The statistical analysis of functional data is a growing need in many research areas. We propose a new depth notion for functional observations based on the graphic representation of the curves. Given a collection of functions, it allows to establish the “centrality” of a function and provides a natural center-outward ordering of the sample curves. Robust statistics such as the median function ...

We show that Nechiporuk’s method [14] for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an Ω(n2/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [15] states that the majority function does not have a linear–size quantum formula.

Quantum dot cellular Automata technology is used in this paper which overcomes the design constraints of nanoscale CMOS circuits. This paper presents the analysis of 2:4 decoder circuit using four different methodologies. QCA based Decoder circuit is implemented using coupled majority voter minority gate, 45 0 rotated cells, multilayer wire crossings and five input Majority Voter gate. Comparat...

We extend graded modal logic (GML) to a logic that captures the concept of majority. We provide an axiomatization for majority logic, MJL, and sketch soundness and completeness proofs. Along the way, we must answer the question what is a majority of an infinite set? Majority spaces are introduced as a solution to this question.

in this note we point out and rectify some errors in a recently published paper “n. singh, r. jain: coupled fixed point results for weakly related mappings in partially ordered metric spaces, bull. iranian math. soc. 40 (2014), no. 1, 29-40”.

in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.