# Volume 28 (2020), Issue 3

### 1. On a question of Schmidt and Summerer concerning 3-systems

Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper 3-system (P 1,P 2,P 3) with the property ̄φ 3 = 1. In fact, our method generalizes to provide n-systems with ̄φn = 1, for arbitrary n ≥ 3. We visualize our constructions with graphics. We further present explicit examples of numbers ξ 1,...,ξn −1 that induce the n-systems in question.

### 2. Deformations of Metrics and Biharmonic Maps

We construct biharmonic non-harmonic maps between Riemannian manifolds (M, g) and (N, h) by first making the ansatz that φ:(M, g) → (N, h) be a harmonic map and then deforming the metric on N by h ˜ α = α h + ( 1 - α ) d f ⊗ d f {\tilde h_\alpha } = \alpha h + \left( {1 - \alpha } \right){\rm{d}}f \otimes {\rm{d}}f to render φ biharmonic, where f is a smooth function with gradient of constant norm on (N, h) and α […]

### 3. Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus

The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon’s Inequality, Bergström’s Inequality, Schlömilch’s Inequality and Rogers-Hölder’s Inequality on time scales in comprehensive form.

### 4. Generalization of uniqueness and value sharing of meromorphic functions concerning differential polynomials

The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13].

### 5. A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra

For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree.

### 6. Finite groups with prime graphs of diameter 5

In this paper we consider a prime graph of finite groups. In particular, we expect finite groups with prime graphs of maximal diameter.