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In this paper, we study the tangential touch and C¹ regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a/2 xn² or a/2 xn² + bxnx1 for some b ∈ ℝ, b ≠ 0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied. [ABSTRACT FROM AUTHOR]

The ancient Vedic mathematics is well known for quicker handy multiplications but its recognition as an integrated circuit core against existing hardware multipliers is not established. As optimized hardware implementation of binary multiplier is one of the prominent unsolved problems in computer architecture, this paper proposes efficient Urdhava Tiryakbhyam Vedic multiplier architecture and compares it with the set of hierarchical multiplication algorithms which generate multiplication result in a single clock cycle. Two innovative algorithms are proposed here, one with a compact structure and another for faster execution. Also, its optimized transistor level layout is designed and implemented. To maintain homogeneity for comparison, all the algorithms are programmed on a common HDL language platform and analyzed with the same tool and technology. Final results indicate that the proposed architecture delivers 15.5% less power delay product (PDP) compared to closest competitor algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a Domain Specific Language to describe in a synthetic and comprehensive way, complex control problems for robotic systems. The proposed language, named Math of Tasks, abstracts from the mathematical description of the problem, which heavily depends on the particular algorithm chosen to solve it, relying on a set of operators and entities which instead, composed together, describes the behavior of the control problem. The Math of Tasks can describe any type of instantaneous controller regardless of the particular controlled variable (e.g., joint velocity, joint acceleration, contact forces). This paper shows the convenience of the proposed formalism using examples from classical control problems for different types of robotic platforms such as manipulators, humanoid bipeds, and quadrupeds. [ABSTRACT FROM AUTHOR]

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including U -pattern, X -pattern, O -pattern, A -pattern, and V -pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium's parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs. [ABSTRACT FROM AUTHOR]

In this paper, we study the maximum number of limit cycles for the unfolding of codimension-3 planar singularities with nilpotent linear parts. In [J. Math. Anal. Appl.499 (2017)], the authors proved that when parameter a ∈ (− 1 , 1) \ { 0 , − 2 / 3 } is rational, the corresponding problem could be transformed to solving semi-algebraic systems. At the same time, it is pointed out that when a = − 2 / 3 , the logarithmic function will appear according to the method, which makes it impossible to solve the problem. In this paper, we use some techniques to avoid the occurrence of logarithmic function, and get the corresponding system to produce at most two limit cycles. [ABSTRACT FROM AUTHOR]

Let K be a number field. The Pólya field concept is used to know when the module of integer-valued polynomials over the ring of integers K of K has a regular basis. In [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory  229 (2021) 386–398], the author used cohomological results from [C. B. Setzer, Units over totally real C 2 × C 2 fields, J. Number Theory  12 (1980) 160–175] to answer questions raised in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory  133 (2013) 59–71] on biquadratic Pólya fields. Here we first prove that number fields were omitted from the list of exceptional fields cited in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory  133 (2013) 59–71]. We therefore identify new biquadratic Pólya fields, where the prime number 2 is totally ramified. This result corrects and completes some others on the literature. On the other hand, we show that the main results of [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory  229 (2021) 386–398] and this paper can be proved with a single method using Kuroda/Kubota's unit formula without cohomological results of [C. B. Setzer, Units over totally real C 2 × C 2 fields, J. Number Theory  12 (1980) 160–175]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various properties (e.g. nonexistence, asymptotic behavior, uniqueness and integral representation formula) of positive solutions to nonlinear tri-harmonic equations in ℝn (n ≥ 2) and bi-harmonic equations in ℝ² with negative exponents. Such kind of equations arise from conformal geometry. [ABSTRACT FROM AUTHOR]

The Alperin weight conjecture is central to the modern representation theory of finite groups, and it is still open, despite many different approaches from different points of view. This paper surveys methods and results relating the Alperin weight conjecture, especially the recent developments in the inductive investigation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron Δ-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron Δ-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the boundedness of solutions for a class of fractional elliptic equations driven by the relativistic Schrôdinger operator (--Δ + I)s, with s ∈ (0, 1). The proof relies on a distributional Kato's inequality for (--Δ + I)s and on some properties of the Bessel kernel. [ABSTRACT FROM AUTHOR]

