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It is well known that M-estimation is a widely used method for robust statistical inference and the varying coefficient models have been widely applied in many scientific areas. In this paper, we consider M-estimation and model identification of bivariate varying coefficient models for longitudinal data. We make use of bivariate tensor-product B-splines as an approximation of the function and consider M-type regression splines by minimizing the objective convex function. Mean and median regressions are included in this class. Moreover, with a double smoothly clipped absolute deviation (SCAD) penalization, we study the problem of simultaneous structure identification and estimation. Under approximate conditions, we show that the proposed procedure possesses the oracle property in the sense that it is as efficient as the estimator when the true model is known prior to statistical analysis. Simulation studies are carried out to demonstrate the methodological power of the proposed methods with finite samples. The proposed methodology is illustrated with an analysis of a real data example. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. [ABSTRACT FROM AUTHOR]

In this paper we apply empirical likelihood method to the error density estimators in first-order autoregressive models under some mild conditions. The log-likelihood ratio statistic is shown to be asymptotically chi-squared distributed at a fixed point. In simulation, we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy which is better than normal approximation. [ABSTRACT FROM AUTHOR]

This paper focuses on the variable selections for a varying coefficient models with missing response at random. A procedure is presented by basis function approximations with smooth-threshold estimating equations. Furthermore, the proposed method selects significant variables and estimates coefficients simultaneously avoiding the problem of solving a convex optimization, which reduced the burden of computation. Compared to existing equation based approaches, our procedure is more efficient and quick. With proper choices the regularization parameter, the resulting estimates perform an oracle property. A cross-validation for tuning parameter selection is also proposed, a numerical study confirms the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The comonotonicity and countermonotonicity provide intuitive upper and lower dependence relationship between random variables. This paper constructs the shuffle of min’s random variable approximations for a given Uniform [0, 1] random vector. We find the two optimal orders under which the shuffle of min’s random variable approximations obtained are shown to be extensions of comonotonicity and countermonotonicity. We also provide the rate of convergence of these random vectors approximations and apply them to compute value-at-risk. [ABSTRACT FROM AUTHOR]

In this paper, trigonometrically fitted multi-step hybrid (TFMSH) methods for the numerical integration of oscillatory special second-order initial value problems are proposed and studied. TFMSH methods inherit the frame of multi-step hybrid (MSH) methods and integrate exactly the differential system whose solutions can be expressed as the linear combinations of functions from the set or equivalently the set , where w represents an approximation of the main frequency of the problem. The corresponding order conditions are given and two explicit TFMSH methods with order six and seven, respectively, are constructed. Stability of the new methods is examined and the corresponding regions of stability are depicted. Numerical results show that our new methods are more efficient in comparison with other well-known high quality methods proposed in the scientific literature. [ABSTRACT FROM AUTHOR]

In this paper, Legendre wavelet collocation method is applied for numerical solutions of the fractional-order differential equations subject to multi-point boundary conditions. The explicit formula of fractional integral of a single Legendre wavelet is derived from the definition by means of the shifted Legendre polynomial. The proposed method is very convenient for solving fractional-order multi-point boundary conditions, since the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces equations to those of solving a system of algebraic equations which greatly simplifies the problem. Several numerical examples are solved to demonstrate the validity and applicability of the presented method. [ABSTRACT FROM AUTHOR]

In this contribution, a new framework for -optimal reduction is presented, motivated by the local nature of both (tangential) interpolation and -optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup in -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing -optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatory reduction. [ABSTRACT FROM AUTHOR]

Unlike traditional Type I and II censoring, progressive censoring allows for removal of surviving units throughout the life test. This feature has several benefits and in the literature, much work has been done on inference based on progressively censored samples and identifying optimal progressive censoring schemes. In this paper, we introduce restricted progressive censoring and within this class, the problem of identifying optimal schemes under different minimum variance criteria. We explore these plans geometrically as well as provide some useful properties. In particular, we look at the vertices of the set of admissible plans and their role in approximating optimal plans. We also provide computational results for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper presents efficient alternative numerical methods for an implicit solution of the harmonic balance equation system for analysing temporal periodic unsteady flows. The proposed method employs approximate factorisation to decouple the common residual term and the time spectral source term of a harmonic balance equation system when it is discretised implicitly. With this approximate factorisation, the complexity of implicit solution of the discrete system is greatly reduced. The common residual term can be dealt with using a lower-upper symmetric-Gauss-Seidel (LU-SGS) method and the time spectral source term is integrated using a Jacobi iteration (JI) or one step Gauss-Seidel (GS) iteration, leading to the LU-SGS/JI method or LU-SGS/GS method. The NASA stage 35 compressor and the 1.5 stage Aachen turbine were used to demonstrate the effectiveness of the proposed methods in stabilising solution and its advantages in comparison with the existing lower-upper symmetric-Gauss-Seidel/block Jacobi (LU-SGS/BJ) method. The LU-SGS/GS method and the LU-SGS/JI method are more robust than the LU-SGS/BJ method in stabilising solution. The LU-SGS/GS method also has faster and tighter convergence and lower memory consumption in comparison with the LU-SGS/BJ method. [ABSTRACT FROM AUTHOR]

