# Master's Degrees Awarded

### 2015

**Azizah Alqhtani**(Rafal Ablamowicz, O'Connor, Chambers)*On Decomposing CG-Modules of Finite Groups Using Irreducible Characters***Leah Frauendienst**(Padmini Veerapen, Hetzel, Ablamowicz)

*Notion of Rank of Noncommutative Quadratic Forms On Four Generators***Bernardino BJ Guerrero**(Matoya Machida, D. Smith, Allen)*The Martingale Framework For Two Sample Problems***Maged Joseph**(Brian O'Connor, Liu, Davis)*The Use of Numerical Software Packages to Evaluate or Approximate the Integrals Corresponding to the Laplace Transform and the Inverse Laplace Transform***Ashley Lawson**(Andew Hetzel, Chambers, Veerapen)

*The Self-Representing Muse: Autobiographical Productions of Women in Artistic Partnerships***Christopher Newton**(Michael Allen, D. Smith, Machida)**Non-thesis****David Tidwell**(Damian Kubiak, Mills, Norden)

*Steinhaus' Property in Banach Spaces*

### 2014

**Forrest Garwood**(Allan Mills, Hetzel, Norden)*A Survey of the Concepts of N-Connectedness of Graphs and Vertical N-Connectedness of Matroids***Eric Morgan**(Andrew Hetzel, Ablamowicz, Mills)*Analogues of the Prime Number Theorem in Certain Rings of Integers*

### 2013

**Christopher Hatcher**(Michael Allen, Hetzel, Liu)*Fractional Derivatives, Fractional Differential Equations, and Their Numerical Approximation***Kehelwala D. Gayan Maduranga**(Rafal Ablamowicz, Hetzel, Chambers)*Representations and Characters of Salingaros' vee Groups***William Wilhoite**(Brian O'Connor, Shibakov, Hetzel)**Non-thesis**

### 2012

**Jeremy Daniel**(Motoya Machida, D. Smith, O'Connor)*A Study of Association Measures in Large Frequency Tables***Curtis Dale Hobbs**(Amy Chambers, Machida, O'Connor)*C*-algebras and Their Representations as Bounded Operators on Hilbert Spaces***Michael Holloway**(Andrew Hetzel, Ablamowicz, Mills)*On Commutative Rings Without Prime Ideals***Eric L. Jones**(Andrzej Gutek, Liu, O'Connor, Chambers)*Curvature and Circles: A Complex and Real Approach*

### 2011

**Aaron Hogancamp**(Allan Mills, Hetzel, Smith)*Two Well-Known Graph Theory Results And Their Relationship To Matroid Theory***Srikanth Potukuchi**(Yung-Way Liu, O'Connor, Allen)*A Study Of Some New Approaches To A Lyapunov Stability Problem*

### 2010

**Quinton Westrich**(Alexander Shibakov, Gutek, Norden, Savage)*Differential Topology and the h-Cobordism Theorem***Lily L. Li**(Allan Mills, Allen, Chambers)*Some Well-known Properties of the Relaxation Operation in Matroid Theory*

### 2009

**Sheela Brachey**(Rafal Ablamowicz, Allen, O'Connor)*Non-thesis***Matthew Houston**(Andrew Hetzel, Ablamowicz, Mills)*Ahmes Expansions over Certain Euclidean Domains***Stephen Hoyer**(Yung-Way Liu, Ablamowicz, O'Connor)*Non-thesis***Jason Knight**(Rafal Ablamowicz, Mills, Murdock)*Various Methods for Calculating Reducible and Irreducible Representations of the Symmetric Group***Bertin Nono**(David Smith, Allen, Machida)

*Applications of Bayesian Statistics*

### 2008

**Seun Akinwumi**(Richard Le Borne, S. Le Borne, D. Smith)*Numerical Behavior of the QR-Decomposition Approach to Solving the Recursive Adaptive Filter Problem***Eric Bouldin**(Brian O'Connor, Liu, Hetzel)*Non-thesis***Troy Brachey**(Rafal Ablamowicz, Hetzel, O'Connor)*Grobner Basis Algorithms for Grassmann Algebras in a Maple Package***Che G. Ngufor**(Sabine Le Borne, O'Connor, Chambers)*An Approximation Inverse Preconditioner for Saddle Point Problems Applied to Groundwater Flow***Brad Schwer**(Alexander Shibakov, Norden, Savage)*Characterizing Topological Spaces Using Topological or Algebraic Invariants***Donna Tucker**(Michael Allen, Anthony, Talbert)*The Intelligence of Statistical Learning Algorithms***Songfei Wu**(Michael Allen, Machida, D. Smith)*A Combination Procedure of Universal Kriging and Logistic Regression*

