Sentence examples for are of the same dimension from inspiring English sources

Let us consider the case where both and are of the same dimension.

From isomorphisms (5.2), sequence (5.4), and sequence (5.5), it follows that the spaces H i ( C · ) Open image in new window and H i ( ( X, Y ), R ) Open image in new window are of the same dimension for each i.

The bound molecules are detected on autoradiographs by the failure of binding of a radio labeled form of the peptide under study; the probes are of the same dimensions as glass microelectrodes and hence are relatively atraumatic.

Viète retained the classical principle of homogeneity, according to which terms added together must all be of the same dimension.

Thus, Viète did not break the important Greek tradition whereby the terms equated must always be of the same dimension.

In our study, it is of the same dimension as of the bottom photovoltaic panel.

The core-shell cylinders are assumed to be of the same dimension and composition.

In homogeneous transfer learning, the feature spaces of the data in the source and target domains are represented by the same attributes (Xs = Xt) and labels (Ys = Yt) while the space itself is of the same dimension (d s = d t).

Furthermore, particle S2 with a 80 nm Ti under-layer is of the same dimension as particles R1 and R2.

Yet, the recent invasion of Europe by Ae. albopictus mosquitoes (5 ) and the marked ecology of this mosquito make emergence of a new DF epidemic possible, even if the impact of such an event is not expected to be of the same dimension as the epidemic described here.

In general, the ith model takes the form (1) where u is a q-dimensional vector denoting the input, x i is an n i -dimensional vector denoting the state, y i is an ℓ-dimensional vector denoting the output (which is of the same dimension for each model) and g i is matrix-valued, with size n i × q.