Model selection methods are important to identify the best approximating model. To identify the best meaningful model, purpose of the model should be clearly pre-stated. The focus of this paper is model selection when the modelling purpose is classification. We propose a new model selection approach designed for logistic regression model selection where main modelling purpose is classification. The method is based on the distance between the two clustering trees. We also question and evaluate the performances of conventional model selection methods based on information theory concepts in determining best logistic regression classifier. An extensive simulation study is used to assess the finite sample performances of the cluster tree based and the information theoretic model selection methods. Simulations are adjusted for whether the true model is in the candidate set or not. Results show that the new approach is highly promising. Finally, they are applied to a real data set to select a binary model as a means of classifying the subjects with respect to their risk of breast cancer. [ABSTRACT FROM AUTHOR]

The article is devoted to new properties of Aumann, Lebesgue, and Itô set-valued stochastic integrals considered in papers [1,2]. In particular, it contains some approximation theorems for Aumann and Itô set-valued stochastic integrals. Hence, in particular, it follows that Aumann and Lebesgue set-valued stochastic integrals cover a.s., both for measurable and IF-nonanticipative integrably bounded set-valued stochastic processes. [ABSTRACT FROM AUTHOR]

This paper provides Bayesian analysis of absolute continuous Marshall–Olkin bivariate Pareto distribution. We consider only three parameters for this Marshall–Olkin bivariate Pareto distribution. We take two types of prior—reference prior and gamma prior for our analysis. Bayesian estimate of the parameters are calculated based on slice cum Gibbs sampler and Lindley approximation. Credible intervals are also provided for all methods and all prior distributions. A real-life data analysis is shown for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper,weintroduce a partially linear single-index additive hazards model with current status data. Both the unknown link function of the single-index term and the cumulative baseline hazard function are approximated by B-splines under a monotonicity constraint on the latter. The sieve method is applied to estimate the nonparametric and parametric components simultaneously. We show that, when the nonparametric link function is an exact B-spline, the resultant estimator of regression parameter vector is asymptotically normal and achieves the semiparametric information bound and the rate of convergence of the estimator for the cumulative baseline hazard function is optimal. Simulation studies are presented to examine the finite sample performance of the proposed estimation method. For illustration, we apply the method to a clinical dataset with current status outcome. [ABSTRACT FROM AUTHOR]

In this paper an estimator of the finite population mean using auxiliary information in sample surveys has been proposed. The bias and mean squared error are obtained under large sample approximation. It has been shown that the proposed estimator performs better than some recently published estimators. [ABSTRACT FROM AUTHOR]

The paper considers split equilibrium problems (EPs) in Hilbert spaces and proposes two hybrid algorithms for finding their solution approximations. Three methods including the diagonal subgradient method, the projection method and the proximal method have been used to design the algorithms. Using the diagonal subgradient method for EPs has allowed us to reduce complex computations on bifunctions and feasible sets. The first algorithm is designed with two projections on feasible set and with the prior knowledge of operator norm while the second algorithm is simpler in computations where only one projection on feasible set needs to be implemented and the information of operator norm is not necessary to construct solution approximations. The strongly convergent theorems are established under suitable assumptions imposed on equilibrium bifunctions. The computational performance of the proposed algorithms over existing methods is also illustrated by several preliminary numerical experiments. [ABSTRACT FROM PUBLISHER]

