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In this paper, some new theorems for various cyclic contractions are established in Gb-metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α-ψφ-contractive mappings in Gb-metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results.

The aim of this paper is to propose a new φ -coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ -coupled fixed point and modified F -control function. Our obtained results are applied to derive some φ -coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results.

As a generalization of hesitant fuzzy sets (HFSs) and hesitant fuzzy linguistic term sets (HFLTSs), linguistic hesitant fuzzy sets (LHFSs) establish a proper interpretation of the hesitancy, inconsistency and uncertainty of experts in evaluating decision alternatives. In this paper, based on the cloud model, we discuss multiple attribute decision-making problems with linguistic hesitant fuzzy information. To extend the applicability of LHFSs, we introduce the concept of a comprehensive cloud of LHFSs that is based on which form of LHFSs with different length can be unified. Utilizing the comprehensive cloud, we define the distance measure between two LHFSs, which makes the support measure of two LHFSs possible. By extending the power operators to the linguistic hesitant fuzzy environment, a series of linguistic hesitant fuzzy power aggregation operators are established. We also study the properties and applications of these aggregation operators and develop two approaches for linguistic hesitant fuzzy multiple attribute decision-making. Finally, two practical examples are given to demonstrate the applicability and effectiveness of the proposed approach.

In this paper, we consider the following Kirchhoff equation − a + b ∫ R 3 | ∇ u | 2 d x Δ u + V ( x ) u = f ( u ) + λ | u | p − 2 u , in R 3 , where a , b > 0 are constants, λ > 0 is a real parameter, p ≥ 6 and V , f satisfy suitable conditions. By using a truncation argument, we prove that the existence of a sign-changing solution for this equation. Our results can be regarded as the complementary work of Li et al. (2017) and Li and Geng (2019).

The strengthening effects of (0 0 1) Ni/Ni3Al interface alloying with Re, Ta and W in Ni-based single crystal superalloys were studied using first-principles density functional theory. By placing alloying elements on (0 0 1) Ni/Ni3Al interface, the substitution formation energy, the Griffith work, the generalized stacking fault energies, the partial density of states and the charge density difference were all calculated. It is figured out that Re, Ta and W atoms prefer to substitute Al positions of γ ' phase. It is consistent with the experimental results. The strengthening effect of Re atom on (0 0 1) Ni/Ni3Al interface is stronger than that of Ta and W atoms addition. The order of strengthening effects of Re, Ta and W atoms from our calculations is consistent with relevant experimental observations. By analyzing the charge density difference and the partial density of states, our results show that the hybridization between Re atom and the nearest neighbor Ni atoms is the strongest, which is conducive to explore the essential reason for the different strengthening effects of alloying atoms at electronic level.

The tension between unitarity and wave-packet collapse is an annoying problem in quantum mechanics, while a breakthrough was made by Zurek recently from the point of view of information transfer. In this paper, we reconsider Zurek's derivation in the setting of generalized probabilistic theories (GPT), and establish that actionable information about a system can be repeatedly passed on to other systems only when the chosen states of the system have mutual zero fidelity. This may be interpreted as an extension of Zurek's result to GPT.

Information flows in a network where individuals influence each other. In this paper, we study the influence maximization problem of finding a small subset of nodes in a social network that could maximize the spread of influence. We propose a novel information diffusion model CTMC - ICM , which introduces the theory of Continuous-Time Markov Chain (CTMC) into the Independent Cascade Model (ICM). Furthermore, we propose a new ranking metric named SpreadRank generalized by the new information propagation model CTMC-ICM. We experimentally demonstrate the new ranking method that can, in general, extract nontrivial nodes as an influential node set that maximizes the spread of information in a social network and is more efficient than a distance-based centrality.

In this note, the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique. Some sufficient conditions are established for the concerned problem, and some existing results are generalized and improved. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

Over the last few years, online forums have gained massive popularity and have become one of the most influential web social media in our times. The forum document corpus can be seemed to be composed of various topics evolved over time, and every topics is reflected on a volume of keywords and social actors. In this paper, we attempt to study the interesting problem: for the evolving topics, were there any correlation between them? We propose a method for discovering the dependency relationship between the topics of documents in adjacent time stamps based on the knowledge of content semantic similarity and social interactions of authors and repliers. We introduce mutual information measure to estimate the correlation between the topics. Applied to the realistic forum data, we show how topics are related and which postings can be recommended to another as similar topics. We also show how the authors impact the topics and propose a new way for evaluating author impact.

Understanding the individual behavior has shown to be of paramount importance to the triumph of the telecommunication operators to retain customers, enhance their purchasing capacity, and predict the churn rate. Different behavior patterns can be observed for different groups of users. Hence, there is an interesting problem posted in telecommunication network that how to define the users' role according to their behavior patterns. Traditionally, user behavior characterization methods generally based on their call detail record (CDR), which are user's individual features, are not appropriate to identify the role in network. In this paper, we develop a new methodology for identifying users' role based on their behaviors in telecommunication network using the social features instead of their individual features. Experiments have tested on synthetic data and large real datasets, and reveal good results on both of them. Finally, the methodology is not only limited to call graphs but also apply to other networks for role defining.

In this paper, we mainly investigate the calculation problems of a random fixed point index and get some new results, part of which generalizes a previous result.

In the paper, the new concepts of bifurcation points and asymptotic bifurcation points of the compact continuous operator T are introduced in M-PN spaces. Some sufficient conditions for the existence of bifurcation points and asymptotic bifurcation points are obtained, and some theorems on the existence of intrinsic values are obtained. Meanwhile some theorems are generalized.

In this paper, we discuss some problems for nonlinear operators in the Menger PN space. Meanwhile, we prove existence theorems for the solution of an operator equation, and obtain some new results by means of the theory of topological degree for the Z-P-S space.

In this work, we prove several important inequalities, and investigate the solution of an operator equation by means of the fixed point index in the theory of topological degree. For operator equations with different boundary conditions, the same conclusion is obtained. Meanwhile, the famous Rothe’s Theorem is generalized. Finally, an example is given to show the application of Theorem 3 .

In this paper, we investigate some nonlinear operator problems and the theory of topological degree. Meanwhile, we obtain some new fixed point theorems in the M-PN space.

In this work, the fixed point theorems of Krasnoselskii and Petryshyn are generalized to inner product spaces. An example is given to show the applications of the theorem.

Driessel [K.R. Driessel, Private communication, 1991] posed the following open-problem: Characterize all n -tuples of real numbers which can serve as n -tuples of eigenvalues of some n × n real Hankel matrices. Miroslav Fiedler has given two necessary conditions for this problem in [M. Fiedler, Spectral properties of real Hankel matrices, Contemporary Mathematics 280 (2001) 313–320]. In this paper we shall completely present the necessary conditions for such spectral and generalize partial results of [M. Fiedler, Spectral properties of real Hankel matrices, Contemporary Mathematics 280 (2001) 313–320].