In this paper, for the Stratified Median Ranked Set Sampling (SMRSS), proposed by Ibrahim et al. (2010), we examine the proportional and optimum sample allocations that are two well-known methods for sample allocation in stratified sampling. We show that the variances of the mean estimators of a symmetric population in SMRSS using optimum and proportional allocations to strata are smaller than ...

A variety of group 4 metal catalytic systems (C2-symmetric {EBTHI}-, {SBI}-type zirconocene complexes (C2-1–4); C1-symmetric (C1-5–8) and Cs-symmetric (Cs-9) {Cp/Flu}-type zirconocene complexes; Cp*2ZrCl2 (Cp* 2-10)), half-metallocene complexes (CpTiCl3, HM-11), constrained-geometry (CGC-12) titanium catalysts) and post-metallocene catalysts (Dow’s ortho-metallated amido-pyridino hafnium comple...

Numerical methods for solving weakly damped Hamiltonian systems are constructed using the popular Störmer-Verlet and implicit midpoint methods. Each method is shown to preserve dissipation of symplecticity and dissipation of angular momentum of an N -body system with pairwise distance dependent interactions. Necessary and sufficient conditions for second order accuracy are derived. Analysis for...

Multisymplecticity and the variational bicomplex are two subjects which have developed independently. Our main observation is that re-analysis of multisymplectic systems from the view of the variational bicomplex not only is natural but also generates new fundamental ideas about multisymplectic Hamiltonian PDEs. The variational bicomplex provides a natural grading of differential forms accordin...

The multi-symplectic form for Hamiltonian PDEs leads to a general framework for geometric numerical schemes that preserve a discrete version of the conservation of symplecticity. The cases for systems or PDEs with dissipation terms has never been extended. In this paper, we suggest a new extension for generalizing the multi-symplectic form for Hamiltonian systems to systems with dissipation whi...

A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...

NTRU is a very efficient public-key cryptosystem based on polynomial arithmetic. Its security is related to the hardness of lattice problems in a very special class of lattices. This article is motivated by an interesting peculiar property of NTRU lattices. Namely, we show that NTRU lattices are proportional to the so-called symplectic lattices. This suggests to try to adapt the classical reduc...

in future high-speed self-routing photonic networks based on all-optical time division multiplexing (otdm) it is highly desirable to carry out packet switching, clock recovery and demultplexing in the optical domain in order to avoid the bottleneck due to the optoelectronics conversion. in this paper we propose a self-routing otdm node structure composed of an all-optical router and demultiplex...

Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact of popular integration methods, we consider a scenario where soft and hard constraints are added to a custom designed deformable linear object. Since the go...