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31. Summary of Background Data . Irreducible atlantoaxial dislocation is typically a chronic process that requires surgical treatment.

32. The Helmholtz free energy expansion of the Rochelle salt crystal is obtained by the basis function of the irreducible representations ofthe paraelectric phase group D2.

33. That which is irreducible to the self begins to come into focus e-e-e-e and a way of expressing this is to say e-e-e-e which is perhaps in some way or another a mask or a simulacrum of he-he-he-he.

34. Aim aimed at finding out the solution to judging an irreducible matrix as an H - matrices.

35. Most important, omega supplies us with an infinite number of these irreducible bits.

36. Unlust, on the other hand, is what remains unassimilable, irreducible to the pleasure principle.

37. We give a method of determining irreducible polynomials over a unique factorization domain.

38. Consequently a practical algorithm is provided for spread spectrum communication and channel code to use irreducible polynomials.

39. Futures used to be called commodities, the irreducible building blocks of the economy.

40. A British historian, Herbert Butterfield, called this the “absolute predicament and irreducible dilemma”.

41. Our estimate k - 17 reference your 18 th price irreducible as marker cost increase hardly accepted.

42. An " irreducible " element is one that can not be quantified.

43. By indirectly applying the Eisenstein discriminant method, this paper explores and discusses two ways of judging the integral coefficients polynomials to be irreducible over the rational number field.

44. The calculation of characters of group representation is the basis of studying the irreducible representation of groups.

45. Other advantages include ease of reconstruction of the comminuted irreducible intra-articular fracture, and in delayed reconstruction of intra- and extra-articular fractures.

46. The stinkiness of poop is not an irreducible fact about the universe.

47. A complete lattice L is called a C-lattice iff it is distributive and has a base consisting of irreducible elements. Some properties of C-lattices have been discussed in this paper.

48. Spectral radius is an important global characteristics of an irreducible Markov chain.

49. To have at least one sheep constituted an irreducible minimum, a sufficient condition for the activity to occur.

50. It is the metaphor for individuality: atomic. It is the irreducible seat of strength.

51. In this paper, we give some conditions that a subdirectly irreducible ring is a primitive ring, simple ring with identity, full matrix ring, or a division ring.

52. All elements of the organic whole were integrally linked as expressions of an irreducible essence.

53. Expenditure on road repair has been cut to an irreducible minimum.

54. Objective To investigate the traumatic pathologic cause, treatment and prognosis in the irreducible dislocation of the proximal interphalangeal joint.

55. The special matrices included inverse M - matrices, inverse Z - matrices, tridiagonal matrices and nonnegative irreducible matrices.

56. The subdirectly irreducible Clifford semigroups are characterized by means of the structure of congruence.

57. Character is used to mark the non-equivalent irreducible representation in group representation.

58. The total antisymmetric basis functions are constructed for irreducible representation of S3 permutation group from nine- dimensional hyperspherical harmonics.

59. Let us by all means see how much of the physicalistic conceptual scheme can be reduced to a phenomenalistic one; still, physics also naturally demands pursuing(sentence dictionary), irreducible in toto though it be.