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• Convolutional code is widely used in communication systems. • NFSR is the main component of the convolutional decoder. • STP is a new mathematical tool with a wide range of applications. • NFSR can be modeled very well with STP, enabling the discussion in mathematics. The nonlinear feedback shift register (NFSR) is the main component of the convolutional decoder. This paper provides a novel method for investigating the driven stability of NFSRs with input via semi-tensor product (STP). By using the STP method, a backward state transition matrix, as well as a backward NFSR, is constructed. Backward NFSRs can help to find the predecessors of any states so that an algorithm for the global stability of autonomous NFSRs is designed. On this basis, two algorithms are proposed for the driven stability of NFSRs with input, and they have lower computational complexity than the existing methods. Meanwhile, some numerical examples are presented to support the results of this paper. Finally, the relationship between stability and connectedness is discussed fully, which derives some interesting results. [ABSTRACT FROM AUTHOR]

The mid-point quadrature rule is often used to solve the nonlocal integral differentiation equations, in which a central material point is used to calculate the integral of the subdomain in the meshless geometry. However, it can only achieve the linear approximation and the first order convergence rate, and it is only accurate enough when the entire cell overlaps with the neighborhood of a material point. In this paper, to achieve the higher precision and the higher rate of convergence speed, a novel coupling method of reproducing kernel particle method and Gaussian-Legendre quadrature scheme is proposed to solve the nonlocal integral differentiation equations in the meshless geometry, in which the mid-point quadrature scheme is replaced with Gauss quadrature scheme to calculate the integral of the subdomain in the meshless geometry, the reproducing kernel particle method is employed to construct the shape functions for material points in the nonlocal model, and to approximate the value of the Gaussian quadrature node. Moreover, the meshless solution for the peridynamic equation is derived detailedly based on the proposed method. Compared with the traditional meshless solution for the nonlocal equations, the proposed solution has higher precision and higher rate of convergence speed in different problems. The numerical results demonstrate improved results in both mathematics and mechanical problems using the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a G -Hausdorff space and show how the results established in the usual metric space can be generalized to the G -metric space. The proven results are used to propose an iterated function system (IFS) called G -IFS. Additionally, the existence of the fractal associated with this construction is demonstrated. This paper shows how non-affine transformations and fractal interpolation functions (FIFs) can be used to approximate fractals by G -IFS. This paper contributes to the understanding of fractal geometry and its applications in mathematics and other fields. • The research paper introduces the concept of a Hausdorff space. • It shows how the results established in the usual metric space can be extended to a more general G metric space. • An iterative function system (IFS) is constructed using the proven results, and a G -IFS is proposed. • The existence of fractals associated with this construction is demonstrated. [ABSTRACT FROM AUTHOR]

Abstract In this paper we continue our study of the shape parameter c contained in the famous multiquadrics (− 1) ⌈ β ⌉ (c 2 + ∥ x ∥ 2) β , β > 0 , and the inverse multiquadrics (c 2 + ∥ x ∥ 2) β , β < 0. The theoretical ground is akin to our previous papers. However, we remove some unnecessary restrictions, making it much more accessible and useful, especially for nonmathematicians [ABSTRACT FROM AUTHOR]

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Statistical matching aims at combining information available in distinct sample surveys referred to the same target population. The matching is usually based on a set of common variables shared by the available data sources. For matching purposes just a subset of all the common variables should be chosen, the so called matching variables. The paper presents a novel method for selecting the matching variables based on the analysis of the uncertainty characterizing the matching framework. The uncertainty is caused by unavailability of data for estimating parameters describing the association between variables not jointly observed in a single data source. The paper focuses on the case of categorical variables and presents a sequential procedure for identifying the most effective subset of common variables in reducing the overall uncertainty. [ABSTRACT FROM AUTHOR]

