Castro-Martin, LuisRueda, Mara del MarFerri-Garcia, Ramon
8页
查看更多>>摘要：The convenience of online surveys has quickly increased their popularity for data collection. However, this method is often non-probabilistic as they usually rely on selfselection procedures and internet coverage. These problems produce biased samples. In order to mitigate this bias, some methods like Statistical Matching and Propensity Score Adjustment (PSA) have been proposed. Both of them use a probabilistic reference sample with some covariates in common with the convenience sample. Statistical Matching trains a machine learning model with the convenience sample which is then used to predict the target variable for the reference sample. These predicted values can be used to estimate population values. In PSA, both samples are used to train a model which estimates the propensity to participate in the convenience sample. Weights for the convenience sample are then calculated with those propensities. In this study, we propose methods to combine both techniques. The performance of each proposed method is tested by drawing nonprobability and probability samples from real datasets and using them to estimate population parameters. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we consider a parabolic partial differential equation with fractional diffusion that generalizes the well-known Fisher's and Hodgkin-Huxley equations. The spatial fractional derivatives are understood in the sense of Riesz, and initial-boundary conditions on a closed and bounded interval are considered here. The mathematical model is presented in an equivalent form, and a finite-difference discretization based on fractional-order centered differences is proposed. The scheme is the first explicit logarithmic model proposed in the literature to solve fractional diffusion-reaction equations. We establish rigorously the capability of the technique to preserve the positivity and the boundedness of the methodology. Moreover, we propose conditions under which the monotonicity of the numerical model is also preserved. The consistency, the stability and the convergence of the scheme are also proved mathematically, and some a priori bounds for the numerical solutions are proposed. We provide some numerical simulations in order to confirm that the method is capable of preserving the positivity and the boundedness of the approximations, and a numerical study of the convergence of the technique is carried out confirming, thus, the analytical results. (c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：Fractal interpolation functions (FIFs) supplement and subsume all classical interpolants. The major advantage by the use of fractal functions is that they can capture either the irregularity or the smoothness associated with a function. This work proposes the use of cubic spline FIFs through moments for the solutions of a two-point boundary value problem (BVP) involving a complicated non-smooth function in the non-homogeneous second order differential equation. In particular, we have taken a second order linear BVP: y'(x) + Q(x)y'(x) + P(x)y(x) = R(x) with the Dirichlet's boundary conditions, where P(x) and Q(x) are smooth, but R(x) may be a continuous nowhere differentiable function. Using the discretized version of the differential equation, the moments are computed through a tridiagonal system obtained from the continuity conditions at the internal grids and endpoint conditions by the derivative function. These moments are then used to construct the cubic fractal spline solution of the BVP, where the non-smooth nature of y' can be captured by fractal methodology. When the scaling factors associated with the fractal spline are taken as zero, the fractal solution reduces to the classical cubic spline solution of the BVP. We prove that the proposed method is convergent based on its truncation error analysis at grid points. Numerical examples are given to support the advantage of the fractal methodology. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper focuses on the numerical solutions of nonlinear delay-differential-algebraic equations with proportional delay, which are transformed into nonlinear delaydifferential-algebraic equation with constant delay through exponential transformation. Block boundary value methods are extended to solve this type of equation, and their unique solvability, convergence, and stability are rigorously proved, respectively. The computational effectiveness of the methods and correctness of the theoretical result are illustrated through numerical examples. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Positone and semipositone boundary value problems are semilinear elliptic partial differ-ential equations (PDEs) that arise in reaction-diffusion models in mathematical biology and the theory of nonlinear heat generation. Under certain conditions, the problems may have multiple positive solutions or even nonexistence of a positive solution. We develop analytic techniques for proving admissibility, stability, and convergence results for simple finite difference approximations of positive solutions to sublinear problems. We also develop guaranteed solvers that can detect nonuniqueness for positone problems and nonexistence for semipositone problems. The admissibility and stability results are based on adapting the method of sub-and supersolutions typically used to analyze the underlying PDEs. The new convergence analysis technique directly shows that all pointwise limits of finite difference approximations are solutions to the boundary value problem eliminating the possibility of false algebraic solutions plaguing the convergence of the methods. Most known approximation methods for positone and semipositone boundary value problems rely upon shooting techniques; hence, they are restricted to one-dimensional problems and/or radial solutions. The results in this paper will serve as a foundation for approximating positone and semipositone boundary value problems in higher dimensions and on more general domains using simple approximation methods. Numerical tests for known applied problems with multiple positive solutions are pro-vided. The tests focus on approximating certain positive solutions as well as generating discrete bifurcation curves that support the known existence and uniqueness results for the PDE problem. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we use Newton-type iterative schemes to obtain a domain of existence of solution, approximate the solution of Chandrasekhar H-equations and deal with the case of nonlinear integral equations with non-separable kernels. A change of variable in the Chandrasekhar H-equation allows us to apply a previous study by describing nonlinear integral equations of Hammerstein-type with non-separable kernel. We use the Bernstein polynomials for approximating the non-separable kernel and then we apply a semilocal converge study done previously to the Chandrasekhar H-equation. Moreover, we apply Newton-type iterative schemes for some specific Chandrasekhar H-equations to approximate the H-function solution and compare our results with others obtained previously. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary nonuniform mesh. The scheme comprises of an implicit difference operator for the derivative term and an appropriate quadrature rule for the integral term. We establish both a priori and a posteriori error estimates for the scheme that hold true uniformly in the small perturbation parameter. Numerical experiments are performed and results are reported for validation of the theoretical error estimates. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We propose an efficient iterative scheme to solve numerically a quadratic matrix equation related to the noisy Wiener-Hopf problems for Markov chains. We improve the efficiency and the accuracy of the well-known Newton's method, frequently used in the literature. We provide a semilocal convergence result for this iterative scheme, where we establish domains of existence and uniqueness of solution. Finally, we apply this efficient method to approximate the solution of a particular noisy Wiener-Hopf problem and we compare it with Newton's method. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is called attribute reduction. Recently, the attribute reduction mechanism has been complemented with the use of local congruences in order to obtain robust clusters of concepts, which form convex sublattices of the original concept lattice. Since the application of such local congruences modifies the quotient set associated with the attribute reduction, it is fundamental to know how the original context (attributes, objects and relationship) has been modified in order to understand the impact of the application of the local congruence in the attribute reduction. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Arana-Jimenez, ManuelSnchez-Gil, M. CarmenLozano, Sebastian
12页
查看更多>>摘要：This paper deals with the problem of efficiency assessment using Data Envelopment Analysis (DEA) when the input and output data are given as fuzzy sets. In particular, a fuzzy extension of the measure of inefficiency proportions, a well-known slacks-based additive inefficiency measure, is considered. The proposed approach also provides fuzzy input and output targets. Computational experiences and comparison with other fuzzy DEA approaches are reported. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
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