The Laplace transform order of reversed residual life, introduced by [I. Elbatal, The Laplace order and ordering of reversed residual life, Appl. Math. Sci.36 (2007) 1773–1788.] is used in the stochastic comparison of two life distributions. In this paper, we aim to study new notions of stochastic comparisons based on bivariate Laplace transform order of reversed residual lives. We investigate relationships the new stochastic order has with other existing bivariate orders. The interpretation of the new orders and their applications in different contexts are also pointed out. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) and a set S ⊆ V (G) of size at least 2 , a path in G is said to be an S -path if it connects all vertices of S. Two S -paths P 1 and P 2 are said to be internally disjoint if E (P 1) ∩ E (P 2) = ∅ and V (P 1) ∩ V (P 2) = S. Let π G (S) denote the maximum number of internally disjoint S -paths in G. The k -path-connectivity π k (G) of G is then defined as the minimum π G (S) , where S ranges over all k -subsets of V (G). In [M. Hager, Path-connectivity in graphs, Discrete Math. 59 (1986) 53–59], the k -path-connectivity of the complete bipartite graph K a , b was calculated, where k ≥ 2. But, from his proof, only the case that 2 ≤ k ≤ min { a , b } was considered. In this paper, we calculate the situation that min { a , b } + 1 ≤ k ≤ a + b and complete the result. [ABSTRACT FROM AUTHOR]

The g -extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464–473] determined the 3 -extra edge-connectivity of balanced hypercubes B H n and conjectured that the g -extra edge-connectivity of B H n is λ g ( B H n) = 2 (g + 1) n − 4 g + 4 for 2 ≤ g ≤ 2 n − 1. In this paper, we confirm their conjecture for n ≥ 6 − 1 2 g + 1 and 2 ≤ g ≤ 8 , and disprove their conjecture for n ≥ 3 e g ( B H n) g + 1 and 9 ≤ g ≤ 2 n − 1 , where e g ( B H n) = max { | E ( B H n [ U ]) | | U ⊆ V (B H n) , | U | = g + 1 }. [ABSTRACT FROM AUTHOR]

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each subsection of the chain. Subsequently, the research findings allowed the division of supply-chain components into subsections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management. [ABSTRACT FROM AUTHOR]

This paper reports that synergetics are used to analyze the crazing evolution. On this basis, chaotic effect is explored. The chaos equation is established and verified. The theoretical derivation are consistent with the experimental results. We design a special specimen with a special loading mode, the transient monitoring function of acoustic emission (AE) technology is used to track and detect the crazing inside the PMMA in real time, and the experiments show that synergetics can explain the crazing properties of polymer. Importantly, the mathematical explanation is also given. The AE analysis, synergetics, and craze photo reached a conclusion that the crazing has chaotic behavior. After analyzing the AE events and crazing at different stress levels, the accuracy of synergetic approach for crazing is verified. By studying the course of AE events and crazing, the self-organization effect is proposed. The research results will provide data support for the application of PMMA in ship, aircraft, and precision instruments. [ABSTRACT FROM AUTHOR]

Liu's inference is a process of deriving consequences from uncertain knowledge or evidence via the tool of conditional uncertainty. Using membership functions, this paper derives some expressions of Liu's inference rule for uncertain systems. This paper also discusses Liu's inference rule with multiple antecedents and with multiple if-then rules. [ABSTRACT FROM AUTHOR]

In this paper we discuss two modifications of the surrogate data method based on phase randomization, see [Theiler et al., 1992]. By construction, phase randomized surrogates are circular stationary. In this respect they differ from the original time series. This can cause level inaccuracies of surrogate data tests. We will illustrate this. These inaccuracies are caused by end to end mismatches of the original time series. In this paper we will discuss two approaches to remedy this problem: resampling from subsequences without end to end mismatches and data tapering. Both methods can be understood as attempts to make non-circular data approximately circular. We will show that the first method works quite well for a large range of applications whereas data tapering leads only to improvements in some examples but can be very unstable otherwise. [ABSTRACT FROM AUTHOR]

