In this paper, by introducing some parameters and by employing a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder’s theorem is given.

The “kissing number problem” asks for the maximal number of white spheres that can touch a black sphere of the same size in n-dimensional space. The answers in dimensions one, two and three are classical, but the answers in dimensions eight and twenty-four were a big surprise in 1979, based on an extremely elegant method initiated by Philippe Delsarte in the early seventies, which concerns ineq...

This material is dedicated to the estimation of the chromatic number and class of the conjugated triangulation and of the second conversion of the planar triangulation. This estimation may through some light on the difficulties, connected with the proof of Four Color Problem. Also this paper introduces some new hypotheses, which are equivalent to Four Color Problem.

A notice appeared in the Bristol Medico-Chirurgical Journal of February 1986 proposing "the formation of a new society with an interest in the History of Medicine". The proposers "wished to see a small group, all of whom would be willing to give a paper from time to time", so that members would be stimulated to research their special interests; and instead of relying on invited speakers with ex...

Between June 1983 and March 1992, we performed a capsular reconstruction procedure through an anterior approach in ten patients (ten shoulders) who had multidirectional laxity of the shoulder and symptomatic atraumatic posterior glenohumeral instability. The procedure included closure of the capsule in the rotator interval and imbrication of the anterior, inferior, and posteroinferior aspects o...

This paper extends the scenario of the Four Color Theorem in the following way. LetHd,k be the set of all k-uniform hypergraphs that can be (linearly) embedded into Rd . We investigate lower and upper bounds on the maximum (weak and strong) chromatic number of hypergraphs in Hd,k. For example, we can prove that for d ≥ 3 there are hypergraphs inH2d−3,d on n vertices whose weak chromatic number ...