116788453
On an open problem of Paul Turán concerning 3-graphs
The third of Paul Turan’s 1961 list of Research Problems [4] reads: 
“If 2 ≦ l < k < n, then what is the minimal number μ of combinations C 1,C 2,..., C μ taken l at a time out of 1, 2,..., n with the property that each combination taken k at a time out of 1, 2,..., n contains at least one C j ? (For l = 2 the question is settled with exhibiting the only minimal C-system in my paper “Egy grafelmeleti szelsőertek-feladatrol”, Mat. es Fiz. Lapok (1941) 436–451, in Hungarian with German abstract.)”
124310136
A new proof of a theorem of Dirac
121338541
Enumeration of Triangulations of the Disk
A method of draining oil from a transmission housing, of an oil-injected screw compressor comprising a compressor housing containing rotor means and a transmission housing. A shaft of the compressor extends into the transmission housing from the compressor housing and the transmission housing is underslung relative to the compression housing. The first portion of the compressor intake stroke, or rotation, is prevented from being filled with intake gas such that a depression is created. Said depression is applied via a bore to a sump portion of the transmission housing, so that the absolute pressure differential between the sump and the suction portion of the rotor means draws oil out of the sump and into the rotor spaces. A compressor employing this method of draining oil is also described.
121690558
On a hierarchy of generalized diagonal dominance properties for complex matrices
ABSTRACT. This article concerns dominance conditions for an nXm matrix. In the simplest kind of dominance, the (absolute) value of the diagonal element exceeds the sum of the absolute values of the nondiagonal elements on the same row. This condition has been generalized in the literature in several ways, of which we consider ways in which the rows of the matrix cooperate. Our work amounts to a sorting out of certain dominance conditions that belong to a class e of dominance conditions. We prove a theorem characterizing all true statements of the form
122388919
Enumeration of quadrangular dissections of the disk
124628297
On the non-existence of a type of regular graphs of girth $5$
123473446
Hesse's theorem for a quadrilateral whose sides touch a conic