• Introduction of the Common Prime RSA and a brief description of its background mathematics. • An overview and explanation of previous CP-RSA cryptanalytic attacks. • Formulation of new cryptanalytic attack on CP-RSA using Lattice Basis Reduction method. • Explanation and detail description of new Cryptanalytic attack solution on CP-RSA. • CP-RSA Speed and efficiency measures w.r.t practical and asymptotic aspects. • Detail explanation and comparison results with the previous CP-RSA cryptanalytic attacks. Standard RSA cryptosystem becomes vulnerable, when private key d < N 0.292 is used inside CryptoChips of constrained devices, thus an alternate scheme is the Common Prime RSA (CP-RSA) variant, which provides cryptographic (decryption/signing) operations. In this paper, we perform a cryptanalytic attack on CP-RSA using lattice basis reduction method that is used to exploit possible vulnerabilities of RSA small private key attacks. In addition, we performed detail experiments on CP-RSA weak or overestimated bounds and compare results to the past studies. Our implemented cryptanalytic attack implicates more precise and direct method to exploit the CP-RSA existing theoretical and experimental bounds. Also, our results prove that CP-RSA is an effective approach that provides resistance against standard RSA small private key attacks. [ABSTRACT FROM AUTHOR]

The paper by C. Lubich in Numer. Math. 2(52):129–145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools. In the present paper it will be shown that this lemma can be quickly proved in an elementary way; moreover, the new proof includes those cases that were excluded from the 1988 paper, and the bounds obtained are shown to be sharp. [ABSTRACT FROM AUTHOR]

In the existing multi-factor one-order (MFOO) forecasting models, each fuzzy logical relation (FLR) has one consequent and more than one premise reflecting the association between the fuzzy values at two consecutive moments, and its premises are related to all the factors involved in forecasting. When using such FLRs to realize prediction, no matched FLR cases happened often and thus no logical prediction can be made. Two shortcomings are found for that: one is that more premises make FLRs matching more difficult; the other is that there are no enough FLRs. To overcome these shortcomings, this paper proposes two kinds of FLRs: short cross-association FLRs and long cross-association FLRs, which mean the influence on the consequent is from a part of the factors instead of all the factors. Specifically, the long cross-association FLRs aim at finding the association between fuzzy values at two non-consecutive moments. Such cross-associations exist in reality, the construction of them allows more FLRs to be mined from history observations. They can raise the possibility of finding available FLRs for forecasting. Based on the proposed FLRs, two MFOO forecasting models are proposed. Experiments show the advantage of the new FLRs and the good performance of the proposed models. [ABSTRACT FROM AUTHOR]

In order to explore a unified theory of three-way decisions proposed by Yao, Hu introduced three-way decision spaces through an axiomatic method, established the corresponding three-way decisions, and proposed two open problems on the changes of decision parameters in definition of three-way decisions. For answering these two questions, this paper firstly discusses the parameter changes in the assumptions from 0 ≤ β < α ≤ 1 to 0 ≤ β ≤ α ≤ 1 and inequality E ( A ) ( x ) ≤ β in the rejection region is replaced by E ( A ) ( x ) < β . Under the circumstance, this paper introduces new type of three-way decisions in three-way decision spaces and discusses properties of the three-way decisions, lower and upper approximations induced by three-way decisions, aggregation three-way decisions over multiple three-way decision spaces and dynamic three-way decisions on three-way decision spaces. Then this paper discusses another question on refusal decision region when the uncertain region is defined by using inequality β < E ( A ) ( x ) < α and gives one example to illustrate the similarity and difference among these three-way decisions based on three-way decision spaces. [ABSTRACT FROM AUTHOR]

Abstract Let X 1 , X 2 , ... be independent and identically distributed random variables with support on non-negative integers and X (n) (n ≥ 1) denote the corresponding sequence of discrete record values. In the present paper, we derive weak and strong limit results for the spacings of discrete record values X (n + m) − X (n) (n → ∞) and discuss generation algorithms of discrete records. [ABSTRACT FROM AUTHOR]

Abstract In Yano et al. (2009), limit theorems (so called, Feynman–Kac penalizations) for the one-dimensional recurrent symmetric α -stable process weighted and normalized by negative (killing) Feynman–Kac functionals with small potential are studied. In this paper, we deal with the same problem for negative potentials diverging at infinity. [ABSTRACT FROM AUTHOR]

