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...

Background The prevalence of urolithiasis in both infants and children is increasing. The metabolic features contributing to urolithiasis formation in children may vary from those in adult patients. The purpose of this study is to determine the prevalence of urinary metabolic abnormalities and related factors in infants and children with urolit...

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 ...

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 ...

When switching tasks, occasionally responding to bivalent stimuli (i.e., stimuli with relevant features for two different tasks) slows performance on subsequent univalent stimuli, even when they do not share relevant features with bivalent stimuli. This performance slowing is labelled the bivalency effect. Here, we investigated whether the bivalency effect results from an orienting response to ...

Identification of cell surface molecules that play a role in cell-cell adhesion (here called cell adhesion molecules) has been achieved by demonstrating the inhibitory effect of univalent antibodies that bind these molecules in an in vitro assay of cell-cell adhesion. A more convenient reagent, intact (divalent) antibody, has been avoided because it might agglutinate the cells rather than block...