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 ...

The terminal velocity of rising microbubbles is a sensitive function of the bubble size and the surface concentration of mobile insoluble surfactants at the gas/liquid interface due to the Marangoni effect. With a model that allows for surface convection and diffusion, we delineate the regimes when the terminal velocity varies between the fully mobile (Hadamard-Rybczynski) and the fully immobil...

To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to these observers, and show that, for any locally inertial frame, the speed of a freely falling material particle is always less than the speed of light at the Schwarzschild black ...

To prevent the pilgrims or local people before falling of landslides we create an alert system for it by using modified particle filtering algorithm.in this we detect the change in position and velocity in the video image of rocks of mountain using modified particle filtering algorithm by tracking the movement of particles by using its likelihoods.

The aims of this work are to elucidate the effects that bulk solids properties have on effective drag experienced by large spheres immersed in an emulsion group-B under minimum fluidization conditions and analyze ways which different suspensions react towards applied shear rates. To investigate this, magnetic particle tracking was resolve trajectory falling-sphere measurements size, density, sp...

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.

OBJECTIVE To investigate balance, gait, falls, and fear of falling in patients with the hypermobility type of Ehlers-Danlos syndrome (EDS-HT). METHODS Twenty-two women with EDS-HT and 22 sex- and age-matched healthy control subjects participated in the study. Each subject performed the modified Clinical Test of Sensory Interaction on Balance (mCTSIB) and the Tandem Stance test (TS) on an Accu...

Drops, globules of a liquid in another liquid, are extremely important in many natural processes and industrial applications. The purpose of this study was to devise a method to measure the terminal velocity of drops rising in water due to buoyancy, and to compare observed values with the theoretical. Two questions were explored: (1) Do these drops continue to accelerate upward from a depth of ...