This is a reply to Ramon Ferrer-I-Cancho's paper in this issue "Some Word Order Biases from Limited Brain Resources: A Mathematical Approach." In this reply, I challenge the Euclidean distance model proposed in that paper by proposing a simple alternative model based on linear ordering. [ABSTRACT FROM AUTHOR]

The longest common subsequence is a well known and popular method for measuring similarity between sequences. It advocates the use of information contained in the longest common subsequence as an indication of similarity. In this paper we consider the count of all common subsequences as a measure of sequence similarity with the view that all common information is captured. This measure is inspired and derived from a generic similarity measure, neighborhood counting metric. The close connection of the neighborhood counting metric with probability and the Bayes classifier helps gain an insight from the probabilistic perspective into the all-common subsequences measure. We design algorithms to calculate this measure and we also carry out an experiment in the framework of k-nearest neighbors on a gene sequence classification task. The experiment shows that the all-common subsequences measure and the longest common subsequence measure have little difference for small k values, but differ significantly for large k values. The performance of the all-common subsequences measure remains steady as k gets larger, but the performance of the longest common subsequence measure drops sharply as k gets larger. Such a property may be useful for those tasks where we are interested not only in the nearest neighbor, but also in the first k nearest neighbors. The main contribution of this paper is a suite of algorithms for finding all common subsequences. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of nonautonomous, almost-periodic discrete FitzHugh–Nagumo system defined on infinite lattices. We prove that the nonautonomous infinite-dimensional system has a uniform attractor which attracts all solutions uniformly with respect to the translations of external terms. We also establish the upper semicontinuity of uniform attractors when the infinite-dimensional system is approached by a family of finite-dimensional systems. This paper is based on a uniform tail method, which shows that, for large time, the tails of solutions are uniformly small with respect to bounded initial data as well as the translations of external terms. The uniform tail estimates play a crucial role for proving the uniform asymptotic compactness of the system and the upper semicontinuity of attractors. [ABSTRACT FROM AUTHOR]

When a CDMA signal is passed through an RF transmitter, nonlinear elements cause spectral regrowth which result in reduction of spectral efficiency. CDMA signal has a pseudo noise nature; hence its mathematical treatment is too complex to analysis. In this paper, first it will be shown how to simplify the complex mathematics of CDMA signal. Then, a deterministic signal replaces the CDMA signal and the system response to both of them is calculated. In this paper, for the first time, ACPR is explicitly calculated for both the CDMA and deterministic signals. ACPR is calculated in terms of the nonlinear system coefficients and input power, and therefore, can be used in design objectives. In addition, it will be shown that if input power of the deterministic signal is multiplied by $\sqrt{20}$ (i.e., correction factor), ACPR error of these kinds of signals in -55 dBc is less than 2.2% for the system nonlinearity orders up to 13. This correction factor is obtained by both theoretical and simulation methods. [ABSTRACT FROM AUTHOR]

In this paper, attribute reduction in variable precision rough set model is discussed. Several kinds of reducts preserving some of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Relations among those kinds of reducts are investigated. As a basis for reduct computation, Boolean function representations of the preservation of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Throughout this paper, the great difference between the analysis using variable precision rough sets and the classical rough set analysis is emphasized. [ABSTRACT FROM AUTHOR]

In this paper, the author discusses estimation procedures for K independent, homogeneous geometric processes (GPs), parallel to those for K independent, homogeneous arithmetic processes (APs) derived by Leung.3 In addition, he corrects two minor mistakes appearing in Leung,3 on pp. 231–232. In the course of developing the fourth and fifth estimators for $\mu_{\bar {G}_1}$, the mean of $\bar {G}_1$, the author was inspired to derive two additional corresponding estimators for $\mu_{\bar {A}_1}$, the mean of $\bar {A}_1$. For the reader's easy reference, the results of both the APs derived in Leung3 and GPs derived in this paper are summarized in a table. Finally, the author draws some conclusions of the applicability of an AP and/or a GP based on partial findings of two real case studies. [ABSTRACT FROM AUTHOR]

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel. [ABSTRACT FROM AUTHOR]

