Chang ‐ Shou Lin

Chang ‐ Shou Lin's AcademicInfluence.com Rankings

Chang ‐ Shou Lin

Mathematics

#7213

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Applied Mathematics

#310

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#335

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Measure Theory

#1952

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#2374

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Mathematics

Chang ‐ Shou Lin's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics National Taiwan University

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Chang ‐ Shou Lin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Large amplitude stationary solutions to a chemotaxis system (1988) (681)
A classification of solutions of a conformally invariant fourth order equation in Rn (1998) (471)
Topological degree for a mean field equation on Riemann surfaces (2003) (288)
Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces (2002) (266)
Estimates of the conformal scalar curvature equation via the method of moving planes (1997) (193)
Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates (2004) (184)
Elliptic functions, Green functions and the mean field equations on tori (2006) (158)
Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation (2002) (141)
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004) (140)
Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions (2005) (132)
Interpolation inequalities with weights (1986) (118)
Uniqueness of the ground state solutions of △u+f(u)=0 in Rn, n≥3 (1991) (113)
On the diffusion coefficient of a semilinear Neumann problem (1988) (107)
The local isometric embedding in R3 of two‐dimensional riemannian manifolds with gaussian curvature changing sign cleanly (1986) (97)
Mean Field Equation of Liouville Type with Singular Data: Topological Degree (2015) (93)
Estimate of the conformal scalar curvature equation via the method of moving planes. II (1998) (92)
A counterexample to the nodal domain conjecture and a related semilinear equation (1988) (92)
Classification and nondegeneracy of SU(n+1) Toda system with singular sources (2011) (91)
On the prescribed scalar curvature problem in RN, local uniqueness and periodicity (2015) (89)
Concentration phenomena of two-vortex solutions in a Chern-Simons model (2004) (87)
Mean field equations of Liouville type with singular data: Sharper estimates (2010) (85)
Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent (1995) (83)
Mean field equations, hyperelliptic curves and modular forms: I (2015) (81)
Uniqueness of Solutions to the Mean Field Equations for the Spherical Onsager Vortex (2000) (73)
The local isometric embedding in $\mathbf{R}^3$ of 2-dimensional Riemannian manifolds with nonnegative curvature (1985) (73)
Bubbling Solutions for Relativistic Abelian Chern-Simons Model on a Torus (2010) (72)
Topological degree for mean field equations on S2 (2000) (68)
Existence of Bubbling Solutions for Chern–Simons Model on a Torus (2013) (67)
Extremal Functions for a Mean Field Equation in Two Dimension (2003) (66)
Minimizers of Caffarelli–Kohn–Nirenberg Inequalities with the Singularity on the Boundary (2010) (64)
Uniqueness of least energy solutions to a semilinear elliptic equation in ℝ2 (1994) (60)
A system of elliptic equations arising in Chern-Simons field theory (2007) (59)
The Existence of Convex Body with Prescribed Curvature Measures (2009) (57)
Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities (2004) (57)
Existence of self-dual non-topological solutions in the Chern–Simons Higgs model (2011) (56)
Profile of bubbling solutions to a Liouville system (2009) (56)
Classification of blowup limits for SU(3) singular Toda systems (2013) (55)
On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in R2 (1997) (54)
Revisiting an idea of Brézis and Nirenberg (2010) (53)
Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa (2010) (51)
Prescribing Scalar Curvature on $S^N$, Part 1: Apriori Estimates (2001) (51)
Application of the method of moving planes to conformally invariant equations (2004) (50)
A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents (2011) (50)
The Christoffel-Minkowski Problem II: Weingarten Curvature Equations* (2006) (50)
Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons System with Two Higgs Particles (2010) (50)
Existence and uniqueness for mean field equations on multiply connected domains at the critical parameter (2012) (50)
An expository survey on the recent development of mean field equations (2007) (50)
