Rook theory has been investigated by many people since its introduction by Kaplansky and Riordan in 1946. Goldman, Joichi and White in 1975 showed that the sum over k of the product of the (n− k)-th rook numbers multiplied by the k-th falling factorial polynomials factorize into a product. In the sequel, different types of generalizations and analogues of this product formula have been derived ...

We investigate the coefficients generated by expressing the falling factorial (xy) as a linear combination of falling factorial products xy for l, m = 1, . . . , k. Algebraic and combinatoric properties are discussed, some in relation to Stirling numbers.

The wheelchair is the major means of transport for physically disabled people. However, it cannot overcome architectural barriers such as curbs and stairs. In this paper, the authors proposed a method to avoid falling down of a wheeled inverted pendulum type robotic wheelchair for climbing stairs. The problem of this system is that the feedback gain of the wheels cannot be set high due to model...

It has long been known that a simple rigid pendulum can be stabilized against small disturbances in its upside-down state by rapid vertical oscillations of its pivot. Over part of the parameter range for which this happens we find that there is a second, quite different way in which the pendulum can avoid falling over, namely by getting trapped in a limit cycle oscillation about the upward vert...

Falling rule lists are classification models consisting of an ordered list of if-then rules, where (i) the order of rules determines which example should be classified by each rule, and (ii) the estimated probability of success decreases monotonically down the list. These kinds of rule lists are inspired by healthcare applications where patients would be stratified into risk sets and the highes...

Although many papers have been published on visual tracking and visual servoing for vision‐based robotics, there are only a few research projects studying using vision to improve standing and walking stabilization for legged robots. In this paper, we proposition a “Visual Lifting Bipedal Walking” strategy, which uses visually measured information to control the robot to...

Introduction. We know little about how environmental challenges beyond home exacerbate difficulty moving, leading to falls among people with Parkinson's (PwP). Aims. To survey falls beyond home, identifying challenges amenable to behaviour change. Methods. We distributed 380 questionnaires to PwP in Southern England, asking participants to count and describe falls beyond home in the previous 12...

Previous studies on tones suggest that Mandarin listeners are more sensitive to pitch direction and slope while English listeners primarily attend to pitch height. In this study, just noticeable differences were established for pitch discrimination using a three-interval, forced-choice procedure with a two-down, one-up staircase design. A high rising and a high falling Mandarin tone were manipu...

Our study aimed to determine the level of fear of falling in elderly nursing home residents. The research population consisted of all the elderly residents of Manisa Municipal Nursing Home between November 2011 and February 2012. The 76 elderly people who agreed to participate were included in the study. A demographics form and the Tinetti Falls Efficacy Scale were used in data collection. The ...