Approximate method for predicting the permanent set in a beam in vacuo and in water subject to a shock wave

An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions

Fairness and Annuitisation Divisors for Notional Defined Contribution Pension Schemes

The use of a gender-neutral annuity divisor introduces an intra-generational redistribution from short-lived towards long-lived individuals; this entails a transfer of wealth from males to females and from low socioeconomic groups to high socioeconomic groups. With some subpopulations consisting of females from low socioeconomic groups (or males from high groups), the net effect of the redistribution is unclear. The study aims to quantify the lifetime income redistribution of a generic NDC system using two types of divisor—the demographic and the economic—to compute the amount of an initial pension. With this in mind, the redistribution (actuarial fairness) among subpopulations is assessed through the ratio between the present value of expected pensions received and contributions paid. We find that all subgroups of women and men with high educational attainment benefit from the use of the unisex demographic divisor. This paper also shows that the value of the economic divisor depends markedly on population composition. When mortality differentials by gender and level of education are considered, economic divisors are mostly driven by the longevity effect corresponding to gender

Retrotransposons Are the Major Contributors to the Expansion of the Drosophila ananassae Muller F Element

The discordance between genome size and the complexity of eukaryotes can partly be attributed to differences in repeat density. The Muller F element (~5.2 Mb) is the smallest chromosome in Drosophila melanogaster, but it is substantially larger (\u3e18.7 Mb) in Drosophila ananassae. To identify the major contributors to the expansion of the F element and to assess their impact, we improved the genome sequence and annotated the genes in a 1.4 Mb region of the D. ananassae F element, and a 1.7 Mb region from the D element for comparison. We find that transposons (particularly LTR and LINE retrotransposons) are major contributors to this expansion (78.6%), while Wolbachia sequences integrated into the D. ananassae genome are minor contributors (0.02%). Both D. melanogaster and D. ananassae F element genes exhibit distinct characteristics compared to D element genes (e.g., larger coding spans, larger introns, more coding exons, lower codon bias), but these differences are exaggerated in D. ananassae. Compared to D. melanogaster, the codon bias observed in D. ananassae F element genes can primarily be attributed to mutational biases instead of selection. The 5’ ends of F element genes in both species are enriched in H3K4me2 while the coding spans are enriched in H3K9me2. Despite differences in repeat density and gene characteristics, D. ananassae F element genes show a similar range of expression levels compared to genes in euchromatic domains. This study improves our understanding of how transposons can affect genome size and how genes can function within highly repetitive domains

A Survey of the Development of the German Lied

The purpose of this paper is to identify the pertinent factors that established the German Lied, to see how the most important composers developed and used these factors, and to gain a perspective of the history and the composers of the German Lied

Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Vector-soliton collision dynamics in nonlinear optical fibers

We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schroedinger equations. We study a low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the two-bounce or two-pass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these "resonance windows." Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.Comment: 32 pages, submitted to Physical Review