Abstract In this short paper we find that the Sobolev inequality 1 p − 2 ∫ f p d μ 2 p − ∫ f 2 d μ ≤ C ∫ | ∇ f | 2 d μ (p ≥ 0) is equivalent to the exponential convergence of the Markov diffusion semigroup (P t) to the invariant measure μ , in some Φ -entropy. We provide the estimate of the exponential convergence in total variation and a bounded perturbation result under the Sobolev inequality. Finally in the one-dimensional case we get some two-sided estimates of the Sobolev constant by means of the generalized Hardy inequality. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to establish two new types of rough set structures associated with the Marcus–Wyse (MW -, for brevity) topology, such as an M -rough set and an MW -topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in Z 2 , where Z is the set of integers. These two rough set structures are related to each other via an M -digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC -, for short) space (U , C) and a subset X of U , we firstly introduce a new neighborhood system on U related to X. Next, we formulate the lower and upper approximations with respect to X , where all of the sets U and X (⊆ U) need not be finite and the covering C is locally finite. Actually, the notion of M -digitization of a 2-dimensional Euclidean space plays an important role in developing an M -rough and MW -topological rough set structures. Further, we prove that M -rough set operators have a duality between them. However, each of MW -topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW -topology. [ABSTRACT FROM AUTHOR]

Abstract The study of properties of gradual evaluation methods in argumentation has received increasing attention in recent years, with studies devoted to various classes of frameworks/ methods leading to conceptually similar but formally distinct properties in different contexts. In this paper we provide a novel systematic analysis for this research landscape by making three main contributions. First, we identify groups of conceptually related properties in the literature, which can be regarded as based on common patterns and, using these patterns, we evidence that many further novel properties can be considered. Then, we provide a simplifying and unifying perspective for these groups of properties by showing that they are all implied by novel parametric principles of (either strict or non-strict) balance and monotonicity. Finally, we show that (instances of) these principles (and thus the group, literature and novel properties that they imply) are satisfied by several quantitative argumentation formalisms in the literature, thus confirming the principles' general validity and utility to support a compact, yet comprehensive, analysis of properties of gradual argumentation. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. Several examples are also presented along with the theory. [ABSTRACT FROM AUTHOR]

Abstract Consider the processes { L t ; t ≥ 0 } and { λ t ; t ≥ 0 } associated with a marked Hawkes process and its conditional intensity. In the present paper, the integration by parts formulas for those processes are constructed, and applied to the study on the absolute continuity for their conditional laws. Moreover, the sensitivity formulas for those processes with respect to the parameters are given. [ABSTRACT FROM AUTHOR]

Abstract This paper develops the asymptotic properties of a recently proposed measure of inequality emphasizing the status of the poor relative to the rich. A simulation confirms the asymptotic results are applicable in practice. [ABSTRACT FROM AUTHOR]

Abstract In intelligent systems, belief function is a common approach to modelling uncertain and imperfect information obtained constantly while knowledge bases are used to encapsulate multiple static information items. In the literature, many different approaches have been proposed for combining belief functions (resp. merging knowledge bases) when there are multiple belief functions (resp. knowledge bases) generated from different sources depicting the same issue of interest. However, the connection between belief function combination and knowledge base merging is not adequately explored. In this paper, we aim to study the correspondence between the two lines of research. By introducing a numerical characteristic function for each knowledge base, we show that there is one to one correspondence between a set of combination rules of belief functions and merging methods of weighted knowledge bases. [ABSTRACT FROM AUTHOR]

Abstract This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies the rendezvous strategy for a group of unicycle systems with connectivity preservation and collision avoidance. Based on the method of potential functions, a novel distributed control algorithm is proposed for all unicycles. By tuning the design parameters, the unicycles finally aggregate so that the average of the distances is bounded by a pre-specified positive number. It is proved that the connectivity of a minimum spanning tree in the initial topology is guaranteed. The result is then extended to multiple unicycles with heterogenous input disturbances. Potential function is further modified to handle the disturbances. Illustrative example is presented to show the improvements and effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

We consider a Lévy risk process and a Sparre-Andersen risk process with Parisian ruin in the presence of a constant dividend barrier. We demonstrate that with few exceptions, ruin occurs with probability one. Subsequently, generalizations to certain dependent risk processes are discussed. Despite the mathematical nature of this paper, its goal is to convey some simple conclusions to the actuarial community. The reader may focus solely on the introduction and conclusion sections (Sections 1 and 5, respectively) as well as the numerical illustrations. [ABSTRACT FROM AUTHOR]