Blowing up with infinite energy of conformal metrics on Sn (1999) (47)
On the asymptotic symmetry of singular solutions of the scalar curvature equations (1999) (46)
Locating the peaks of solutions via the maximum principle: I. The Neumann problem (2001) (46)
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations (1999) (45)
A topological degree counting for some Liouville systems of mean field type (2011) (44)
Sign-changing Solutions and Phase Separation for an Elliptic System with Critical Exponent (2014) (44)
On the second eigenfunctions of the Laplacian in R2 (1987) (43)
Schouten tensor and some topological properties (2005) (43)
Bubbling Solutions for the SU(3) Chern‐Simons Model on a Torus (2013) (43)
Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature (2003) (41)
Estimates for boundary-bubbling solutions to an elliptic Neumann problem (2002) (41)
Local Uniqueness and Refined Spike Profiles of Ground States for Two-Dimensional Attractive Bose-Einstein Condensates (2016) (40)
On the symmetry of blowup solutions to a mean field equation (2001) (40)
Non-Abelian Multiple Vortices in Supersymmetric Field Theory (2011) (39)
The symmetry of least-energy solutions for semilinear elliptic equations (2003) (38)
Vortex Condensates for Relativistic Abelian Chern-Simons Model with Two Higgs Scalar Fields and Two Gauge Fields on a Torus (2009) (36)
A sharp sup + inf inequality for a nonlinear elliptic equation in R 2 (2016) (35)
Green function, Painlevé VI equation, and Eisenstein series of weight one (2018) (35)
A sharp sup + inf inequality for a nonlinear elliptic equation in R 2 (2016) (35)
Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa I. Stokes Data (2012) (35)
Mean field equations, hyperelliptic curves and modular forms: II (2017) (34)
Estimates of the scalar curvature equation via the method of moving planes III (2000) (34)
Conformal metrics in R 2 with prescribed Gaussian curvature with positive total curvature (1999) (34)
Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon (2011) (33)
Explicit construction of extremal Hermitian metrics with finite conical singularities on $S^2$ (2002) (33)
On the Entire Radial Solutions of the Chern–Simons SU(3) System (2013) (32)
Locating the peaks of solutions via the maximum principle II: A local version of the method of moving planes (2003) (32)
Sharp estimates for fully bubbling solutions of a SU(3) Toda system (2012) (32)
Uniqueness of solutions for a mean field equation on torus (2006) (32)
Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann–Hilbert Problem (2013) (32)
Sharp existence and uniqueness theorems for non-Abelian multiple vortex solutions (2011) (32)
Monotonicity and nonexistence results to cooperative systems in the half space (2014) (31)
On Liouville systems at critical parameters, Part 1: One bubble (2013) (31)
On Liouville theorem and apriori estimates for the scalar curvature equations (1998) (29)
On Non-Topological Solutions of the A2 and B2 Chern-Simons System (2016) (29)
MINIMIZING PROBLEMS FOR THE HARDY-SOBOLEV TYPE INEQUALITY WITH THE SINGULARITY ON THE BOUNDARY (2012) (29)
Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations (2013) (29)
On the Best Constant in the Moser-Onofri-Aubin Inequality (2009) (27)
One-dimensional symmetry of periodic minimizers for a mean field equation (2007) (26)
Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system (2012) (25)
Sharp estimates for bubbling solutions of a fourth order mean field equation (2007) (25)
On the 2-scalar curvature (2010) (25)
Removable singularity of positive solutions for a critical elliptic system with isolated singularity (2014) (24)
Chern–Simons vortices in the Gudnason model (2013) (24)
Degree counting and shadow system for $SU(3)$ Toda system: one bubbling (2014) (23)
Positive radial solutions for and related topics (1990) (23)
A sharp $\mathrm{sup} + \mathrm{inf}$ inequality for a nonlinear elliptic equation in $\mathbb{R}^2$ (1998) (22)
On rank-2 Toda systems with arbitrary singularities: local mass and new estimates (2016) (22)
Estimates of the mean field equations with integer singular sources: Non-simple blowup (2016) (22)
On the Conformal Gaussian Curvature Equation inR2 (1998) (21)
Uniqueness and solution structure of nonlinear equations arising from the Chern–Simons gauged O(3) sigma models (2013) (21)
Asymptotic symmetry and local behaviors of solutions to a class of anisotropic elliptic equations (2011) (20)
Segregated Vector Solutions for linearly coupled Nonlinear Schr\"odinger Systems (2013) (19)
