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Nonprofit organizations face challenges recruiting volunteers for morally important activities that may generate fear, such as firefighting, aid work and delinquent counseling. The purpose of this study is to examine how voluntary organizations can instill the virtue of courage among potential volunteers and motivate them to participate in such activities.

Three experimental studies examined how fear, hope and courage relate to the likelihood of volunteering. Study 1 investigated how integral hope (hope related to the context, i.e. hope emanating from volunteering activities) and incidental hope (hope unrelated to the context, i.e. a general hopeful feeling) affect volunteering intentions when there is low vs high fear. Study 2 examined whether courage mediated the effects of hope on volunteering intentions when there is low vs high fear. Study 3 replicated the findings in a different volunteering context.

Integral hope (but not incidental hope) in the face of high fear generates courage leading to intentions to volunteer. Both integral hope and incidental hope motivate volunteering intentions through positive affect (but not through courage) in low fear contexts.

The hypothetical volunteering scenarios and the gender distribution in the samples restrict the external validity of the findings. Family background in volunteering was not controlled for. Moral courage, physical courage and psychological courage were not separately measured.

Nonprofit organizations recruiting volunteers for risky voluntary activities that induce high fear should use integral hope in their marketing communications to instill courage among potential volunteers. For voluntary activities that are not very risky and generate low levels of fear among potential volunteers, nonprofit organizations can recruit volunteers through communications that use either integral hope or incidental hope.

This research shows that hope and fear are critical emotions in relation to courage – an essential virtue for volunteers. Courage is manifested when there is high fear and integral hope. Findings contribute to the research literatures on the marketing of volunteering and the moral psychology of courage.

The purpose of this paper is to present a new approach to solve nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

The authors first transform the given nonlocal boundary value problems of first‐ and second‐order differential equations into local boundary value problems of second‐ and third‐order differential equations, respectively. Then a modified Adomian decomposition method is applied, which permits convenient resolution of these equations.

The new technique, as presented in this paper in extending the applicability of the Adomian decomposition method, has been shown to be very efficient for solving nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

The paper presents a new solution algorithm for the nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

EASE of maintenance is a major consideration in the design of the Rolls‐Royce RB.211 three‐shaft turbofan, and one of the most important aspects of the advance in technology which the engine represents compared with engines at present in airline service.

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

AN approximate solution of the boundary layer equations recently completed involved the assumption of a velocity profile through the boundary layerdepending on two parameters. As a result the problem was reduced to that of the construction and solution of two equations governing the variation of these parameters around the surface of the cylinder considered. Earlier solutions, such as Pohlhauscn's, have made use of a single parameter only and have employed Kármán's momentum integral for its determination, but the additional, parameter now introduced necessitates the use of a further equation. It is the purpose of the present note to discuss and illustrate the properties of the second condition that was selected.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

This paper aims to investigate the existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions. With regard to this nonlinear boundary value problem, three popular fixed point theorems, namely, Krasnoselskii’s theorem, Leray–Schauder’s theorem and Banach contraction principle, are employed to theoretically prove and guarantee three novel theorems. The main outcomes of this work are verified and confirmed via several numerical examples.

In order to accomplish our purpose, three fixed point theorems are applied to the problem under consideration according to some conditions that have been established to this end. These theorems are Krasnoselskii's theorem, Leray Schauder's theorem and Banach contraction principle.

In accordance to the applied fixed point theorems on our main problem, three corresponding theoretical results are stated, proved, and then verified via several numerical examples.

The existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions are studied. To the best of the authors’ knowledge, this work is original and has not been published elsewhere.

Piezoelectric ceramics are often combined with other materials to fabricate composites, which are used for constructions of intelligent systems. This paper is concerned with the fracture of a piezoelectric fiber embedded in an elastic matrix of finite radius. The fiber composite medium is subjected to the axially symmetric mechanical and electrical loads. Fourier and Hankel transforms are used to reduce the problem to the solution of a system of integral equations. Numerical solutions for the crack tip fields are obtained for various crack sizes and different piezoelectric fiber volume fractions. Both impermeable and permeable crack‐face electrical boundary conditions are considered. Applicability and effect of the crack‐face electrical boundary conditions are discussed.