The Space-fractional wave equations (SFWE) have been found to be very adequate in describing anomalous transport and dispersion phenomena. Due to the non-local property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model. In this paper, a meshless analysis of two-dimensional two-sided SFWE is proposed based on the improved moving least-squares (IMLS) approximation. The trial function for the SFWE is constructed by the IMLS approximation, where the resulting algebraic equation system to obtain the shape functions is no more ill conditioned and has high computational efficiency. The Riemann–Liouville operator is discretized by the Grünwald formula. The centre difference method and the strong-forms of the SFWE are used to obtain the final fully discrete algebraic equation. And the essential boundary conditions can be directly and easily imposed on as a finite element method. Due to the adoption of IMLS approximation and strong-forms, this method will be highly accurate and efficient. Numerical results demonstrate that this method is highly accurate and computationally efficient for SFWE. Moreover, the convergence and error estimate have been analysed in our study. [ABSTRACT FROM PUBLISHER]

In this paper, new perturbation bounds for linear complementarity problems are presented based on the sign patterns of the solution of the equivalent modulus equations. The new bounds are shown to be the generalization of the existing ones. [ABSTRACT FROM AUTHOR]

Dynamic optimisation problem with characteristic times, widely existing in many areas, is one of the frontiers and hotspots of dynamic optimisation researches. This paper considers a class of dynamic optimisation problems with constraints that depend on the interior points either fixed or variable, where a novel direct pseudospectral method using Legendre–Gauss (LG) collocation points for solving these problems is presented. The formula for the state at the terminal time of each subdomain is derived, which results in a linear combination of the state at the LG points in the subdomains so as to avoid the complex nonlinear integral. The sensitivities of the state at the collocation points with respect to the variable characteristic times are derived to improve the efficiency of the method. Three well-known characteristic time dynamic optimisation problems are solved and compared in detail among the reported literature methods. The research results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an admittance control scheme for a user-in-charge exoskeleton is presented. The controller basically consists of a composite adaptive controller implementing a feedback law to estimate the structured uncertainties and to modify the apparent dynamics of the robot, and an LWPR estimator which tries to give an appropriate approximation of unmodeled uncertainty along with a robust term aiming to overcome the approximation residue. The control scheme offers a unified general control structure that explains the effect of each control component on the others. It is proved that based on the developed controller, the tracking and estimation errors converge to small boundaries with ultimate boundedness property due to the presence of the unstructured uncertainty. Based on simulations of a 2-DOF leg, the effectiveness of the controller is investigated. The results show the effectiveness of employing a universal approximator alongside a robust adaptive control and the success of the recommended approach in estimating model parameters and unmodeled dynamics simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, a new type of stepsize, approximate optimal stepsize, for gradient method is introduced to interpret the Barzilai–Borwein (BB) method, and an efficient gradient method with an approximate optimal stepsize for the strictly convex quadratic minimization problem is presented. Based on a multi-step quasi-Newton condition, we construct a new quadratic approximation model to generate an approximate optimal stepsize. We then use the two well-known BB stepsizes to truncate it for improving numerical effects and treat the resulted approximate optimal stepsize as the new stepsize for gradient method. We establish the global convergence andR-linear convergence of the proposed method. Numerical results show that the proposed method outperforms some well-known gradient methods. [ABSTRACT FROM PUBLISHER]

We introduce a new class of Monte Carlo-based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically introduce a bias. In this paper, we show how to remove that bias, by introducing a new version of multi-index Monte Carlo (MIMC) that has the added advantage of reducing the computational effort, relative to i.i.d. sampling from the most precise discretization, for a given level of error. We cover extensions of results regarding variance and optimality criteria for the new approach. We apply the methodology to the problem of computing an unbiased mollified version of the solution of a partial differential equation with random coefficients. A second application concerns the Bayesian inference (the smoothing problem) of an infinite-dimensional signal modeled by the solution of a stochastic partial differential equation that is observed on a discrete space grid and at discrete times. Both applications are complemented by numerical simulations. [ABSTRACT FROM PUBLISHER]

In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result. [ABSTRACT FROM PUBLISHER]

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPFbased control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method. [ABSTRACT FROM AUTHOR]

The problem of density estimation arises naturally in many contexts. In this paper, we consider the approach using a piecewise constant function to approximate the underlying density. We present a new density estimation method via the random forest method based on the Bayesian Sequential Partition (BSP) (Lu, Jiang, and Wong 2013). Extensive simulations are carried out with comparison to the kernel density estimation method, BSP method, and four local kernel density estimation methods. The experiment results show that the new method is capable of providing accurate and reliable density estimation, even at the boundary, especially for i.i.d. data. In addition, the likelihood of the out-of-bag density estimation, which is a byproduct of the training process, is an effective hyperparameter selection criterion. [ABSTRACT FROM AUTHOR]

