scholarly journals Fractional variation of Hölderian functions

Author(s):  
Dimiter Prodanov

AbstractThe paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Hölderian functions. In particular, it is established that a class of such functions exhibits singular behavior under the action of fractal variation operators in infinitesimal limit. The link between the limit of the fractal variation of a function and its derivative is demonstrated. The paper presents a number of examples, including the calculation of the fractional variation of Cauchy sequences leading to the Dirac’s delta-function.

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll

Author(s):  
Andrea Lucibello ◽  
Christopher Hardly Joseph ◽  
Emanuela Proietti ◽  
Giovanni Maria Sardi ◽  
Giovanni Capoccia ◽  
...  

2021 ◽  
Author(s):  
Choolwe Muzyamba

Abstract Background The onset of the covid19 pandemic has sparked heated debate among scholars on the relevance of lockdowns. There are those in favor of the lockdown and others who are critical of it. However, despite the increased interest in understanding the relevance of lockdowns, there still has not been much focus on its relevance in low income countries like Zambia. Thus with the help of the SRT, we set out to explore and document the local characterization of the lockdown by residents of Lusaka, Zambia.Methods A qualitative study in the form of interviews was conducted in Lusaka, Zambia involving a sample of 68 participants. Due to the lockdown measures that were in place during the study, the interviews were conducted via phone calls and the data collected were later analyzed by use of thematic analysis technique.Results The lockdown was on one hand lauded for slowing down the incidence rates, preventing fatalities, and for protecting the healthcare system from collapse. On the other hand, it was criticized for exacerbating poverty levels, unemployment rates, increasing the rate of mental health problems, aiding gender based violence, and intensifying political repression and corruption. The results speak to the complexity in the characterization of the lockdown as a response to covid19 in Zambia. This observation demonstrates the folly of viewing, applying and characterizing the covid19 lockdown as a ‘one-size-fits-all’ approach in Zambia.Conclusion Thus rather than definitely establishing the lockdown as an incontestable good, as it is depicted by some scholars or as useless by its critics, our findings instead demonstrate the diversity and complexity in how it is locally viewed by Zambians. The study provides grounds for caution on simplistic and binary characterization of lockdowns. It indicates the need for careful dialog between the designers of lockdowns and citizens in order to tailor such interventions to local realities in context-specific ways. It also shows that though the development of such interventions, all the various and complex elements it embodies must be taken into account in order to realize optimum outcomes.


2020 ◽  
Vol 117 (25) ◽  
pp. 252601
Author(s):  
Dirk Wulferding ◽  
Geunyong Kim ◽  
Hoon Kim ◽  
Ilkyu Yang ◽  
E. D. Bauer ◽  
...  

2018 ◽  
Vol 154 (9) ◽  
pp. 2005-2019 ◽  
Author(s):  
Amine Marrakchi

An ergodic probability measure preserving (p.m.p.) equivalence relation ${\mathcal{R}}$ is said to be stable if ${\mathcal{R}}\cong {\mathcal{R}}\times {\mathcal{R}}_{0}$ where ${\mathcal{R}}_{0}$ is the unique hyperfinite ergodic type $\text{II}_{1}$ equivalence relation. We prove that a direct product ${\mathcal{R}}\times {\mathcal{S}}$ of two ergodic p.m.p. equivalence relations is stable if and only if one of the two components ${\mathcal{R}}$ or ${\mathcal{S}}$ is stable. This result is deduced from a new local characterization of stable equivalence relations. The similar question on McDuff $\text{II}_{1}$ factors is also discussed and some partial results are given.


Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1463
Author(s):  
Sumin Kim ◽  
Jongrak Lee

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).


2009 ◽  
Vol 58 (6) ◽  
pp. 2661-2672 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Pascal J. Thomas ◽  
Wlodzimierz Zwonek

Author(s):  
Omar Besbes ◽  
Francisco Castro ◽  
Ilan Lobel

We consider the pricing problem faced by a revenue-maximizing platform matching price-sensitive customers to flexible supply units within a geographic area. This can be interpreted as the problem faced in the short term by a ride-hailing platform. We propose a two-dimensional framework in which a platform selects prices for different locations and drivers respond by choosing where to relocate, in equilibrium, based on prices, travel costs, and driver congestion levels. The platform’s problem is an infinite-dimensional optimization problem with equilibrium constraints. We elucidate structural properties of supply equilibria and the corresponding utilities that emerge and establish a form of spatial decomposition, which allows us to localize the analysis to regions of movement. In turn, uncovering an appropriate knapsack structure to the platform’s problem, we establish a crisp local characterization of the optimal prices and the corresponding supply response. In the optimal solution, the platform applies different treatments to different locations. In some locations, prices are set so that supply and demand are perfectly matched; overcongestion is induced in other locations, and some less profitable locations are indirectly priced out. To obtain insights on the global structure of an optimal solution, we derive in quasi-closed form the optimal solution for a family of models characterized by a demand shock. The optimal solution, although better balancing supply and demand around the shock, quite interestingly also ends up inducing movement away from it. This paper was accepted by David Simchi-Levi, optimization.


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