Mathematics, Volume 8, Issue 3 (March 2020) – 159 articles

The importance of cybersecurity has recently been increasing. A malware coder writes malware into normal executable files. A computer is more likely to be infected by malware when users have easy access to various executables. Malware is considered as the starting point for cyber-attacks; thus, the timely detection, classification and blocking of malware are important. Malware visualization is a method for detecting or classifying malware. A global image is visualized through binaries extracted from malware. The overall structure and behavior of malware are considered when global images are utilized. However, the visualization of obfuscated malware is tough, owing to the difficulties encountered when extracting local features. This paper proposes a merged image-based malware classification framework that includes local feature visualization, global image-based local feature visualization, and global and local image merging methods. This study introduces a fastText-based local feature visualization method: First, local features such as opcodes and API function names are extracted from the malware; second, important local features in each malware family are selected via the term frequency inverse document frequency algorithm; third, the fastText model embeds the selected local features; finally, the embedded local features are visualized through a normalization process. Malware classification based on the proposed method using the Microsoft Malware Classification Challenge dataset was experimentally verified. The accuracy of the proposed method was approximately 99.65%, which is 2.18% higher than that of another contemporary global image-based approach. Full article

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can be used in the studies of various applications of systems with dependent failures between their elements. Full article

Many decision problems manage linguistic information assessed through several ordered qualitative scales. In these contexts, the main problem arising is how to aggregate this qualitative information. In this paper, we present a multi-criteria decision-making procedure that ranks a set of alternatives assessed by means of a specific ordered qualitative scale for each criterion. These ordered qualitative scales can be non-uniform and be formed by a different number of linguistic terms. The proposed procedure follows an ordinal approach by means of the notion of ordinal proximity measure that assigns an ordinal degree of proximity to each pair of linguistic terms of the qualitative scales. To manage the ordinal degree of proximity from different ordered qualitative scales, we provide a homogenization process. We also introduce a stochastic approach to assess the robustness of the conclusions. Full article

In this paper, a new fuzzy multi-criteria decision-making model for traffic risk assessment was developed. A part of a main road network of 7.4 km with a total of 38 Sections was analyzed with the aim of determining the degree of risk on them. For that purpose, a fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (fuzzy MARCOS) method was developed. In addition, a new fuzzy linguistic scale quantified into triangular fuzzy numbers (TFNs) was developed. The fuzzy PIvot Pairwise RElative Criteria Importance Assessment—fuzzy PIPRECIA method—was used to determine the criteria weights on the basis of which the road network sections were evaluated. The results clearly show that there is a dominant section with the highest risk for all road participants, which requires corrective actions. In order to validate the results, a comprehensive validity test was created consisting of variations in the significance of model input parameters, testing the influence of dynamic factors—of reverse rank, and applying the fuzzy Simple Additive Weighing (fuzzy SAW) method and the fuzzy Technique for Order of Preference by Similarity to Ideal Solution (fuzzy TOPSIS). The validation test show the stability of the results obtained and the justification for the development of the proposed model. Full article

The stress–strain behavior of nano magnesia-cement-reinforced seashore soft soil (Nmcs) under different circumstances exhibits various characteristics, e.g., strain-hardening behavior, falling behavior, S-type falling behavior, and strong softening behavior. This study therefore proposes a REP (reinforced exponential and power function)-based mathematical model to simulate the various stress–strain behaviors of Nmcs under varying conditions. Firstly, the mathematical characteristics of different constitutive behaviors of Nmcs are explicitly discussed. Secondly, the conventional mathematical models and their applicability for modeling stress–strain behavior of cemented soil are examined. Based on the mathematical characteristics of different stress–strain curves and the features of different conventional models, a simple mathematical REP model for simulating the hardening behavior, modified falling behavior and strong softening behavior is proposed. Moreover, a CEL (coupled exponential and linear) model improved from the REP model is also put forth for simulating the S-type stress–strain behavior of Nmcs. Comparisons between conventional models and the proposed REP-based models are made which verify the feasibility of the proposed models. The proposed REP-based models may facilitate researchers in the assessment and estimation of stress–strain constitutive behaviors of Nmcs subjected to different scenarios. Full article