This paper introduces and studies extensions of modal logics by investigating the soundness of classical modal axioms in a weighted framework. It discusses the notion of relevant weight values, in a specific weighted Kripke semantics and exploits accessibility relation properties. Different generalisations of the classical axioms are constructed and, from these, a typology of weighted axioms is built, distinguishing between four types, depending on their relations to their classical counterparts and to the, possibly equivalent, frame conditions. [ABSTRACT FROM AUTHOR]

Handling uncertain knowledge is crucial for modeling many real world domains. Ontologies and ontology-based data access (OBDA) have proven to be versatile methods to capture this knowledge. Multiple systems for OBDA have been developed and there is theoretical work towards probabilistic OBDA, namely identifying efficiently processable queries. These queries are called safe queries. However, there is no analysis on the safeness of probabilistic queries in real-world applications, and there exists no tool support for applying the existing formalisms to the standard query language of SPARQL. In this paper we investigate queries collected from several public SPARQL endpoints and determine the distribution of safe and unsafe queries. This analysis shows that many queries in practice are safe, making probabilistic OBDA feasible and practical to fulfill real-world users' information needs. Furthermore, we design and conduct benchmarks on real-world and generated data sets which show that the approach of answering safe queries in the appropriate way is scalable to large amounts of data. [ABSTRACT FROM AUTHOR]

In this paper we are interested in the use of argumentation for handling inconsistency in inconsistent knowledge bases expressed with existential rules. We propose an instantiation of an argumentation framework and demonstrate it is coherent, relatively grounded and non-trivial, therefore satisfying the rationality postulates from the literature. We demonstrate how argumentation semantics relate to the state of the art of handling inconsistency in this setting, allowing us to propose the first dialectical proof in the literature for a given semantics. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive study on mechanical behavior of non-uniform small scale beams in the framework of nonlocal strain gradient theory is presented. The governing equations and boundary conditions have been developed using Hamilton's principle and solved with the aid of finite element method for introducing the bending, buckling and free vibration response of nano-beams. The current formulation could be used for all types of non-uniformities by varying the width and thickness of nano-beams along the length. The accuracy of the current model and formulation is verified by comparing the results with previous literature and those obtained by analytically solving simplified problems. In order to understand the influence of having non-uniform cross section on static and dynamic behavior of small scale beams, parametric study is presented and the effects of different parameters such as non-uniformity, non-local and strain gradient terms on natural frequency, buckling load and deformation are observed and discussed. It is seen that having non-uniform cross section in nonlocal strain gradient beams could lead to significant changes in mechanical behavior of such structures. [ABSTRACT FROM AUTHOR]

Highlights: [•] The tracking consensus analysis method for stochastic MASs is novel. [•] The asymmetric communication delays is focused on in this paper. [•] The delays is time-varying, and one derives its upper bound. [•] This paper also focuses on noise, directed topology, and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

This paper presents a new characterization of subjective possibility theory. Anscombe and Aumann [1] pioneered a multiple-variable approach to characterize the subjective probability on the basis of its relationship with objective probability. We generalize the Anscombe-Aumann approach to define subjective possibility theory. To characterize the uncertainty of the variable of interest ( H ) we consider its relationship with a variable of probability and a variable of ignorance. Our axiomatization assumes that the preference over the acts contingent on the outcomes of the variables is a weak order and satisfies a monotonicity property; the preference over probabilistic lotteries is represented by linear utility; and the preference over acts under ignorance by a recently developed τ -anchor utility theory. We show that if H and the variable of ignorance are completely reversible in Anscombe-Aumann’s sense and H and the variable of probability are partially reversible then the uncertainty of H must obey the laws of possibility theory. We outline a framework to manage heterogeneous uncertainty that includes probability, possibility and ignorance in decision making. [ABSTRACT FROM AUTHOR]

