Sentence examples for essential fixed from inspiring English sources

Thus, the set of essential fixed point classes of (f^{q}) with (qmid n) is the same as that of (f^{q}) with (qmid n_{0}).

Let us still denote operatorname {Ess}(f):=bigl{ xin operatorname {Fix}(f mid xmbox{ is essential}bigr} the set of essential fixed points of f.

After the seminal work for essential fixed points of continuous functions (Brouwer type fixed points) in [18], essential components and essential sets of fixed points were introduced [19, 20].

For any essential fixed point class F of f, since ϕ is sparse, F ∩ S n − 1 contains u ( F ) fixed points p such that i ( S n − 1, ϕ, p ) = 1 and l ( F ) fixed points p such that i ( S n − 1, ϕ, p ) = − 1.

A new definition of essential fixed points is introduced for a large class of multivalued maps.

Then f admits an essential fixed point, i.e. (operatorname {Ess}(f neqemptyset).

In this category, I recommend looking at the top ten business ideas for 2012 selected by Springwise.com, which bills itself as "your essential fix of entrepreneurial ideas".

Also, if your budget becomes bloated, you won't be missing essential fixes like kitchen spruce-ups or basic yard work, and you can push to sell quickly.

From that basis, the show asks the question, "Can a person ever change or is your essential nature fixed forever?" What's the rundown so far?

It is equal to the number of essential (classical) fixed point classes F of f with F ∩ S n − 1 = ∅.

The smooth extension number N 1 ( f | ϕ ) is the number of essential (classical) fixed point classes F of f which are not representable on S n − 1.