Extremal system for control the intensity of the rotary oscillator emission

Author(s):  
Andrey A. Kapelyuhovskiy
Keyword(s):  

1969 ◽  
Vol 12 (7) ◽  
pp. 803-807
Author(s):  
N. N. Leonov


1970 ◽  
Vol 13 (11) ◽  
pp. 1259-1263 ◽  
Author(s):  
N. N. Leonov




2019 ◽  
Vol 19 (07) ◽  
pp. 2050137 ◽  
Author(s):  
Felix Gotti

Let [Formula: see text] be an atomic monoid. For [Formula: see text], let [Formula: see text] denote the set of all possible lengths of factorizations of [Formula: see text] into irreducibles. The system of sets of lengths of [Formula: see text] is the set [Formula: see text]. On the other hand, the elasticity of [Formula: see text], denoted by [Formula: see text], is the quotient [Formula: see text] and the elasticity of [Formula: see text] is the supremum of the set [Formula: see text]. The system of sets of lengths and the elasticity of [Formula: see text] both measure how far [Formula: see text] is from being half-factorial, i.e. [Formula: see text] for each [Formula: see text]. Let [Formula: see text] denote the collection comprising all submonoids of finite-rank free commutative monoids, and let [Formula: see text]. In this paper, we study the system of sets of lengths and the elasticity of monoids in [Formula: see text]. First, we construct for each [Formula: see text] a monoid in [Formula: see text] having extremal system of sets of lengths. It has been proved before that the system of sets of lengths does not characterize (up to isomorphism) monoids in [Formula: see text]. Here we use our construction to extend this result to [Formula: see text] for any [Formula: see text]. On the other hand, it has been recently conjectured that the elasticity of any monoid in [Formula: see text] is either rational or infinite. We conclude this paper by proving that this is indeed the case for monoids in [Formula: see text] and for any monoid in [Formula: see text] whose corresponding convex cone is polyhedral.







2018 ◽  
Vol 0 (18) ◽  
pp. 9-14
Author(s):  
A. M. Sotnikov ◽  
A. I. Timochko ◽  
A. B. Tancyra ◽  
A. V. Fedin
Keyword(s):  


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