### 2007

**Jared C. Daniels**(Allan D. Mills, Chambers, Liu)*Two Alternative Proofs of a Matroid Reconstruction Result***Bennie Hodges**(Rafal Ablamowicz, Kosa, Mills, Norden)*Application of Category Theory to Basic Principles of Automata Theory***Rebeca Lewis**(Andrew Hetzel, Ablamowicz, Mills)*Sufficient Conditions for a Finite Semiring to be a Ring***Ronald Smitty**(Rafal Ablamowicz, O'Connor, D. Smith)*Non-thesis*

### 2006

**Barry Thomas Elliott**(Richard P. Savage, Jr., Gutek, Mills)*Overlapping Congruent Isosceles Triangles***Yu "Leo" Liu**(Yung-Way Liu, Ablamowicz, D. Smith)*Non-thesis***Dustin Long**(Michael R. Allen, D. Smith, Mills)*A Semiparametric Approach to Linear Regression***Dorothy Leann Long**(David D. Smith, Allen, Machida)*Estimating Confidence Intervals for the Fay-Herriot Model***Gary Starnes**(Brian M. O'Connor, Savage, Liu)*An Investigation of Numerical Methods for Approximating the Laplace Transform and the Inversion Integral*

### 2005

**Matthew Estes**(Alexander Shibakov, Norden, Mills, M. Rogers)*Properties of Infinite Languages and Grammars***Aparna Sonar**(Sabine Le Borne, Ablamowicz, O'Connor)*Domain Decomposition Based Hierarchical Matrices***Jianfeng Zhang**(Matoya Machida, Allen, Smith)*Statistical Data Mining Methods in Adverse Drug Reaction Database*

### 2004

**Rolando Navarro**(David Smith, R. Le Borne, Mills)*Non-thesis***Cheryl Swafford**(David Smith, Machida, Allen)*An Order Statistics Approach for Testing Normality***Jun Ye**(David Smith, Machida, R. Le Borne)*Robust Estimation of Extremes***Ping Ye**(Yung-Way Liu, Murdock, Garimella)*Bound States in Two and Three Quantum Waveguides Coupled Laterally through Boundary Windows with Different Channel Widths***Qiang Zhang**(Ramesh Garimella, Liu, Ablamowicz)*Matrix Operator on Some LP Spaces***Shiwei "Devin" Zhang**(Rafal Ablamowicz, Garimella, Machida)*Non-thesis*

### 2003

**Lynda Buck**(Michael Allen, O’Connor, McHenry)*Edgeworth Expansions of Some Well Known Distributions and the Relationships Between These Distributions with Respect to Convergence***James Lindsay**(Yung-Way Liu, Murdock, O’Connor, Norden)*Bound States in Three Quantum Waveguides Coupled Laterally through Boundary Windows***Sean Tunney**(Rafal Ablamowicz, Mills, Garimella)*On the Continuous Families of Idempotents in the Clifford Algebra of the Euclidian Plane***David Young**(Alexander Shibakov, Norden, Garimella, Savage, Jr.)*Infinite Dimensional Topology and Homogeneity of the Hilbert Cube*

### 2002

**Jiang Chang**(Yung-Way Liu, O’Connor, Garimella, Ablamowicz)*Image Restoration Using Total Variation Norm***Zhongming Huang**(Yung-Way Liu, O’Connor, Garimella, Ablamowicz)*Reliability of the Solutions of Bidiagonal Systems with Applications***Jianying Zhang**(Yung-Way Liu, O’Connor, Garimella, Ablamowicz)*Total Variation Based Digital Image Restoration*

### 2001

**Scott Baker**(Annie Selden, Mason, Savage, Jr., O’Connor)*Proofs and Logic: An Examination of Mathematics Bridge Course Proofs*

