A model of the equations of two dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a Mode-I Crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half- space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lor...

The mode of a multiset of labels, is a label that occurs at least as often as any other label. The input to the range mode problem is an array A of size n. A range query [i, j] must return the mode of the subarray A[i], A[i+ 1], . . . , A[j]. We prove that any data structure that uses S memory cells of w bits needs Ω( log n log(Sw/n) ) time to answer a range mode query. Secondly, we consider th...

This paper describes a novel search engine, WithAir that provides contents retrieval for i-mode, the most popular cell-phone service in Japan. WithAir allows users to complete typical search tasks with 4.4 keystrokes on average through keyword/purpose-predictive navigation. These two forms of navigation simplify, respectively, keyword input and search result output. WithAir has been used to sea...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...