In 2013, Döbler used Stein’s method to obtain the uniform bounds in half-normal approximation for three statistics of a symmetric simple random walk; the maximum value, the number of returns to the origin and the number of sign changes up to a given timen. In this paper, we give the non-uniform bounds for these statistics by using Stein’s method and the concentration inequality approach. [ABSTRACT FROM AUTHOR]

The rough sets based onL-fuzzy relations andL-fuzzy coverings are the two most well-knownL-fuzzy rough sets. Quite recently, we prove that some of these rough sets can be unified into one framework—rough sets based onL-generalized fuzzy neighborhood systems. So, the study on the rough sets based onL-generalized fuzzy neighborhood system has more general significance. Axiomatic characterization is the foundation ofL-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence ofL-fuzzy relations,L-fuzzy coverings that reproduce the approximation operators. In this paper, we shall give an axiomatic study onL-generalized fuzzy neighborhood system-based approximation operators. In particular, we will seek the axiomatic sets to characterize the approximation operators generated by serial, reflexive, unary and transitiveL-generalized fuzzy neighborhood systems, respectively. [ABSTRACT FROM PUBLISHER]

Let r2(n) denote the number of representations of the positive integer n as a sum of two squares, and let d(n) denote the number of positive divisors of n. Gauss and Dirichlet were evidently the first mathematicians to derive asymptotic formulas for ***n≤x r2(n) and ***n≤x d(n), respectively, as x tends to infinity. But what is the error made in such approximations? Number theorists have been attempting to answer these two questions for over one and one-half centuries, and although we think that we essentially "know" what these errors are, progress in proving these conjectures has been agonizingly slow. Ramanujan had a keen interest in these problems, and although, to the best of our knowledge, he did not establish any bounds for the error terms, he did give us identities that have been used to derive bounds, and two further identities that might be useful, if we can figure out how to use them. In this paper, we survey what is known about these two famous unsolved problems, with a moderate emphasis on Ramanujan's contributions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of the stability of upper semi-Browder, lower semi-Browder and Browder linear relations which satisfy the stabilization property, under commuting Riesz operator perturbations. As applications, we infer the invariance of the corresponding Browder’s essential approximate point spectrum, Browder’s essential defect spectrum and Browder’s essential spectrum under commuting Riesz operator perturbations. [ABSTRACT FROM PUBLISHER]

In topic modelling, the main computational problem is to approximate the posterior distribution given an observed collection. Commonly, we must resort to variational methods for approximations; however, we do not know which variational variant is the best choice under certain settings. In this paper, we focus on four topic modelling inference methods, including mean-field variation Bayesian, collapsed variational Bayesian, hybrid variational-Gibbs and expectation propagation, and aim to systematically compare them. We analyse them from two perspectives, i.e. the approximate posterior distribution and the type of-divergence; and then empirically compare them on various data-sets by two popular metrics. The empirical results are almost matching our analysis, where they indicate that CVB0 may be the best variational variant for topic models. [ABSTRACT FROM PUBLISHER]

Phase compensation for high-order repetitive control (HORC) can improve system transient and steady-state performances. The phase compensator is often designed as the inverse transfer function of a closed-loop system. No other phase compensation methods for HORC have been reported up to now. Hence, in this paper, a simple approximate phase cancellation second-order repetitive control (RC) is proposed. The compensator is a linear combination of two different linear phase lead compensators, which can better fit the inverse of a plant model phase curve compared with the conventional linear phase compensator. Optimisation is introduced to design the parameters of the approximate phase cancellation second-order RC. Analysis and design of the second-order repetitive controlled pulse width modulation inverter system are presented. Simulations and experiments are provided to demonstrate the effectiveness of the optimisation method and verify the advantage of the approximate phase cancellation compensator. [ABSTRACT FROM AUTHOR]