### 2000

**Devrim Bilgili**(Ramesh Garimella, Patil, Breen)*Inequalities Involving the Maximum Modulus of a Polynomial***Ben Howard**(Jeffrey Norden, Shibakov, Breen, Gutek)*Set Theory and the Method of Forcing***Volodymyr Hrynkiv**(Rafal Ablamowicz, Garimella, Liu, O'Connor)*On the Invertibility of some Operators on Hilbert Spaces***Ellen Smyth**(Michael Breen, Mills, McHenry, Ablamowicz, Norden)*RSA Compatibility with Composite Integers*

### 1999

**David W. Caughran, Jr.**(Nizam Uddin, Breen, McHenry, Patil)*Some Optimal Row Column Designs in the Presence of Correlated Errors***Hanif Talukder**(Nizam Uddin, McHenry, Patil)*Constructions of Optimal Two-Dimensional Block Designs for Correlated Errors*

### 1998

**Russell Jenkins**(Ramesh Garimella, Breen, O’Connor)*On Inclusions of L^p-Spaces***Joanna Leete**(Michael Breen, Mazeres, Garimella)*Maximal Length of a Chain of Principal Ideals in the Semigroup of NxN Boolean Matrices***Honghong Zhu**(Yung-Way Liu, Linos, Norden, Garimella)*A Formal Study of Dependencies Found in Computer Programs*

### 1997

**Tina Anderson**(Edmond Dixon, Mazeres, Khleif)*The Matrix Equation AX + XA = 0***Noah T. Colson**(Brian M. O'Connor, Dixon, Liu )*Canonical Forms For Second Order Partial Differential Equations***Hongxing Lai**(S. A. Patil, Liu, Uddin)*Poisson Process of Order k with Waiting Time*

### 1996

**Eric Trees**(Michael Breen, Linos, Gutek, Mazeres)*Characterization of Layered Graphs and Optimization of Their Edge Intersections*

### 1995

**Bobbi Jo Butler**(Yung-Way Liu, O’Connor, McHenry)*The Transportation Problem***Qianyu Chen**(Nizam Uddin, Patil, O’Connor, Liu)*Construction of Universally Optimal Nested Row-Column Design with Unequal Block Sizes***Leann Link**(Jacob T. Beard, Mazeres, Garimella)*Iterated Sums of Polynomial Divisors over GF(p)***Kenneth Selvidge**(Ramesh Garimella, O’Connor, Dixon)*A Study of Functions of Bounded Variation and Generalized Hellinger Integrals*

### 1994

**Aditi Badve**( S. A. Patil, Liu, McHenry)*Hybrid Transform and Related Distributions***Frank Bin Lu**(Yung-Way Liu, O’Connor, Beard)*Some Bifurcation Properties in the Lorenz Systems***Angela Neal**(S. B. Khleif, O’Connor, Mazeres, Liu)*Duality in Linear Algebra with an Application to Linear Programming***Ren Shan**(Brian O’Connor, Breen, Liu)*Finding the Shortest Paths in a Parking Lot using a Successive Approximation Method*

### 1993

**Marc Campbell**(Jeffrey Norden, Mazeres, Mason)*A Study of Paracompactness in General Topological Spaces*

### 1992

**John Benjamin Daley**(Ed Dixon, Beard, Norden)*Almost Commutative Matrices***Mohamad Diab**(Edmond Dixon, Mason, O’Connor)*Almost L-Commutative Matrices***Leisa Hopkins**(Reginald Mazeres, Ramsier, O’Connor)*Some Properties of Cyclic Group Generators from 2x2 Matrices MOD P***Beth Riter**(Steve Ramsier, Patil, Liu)*A Correlation Coefficient test for Normality***Kokesh Kadakia**(S. A Patil, Ramsier, Liu)*The Generalized Poisson Process, Negative Factorial Moments and Limiting Distributions for some Discrete Distributions*

### 1991

**Michael Allen**(S.A. Patil, Ramsier, Liu)*Distributions of Two and Three State Markov Chains with Applications***Dollena Hawkins**(S.A. Patil, McHenry, Norden, Mason)*Distribution of Ratios of Uniform Random Variables with Applications to Roots of Polynomials***Pamela Nickrand**(Andrzej Gutek, Norden, Purisch)*Transitive and Almost Transitive Homeomorphisms on the Cantor Set***Craig Knuckles**(Steve Purisch, Norden, J. Selden, Savage Jr.)*Nonarchemedian Topological Spaces***Stacy Williams**(Brian O’Connor, Savage, Jr., Liu)*Analysis of Subseries of the Harmonic Series***Maria Pantazopoulou**(Alice Mason, O’Connor, K. Kumar)*Applications of Topology in the Study of Defects in Condensed Matter Physics*

