Succinyl CoA synthetase from Nicotiana tabacum exhibited a requirement for univalent and divalent cations. Mn(2+) replaced Mg(2+) in the assay medium and Co(2+) and Ca(2+) partially replaced Mg(2+). Addition of Zn(2+) resulted in no enzyme activity. The enzyme was activated by univalent cations K(+), Rb(+), NH(4) (+), and Na(+); Li(+) showed little or no activation. Maximum enzyme activity vari...

A normalized univalent function f is called Ma–Minda starlike or convex if zf ðzÞ=f ðzÞ uðzÞ or 1þ zf ðzÞ=f 0ðzÞ uðzÞ where u is a convex univalent function with uð0Þ 1⁄4 1. The class of Ma–Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and clo...

A model theory in the framework of Univalent Foundations requires a logic that allows us to define structures on homotopy (n-)types, similar to how first-order logic can define structures on sets. We define such an “n-level” logic for finite n. The syntax is based on a generalization of Makkai’s FOLDS, obtained by an operation that allows us to add equality sorts to FOLDS-signatures. We then gi...

The well-known Schwarz-Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ ′ (z)| ≤ 1 − |φ(z)| 2 1 − |z| 2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent map-pings. The lower estimate is |φ ′ (z)| ≥ 0 generally or |φ ′ (z)| > 0 for univa-lent functions. To make the lower estimate non-trivial we consider univalen...

For the standard class S of normalized univalent functions f analytic in the unit disk U , we consider a problem on the minimal area of the image f(U) concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect ...

The subjective experience of ambivalence results from possessing both positive and negative reactions. Why do individuals sometimes experience ambivalence when they possess only positive or only negative reactions (i.e., univalent attitudes)? This research advances and provides support for the notion that anticipated conflicting reactions underlie such ambivalence. Anticipated conflicting react...

Thermal behavior of various solid feldspars are different, namely those of bivalent cations show no change in the distribution of Al and Si atoms, whereas feldspars of univalent cations become more disordered with raising temperature. In the latter case Al atoms migrate from the sites they occupe at low temperatures and interchange positions with the Si atoms. At high temperatures (but stil...

In this work, we obtain the Fekete-Szegö inequalities for the class $P_{Sigma }left( lambda ,phi right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.