The results show that by importing material, energy and information, the complex system evolves to the direction of order and dynamic balance.
Valiron [15] proved that every meromorphic function of finite order ρ > 0 has at least one Borel direction of order ρ.
A ray arg z = θ ( 0 ≤ θ < 2 π ) starting from the origin is called a Borel direction of order σ of f ( z ) if the following equality: lim sup r ⟶ ∞ log n ( Ω ( θ, ε, r ), f = a ) log r = σ.
Block copolymer (BCP) self-assembly has been extensively used for soft templating or structure direction of ordered mesoporous transition metal oxides.
Unlike previous alternating direction methods of order higher than one, which only deliver unconditional stability for rectangular domains, the new high-order FC-AD (Fourier-Continuation Alternating-Direction) algorithm yields unconditional stability for general domains at an O(Nlog(N)) cost per time-step for an N point spatial discretization grid.
Remark 1.1 Chuang [16] proved that every meromorphic function f with infinite order ρ ( r ) has as least one Borel direction of infinite order ρ ( r ).
By the second half of the 15th century, the Augustinian order had become divided into two factions, one seeking reform in the direction of the order's original strict rule, the other favouring modifications.
One such structure is the ionospheric trough, which is a large-scale depletion in the F region plasma with a width in the latitudinal direction of the order of 5° 10° (for review, see Rodger et al. 1992).
The means of β ¯ b and β ¯ c did not differ systematically, consistent with the direction of the order effect being arbitrary and dataset dependent.
The parameter s∈{1,−1} indicates the direction of first-order filters, where s=1 corresponds to a recursive operation from left to right in g + and right to left for g −.
Number pairs were adapted from Moeller, Fischer, Nuerk, and Willmes (2009) and were balanced such that both relevant groups of stimuli (i.e. compatible versus incompatible trials) yielded statistically similar measures of multiple factors including overall numerical distance, unit distance, decade distance, problem size, correct hand response, and within-pair direction of numerical ordering.