### 1990

**Vesna Cavka**(Yung-Way Liu, Patil, McHenry)*Liapuunov’s Functions and Applications on Stability***Bhavna Vyas**(Steve Purisch, Liu, Mason, Patil)*Sequential and Subsequential Spaces***Robert Hebble**(John Selden, Mason, Savage, Jr.)*Locally Compact Closures of the Semilattice of Positive Integers***Barry Hamilton**(Yung-Way Liu, O’Connor, B. Briggs)*The Singular Perturbation Method of a Satellite Problem*

### 1989

**Umaru Saleh**(Yung-Way Liu, Patil, Mazeres)*Integral Equation Method of Solving Boundary Value Problems for Laplace’s Equations*

### 1988

**Ayman Badawi**(Jacob. T. Beard, Dixon, Mason)*Non-Unitary Perfect Polynomials over GF(p)***Kim McFadden**(S.A. Patil, McHenry, Mason)*Poisson Process and Reliability Relationships Applicable to Bathtub-Shaped Hazard Rate Functions***Ali Noureddine**(Brian O’Connor, Savage, Jr., Dixon, C. Ventrice)*Methods Relating Integral and Differential Equations*

### 1987

**Shelly Forgey**(Alice Mason, O'Connor, Mazeres)*Upper Semi-Continuous Collections***Shankang Qu**(Claude McHenry, Mason, Patil)*The Distribution of Most Significant Digits For Values of Certain Random Variables***Robert G. Wynegar**(Reginald Mazeres, Mason, McHenry)*Strategies For The Niven Dice Game*

### 1986

**Felix Fernandez**(Brian O'Connor, Long, McHenry)*Laplace Transform Solutions of Ordinary Differential Equations with Linear Coefficients***Martha Emily Hill**(Brian O'Connor, McHenry, Long)*The Methods of Jumps as Applied to Fourier Series, Legendre Polynomial Series, and Laplace Transforms***Raghuram K. Machiraju**(S. A. Patil, Mason, McHenry)*The Reliability Analysis of Nonrepairable Systems and the Development of a New Failure Model***Fadhilah Abd. Razak**(S. A. Patil, O'Connor, McHenry)*Some Compound Discrete Distributions***Dewey Dickson Thurman**(Richard Savage, Jr., Mason, Mazeres, Dixon)*Overlapping Rectangles of the Same Width*

### 1984

**Mohammad R. Kafai**(S. A. Patil, McHenry, O'Connor)*One-Sided R-Reliable Intervals and Their Associated Confidences on the Sum of Two Continuous, Independent, Random Variables*

### 1983

**Demetrois P. Kanoussis**(S. B. Khleif, O'Connor, C. Ventrice, McHenry)*Boundary-Initial Value Problems in Elliptic Coordinates*

### 1982

**Lloyd Rabindra Jaisingh**(C. E. McHenry, Patil, O'Connor)*Some Geometrical Interpretations of Least Squares***Frances Eubank Crawford**(Reginald Mazeres, Long, Dixon)*Concerning Paths in a Rectangular Grid*

### 1981

**Coral Thomas Wallace, Jr.**(Edmond Dale Dixon, Long, McHenry)*The Matrix Equations AX = XA and A*X = XA****Wynella Meachum Mathes**(Leland L. Long, Ramsey, Romine)*Power Spectral Density Techniques in Modeling Water Temperature Regimes of Large Rivers***Adedeji Bodunde Badiru**(Leland L. Long, Lessman, Mazeres)*Stochastic Modeling of Energy Consumption at Tennessee Technological University*

### 1980

**Gary Lynn Slagle**(Reginald Mazeres, Savage, Long)*Extension of the Kaplansky Property to Special Types of Four-by-Four Matrices***Debra L. R. Hall**( Leland Long, McHenry, Patil)*Approaches to an Analysis of Covariance Linear Model***Sharon Reed Lee**( Reginald Mazeres, Dixon, Savage)*Concerning Square and Triangular Matrices***Lai Chu-Ai Jen**( S.A. Patil, McHenry, Long)*Distributions of Ratio Statistics for a Sample from the Two-Parameter Exponential and Gamma Distributions with Applications*

