Analysis of a new variational model for image multiplicative denoising

In this paper, we study the mathematical properties of a new variational model for image multiplicative noise removal. Some important properties of the model, including the lower semicontinuity, the differential property, the convergence and regularization property, are established for the first time. The existence and uniqueness of a solution for the problem as well as a comparison principle have also been established

Deforming black holes with even multipolar differential rotation boundary

Motivated by the novel asymptotically global AdS$_4$ solutions with deforming horizon in [JHEP {\bf 1802}, 060 (2018)], we analyze the boundary metric with even multipolar differential rotation and numerically construct a family of deforming solutions with quadrupolar differential rotation boundary, including two classes of solutions: solitons and black holes. In contrast to solutions with dipolar differential rotation boundary, we find that even though the norm of Killing vector $\partial_t$ becomes spacelike for certain regions of polar angle $\theta$ when $\varepsilon>2$, solitons and black holes with quadrupolar differential rotation still exist and do not develop hair due to superradiance. Moreover, at the same temperature, the horizonal deformation of quadrupolar rotation is smaller than that of dipolar rotation. Furthermore, we also study the entropy and quasinormal modes of the solutions, which have the analogous properties to that of dipolar rotation.Comment: 18 pages, 21 figure

2-Amino-4-(4-hy­droxy-3,5-dimeth­oxy­phen­yl)-6-phenyl­nicotinonitrile

In the title compound, C20H17N3O3, the dihedral angles between the central pyridine ring and the two terminal rings are 15.07 (3) and 43.24 (3)°. The dihedral angle between the two terminal rings is 37.49 (4)° In the crystal, inter­molecular amine N—H⋯Nnitrile hydrogen-bonding inter­actions form inversion dimers, which are linked into chains through amine N—H⋯Ometh­oxy hydrogen bonds

3-Hy­droxy-2-[(4-hy­droxy-3,5-dimeth­oxy­phen­yl)(2-hy­droxy-4,4-dimethyl-6-oxo­cyclo­hex-1-en-1-yl)meth­yl]-5,5-dimethyl­cyclo­hex-2-en-1-one

In the title compound, C25H32O7, the 3-hy­droxy-5,5-dimethyl­cyclo­hex-2-enone rings adopt slightly distorted envelope conformations with the two planes at the base of the envelope forming dihedral angles of 57.6 (4) and 53.9 (9)° with the benzene ring. There is an intra­molecular hy­droxy–ketone O—H⋯O inter­action between the two substituted cyclo­hexane rings as well as a short intra­molecular phenol–meth­oxy O—H⋯O inter­action

2,2′-{[4,6-Bis(octyl­amino)-1,3,5-triazin-2-yl]aza­nedi­yl}diethanol

In the title compound, C23H46N6O2, the two hy­droxy groups are located on opposite sides of the triazine ring. One of the hy­droxy groups links with the triazine N atom via an intra­molecular O—H⋯N hydrogen bond. Inter­molecular O—H⋯N and N—H⋯O hydrogen bonding is observed in the crystal structure. π–π stacking is also observed between parallel triazine rings of adjacent mol­ecules, the centroid–centroid distance being 3.5944 (14) Å

Exact solution of gyration radius of individual's trajectory for a simplified human mobility model

Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that individual has constant travel speed and inferior limit of time at home and work, we prove that the daily moving area of an individual is an ellipse, and finally get an exact solution of the gyration radius. The analytical solution well captures the empirical observation reported in [M. C. Gonz`alez et al., Nature, 453 (2008) 779]. We also find that, in spite of the heterogeneous displacement distribution in the population level, individuals in our model have characteristic displacements, indicating a completely different mechanism to the one proposed by Song et al. [Nat. Phys. 6 (2010) 818].Comment: 4 pages, 4 figure

Deforming charged black holes with dipolar differential rotation boundary

Motivated by the recent studies of the novel asymptotically global AdS$_4$ black hole with deforming horizon, we consider the action of Einstein-Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge $q$ and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. We also study the entropy and quasinormal modes of deforming charged AdS black hole. It is interesting to find there exist two families of black hole solutions with different horizon radius for a fixed temperature, but these two black holes have same horizon geometry and entropy. Due to the existence of charge $q$, the phase diagram of entropy is more complicated.Comment: 19 pages, 9 figure