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...

Ruscheweyh‘and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve...

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 ,...

and Applied Analysis 3 In contrast to the modified Roper-Suffridge extension operator in the unit ball, it is natural to ask if we can modify the Roper-Suffridge extension operator on the Reinhardt domains. In this paper, we will introduce the following modified operator: F z ⎛ ⎝f z1 f ′ z1 n ∑ j 2 ajz pj j , ( f ′ z1 2z2, . . . , ( f ′ z1 nzn ⎞ ⎠ ′ 1.5 on the Reinhardt domainΩn,p2,...,pn . Wew...

The main purpose of the present paper is to derive a new criterion for mul-tivalent starlike functions by applying Jack's lemma.

In this note, we provide a starlike and normal tiling in any separable Banach space. That means, there are positive constants r R (not depending on the space) such that every tile of is starlike, contains ball radius contained .