where Ω is a domain in RN . When Ω is a bounded domain in RN being convex in the zi direction and symmetric with respect to the hyperplane {zi = 0}, the famous theorem by Gidas, Ni, and Nirenberg [6] (or see Han and Lin [7]): if u is a positive solution of (1.1) belonging to C2(Ω) ∩C(Ω), then u is axial symmetric in zi. However, the axially symmetry of positive solution generally fails if Ω is ...

I hereby declare that the work submitted for assessment is original and my own work, except where acknowledged in the submission. Abstract This report presents the measurement of vehicular speed using a smartphone camera. The speed measurement is accomplished by detecting the position of the vehicle on a camera frame using OpenCV's library LBP cascade classifier, the displacement of the detecte...

Magnetic order and low-energy spin dynamics in the zero field ground state of Ni3V2O8 are revealed in elastic and inelastic neutron scattering experiments. Neutron diffraction shows that below T = 2.3 K the Ni2+ moments (spin S = 1) order in a cycloid pattern with incommensurate wave vector kICM = (0,1,τ ), where τ = 0.4030 ± 0.0004, which is superimposed on a commensurate antiferromagnetic spi...

A new computer-based platform has been proposed whose novelty consists in modeling the local site effects of the ground motion propagation using a hybrid approach based on an equivalent linear model. The soil behavior is modeled assuming that both the shear modulus and the damping ratio vary with the shear strain amplitude. So, the hysteretic behavior of the soil is described using the shear mo...

In human osteo-arthritis there is a loss of matrix ground substance in the fibrillated cartilage (Matthews, 1953; Collins and McElligott, 1960). Studies using radioactive sulphate have indicated that the loss of ground substance is accompanied by a reactive increase in the synthesis of sulphated matrix by all but the more superficial chondrocytes in fibrillated areas (Collins and McElligott, 19...

We consider the problem of optimally filtering (or rating) a set of items based on predicates (or scoring) requiring human evaluation. Filtering and rating are ubiquitous problems across crowdsourcing applications. We consider the setting where we are given a set of items and a set of worker responses for each item: yes/no in the case of filtering and an integer value in the case of rating. We ...

Local-density-approximation calculations are used to show that the metal-metal distance along the chains controls the charge-density wave (CDW) in halogen-bridged transition-metal linear-chain (MX) compounds. The strength of the CDW can be understood in terms of a two band Su-Schrieffer-Heeger model if a hard-core ion-ion repulsion potential is also added. We predict a second-order phase transi...