### 1979

**Debra Tibbels**(Richard P. Savage, Mazeres, Swong)*Congruences with Composite Moduli***Gordon L. Freeman, Jr.**(S .A. Patil, Long, Ramsey)*The Development of the Covariance Matrix of the Order Statistics of a Generalized Logistic Distribution and Applications*

### 1977

**Linda Brown Draper**(S.A. Patil, Swong, Yoon, Fletcher)*Mean Square Errors of Estimators in the Presences of an Outlier***Lisa Randolph Gentry**(Reggie Mazeres, Khleif, Dixon)*Some Properties of Characteristic Equations and Characteristic Roots of Two by Two Matrices***David Wayne Jessee, Jr.**(Reggie Mazeres, Savage, Dixon)*Concerning Free Groups of Finite Order***Albert Han-Chu Liu**(S.A. Patil, Ramsey, Lessman)*On the Distribution of the Studentized Bivariate Range from Correlated Sample***Claudia Torgerson Mitchell**(Edmond Dixon, Savage, Mazeres)*The Power Method for Determining the Maximal Eigenvalue for a Matrix*

### 1976

**Peggy Bishop**(S. A. Patil, Buck, Long)*Biases and Some Mean Square Errors of Certain Statistics in the Presence of an Outlier***Michael Howard Alexander**(James Harris, Long, Ramsey)*Linked List Structures Applied to a Student File Maintenance Program***Diane Coleman**(Daniel Buck, Long, Mazeres)*Numerical Solution of Elliptic Partial Differential Equations Using Successive Over-Relaxation***Marilyn Sieben McIntosh**(Richard Savage, Mazeres, Briggs)*Pythagorean Triples and Obtuse Pythagorean Triples***Dilip Patel**(S. A. Patil, Savage, Harris)*On the Bivariate Truncated Poisson Distribution*

### 1975

**Shelia Ray Tallent**(Reggie Mazeres, Khleif, Savage)*Simple Semigroups and Related Concepts***Kin-wing Wong**(James Harris, Buck, Long)*Study of A-Stable Multistep-Multiderivative Integration Formulas for Solving Stiff Differential Equations***Stephen N. Estes**(S.B. Khleif, Mazeres, Savage, Swong)*Positive Definite Matrices and Associated Hermitian Forms***Lynne Hanson Moorer**(S. B. Khleif, Mazeres, Savage)*On Normal Matrices***Charles Edward Stevens**(Leland Long, Buck, Jones)*Meta-Functions*

### 1974

**Maw-Wen Lin**(S.A. Patil, Long, Buck)*Estimation and Testing of the Pareto and Exponential and Related Families***Iris Cauthen McMurtry**(Richard Savage, Mazeres, Swong)*Fibonacci Numbers: Identities and Divisibility Properties***Evangelos Theodore Skoumbourdis**(Reggie Mazeres, Culp, Dixon, Buck)*Semigroups, Right Groups, and Groups***Teresa Tzong Yang**(S.A. Patil, Savage, Buck)*The Distribution of the Ratio of Sample Variances of Components of Correlated Normal Population with Different Scale Parameters***Eddie Bingham**(Reggie Mazeres, Savage, Briggs)*Properties and Interrelationships of Regular, Inverse, and Cancellative Semigroups***Ei-Hu Shen**(S.A. Patil, Buck, Mazeres)*The Bivariate Distribution of the First Passage Time in Brownian Motion*

### 1973

**Linda Dianne Goulder**(Reggie Mazeres, Buck, Savage)*Relationships Between Semigroups and Groups***Marcellus Hebron Graham**(Robert Briggs, Mazeres, Briggs)*A Comparison of Second Countable, Hereditarily Separable, Lindelof, and Aleph-compact Spaces***Dennis Nolan Bean**(Robert Briggs, Savage, Dixon)*A Study of Compactness in Moore Spaces***Carolyn May Bingham**(Donald Ramsey, Mazeres, Briggs)*Generation Polynomials for Finite Semigroups***Leslie Irene Hale**(S.A. Patil, Buck, Ramsey)*The Distribution and the Moments of Order Statistics of a Mulivariate Normal Population with Common Correlation and Their Applications*

