A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in Cn are introduced. Basic properties such as the chain rule, multiplicative invariance affine proved these operators. It is shown that stable only with respect to rotations of identity. characterization given case when holomorphic. Furthermore, it if mapping vanishes then analytic part this Möbius transf...

FMN and flavodoxin, when reduced by the action of ferredoxin-TPN+ oxidoreductase, have been shown to cause both univalent and divalent reductions of oxygen. Superoxide radicals, so generated, were detected by their abilities to oxidize epinephrine to adrenochrome and to reduce cytochrome c. Superoxide dismutase inhibited these actions of the superoxide radical. The ratio of the univalent reduct...

The reaction of the bivalent rabbit antibody molecule with papain (1, 2) or pepsin (3) and a reducing agent results in the release of two univalent fragments. The evidence for univalence is provided by the capacity of the fragments of hydrolyzed antiprotein antibody to inhibit specifically the homologous precipitin reaction (2), and by direct measurements of the maximal number of moles of hapte...

The role of bivalence of antibody in its capacity to neutralize virus was studied with rabbit antibodies to the bacteriophage, phiX174. Univalent Fab or Fab' fragments of IgG isolated from antiviral antisera obtained early in the immunization schedule had virtually no activity compared to that of the intact IgG. When the antibodies were isolated from antisera of the same rabbits several months ...

We establish a close connection between a reversible programming language based on type isomorphisms and a formally presented univalent universe. The correspondence relates combinators witnessing type isomorphisms in the programming language to paths in the univalent universe; and combinator optimizations in the programming language to 2-paths in the univalent universe. The result suggests a si...

A continuous complex-valued function f u iv is said to be harmonic in a simply connected domain D if both u and v are real harmonic in D. In any simply-connected domain we can write f h g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h′ z | > |g...

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...