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This paper provides a new analytic test to check strong accessibility of nonlinear control systems. This test can be applied to nonlinear systems described by meromorphic vector fields (whose components are fractions of analytic functions). The test consists in checking the rank of a certain finite matrix (which extends to a nonlinear case the classical “controllability matrix” of linear systems theory) and, unlike the classical accessibility test, always terminates giving an exhaustive answer (yes/no) within a fixed number of steps. Further, a generic feature of accessibility is proven: the accessibility from a point $p$ of the system analyticity domain implies the accessibility from almost every point of the domain (generic strong accessibility). The paper provides two simple examples, which illustrate the proposed analytic test and its advantages with respect to the existing results. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation. Design/methodology/approach: The newly developed time-dependent model has been handled by using the Hirota's direct method. The authors also use the complex Hirota's criteria for deriving multiple complex soliton solutions. Findings: The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient. Research limitations/implications: The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions. Practical implications: The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function. Social implications: The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived. Originality/value: This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test. [ABSTRACT FROM AUTHOR]

• The stratification and anisotropy of the soil are taken into consideration. • The impact of the bedrock underlying the soil is taken into account. • The stiffness of the footing is considered. • Explicit expressions for stress and displacement are provided. This paper presents explicit expressions of stress and displacement in the physical domain of layered transversely isotropic soil under strip footing for the first time. The method proposed in this study is not only applicable to analysing problems related to flexible footings, but can also be utilized for analysing problems related to rigid footings. The stress function of each layer can be represented by two single-valued analytic functions. Each layer of soil is mapped to a unit circle using affine and conformal transformations. Within the unit circle, the single-valued analytic function can be expanded into a Taylor series with unknown coefficients. By establishing equations based on the boundary conditions and stress-displacement continuity conditions, the unknown coefficients can be determined. To validate the proposed method, the calculation results were compared with ANSYS finite element results. [ABSTRACT FROM AUTHOR]

In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice continuously differentiable) functions. In this paper, a generalized circuit is introduced (G-NPC), which is aimed at solving in real time a much wider class of nonsmooth nonlinear programming problems where the objective function and the constraints are assumed to satisfy only the weak condition of being regular functions. G-NPC, which derives from a natural extension of NPC, has a neural-like architecture and also features the presence of constraint neurons modeled by ideal diodes with infinite slope in the conducting region. By using the Clarke's generalized gradient of the involved functions, G-NPC is shown to obey a gradient system of differential inclusions, and its dynamical behavior and optimization capabilities, both for convex and nonconvex problems, are rigorously analyzed in the frame- work of nonsmooth analysis and the theory of differential inclusions. In the special important case of linear and quadratic pros gramming problems, salient dynamical features of G-NPC, namely the presence of sliding modes, trajectory convergence infinite time, and the ability to compute the exact optimal solution of the problem being modeled, are uncovered and explained in the developed analytical framework. [ABSTRACT FROM AUTHOR]

This paper expands the method of fundamental solutions (MFS) to solve the anti-plane crack problems based on the traditional fundamental solution by the conformal mapping technique without using the domain decomposition technique and/or the crack Green's function. Based on the complex analysis and the conformal mapping technique, the approximate solution of the complex analytic function is derived for the MFS. The modified boundary conditions are deduced to construct the interpolation equations of the MFS. The conformal mapping technique naturally introduces singularities of the stress fields and the stress intensity factors (SIFs) for the anti-plane crack problems without using the crack Green's function and the domain-decomposition technique. The obtained numerical examples illustrate the validity and accuracy for the anti-plane crack problems. The proposed method is an expansion of the traditional MFS, and can be applied for many anti-plane elastic problems with the simple concept and the easy numerical implementation. [ABSTRACT FROM AUTHOR]

This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

Abstract The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly infinite families of probability densities with the same sequence of moments. In this paper, the notion of q -moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either q -moment determinate or indeterminate in terms of its q -density have been obtained. Also, a q -analogue of Stieltjes classes is defined for q -distributions and q -Stieltjes classes have been constructed for a family of q -densities of q -moment indeterminate distributions. [ABSTRACT FROM AUTHOR]

