically complementary pyridine ligands self-assembles to form an unusually stable complex with approximately 12 porphyrin monomers arranged in a macrocyclic array.     

Differential inhibition of postnatal brain,spinal cord and body growth by a growth hormone antagonist

Background  

Growth hormone (GH) plays an incompletely understood role in the development of the central nervous system (CNS). In this study, we use transgenic mice expressing a growth hormone antagonist (GHA) to explore the role of GH in regulating postnatal brain, spinal cord and body growth into adulthood. The GHA transgene encodes a protein that inhibits the binding of GH to its receptor, specifically antagonizing the trophic effects of endogenous GH.