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Preprint Archives

2019
Paper Number Title Author
1 Population Dynamics with Immigration Dan Han
2 Schwarz methods for fourth-order problems containing singularities Birce Palta
3 On the discrete spectrum of exterior elliptic problems Rajan Puri
4 On the spectral theory of 1-D Schrodinger Operator with sparse random potentials Thomas A. Cook
5 Estimation of semi-varying coefficient models for counting process with applications Liqiu Deng
6 Jensen-Shannon Divergence: Estimation and Hypothesis Testing Ann Marie Stewart
7 Inverse source problems for elliptic and parabolic equations Qitong Li
8 Dynamic modeling of incomplete event history data Fei Heng
9 Non-parametric estimation of information-theoretic quantities in entropic perspective Jialin Zhang
10 Statistical estimation and inference for the associations of multivariate recurrent event processes Peilin Chen
11 Optimal strategies in "Locks, Bombs, and Testing" (LBT) problem for the case of independent protection Li Liu
12 Goodness-of-fit tests under permutations Chen Chen
13 Invariants of rational links represented by reduced alternating diagrams Yuanan Diao, Claus Ernst and Gabor Hetyei
14 Unifying estimation of varying-coefficient models Weitong Yin
15 Isomorphism in Wavelets II Xingde Dai, Wei Huang and Zhongyan Li

2018
Paper Number Title Author
1 Option Valuation Under A Regime-Switching Model Using the Fast Fourier Transform Elham Sohrabi
2 Interval Estimation for Semiparametric Predictive Regression Shaoxin Hong
3 Estimates For the Number of Eigenvalues of Non-self-adjoint Operators Artem Hulko
4 Improving Semiparametric Estimation of Longitudinal Data with Covariance Function Fang Fang
5 The braid indices of alternating links Pengyu Liu
6 Robust generalized likelihood ratio test based on penalization Meijiao Zhang
7 Accurate and efficient calculation of singular electrostatic potentials in charge-dielectric spherical and Janus particle systems Caylah N. Retz
8 High confidence set regularization in sparse high dimensional logistic regression with measurement error Maorong Rao
9 Uniform flag triangulations of the Legendre polytope Richard Ehrenborg, Gabor Hetyei and Margaret Readdy

2017
Paper Number Title Author
1 The Braid Index Of Alternating Links Yuanan Diao, Gabor Hetyei and Pengyu Liu
2 Parallel computing for Markov chains with islands and ports Amod Basnet
3 Optimal multiple stopping: theory and applications Gary Wayne Crosby
4 Non-nested model selection via empirical likelihood Cong Zhao
5 American options pricing using HJM methodology Wedige Sandesh Kushantha Fernando
6 Alternation acyclic tournaments Gabor Hetyei
7 Counting partitions of a fixed genus Robert Cori and Gabor Hetyei

2016
Paper Number Title Author
1 Limit theorems for random exponential sums and their applications to insurance and random energy model Huseyin Erturk
2 High-order Integral Equations for Electromagnetic Problems in Layered Media with Applications in Biology and Solar Cells Brian Zinser
3 Limit theorems for one class of ergodic Markov chains Nezihe Turhan
4 Frame Wavelets in High Dimension Wei Huang
5 Analysis of semiparametric regression models for the cumulative incidence functions under the two-phase sampling designs Unkyung Lee
6 The Braid Index of Reduced Alternating Braids Pengyu Liu, Yuanan Diao and Gabor Hetyei
7 Estimation of Standardized Mutual Information Zhiyi Zhang and Ann M. Stewart
8 Simion's type B associahedron is a pulling triangulation of the Legendre polytope Richard Ehrenborg, Gabor Hetyei and Margaret Readdy
9 Path intergal methods using Feynman-Kac formula and reflecting Brownian motions for Neumann and Robin Problems Yijing Zhou
10 Intermittency for Branching Random walks with Heavy Tails Asmaa Getan
11 Isogeometric collocation method for elasticity problems containing singularities Puja Rattan
12 High order H(div) discontinuous Galerkin methods for MHD equations Jian Wu
13 Nonparametric predictive regression Xintian Yu
14 Partition of unity isogeometric analysis for singularly perturbed problems and fourth order differential equations containing singularities Sinae Kim

