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.     

Preferential hydrophobic interactions are responsible for a preference of D-amino acids in the aminoacylation of 5'-AMP with hydrophobic amino acids.

We have studied the chemistry of aminoacyl AMP to model reactions at the 3' terminus of aminoacyl tRNA for the purpose of understanding the origin of protein synthesis. The present studies relate to the D, L preference in the esterification of 5'-AMP. All N-acetyl amino acids we studied showed faster reaction of the D-isomer, with a generally decreasing preference for D-isomer as the hydrophobicity of the amino acid decreased. The beta-branched amino acids, Ile and Val, showed an extreme preference for D-isomer. Ac-Leu, the gamma-branched amino acid, showed a slightly low D/L ratio relative to its hydrophobicity. The molecular basis for these preferences for D-isomer is understandable in the light of our previous studies and seems to be due to preferential hydrophobic interaction of the D-isomer with adenine. The preference for hydrophobic D-amino acids can be decreased by addition of an organic solvent to the reaction medium. Conversely, peptidylation with Ac-PhePhe shows a preference for the LL isomer over the DD isomer.     

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.     

The effect of ethanol on the biosynthesis and regulation of opioid peptides

Summary Alcoholism and alcohol abuse are serious health problems. Alcohol is known to influence the activity of a number of biological systems, for example the hormonal and neuronal systems. One of the biological systems whose activity is greatly influenced by alcohol is the endogenous opiate system. Alcohol modifies the function of both opiate receptors and opioid peptides. In fact it has been proposed that many of the effects of ethanol are mediated by its effects on the endogenous opiate system. This review will present results from various laboratories on the effects of acute and chronic ethanol treatments on various species, and on the release, biosynthesis and post-translational processing of the endorphins, enkephalins and dynorphins, the three known families of endogenous opioid peptides. Furthermore, the effect of acute and chronic ethanol consumption on the -endorphin system in man, and the possible implications of the functional activity of the endogenous opiate system for the genetic predisposition to alcoholism will be discussed.