Type synthesis of 90°/180° dual-function upenders for large shell units of nuclear reactor

In this paper, unit vectors collinear with the axes of large shell units of nuclear reactors were used to represent the poses of the workpieces. Based on the motion operator interpretation of the rotation matrix, 60 kinds of rotation matrix permutations with 90° turns as the step length to achieve 180° flipping of the workpiece were obtained. After eliminating invalid permutations and merging homogenous permutations, class I, II, and III flipping motion models were obtained. By calculating the Lie algebra of each step of rigid body motion in the flipping motion model, the twist and the motion pair property for each step were obtained. By means of the permutation and combination theory, the sequence of the motion pairs for different configurations was determined, and the rules between sequential transformations and axis changes of the motion pairs under the initial configuration were stipulated. Three classes of 19 initial configurations of 90°/180° dual-function upenders were constructed. For three of them, taking into account the characteristics of the axial dimension variation of workpieces, prismatic pairs were added along the workpiece’s axis (vector), and 15 overall configurations of 90°/180° dual-function upenders were synthesized. This provides the basic theoretical support for the innovative design of upenders with independent intellectual property rights.

NORMAL PAIRS WITH ZERO-DIVISORS

Results of Davis on normal pairs (R, T) of domains are generalized to (commutative) rings with nontrivial zero-divisors, particularly complemented rings. For instance, if T is a ring extension of an almost quasilocal complemented ring R, then (R, T) is a normal pair if and only if there is a prime ideal P of R such that T = R[P], R/P is a valuation domain and PT = P. Examples include sufficient conditions for the "normal pair" property to be stable under formation of infinite products and ⋈ constructions.

Structural and Transformational Properties of All-Interval Tetrachords

An analysis (from Guy Capuzzo’s 1999 dissertation) of Elliott Carter’sScrivo in Ventofor solo flute serves as a point of departure for the consideration of certain properties of all-interval tetrachords (AITs). First, the roles of the individual (and a priori distinct) dyads are examined in light of the complement-union pair property exhibited by AITs. Second, a systematic means of describing common-tone relationships among AITs is proposed and studied. Examples from two works by Carter (Shard andScrivo in Vento) show the flexibility and usefulness of the system.

GRAPH PRODUCTS AND CANNON PAIRS

A pair (G, A) consisting of a group G and a finite generating set A is a Cannon pair if the language of all geodesics in the associated Cayley graph is regular. We prove that the Cannon pair property is preserved by graph products and indicate applications of this result to the geodesic and spherical growth series of graph products.