Is human life limited or unlimited? (A discussion of the paper by Holger Rootzén and Dmitrii Zholud)

We thank Holger Rootzén and Dmitrii Zholud’s for their stimulating work, that led us to further investigate the problem of best fitting the human life span distribution. Their assertion “human life is unlimited but short” is based on their conclusion that the exponential model is the best to fit. We provide results based on standard Extreme Value approaches, the Block Maxima and Peaks-over-Threshold, and on the whole data available in the IDL database (IDL A, B validations and GRG). We verify that negative values for the extreme value index are more likely, supporting the conclusion that models with finite endpoint seem better to fit to the human life span distribution.     

Rejoinder to discussion of the paper “Human life is unlimited—but short”

What can be learned from data about human survival at extreme age? In this rejoinder we give our views on some of the issues raised in the discussion of our paper Rootzén and Zholud (Extremes 20(4), 713–728, 2017).     

Quasirecognition by prime graph of 2 D n (3α) where n = 4m + 1 ≥ 21 and α is odd

Let G be a finite group. The prime graph of G is denoted by Γ(G). In this paper, as the main result, we show that if G is a finite group such that Γ(G) = Γ(² D _n (3^α)), where n = 4m+ 1 and α is odd, then G has a unique non-Abelian composition factor isomorphic to ² D _n (3^α). We also show that if G is a finite group satisfying |G| = |² D _n (3^α)|, and Γ(G) = Γ(² D _n (3^α)), then G ? ² D _n (3^α). As a consequence of our result, we give a new proof for a conjecture of Shi and Bi for ² D _n (3^α). Application of this result to the problem of recognition of finite simple groups by the set of element orders are also considered. Specifically, it is proved that ² D _n (3^α) is quasirecognizable by the spectrum.     

Discussion on paper “An Overview of Some Classical Models and Discussion of the Signature-based Models of Preventive Maintenance”

Possible generalizations of models and techniques of signature-based preventive Maintenance have been, in particular, advocated in the extended survey recently published on ASMBI. In view of future work in this direction by the reliability community a few conceptual aspects, related with concepts of system signature, will be recalled here.     

Generalized Hénon Mappings and Foliation by Injective Brody Curves

We consider a finite composition of generalized Hénon mappings \({\mathfrak {f}}:{\mathbb {C}}^2\rightarrow {\mathbb {C}}^2\) and its Green function \({\mathfrak {g}}^+:{\mathbb {C}}^2\rightarrow {\mathbb {R}}_{\ge 0}\) (see Sect. 2). It is well known that each level set \(\{{\mathfrak {g}}^+=c\}\) for \(c>0\) is foliated by biholomorphic images of \({\mathbb {C}}\) and each leaf is dense. In this paper, we prove that each leaf is actually an injective Brody curve in \(\mathbb {P}^2\) (see Sect. 4). We also study the behavior of the level sets of \({\mathfrak {g}}^+\) near infinity.     

Discussion: “On interactive buckling in a sandwich structure” by C. D. Coman

A recent article by Coman (Z Angew Math Phys 2009) on the response of compression sandwich struts made some claims on the quality of the simplified version of the interactive buckling model presented in Hunt and Wadee (Proc R Soc A 454(1972):1197–1216, 1998). Some of these claims are examined in detail herein; it is concluded that great care must be exercised when performing parametric studies with equations that have been derived from simplifying a mechanical model. This is because the resulting system of equations does not necessarily describe the original mechanical system in full, since the key assumptions necessarily change.     

Discussion: “On interactive buckling in a sandwich structure” by C. D. Coman

A recent article by Coman (Z Angew Math Phys 2009) on the response of compression sandwich struts made some claims on the quality of the simplified version of the interactive buckling model presented in Hunt and Wadee (Proc R Soc A 454(1972):1197–1216, 1998). Some of these claims are examined in detail herein; it is concluded that great care must be exercised when performing parametric studies with equations that have been derived from simplifying a mechanical model. This is because the resulting system of equations does not necessarily describe the original mechanical system in full, since the key assumptions necessarily change.     

-Decompositions of and D v ∪P where P is a 2-Regular Subgraph of D v

In this paper, we extend the study of C₄-decompositions of the complete graph with 2-regular leaves and paddings to directed versions. Mainly, we prove that if P is a vertex-disjoint union of directed cycles in a complete digraph D_v, then and D_v∪P can be decomposed into directed 4-cycles, respectively, if and only if v(v−1)−|E(P)|≡0(mod 4) and v(v−1)+|E(P)|≡0(mod 4) where |E(P)| denotes the number of directed edges of P, and v≥8.     

Exponential mixing of 2D SDEs forced by degenerate Lévy noises

We modify the coupling method established in Shirikyan (Exponential mixing for randomly forced partial differential equations: method of coupling, Springer, New York, 2008) and Shirikyan (J Math Fluid Mech 6(2):169–193, 2004) and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Lévy noises. In particular, these Lévy noises include α-stable noises (0 < α < 2). Thanks to the stimulating discussion (Nersesyan in Private communication 2011), this technique is promising to study the exponential mixing problem of SPDEs driven by degenerate symmetric α-stable noises.