Sentence examples for which are generalized from inspiring English sources

First, we introduce some results of nonnegative tensors [10 12], which are generalized from nonnegative matrices.

The example demonstrates that our main result is an actual improvement over the results which are generalized.

In this paper, a further family of refinable functions is constructed, which includes pseudo-splines of Type II, based on refinement masks, which are generalized Bernstein polynomials.

Furthermore, a sequence { u n } in A converges to x if there is a sequence of positive numbers { ϵ n } such that lim n → ∞ ϵ n = 0 and d ( u n + 1, z n + 1 ) ≤ ϵ n, where z n + 1 ∈ A satisfies the condition that d ( z n + 1, S u n ) = d ( A, B ). Next, we establish a result for non-self-mappings which are generalized proximal contractions of the first kind and the second kind.

In vertebrates pair bonding probably initiated a qualitative shift from loose aggregations of individuals to complex negotiated relationships which are generalized to all social partners in only a few taxa, for example in anthropoid primates (Shultz & Dunbar 2007).

Theorem 3.5 gives the existence of such functions (U^{s}_{n}(xi,eta)) which are generalized solutions of problem (mathit {PK}_{2}) in D. In that way we found functions (u_{n}^{r}(r,t)=r^{-1}U_{n}^{s}(xi r,t),eta r,t))) which are generalized solutions of problem (mathit {PK}_{1}) in (G_{m}).

C1 summability which was generalized by various investigators using different summability methods with different sets of conditions.

The shape factor of every sample was calculated using Eq. 2, which was generalized based on the circularity factor defined by ISO 9276-6 [26].

Harris ([1915]) developed the first inventory model, Economic Order Quantity, which was generalized by Wilson ([1934]) who gave a formula to obtain economic order quantity.

In particular, a very powerful tool is the Banach fixed point theorem, which was generalized and extended in various directions (see [1 37]).

Then they proved a weak convergence theorem which is generalized simultaneously theorems of Browder and Petryshyn [12] and Gol'shteĭn and Tret'yakov [13].