the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope α, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A Sturmian word s of slope α can be written as a product of these six minimal squares: s = X2 1X 2 2X 2 3 · · · . The square root of s is defined to be the word √ s = X1...

as a medium between people and the city, urbanscape makes a mental connection between individuals and their surroundings. it is usually difficult to conceive this mental relationship and its corresponding processes with usual methods. this study seeks to address the mental aspects of urbanscape and highlight its role and importance by using an innovative method. in this study, map-based methods...

Species range maps based on extents of occurrence (EOO maps) have become the basis for many analyses in broad-scale ecology and conservation. Nevertheless, EOO maps are usually highly interpolated and overestimate small-scale occurrence, which may bias research outcomes. We evaluated geographical range overestimation and its potential ecological causes for 1158 bird species by quantifying EOO m...