Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n≥ 0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A trapezoidal word is closed if its longest repeated prefix has exactly two occurrences in the word, the second one being a suffix of the word. Otherwise it is open...

The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function...

Abstract In embedded systems that necessarily require a steady source of power and (or) attaches to sensor(s), there are opportunities mix small batteries supply such power. The aim this research is optimize the geometry shape piezoelectric cantilevers harvest more Several cantilever geometries with various shapes (rectangular, triangular, circular, trapezoidal cross section) tested in COMSOL m...

The present study investigates the peristaltic transport of non-Newtonian fluid, modeled as power law and Bingham fluid, in a diverging tube with different wall wave forms: sinusoidal, multi-sinusoidal, triangular, trapezoidal and square waves. Fourier series is employed to get the expressions for temporal and spatial dependent wall shapes. Solutions for time average pressure rise — flow rate r...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

Methods for aggregating intuitionistic trapezoidal fuzzy information are investigated. Some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy ordered weighted averaging (ITFOWA) operator and intuitionistic trapezoidal fuzzy hybrid aggregation (ITFHA) operator, are p...

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the capsid of a T=1 virus. Growth occurs in the presence of an atomistic solvent and, under suitable conditions, achieves a high yield of complete shells. The s...

Frictional resistance across rough surfaces depends on the existence of slip on the liquid-gas interface; therefore, prolonging the existence of liquid-gas interface becomes relevant. In this work, we explore manipulation of the cavity shape in order to delay the wetting transition. We propose that liquid-driven vortices generated in the air cavity dissipate sufficient energy to delay the Cassi...

The role of environmental geometry in maintaining spatial orientation was measured in immersive virtual reality using a spatial updating task (requiring maintenance of orientation during locomotion) within rooms varying in rotational symmetry (the number of room orientations providing the same perspective). Spatial updating was equally good in trapezoidal, rectangular and square rooms (one-fold...