A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Multi-frequency AOM for multi-beam laser scanning exposure system

Digital printing systems recorded on films or computer to plates (CTPs) have been required to improve their productivity and image quality. Under the circumstance, a printing technology of the multi-beam laser scanning for the drum capstan system, which is almost the same as optics configuration as the flat bed system, was developed using a newly developed multi-frequency acousto–optic modulator (AOM) as a key device instead of ultra-fast scanning devices toward a main scan direction. The multi-frequency AOM was developed with phased array-type transducers, achieving a wider bandwidth of over 160 MHz. The design consisted of a simultaneous three beams generation with interlace scan to avoid the beat effect by adjacent Doppler-shifted beams, which consequently attained the fastest recording speed of 5.0 mm/s compared with 2.0–3.0 mm/s of existing systems in those days. Furthermore, a couple of critical parameters of the multi-frequency AOM are studied, for example, a treatment of third-order intermodulation and also beat effect in connection with photosensitive media. As a result, the necessity of interlaces scanning to obtain good image quality without beat effect and also to allow a lower laser power to apply is proposed.     

Superintegrable cases of four-dimensional dynamical systems

Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.     

Magnetic Properties of Pt-Based Nanoalloys: A Critical Review

In recent years, magnetic nanoalloys (MNAs) have attracted many attentions from all over the world, due to their potential applications in the broad fields of magneto-optics, data storage, engineering, and biology. Among these MNAs, Pt–M (M = Fe, Co, Ni) MNAs have been considered to be the most promising ones, due to their superparamagnetism and response to a magnetic field. Here, we firstly review the experimental work on the synthesis, characterization, and magnetic properties of Pt–Fe, Pt–Co, and Pt–Ni MNAs. Then, we discuss the recent theoretical work on Pt–Fe, Pt–Co, and Pt–Ni MNAs. Moreover, we also review the main applications of Pt–Fe, Pt–Co, and Pt–Ni MNAs in the fields of biology, information storage, and magnetic separation. It is found that the size, shape, and composition of Pt–Fe, Pt–Co, and Pt–Ni MNAs play a critical role on their fundamental magnetic properties from both the experimental and theoretical points of view. It is expected that this review could be a valuable resource for both experimental and theoretical researchers, who are interested in Pt-based MNAs.     

A longitudinal study of evolving networks in response to natural disaster

In this study, we present a longitudinal analysis of the evolution of interorganizational disaster coordination networks (IoDCNs) in response to natural disasters. There are very few systematic empirical studies which try to quantify the optimal functioning of emerging networks dealing with natural disasters. We suggest that social network analysis is a useful method for exploring this complex phenomenon from both theoretical and methodological perspective aiming to develop a quantitative assessment framework which could aid in developing a better understanding of the optimal functioning of these emerging IoDCN during natural disasters. This analysis highlights the importance of utilizing network metrics to investigate disaster response coordination networks. Results of our investigation suggest that in disasters the rate of communication increases and creates the conditions where organizational structures need to move at that same pace to exchange new information. Our analysis also shows that inter-organizational coordination network structures are not fixed and vary in each period during a disaster depending on the needs. This may serve the basis for developing preparedness among agencies with an improved perspective for gaining effectiveness and efficiency in responding to natural disasters.     

The Kervaire invariant problem

The history and solution of the Kervaire invariant problem is discussed, along with some of the future prospects raised by its solution.