2015
Paper Number Title Author
1 Spectral theorems for Schrodinger operator on general graphs Lukun Zheng
2 Generalized semiparametric varying-coefficient models for longitudinal data Li Qi
3 Approximating solutions of boundary value problems Hamid Semiyari
4 Symmetry and constraints in hydrodynamics and mechanical locomotion Michael J. Fairchild
5 Efron's coins and the Linial arrangement Gabor Hetyei

2014
Paper Number Title Author
1 Generalized Tchebyshev triangulations Gabor Hetyei and Eran Nevo
2 Image Charge Solvation Model (ICSM) for Simulating Biomolecules and KcsA Ion-Channels Katherine A. Baker
3 Generating Random Walks and Polygons with Stiffness in Confinement Y. Diao, C. Ernst, S. Saarinen, and U. Ziegler
4 Orientation of DNA minicircles balances density and topological complexity in kinetoplast DNA Y. Diao, V. Rodriguez, M. Klingbeil and J. Arsuaga
5 The effect of volume exclusion on the formation of DNA minicircle networks Y. Diao, K. Hinson and J. Arsuaga

2013
Paper Number Title Author
1 Isogeometric analysis and patchwise reproducing polynomial particle method for plates Hyunju Kim
2 The Asymptotic Approximation of the Transition Probability for the Random Walks with Heavy Tails Andu Agbor
3 Asymptotic normality of entropy estimators Xing Zhang
4 The toric h-vector of a cubical complex in terms of noncrossing partition statistics Sarah Birdsong and Gábor Hetyei
5 On the structure and invariants of cubical complexes Sarah J. Birdsong
6 Binary Edwards Curves in Elliptic Curve Cryptography Graham Enos
7 Generalized quasi-likelihood ratio tests for varying codfficient quantile regression models Yonggang Wang
8 Counting genus one partitions and permutations Robert Cori and Gabor Hetyei
9 Generalized Quasi-likelihood Ratio Statistics for Multivariate Time-varying Coefficient Regression Models Yi Liu
10 The center and cyclicity problems in a family of three dimensional polynomial systems of ordinary differential equations Kokouvi Hounkanli
11 Consistent Nonparametric Test on Nonlinear Regression Models With Near-Integrated Covariates Li Wu
12 Curvature of random walks and random polygons in confinement Y. Diao, C. Ernst, A. Montemayor, and U. Ziegler
13 Percolation phenomena in disordered topological networks V. Rodriguez, Y. Diao and J. Arsuaga
14 Random walks and polygons in tight confinement Y. Diao, C. Ernst and U. Ziegler
15 The Knot Spectrum of Confined Random Equilateral Polygons Y. Diao, C. Ernst, A. Montemayer, E. Rawdon and U. Ziegler
16 Properties of Topological Networks of Flexible Polygonal Chains J. Arsuaga, Y. Diao, M. Klingbeil, V. Rodriguez
17 A Random Hierarchical Laplacian Elijah E. Ray

2012
Paper Number Title Author
1 A Multivariate Normal Law for Turing's Formulae Zhiyi Zhang
2 Relative Tutte polynomials of tensor products of colored graphs Yuanan Diao and Gábor Hetyei
3 Variable selection for functional index coefficient models and its application in finance and engineering Bingduo Yang
4 Semiparametric time-varying coefficient regression model for longitudinal data with censored time origin Shou, Qiong
5 Branching processes in random trees Yanjmaa Jutmaan
6 Sampling Adjusted Semiparametric Regression for Panel Data Yanqing Sun, Liuquan Sun, and Jie Zhou
7 Hybrid solvation model for electrostatic interactions in molecular dynamics simulation of ionic solvent Ming Xiang
8 A Unified Treatment of Derivative Pricing and Forward Decision Problems within the HJM Framework Wenhua Zhou
9 Generating equilateral random polygons in confinement II Y. Diao, C. Ernst, A. Montemayor, and U. Ziegler
10 Generating equilateral random polygons in confinement III Y. Diao, C. Ernst, A. Montemayor, and U. Ziegler
11 Hurwitzian continued fractions containing a repeated constant and an arithmetic progression G. Hetyei