### 1972

**Ching-ta Kao**(James Harris, Savage, Buck)*Comparison of a Pece Method and Liniger and Willoughby's Method for Solving Stiff Ordinary Differential Equations***Natavarbhai Gordhanbhai Patel**(James Harris, Ramsey, Buck)*Study of Cyclic Methods for Solving Ordinary Differential Equations***Arvindkumar Kantilal Shah**(Richard Savage, Briggs, Mazeres)*Some Partition Identities and Generating Functions***David Allen Stults**(Reggie Mazeres, Savage, Dixon)*Properties of E-Inversive and Rectangular Semigroups*

### 1971

**Margaret Clift Hairston**(Richard Savage, Briggs, Mazeres)*Periodicity of the Fibonacci Sequence***Richard Lee Melhorn**(Richard Savage, Briggs, Mazeres)*Fibonacci-Type Sequence***Devendra C. Patel**(S.A. Patil, Savage, Dixon)*Distribution of Maximum Likelyhood Estimator of p in the Multivariate Normal Population Having Uniform and Circular Covariance Matrix***Pi-choa Ko**(S.A. Patil, Savage, Mazeres)*Applications of Waiting Time to Counting Processes***Edward Wu-Chieh Tseng**(S.A. Patil, Jones, Dixon)*The Minimum Variance Unbiased Estimators for Some Special Density Function and Their Variances***James Martin Stephens White, Jr.**(Bobby Wilder, Briggs, Mazeres, VanCleave)*Reflexive Linear Spaces***Nancy Wei-dz Wong**(Edmond Dixon, Mazeres, Savage)*K-Commutativity of Matrices***Felix R. Hoots, Jr.**(Robert Briggs III, Dixon, Swong)*A Comparison of Covering Properties in Moore Spaces***James Richard Harville**(Edmond Dixon, Savage, Ward)*K-Commutativity in a Ring*

### 1970

**J. B. Patel**(S.A. Patil, Swong, Jones)*On the Minimum Unbiased Estimator of Common Variance of Multivariate Normal Population***Francis Ermon Little**(Robert Briggs III, Dixon, Ward)*A Study of Compactness in Metric Spaces***Gerald Walter Haynes**(Bobby Wilder, Briggs, Savage, VanCleave)*Finite Dimensional Linear Spaces*

### 1969

**Josefino W. Y. Huang**(Edmond Dixon, Swong, Patil)*K-Commutative Matrices***Shirley H. Liao**(S.A. Patil, Savage, Dixon)*The Exact Distribution of the Ratio of the Mean to the Square Root of the Sum of Squares From a Normal Population***Te-chi Wu**(S.A. Patil, Savage, Dixon, Swong)*A Tetravariate Generalization of Student's t-Distribution***Shyue C. Tao**(S. A. Patil, Swong, Dixon)*Inversion of Certain Matrices and Their Applications to Maximum Likelihood Estimators of Regression Coefficients***Dong Gill Lee**(Ralph Boles, Jones, Swong, Dixon)*Legendre Polynomials and Applications*

### 1968

**Franklin D. Cheatham**(Edmond Dixon, Savage, Ward)*Theorems on Semigroups***Patricia Rhea Ware Daggett**(A. R. VanCleave, Jr., Swong, Dixon)*Concerning Topological Properties of Product Spaces***Julia Ann Watts**(Edmond Dixon, Sublett, Ward)*Some Theorems on Higher Commutators in a Ring***Tony M. Hinson**(Edmond Dixon, Savage, Ward)*Determinants of Special Matrices***Leon Harold Darby**(Edmond Dixon, Mazeres, Jones)*Some Theorems on Idempotents in Various Algebraic Structures*

### 1967

**Jacob T. B. Beard, Jr.**(Edmond Dixon, Boles, Mazeres)*Maximal Matric Fields Over a Finite Field***Elzie G. McBride, Jr.**(C. G. Phipps, Dixon, Mazeres, Doran, Boles)*Hyberbolic Geometry in Two and Three Dimensions***Bethel Carlton Flatt**(Edmond Dixon, Mazeres, Ward, Boles)*Theorems on Commutator Subgroups*

### 1965

**James W. Lea, Jr.**(Cecil Phelps, Boles, Clark)*The Well-Ordering Theorem and Some Equivalents*