In this paper we carry out a nonlinear self-adjoint classification with differential substitutions of a class of dispersive equations with three arbitrary functions. As a particular case, we obtain the sub families of the C 1 ( m , a + b ) equations which are nonlinearly self-adjoint. Conservation laws for these last families are established using the techniques for finding conserved vectors proposed by Ibragimov. [ABSTRACT FROM AUTHOR]

In this paper, an order induced by uninorms on bounded lattices is given and discussed. By defining such an order, the T -partial order is extended to a more general form. The relationship between the order induced by the underlying t -norm and t -conorm and the order induced by a uninorm is studied. Finally, the order is extended to the order induced by n -uninorms on chains. [ABSTRACT FROM AUTHOR]

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (N a ˙ sell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. [ABSTRACT FROM AUTHOR]

Environmental changes can affect the functioning of an ecosystem directly, through the response of individual life forms, or indirectly, through interspecific interactions and community dynamics. The feasibility of a community-level response has motivated numerous studies aimed at understanding the mutual relationships between three elements of ecosystem dynamics: the abiotic environment, biodiversity and ecosystem function. Since ecosystems are inherently nonlinear and spatially extended, environmental changes can also induce pattern-forming instabilities that result in spatial self-organization of life forms and resources. This, in turn, can affect the relationships between these three elements, and make the response of ecosystems to environmental changes far more complex. Responses of this kind can be expected in dryland ecosystems, which show a variety of self-organizing vegetation patterns along the rainfall gradient. This paper describes the progress that has been made in understanding vegetation patterning in dryland ecosystems, and the roles it plays in ecosystem response to environmental variability. The progress has been achieved by modeling pattern-forming feedbacks at small spatial scales and up-scaling their effects to large scales through model studies. This approach sets the basis for integrating pattern formation theory into the study of ecosystem dynamics and addressing ecologically significant questions such as the dynamics of desertification, restoration of degraded landscapes, biodiversity changes along environmental gradients, and shrubland–grassland transitions. [ABSTRACT FROM AUTHOR]

The paper aims at providing a general theoretical frame bridging the macroscopic growth law with the complex heterogeneous structure of real tumors. We apply the “Phenomenological Universality” approach to model the growth of cancer cells accounting for “populations”, which are defined not as biologically pre-defined cellular ensemble but as groups of cells behaving homogeneously with respect to their position (e.g. primary or metastatic tumor), growth characteristics, response to treatment, etc. Populations may mutually interact, limit each other their growth or even mutate into another population. To keep the description as simple and manageable as possible only two populations are considered, but the extension to a multiplicity of cell populations is straightforward.Our findings indicate that the eradication of the metastatic population is much more critical in the presence of mutations, either spontaneous or therapy-induced. Furthermore, a treatment that eradicates only the primary tumor, having a low kill rate on the metastases, is ultimately not successful but promotes a “growth spurt” in the latter. [ABSTRACT FROM AUTHOR]

Susceptible Exposed Infectious and Recovered epidemic model endowed with a treatment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease. This paper focuses on the nonlinear observer design for a class of nonlinear piecewise systems including SEIR-T models. For this purpose, two changes of coordinates are provided to transform the considered systems into an extended nonlinear observer normal form, on which a high gain observer can be applied. Then, the proposed method is applied to a SEIR-T model. Finally, simulation results are given to show its efficiency. [ABSTRACT FROM AUTHOR]

This paper discusses the asymptotical synchronization and H ∞ synchronization of coupled neutral-type delay partial differential systems (NDPDSs). A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. By using the method of a nonsingular matrix transformation, we decouple the coupled error dynamical systems. Then, sufficient conditions that guarantee the asymptotic stability of decoupled synchronization error dynamical systems are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and by using Jensen׳s inequality and reciprocally convex combination technique, which implies the asymptotical synchronization of the coupled NDPDSs. Moreover, the stability criteria for the H ∞ stabilization of decoupled synchronization error dynamical systems with external disturbances are also derived in terms of LMIs, which guarantee the H ∞ synchronization of the coupled NDPDSs. The equivalence between the H ∞ stability of decoupled synchronization error dynamical systems and the H ∞ synchronization of coupled NDPDSs is also proved by mathematical analysis. Finally, numerical examples are provided to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper presents the finite-time adaptive fuzzy control to regulate thruster faults in rigid spacecraft system. The considered faults are that the thrusters losing power partially or even totally. Fuzzy logic systems are used to approximate the unknown nonlinear function which is produced by the external disturbances, unknown inertia matrix and thrusters faults. Uniting fast nonsingular terminal sliding mode surface (FNTSMS) and the fault-tolerant control (FTC), two novel adaptive fuzzy finite-time FTC schemes are developed. It has been testified that this control method can make sure that the rigid spacecraft has excellent property of fault-tolerant and all the signals are finite-time convergence. Simulation examples on a rigid body spacecraft with three thrusters and six thrusters are done to indicate that the finite-time FTC schemes are available in achieving high attitude tracking with faults and uncertainty of the system. [ABSTRACT FROM AUTHOR]