Self-Dual Symmetric Nontopological Solutions in the SU(3) Model in $${\mathbb{R}^2}$$R2 (2015) (19)
Method of rotating planes applied to a singularly perturbed Neumann problem (2001) (18)
Liouville–type theorems for semilinear elliptic equations involving the Sobolev exponent (1998) (18)
Hamiltonian system for the elliptic form of Painlev\'{e} VI equation (2015) (18)
Asymptotic behavior of SU(3) Toda system in a bounded domain (2012) (18)
Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa III: Iwasawa Factorization and Asymptotics (2017) (18)
Tropical atmospheric circulations with humidity effects (2011) (18)
Degree counting and Shadow system for Toda system of rank two: One bubbling (2017) (17)
On the Minimality of Extra Critical Points of Green Functions on Flat Tori (2016) (17)
BLOW-UP BEHAVIOR FOR A PARABOLIC EQUATION WITH SPATIALLY DEPENDENT COEFFICIENT (2010) (17)
Critical points of the classical Eisenstein series of weight two (2017) (16)
Uniqueness of conformal metrics with prescribed total curvature in $R^2$ (2000) (16)
Classification of the entire radial self-dual solutions to non-Abelian Chern–Simons systems (2014) (16)
When “blow-up” does not imply “concentration”: A detour from Brézis–Merle's result (2016) (16)
Blow-up for a reaction-diffusion equation with variable coefficient (2013) (16)
On regular solutions of second order degenerate elliptic–parabolic equations (1990) (16)
Asymptotic Behavior of Least Energy Solutions for a Critical Elliptic System (2015) (16)
Recent advances in elliptic and parabolic problems (2005) (15)
On the Cauchy problem of degenerate hyperbolic equations (2005) (15)
A Topological Degree Counting for some Liouville Systems of Mean Field Equations (2010) (15)
Bubble accumulations in an elliptic Neumann problem with critical Sobolev exponent (2007) (15)
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations (2001) (14)
Some tt* structures and their integral Stokes data (2012) (14)
On Non-topological Solutions of the ${\bf G}_2$ Chern-Simons System (2014) (14)
Resolution of Chern–Simons–Higgs Vortex Equations (2015) (14)
On the mean field type bubbling solutions for Chern–Simons–Higgs equation (2018) (14)
Recent advances in geometric analysis (2010) (13)
Energy concentration and a priori estimates for $B_2$ and $G_2$ types of Toda systems (2015) (13)
On compactness and completeness of conformal metrics in $\mathbf{R}^N$ (1997) (12)
Uniqueness and structure of solutions to the Dirichlet problem for an elliptic system (2009) (12)
New type of nontopological bubbling solutions in the SU(3) Chern–Simons model in R2 (2016) (12)
Asymptotic analysis of solutions to a gauged O(3) sigma model (2013) (12)
Classification of Radial Solutions to Liouville Systems with Singularities (2013) (11)
Local profile of fully bubbling solutions to SU(n+1) Toda Systems (2013) (11)
Bubbling solutions for the Chern-Simons gauged $O(3)$ sigma model in $\mathbb{R}^2$ (2013) (11)
Mixed Type Solutions of the $${SU(3)}$$SU(3) Models on a Torus (2016) (11)
A priori estimates of Toda systems, I: the Lie algebras of $\mathbf{A}_n$, $\mathbf{B}_n$, $\mathbf{C}_n$ and $\mathbf{G}_2$ (2020) (11)
Sharp Nonexistence Results for Curvature Equations with Four Singular Sources on Rectangular Tori (2017) (11)
Degree counting for Toda system with simple singularity: One point blow up (2017) (10)
Local profile of fully bubbling solutions to $\mathrm {SU} (n+1)$ Toda systems (2016) (10)
The geometry of generalized Lamé equation, I (2017) (10)
Sharp estimates for solutions of mean field equations with collapsing singularity (2017) (10)
Existence of mixed type solutions in the SU(3) Chern–Simons theory in $$\mathbb {R}^2$$R2 (2017) (10)
Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains (2018) (9)
Existence of mixed type solutions in the Chern–Simons gauge theory of rank two in R2 (2017) (9)
Harnack type inequality and a priori estimates for solutions of a class of semilinear elliptic equations (2008) (9)
Sharp existence results for mean field equations with singular data (2012) (9)
The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application (2018) (8)
Geometric quantities arising from bubbling analysis of mean field equations (2016) (8)
Existence, uniqueness and stability of positive solutions to sublinear elliptic systems (2011) (8)
LOCAL GRADIENT ESTIMATES FOR QUOTIENT EQUATIONS IN CONFORMAL GEOMETRY (2007) (8)
Real-root property of the spectral polynomial of the Treibich–Verdier potential and related problems (2016) (8)
