Trapezoidal words are words having at most n+1 distinct factors of length n for every n ≥ 0. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a p...

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, a new decision making analysis method is developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced, and the com...

In this article, stress analysis and energy estimation during cold-roll forming of symmetrical channel sections have been discussed. Geometry of sheet strip is pre-estimated by a shape function. Then longitudinal, transversal and shear strains have been calculated. Using both the Levy-Mises and the Prandtl Reuss equations, and also considering the Bauschinger effect, stress distributions have b...

Numerous factors influence the leftward bias (pseudoneglect) in perceived line midpoint of normal subjects in line bisection tasks. Cues are a potent factor; left and right cues promote shifts in perceived midpoint to the left and right, respectively. Trapezoidal lines have recently been shown to influence perceived line midpoint, displacing it toward the larger side. The present experiments te...

To obtain a higher heat transfer in the low Reynolds number flows, wavy channels are often employed in myriad engineering applications. In this study, the geometry of grooves shapes is parameterized by means of four angles. By changing these parameters new geometries are generated and numerical simulations are carried out for internal fully developed flow and heat transfer. Results are compared...