Illuminative deformation patterns of a honeycomb structure are presented. A representative volume element of a honeycomb structure consisting of 2 × 2 hexagonal cells is modeled to be a ${\rm D}_6\dot{+}({\rm C}_2\times\tilde{\rm C}_2)$-equivariant system. The bifurcation mechanism and an exhaustive list of possible bifurcated patterns are obtained by group-theoretic bifurcation theory. A flower mode of the honeycomb is shown to have the same symmetry as the so-called anti-hexagon in the Rayleigh–Bénard convection. A numerical bifurcation analysis is conducted on an elastic in-plane honeycomb structure consisting of 2×2 cells to produce beautiful wallpapers of bifurcating deformation patterns and, in turn, to highlight the achievement of the paper. New deformation patterns of a honeycomb structure have been found and classified in a systematic manner. Knowledge of the symmetries of the bifurcating solutions has turned out to be vital in the successful numerical tracing of the bifurcated paths. This paper paves the way for the introduction of the results hitherto obtained for flow patterns in fluid dynamics into the study of patterns on materials. [ABSTRACT FROM AUTHOR]

The subject of this paper is a generalized approach to relative scalar cardinalities of fuzzy sets. In the main part of the paper, we discuss basic properties of triangular norm-based relative cardinality such as valuation property, the cartesian product rule and complementary rule. Examples of cardinalities satisfying those properties are also given. [ABSTRACT FROM AUTHOR]

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable. [ABSTRACT FROM AUTHOR]

By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of Chen's attractor. [ABSTRACT FROM AUTHOR]

In this paper we study phase space relations in a certain class of discrete dynamical systems over graphs. The systems we investigate are called Sequential Dynamical Systems (SDSs), which are a class of dynamical systems that provide a framework for analyzing computer simulations. Specifically, an SDS consists of (i) a finite undirected graph Y with vertex set {1,2,…,n} where each vertex has associated a binary state, (ii) a collection of Y-local functions (Fi,Y)i∈v[Y] with $F_{i,Y}: \mathbb{F}_2^n\to \mathbb{F}_2^n$ and (iii) a permutation π of the vertices of Y. The SDS induced by (i)–(iii) is the map \[ [F_Y,\pi] = F_{\pi(n),Y} \circ \cdots \circ F_{\pi(1),Y}\,. \] The paper is motivated by a general reduction theorem for SDSs which guarantees the existence of a phase space embedding induced by a covering map between the base graphs of two SDSs. We use this theorem to obtain information about phase spaces of certain SDSs over binary hypercubes from the dynamics of SDSs over complete graphs. We also investigate covering maps over binary hypercubes, $Q_2^n$, and circular graphs, Circn. In particular we show that there exists a covering map $\phi: Q_2^n\to K_{n+1}$ if and only if 2n≡0 mod n+1. Furthermore, we provide an interpretation of a class of invertible SDSs over circle graphs as right-shifts of length n-2 over {0,1}2n-2. The paper concludes with a brief discussion of how we can extend a given covering map to a covering map over certain extended graphs. [ABSTRACT FROM AUTHOR]

An emulated digital CNN-UM (CASTLE) architecture was published few years ago.1 Different emulated digital CNN-UM architectures are analyzed in the paper. These new modified architectures are optimized according to the silicon area, operating speed or dissipated power. A reconfigurable arithmetic core will also be shown in the paper, by which solution of the neighborhood size can be changed. An advanced CASTLE with pipe-lining is presented. The operation frequency is increased by using this solution in approximately 10 times. [ABSTRACT FROM AUTHOR]

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper. [ABSTRACT FROM AUTHOR]

Passive synthesis of fractional driving-point immittance function is one of the most important research topics in fractional circuits. The synthesis method for a class of fractional driving-point immittance function is proposed in this paper. Firstly, the immittance function of passive fractional circuit is transformed to multivariable positive-real function by proper variable substitution. Secondly, to synthesize the function, except one variable, other high-order variables are transformed to the combination of products of different one-order variables by introducing new variables. Thirdly, synthesize the new function by traditional method. At last, substitute elements inversely twice and the final circuit for fractional driving-point immittance function can be achieved. The method is verified by giving synthesis demonstration. [ABSTRACT FROM AUTHOR]

