This research clarifies the characteristics of radiation fields associated with biophotons on the basis of Hamiltonian dynamics which describes phenomenological aspects of biophotons signals.

In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our results generalize the previous result by T. Cai (2001)

The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase separation in binary alloys by Cahn and Hilliard. Since then the equation has been extended to a variety of chemical, physical, biological, and other engineering fields such as spinodal decomposition, diblock copolymer, image inpainting, multiphase fluid flows, microstructures with elastic inhomogeneity, tumor growth simulation, and topology optimization. Therefore, it is important to understand the basic mechanism of the CH equation in each modeling type. In this paper, we review the applications of the CH equation and describe the basic mechanism of each modeling type with helpful references and computational simulation results.

Cryptographic primitives are fundamental building blocks for designing security protocols to achieve confidentiality,authentication, integrity and non-repudiation. It is not toomuch to say that the selection and integration of appropriate cryptographic primitives into the security protocols determines the largest part of the efficiency and energy consumption of the wireless sensor network (WSN). There are a number of surveys on security issues on WSNs, which, however, did not focus on public-key cryptographic primitives in WSNs. In this survey, we provide a deeper understanding of public-key cryptographic primitives in WSNs including identity-based cryptography and discuss their main directions and some open research issues that can be further pursued. We investigate state-of-the-art software implementation results We investigate state-of-the-art software implementation results of public-key cryptographic primitives in terms of execution time, energy consumption and resource occupation on constrained wireless devices choosing popular IEEE 802.15.4-compliant WSN hardware platforms, used in real-life deployments. This survey provides invaluable insights on public-key cryptographic primitives on WSN platforms, and solutions to find tradeoffs between ost, performance and security for designing security protocols in WSNs.

Our algorithm precomputes a primitive rs-th root of unity   where s is the largest positive integer satisfying rsjq   1, and is applicable for the cases when s is small.
The proposed algorithm requires one exponentiation for the r-th root computation and is favorably compared to the existing algorithms..
Our algorithm precomputes a primitive rs-th root of unity   where s is the largest positive integer satisfying rsjq   1, and is applicable for the cases when s is small.
The proposed algorithm requires one exponentiation for the r-th root computation and is favorably compared to the existing algorithms.