In this study, we design an efficient identity-based QER cryptographic scheme using the property of DLP with distinct discrete exponent and IFP.
It is revealed that the relationship of minimum creep rate versus applied engineering stress exhibits distinct power exponent n in three stress regions, which are associated with different deformation mechanisms.
The cumulative distribution of l displays power-law tails with two distinct exponents, αB=2 and αR=3.
That is, it is conceivable that on some more fundamental level there are only a small number of distinct exponents, for example α = 0, α = 1, and α = 2, and that the observed scaling laws with more complex exponents are different mixtures of these more fundamental scaling laws.
A distinct rate exponent is identified for grain orientations that have a propensity for slip on second-order pyramidal planes, highlighting the capability to capture the simultaneous action of different deformation mechanisms through HEXD.
Suppose Φ ( t ) = t α 1 + μ 2 t α 2 + ⋯ + μ n t α n and φ ∈ F, where μ 2, …, μ n are real parameters, and α 1, …, α n are distinct positive (not necessarily integer) exponents.
Let Φ ( t ) = t α 1 + μ 2 t α 2 + ⋯ + μ n t α n and Ψ ∈ C 1 ( [ a, b ] ), where μ 2, …, μ n are real parameters, and α 1, …, α n are distinct positive (not necessarily integer) exponents.
Definition 1.5 The p-iterated exponent of convergence of distinct zero-sequence of f ( z ) − φ ( z ) and the p-iterated exponent of convergence of distinct fixed points of f ( z ) are respectively defined to be λ ¯ p ( f − φ ) = lim r → ∞ ¯ log p N ¯ ( r, 1 f − φ ) log r, λ ¯ p ( f − z ) = lim r → ∞ ¯ log p N ¯ ( r, 1 f − z ) log r. (1.9).
Similar to Definition 1.6, we can also define the [ p, q ] − φ exponent of convergence of the (distinct) zero-sequence of a meromorphic function f ( z ).
Clearly, if g ( z ) = z, then Definition 1.1 is equivalent to the definition of the exponent of convergence of the sequence of distinct fixed points of f ( z ).
