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1            Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k.
2 ary, but time independent and ergodic (i.e., irreducible and aperiodic).
3 is based upon the rich and deep formalism of irreducible biochemical networks.
4     The resulting representation is normally irreducible, but splits in the case of the K0 into two P
5 omprised of six basic (i.e., psychologically irreducible) categories, and instead suggesting four.
6                               A functionally irreducible complex contains multiple copies of three pr
7 ng frames, can be regarded as an example of "irreducible complexity." To address the biochemical func
8 but splits in the case of the K0 into two P0-irreducible components that are mixed by the excess of t
9 at exhibits the decomposition of R* into its irreducible components.
10 at an identity: an experience is a maximally irreducible conceptual structure (MICS, a constellation
11 ategies.We also developed a method to detect irreducible differences between the best possible automa
12 asizes the extent to which any network is an irreducible entity.
13 tion, with l parts, and let F(lambda) be the irreducible finite dimensional representation of GL(m) a
14 ain; we should expect to see a great deal of irreducible functional diversity in the brain at multipl
15      Therefore, we should expect a degree of irreducible imprecision in quantitative correspondences
16 ecently, it has been suggested that there is irreducible imprecision in such climate models that mani
17 y, and models with a significant new type of irreducible imprecision involving many fast, unstable mo
18      A systematic approach to deal with this irreducible imprecision is advocated through algorithms
19 s allow an estimate of the level of relevant irreducible imprecision.
20                                The amount of irreducible internal noise in spike trains, an important
21     If G is such a Lie group and Gamma is an irreducible lattice of G it turns out that the subgroup
22 nd in parallel, give rise to intertwined and irreducible mechanisms describing the complex chemical t
23 e 4-point propagators that contribute to the irreducible memory function into products of independent
24 pproximations are formulated in terms of the irreducible memory function, and we assess their efficac
25 eactions on the surface of catalysts with an irreducible metal-lanthanum, which is significantly diff
26 omputations that have evolved in response to irreducible noise during neural information processing.
27 d not be assumed to arise from fundamentally irreducible noise sources.
28 ntial to improve decoding in the presence of irreducible noise.
29 neral assumptions on g and D we construct an irreducible nonsingular variety U(c), a finite etale mor
30 pe states, treating the genotype variable as irreducible or unaltered by other colocalizing forms of
31 aph, we show how to output directly only the irreducible overlaps, significantly shrinking memory req
32 eafloor diking-eruptive events represent the irreducible, quantum events of upper oceanic crustal acc
33 eafloor diking-eruptive events represent the irreducible, quantum events of upper oceanic crustal acc
34 te magnetic structure consistent with Gamma3 irreducible representation appears, and the k component
35 the possibility that quantum states of other irreducible representation are mixed into the ground sta
36 uency mode that transforms as the asymmetric irreducible representation of the group.
37                       Ideal knots provide an irreducible representation of the knot, and they have so
38  We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but
39                   To each finite dimensional irreducible representation Vlambda of F we assign a mult
40 ic peaks develop, consistent with the Gamma4 irreducible representation, along with a splitting of th
41 ich we conjecture that the multiplicities of irreducible representations in various bi-degrees are gi
42 tation Vlambda of F we assign a multiplet of irreducible representations of B with m elements in each
43                    It is also shown that the irreducible representations of orbifolds of rank one lat
44 al of work has gone into construction of the irreducible representations of the symmetric group n (an
45 ntroduce the theory of the partially reduced irreducible representations which we use to obtain a sim
46 s in large Poincare systems leads to complex irreducible spectral representations for the Liouville-v
47 on at this synapse, and gain varies with the irreducible statistical fluctuations in photon arrival.
48  the single-site gold species is the same on irreducible supports as on reducible ceria, iron oxide,
49 ar (beta(J)(=1)) and octupolar (beta(J)(=3)) irreducible tensor contributions to the overall beta ten
50 iences; integration says that it is unified--irreducible to non-interdependent components; exclusion
51 rs of complex biomolecular systems are often irreducible to the elementary properties of their indivi
52                                              Irreducible uncertainties regarding the dose-response cu
53 to signals under conditions of reducible and irreducible uncertainty.
54 kin conductance all tracked the evolution of irreducible uncertainty.
55 he matrices formed by the fusion rules among irreducible V-modules are diagonalized by the matrix giv
56 n V satisfies in addition the condition that irreducible V-modules not equivalent to V have no nonzer
57 au |--> -1/tau on the space of characters of irreducible V-modules.

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