On complex multiplicative differentiation

In the present paper we discuss multiplicative differentiation for complexvalued functions. Some drawbacks, arising with this concept in the real case, are explained satisfactorily. Some new difficulties, coming from the complex nature of variables, are discussed and they are outreached. Multiplicative Cauchy–Riemann conditions are established. Properties of complex multiplicative derivatives are studied.The paper is a part of B-type project MEKB-09-05Publisher's Versio

A Realizable Quantum Three-Pass Protocol Authentication Based on Hill-Cipher Algorithm

A realizable quantum three-pass protocol authentication based on Hill-cipher algorithm is presented by encoded and decoded plaintext using classical Hill-cipher algorithm. It is shown that the encoded message transferred to the particles called quantum state where we assumed that a photon is used as a qubit and after the encoded message is transferred into photons, the polarization of each photon is rotated by an angle θj, which is chosen randomly for each qubit. The sender and receiver agree over a Hill-cipher key, the encryption occurs by utilization of the quantum three-pass protocol (QTPP), the decryption will be illustrated, and an example shows how the algorithm will work. Finally, the security of this algorithm is analyzed in detail

Intracell interference characterization and cluster interference for D2D communication

The homogeneous spatial Poisson point process (SPPP) is widely used for spatial modeling of mobile terminals (MTs). This process is characterized by a homogeneous distribution, complete spatial independence, and constant intensity measure. However, it is intuitive to understand that the locations of MTs are neither homogeneous, due to inhomogeneous terrain, nor independent, due to homophilic relations. Moreover, the intensity is not constant due to mobility. Therefore, assuming an SPPP for spatial modeling is too simplistic, especially for modeling realistic emerging device-centric frameworks such as device-to-device (D2D) communication. In this paper, assuming inhomogeneity, positive spatial correlation, and random intensity measure, we propose a doubly stochastic Poisson process, a generalization of the homogeneous SPPP, to model D2D communication. To this end, we assume a permanental Cox process (PCP) and propose a novel Euler-Characteristic-based approach to approximate the nearest-neighbor distribution function. We also propose a threshold and spatial distances from an excursion set of a chi-square random field as interference control parameters for different cluster sizes. The spatial distance of the clusters is incorporated into a Laplace functional of a PCP to analyze the average coverage probability of a cellular user. A closed-form approximation of the spatial summary statistics is in good agreement with empirical results, and its comparison with an SPPP authenticates the correlation modeling of D2D nodes