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results. Full article

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results. Full article

A possible solution with which to alleviate the range anxiety of electric vehicle (EV) drivers could be a mobile charging station which moves in different places to charge EVs, having a charging time of even half an hour. A problem that arises is the impossibility of charging in any location due to heavy traffic or limited space constraints. This paper proposes a new operational mode for the mobile charging station through temporarily stationing it at different places for certain amounts of time. A mathematical model, in the form of an optimization problem, is built by modeling the mobile charging station as a queuing process, the goal of the problem being to place a minimum number of temporary service centers (which may have one or more mobile charging stations) to minimize operating costs and the charger capacity of the mobile charging station so that the service offered is efficient. The temporary locations obtained are in areas with no or few fixed charging stations, making the mobile station infrastructure complementary to the fixed charging station infrastructure. The temporary location operational mode, compared to current moving operational mode, is more efficient, having a small miss ratio, short mean response time and short mean queuing time. Full article

In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper, we introduce a new fractional Newton-type method with order of convergence $\alpha +1$ and compare it with the existing fractional Newton method with order $2\alpha$ . Moreover, we also introduce a multipoint fractional Traub-type method with order $2\alpha +1$ and compare its performance with that of its first step. Some numerical tests and analysis of the dependence on the initial estimations are made for each case, including a comparison with classical Newton ( $\alpha =1$ of the first step of the class) and classical Traub’s scheme ( $\alpha =1$ of fractional proposed multipoint method). In this comparison, some cases are found where classical Newton and Traub’s methods do not converge and the proposed methods do, among other advantages. Full article

We investigate the extent to which the United States and the countries of Europe have achieved economic convergence of their corporate sector. We define convergence as the homogenization of economic performance, institutional arrangements, and market valuation taking place at the meso-economic level. We perform a cluster analysis along industry lines and find that industries and corporations on both continents cluster in four groups, based on six variables measuring operating performance, ownership, and market valuation. The clusters resulted from the US data are more unstable than those resulted from European data. We are also able to pair a handful of highly similar clusters between the US and European data. These findings suggest a complex dynamic. It seems that the US corporate sector is more homogeneous than the European one. Moreover, some degree of convergence between the European Union and the United States appears to have already occurred. Full article

The theory of exact resonances (kinematics and dynamics) is well developed while even the very concept of detuned resonance is ambiguous and only studies of their kinematic characteristics (that is, those not depending on time) are available in the literature. In this paper, we report novel effects enforced by the resonance detuning on solutions of the dynamical system describing interactions of three spherical planetary waves. We establish that the energy variation range can significantly exceed the range of the exact resonance for suitably chosen values of the detuning. The asymmetry of system’s solutions with respect to the sign of the detuning parameter is demonstrated. Finally, a non-monotonic dependence of the energy oscillation period with respect to detuning magnitude is discovered. These results have direct implications in physics of atmosphere, e.g., for prediction of weather extremes in the Northern Hemisphere midlatitudes (Proc. Nat. Acad. Sci. USA 2016, 133(25), 6862–6867). Moreover, similar study can be conducted for a generic three-wave system taken in the Hamiltonian form which makes our results applicable for an arbitrary Hamiltonian three-wave system met in climate prediction theory, geophysical fluid dynamics, plasma physics, etc. Full article

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student’s t-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to portfolio construction as an alternative of existing nonlinear factor models. To test the performance of the proposed method, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model. Full article

With the spread of the Internet, the speed of data spread is getting faster and faster. It benefits us a lot but also brings us many potential security problems, especially the problem of privacy leakage. For example, more and more people choose to store their private images in the cloud. Secret image sharing as a significant method has been widely applied in protecting images in the cloud, which reduces the risks of data leakage and data loss. Generally, the secret image sharing scheme would encrypt the secret image into a series of shares and then stored these shares in a cloud. However, when this cloud has been attacked, the secret may meet a risk of leakage. A solution to solve the problem is that the generated shares are distributed storage in multiple clouds. Each cloud is independent and all clouds can have a collaboration to manage the secret image. To address this issue, a novel hierarchical secret image sharing scheme with multi-group joint management is proposed in this paper, which is suitable for protecting the security of the secret image by distributed storage over multiple clouds. In the proposed scheme, the secret image would be shared among multiple groups with different thresholds. The number of each group’s shareholders is determined by a sequence of thresholds. Therefore, the proposed scheme is a hierarchical secret image sharing scheme in which the secret image can be reconstructed if and only if the number of shares has met all threshold conditions. In addition, the generated shares have the same weight, which is more suitable for universal applicability. Both the system analysis and the simulation results prove that the proposed scheme is efficient and practical. Full article

In this paper, we study a hybrid forward–backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the application in the field of signal processing. Full article

