In the paper λ-method Mitrinovi´c-Vasi´c is applied aiming to improve Fink's inequality, and Shafer's inequality for arcus sinus function is observed. In monography [1, p. 247] Shafer's inequality is stated: (1) 3x 2 + √ 1 − x 2 ≤ asin x (0 ≤ x ≤ 1). The equality holds only for x = 0. In paper [2] Fink has proved the inequality: (2) asin x ≤ πx 2 + √ 1 − x 2 (0 ≤ x ≤ 1). The equality holds at b...

Natural human activities involve using and manipulating objects, often several at a time, simultaneously and continuously. For example, changing lanes while driving requires using a steering wheel and pedals, all while observing the road and making sure that lanes are clear. Not only are we recognizing these objects, but we know what to do with them (i.e., we can perceive object affordances). W...

We study the three-dimensional topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The three-dimensional lowest Landau level wave functions exhibit the quaternionic analyticity as a generalization of the complex analyticity of ...