Min-max minimal surfaces, horizons and electrostatic systems

We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality relating the area and the charge of a minimal surface of index one in a Cauchy data satisfying the Dominant Energy Condition for non-electromagnetic matter fields. Moreover, we explore a global version of this inequality, and the rigidity in the case of the equality, using a result proved by Marques and Neves.Comment: References updated. We added more details to the proof of the results in Section 6. arXiv admin note: text overlap with arXiv:1706.01037, arXiv:1202.6036, arXiv:1503.02938 by other author

Approximation of Fractional Order Conflict-Controlled Systems

We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov formulas, we propose an approximation of the considered system by a system described by a functional-differential equation of a retarded type. A mutual aiming procedure between the initial conflict-controlled system and the approximating system is given that guarantees the desired proximity between their motions. This procedure allows to apply, via the approximating system, the results obtained for functional-differential systems for solving control problems in fractional order systems. Examples are considered, results of numerical simulations are presented.Comment: Submitted to Progress in Fractional Differentiation and Application

Sponsored content advertising in a two-sided market

Sponsored content advertising, also known as native advertising, is a new ad format in which a brand's content takes the same form and qualities of the publisher's original content. While many advertisers have largely embraced this new advertising format, consumers seem to react negatively towards sponsored content ads. In this paper, we present an analytical model that studies the strategic role of sponsored content advertising in a two-sided media market. We identify conditions under which competing platforms would choose sponsored content advertising over traditional advertising. Despite consumers' negative sentiment towards sponsored content ads, they can be better off together with the advertisers when both platforms choose this ad format. In fact, we show that a certain degree of consumer disliking is necessary to make both advertisers and consumers better off with sponsored content ads. However, both competing platforms offering sponsored content ads may also result in a Prisoner's Dilemma equilibrium outcome generating sub-optimal profits. We further show that two symmetric media platforms can choose different advertising strategies, leading to an asymmetric equilibrium outcome. Lastly, we analyze how the presence of multi-homing advertisers as well as an incomplete ad market coverage would affect the sponsored content ad equilibrium

Network Non-neutrality Debate: An Economic Analysis

This paper studies the economic utilities and the quality of service (QoS) in a two-sided non-neutral market where Internet service providers (ISPs) charge content providers (CPs) for the content delivery. We propose new models on a two-sided market which involves a CP, an ISP, end users and advertisers. The CP may have either the subscription revenue model (charging end users) or the advertisement revenue model (charging advertisers). We formulate the interactions between the ISP and the CP as a noncooperative game problem for the former and an optimization problem for the latter. Our analysis shows that the revenue model of the CP plays a significant role in a non-neutral Internet. With the subscription model, both the ISP and the CP receive better (or worse) utilities as well as QoS in the presence of side payment at the same time. However, with the advertisement model, the side payment impedes the CP from investing on its contents.Comment: 15 pages, 10 figure

Some nonlinear inequalities and applications

Sufficient conditions are given for the relation $\lim_{t\to\infty}y(t) = 0$ to hold, where $y(t)$ is a continuous nonnegative function on $[0,1)$ satisfying some nonlinear inequalities. The results are used for a study of large time behavior of the solutions to nonlinear evolution equations. Example of application is given for a solution to some evolution equation with a nonlinear partial differential operator.Comment: 16 page