This paper studies the following two non-Newtonian equations with nonlinear boundary conditions. Firstly, we show that finite time blow up occurs on and get a rate an estimate for of equation $k_{t}=(\left \vert k_{x}\right ^{r-2}k_{x})_{x}$, $(x,t)\in (0,L)\times (0,T)\ $with $k_{x}(0,t)=k^{\alpha }(0,t)$, $k_{x}(L,t)=k^{\beta }(L,t)$,$\ t\in $and initial function $k\left(x,0\right) =k_{0}\lef...

The domain of spatiotemporal applications is a treasure trove of new types of data and queries. However, work in this area is guided by related research from the spatial and temporal domains, so far, with little attention towards the true nature of spatiotemporal phenomena. In this work, the focus is on a spatiotemporal sub-domain, namely the trajectories of moving point objects. We present new...

A lot of recent work has studied strategies related to bulk loading of large data sets into multidimensional index structures In this paper we address the problem of bulk insertions into existing index struc tures with particular focus on R trees which are an important class of index structures used widely in commercial database systems We pro pose a new technique which as opposed to the curren...

Finding the most accessible locations has a number of applications. For example, a user may want to find an accommodation that is close to different amenities such as schools, supermarkets, and hospitals etc. In this paper, we study the problem of finding the most accessible locations among a set of possible sites. The task is converted to a top-k query that returns k points from a set of sites...

Constraint search trees are a generic approach to search trees where all operations are defined in terms of constraints. This abstract viewpoint makes clear the fundamental operations of search trees and immediately points to new possibilities for search trees. In this paper we present height-balanced constraint search trees (HCSTs), a general approach to building height-balanced index structur...

Spatial databases have been increasingly and widely used in recent years. The R-tree proposed by Guttman is probably the most popular dynamic index structure for eciently retrieving objects from a spatial database according to their spatial locations. However, experiments show that only about 70% storage utilization can be achieved in Guttman's R-tree and its variants. In this paper, we propos...

Given a group G, RF-theory constructs a new group RF(G) and an action RF(G) → Isom(XG) by isometries of RF(G) on a canonically associated R-tree XG. We give an overview mostly focusing on the more basic aspects of this theory, up to and including the universal property of RF-groups and their associated R-trees.

Recently there has been an increasing interest in supporting bulk operations on multidimensional index structures. Bulk loading refers to the process of creating an initial index structure for a presumably very large data set. In this paper, we present a generic algorithm for bulk loading which is applicable to a broad class of index structures. Our approach differs completely from previous one...

Computational psychology has the aim to explain human cognition by computational models of cognitive processes. The cognitive architecture Adaptive Control of Thought – Rational (ACT-R) is popular to develop such models. Although ACT-R has a well-defined psychological theory and has been used to explain many cognitive processes, there are two problems that make it hard to reason formally about ...