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Submissions from 2018

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The Method of Particular Solutions for Solving Nonlinear Poisson Problems, Fangfang Dou, Yanshan Liu, and Ching-Shyang Chen

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An Extension of the Method of Brackets: Part 1, Ivan Gonzalez, Karen T. Kohl, Lin Jiu, and Victor H. Moll

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Improved Kansa RBF Method for the Solution of Nonlinear Boundary Value Problems, Malgorzata A. Jankowska, Andreas Karageorghis, and Ching-Shyang Chen

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A Maximum Entropy Method for Solving the Boundary Value Problem of Second Order Ordinary Differential Equations, Congming Jin and Jiu Ding

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Particular Solutions of Products of Helmholtz-Type Equations Using the Matern Function, Xiao-Yan Liu, Ching-Shyang Chen, Wen Li, and Ming Li

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Diagonalization of 1-D Differential Operators With Piecewise Constant Coefficients Using the Uncertainty Principle, Sarah D. Long, Somayyeh Sheikholeslami, James V. Lambers, and Carley Walker

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A Continuum of Periodic Solutions to the Planar Four-Body Problem With Two Pairs of Equal Masses, Tiancheng Ouyang and Zhifu Xie

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Modeling of First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami and James V. Lambers

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The Method of Particular Solutions Using Trigonometric Basis Functions, Zhaolu Tian, Xinxiang Li, C.M. Fan, and Ching-Shyang Chen

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Nodal Superconvergence of the Local Discontinuous Galerkin Method for Singularly Perturbed Problems, Huiqing Zhu and Fatih Celiker

Submissions from 2017

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Corrigendum to "The F5 Criterion Revised", Alberto Arri and John Perry

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Integrals of Frullani Type and the Method of Brackets, Sergio Bravo, Ivan Gonzalez, Karen T. Kohl, and Victor H. Moll

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Polynomial Particular Solutions for Solving Elliptic Partial Differential Equations, Thir R. Dangal, Ching-Shyang Chen, and Ji Lin

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Generalizing a Caccioppoli-Type Inequality, Jiu Ding, Vilmos Komornik, and Bernd S.W. Schröder

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From Integrals to Multi-Sum Identities, Karen T. Kohl

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Method of Particular Solutions Using Polynomial Basis Functions for the Simulation of Plate Bending Vibration Problems, Ji Lin, Ching-Shyang Chen, Fajie Wang, and Thir Dangal

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The MFS Versus the Trefftz Method for the Laplace Equation In 3D, Hui Lv, Fang Hao, Yong Wang, and Ching-Shyang Chen

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The MFS and MAFS for Solving Laplace and Biharmonic Equations, Xiangnan Pei, Ching-Shyang Chen, and Fangfang Dou

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The Fixed Point Property for Ordered Sets of Interval Dimension 2, Bernd S.W. Schröder

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Analysis of the Method of Fundamental Solutions for the Modified Helmholtz Equation, Zhaolu Tian, Zi-Cai Li, Hung-Tsai Huang, and Ching-Shyang Chen

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A Modified Method of Approximate Particular Solutions for Solving Linear and Nonlinear PDEs, Guangming Yao, Ching-Shyang Chen, and Hui Zheng

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Solving the Yang-Baxter-Like Matrix Equation for Rank-Two Matrices, Duanmei Zhou, Guoliang Chen, and Jiu Ding

Submissions from 2016

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Solution of Nonlinear Time-Dependent PDEs Through Componentwise Approximation of Matrix Functions, Alexandru Cibotarica, James V. Lambers, and Elisabeth M. Palchak

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Solving Fredholm Integral Equations via a Piecewise Linear Maximum Entropy Method, Congming Jin and Jiu Ding

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Error Analysis of an HDG Method for a Distributed Optimal, Huiqing Zhu and Fatih Celiker

Submissions from 2015

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Solution of Time-Dependent PDE Through Rapid Estimation of Block Gaussian Quadrature Nodes, Elisabeth M. Palchak, Alexandru Cibotarica, and James V. Lambers

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A Piecewise Quadratic Maximum Entropy Method for the Statistical Study of Chaos, Tulsi Upadhyay, Jiu Ding, and Noah H. Rhee

Submissions from 2014

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Reducing the Size and Number of Linear Programs in a Dynamic Gröbner Basis Algorithm, Massimo Caboara and John Edward Perry III

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Localized Method of Approximate Particular Solutions with Cole-Hopf Transformation for Multi-Dimensional Burgers Equations, C. Y. Lin, M. H. Gu, D. L. Young, and C. S. Chen

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Genome-Wide Gene Expression Profiles in Lung Tissues of Pig Breeds Differing in Resistance to Porcine Reproductive and Respiratory Syndrome Virus, Jinyi Xing, Feng Xing, Chenhua Zhang, Yujie Zhang, Nan Wang, Yanping Li, Lijuan Yang, and Chenglan Jiang

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Local Method of Approximate Particular Solutions for Two-Dimensional Unsteady Burgers' Equations, Xueying Zhang, Haiyan Tian, and Wen Chen