The finite-time control for a class of discrete impulsive switched positive time-delay systems under asynchronous switching is discussed in this paper. First, by choosing a Lyapunov–Krasovskii functional, some sufficient conditions for the existence of a family of asynchronously switched controllers are derived such that the resulting closed-loop system is finite-time stable based on the mode-dependent average dwell time approach. Second, the specific form of desired controller gains is given. Moreover, all the obtained results are formulated in terms of algebraic matrix inequalities which can be solved by virtue of LP toolbox. Finally, a numerical example is exploited to show that the obtained results are effective. [ABSTRACT FROM AUTHOR]

Decentralised local variable structure observers are proposed for a class of nonlinear interconnected systems in which the system states experience time delay while the inputs and outputs are delay free. The interconnections are nonlinear, unknown and time delayed, which provides particular challenge for the case of decentralised observation. It is not required that the bounds on the uncertainties in the isolated subsystems are functions of the system outputs. Unlike much of the existing work where the designed observer is an interconnected system, the observers designed in this paper are a set of decoupled dynamics and thus decentralised, which is more reliable in real implementation. A set of sufficient conditions are derived such that in the considered domain the corresponding error dynamics are asymptotically stable where the Lyapunov Razumikhin approach is employed to deal with the time delay. The delays are time varying, and there is no limitation on the rate of change of the time delays. A numerical example is presented to show the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with collision-free second-order vehicle formation control when the inter-vehicle network topology is time-varying. The proposed control law has two parts: one for converging to a desired formation (no collision avoidance considered); the other for achieving collision avoidance. Unlike existing works, the proposed control law uses a fixed (so easy-to-implement) set of time-invariant control gains for achieving the desired formation and the gradient of a distance-based edge-tension function for collision avoidance. This simple combination of the two parts provably allows for collision-free formation control under time-varying network topologies. Theoretical and numerical evidences are provided to justify the effectiveness of the developed control law. [ABSTRACT FROM AUTHOR]

In this paper, we focus on optimal H 2 model reduction methods for bilinear systems. The optimal H 2 model reduction problem can be viewed as a minimization problem on Grassmann manifold. By utilizing the geometry of Grassmann manifold, a gradient descent model reduction algorithm and a conjugate gradient model reduction algorithm based on Grassmann manifold are given. These two algorithms can simulate well the behavior of the original system and the order-reduced systems generated by our algorithms can satisfy the minimal stability requirement. Numerical examples are given to illustrate the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

