We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a ...

In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...