On the structure of the solution set of a generalized Euler–Lambert equation

Mező, István

doi:10.1016/j.jmaa.2017.05.061

Cited by 20 publications

(6 citation statements)

References 32 publications

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“…This is a rewritten form of the generalized Euler-Lambert or r-Lambert equation [12]. The solution to the above equation is denoted by the r-Lambert function of the parameter α: W r (α).…”

Section: High Energy Structure and Markovianity: M = 0 L < ∞ Casementioning

confidence: 99%

Non-Markovianity in atom-surface dispersion forces

Intravaia¹,

Behunin

Henkel

et al. 2016

Phys. Rev. A

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We discuss the failure of the Markov approximation in the description of atom-surface fluctuationinduced interactions, both at equilibrium (Casimir-Polder forces) and out-of-equilibrium (quantum friction). Using general theoretical arguments, we show that the Markov approximation can lead to erroneous predictions of such phenomena with regard to both strength and functional dependencies on system parameters. Our findings highlight the importance of non-Markovian effects in dispersion interactions. In particular, we show that the long-time power-law tails of temporal correlations, and the corresponding low-frequency behavior, of two-time dipole correlations, neglected in the Markovian limit, dramatically affect the prediction of the force.

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Section: High Energy Structure and Markovianity: M = 0 L < ∞ Casementioning

confidence: 99%

Non-Markovianity in atom-surface dispersion forces

Intravaia¹,

Behunin

Henkel

et al. 2016

Phys. Rev. A

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“…The r-Lambert W function, e.g., [16][17][18], denoted h −1 r or W r , is the inverse of h r defined according to h r (w) = rw + we w . (…”

Section: Definitionsmentioning

confidence: 99%

“…Whilst such a relationship is important, it does not directly facilitate finding approximations for the inverse Langevin function as the generalized Lambert W function does not have an explicit analytical form. The contribution of this paper is to detail a relationship between the inverse Langevin function and the r 0 -r 1 -Lambert W function which is a generalization of the r-Lambert W function that has been considered by Mező [16], Mező and Baricz [17], and Jamilla [18]. The derived relationship leads to new approximations for the inverse Langevin function with potentially lower relative error bounds than comparable approximations.…”

Section: Introductionmentioning

confidence: 99%

Relationship between Inverse Langevin Function and r0-r1-Lambert W Function

Howard

2024

AppliedMath

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The relationship between the inverse Langevin function and the proposed r0-r1-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable published approximations. High accuracy approximations, based on Schröder’s root approximations of the first kind, are detailed. Several applications are detailed.

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“…For details and properties of the generalized Lambert W function see Siewert and Burniston (1974), Mező (2017), and Wright (1961.…”

Section: A6 Overcapacity and Queuing Effectsmentioning

confidence: 99%

Product Selling vs. Pay-Per-Use Service: A Strategic Analysis of Competing Business Models

2022

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We present a model that suggests possible explanations for the observed proliferation of “pay-per-use” (PPU) business models over the last two decades. Delivering “fractions” of a product as a service offers a cost advantage to customers with lower usage but requires extra delivery costs. Previous research focused on information goods (with negligible production costs) and predicted that PPU, when arising as a differentiation to selling in equilibrium, would fundamentally achieve lower profits than selling. We extend the theory by covering goods with any production cost in duopolistic competition. We show that PPU business models can be more profitable than selling (especially at midrange production costs), as long as their delivery costs are not too high, a requirement that is more easily fulfilled as new technologies reduce these costs. Moreover, if firms are imperfectly informed about their customers’ usage profiles, PPU’s effective pricing of customers’ varying usage offers an additional advantage over selling. This requires companies to employ accounting methods that do not inappropriately allocate production costs over stochastic usage levels. If PPU service provision suffers from queueing inefficiencies, this does not fundamentally change the relative profitability of the PPU and selling models, provided that PPU providers can attract sufficiently high demand to benefit from pooling economies. This paper was accepted by Charles Corbett, operations management.

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On the structure of the solution set of a generalized Euler–Lambert equation

Cited by 20 publications

References 32 publications

Non-Markovianity in atom-surface dispersion forces

Non-Markovianity in atom-surface dispersion forces

Relationship between Inverse Langevin Function and r0-r1-Lambert W Function

Product Selling vs. Pay-Per-Use Service: A Strategic Analysis of Competing Business Models

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