Mixed method for the product integral on the infinite interval

In this note, quadrature formula is constructed for product integral on the infinite interval I(f) = ∫ w(x)f(x)dx, where w(x) is a weight function and f(x) is a smooth decaying function for x > N (large enough) and piecewise discontinuous function of the first kind on the interval a ≤ x ≤ N. For the approximate method we have reduced infinite interval x [a, ∞) into the interval t[0,1] and used the mixed method: Cubic Newton’s divided difference formula on [0, t3) and Romberg method on [t3,1] with equal step size, ti = t0+ih,i=0, …,n, h=1/n, where t0 = 0,tn=1. Error term is obtained for mixed method on different classes of functions. Finally, numerical examples are presented to validate the method presented

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

A multi-country test of brief reappraisal interventions on emotions during the COVID-19 pandemic

The COVID-19 pandemic has increased negative emotions and decreased positive emotions globally. Left unchecked, these emotional changes might have a wide array of adverse impacts. To reduce negative emotions and increase positive emotions, we tested the effectiveness of reappraisal, an emotion-regulation strategy that modifies how one thinks about a situation. Participants from 87 countries and regions (n = 21,644) were randomly assigned to one of two brief reappraisal interventions (reconstrual or repurposing) or one of two control conditions (active or passive). Results revealed that both reappraisal interventions (vesus both control conditions) consistently reduced negative emotions and increased positive emotions across different measures. Reconstrual and repurposing interventions had similar effects. Importantly, planned exploratory analyses indicated that reappraisal interventions did not reduce intentions to practice preventive health behaviours. The findings demonstrate the viability of creating scalable, low-cost interventions for use around the world

A global experiment on motivating social distancing during the COVID-19 pandemic

Significance Communicating in ways that motivate engagement in social distancing remains a critical global public health priority during the COVID-19 pandemic. This study tested motivational qualities of messages about social distancing (those that promoted choice and agency vs. those that were forceful and shaming) in 25,718 people in 89 countries. The autonomy-supportive message decreased feelings of defying social distancing recommendations relative to the controlling message, and the controlling message increased controlled motivation, a less effective form of motivation, relative to no message. Message type did not impact intentions to socially distance, but people’s existing motivations were related to intentions. Findings were generalizable across a geographically diverse sample and may inform public health communication strategies in this and future global health emergencies. Abstract Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

A global experiment on motivating social distancing during the COVID-19 pandemic

Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e. a controlling message) compared to no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly-internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared to the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly-internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing: Controlled motivation was associated with more defiance and less long-term behavioral intentions to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

Threshold resonances and eigenvalues of some schrödinger operators on lattices

The discrete Schrodinger operator Hλμ on the subspace of even functions of the Hilbert space ℓ2(Zn), with finite potential depending on λμ εR>0, is considered.The dependence of the threshold resonance and eigenvalues on theparameters λμ and n are explicitly derived