The phrase "a sequence of distinct" is correct and usable in written English.
It can be used when describing a series of items or elements that are unique or different from one another.
Example: "In mathematics, a sequence of distinct numbers can be used to illustrate various properties of functions."
Alternatives: "a series of unique" or "a list of different".
A loop is a sequence of distinct edges forming a path from a node back to itself.
The method constructs a periodic response assuming that each period is comprised of a sequence of distinct phases for which analytical solutions are known.
Let be a sequence of distinct points on the unit circle, and let We now define a continuous fixed-point free map for which.
admits a sequence of distinct eigenvalues of finite multiplicity 0 < λ 1 ( A ) < λ 2 ( A ) < ⋯ < λ k ( A ) < ⋯. such that λ k ( A ) → ∞ as k → ∞.
(LA) has a sequence of distinct eigenvalues 0 < λ 1 ( A ) < λ 2 ( A ) < ⋯ < λ k ( A ) < ⋯ → ∞, and each eigenvalue λ ( A ) of (LA) has a finite multiplicity.
Then system (1.1) has a sequence of distinct periodic solutions with period (k_{n}T) satisfying ({k_{n}}inmathbb{N}) and (k_{n}rightarrow+infty) as (nrightarrow +infty).
For example, 5 can be thought of as five times 1 instead of a sequence of five distinct counting acts.
there is a sequence of pairwise distinct critical points (local minima) of (Phi-lambda J) which weakly converges to a global minimum of Φ.
(c) If (gamma_{2}<+infty) then, for each (lambdain (0,frac{1}{gamma_{2}})), the following alternative holds: either (c1): there is a global minimum of Φ which is a local minimum of (Phi-lambda J), or (c2): there is a sequence of pairwise distinct critical points (local minima) of (Phi-lambda J) which weakly converges to a global minimum of Φ. .
(c) If (delta<+infty) then, for each (lambdain,]0,frac{1}{delthe[), the following alternative holds: either (c1): there is a global minimum of Φ which is a local minimum of (I_{lambda}), or (c2): there is a sequence of pairwise distinct critical points (local minima) of (I_{lambda}) which weakly converges to a global minimum of Φ. .
Here, F t i denotes the partial derivative of F with respect to t i. Precisely, under appropriate hypotheses on the behavior of the nonlinear term F at infinity, the existence of an interval Λ such that, for each λ ∈ Λ, the system (1) admits a sequence of pairwise distinct weak solutions is proved; (see Theorem 3.1).
