For a tree T , let iT (t) be the number of independent sets of size t in T . It is an open question, raised by Alavi, Malde, Schwenk and Erdős, whether the sequence (iT (t))t≥0 is always unimodal. Here we answer the question in the affirmative for some recursively defined families of trees, specifically paths with auxiliary trees dropped from the vertices in a periodic manner. In particular, ex...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

The main issue addressed in this paper is how to help learners navigate in existing web-based learning resources. Towards this issue, we introduce a learner-centered navigation path planning. The key idea is to provide learners with a space, in which they can see through WWW pages to plan a navigation path. In this paper, we also demonstrate an assistant system, which is composed of hyperspace ...

Over repeated viewings of motion along a quasi-random path, ability to reproduce that path from memory improves. To assess the role of expectations and sequence context on such learning, subjects eye movements were measured while trajectories were viewed for subsequent reproduction. As a sequence of motions was repeated, subjects' eye movements became anticipatory, leading the stimulus' motions...

The pointwise traversal of a given path is a popular task in the area of robotics, e.g. in mobile, industrial or surgical robotics. The easiest method to describe paths is by a sequence of linear segments, and for many tasks the precision of a path approximated by linear segments is sufficient. The movements to be accomplished by a mobile robot or the robot’s end-effector are described by a seq...

The learning of the concept infinity, mediated by information and communications technology (ICT) under a didactic engineering approach, has been objective this research. Didactic engineering, with its different phases, shown path toward understanding concept, which true challenge for many mathematicians throughout history in terms comprehension application within various mathematical framework...

If the algorithm has in its memory two points x + ; x ? then the algorithm performs a binary search on the path connecting x + and x ? as follows: the algorithm picks the node y 2 which is the middle point on the path connecting x + and x ? ; the algorithm deenes an hypothesis h using the branch leading to y 2 and asks an equivalence query EQ(h). If the answer to the query is \YES" it stops wit...

This paper treats a high-level, algebraic programming method for the on-line control of actions in a realtime, parallel processing environment. The method is based on interaction of path expressions. On the basis of a set of path expressions evocation of actions can be controlled in realtime in a fully automated way. It is shown how intelligent system behaviour can be obtained by a combination ...

The problem of generating a smooth reference path, given a finite family of discrete, locally optimal paths, is investigated. A finite discretization of the environment results in a sequence of obstacle-free square cells. The generated path must lie inside the channel generated by these obstacle-free cells, while minimizing certain performance criteria. Two constrained optimization problems are...

Recently, DQDB (IEEE 802.6) MAN has been proposed as a component of the Personal Communication Networks, in which base stations of wireless infrastructures are connected by a number of DQDBs which in turn are connected by bridges. We propose a protocol for call setup and path migration in a cluster of DQDBs. To pursue simplicity, eeciency, and fastness in path setup, we use a link-state-like ro...