Sparse representation classification (SRC) has been successfully applied into hyperspectral image (HSI). A test sample (pixel) can be linearly represented by a few training samples of the training set. The class label of the test sample is then decided by the reconstruction residuals. To incorporate the spatial information to improve the classification performance, a patch matrix, which includes a spatial neighborhood set, is used to replace the original pixel. Generally, the objective function of the reconstruction residuals is represented as Frobenius-norm, which actually treats the elements in the reconstruction residuals in the same way. However, when a patch locates in the image edge, the samples in the patch may belong to different classes. Frobenius-norm is not suitable to compute the reconstruction residuals. In this paper, we propose a robust patch-based sparse representation classification (RPSRC) based on -norm. An iteration algorithm is given to compute RPSRC efficiently. Extensive experimental results on two real-life HSI datasets demonstrate the effectiveness of RPSRC. [ABSTRACT FROM AUTHOR]

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [ABSTRACT FROM AUTHOR]

This paper studies the problem of achieving an energy efficient walking on an uneven surface for a compass-like biped robot with flat feet. To this end, reference walking gaits, which consist of two phases including the static foot phase and the foot rotation phase, are designed on several typical slopes via minimizing the dimensionless specific mechanical cost of transport. Moreover, for other slopes, a simple transformation method is proposed to generate interim reference walking gaits from the reference ones on those typical slopes. Then an input-output feedback linearization approach is considered to design a tracking control law in the static foot phase and a time-scaling approach is adopted to construct a tracking control law in the foot rotation phase as the dynamics in this phase is underactuated. By switching the control law at different phases and switching the reference walking gaits on different slopes, a compass-like robot can achieve energy efficient walking on uneven surfaces. The validity of our method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied. [ABSTRACT FROM AUTHOR]

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner-KP equation are obtained via an auxiliary function method. [ABSTRACT FROM AUTHOR]

Under an interpretation of the principles of non-contradiction and excluded-middle based on the concept of self-contradiction, this paper mainly deals with the principles' verification in the case of the unit interval of the real line. Such verification is done in the three following cases: (1) The unit interval is totally ordered by the restriction to it of the usual order of the real line, (2) the unit interval is partially ordered by the sharpened order, and (3) the unit interval is under a new particular preorder. The first case is immediately extended to characterize the case of fuzzy sets. [ABSTRACT FROM AUTHOR]

One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity. [ABSTRACT FROM AUTHOR]

Many papers have addressed the task of proposing a set of convenient axioms that a good rule interestingness measure should fulfil. We provide a new study of the principles proposed until now by means of the logic model proposed by Hájek et al.14 In this model association rules can be viewed as general relations of two itemsets quantified by means of a convenient quantifier.28 Moreover, we propose and justify the addition of two new principles to the three proposed by Piatetsky-Shapiro.27 We also use the logic approach for studying the relation between the different classes of quantifiers and these axioms. We define new classes of quantifiers according to the notions of strong and very strong rules, and we present a quantifier based on the certainty factor measure,317 studying its most salient features. [ABSTRACT FROM AUTHOR]

The generation of Pareto optimal solutions for complex systems with multiple conflicting objectives can be easier if the problem can be decomposed and solved as a set of smaller coordinated subproblems. In this paper, a new decomposition-coordination method is proposed, where the global problem is partitioned into subsystems on the basis of the connection structure of the mathematical model, assigning a relative importance to each of them. In order to obtain Pareto optimal solutions for the global system, the aforementioned subproblems are coordinated taking into account their relative importance. The scheme that has been developed is an iterative one, and the global efficient solutions are found through a continuous information exchange process between the coordination level (upper level) and the subsystem level (lower level). Computational experiments on several randomly generated problem instances show that the suggested algorithm produces efficient solutions within reasonable computational times. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of the solutions u(x,t) of the Swift–Hohenberg equation with quintic nonlinearity on a one-dimensional domain (0, L). With α and the length L of the domain regarded as bifurcation parameters, branches of nontrivial solutions bifurcating from the trivial solution at certain points are shown. Local behavior of these branches are also studied. Global bounds for the solutions u(x,t) are established and then the global attractor is investigated. Finally, with the help of a center manifold analysis, two types of structures in the bifurcation diagrams are presented when the bifurcation points are closer, and their stabilities are analyzed. [ABSTRACT FROM AUTHOR]