In this paper, we study the synchronization of a nonlinear fractional system, and analyze its time response and chaotic behaviors. We represent a solution for considered system by employing the Mittag-Leffler matrix function and Jacobian matrix. Thereafter, we prove synchronization of error system between drive-response systems using stability theory and linear feedback control methods. Finally, numerical simulations are presented to show the effectiveness of the theoretical results. Full article

In the present note we introduce a Pythagorean-like formula for surfaces immersed into 3-dimensional space forms ${\mathbb{M}}^3\left(c\right)$ of constant sectional curvature $c=-1,0,1.$ More precisely, we consider a surface immersed into ${\mathbb{M}}^3\left(c\right)$ satisfying ${\mathrm{I}}^2+{\mathrm{II}}^2={\mathrm{III}}^2,$ where $\mathrm{I}$ , $\mathrm{II}$ and $\mathrm{III}$ are the matrices corresponding to the first, second and third fundamental forms of the surface, respectively. We prove that such a surface is a totally umbilical round sphere with Gauss curvature $\phi +c,$ where $\phi$ is the Golden ratio. Full article

A model is developed to simulate micro-scale turbulence driven Zonal Flows (ZFs), and their impact on the Magnetohydrodynamic (MHD) tearing and kink modes is examined. The model is based on a stochastic representation of the micro-scale ZFs with a given Alfvén Mach number, M_S. Two approaches were explored: (i) passive stochastic model where the ZFs amplitudes are independent of the MHD mode amplitude, and (ii) the semi-stochastic model where the amplitudes of the ZFs have a dependence on the amplitude of the MHD mode itself. The results show that the stochastic ZFs can significantly stabilise the (2,1) and (1,1) MHD modes even at very low kinematic viscosity, where the mode is linearly unstable. Our results therefore indicate a possible mechanism for stabilisation of the MHD modes via small-scale perturbations in poloidal flow, simulating the turbulence driven ZFs. Full article

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully. Full article

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight. Full article

Certain new classes of q-convex and q-close to convex functions that involve the q-Janowski type functions have been defined by using the concepts of quantum (or q-) calculus as well as q-conic domain $\left({\Omega }_{k,q}[\lambda ,\alpha ]\right)$ . This study explores some important geometric properties such as coefficient estimates, sufficiency criteria and convolution properties of these classes. A distinction of new findings with those obtained in earlier investigations is also provided, where appropriate. Full article

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework. Full article

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov’s sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied. Full article

Wireless Sensor Networks (WSN) are of great current interest in the proliferation of technologies. Since the location of the sensors is one of the most interesting issues in WSN, the process of node localization is crucial for any WSN-based applications. Subsequently, WSN’s node estimation deals with a low-rank matrix which gives rise to the application of the Nuclear Norm Minimization (NNM) method. This paper will focus on the localization of 2-dimensional WSN with objects (obstacles). Recent studies introduce Nuclear Norm Minimization (NNM) for node estimation instead of formulating the rank minimization problem. Common way to tackle this problem is by implementing the Semidefinite Programming (SDP). However, SDP can only handle matrices with a size of less than 100 × 100. Therefore, we introduce the method of Singular Value Thresholding (SVT) which is an iterative algorithm to solve the NNM problem that produces a sequence of matrices $\{X^k,Y^k\}$ and executes a soft-thresholding operation on the singular value of the matrix $Y^k$ . This algorithm is a user-friendly algorithm which produces a low computational cost with low storage capacity required to give the lowest-rank minimum nuclear norm solution. Full article

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting. Full article

In this paper, using a new shrinking projection method, we deal with the strong convergence for finding a common point of the sets of zero points of a maximal monotone mapping, common fixed points of a finite family of demimetric mappings and common zero points of a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we get well-known and new strong convergence theorems in a Hilbert space. Full article

In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When $\alpha =1$ we obtain some well-known time-scale inequalities due to Hardy, Copson, Bennett and Leindler inequalities. Full article

The aim of the work is to connect individual behavior of drivers with traffic intensity. By diversifying the populations of drivers into two categories, often considered in this type of an analysis, CO (cooperative) and DE (defective), the tendency of drivers from each of these groups to deviate from compliance with traffic rules is established. The effective driver behavior translates into disrupting traffic by slowing it down. Participant interactions are described using game theories that provide information for simulations algorithms based on cellular automata. Three different ways of using this combination of descriptions of traffic participants to examine the impact of their behavior on the traffic dynamics are shown. Directions of the further, detailed analysis are indicated, which requires basic research in the field of game theory models. Full article

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid. Full article

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results. Full article