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The author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.

The author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.

The author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).

To the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

The purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.

The paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.

The geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.

All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

This study aims to study the gas film stiffness of the spiral groove dry gas seal.

The present study represents the first attempt to calculate gas film stiffness in consideration of the slipping effect by using the new test technology for dry gas seals. First, a theoretical model of modified generalized Reynolds equation is derived with slipping effect of a micro gap for spiral groove gas seal. Second, the test technology examines micro-scale gas film vibration and stationary ring vibration to determine gas film stiffness by establishing a dynamic test system.

An optimum value of the spiral angle and groove depth for improved gas film stiffness is clearly seen: the spiral angle is 1.34 rad (76.8º) and the groove depth is 1 × 10^–5 m. Moreover, it can be observed that optimal structural parameters can obtain higher gas film stiffness in the experiment. The average error between experiment and theory is less than 20%.

The present study represents the first attempt to calculate gas film stiffness in consideration of the slipping effect by using the new test technology for dry gas seals.

This study highlights areas of key importance for building event resilience and provides best-practice industry examples that foster innovative, adaptable and transformative event environments, which are areas of high academic and managerial relevance in times of uncertainty.

The study employs a multicase study research design that draws on interviews with the leaders of four event organizations in Denmark and Norway: (1) the Steinkjer Festival, (2) Run Alone Denmark, (3) FC Midtjylland and (4) the Bergen International Festival.

The events demonstrated the critical necessity of understanding innovation and its contribution to resilience in the event sector, particularly in times of uncertainty, such as the COVID-19 pandemic. These organizations achieved success by continuously fostering innovative environments before COVID-19 by being value-driven and customer-centric organizations. Digital technologies were not used as makeshift solutions but rather to enhance event attendees' experiential platforms and expand each event's business potential.

The paper answers the call for event and festival research during the COVID-19 pandemic to explore the importance of understanding failure, crisis, innovation and recovery.

The paper's contributions to event management research are (1) adding to the ongoing discussion about building a resilient event sector in times of uncertainty, (2) screening how event organizers achieve innovation in their organizations and (3) providing insights on future requirements for events in a post-COVID world.