(1) The irreducibility thesis, in its general outline, might be summed up thus.

(2) The strong irreducibility of infinite multiplicity operator weighted shifts with weighted sequence of inverse operators are discussed.

(3) One-dimension uniformity testing is extended, irreducibility and frequency slots lingering are suggested. Frequency slots lingering is put forward to test the performance of DFH patterns.

(4) Main Outcome Measures: Clinical and radiographic markers of irreducibility, surgical findings, fixation methods, reduction accuracy, and injury- and treatment-related complications.

(5) Then for comparison, entertainment and for later examination we offer a more novel approach which apparently uses only irreducibility.

(6) Queueing network models of re-entrant lines are developed, and are converted to the canonical forms that are solvable by non-linear matrix equations. Irreducibility of such systems is studied.

(7) Multiple cultures mainly contain two implications: the coexistence of many cultures and irreducibility.

(8) This paper gives an effective algorithm for deciding of irreducibility and aperiodicity of nonnegative matrices.

(9) The system of educational activities is a special complex system, it has the characteristics of nonlinear, irreducibility, self organization, contingency etc.

(10) This paper is a further effort to investigate the irreducibility of this semigroup.

(11) It is also a form of dualism , because it allows the irreducibility of mental states and properties.

(12) In the meantime, the matrix's eigenwert and nonsingular problem was analyzed under the condition of irreducibility and diagonally dominance.

(13) As known today, brain, one of a classic giant system, is characterized by open complexity. While mind, brain's advances functional property, is irreducibility.

(14) But this theory is still full of problems, mainly in the argument analogy, the state of mind ontological irreducibility on the causes and free will.

(15) The system of teaching activities is a special complex system; it has the characteristics of non-linear, irreducibility, self-organization, contingency, openness etc.