On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been proven that the eigenvalue-based inconsistency (proposed as a part of AHP) is incorrect.Comment: Enhanced text, with 21 pages and 3 figures, proves that arbitrarily inaccurate pairwise matrices are considered acceptable by theories with a inconsistency based on the principal eigenvalue (e.g., AHP). CPC (corner pairwise comparisons) matrix is the crucial part of this study as it invalidates any eigenvalue-based inconsistency. All comments are highly appreciate

The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Nonconvolution nonlinear integral Volterra equations with monotone operators

Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear Volterra integral equations with convolution kernels and some comparison techniques. Therefore, this paper is devoted to find a wide class of nonconvolution Volterra integral equations where their solutions behave like those of Volterra equations with convolution kernels.Comment: 13 page

Group Pregnancy Care for refugee background women: a codesigned, multimethod evaluation protocol applying a community engagement framework and an interrupted time series design.

IntroductionPregnancy and early parenthood are key opportunities for interaction with health services and connecting to other families at the same life stage. Public antenatal care should be accessible to all, however barriers persist for families from refugee communities to access, navigate and optimise healthcare during pregnancy. Group Pregnancy Care is an innovative model of care codesigned with a community from a refugee background and other key stakeholders in Melbourne, Australia. Group Pregnancy Care aims to provide a culturally safe and supportive environment for women to participate in antenatal care in a language they understand, to improve health literacy and promote social connections and inclusion. This paper outlines Froup Pregnancy Care and provides details of the evaluation framework.Methods and analysisThe evaluation uses community-based participatory research methods to engage stakeholders in codesign of evaluation methods. The study is being conducted across multiple sites and involves multiple phases, use of quantitative and qualitative methods, and an interrupted time series design. Process and cost-effectiveness measures will be incorporated into quality improvement cycles. Evaluation measures will be developed using codesign and participatory principles informed by community and stakeholder engagement and will be piloted prior to implementation.Ethics and disseminationEthics approvals have been provided by all six relevant authorities. Study findings will be shared with communities and stakeholders via agreed pathways including community forums, partnership meetings, conferences, policy and practice briefs and journal articles. Dissemination activities will be developed using codesign and participatory principles

Molecular dynamics simulations of the growth of poly(chloro-para-xylylene) films

Parylene C, poly(chloro-para-xylylene) is the most widely used member of the parylene family due to its excellent chemical and physical properties. In this work we analyzed the formation of the parylene C film using molecular mechanics and molecular dynamics methods. A five unit chain is necessary to create a stable hydrophobic cluster and to adhere to a covered surface. Two scenarios were deemed to take place. The obtained results are consistent with a polymer film scaling growth mechanism and contribute to the description of the dynamic growth of the parylene C polymer

Production of deuterium, tritium, and 3^3He in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV at the CERN SPS

Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.Comment: 22 pages, 29 figures, 8 tables, for submission to Phys. Rev.

Phase-space dependence of particle-ratio fluctuations in Pb+Pb collisions from 20A to 158A GeV beam energy

A novel approach, the identity method, was used for particle identification and the study of fluctuations of particle yield ratios in Pb+Pb collisions at the CERN Super Proton Synchrotron (SPS). This procedure allows to unfold the moments of the unknown multiplicity distributions of protons (p), kaons (K), pions ($\pi$) and electrons (e). Using these moments the excitation function of the fluctuation measure $\nu_{\text{\text{dyn}}}$[A,B] was measured, with A and B denoting different particle types. The obtained energy dependence of $\nu_{\text{dyn}}$ agrees with previously published NA49 results on the related measure $\sigma_{\text{dyn}}$. Moreover, $\nu_{\text{dyn}}$ was found to depend on the phase space coverage for [K,p] and [K,$\pi$] pairs. This feature most likely explains the reported differences between measurements of NA49 and those of STAR in central Au+Au collisions

Measurement of event-by-event transverse momentum and multiplicity fluctuations using strongly intensive measures Δ[PT,N]\Delta[P_T, N] and Σ[PT,N]\Sigma[P_T, N] in nucleus-nucleus collisions at the CERN Super Proton Synchrotron

Results from the NA49 experiment at the CERN SPS are presented on event-by-event transverse momentum and multiplicity fluctuations of charged particles, produced at forward rapidities in central Pb+Pb interactions at beam momenta 20$A$, 30$A$, 40$A$, 80$A$, and 158$A$ GeV/c, as well as in systems of different size ($p+p$, C+C, Si+Si, and Pb+Pb) at 158$A$ GeV/c. This publication extends the previous NA49 measurements of the strongly intensive measure $\Phi_{p_T}$ by a study of the recently proposed strongly intensive measures of fluctuations $\Delta[P_T, N]$ and $\Sigma[P_T, N]$. In the explored kinematic region transverse momentum and multiplicity fluctuations show no significant energy dependence in the SPS energy range. However, a remarkable system size dependence is observed for both $\Delta[P_T, N]$ and $\Sigma[P_T, N]$, with the largest values measured in peripheral Pb+Pb interactions. The results are compared with NA61/SHINE measurements in $p+p$ collisions, as well as with predictions of the UrQMD and EPOS models.Comment: 12 pages, 14 figures, to be submitted to PR