Abstract-The paper deals with definitions of zeros and poles and their features in finite-dimensional linear continuous-time periodic (FDLCP) systems under a harmonic framework. More precisely, system and transfer zeros and poles in the harmonic wave-to-wave sense are defined on what we call the regularized harmonic system operators and the harmonic transfer operators of FDLCP systems by means of regularized determinants; then their composition and properties related to system structures are examined via the Floquet theory and controllability/observability decompositions of FDLCP systems. The study shows that under mild assumptions, the harmonic transfer operators of FDLCP systems are analytic and meromorphic, on which zeros and poles are well-defined. Basic zero/pole relationships are established, which are similar to their linear time-invariant counterparts and in particular explicate some interesting harmonic wave-to-wave behaviors of FDLCP systems. The results are significant in analysis and synthesis of FDLCP systems when the harmonic approach is adopted. [ABSTRACT FROM AUTHOR]

We present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint. Performance is cast as an interpolation problem with bounded analytic functions. Minimizers of a certain weighted-entropy functional provide interpolants having degree less than the number of constraints. The choice of weight parameterizes all such bounded degree solutions. However, the relationship between the weights and the shape of corresponding transfer functions is not direct. Thus, in this paper we develop a formalism that guides weight selection. [ABSTRACT FROM AUTHOR]

Abstract: The effective elastic properties of periodic fibre-reinforced media with complex microstructure are determined by the method of asymptotic homogenization via a novel solution to the cell problem. The solution scheme is ideally suited to materials with many fibres in the periodic cell. In this first part of the paper we discuss the theory for the most general situation—N arbitrarily anisotropic fibres within the periodic cell. For ease of exposition we then restrict attention to isotropic phases which results in a monoclinic composite material with 13 effective moduli and expressions for each of these are determined. In the second part of this paper we shall discuss results for a variety of specific microstructures. [Copyright &y& Elsevier]

The paper is devoted to the numerical solution of both elliptic and parabolic problems by overlapping Schwarz methods. It demonstrates that while the two-level Schwarz method is necessary for the efficient solution of discrete elliptic problems, the one-level Schwarz method can be sufficiently efficient in the parabolic case. The paper includes results from numerical simulations of a large-scale model of the performance of a nuclear waste repository. [Copyright &y& Elsevier]

A neural network is said to be convergent (or completely stable) when each trajectory tends to an equilibrium point (a stationary state). A stronger property is that of absolute stability, which means that convergence holds for any choice of the neural network parameters, and any choice of the nonlinear functions, within specified and well characterized sets. In particular, the property of absolute stability requires that the neural network be convergent also when, for some parameter values, it possesses nonisolated equilibrium points (e.g., a manifold of equilibria). Such a property, which is really well suited for solving several classes of signal processing tasks in real time, cannot be in general established via the classical LaSalle approach, due to its inherent limitations to study convergence in situations where the neural network has nonisolated equilibrium points. In this paper, a new method to address absolute stability is developed, based on proving that the total length of the neural network trajectories is finite. A fundamental result on absolute stability is given, under the hypothesis that the neural network possesses a Lyapunov function, and the nonlinearities involved (neuron activations, inhibitions, etc.) are modeled by analytic functions. At the core of the proof of finiteness of trajectory length is the use of some basic inequalities for analytic functions due to Łojasiewicz. The result is applicable to a large class of neural networks, which includes the networks pro- posed by Vidyasagar, the Hopfield neural networks, and the standard cellular neural networks introduced by Chua and Yang. [ABSTRACT FROM AUTHOR]

We introduce a general bivariate fractional calculus, defined using a kernel based on an arbitrary univariate analytic function with an appropriate bivariate substitution. Various properties of the introduced general operators are established, including a series formula, function space mappings, and Fourier and Laplace transforms. A major result of this paper is a fractional Leibniz rule for the new operators, the derivation of which involves correcting a minor error in one of the classic textbooks on fractional calculus. We also solve some fractional differential equations using transform methods, revealing an interesting connection between bivariate type Mittag-Leffler functions. • Bivariate fractional integrals using general analytic kernel functions. • A fractional Leibniz rule is proved for the new operators. • Corresponding bivariate fractional derivative operators are constructed. • Double Laplace transforms used to solve partial integro-differential equations. [ABSTRACT FROM AUTHOR]

Our attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a (α) (t − s) b (α) of order α ∈ (0 , 1). We determine analytic functions a (α) and b (α) such that when α → 0 + , the corresponding operator becomes identity operator, and when α → 1 − the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared. • A class of linear fractional operators that behave like an integer order derivative is obtained. • Inverse and Laplace transforms of introduced fractional derivatives are investigated. • The relaxation equation with diverse fractional operators is solved analytically. [ABSTRACT FROM AUTHOR]

