Sentence examples for equal components from inspiring English sources

Formally, Poland and Lithuania were to be distinct, equal components of the federation, each retaining its own army, treasury, civil administration, and laws; the two nations agreed to cooperate with each other on foreign policy and to participate in a joint Diet.

We hope that it will be clear from the context whether a scalar is intended or a vector with equal components is intended.

Given a potential symmetric equilibrium price-vector (underline {p}) with equal components

where λ ∈ ( 0, 1 ), converges (strongly) to a coupled fixed point of F. Proof By Theorem 2, F has at least one coupled fixed point with equal components, ( x ¯, x ¯ ) ∈ C × C. We first show that the sequence { x n − F ( x n, x n ) } n ∈ N converges strongly to zero.

This also indicates that it is not necessary to consider only the case of a double sequence with equal components { ( x n, x n ) } in Theorems 3-6 (buthehe proof of a convergence theorem for such an iterative method will be essentially different from the one given in this paper).

Example 2 Let X = R (with the usual metric), C = [ − 4, 4 ] and F : C 2 → X be defined by F ( x, y ) = 4 − x 2 − 2 y, ∀ x, y ∈ C. Then F is weakly Lipschitzian with constants a = 8 and b = 2 (in the sense of Definition 1) and F possesses two coupled fixed points ( − 4, − 4 ), ( 1, 1 ) with equal components and two coupled fixed points with unequal components, ( − 1, 2 ) and ( 2, − 1 ).

Therefore, optimal maintenance decisions for suspension bridges designed according to allowable stress method are not consistent with those based on equal component reliability values.

As a result, we arrive at a definition of the symmetry of a geometrical figure in terms of its invariance when equal component parts are exchanged according to one of the specified operations.

We assessed the evidence against equal component risks using a chi-square statistic applied to the national average estimates.

Hence, although a larger proportion of end-sequences may have been genuine bodonid non-coding sequences (without representation in sequence databases), the library included a considerable, perhaps equal, component of bacterial DNA.

Because the values for Ni and Co are so similar, (9.14 times 10^{22}) and (9.09 times 10^{22}) cm(^{-3}) respectively, an average value of (rho ^*) was used to calculate the axis in the figure, corresponding to the assumption of an equal-component alloy.