2011
Paper Number Title Author
1 The Center Problem on a Center Manifold in R3 V.F. Edneral, A. Mahdi, V.G. Romanovski, and D.S. Shafer
2 Centers On Center Manifolds in the Lü System Adam Mahdi, Claudio Pessoa, and Douglas S. Shafer
3 The Study of "Loop" Markov Chains Perry L. Gillespie Jr.
4 Integrability of the Nosé-Hoover equation Adam Mahdi and Claudia Valls
5 Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -2 Jaume Llibre, Adam Mahdi and Claudia Valls
6 Gevrey regularity for a class of dissipative equations Animikh Biswas
7 Analysis of Failure Time Data with Missing and Informative Auxiliary Covariates Lipika Gosh
8 Essays on lambda-quantile dependent convex risk measures Lihong Xia
9 Statistical Analysis of Mark-Specific Proportional Hazards Model Mei Li
10 Nonparametric Pricing Kernel Models Linman Sun
11 Meshless boundary particle methods for boundary integral equations and meshfree particle methods for plates Christopher Bard Davis
12 Limit theorems for reaction diffusion models Yaqin Feng
13 Gevrey reguarity for a class of dissipative equations with analytic nonlinearity Hantaek Bae and Animikh Biswas
14 Consistency Results in the Theory of Continuous Functions and Selective Separability Doyel Barman
15 Polynomial integrability of Hamiltonian systems with homogeneous potential of degree -3 Jaume Llibre, Adam Mahdi and Claudia Valls
16 Asymptotic analysis of the Andersson parabolic problem and the Moser's type optimal stopping prblem Hao Zhang
17 On $s$-elementary Super Frame Wavelets and their Path-connectedness Yuanan Diao and Zhongyan Li
18 Generating equilateral random polygons in confinement Y. Diao, C. Ernst, A. Montemayor, and U. Ziegler
19 Nullification of knots and links Y. Diao, C. Ernst and A. Montemayor
20 The effect of angle restriction on the topological characteristics of minicircle networks J. Arsuaga, Y. Diao and K. Hinson
21 Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice K. Ishihara, R. Scharein, Y. Diao, J. Arsuaga, M. Vazquez and K. Shimokawa
22 The growth of minicircle networks on regular lattices J. Arsuaga, Y. Diao and K. Hinson
23 Continue, quit, restart probability model and related problems Constantine Steinberg
24 A Gray Code for the Shelling Types of the Boundary of a Hypercube Sara Birdsong and Gábor Hetyei

2010
Paper Number Title Author
1 The short toric polynomial Gabor Hetyel
2 Level Eulerian posets Richard Ehrenborg, Gabor Hetyei, and Margaret Readdy
3 A note on the Stefanescu conjecture Adam Mahdi and Claudia Valls
4 The effects of confinement on the structure of the mitochondrial DNA from trypanosomes J. Arsuaga, Y. Diao and R. Kaplan
5 The mean squared writhe of alternating random knot diagrams C. Ernst, K. Hinson and U. Ziegler
6 On the mean and variance of the writhe of random polygons J. Portillo, Y. Diao, R. Scharein, J. Arsuaga and M. Vazquez
7 A Convertible-Bond-Pricing Method Based on Bond Prices on Markets Quang Shi

2009
Paper Number Title Author
1 Meixner polynomials of the second kind and quantum algebras representing SU(1,1) Gábor Hetyei
2 Enumeration by kernel positions for strongly Bernoulli type truncation games on words Gábor Hetyei
3 Assessing cumulative incidence functions under the semiparametric additive risk model Seunggeun Hyun, Yanqing Sun, Rajeshwari Sundaram
4 Bounds for minimal step number of knots in the simple cubic lattice R. Scharein, K. Ishihara, J. Arsuaga, Y. Diao, K. Shimokawa and M. Vazquez
5 On the Direct Path Problem of s-elementary Frame Wavelets X. Dai, Y. Diao, and X. Guo
6 The Growth of the Mean Average Crossing Number of Equilateral polygons in Confinement R.J. Arsuaga, B. Borgo, Y. Diao and R. Scharein
7 The poset of bipartitions Gábor Hetyei and Christian Krattenthaler
8 Intrinsic s-elementary Parseval Frame Multiwavelets in L2(R)d Zhongyan Li, X. Dai and Y. Diao
9 The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers Y. Diao, C. Ernst, Attila Por and U. Ziegler
10 Modeling of Chromosome Intermingling by Partially Overlapping Uniform Random Polygons T. Blackstone, R. Scharein, B. Borgo, R. Varela, Y. Diao and J. Arsuaga