Asymptotic symmetry of singular solutions of semilinear elliptic equations (2008) (8)
Variational justification of the dimensional-scaling method in chemical physics: the H-atom (2010) (8)
Erratum to “Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities” (2004) (8)
Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I (2016) (7)
Toda systems and hypergeometric equations (2016) (7)
Self-dual radial non-topological solutions to a competitive Chern–Simons model (2018) (7)
Multiplicity for Self-Dual Condensate Solutions in the Maxwell-Chern-Simons O(3) Sigma Model (2014) (7)
ON TODA SYSTEM WITH CARTAN MATRIX G 2 (2014) (7)
Compactness of conformal metrics with positive gaussian curvature in $\mathbb {R}^2$ (1998) (7)
Green function, mean field equation and Painlevé VI equation (2015) (7)
Bubbling solutions for the Chern–Simons gauged $$O(3)$$O(3) sigma model on a torus (2015) (7)
Solutions to the Master Equations Governing Fractional Vortices (2012) (7)
Mathematical analysis of the dimensional scaling technique for the Schrödinger equation with power-law potentials (2010) (6)
Uniqueness of non-topological solutions for the Chern-Simons system with two Higgs particles (2014) (6)
Exact number and non-degeneracy of critical points of multiple Green functions on rectangular tori (2021) (6)
Classification of solutions to general Toda systems with singular sources (2016) (6)
On Toda system with Cartan matrix (2015) (6)
Uniqueness of topological multi-vortex solutions for a skew-symmetric Chern-Simons system (2014) (6)
Conformal metrics with prescribed nonpositive Gaussian curvature on ${\mathbb R}^2$ (2000) (6)
Existence of non-topological solutions for a skew-symmetric Chern-Simons system (2014) (6)
Topological degree for solutions of fourth order mean field equations (2011) (6)
Simple zero property of some holomorphic functions on the moduli space of tori (2017) (6)
A priori estimates for D4 and F4 Toda systems (2020) (5)
A FUNCTION THEORETIC VIEW OF THE MEAN FIELD EQUATIONS ON TORI (2008) (5)
Multiple solutions of conformal metrics with negative total curvature (2000) (5)
Convergence rate, location and $\partial_z^2$ condition for fully bubbling solutions to SU(n+1) Toda Systems (2014) (5)
ON THE CHERN-SIMONS-HIGGS EQUATION : PART II , LOCAL UNIQUENESS AND EXACT NUMBER OF SOLUTIONS (2014) (5)
The SU(3) Toda system with multiple singular sources (2019) (5)
On axisymmetric solutions of the conformal scalar curvature equation on $S^n$ (2000) (5)
On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations (2018) (5)
Bubbling solutions for a skew-symmetric Chern–Simons system in a torus (2017) (5)
On condensate of solutions for the Chern–Simons–Higgs equation (2017) (5)
Self-Dual Symmetric Nontopological Solutions in the SU(3) Model in R 2 (2015) (4)
Existence and non-existence of solutions of the mean field equations on flat tori (2017) (4)
Mean field equations and premodular forms, I: at critical parameter $16\pi$ (2016) (4)
Non-existence of solutions for a mean field equation on flat tori at critical parameter $16 \pi$ (2016) (4)
A new type of non-topological bubbling solutions to a competitive Chern-Simons model (2014) (4)
Liouville Systems of Mean Field Equations (2011) (4)
Small divisors in nonlinear elliptic equations (2003) (4)
Sharp Estimate for the Critical Parameters of SU(3) Toda System with Arbitrary Singularities, I (2020) (4)
Existence of bubbling solutions without mass concentration (2018) (4)
Existence of non-Abelian vortices with product gauge groups (2014) (4)
On the attainability for the best constant of the Sobolev-Hardy type inequality (Progress in Variational Problems : New Trends of Geometric Gradient Flow and Critical Point Theory) (2011) (3)
Metrics with Positive constant curvature and modular differential equations (2021) (3)
Spectrum of the Lamé operator and application, I: Deformation along Reτ=12 (2021) (3)
Spectrum of the Lamé Operator and Application, II: When an Endpoint is a Cusp (2020) (3)
Existence of Radial Mixed Type Solutions in Chern–Simons Theories of Rank 2 in $$\mathbb {R}^2$$R2 (2019) (3)
The geometry of generalized Lamé equation, III: One-to-one of the Riemann–Hilbert correspondence (2020) (2)
BLOWUP BEHAVIOR OF MEAN FIELD TYPE EQUATIONS (2000) (2)
A uniqueness result for a Neumann problem involving the critical Sobolev exponent (2003) (2)
Uniqueness of bubbling solutions with collapsing singularities (2017) (2)
On reducible monodromy representations of some generalized Lamé equation (2016) (2)
