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The author corrects the proof of Theorem 2.1 in the above titled paper. Also, the conditions for extinction and persistence of the disease become identical in particular case. This situation should be avoided. The author apologizes for any inconvenience that may have been caused. [ABSTRACT FROM AUTHOR]

• 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]

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]

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]

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]

In this paper, we investigate the data-driven localized solutions of Kadomtsev–Petviashvili (KP) and modified KP equation. Through the two-dimensional Miura transformation, the solutions of modified KP equation can be converted into the solutions of KP equation, but the process is not invertible in mathematics. Based on the neural network, the localized waves of modified KP equation are obtained under an unsupervised training with the aid of two-dimensional Miura transformation and the initial and boundary conditions of solution of the KP equation. As the result of the different hyperparameters, three types of localized waves are found after the training, including the shape of kink, dark and kink-bell. The evolution and error dynamics of the predicted solutions are analyzed through the graphics. • Solutions of mKP equation are studied via PINN with 2D Miura transformation. • The numerical solutions are predicted under the unsupervised training. • Different solutions are obtained based on the same initial and boundary condition. [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]

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]

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]

• 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]

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]

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]

Abstract: This paper is motivated from some recent papers treating the impulsive Cauchy problems for some differential equations with fractional order q ∈(1,2). A better definition of solution for impulsive fractional differential equation is given. We build up an effective way to find natural solution for such problems. Then sufficient conditions for existence of the solutions are established by applying fixed point methods. Four examples are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]

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: For linear elastostatics, the particular solutions and the fundamental solutions can be used for the admissible functions, so that only the boundary conditions need to be satisfied, thus called the boundary methods (or Trefftz methods). Hence, how to couple the boundary conditions is a crucial issue. There are basically two types of boundary conditions: (I) the displacement (i.e., Dirichlet) condition and (II) the traction (i.e., Neumann) condition. In this paper, the coupling techniques for the traction (i.e., Neumann condition) are the main theme for boundary methods, because the traction condition may be regarded as the basic condition and the displacement condition as the natural condition. The Lagrange multiplier used for the displacement (i.e., Dirichlet) condition is well known in mathematics community (see Babuška, 1973 ; Babuška et al., 1978 ; Li, 1998 ; Pitkäranta, 1979 ), but the Lagrange multiplier used for the traction (i.e., Neumann) condition is popular for elasticity problems by the Trefftz method in engineering community, which is called the hybrid Trefftz method (HTM) (see de Freitas, 1998 ; de Freitas and Ji, 1996 ; Jirousek, 1978 ; Jirousek and Venkstesh, 1992 ; Jirousek and Wroblewski, 1996 ; Qin, 2000 ). On the other hand, the collocation Trefftz method (CTM) can also be used to directly couple the traction condition without extra-multipliers. In this paper, a brief error analysis for the HTM is given, to provide the optimal convergence rates. Numerical experiments of simple models are carried out to support this analysis. The HTM has the merits: flexibility and robustness, so that it has been widely used in engineering problems. Since the optimal convergence rates are the most important criterion in evaluation of numerical methods, the global performance of the HTM is as good as that of the CTM, although the HTM causes larger condition numbers and requires more CTU time for the computation of the simple models in this paper. More numerical comparisons also show that using the particular solutions is more advantageous than using the fundamental solutions in both HTM and CTM. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a summability factor theorem for summability ∣A, δ∣ k as defined in . This paper is an extension of the main result of Savaş and Rhoades [Savaş E, Rhoades B. On absolute summability factors for a triangular matrix. Int J Diff Equat 2006;1:155–63]. [Copyright &y& Elsevier]

Abstract: This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included. [Copyright &y& Elsevier]

Abstract: Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2006;28:902–5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new. [Copyright &y& Elsevier]

Abstract: A few reduced equations from the self-dual Yang–Mills equations are presented, which are seemly extended zero curvature equations. As their applications, a good many nonlinear evolution equations could be obtained. In this paper, a (2+1)-dimensional AKNS hierarchy of soliton equations is generated from one of reduced equations of the self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable model (actually, its integrable couplings) is worked out by using the quadratic-form identity, which is Liouville integrable. The way presented in the paper has extensive applications. That is to say, making use of the approach specially a few higher-dimensional zero curvature equations in the paper could produce a lots of higher-dimensional integrable coupling systems and their corresponding Hamiltonian structures. [Copyright &y& Elsevier]