2008
Paper Number Title Author
1 The Particle Shape functions that Reproduce singular functions Reproducing Polynomial(Singularity) Particle Methods and Adaptive Meshless Methods for 2-Dim Elliptic Boundary Value Problems Hae-Soo Oh and Jae Woo Jeong
2 DNA Knotting in Spooling Like Conformations in Bacteriophages J. Arsuaga and Y. Diao
3 Jones Polynomials of Knots Formed by Repeated Tangle Replacement Operations Y. Diao, C. Ernst and U. Ziegler
4 Multipliers, Phases and Connectivity of Wavelets in L2(R2) Zhongyan Li, Xingde Dai , Yuanan Diao and Jianguo Xin
5 Exploring alternative mathematics assessments with Latino/a students Anthony Fernandes, Cynthia Anhalt, and Marta Civil
6 Relative Tutte Polynomials for Colored Graphs and Virtual Knot Theory Yuanan Diao and Gábor Hetyei
7 The Path-Connectivity of MRA Wavelets in L2(Rd) Zhongyan Li, Xingde Dai, Yuanan Diao and Wei Huang
8 Wavelets with Frame Multiresolution Analysis X. Dai, Y. Diao, Q. Gu, and D. Han
8 Shifted Jacobi polynomials and Delannoy numbers Gábor Hetyei
9 The Linearity of the Ropelenghts of Conway Algebraic Knots in Terms of Their Crossing Numbers Y. Diao, C. Ernst and U. Ziegler
10 A second look at the toric h-polynomial of a cubical complex Gábor Hetyei
11 Mathematical methods in DNA topology: applications to chromosome organization and site-specific recombination Javier Arsuaga, Yuanan Diao, and Mariel Vazquez
12 The Path-Connectivity of s-Elementary Frame Wavelets with Frame MRA Xingde Dai, Yuanan Diao, and Zhongyan Li
13 Almost Everywhere Partition of Unity to deal with Essential Boundary Conditions in Meshless Methods Hae-Soo Oh and Jae Woo Jeong
14 A Fast Ergodic Algorithm for Generating Ensembles of Equilateral Random Polygons R. Varela, K. Hinson, J. Arsuaga, and Y. Diao
15 A Tutte-style Proof of Brylawski’s Tensor Product Formula Y. Diao, G. Hetyei, and K. Hinson

2007
Paper Number Title Author
1 Linking of Uniform Random Polygons in Confined Spaces J. Arsuaga, T. Blackstone, Y. Diao, E. Karadayi and M. Saito
2 Generating 4-regular Hamiltonian Plane Graphs O. Ascigil, Y. Diao, C. Ernst, D. High and U. Ziegler
3 Proportional hazards models with continuous marks Yanqing Sun, Peter B. Gilbert and Ian W. McKeague
4 The two-sample problem for failure rates depending on a continuous mark: an application to vaccine efficacy Peter B. Gilbert, Ian W. McKeague and Yanqing Sun
5 Maximum likelihood estimation for tied survival data under Cox's regression model via the EM algorithm Thomas H. Scheike and Yanqing Sun
6 Tutte Polynomials of Tensor Products of Signed Graphs and their Applications in Knot Theory Yuanan Diao, Gábor Hetyei and Kenneth Hinson
7 The Piecewise Polynomial Partition of Unity Functions for the Generalized Finite Element Methods (II) Hae-Soo Oh, June G. Kim, and Won-Tak Hong
8 Invariants of composite networks arising as a tensor product Y. Diao, G. Hetyei, and K. Hinson
9 Enumeration by kernel positions G. Hetyei
10 Sampling Large Random Knots in a Confined Space J. Arsuaga, T. Blackstone, Y. Diao, K. Hinson E. Karadayi and M. Saito
11 Delannoy orthants of Legendre polytopes G. Hetyei
12 Building Alliances: A partnership between a middle school mathematics teacher and a researcher Anthony M. A. Fernandes
13 Almost Everywhere Partition of Unity to deal with Essential Boundary Conditions in Meshless Methods Hae-Soo Oh and Jae Woo Jeong

