On the dual and inverse problems of scheduling problems with minimizing the maximum job penalty
In the modern world, a high-speed wireless Internet connection is a necessity rather than a luxury. To improve the efficiency of Wi-Fi networks in dense deployment, a novel amendment to the Wi-Fi standard, namely IEEE 802.11ax introduces Orthogonal frequency-division multiple access (OFDMA). In contrast to legacy Wi-Fi, where performance of a station to a considerable degree depends on rate control, aggregation and other decision-making algorithms implemented at the station, in 11ax networks it is the access point that schedules channel time and specifies transmission parameters for both uplink and downlink. Although OFDMA scheduling in 11ax has much in common with that in cellular networks, e.g. LTE, 11ax has some peculiarities, especially for uplink transmission. Focusing on such peculiarities, in this paper, we investigate the scheduling problem in 11ax, propose a set of schedulers for 11ax, compare their performance and determine the gain achievable by the usage of OFDMA.
In the article the theory of schedule, which the author offers to use for the optimization of logistic management of investment activity, is discerned.
To prepare cosmonauts for the mission on the International Space Station Cosmonaut Training Center must provide trainings for all sorts of the operations and emergencies. All the operations and emergencies combined into sets named onboard systems.
The following classical NP-complete scheduling problem is considered.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.