Abstract: The paper is a continuation of our previous work towards the use of probability information in interval computations. While in the previous work, bounds on the first order moments are taken into account, the contribution of this article is to deal with correlations. Specifically, in this paper, we develop a new method that takes into account both correlation among measured parameters and bounds on their expected values when doing interval computation. [Copyright &y& Elsevier]

Abstract: This paper presents some comments on the above paper regarding the manipulation of Gaussian fuzzy sets and provides two useful generalized formulas for both of similarity and similarity/possibility relationships of Gaussian fuzzy sets with different widths. [Copyright &y& Elsevier]

Abstract: The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and also a stress tensor. Correspondingly, a viscous double-layer potential is defined. The properties of all these potentials are investigated. By representing the scattered field as a combination of a single-layer viscous potential and a double-layer viscous potential the problem is reduced to the solution of a singular vectorial integral equation of Fredholm type of the second kind. In the case where the stress vector on the boundary is the main quantity of interest the corresponding boundary singular integral equation is proved to have a unique solution. [Copyright &y& Elsevier]

Abstract: The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh’s extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with particular types of fuzzy intervals. Recently, Dombi and Győrbíró [J. Dombi, N. Győrbíró, Additions of sigmoid-shaped fuzzy intervals using the Dombi operator and infinite sum theorems, Fuzzy Sets and Systems 157 (2006) 952–963] proved that addition is closed if the Dombi t-norm is used with sigmoid-shaped fuzzy intervals. In this paper, we define a broader class of sigmoid-shaped fuzzy intervals. Then, we study t-norms that are consistent with these particular types of fuzzy intervals. Dombi and Győrbíró’s results are special cases of the results described in this paper. [Copyright &y& Elsevier]

Abstract: This paper studies a multi-level multi-objective decision-making (ML-MODM) problems with linear or non-linear constraints. The objective functions at each level are non-linear functions, which are to be maximized or minimized. This paper presents a three-level multi-objective decision-making (TL-MODM) model and an interactive algorithm for solving such a model. The algorithm simplifies three-level multi-objective decision-making problems by transforming them into separate multi-objective decision making problems at each level, thereby avoiding the difficulty associated with non-convex mathematical programming. Our algorithm is an extension of the work of Shi and Xia [X. Shi, H. Xia, Interactive bi-level multi-objective decision making, Journal of the Operational Research Society 48 (1997) 943–949], which dealt with interactive bi-level multi-objective decision-making problems, with some modifications in assigning satisfactoriness to each objective function in all the levels of the TL-MODM problem. Also, we solve each separate multi-objective decision making problem of the TL-MODM problem by the balance space approach. A new formula is introduced to interconnect the satisfactoriness and the proportions of deviation needed to reflect the relative importance of each objective function. Thus, we have the proportions of deviation including satisfactoriness. In addition, we present new definitions for the satisfactoriness and the preferred solution in view of singular-level multi-objective decision making problems that corresponds to the η-optimal solution of the balance space approach. Also, new definitions for the feasible solution and the preferred solution (η-optimal point) of the TL-MODM problem are presented. An illustrative numerical example is given to demonstrate the algorithm. [Copyright &y& Elsevier]

Abstract: Fusion of sensor and communication data currently can only be performed at a late processing stage after sensor and textual information are formulated as logical statements at appropriately high level of abstraction. Contrary to this it seems, the human mind integrates sensor and language signals seamlessly, before signals are understood, at pre-conceptual level. Learning of conceptual contents of the surrounding world depends on language and vice versa. The paper describes a mathematical technique for such integration. It combines fuzzy dynamic logic with dual cognitive-language models. The paper briefly discusses relationships between the proposed mathematical technique, working of the mind and applications to understanding-based search engines. [Copyright &y& Elsevier]

Abstract: Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce a theory of fuzzily defined complement operations on nonempty sets equipped with fuzzily defined ordering relations. Many-valued equivalence relation-based fuzzy ordering relations (also called vague ordering relations) provide a powerful and a comprehensive mathematical modelling of fuzzily defined partial ordering relations. For this reason, starting with a nonempty set X equipped with a many-valued equivalence relation and a vague ordering relation, a fuzzily defined complement operation (called a vague complement operation) on X will be formulated by means of the underling many-valued equivalence relation and vague ordering relation. Because of the fact that the practical implementations of vague complement operations basically depend on their representation properties, a considerable part of this paper is devoted to the representations of vague complement operations. In addition to this, the present paper provides various nontrivial examples for vague complements, and introduces a many-valued logical interpretation of quantum logic as a real application of vague complements. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the computation of Asian options when the underlying asset has a jump. In the Black and Scholes model, Geman and Yor give a closed-form of formula for the price of an Asian option at a random exponential distributed maturity (it then “suffices” to invert the Laplace transform to have the price at a fixed time). The aim of this paper is to obtain such a formula in a model (which seems more realistic) of Black and Scholes with a jump at a random time, which extends the well-known case of the continuous Black and Scholes model. Furthermore, we treat the multi-jump case. Here we also develop a formula for pricing such an option. [Copyright &y& Elsevier]