2006
Paper Number Title Author
1 On Frame Wavelet Sets and Some Related Topics X. Dai and Y. Diao
2 The Path-Connectivity of Wavelets and Frame Wavelets X. Dai and Y. Diao
3 The Path-Connectivity of s-Elementary Tight Frame Wavelets X. Dai and Y. Diao
4 The Closed Form Reproducing Kernel Particle Shape Functions: Part 1. Basic Consctructions: Uniformly Distributed Particles June G. Kim, Hae-Soo Oh, and Jaewoo Jeong
5 The Closed Form Reproducing Kernel Particle Shape Functions: Part 2. Non-Uniformly Distributed Particles June G. Kim, Hae-Soo Oh, and Jaewoo Jeong
6 Numerical Upper Bounds on Ropelengths of Large Physical Knots Y. Diao, C. Ernst, V. Kavuluru and U. Ziegler
7 The Smooth Piecewise Polynomial Particle Shape Functions corresponding to Patch-wise Non-Uniformly Spaced Particles for Meshfree Particle Methods Hae-Soo Oh, June G. Kim, and Jaewoo Jeong
8 Hypotheses Tests of Strain-Specific Vaccine Efficacy Adjusted for Covariate Effects Seunggeun Hyun and Yanqing Sun
9 Tutte Polynomials of Signed Graphs and Jones Polynomials of Some Large Knots Yuanan Diao, Gábor Hetyei and Kenneth Hinson
10 The Reproducing Singularity Particle Shape Functions for Problems Containing Singularities Hae-Soo Oh, Jae Woo Jeong and June G. Kim
11 Tchebyshev triangulations of stable simplicial complexes Gábor Hetyei
12 A Partial Ordering of Knots Through Diagrammatic Unknotting Y. Diao, C. Ernst and A. Stasiak

2005
Paper Number Title Author
1 Lipschitz Stability for Hyperbolic Inequalities in Octants With the Lateral Cauchy Data and Refocusing in Time Reversal Michael Klibanov
2 Central Delannoy numbers and balanced Cohen-Macaulay complexes Gábor Hetyei
3 On the Recovery Of a 2-D Function From the Modulus Of Its Fourier Transform Michael Klibanov
4 On the General Intertwining Lifting Problem - I A. Biswas, C. Foias
5 An Alternative and Surprising Solution to Olbers' Paradox Y. Diao and A. Stasiak
6 Weyl-Heisenberg Frame Wavelets with Basic Supports Xunxiang Guo, Yuanan Diao and Xingde Dai
7 Ropelengths of Closed Braids Yuanan Diao and C. Ernst
8 The Average Inter-crossing Number of Equilateral Random Walks and Polygons Y. Diao, A. Dobay and A. Stasiak
9 Total Curvature, Ropelength and Crossing Number of Thick Knots Yuanan Diao and C. Ernst
10 From Weyl-Heisenberg Frames to Infinite Quadratic Forms Xunxiang Guo, Yuanan Diao and Xingde Dai.
11 Approximate Globally-Regular Solutions of the Navier-Stokes Equations via Spectral Methods Joel Avrin

2004
Paper Number Title Author
1 Global uniqueness for a non-overdetermined inverse conductivity problem in unbounded domains Michael Klibanov and Alexandre Timonov
2 Orthogonal polynomials represented by CW-spheres Gábor Hetyei
3 Lipschitz Stability of an Inverse Problem for an Acoustic Equation Michael Klibanov and Masahiro Yamamoto
4 Global uniqueness for a 3-D/2-D inverse conductivity problem in tube domains via Carleman estimates Michael Klibanov and Alexandre Timonov
5 Scaling of the average crossing number in equilateral random walks, knots and proteins A. Dobay, Y. Diao, Jacques Dubochet and A. Stasiak
6 How complex can a land suitability map be? Y. Diao and W-N. Xiang
7 Hamiltonian Cycles and Ropelengths of Conway Algebraic Knots Y. Diao and C. Ernst
8 Quadrisecants Give New Lower Bounds for the Ropelength of a Knot E. Denne, Y. Diao and J. M. Sullivan
9 Braid Index, Genus and Crossing Number of Links Y. Diao and C. Ernst
10 Polyspherical Complexes Gábor Hetyei
11 Face Enumeration Using Generalized Binomial Coefficients Gábor Hetyei