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The Method of Approximate Particular Solutions for Solving Anisotropic Elliptic Problems, Huiqing Zhu

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Uniform Convergence of the LDG Method for a Singularly Perturbed Problem with the Exponential Boundary Layer, Huiqing Zhu and Zhimin Zhang

Submissions from 2013

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On the Convergence of the MFS-MPS Scheme for 1D Poisson's Equation, C. S. Chen, C. S. Huang, and K. H. Lin

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Spectral Solutions of the Yang-Baxter Matrix Equation, Jiu Ding and N.H. Rhee

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Further Solutions of a Yang-Baxter-like Matrix Equation, Jiu Ding, Chenhua Zhang, and Noah H. Rhee

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Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona-Malik Type with Applications to Satellite Image Enhancement, Patrick Guidotti, Yunho Kim, and James Lambers

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A Numerical Method for 1D Time-Dependent Schrodinger Equation Using Radial Basis Functions, Tongsong Jiang, Zhaolin Jiang, and Joseph Kolibal

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Fast Multipole Accelerated Boundary Knot Method for Inhomogeneous Helmholtz Problems, Xinrong Jiang, Wen Chen, and C. S. Chen

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Domain Type Kernel-Based Meshless Methods for Solving Wave Equations, L. H. Kuo, M. H. Gu, D. L. Young, and C. Y. Lin

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The MFS for the Solution of Harmonic Boundary Value Problems with Non-Harmonic Boundary Conditions, Ming Li, C. S. Chen, and A. Karageorghis

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The Localized RBFs Collocation Methods for Solving High Dimensional PDEs, Ming Li, Wen Chen, and C. S. Chen

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Fast Boundary Knot Method for Solving Axisymmetric Helmholtz Problems with High Wave Number, Jun Lin, Wen Chen, Ching-Shyang Chen, and Xinrong Jiang

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A Discontinuous Galerkin Least-Squares Finite Element Method for Solving Fisher's Equation, Runchang Lin and Huiqing Zhu

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Laughing at the Looking Glass: Does Humor Style Serve as an Interpersonal Signal?, Virgil Zeigler-Hill, Avi Besser, and Stephanie E. Jett

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A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows, Xueying Zhang, Haiyan Tian, Lei-Hsin Kuo, and Wen Chen

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L-infinity Estimation of the LDG Method for 1-D Singularly Perturbed Convection-Diffusion Problems, Huiqing Zhu and Runchang Lin

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Convergence Analysis of the LDG Method Applied to Singularly Perturbed Problems, Huiqing Zhu and Zhimin Zhang

Submissions from 2012

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Nodal Superconvergence of SDFEM for Singularly Perturbed Problems, Fatih Celiker, Zhimin Zhang, and Huiqing Zhu

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The Method of Approximate Particular Solutions For Solving Certain Partial Differential Equations, Ching-Shyang Chen, Chia-Ming Fan, and Pihua Wen

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A Piecewise Constant Method for Frobenius-Perron Operators via Delta Function Approximations, Suanrong Chen and Jiu Ding

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A Generalization of a Classic Theorem in the Perturbation Theory for Linear Operators, Jiu Ding and L.J. Huang

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On the Norm Convergence of a Piecewise Linear Least Squares Method for Frobenius-Perron Operators, Jiu Ding and Noah H. Rhee

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On the Independent Domination Number of Regular Graphs, Wayne Goddard, Michael A. Henning, Jeremy Lyle, and Justin Southey

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Independent Dominating Sets In Triangle-Free Graphs, Wayne Goddard and Jeremy Lyle

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The Method of Particular Solutions for Solving Inverse Problems of a Nonhomogeneous Convection-Diffusion Equation With Variable Coefficients, Tongsong Jiang, Ming Li, and Ching-Shyang Chen

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Parallel Computational Models For Composites Reinforced by CNT-fibres, Vladimír Kompiš, Quin-Hua Qin, Zhuo-Jia Fu, Ching-Shyang Chen, Peter Droppa, Miroslav Kelemen, and Wen Chen

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Explicit High-Order Time Stepping Based on Componentwise Application of Asymptotic Block Lanczos Iteration, James V. Lambers

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A Regularization Method for the Approximate Particular Solution of Nonhomogeneous Cauchy Problems of Elliptic Partial Differential Equations with Variable Coefficients, Ming Li, Wen Chen, and C. H. Tsai

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Asymptotic Properties of the Tail Distribution and Hill's Estimator for Shot Noise Sequence, Chenhua Zhang and William P. McCormick

Submissions from 2011

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The F5 Criterion Revised, Alberto Arri and John E. Perry

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The Method of Approximate Particular Solutions for Solving Elliptic Problems with Variable Coefficients, Ching-Shyang Chen, Chia-Ming Fan, and Pihua Wen

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A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings, Jiu Ding, Congming Jin, Noah H. Rhee, and Aihui Zhou

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A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators, Jiu Ding and Noah H. Rhee

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On the Equality of Algebraic and Geometric Multiplicities of Matrix Eigenvalues, Jiu Ding and Noah H. Rhee