Sparse channel estimation problem is one of challenge technical issues in broadband wireless communications. Square error criterion based adaptive sparse channel estimation (SEC-ASCE) algorithms, e.g., zero-attracting least mean square (ZA-LMS) and reweighted ZA LMS (RZA-LMS), have been proposed to mitigate noises as well as to exploit the channel sparsity. However, the conventional SEC-ASCE algorithms are vulnerable to performance deteriorate due to 1) random scaling of input training signal, and 2) unable to balance between convergence speed and transient-state mean square error (MSE) performance. In this paper, a mixed square/fourth error criterion (SFEC) based ASCE algorithms (SEFC-ASCE), i.e., zero-attracting least mean square/fourth error (ZA-LMS/F) and reweighted ZA-LMS/F (RZA-LMS/F), are proposed to enhance estimation performance while without exhausting a lot computational complexity. First, regularization parameters of the ZA-LMS/F and RZA-LMS/F algorithms are selected by means of Monte-Carlo simulations. Second, lower bounds of the proposed channel estimation algorithms are derived and analyzed. Finally, simulation results are given to show that the proposed sparse LMS/F-type algorithms achieve better estimation performance than the conventional algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of vibration suppression for seismic-excited buildings in finite frequency domain, and the possible faults caused by actuators are also considered in controller׳s design to improve the stability of the system. Firstly, with the consideration of seismic wave׳s effect, a mathematical model of building structure system is established. Then the finite frequency theory is introduced to the process of controller design in order to reduce seismic-excited building vibration over a certain frequency band and enhance disturbance suppression performance. Furthermore, taking actuators׳ faults into account, the active fault tolerance control method is also added to the finite frequency domain controller to compensate for the faults effect and remain the performance of building system at an acceptable level when faults occur. Finally, simulation of a three-degree-of-freedom linear building structure under earthquake excitation is given to illustrate the effect of the proposed approach. [ABSTRACT FROM AUTHOR]

This letter shows an incorrect application of the chain rule for fractional order derivatives reported in paper (Chen et al., 2014). Due to this misleading application, the proof of Theorem 2 and Theorem 5 in Chen et al., (2014) are incorrect. However, the mentioned Theorem 2 is a straightforward conclusion from results already available in literature (Jarad et al., 2013; Matignon 1996), and consequently there is no need to prove it, as it is stated in this letter. In the same way, although the proof of Theorem 5 in Chen et al. (2014) is not valid, Theorem 5 is indeed true, and a recommendation as to how to prove it is made to the authors. Besides, this letter shows that the proposed Theorem 1 in Chen et al., (2014) is also a straightforward conclusion from well known results available in literature (Jarad et al., 2013; Slotine and Li, 1999), so no demonstration is needed for this result neither. [ABSTRACT FROM AUTHOR]

This paper is devoted in the study of (2 + 1) dimensional KP–BBM equation. A small dispersion of waves is included and the nature of the solutions are examined under this effect using the theory of dynamical system. We prove that in the presence of dispersion effect on the equation, yet there exists bounded traveling wave solutions in different classes in terms of solitary waves, periodic and elliptic functions in certain regions. We obtain the general solution of the equation with or without the dispersion effect in terms of Weirstrass ℘ functions and Jacobi elliptic functions. A new technique based on the application of factorization method and the use of functional transformation yields new form of solutions. Finally, we discuss the stability analysis which shows that the traveling wave speed is a bifurcation parameter, which modulates between different classes of waves. Using phase plane analysis, we show that the solution has a transcritical bifurcation at a critical velocity. [ABSTRACT FROM AUTHOR]

Let f : M → M be a diffeomorphism of a compact smooth manifold M. Herein, we demonstrate that (i) if f has the C 1 robustly inverse pseudo orbit tracing property on the chain recurrent set CR (f) , then CR f is hyperbolic of f and (ii) if f has the C 1 robustly inverse pseudo orbit tracing property on a nontrivial transitive set Λ ⊂ M , then Λ is hyperbolic for f. 1 1 1991 Mathematics Subject Classification. 37C50; 37D20. • In Section 1, we give an introduction about the paper. • In Section 2, we have introduced the concepts for the inverse pseudo orbit tracing property. • In Section 3, we introduced basic notions and Theorem A and Theorem B. • In Section 4, we prove Theorem A. • In Section 5, we prove Theorem B. [ABSTRACT FROM AUTHOR]

Highlights: [•] Discrete zero-curvature representation from new 4-order matrix spectral problem is introduced. [•] Bargmann symmetry constraint and integrable symplectic map about the 4-field lattice equation in this paper is constructed first. [•] The integrable finite-dimensional systems in the Liouville sense are obtained. [ABSTRACT FROM AUTHOR]

a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model using the concept of fractional differential operator. A numerical method based on the Lagrange polynomial was used to solve the system equations depicting the spread of COVID-19. A detailed investigation of stability including reproductive number using the next generation matrix, and the Lyapunov were presented in detail. Numerical simulations are depicted for various fractional orders. [ABSTRACT FROM AUTHOR]