Chaotic system constructed by product trigonometric function and polynomial and applied to color image encryption

In the applied research of nonlinear system, the low degree of chaos in the dynamical system leads to the limitation of using the chaos method to solve some practical problems. In this paper, we use the product trigonometric function and ternary polynomial to build a dynamical system, which has strong chaotic characteristics. The dynamical system is constructed by two product trigonometric functions and a ternary linear equation, and its chaotic properties are verified by bifurcation diagrams, Lyapunov exponents, fractal dimensions, etc. The system has many parameters and large parameter intervals and is not prone to cycles. The conditions for the non-divergence of this system are given by mathematical derivation, and it is found that the linear part of the system can be replaced by an arbitrary ternary polynomial system and still not diverge, and the bifurcation diagram is drawn to verify it. Finally, the chaotic sequence is distributed more uniformly in the value domain space by adding the modulo operation. Then, the bit matrix of multiple images is directly permuted by the above system, and the experiment confirms that the histogram, information entropy, and pixel correlation of its encrypted images are satisfactory, as well as a very large key space.

On Markov Moment Problem and Related Results

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an space, where is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

Development of an algorithm to protect user communication devices against data leaks

In order to identify ways used to collect data from user communication devices, an analysis of the interaction between DNS customers and the Internet name domain space has been carried out. It has been established that the communication device's DNS traffic is logged by the DNS servers of the provider, which poses a threat to the privacy of users. A comprehensive algorithm of protection against the collection of user data, consisting of two modules, has been developed and tested. The first module makes it possible to redirect the communication device's DNS traffic through DNS proxy servers with a predefined anonymity class based on the proposed multitest. To ensure a smooth and sustainable connection, the module automatically connects to a DNS proxy server that has minimal response time from those available in the compiled list. The second module blocks the acquisition of data collected by the developers of the software installed on the user's communication device, as well as by specialized Internet services owned by IT companies. The proposed algorithm makes it possible for users to choose their preferred level of privacy when communicating with the Internet space, thereby providing them with a choice of privacy level and, as a result, limiting the possibility of information manipulation over their owners. The DNS traffic of various fixed and mobile communication devices has been audited. The analysis of DNS traffic has enabled to identify and structure the DNS requests responsible for collecting data from users by the Internet services owned by IT companies. The identified DNS queries have been blocked; it has been experimentally confirmed that the performance of the basic and application software on communication devices was not compromised.

Energy and Charge Transport in 2D Atomic Layer Materials: Raman-Based Characterization

As they hold extraordinary mechanical and physical properties, two-dimensional (2D) atomic layer materials, including graphene, transition metal dichalcogenides, and MXenes, have attracted a great deal of attention. The characterization of energy and charge transport in these materials is particularly crucial for their applications. As noncontact methods, Raman-based techniques are widely used in exploring the energy and charge transport in 2D materials. In this review, we explain the principle of Raman-based thermometry in detail. We critically review different Raman-based techniques, which include steady state Raman, time-domain differential Raman, frequency-resolved Raman, and energy transport state-resolved Raman techniques constructed in the frequency domain, space domain, and time domain. Detailed outlooks are provided about Raman-based energy and charge transport in 2D materials and issues that need special attention.

An adversarial learning approach for discovering social relations in human-centered information networks

The analytics on graph-structured data in cyber spaces has advanced many human-centered computing technologies. However, if only utilizing the structural properties, we might be prohibited from unraveling unknown social relations of nodes especially in the structureless networked systems. Up-to-date ways to unfold latent relationships from graph-structured data are network representation learning (NRL) techniques, but it is difficult for most existing ones to deal with the network-structureless situations due to the fact that they largely depend on the observed connections. With the ever-broader spectrum of human-centered networked systems, large quantities of textual information have been generated and collected from social and physical spaces, which may provide the clues of hidden social relations. In order to discover latent social relations from the accompanied text resources, this paper attempts to bridge the gap between text data and graph-structured data so that the textual information can be encoded to substitute for those incomplete structural information. Generative adversarial networks (GANs) are employed in the cross-modal framework to make the transformed data indistinguishable in graph-domain space and also capable of depicting structure-aware relationships with network homophily. Experiments conducted on three text-based network benchmarks demonstrate that our approach can reveal more realistic social relations from text-domain information compared against the state-of-the-art baselines.

From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the following problems: (1) pointing out a previously published sandwich theorem of the type f ≤ h ≤ g, where f, −g are convex functionals and h is an affine functional, over a finite-simplicial set X, and proving a topological version for this result; (2) characterizing isotonicity of convex operators over arbitrary convex cones; giving a sharp direct proof for one of the generalizations of Hahn–Banach theorem applied to the isotonicity; (3) extending inequalities assumed to be valid on a small subset, to the entire positive cone of the domain space, via Krein–Milman or Carathéodory’s theorem. Thus, we point out some earlier, as well as new applications of the Hahn–Banach type theorems, emphasizing the topological versions of these applications.