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.     

Rapid-time-course miniature and evoked excitatory currents at cerebellar synapses in situ.

Neurotransmission from mossy fibre terminals onto cerebellar granule cells is almost certainly mediated by L-glutamate. By taking advantage of the small soma size, limited number of processes and short dendrite length of granule cells, we have obtained high-resolution recordings of spontaneous miniature excitatory postsynaptic currents (m.e.p.s.cs) and evoked currents in thin cerebellar slices. Miniature currents have a similar time-course and pharmacology to evoked currents and consist of an exceptionally fast non-NMDA (N-methyl-D-aspartate) component (measured rise-time, 200 microseconds; estimated pre-filtered rise-time less than 100 microseconds; decay time constant, tau = 1.0 ms), followed by 50 pS NMDA channel openings that are directly resolvable. We could find no evidence for the recent proposal that miniature currents in granule cells are mediated solely by NMDA channels with a novel time course. The non-NMDA receptor component of m.e.p.s.cs has a skewed amplitude distribution, which suggests potential complications for quantal analysis. The difference in time course between the m.e.p.s.cs reported here and other synaptic currents in the brain could reflect differences in synaptic function or electrotonic filtering; the relative contribution of these possibilities has yet to be established.     

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.