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.     

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.     

Algorithmic compression of empirical data: reply to Twardy, Gardner, and Dowe

This discussion note responds to objections by Twardy, Gardner, and Dowe to my earlier claim that empirical data sets are algorithmically incompressible. Twardy, Gardner, and Dowe hold that many empirical data sets are compressible by Minimum Message Length technique and offer this as evidence that these data sets are algorithmically compressible. I reply that the compression achieved by Minimum Message Length technique is different from algorithmic compression. I conclude that Twardy, Gardner, and Dowe fail to establish that empirical data sets are algorithmically compressible.     

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.     

Induction of hemopoietic chimerism in the caprine fetus by intraperitoneal injection of fetal liver cells

Summary Intraperitoneal injection of allogeneic liver cells from 43-day-old male fetuses into normal 60-day female goat fetuses resulted in persistent hemopoietic chimerism in surviving recipients without clinical evidence of graft-versus-host disease. Transplantation of normal fetal liver cells into preimmunocompetent goat fetuses affected with -D-mannosidosis may provide an alternative strategy for evaluating hemopoietic stem cell transplantation in the treatment of human lysosomal storage diseases.