We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously, is a function f of the size of the piles. Wythoff’s game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences, some of which are related to well-known sequences, but most are new. The main result is a theorem giving ...

E. Thorp introduced the following card shuffling model. Suppose the number of cards n is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue this way until both piles are empty. We show that if n is a power of 2 then the mixing time of the Thorp shuffle is O(l...

This study examines the capability of the Relevance Vector Machine (RVM) and Multivariate Adaptive Regression Spline (MARS) for prediction of ultimate capacity of driven piles and drilled shafts. RVM is a sparse method for training generalized linear models, while MARS technique is basically an adaptive piece-wise regression approach. In this paper, pile capacity prediction models are developed...

One of the greatest challenges to be faced in the fight against climate change in the construction sector is the fact that (non-traditional) conventional solutions are routinely accepted despite their high environmental impact. In particular, reinforced or mass concrete foundations are used at almost all sites, but they require a large amount of material, involve high emissions (some toxic), ar...

INTRODUCTION Ayurveda, the Indian system of medicine comprises of eight different sp cialties in which Shalyatantra, the surgical school of thoughts has got prime impo tance. Acharya Sushruta, (Su.Su.33/4 father of surgery has considered (haemorrhoids) in Ashta-mahagada major diseases). The incidence of h rhoids is common among all economical classes of population. Though the disease is within ...

In recent years, determining bearing capacity of piles from in-situ testing data as a complement to static and dynamic analysis has been used by geotechnical engineers. In this paper, different approaches for estimating bearing capacity of piles from SPT data are studied and compared. A new method based on N value from SPT is presented. Data averaging, failure zone and plunging failure of pil...

Sonic Echo (SE) testing method is a well-known, versatile method to gather information pertaining to unknown bridge foundations. Many studies on the applicability and methodology improvement of SE tests to evaluate individual piles and foundations supporting the superstructure have been reported previously. However, there is a rare opportunity for obtaining the performance of SE tests without t...

Retrofitting works are immensely essential for deteriorated and damaged structures in Engineering and Medical fields, in order to keep, or return to, the originality for safe guarding the structures and consumers. In this paper, different types of methods of retrofitting review notes are given based on the experimental, numerical and analytical methods results on strengthening the Reinforced ce...

We study the surface shape of two-dimensional piles using experiments and a continuum theory for surface flows of granular materials (the BCRE equations). We first obtain an analytical solution to the BCRE equations with a simple transformation and show that the surface shapes thereby predicted are in good agreement with the experimental results. By means of such an analytical solution, we find...