Uniqueness of Multiple-spike Solutions via the Method of Moving Planes (2007) (2)
On number and evenness of solutions of the $SU(3)$ Toda system on flat tori with non-critical parameters (2021) (2)
On Non-topological Solutions of the Chern-Simons SU ( 3 ) System (2011) (2)
Lectures on Partial Differential Equations: Proceedings in honor of Louis Nirenberg's 75th Birthday (2003) (2)
On Algebro-Geometric Simply-Periodic Solutions of the KdV Hierarchy (2020) (2)
Uniqueness of topological solutions of self-dual Chern-Simons equation with collapsing vortices (2014) (1)
Modular Ordinary Differential Equations on SL(2,Z) of Third Order and Applications (2021) (1)
Asymptotic behavior of SU(3) Toda system in a bounded domain (2011) (1)
A NECESSARY AND SUFFICIENT CONDITION FOR THE DARBOUX-TREIBICH-VERDIER POTENTIAL WITH ITS SPECTRUM CONTAINED IN R (2020) (1)
Quasimodular forms and modular differential equations which are not apparent at cusps: I (2021) (1)
The existence of positive solutions to the semilinear elliptic equation involving the Sobolev and the Sobolev-Hardy critical terms (Harmonic Analysis and Nonlinear Partial Differential Equations) (2011) (1)
Blow up at infinity in the SU(3) Chern-Simons model, part I (2020) (1)
A MINIMIZATION PROBLEM ASSOCIATED WITH THE CHERN-SIMONS MODEL WITH DOUBLE VORTEX POINTS ON A TORUS (2013) (1)
The tt*-Toda equations of A_n type (2023) (1)
Compactness of conformal metrics with positive gaussian curvature in R2 (2019) (1)
The existence of positive solutions to the semilinear elliptic equation involving the Sobolev and the Sobolev ‐ Hardy critical terms (2018) (1)
Proof of a conjecture of Dahmen and Beukers on counting integral Lam\'{e} equations with finite monodromy (2021) (0)
Asymptotic analysis of solutions to a gauged $ \mathrm{O}(3)$ sigma model (2015) (0)
Elliptic KdV potentials and conical metrics of positive constant curvature, I (2023) (0)
On the blow-up behavior of solutions of scalar curvature equation and its application (1999) (0)
On reducible monodromy representations of some generalized Lamé equation (2017) (0)
A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in ℝ (2022) (0)
Simple zero property of some holomorphic functions on the moduli space of tori (2019) (0)
Monodromy of a generalized Lame equation of third order (2022) (0)
Recent advances in nonlinear analysis : proceedings of the International Conference on Nonlinear Analysis, Hsinchu, Taiwan, 20-25 Novemver 2006 (2008) (0)
Title The existence of positive solutions to the semilinear elliptic equation involving the Sobolev and the Sobolev-Hardy critical terms ( Harmonic Analysis and Nonlinear Partial Differential Equations ) (2018) (0)
A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$ (2020) (0)
Existence of Bubbling Solutions for Chern–Simons Model on a Torus (2012) (0)
Asymptotic behavior of solutions of A 2nth order nonlinear differential equation (2002) (0)
STRUCTURES AND THEIR INTEGRAL STOKES DATA (2012) (0)
Recent advances in elliptic and parabolic problems : Proceedings of the International Conference, Hsinchu, Taiwan 16-20 February 2004 (2005) (0)
THE CHRISTOFFEL-MINKOWSKI PROBLEM III: EXISTENCE PROBLEM FOR CURVATURE MEASURES (2003) (0)
Resolution of Chern–Simons–Higgs Vortex Equations (2016) (0)
Removable singularity of positive solutions for a critical elliptic system with isolated singularity (2015) (0)
Co-axial metrics on the sphere and algebraic numbers (2022) (0)
Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann–Hilbert Problem (2015) (0)
Sharp upper bound of the number of solutions for the SU(N + 1) Toda system on torus with non-critical parameters (2022) (0)
Sharp estimates for fully bubbling solutions of a SU(3) Toda system (2012) (0)
Even solutions of some mean field equations at non-critical parameters on a flat torus (2022) (0)
On the Entire Radial Solutions of the Chern–Simons SU(3) System (2014) (0)
Classification and nondegeneracy of SU(n+1) Toda system with singular sources (2012) (0)
A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents (2011) (0)
Non-degeneracy and uniqueness of solutions to general singular Toda systems on bounded domains (2022) (0)
degree counting formula for non-symmetric Toda systems of rank two (2022) (0)
PHASE SEPARATION OF BOUND STATE SOLUTIONS OF A SYSTEM OF NONLINEAR SCHRÖDINGER EQUATIONS (2005) (0)
Existence and uniqueness for mean field equations on multiply connected domains at the critical parameter (2013) (0)

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Chang ‐ Shou Lin's AcademicInfluence.com Rankings