The probability of occurrence of extremely large energetic particle (SEP) events is determined by both the general properties of the distribution function, and the character of this function in the region of large particle fluxes (fluences and peak fluxes).
Initial fitting does not have to be as accurate as in the L-Q method, but the rate at which the solution converges to a minimum in the L-M method strongly depends on the character of the function and its use is recommended in the "final" stage of the process in order to optimize the solution.
It is known that the integer-order calculus is only determined by the local character of the function, while the fractional-order one can gather the global information of the function in the weighted form [13].
"The initial confrontation on the United States Supreme Court with the astounding differences in function and character of role, and the necessity for learning entirely new criteria for decisions, can be a traumatic experience for the neophyte".
The majority opinion would make no distinction whatsoever between the character of the function of the water system when it furnishes water for domestic and household use and when it is employed as a vehicle to bring water to the scene of a fire.
Using the monotonic character of the function from Lemma 3.2, in each of the intervals in Lemmas 3.3 3.6, together with Lemmas 4.3 and 4.4, it is easy to obtain the following results concerning semicycle analysis.
Note that, in cases (16) and (17), it is not necessary to assume the nondecreasing character of the function ϕ since, using that ϕ ∈ Φ, we deduce (14) and (15), respectively.
This proves that T satisfies the contractive condition of Theorem 1. Finally, the nonnegative character of the function G t, s) and f t, x) [assumption (H1)] gives us ( T 0 ) ( t ) = ∫ 0 1 G ( t, s ) f ( s, 0 ) d s ≥ 0, where 0 denotes the zero function.
The present data provide a striking demonstration of pulse and its subjective nature, characteristic for the proactive, predictive, and hypothesis-testing character of brain function in general [33], [34].
Due to the oscillating character of modal functions and because we consider only modal function modulus, there exist "mirror" depths which give secondary peaks in the contrast function (Figure 14(a)).
