Sentence examples for which satisfies in from inspiring English sources

Let be a point which satisfies in the parts (i) and (ii) with.

After Iteration 1, there is only one cluster left, which satisfies in step (4.4) of Algorithm 1.

In the following theorem we show that if ϕ ( I ) is an injective operator and ϕ is an additive map which satisfies in (2.1), then the restriction of ϕ is a Jordan homomorphism multiplied by ϕ ( I ).

Evidently, A is a (cofinite) maximal m-open extension of S. For the converse, suppose that B is a nonempty proper cofinite m-open set, B c is a finite m-closed set which satisfies in all conditions of Theorem 3.5.

It is proved that finding all of the real solutions which satisfy in a system with interval coefficients is NP-hard.

Then, the following properties hold provided that ;. (i) ; are all composed -cyclic -contraction self-mappings which satisfy, in addition, ; (i.e., and ; ) and which possess common fixed points in, that is, ;.   (ii) There is a unique set satisfying the constraints, subject to, for any given and for any given.

(iv) If is a complete metric space, then there is a unique set satisfying ; with for any and any given.  . ; are all composed -cyclic -contraction self-mappings which satisfy, in addition, ; (i.e., and ; ) and which possess common fixed points in, that is, ;.

These are "foods" which satisfy in the short-term, but lead to long-term malnutrition and a host of dietary illness.

Now we use in place of in (1.3), then (1.1) satisfying (1.3) is equivalent to (5) which satisfies (6) in [1], we can obtain the following result which is the improving result of [1, Theorem  2].

Let (B=(b_{ij})_{ntimes n}) be a real symmetric matrix which satisfies conditions in Theorem  3.1.

The SiC ceramics were successfully joined at a low temperature of 1000 °C with a flexural strength of 168.2 MPa, which satisfies applications in corrosive environments.