Sentence examples for a sequence of negative from inspiring English sources

Then Ψ has a sequence of negative critical values converging to 0. Now we give the proof of Theorem 1.3.

In critical point theory, Clark's theorem [16] asserts the existence of a sequence of negative critical values tending to 0 for even coercive functionals.

The phenomena of the lateral diffusion can be suppressed, however, by applying an AC voltage with a sequence of negative and positive voltages.

(ii) If a ≺ 0, then Σ p D ( a ) contains no positive eigenvalues, and it consists of a sequence of negative eigenvalues ( 0 > ) λ − 1 D ( a ) > λ − 2 D ( a ) > ⋯ > λ − k D ( a ) > ⋯.

(A5) d k : = inf u ∈ Z k, u ≤ ρ k φ ( u ) → 0, as k → ∞; (A6) i k : = max u ∈ Y k, u = r k φ ( u ) < 0 ; (A7) inf u ∈ Z k, u = ρ k φ ( u ) ≥ 0 ; (A8) ϕ satisfies the (PS) c * condition for every c ∈ [dk 0, 0). Then ϕ has a sequence of negative critical values converging to 0. Remark 2.3.

There is a layer in our mind which, if left it idle, begins to gnaw on you(gnaw in the sense it triggers a sequence of negative and unwanted thoughts which lead to frustration. So always keep doing something and make activity a habit. Smile freely and often. Smiles act as a lubricant and catalyst that helps you maintain an aroused, joyous state. Maintain a healthy emotional state.

The crash was caused by a sequence of incredibly negative circumstances.

We apply the method to US real GDP for the 1947 1 2013 3 period and find that a sequence of mostly negative shocks, rather than a few extraordinary large ones, are responsible for the changes in the US real GDP trend.

(i) If a ≻ 0, then Σ p N ( a ) contains no negative eigenvalues, and it consists of a sequence of non-negative eigenvalues 0 < λ 1 N ( a ) < λ 2 N ( a ) < ⋯ < λ k N ( a ) < ⋯.

If {a m } is a a sequence of non-negative real numbers and.

Let { a n } be a sequence of non-negative real numbers.