In this paper, radiation characteristics of an isosceles 45°-45°-90° triangular microstrip antenna (TMA) are presented using simple extension of cavity model considering field variation in all dimensions for the first time along with physical explanation. Eigenfunctions, eigenvalues, input impedance, far-field radiation patterns, etc. are discussed. Approximate expression is given here to predict the resonant frequency with accuracy better than 1%. Theoretical results are verified with experimental data to show the accuracy of our theory. The study of 45°-45°-90° TMA is important because (1) the area occupied by the antenna is just half of that compared to a square patch antenna for a given resonant frequency, (2) mode suppression (including fundamental mode) of the antenna is quite easy compared to other conventional shaped patch antennas, (3) all modes of the antenna are dual polarized, and (4) four modes out of first five modes of the antenna produce a peak in the broadside direction. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new diagnosing technique for chronic kidney disease by using Artificial Neural Network (ANN). Where, the required data for the computational health-care system is collected from various hospitals at Jazan region, Saudi Arabia. Furthermore, in order to prove the convergence of this method, a ridge function is used in the hidden layer as a basis for the neurons. The technique applied for different number of neurons, and in each case a least square error is provided for choosing the best possible approximation. [ABSTRACT FROM AUTHOR]

In this work, we consider a nonlinear resolvent integro-differential evolution inclusions in Hilbert spaces. This paper deals with the approximate controllability for nonlinear resolvent integro-differential inclusions in Hilbert spaces. We use Bohnenblust–Karlin's fixed-point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro-differential inclusions in Hilbert spaces. Further, we extend the result to study the approximate controllability concept with non-local conditions. An example is presented to demonstrate the obtained theory. [ABSTRACT FROM AUTHOR]

Let (Xn) be a sequence of independent identically distributed random variables with. A symmetric simple random walk is a discrete-time stochastic process (Sn)n ⩾ 0defined byS0= 0 andSn= ∑ni = 1Xiforn⩾ 1.Knis called the number of returns to the origin if. Döbler (2015) showed that the distribution ofKncan be approximated by half-normal distribution and he also gave a uniform bound in terms of. After that, Sama-ae, Neammanee, and Chaidee (2016) gave a non uniform bound in terms of. Observe that, the exponent ofzis 3. In this paper, we improve the exponent ofzto be any natural numberkwhich make the better constant than before. [ABSTRACT FROM AUTHOR]

The nonconvexregularization, which has superiority on sparsity-inducing over the convex counterparts, has been proposed in many areas of engineering and science. In this paper, we present an acceleratedregularization thresholding algorithm for sparse signal recovery, which can be viewed as an extension of the well-known Nesterov's accelerated gradient method from convex optimization to nonconvex case. It has shown numerically that the proposed algorithm keeps fast convergence, and also maintains high recovery precision. Extensive numerical experiments have been to demonstrate the effectiveness of the proposed algorithm. It is also mentioned that the proposed algorithm has much faster convergence and higher recovery precision in sparse signal recovery over the commonly non-acceleratedthresholding algorithm. [ABSTRACT FROM PUBLISHER]

Let X = Lp(Ω,μ) (1

In this paper, the multiple kernel learning (MKL) is formulated as a supervised classification problem. We dealt with binary classification data and hence the data modelling problem involves the computation of two decision boundaries of which one related with that of kernel learning and the other with that of input data. In our approach, they are found with the aid of a single cost function by constructing a global reproducing kernel Hilbert space (RKHS) as the direct sum of the RKHSs corresponding to the decision boundaries of kernel learning and input data and searching that function from the global RKHS, which can be represented as the direct sum of the decision boundaries under consideration. In our experimental analysis, the proposed model had shown superior performance in comparison with that of existing two stage function approximation formulation of MKL, where the decision functions of kernel learning and input data are found separately using two different cost functions. This is due to the fact that single stage representation helps the knowledge transfer between the computation procedures for finding the decision boundaries of kernel learning and input data, which inturn boosts the generalisation capacity of the model. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of delay dependent stability andH∞performance for a class of linear systems with interval time-varying delay. A new model transformation is first proposed by employing a three-terms approximation of delayed state variables, for a better approximation of delayed state. By using scaled small gain theorem and a simple Lyapunov–Krasovskii functional, new stability andH∞performance criteria are proposed in terms of linear matrix inequalities, which can be easily solved by using standard numerical packages. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The conjugate gradient (CG) method is one of the most popular methods for solving large-scale unconstrained optimization problems. In this paper, a new modified version of the CG formula that was introduced by Polak, Ribière, and Polyak is proposed for problems that are bounded below and have a Lipschitz-continuous gradient. The new parameter provides global convergence properties when the strong Wolfe-Powell (SWP) line search or the weak Wolfe-Powell (WWP) line search is employed. A proof of a sufficient descent condition is provided for the SWP line search. Numerical comparisons between the proposed parameter and other recent CG modifications are made on a set of standard unconstrained optimization problems. The numerical results demonstrate the efficiency of the proposed CG parameter compared with the other CG parameters. [ABSTRACT FROM PUBLISHER]