Watermarking is now considered as an efficient means for assuring copyright protection and data owner identification. Watermark embedding techniques depend on the representation domain of the image (spatial, frequency, and multiresolution). Every domain has its specific advantages and limitations. Moreover, each technique in a chosen domain is found to be robust to specific sets of attack types. So we need to propose more robust domains to defeat these limitations and respect all the watermarking criterions (capacity, invisibility and robustness). In this paper, a new watermarking method is presented using a new domain for the image representation and the watermark embedding: the mathematical Hessenberg transformation. This domain is found to be robust against a wide range of STIRMARK attacks such as JPEG compression, convolution filtering and noise adding. The robustness of the new technique in preserving and extracting the embedded watermark is proved after various attacks types. It is also improved when compared with other methods in use. In addition, the proposed method is blind and the use of the host image is not needed in the watermark detection process. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy set, was introduced by Atanassov, has been applied to many different fields, such as logic programming, pattern recognition, and decision making, etc. However, so far there has been few investigation on how to transform attribute tested values of alternative into a intuitionistic fuzzy number, and then complete decision making by intuitionistic fuzzy information. In this paper, the original attribute value (objective information) are characterized by crisp number which are given by decision maker. We define the concepts of supporting, opposing and neutral set of alternative respectively, develop an approach for transform attribute values into intuitionistic fuzzy number, and determine the order of alternatives based on the score and the degree of accuracy of the intuitionistic fuzzy number. Finally, a practical example is provided to illustrate the developed method. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing the total late work (Σj=1n Vj) on an unbounded batch processing machine, where Vj = min{Tj, pj} and Tj = max{Cj - dj, O}. The batch processing machine can process up to B (B ≥ n) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time, respectively. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the jobs in this batch. In this paper, we prove that the problem 1∣B ≥ n∣ Σj=1nVj is NP-hard. [ABSTRACT FROM AUTHOR]

This paper studies the fluid model of a special kind of multi-type queueing network with type priority. The fluid of the same type in the same station is operated under last buffer first served (LBFS) policy. The stability of this kind of fluid model is proved via the Lyapunov function. [ABSTRACT FROM AUTHOR]

In this paper we investigate, via numerical simulations, the parameter space of the set of autonomous differential equations of a Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode was replaced by a cubic polynomial. As far as we know, we are the first to report that this parameter-space presents islands of periodicity embedded in a sea of chaos, scenario typically observed only in discrete-time models until recently. We show that these islands are self-similar, and organize themselves in period-adding bifurcation cascades. [ABSTRACT FROM AUTHOR]

Chua's circuit is very suitable as a programmable chaos generator because of its robust nonlinearity. In addition to exhibiting a rich variety of bifurcation and chaos phenomenon, this circuit can be modeled and realized with a fixed main system block and many different nonlinear function blocks such as piecewise-linear function, cubic-like function, piecewise-quadratic function and other trigonometric functions. This paper presents a FPAA (Field Programmable Analog Array) based programmable implementation of Chua's circuit. Nonlinear function blocks used in Chua's circuit are modeled with an FPAA and hence a model can be rapidly changed for realization of other nonlinear functions. In this study, four FPAA-based reconfigurable implementations of Chua's circuit have been realized. Experimental results agree with numerical simulation and results obtained from discrete electronic implementations of Chua's circuit. [ABSTRACT FROM AUTHOR]

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a generating subsystem, where each subsystem is based on a single chaotic map. This chaotic map is presented as a 1-D piecewise chaotic map related to the chaotic logistic map. We conduct an analysis of the dynamical behavior of the proposed map to integrate it as a component in the proposed generators subsystems. The output bits of these keystream generators are produced by applying a threshold function to convert the floating-point iterates of the irregularly decimated map into a binary form. The generated keystream bits are demonstrated to exhibit high level of security, long period length, high linear complexity measure and random-like properties at given certain parameter values. Standard statistical tests on the proposed generators, as well as other keystream generators, are performed and compared. [ABSTRACT FROM AUTHOR]

In this paper, we consider a planar dynamical system with a piecewise linear function containing two dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system, with five singular points, can have at most four limit cycles, three of which surround the foci one by one and the fourth limit cycle surrounds all of the singular points of this system. [ABSTRACT FROM AUTHOR]