We have developed a software package based on a genetic algorithm that fits an analytic function to a given set of data points. The code, called GAFit, was also interfaced with the CHARMM and MOPAC programs in order to facilitate force field parameterizations and fittings of specific reaction parameters (SRP) for semiempirical Hamiltonians. The present tool may be applied to a wide range of fitting problems, though it has been especially designed to significantly reduce the hard work involved in the development of potential energy surfaces for complex systems. For this purpose, it has been equipped with several programs to help the user in the preparation of the input files. We showcase the application of the computational tool to several chemical-relevant problems: force-field parameterization, with emphasis on nonbonded energy terms or intermolecular potentials, derivation of SRP for semiempirical Hamiltonians, and fittings of generic analytical functions. Program summary Program title : GAFit Program Files doi : http://dx.doi.org/10.17632/9gy6bjcwk5.1 Licensing provisions : GNU General Public License 3 (GPL) Programming language : Fortran 90, C, Perl and Java Nature of problem : Potential energy surfaces (PESs) have a key role in reaction dynamics and molecular dynamics. Chemical dynamics simulations can be performed by using analytical PESs or by direct dynamics, that is, by computing energies and forces “on-the-fly” by molecular structure calculations. The development of analytical PESs is, quite often, a very complex and tedious task. There are several programs in the literature that may help to develop PESs but, as far as we know, none of them show, at the same time, great generality and flexibility. Solution method : GAFit was designed to help users develop analytical potential energy functions. We made special efforts to write a code that exhibits the three features mentioned above. For this reason, we have also interfaced GAFit with the CHARMM and MOPAC programs. The former is one of the popular packages for molecular dynamics and the latter is a semiempirical quantum chemistry program that may be conveniently used for direct dynamics simulations. Because, in general, the fitting of PESs involves a simultaneous optimization of many nonlinear parameters, we have selected a genetic algorithm as the driver for the parameterizations. As shown in the paper, GAFit may be applied to other fitting problems. [ABSTRACT FROM AUTHOR]

A recent report from the Michigan Psychoanalytics Institute challenges the negative perception of teleanalysis as an inferior and less effective form of therapy. The researchers argue that these views limit the therapeutic potential of teleanalysis and propose that analysts should instead consider them as symbolic expressions of anxieties. By doing so, analysts can improve their understanding and engagement in teleanalysis, leading to more effective treatment. The research has important implications for both current and future analysts. [Extracted from the article]

Abstract: Karamata’s theorem is well known, which examines the integral properties of regular variation functions. In this paper, we obtain the second-order version of Karamata’s theorem, and give its one application in characterizing the second-order regular variation property of a survival function in terms of conditional moments. [Copyright &y& Elsevier]

Abstract: This paper develops the Somigliana type boundary integral equations for fracture of anisotropic thermoelastic solids using the Stroh formalism and the theory of analytic functions. In the absence of body forces and internal heat sources, obtained integral equations contain only curvilinear integrals over the solid’s boundary and crack faces. Thus, the volume integration is eliminated and also there is no need to evaluate integrals over the contours in the mapped temperature domain as it was done before. In addition to finite solids, the case of an infinite anisotropic medium with a remote thermal load is also studied. The dual boundary element method for fracture of anisotropic thermoelastic solids is developed based on the obtained boundary integral equations. Presented numerical examples show the validity and efficiency of the obtained equations in the analysis of both finite and infinite solids with cracks. [Copyright &y& Elsevier]

Abstract: The problem of numerical analytic continuation of an analytic function with complex variable, in general, is ill-posed and frequently encountered in many practical applications. However, there are few results for this problem until now. In the present paper, this problem with a single complex variable is considered on bounded domains. A very simple meshless algorithm based on the method of fundamental solution (MFS) combining with numerical differentiation is established. Some numerical examples verify the feasibility and effectiveness of this method. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the analytical and numerical stability of nonlinear neutral delay integro-differential equations (NDIDEs). First, sufficient conditions for the analytical stability of nonlinear NDIDEs with a variable delay are derived. Then, we show that any A-stable linear multistep method can preserve the asymptotic stability of the analytical solution for nonlinear NDIDEs with a constant delay. At last, we validate our conclusions by numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the integral operator of analytic functions. The order of convexity of this integral operator when is determined. Furthermore, we derive sufficient conditions for this operator to be analytic and univalent in the open unit disc. [Copyright &y& Elsevier]

Abstract: In this paper, we use the first integral method for analytic treatment of the modified Benjamin–Bona–Mahony equation. Some exact new solutions are formally derived. [Copyright &y& Elsevier]

