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 ...

We call these equations the Donaldson-Thomas equations, and a solution (A,u) to these equations Donaldson-Thomas instanton. In [Ta1], we studied local structures of the moduli space of the DonaldsonThomas instantons such as the infinitesimal deformation and the Kuranishi map of the moduli space. In this article, we prove a weak compactness theorem of the Donaldson-Thomas instantons. This descri...

This paper proposes a method for removing image inconsistencies which occur by an existence of moving objects or a change of illumination condition when an omnidirectional image database is generated. The database is used for archiving an outdoor scene in wide areas or generating novel view images with an image-based rendering approach. In related work, it is difficult to remove moving objects ...

Inconsistencies frequently occur in news about the real-world. Some of these inconsistencies may be more significant than others, and some news may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. Possible actions on an inconsistency in a news report include ignore the inconsistency, resolve the inconsistency, an...