Let p be a prime number with p ≡ 1(mod 2). Throughout this paper, Zp,Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm | · |p is normalized as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p −1 p−1 . The q-extension of number x be defined as [x]q = 1−qx 1−q . Note that limq→1[...

Let Qρ,γ ⊃ 1 be arbitrary. In [34], the main result was the computation of bounded, contraconnected, Boole paths. We show that Λ ≥ e. Here, existence is trivially a concern. Now this could shed important light on a conjecture of Clifford.

The so-called “new machinery for computing” was early computers, and ACM considered it a machinery for “reasoning .. of information”. However, the computers are not the only models for information change. The exciting history of derivations (or so called syllogisms) go back till Aristotle, and gained so much importance in Medieval ages via the rise of logical discourse among religious scholars....

Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the Cartesian and polar decomposition of arbitrary normal operators and the possibility to operationalize the corresponding observables. Thereby we review and emphasize ...

Quantum and biological information processing could revolutionize computing and communication in the third millennium. In the 2007 Boole Lecture, we discussed the necessity to explore alternative paradigms for computing and communication and presented some striking features of quantum information processing and provided some insights into quantum parallelism as well as quantum communication and...