2003
Paper Number Title Author
1 On Super-Wavelets Xingde Dai, Yuanan Diao, and Q. Gu
2 Frame Wavelets with Frame Set Support in the Frequency Domain Xingde Dai, Yuanan Diao, and Q. Gu
3 The Additivity of Crossing Numbers Yuanan Diao
4 Realizable Powers of Ropelengths by Nontrivial Knot Families Yuanan Diao and Claus Ernst
5 Tchebyshev posets Gábor Hetyei
6 Matrices of formal power series associated to binomial posets Gábor Hetyei
7 The topology of the independence complex Richard Ehrenborg and Gábor Hetyei
8 The Average Crossing Number of Equilateral Random Polygons Yuanan Diao, A. Dobay, R. B. Kusner, K. Millett, and A. Stasiak
9 Global Uniqueness of a Multidimensional Inverse Problem for a Nonlinear Parabolic Equation by a Carleman Estimate Michael Klibanov
10 Local Existence and Gevrey Regularity of 3-D Periodic NSE with lp initial data Animikh Biswas
11 An intertwining property for positive Toeplitz operators A. Biswas, C. Foias, and A. E. Frazho
12 Generating Large Random Knot Projections Yuanan Diao, Claus Ernst, and Uta Ziegler
13 The Average Crossing Number of Gaussian Random Walks and Polygons Yuanan Diao and Claus Ernst

2002
Paper Number Title Author
1 Non-realcompact products with a metric factor Alan Dow and Neeta Singh
2 Embeddings into P(N})/fin and extension of automorphisms A. Bella, A. Dow, K. P. Hart, M. Hrusak, J. van Mill, and P. Ursino
3 Compact spaces and the pesudoradial property, I Alan Dow
4 Subspaces with Normalized Tight Frame Wavelets in R Xingde Dai, Yuanan Diao, and Qing Gu
5 The Existence of Subspace Wavelet Sets X. Dai, Y. Diao, Q. Gu, and D. Han
6 The lower bounds of the lengths of thick knots Yuanan Diao
7 The Crossing Numbers of Thick Knots and Links Yuanan Diao and Claus Ernst
8 Wavelets with Frame Multiresolution Analysis X. Dai, Y. Diao, Q. Gu, and D. Han
9 Upper bounds on linking numbers of thick links Y. Diao, C. Ernst, and E.J. Janse van Rensburg
10 Frame Wavelet Sets in Rd X. Dai, Y. Diao, Q. Gu, and D. Han
11 Normalized Tight Frame Wavelet Sets in Rd X. Dai, Y. Diao, Q. Gu, and D. Han
12 The s-elementary Frame Wavelets are Path Connected X. Dai, Y. Diao, Q. Gu, and D. Han
13 Button design for map overlays (II) Yuanan Diao and Wei-Ning Xiang
14 The Weighted Riesz-Galerkin Method for Elliptic Boundary Value Problems on Unbounded Domains Hae-Soo Oh, Bongsoo Jang, and Yichung Jou
15 Numerical Methods for Accurate Finite Element Solutions of Elliptic Boundary Value Problems Containing Singularities Hoonjoo Kim, Sung-Jin Lee, and Hae-Soo Oh
16 Three Pile Nim with Blocking Arthur Holshouser and Harold Reiter
17 Generalization of Beatty's Theorem Arthur Holshouser and Harold Reiter
18 Dynamic One-Pile Blocking Nim Arthur Holshouser and Harold Reiter
19 One Pile Nim with Arbitrary Move Function Arthur Holshouser and Harold Reiter
20 Dynamic One-Pile Nim Arthur Holshouser, Harold Reiter, and James Rudzinski
21 (Pilesize) Dynamic One-Pile Nim Arthur Holshouser, Harold Reiter, and James Rudzinski
22 The linear growth in the lengths of a family of thick knots Yuanan Diao, Claus Ernst, and Morwen Thistlewhite.
23 A sequential minimisation algorithm based on the convexification approach Michael Klibanov and Alexandre Timonov.
24 Hamiltonian Knot Projections and Lengths of Thick Knots Yuanan Diao, Claus Ernst, and Xingxing Yu
25 Accurate Mode-Separated Energy Release Rates for Delamination Cracks Hae-Soo Oh