124310136
A new proof of a theorem of Dirac
121210068
On the existence of square roots in certain rings of power series
An apparatus for measuring the pressure in a very small volume, such as a biological cell or a capillary vessel. The apparatus has a space or chamber which is connected with a microcapillary tube, is pressure-tight, and is filled with a nearly incompressible medium, such as silicone oil or the like. To measure the pressure in the space, a device for converting the pressure into electrical values is connected to the space. A body, which partially displaces the medium and is moved from outside the space, extends into the space. The apparatus includes a reference electrode and another electrode which is arranged within the microcapillary tube and extends nearly to the opening of the tube. The two electrodes are electrically connected to a control device which is connected with a drive for moving the body which is provided for partial displacement of the medium. The control device is designed in such a way that by insertion or withdrawal of the body into the space, it regulates the interface (located in the microcapillary tube during the measuring process) between the medium and the fluid which penetrates the capillary tube from the volume of the cell. The regulation by the control device is a function not only of the measured value of the electrical resistance between the two electrodes as input variable, but also of a predetermined rated resistance value.
122388919
Enumeration of quadrangular dissections of the disk
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
124628297
On the non-existence of a type of regular graphs of girth $5$
121671285
Enumeration of non-separable planar maps
123473446
Hesse's theorem for a quadrilateral whose sides touch a conic