Refinement of some inequalities for means
Abstract We consider weighted arithmetic means as, for example \(\alpha G+\left(1-\alpha \right) C\), with \(\alpha \in \left( 0,1\right) ,GC\) being…
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Properties of palindromes in finite words
Abstract We present a method which displays all palindromes of a given length from De Bruijn words of a certain…
Two-dimensional arrays with maximal complexity
Abstract We present natural bounds for the complexity function of two-dimensional arrays, and we study the shape of the maximal…
On Lp norms and the spectral radius of operators in Hilbert spaces
Abstract We prove that \(lim_{p\rightarrow \infty}k\) \(\left \Vert f\right \Vert _{+p}^{+p}\diagup \left \Vert f\right \Vert _{p}^{p}=\left \Vert f\right \Vert _{\infty}\)…
New solutions in the direct problem of dynamics
Abstract Given a planar potential \(V\), we look for families of orbits \(f(x,y)=c\) (determined by their slope function \(\U{3b3} =fy/fx\)),…
Two-dimensional total palindrome complexity
Abstract We initiate a comparative study of the properties of total palindrome complexity for binary words and arrays. From this…
Programmed motion with homogeneity assumptions
Abstract We consider the problem : Given a planar region \(T_{orb}\) described by one inequality \(g(x,y)\leq c_{0}\), find the potentials…
Straight-line solutions in two-dimensional homogeneous potentials
Abstract Within the framework of the inverse problem of Dynamics, we consider the following question with reference to the motion…
Logarithmic mean and weighted sum of geometric and anti-harmonic means
Abstract We consider the problem of finding the optimal values\U{3b1}, \(\U{3b2} \in R\) for which the inequality \(\U{3b1} G(a,b)+(1-\U{3b1} )C(a,b)<L(a,b)<\U{3b2}…
Bilateral inequalities for means
Abstract Let \((M1,M2,M3)\) be three means in two variables chosen from \(H,G,L,I,A,Q,S,C\) so that \(M_{1}(a,b)<M_{2}(a,b)<M_{3}(a,b),0<a<b\). We consider the problem of…