Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Treatment of 6.5-S rabbit antibody with pepsin removes a large inactive fragment. The residual portion of the molecule, which is still bivalent, has a molecular weight of 106,000 and a sedimentation coefficient of 4.6 to 5.0 S (1, 2). Reduction of a single, highly labile disulfide bond cleaves this fragment approximately in half (2, 3). The resulting 3.5-S fragments are univalent and inhibit sp...

While working on the completion of the proof of the Bloch-Kato conjecture I have thought a lot about what to do next. Eventually I became convinced that the most interesting and important directions in current mathematics are the ones related to the transition into a new era which will be characterized by the widespread use of automated tools for proof construction and verification. I have star...

A new filtration of the spaces of tri-/univalent graphs B u m that occur in the theory of finitetype invariants of knots and 3-manifolds is introduced. Combining the results of the two preceding articles, the quotients of this filtration are modeled by spaces of graphs with two types of edges and four types of vertices, and an upper bound for dimB u m in terms of the dimensions of the filtratio...

Since the function z 7→ 1+z 1−z is univalent with image the right half plane, we see that z 7→ ( 1+z 1−z )2 is univalent, so k ∈ S, and the image of k is the entire complex plane except for real numbers ≤ −14 . In 1916, L. Bieberbach [Bi] conjectured that the Koebe function was maximal with respect to the absolute value of the coefficients of its power series. More precisely, he conjectured the...

The human cognitive system is equipped with various processes for dealing with everyday challenges. One of such processes is the inhibition of currently irrelevant goals or mental task-sets, which can be seen as a response to the critical event of information overflow in the cognitive system and challenging the cognitive system's ability to keep track of ongoing demands. In two experiments, we ...

We investigate the relationship between the univalence of f and of h in the decomposition f = h+g of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g with |g| < c|h| is univalent. The notion of a linearly connected domain appea...

It has been shown in the previous publications’ that the eriect of neutral salts on gelatin is repressed in the presence of the salt and that we can study such effects with any profit only when the excess of salt is washed away after it has had a chance to act on the protein. Such gelatin reveals qualities which are masked in the presence of the salt and which allow us to gain a clear insight i...

The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

The interplay of geometry and analysis is perhaps the most fascinating aspect of complex function theory. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior. A function is said to be univalent (or schlichi) if it never takes the same value twice: f(z{) # f(z2) if zx #= z2. The present survey will focus upon the class S ...