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Dense Graphs with Small Clique Number, Wayne Goddard and Jeremy Lyle

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Engineering Presentation of the Stochastic Interpolation Framework and Its Applications, Daniel Howard, Adrian Brezulianu, and Joseph Kolibal

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Genetic Programming of the Stochastic Interpolation Framework: Convection-Diffusion Equation, Daniel Howard, Adrian Brezulianu, and Joseph Kolibal

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A Meshless Method for Solving Nonhomogeneous Cauchy Problems, Ming Li, Ching-Shyang Chen, and Benny Y.C. Hon

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A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform, Antonio Tadeu, Ching-Shyang Chen, J. António, and Nuno Simões

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Numerical Solution of Three-Dimensional Backward Heat Conduction Problems By the Time Evolution Method of Fundamental Solutions, C.H. Tsai, Der-Liang Young, and Joseph Kolibal

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A Localized Approach for the Method of Approximate Particular Solutions, Guangming Yao, Joseph Kolibal, and Ching-Shyang Chen

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A Comparison of Three Explicit Local Meshless Methods Using Radial Basis Functions, Guangming Yao, Bozidar Šarler, and Ching-Shyang Chen

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Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems, Huiqing Zhu, Haiyan Y. Tian, and Zhimin Zhang

Submissions from 2010

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Adaptive Method of Particular Solution for Solving 3D Inhomogeneous Elliptic Equations, Ching-Shyang Chen, T.O. Kwok, and L. Ling

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Piecewise Linear Least Squares Approximations of Frobenius-Perron Operators, Jiu Ding and Noah H. Rhee

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Non-Convexity of the Dimension Function for Sierpinski Pedal Triangles, Jiu Ding and Yifa Tang

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F5C: A Variant of Faugere's F5 Algorithm With Reduced Gröbner Bases, Christian Eder and John E. Perry

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An Analysis of Backward Heat Conduction Problems Using the Time Evolution Method of Fundamental Solutions, Joseph Kolibal, C.H. Tsai, and D.L. Young

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Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients, Ming Li, Ching-Shyang Chen, and C. H. Tsai

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EPDM/tBS Suspension Copolymer for Oil Sorbency Application, Y.P. Liu, B. Wu, M.H. Zhou, and Jiu Ding

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An Extension of Buchberger's Criteria for Gröbner Basis Decision, John Edward Perry III

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The Golden Section Search Algorithm for Finding a Good Shape Parameter for Meshless Collocation Methods, C. H. Tsai, Joseph Kolibal, and Ming Li

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The Method of Particular Solutions For Solving Scalar Wave Equations, Pihua Wen and Ching-Shyang Chen

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The Comparison of Three Meshless Methods Using Radial Basis Functions for Solving Fourth-Order Partial Differential Equations, Guangming Yao, C. H. Tsai, and Wen Chen

Submissions from 2009

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Integral and Non-Negativity Preserving Bernstein-Type Polynomial Approximations, Jiu Ding, Joseph Kolibal, and Noah H. Rhee

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On the Dimension of Sierpinski Pedal Triangles, Jiu Ding and Zhao Li

The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients, Chia-Ming Fan, Ching-Shyang Chen, and Jeannette Monroe

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Driven Diffusion In Solid Media: A Matrix Formalism, Jun-Ichi Inoguchi and Joseph Kolibal

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Lightlike Surfaces in Minkowski 3-Space, Jun-Ichi Inoguchi and Sungwook Lee

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On Immunotherapies and Cancer Vaccination Protocols: A Mathematical Modelling Approach, Badal Joshi, Xueying Wang, Sayanti Banerjee, Haiyan Y. Tian, Anastasios Matzavinos, and Mark A.J. Chaplain

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Matrix Decomposition RBF Algorithm for Solving 3D Elliptic Problems, Andreas Karageorghis, Ching-Shyang Chen, and Yiorgos-Sokratis Smyrlis

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The Binding Number of a Graph and Its Cliques, Jeremy Lyle and Wayne Goddard

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The Method of Particular Solutions for Solving Axisymmetric Polyharmonic and Poly-Helmholtz Equations, Chia-Cheng Tsai, Ching-Shyang Chen, and Tai-Wen Hsu

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Particular Solutions of Splines and Monomials for Polyharmonic and Products of Helmholtz Operators, Chia-Cheng Tsai, A.H.-D. Cheng, and Ching-Shyang Chen

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A Revisit on the Derivation of the Particular Solution for the Differential Operator Delta(2) +/- lambda(2), Guangming Yao, Ching-Shyang Chen, and Chia-Cheng Tsai

Submissions from 2008

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Symmetric Groups and Conjugacy Classes, Edith Adan-Bante and Helena Verrill

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A Quasi-Isometry Invariant Loop Shortening Property for Groups, Stephen G. Brick, Jon M. Corson, and Dohyoung Ryang

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Sierpinski Pedal Triangles, Jiu Ding, Richard Hitt, and Xin-Min Zhang

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A Spectrum Theorem for Perturbed Bounded Linear Operators, Jiu Ding and Aihui Zhou