ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.     

A theoretical model for mid-and low-latitude ionospheric electric fields in realistic geomagnetic fields

The geomagnetic fields, which play important roles in the ionospheric dynamo, can greatly affect the global distribution of ionospheric electric fields, currents and other ionospheric electrodynamics phenomena. In the study of ionospheric electrodynamics phenomena, such as the longitudinal variations of ionospheric electric fields, the non-dipolar component of the geomagnetic fields must be taken into account. In this paper, we deduce a theoretical electric field model for ionospheric dynamo at mid- and low-latitude which adopt a modified magnetic apex coordinates system. In the new electric field model, the geomagnetic fields can be calculated from either the IGRF model or the dipole field model, and the neutral winds and conductivities are calculated based on empirical models. Then the dynamo equation for the electric potential is finally solved in terms of the line-by-line iteration method, and the ionospheric electric fields and currents are derived from the calculated potential. Our model can reproduce the main features of the ionospheric electrodynamics processes, so it will be a useful tool for the investigation of the upper atmosphere and ionosphere.     

Chromosomal localization of a unique gene by non-autoradiographic in situ hybridization

During the past few years, several methods have been developed for the detection of specific nucleic acid sequences by in situ hybridization using non-radioactive labels such as fluorochromes, cytochemically detectable enzymes and electron-dense markers. These methods are preferable to autoradiography in terms of speed of performance and topological resolution. Their limited sensitivity, however, has so far restricted their use to the detection of repeated sequences. Here we report single gene detection with a procedure using 2-acetylaminofluorene (AAF)-modified probes, immunoperoxidase cytochemistry and reflection-contrast microscopy. We confirmed the autoradiographic data on the localization of the human thyroglobulin (Tg) gene to the distal end of the long arm of chromosome 8. A mixture of cosmid cHT2-derived subclones of the 3' part of the Tg gene, 22.3 kilobase pairs (kbp) in total, was used as a hybridization probe. This procedure can be used to map other unique sequences, if genomic clones are available from which clones with an appropriate amount of inserts can be isolated.     

Acquired immunity and epidemiology of Schistosoma haematobium

Human immune responses to schistosome infection have been characterized in detail. But there has been controversy over the relative importance of ecological factors (variation in exposure to infection) and immunological factors (acquired immunity) in determining the relationships between levels of infection and age typically found in areas where infection is endemic. Independent effects of exposure and age on the rates of reinfection with Schistosoma haematobium after chemotherapy have been demonstrated in the Gambia and Zimbabwe. This age effect could be the result of acquired immunity to infection. Indeed, allowing for variation in exposure and age, low rates of reinfection in the Gambia are correlated with high amounts of specific IgE antibodies--human IgE can kill S. mansoni schistosomulae in vitro. Further, animals can acquire immunologically mediated resistance to S. mansoni infection, although nonimmunological factors could also be involved. Acquisition of this immunity seems to be related to the cumulative effects of repeated infection and provides only partial protection. These characteristics are consistent with immuno-epidemiological data for both S. mansoni and S. haematobium infections of humans. We have now analysed age-prevalence data for human infection with S. haematobium, and find patterns of variation that are indeed consistent with the epidemiological effects of acquired immunity predicted by mathematical models.     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

Mutation of the matrix metalloproteinase 2 gene (MMP2) causes a multicentric osteolysis and arthritis syndrome.

The inherited osteolyses or 'vanishing bone' syndromes are a group of rare disorders of unknown etiology characterized by destruction and resorption of affected bones. The multicentric osteolyses are notable for interphalangeal joint erosions that mimic severe juvenile rheumatoid arthritis (OMIMs 166300, 259600, 259610 and 277950). We recently described an autosomal recessive form of multicentric osteolysis with carpal and tarsal resorption, crippling arthritic changes, marked osteoporosis, palmar and plantar subcutaneous nodules and distinctive facies in a number of consanguineous Saudi Arabian families. We localized the disease gene to 16q12-21 by using members of these families for a genome-wide search for homozygous-by-descent microsatellite markers. Haplotype analysis narrowed the critical region to a 1.2-cM region that spans the gene encoding MMP-2 (gelatinase A, collagenase type IV; (ref. 3). We detected no MMP2 enzymatic activity in the serum or fibroblasts of affected family members. We identified two family-specific homoallelic MMP2 mutations: R101H and Y244X. The nonsense mutation effects a deletion of the substrate-binding and catalytic sites and the fibronectin type II-like and hemopexin/TIMP2 binding domains. Based on molecular modeling, the missense mutation disrupts hydrogen bond formation within the highly conserved prodomain adjacent to the catalytic zinc ion.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.