By combining the advantages of quantum computing and soft computing, the paper shows that rough sets can be used with quantum logic for classification and recognition systems. We suggest the new definition of rough set theory as quantum logic theory. Rough approximations are essential elements in rough set theory, the quantum rough set model for set-valued data directly construct set approximation based on a kind of quantum similarity relation which is presented here. Theoretical analyses demonstrate that the new model for quantum rough sets has new type of decision rule with less redundancy which can be used to give accurate classification using principles of quantum superposition and non-linear quantum relations. To our knowledge, this is the first attempt aiming to define rough sets in representation of a quantum rather than logic or sets. The experiments on data-sets have demonstrated that the proposed model is more accuracy than the traditional rough sets in terms of finding optimal classifications. [ABSTRACT FROM PUBLISHER]

Several procedures have been proposed for testing the equality of error distributions in two or more nonparametric regression models. Here we deal with methods based on comparing estimators of the cumulative distribution function (CDF) of the errors in each population to an estimator of the common CDF under the null hypothesis. The null distribution of the associated test statistics has been approximated by means of a smooth bootstrap (SB) estimator. This paper proposes to approximate their null distribution through a weighted bootstrap. It is shown that it produces a consistent estimator. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared to the SB. This study reveals that, from a computational point of view, the proposed approximation is more efficient than the one provided by the SB. [ABSTRACT FROM PUBLISHER]

In this paper, a common zero of a finite family of monotone operators is approximated in Hadamard spaces. Some applications in convex minimization and fixed point theory are also presented. [ABSTRACT FROM AUTHOR]

In this paper we propose a formula to derive the value of a firm which is currently producing a certain product and faces the option to exit the market, whose demand follows a geometric Brownian motion. The problem of optimal exiting is an optimal stopping problem that can be solved using the dynamic programming principle. This is a free-boundary problem. We propose an approximation for the original model and, using the Implicit Function Theorem, we obtain the solution of the original problem. Finally we show, analytically, that the exit threshold is decreasing with the volatility as well as the drift of the geometric Brownian motion. [ABSTRACT FROM AUTHOR]

The modular estimates for the fractional integral operators and thek-plane transforms are obtained in this paper. These estimates are obtained by using the modular estimates of Hardy operators and the modular interpolation theorem. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of adaptive hierarchical control for a class of so-called uncertain output feedback systems. The proposed approach is to design an adaptive output interface dynamic by estimating the uncertainties. With the interface connected to the uncertain nonlinear system and a linear abstract system, the system could track approximately the abstraction. Finally, two examples are presented to illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, applying a novel second-order numerical approximation formula for the Riesz derivative and Crank–Nicolson technique for the temporal derivative, a numerical algorithm is constructed for the two-dimensional spatial fractional diffusion equation with convergence order, whereτ,andare the temporal and spatial step sizes, respectively. It is proved that the proposed algorithm is unconditionally stable and convergent by using the energy method. Meanwhile, by adding the high-order perturbation items for the above numerical scheme, an alternating direction implicit difference scheme is also constructed. Finally, some numerical results are presented to demonstrate the validity of theoretical analysis and show the accuracy and effectiveness of the method described herein. [ABSTRACT FROM AUTHOR]

In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problem needs to have an analytic solution. So we investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numerical methods to show the performance and good accuracy of the methods. The numerical orders of convergence show that the method has exponential rate of convergence. [ABSTRACT FROM AUTHOR]

In the present paper, the positivity of the second order of approximation of the difference operator approximates the second-order differential operator with nonlocal conditions is established. The equivalence of norms of these fractional spaces generated by this operator and Hölder spaces is proved. In applications, the stability of difference schemes for the approximate solution of the boundary value problem for elliptic differential equations is provided. [ABSTRACT FROM AUTHOR]

This paper presents a fourth order of accuracy unconditionally stable difference scheme for the approximate solution of multipoint nonlocal boundary value hyperbolic problem in a Hilbert space with a self-adjoint positive definite operator. Stability estimates for the solution of this difference scheme are established. To support the theoretical statements, some results of numerical experiments are presented using finite difference method. [ABSTRACT FROM AUTHOR]