EXPRESS: Time Periods Feel Longer When They Span More Category Boundaries: Evidence From the Lab and the Field

Seven experiments (total N = 3,509) and a large field dataset (N = 1,820,671) demonstrate that time periods of equal duration are not always perceived as equivalent. We find that periods feel longer when they span more time categories (e.g., hour, month). For example, periods like 1:45pm – 3:15pm and March 31st – April 6th (boundary-expanded) feel longer than, say, 1:15pm – 2:45pm and April 2nd – April 8th (boundary-compressed). Reflecting this, participants anticipated completing more work during boundary-expanded periods than equivalent boundary-compressed periods. This effect appears to result from the salience and placement of time boundaries. As a consequence, participants preferred scheduling pleasant activities for boundary-expanded and unpleasant activities for boundary-compressed periods. Moreover, participants were willing to pay more to avoid—and required more money to endure—a long wait when it was presented as boundary-expanded. Finally, data from over 1.8 million rideshare trips suggest that consumers are more likely to choose independent rides (e.g., UberX) when they are boundary-compressed when the alternative shared option (e.g., UberPool) is boundary-expanded. Together, our studies reveal that time periods feel longer when they span more boundaries, and that this phenomenon shapes consumers’ scheduling and purchasing decisions.

Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed

Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

Numerical implementation of solving a control problem for loaded differential equations with multi-point condition

A linear boundary value problem with a parameter for loaded differential equations with multi-point condition is considered. The method of parameterization is used for solving the considered problem. We offer an algorithm for solving a control problem for the system of loaded differential equations with multi-point condition. The linear boundary value problem with a parameter for loaded differential equations with multi-point condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multi-point condition, and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations concerning the parameters is composed by substituting the values of the corresponding points in the built solutions to the multi-point condition and continuity conditions. The numerical method for finding the solution of the problem is suggested, which based on the solving the constructed system and solving Cauchy problem on the subintervals by Adams method and Bulirsch-Stoer method. The proposed numerical implementation is illustrated by example.

On a mathematical model of dynamics of the elastic wedge-shaped medium with radiating defect

In the paper the mixed boundary value problem of antiplane vibrations is considered in the elastic wedge-shaped medium containing the radiating defect J2. Radiating generators are assumed to be located on defect boundaries and on the interval J1 of the wedge free boundary as well. The problem of reconstructing the wave field in the whole wedgeshaped region with its boundary is stated. A number of problems of analyzing acoustic emission signals by radiating defect are reduced to the problem considered in connections with using non-destructive testing elements of the technological equipment under exploitation. The problem in question is reduced to studying the solvability problems of the equivalent boundary integral equation system both for stress saltus on the defect J2and contact stresses on the interval J1 of the upper plane of the wedge.