This paper will look at the relationship between high girth and high chromatic number in both its finite and transfinite incarnations. On the one hand, we will demonstrate that it is possible to construct graphs with high oddgirth and high chromatic number in all cases. We will then look at a theorem which tells us why, at least in the transfinite case, it is impossible to generalize this to in...

Is is known that a Banach space contains an isomorphic copy of $c_0$ if, and only it can be equivalently renormed to almost square. We introduce study transfinite versions square spaces with the purpose relating them

When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. Linear method does not preserve the known values along the g...

the seismic performance of hybrid braces composed of steel and shape memory alloy (sma) was investigated in this paper. six types of hybrid braces were used, constituted by sma content of 0, 20, 40, 60, 80, and 100%. a nonlinear dynamic analysis was performed under el centro earthquake records, with the maximum acceleration of 0.6g and 0.9g. our results showed that the seismic performance, i.e....

In a general setting, the transfinite interpolation problem requires constructing a single function´Üµ that takes on the prescribed values and/or derivatives on some collection of point sets. The sets of points may contain isolated points, bounded or unbounded curves, as well as surfaces and regions of arbitrary topology. All such closed semi-analytic sets may be represented implicitly by real ...

We show that the space of transfinite words, is, ordinal-indexed over a Noetherian is also Noetherian, under natural topology which we call regular subword topology. characterize its sobrification and specialization ordering