For almost 350 years it was known that 1729 is the smallest integer which can be expressed as the sum of two positive cubes in two different ways. Motivated by a famous story involving Hardy and Ramanujan, a class of numbers called Taxicab Numbers has been defined: Taxicab(k, j, n) is the smallest number which can be expressed as the sum of j kth powers in n different ways. So, Taxicab(3, 2, 2)...

BACKGROUND Taxicab drivers historically have had one of the highest work-related homicide rates of any occupation. In 2010 the taxicab driver homicide rate was 7.4 per 100,000 drivers, compared to the overall rate of 0.37 per 100,000 workers. PURPOSE Evaluate the effectiveness of taxicab security cameras and partitions on citywide taxicab driver homicide rates. METHODS Taxicab driver homici...

The famous story of the number 1729, the smallest integer which can be expressed as the sum of two positive cubes in two different ways, motivated the introduction of Taxicab Numbers. The smallest number expressible as the sum of two cubes in n different ways is called Taxicab(n). So, Taxicab(2) = 1729. Further on, Taxicab(5) = 48988659276962496. Computing Taxicab(n) is challenging and interest...

This paper proposes the Fuzzy Logic Model for Location Decisions of Taxicab Stands (FMOTS), which is a decision support system for decision makers, who wish to alleviate taxicab stand complexity in the short to medium term. In this study, an integrated model of GIS and fuzzy logic for taxicab stand location decision is built. The location decisions of taxicab stands in Ankara (Turkey), where or...

PROBLEM The homicide rate of taxicab-industry is 20 times greater than that of all workers. A NIOSH study showed that cities with taxicab-security cameras experienced significant reduction in taxicab driver homicides. METHODS Minimum technical requirements and a standard test protocol for taxicab-security cameras for effective taxicab-facial identification were determined. The study took more...

Carpooling taxicab services hold the promise of providing additional transportation supply, especially in extreme weather or rush hour when regular taxicab services are insufficient. Although many recommendation systems about regular taxicab services have been proposed recently, little research, if any, has been done to assist passengers to find a successful taxicab ride with carpooling. In thi...

It is well known that RN has subspaces of dimension proportional to N on which the l1 norm is equivalent to the l2 norm; however, no explicit constructions are known. Extending earlier work by Artstein– Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

Let n and n be respectively the uniform empirical and quantile processes , and deene R n = n + n , which usually is referred to as the Bahadur{Kiefer process. The well-known Bahadur{Kiefer theorem connrms the following remarkable equivalence: kR n k= p k n k n ?1=4 (log n) 1=2 almost surely, as n goes to innnity, where kfk = sup 0t1 jf(t)j is the L 1-norm. We prove that kR n k 2 = p k n k 1 n ?...