Abstract: This is the fourth contribution in a series of papers aimed at directing the attention of the prospective E-infinity researcher to the most important mathematical background and sources needed for an easy understanding and successful application of this theory. The present paper is mainly concerned with the mathematical physics relevant to E-infinity theory with emphasis on super Yang–Mills theory and superstrings. [Copyright &y& Elsevier]

Abstract: This paper is a further note which corrects an error of the paper by Park and Won. A new stability criteria which is less conservative than those in the literature is presented. [Copyright &y& Elsevier]

Abstract: In this paper we consider the application of the method of fundamental solutions to solve crack problems. These problems present difficulties, which are not only related to the intrinsic singular nature of the problem, instead they are mainly related to the impossibility in choosing appropriate point sources to write the solution as a whole. In this paper we present: (1) a domain decomposition technique that allows to express a piecewise approximation of the solution using a method of fundamental solutions applied to each subdomain; (2) an enriched approximation whereby singular functions (fully representing the singular behaviour around the cracks or other sources of boundary singularities) are used. An application of the proposed techniques to the torsion of cracked components is carried out. [Copyright &y& Elsevier]

Abstract: The reactive power optimization is an effective method to improve voltage level, decrease network losses and maintain the power system running under normal conditions. This paper provides a method combining particle swarm optimization (PSO) with linear interior point to handle the problems remaining in the traditional arithmetic of time-consuming convergence and demanding initial values. Furthermore, since chaotic mapping enjoys certainty, ergodicity and stochastic property, the paper introduces chaos mapping into the particle swarm optimization, the paper presents a new arithmetic based on a hybrid method of chaotic particle swarm optimization and linear interior point. Thanks to the superior overall exploration ability of particle swarm optimization and the local exploration ability of linear interior point within the neighborhood of the optimal point, the new method can improve the performance of both convergence and results’ precision. Tested by IEEE-30, the new method provided in this paper is proved effective and practical in the optimization of shunt capacitors and tap position of load-ratio voltage transformer. [Copyright &y& Elsevier]

Abstract: In this paper, the Hodgkin–Huxley model is studied with the leakage conductance and the sodium reversal potential selected as parameters for a two-parameter Hopf-bifurcation analysis. The influence of bifurcation on the HH model was also discussed and algebra criterion in high dimension equations was used to identify Hopf bifurcation. In addition, this paper also discuses the bifurcation approach to inherited disorders of ion channels in skeletal muscle excitable membranes. [Copyright &y& Elsevier]

In this paper basic notions of the rough set theory will be given. In fact, the paper concerns a relationship between rough sets and ring theory. We shall introduce the notion of rough subring (resp. ideal) with respect to an ideal of a ring which is an extended notion of a subring (resp. ideal) in a ring, and we shall give some properties of the lower and the upper approximations in a ring. [ABSTRACT FROM AUTHOR]

Trefftz method is the boundary-type solution procedure using regular T-complete functions satisfying the governing equation. Until now, it has been mainly applied to numerical analyses of the problems governed with the homogeneous differential equations such as the two- and three-dimensional Laplace problems and the two-dimensional elastic problem without body forces. On the other hand, this paper describes the application of the indirect Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. Since the Poisson equation has an inhomogeneous term, it is generally difficult to determine the T-complete function satisfying the governing equation. In this paper, the inhomogeneous term containing an unknown function is approximated by a polynomial in the Cartesian coordinates to determine the particular solutions related to the inhomogeneous term. Then, the boundary value problem of the Poisson equation is transformed to that of the Laplace equation by using the particular solution. Once the boundary value problem of the Poisson equation is solved according to the ordinary Trefftz formulation, the solution of the boundary value problem of the Poisson equation is estimated from the solution of the Laplace equation and the particular solution. The unknown parameters included in the particular solution are determined by the iterative process. The present scheme is applied to some examples in order to examine the numerical properties. [Copyright &y& Elsevier]

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]

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]

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]