Origin of laser damage in transparent dielectrics of the plexiglas type

A gasification mechanism is proposed. This mechanism is based on multiphoton photodegradation of the polymer molecules and the resulting formation of free radicals which trigger a chain reaction and the subsequent formation of gas molecules. The kinetics of this process, in which an important part is played by the microstructure of the material, are examined.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 232–238, March–April, 1973.     

Stability of cylindrical plexiglas shells exposed to dynamical axial loads

The dynamical stability of a cylindrical Plexiglas shell exposed to axial compression is studied by means of a nonlinear formulation. Main attention is paid to a study of the waves formed when the stability gets lost. Empirical relationships between the critical load and the geometrical and mechanical parameters of the shell are derived.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 740–743, July–August, 1972.     

Quasi-star-cutsets and some consequences

This paper introduces a structural property of minimal imperfect graphs, no minimal imperfect graph has a quasi-star-cutset, before describing some consequences. First, a large class of perfect graphs is obtained from the class of all bipartite graphs and their line-graphs; this class contains several well-known classes of perfect graphs. The second consequence deals with a composition operation of graphs which preserves perfection and which encompasses the most part of the compositions known to preserve perfection.     

Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible and illustrate that while epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.     

Axiomatization of semigroup consequences

We show (1) the consequence determined by a variety V of algebraic semigroup matrices is finitely based iffV is finitely based, (2) the consequence determined by all 2-valued semigroup connectives, Λ, ∨, ?, +, in other words the collection of common rules for all these connectives, is finitely based. For possible applications see Sect. 0.     

A new Yang number and consequences

Base sequences BS(m, n) are quadruples (A; B; C; D) of {±1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n + 1, n) known as normal and near-normal sequences, NS(n) and NN(n), as well as T-sequences and orthogonal designs play a prominent role in modern constructions of Hadamard matrices. In our previous papers (Doković, Classification of near-normal sequences, arXiv:0903.4390v1 [math.CO] 25 Mar (2009); Doković, Some new near-normal sequences, arXiv:0907.3129v1 [math.CO] 17 Jul (2009)) we have classified the near-normal sequences NN(s) for all even integers s ≤ 32 (they do not exist for odd s > 1). We now extend the classification to the case s = 34. Moreover we construct the first example of near-normal sequences NN(36). Consequently, we construct for the first time T-sequences of length 73. For all smaller lengths, T-sequences were already known. Another consequence is that 73 is a Yang number, and a few important consequences of this fact are given.     

Drug Release Kinetics from Biodegradable Polymers via Partial Differential Equations Models

In order to achieve prescribed drug release kinetics some authors have been investigating bi-phasic and possibly multi-phasic releases from blends of biodegradable polymers. Recently, experimental data for the release of paclitaxel have been published by Lao et al. (Lao and Venkatraman in J. Control. Release 130:9–14, 2008; Lao et al. in Eur. J. Pharm. Biopharm. 70:796–803, 2008). In Blanchet et al. (SIAM J. Appl. Math. 71(6):2269–2286, 2011) we validated a two-parameter quadratic ordinary differential equation (ODE) model against their experimental data from three representative neat polymers. In this paper we provide a gradient flow interpretation of the ODE model. A three-dimensional partial differential equation (PDE) model for the drug release in their experimental set up is introduced and its parameters are related to the ones of the ODE model. The gradient flow interpretation is extended to the study of the asymptotic concentrations that are solutions of the PDE model to determine the range of parameters that are suitable to simulate complete or partial drug release.     

Some consequences of Schanuel's conjecture

We study the algebraic independence of two inductively defined sets. Under the hypothesis of Schanuel's conjecture we prove that the exponential power tower E and its related logarithmic tower L are linearly disjoint.     

Density of specific Strebel points and its consequences

It is a well-known fact that Strebel points (i.e., the equivalence classes of quasiconformal maps satisfying the frame mapping condition of Strebel) are dense in Teichmüller spaces. In various areas, one has to deal with nowhere dense sets in the universal Teichmüller space T, and it is important to knowwhether a given nowhere dense subset E ⊂ T contains the Strebel points and, if so, whether these points are dense in E.     

Constructions for normal graphs and some consequences

Normal graphs can be considered as weaker perfect graphs in several ways. However, only few graphs are known yet to be normal, apart from perfect graphs, odd holes, and odd antiholes of length ≥ 9. Körner and de Simone [J. Körner, C. de Simone, On the odd cycles of normal graphs, Discrete Appl. Math. 94 (1999) 161-169] conjectured that every ()-free graph is normal. As there exist normal graphs containing C₅, C₇, or , it is worth looking for other ways to construct or detect normal graphs. For that, we treat the behavior of normal graphs under certain construction techniques (substitution, composition, and clique identification), providing several ways to construct new normal graphs from normal and even not normal ones, and consider the corresponding structural decompositions (homogeneous sets, skew partitions, and clique cutsets). Our results imply that normal graphs cannot be characterized by means of decomposition techniques as well as by forbidden subgraphs. We address negative consequences for the algorithmic behavior of normal graphs, reflected by the fact that neither the imperfection ratio can be bounded for normal graphs nor a χ-binding function exists. The latter is even true for the class of ()-free graphs and related classes. We conclude that normal graphs are indeed only “normal”.