Abstract: When constructing a Bayesian network classifier from data, the more or less redundant features included in a dataset may bias the classifier and as a consequence may result in a relatively poor classification accuracy. In this paper, we study the problem of selecting appropriate subsets of features for such classifiers. To this end, we propose a new definition of the concept of redundancy in noisy data. For comparing alternative classifiers, we use the Minimum Description Length for Feature Selection (MDL-FS) function that we introduced before. Our function differs from the well-known MDL function in that it captures a classifier’s conditional log-likelihood. We show that the MDL-FS function serves to identify redundancy at different levels and is able to eliminate redundant features from different types of classifier. We support our theoretical findings by comparing the feature-selection behaviours of the various functions in a practical setting. Our results indicate that the MDL-FS function is more suited to the task of feature selection than MDL as it often yields classifiers of equal or better performance with significantly fewer attributes. [Copyright &y& Elsevier]

Abstract: In this paper, we give an analytic solution for the one-loop soliton solution of the Vakhnenko equation, by the use of the homotopy analysis method and via a fractional basis. [Copyright &y& Elsevier]

Abstract: In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of ortho-symplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the special block structure of a Hamiltonian and skew-symmetric matrix to gain a cheaper computation of the functions. First, we will consider an approach based on the numerical solution of structured linear systems and then another one based on the Schur decomposition of the matrix. Splitting techniques are also considered in order to reduce the computational cost. Several numerical tests and comparison examples are shown. [Copyright &y& Elsevier]

Abstract: Two traditional assumptions in shock models are that the failure of a system is related either to the cumulative effect of a large number of shocks or to the maximum magnitude of shocks ever occur. The present paper provide another type (only concentrating on inter-arrivals) of shock model (called -shock model). For the case with underlying homogeneous Poisson process, some results are given, such as, analytic survival function, moment of any order, class properties and asymptotic behavior of the normalized lifetime of a system as . For another case with underlying non-homogeneous Poisson process with periodic intensity , analytic survival function is given as well. Moreover, under practical conditions, moment of any order is proved to be finite, and asymptotic behavior of is obtained as . This shock model has diverse range of applications. [Copyright &y& Elsevier]

In this paper, we study a family of nilpotent cubic systems having an isolated singular point at the origin and we give a characterization of those that accept a certain type of analytic first integrals. For these systems, we also give a characterization of the singular point at the origin; in particular, we see that the origin is never a center. [Copyright &y& Elsevier]

Studies a model validation problem pertaining to linear fractional uncertainty models. Use of simultaneously time- and frequency-domain data; Reduction of the problem to two independent convex feasibility tests; Analytic function interpolation; Convex optimization; Linear matrix inequality.

Analyzes the error coefficients applicable in the integration of periodic analytic functions using the trapezoidal rule. Theoretical and practical values of error coefficients; Roundoff and truncation errors; Davis' derivation of error coefficients.

A regression method for estimating the inverse of a continuous cumulative probability function F(x) is presented. It is assumed that an ordered sample, X1,…, Xn, of identically and independently distributed random variables is available. A reference distribution F0(x) with known inverse F0-1(p) is used to calculate the quantities Wi, = i ln[F0(Xi(Xi)/F0(Xi+10]. These quantities are used to estimate the function γ[p] = pd ln≥F0[F-1( p)]≲/dp from which an estimate of F-1(p) is derived. The method produces an estimate in a form that is convenient for random variate generation. The procedure is illustrated using data from a study of oil and gas lease bidding. [ABSTRACT FROM AUTHOR]

The problem of linear input-output (i/o) equivalence of meromorphic nonlinear control systems, described by implicit higher order difference equations, is studied. It is proved that any system is linearly i/o equivalent to a row-reduced form. The constructive algorithm is given for finding the required transformation. The latter amounts to 1) multiply the set of i/o equations \varphi=0 from left by a unimodular matrix A(\delta), whose entries are non-commutative polynomials in the forward-shift operator \delta, and 2) define certain multiplicative subset of the difference ring of analytic functions which introduces some inequations that should be satisfied. [ABSTRACT FROM AUTHOR]

We present conditions which are necessary and sufficient for a transfer function (or transfer function matrix) to be strictly positive real. A counter-example is given to illustrate that the conditions presented here differ from those previously presented in the literature. The proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state-space realizations. Also, the results are not restricted to rational transfer functions with real coefficients. [ABSTRACT FROM AUTHOR]

When uncertainty is given in parametric form, the QFT templates computation requires time if the number of parameters is high. The latest methods do not solve the problem efficiently. The present note shows a new way to calculate templates by means of analytic functions. The discrete template is replaced by an analytic template, so operations are done with functions, not with points. In such a way, the computation time is reduced and the results can be used to solve other problems such as bounds computation. [ABSTRACT FROM AUTHOR]