Rings based on pure iron have been manufactured by laser powder bed fusion. Different experimental conditions implemented to manufacture simple rings called “bulk”. Selected were used fabricate “structured” rings, made up of stacking lamellae separated weakly densified metal zones or spacers. The magnetic properties these measured in order determine their maximum flux density, permeability and ...

Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first exact method for ...

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute generic fusion rules Grothendieck ring Rep(PSL(2,q)), q prime-power, applying Verlinde-like formula on character table. then prove that this family rings R_q interpolates to all integers q>=2, providing (when not prime-power) first example infinite non group-like simple integral ri...

The notion of strict closedness rings was given by J. Lipman [Amer. Math. 93 (1971), pp. 649–685] in connection with a conjecture O. Zariski. present purpose is to give practical method construction strictly closed rings. It also shown that the Stanley-Reisner simplicial complexes (resp. $F$-pure satisfying condition $(\operatorname {S}_2)$ Serre) are weakly Arf)

Let [Formula: see text] be a commutative ring with text]. We introduce the concept of weakly 1-absorbing primary ideal, which is generalization ideal. A proper ideal said to if whenever nonunit elements and text], we have or number results concerning ideals are given, as well examples ideals. Furthermore, give corrected version result on rings.