A novel class of vivid motion and velocity illusions for contrast-defined shapes is presented and discussed. The illusions concern a starlike wheel that, physically, rotates with constant velocity between stationary starlike inner and outer shapes but that, perceptually, shows pulsations, jolts backwards, jolts forwards, and accelerations, each time it aligns with the inner and outer shapes. Th...

The reverse Wiener index of a connected graph G is defined as Λ(G) = 1 2 n(n− 1)d−W (G), where n is the number of vertices, d is the diameter, and W (G) is the Wiener index (the sum of distances between all unordered pairs of vertices) of G. We determine the n-vertex non-starlike trees with the first four largest reverse Wiener indices for n > 8, and the nvertex non-starlike non-caterpillar tre...

AbstractIn this paper, we introduce a new class K(α, β) of uniformly convex functions defined by a certain fractional calculus operator. The class has interesting subclasses like β-uniformly starlike, βuniformly convex and β-uniformly pre-starlike functions. Properties like coefficient estimates, growth and distortion theorems, modified Hadamard product, inclusion property, extreme points, clos...

This article comprises the study of strongly starlike functions which are defined by using concept subordination. The function φ φ(ζ)=(1+ζ)λ, 0<λ<1 maps open unit disk in complex plane to a domain symmetric with respect real axis right-half plane. Using this mapping, we obtain some radius results for family functions. It is worth noting that all presented sharp.

1. I N T R O D U C T I O N Ordering of graphs with respect to the number of matchings, and finding the graphs extremal with regard to this property, has been the topic of several earlier works [1-4]. These results have chemical applications, in connection with the so-called total 1r-electron energy [5-7]. Let G be a graph without loops and multiple edges. For k being a positive integer, m ( G ,...

This paper is related to notions adapted from fuzzy set theory the field of complex analysis, namely differential subordinations. work aims present new subordinations for which best dominant and subordinate are given, respectively. The original theorems proved in generate interesting corollaries particular choices functions acting as dominant. Here, this article, subordination results obtained ...

In this lecture, we aim at presenting a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function and then investigating its various mapping as well as inclusion properties involving such subclasses of analytic and univalent functions as (for example) k-uniformly convex functions and k-starlike functions. Relevant conne...

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ starlike functions complex order γ connected with cardioid domain. The main contribution article consists derivations sharp inequality, considering belonging to in U. Particularly, bounds first two Taylor–Maclaurin coefficients, estimates Fekete–Szegö-type functionals, and coefficient inequalities are investi...