Smoothness of the Beurling transform in Lipschitz domains

Let D be a planar Lipschitz domain and consider the Beurling transform of the characteristic function of D, B(1_D). Let 11. In this paper we show that if the outward unit normal N on bD, the boundary of D, belongs to the Besov space B_{p,p}^{a-1/p}(bD), then the Beurling transform of 1_D is in the Sobolev space W^{a,p}(D). This result is sharp. Further, together with recent results by Cruz, Mateu and Orobitg, this implies that the Beurling transform is bounded in W^{a,p}(D) if N belongs to B_{p,p}^{a-1/p}(bD), assuming that ap>2.Comment: 32 page

Integrated Land Use Planning and Sustainable Watershed Management

This paper discusses the key issues and concerns regarding sustainable Philippine watershed management. Emphasis is made on the various requisites of a sustainable management with a focus on the critical roles of land use planning.land use planning, land management, watershed

Deep reinforcement learning based approaches for capacity sharing in radio access network slicing

Network slicing has become a fundamental capability for 5G networks to support the expected high variety of service requirements over a common physical network infrastructure. Each network slice can be customized for a specific application, making that the radio resources have to be accordingly managed by the Radio Access Network (RAN) part of the slice. In this thesis, three different Deep Reinforcement Learning (DRL) based approaches are presented to optimize the resource allocation among slices. A RAN slicing simulator scenario is developed, where the DRL mechanisms build knowledge about the network and learn how to optimize the capacity allocation for each tenant at every moment of time. The performance of each approach is studied based on simulation results, and before the comparison between the algorithms, the set of hyperparameters of each approach is tuned to optimize the learning process

Sobre el teorema de Liouville para funciones enteras

La idea del artículo es presentar las pruebas del teorema de Liouville sobre funciones enteras. En este trabajo recalcamos dos importantes aplicaciones, una en la demostración del teorema fundamental del álgebra y otra en el área de las aplicaciones conformes. El presente contiene una breve nota histórica de la vida de Joseph Liouville y su trabajo. También contiene la version del teorema de Liouville para funciones doblemente periódicas, funciones armónicas y aplicaciones cuasiconformes

Antioxidant Capacity and Antimicrobial Activity of Commercial Samples of Guava Leaves (\u3cem\u3ePsidium guajava\u3c/em\u3e)

Psidium guajava is a small tree native to South and Central America. Guava leaves have traditionally been used for treating different illnesses. These benefits can be attributed to phenolics and flavonoids produced by guava. The chemical composition of guava leaf extracts was correlated with biological activity. Total phenolics, total flavonoids, ABTS/DPPH, TZM-bl, plaque reduction, XTT, spectrophotometric and Kirby-Bauer assays were used to test phenols, flavonoids, antioxidant properties, antiviral activity, cytotoxicity, and antibacterial activity, respectively. The median cytotoxicity concentration and half-maximal effective concentration values were obtained in order to determine antiviral selectivity against human immunodeficiency virus type 1 and herpes simplex virus type 1. Antibacterial activity against Escherichia coli and Bacillus subtilis were evaluated using a spectrophotometric assay and Kirby-Bauer test. The guava leaf extracts had a high phenol (0.8 to 2.1 GAE mg/mL) and flavonoid (62.7 to 182.1 Rutin Eq mg/g DW) content that correlated with high antioxidant capacity and selective antiviral activity (therapeutic index values above 10). Results of antibacterial tests indicated that the extracts have activity against gram-negative and gram-positive bacteria

Compared to Mexico, religion's role in US society has hindered progress on legal equality for LGBT people

New research by Caroline Beer and Victor Cruz Aceves examines the puzzling finding that Mexico has offered greater legal equality for LGBT people for a longer period of time than the United States. They argue that this can be explained by the wider separation of church and state in Mexican politics and the strong importance of human rights in new democracies. Examining LGBT rights at the subnational level, they also find that states with more LGBT organizations and governors from left parties are more likely to recognize same sex relationships, but the religious makeup of states only matters in the United States, and not in Mexico