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On the isometric embedding problem for length metric spacesJan 28 2016We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. By an "approximate isometric embedding" we mean an embedding which preserves the energy functional ... More

Power-Central Elements in Tensor Products of Symbol AlgebrasOct 21 2013Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r be cyclic extensions of F such that k_1\otimes_F\cdots \otimes_F k_r is a field. We investigate conditions under which A is a tensor product of symbol algebras where each k_i is in ... More

Real hyperbolic hyperplane complements in the complex hyperbolic planeSep 07 2016Sep 16 2016This paper studies Riemannian manifolds of the form $M \setminus S$, where $M^4$ is a complete four dimensional Riemannian manifold with finite volume whose metric is modeled on the complex hyperbolic plane $\mathbb{C} \mathbb{H}^2$, and $S$ is a compact ... More

Regularity and the Cesaro-Nevai classNov 16 2007We consider OPRL and OPUC with measures regular in the sense of Ullman-Stahl-Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on $[-2,2]$ implies $\lim_{N\to\infty} N^{-1} [\sum_{n=1}^N (a_n-1)^2 ... More

On the Hankel transform of C-fractionsDec 14 2012Dec 17 2012We study the Hankel transforms of sequences whose generating function can be expressed as a C-fraction. In particular, we relate the index sequence of the non-zero terms of the Hankel transform to the powers appearing in the monomials defining the C-fraction. ... More

Zeros of OPUC and Long Time Asymptotics of Schur and Related FlowsOct 31 2006We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: $\alpha_j(t)=(1- |\alpha_j(t)|^2) (\alpha_{j+1}(t)-\alpha_{j-1}(t))$ for $\alpha_{-1}(t)= 1$ boundary conditions and $n=0,1,2,...$, with initial condition $\alpha_j(0)\in ... More

Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficientsDec 16 2004We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to ... More

Laurent Biorthogonal Polynomials and Riordan ArraysNov 10 2013We show that Laurent biorthogonal polynomials whose defining three-term recurrence have constant coefficients have coefficient arrays that are Riordan arrays. For each such family of Laurent biorthogonal polynomials we associate in a natural way a family ... More

Some conjectures on the ratio of Hankel transforms for sequences and series reversionJan 17 2007For each element of certain families of integer sequences, we study the term-wise ratios of the Hankel transforms of three sequences related to that element by series reversion. In each case, the ratios define well-known sequences, and in one case, we ... More

Analogs of the M-Function in the Theory of Orthogonal Polynomials on the Unit CircleNov 04 2003We show that the multitude of applications of the Weyl-Titchmarsh m-function leads to a multitude of different functions in the theory of orthogonal polynomials on the unit circle that serve as analogs of the m-function.

Self-force: Computational StrategiesJan 29 2015Jun 02 2015Building on substantial foundational progress in understanding the effect of a small body's self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of ... More

An orthogonal polynomial coefficient formula for the Hankel transformMar 30 2011We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest, deriving interesting ... More

On the passage from local to global in number theoryJul 01 1993The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).

CMV matrices: Five years afterMar 03 2006CMV matrices are the unitary analog of Jacobi matrices; we review their general theory.

Orthogonal polynomials on the unit circle: New resultsMay 06 2004We announce numerous new results in the theory of orthogonal polynomials on the unit circle.

The Christoffel-Darboux KernelJun 09 2008A review of the uses of the CD kernel in the spectral theory of orthogonal polynomials, concentrating on recent results.

Divisibility of partial zeta function values at zero for degree 2p extensionsJan 07 2013Let K/k be an Abelian extension of number fields, S be a set of places of k, and p be an odd prime number. We continue an earlier investigation of the author into the values at zero of the S-imprimitive partial zeta functions of K/k. An earlier result ... More

Invariant number triangles, eigentriangles and Somos-4 sequencesJul 27 2011Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invariant sequences that arise are conjectured to have Hankel transforms ... More

Approximating continuous maps by isometriesJul 31 2015Jan 28 2016The Nash-Kuiper Theorem states that the collection of $C^1$-isometric embeddings from a Riemannian manifold $M^n$ into $\mathbb{E}^N$ is $C^0$-dense within the collection of all smooth 1-Lipschitz embeddings provided that $n < N$. This result is now known ... More

A Note on d-Hankel Transforms, Continued Fractions, and Riordan ArraysFeb 13 2017The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued fractions in the ... More

On the $f$-Matrices of Pascal-like Triangles Defined by Riordan ArraysMay 06 2018We define and characterize the $f$-matrices associated to Pascal-like matrices that are defined by ordinary and exponential Riordan arrays. These generalize the face matrices of simplices and hypercubes. Their generating functions can be expressed simply ... More

Generalized Eulerian Triangles and Some Special Production MatricesMar 27 2018We show how some special production matrices may be used to define families of generalized Eulerian triangles. We furthermore show that these generalized Eulerian triangles are the coefficient arrays of polynomials which are the moments of families of ... More

On the halves of a Riordan array and their antecedentsJun 14 2019Jun 29 2019Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common context, showing that one may be obtained from the other. We also ask and ... More

Decomposable and Indecomposable Algebras of Degree 8 and Exponent 2Apr 09 2013We study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let $B$ be a biquaternion ... More

3x+1 dynamics on rationals with fixed denominatorApr 13 2002We propose the existence of an infinite class of exact analogues of the 3x+1 conjecture for rational numbers with fixed denominators. For some other denominators, there are several attracting cycles, which exhibit scaling and covariance phenomena. We ... More

Meromorphic Szego functions and asymptotic series for Verblunsky coefficientsFeb 23 2005We prove that the Szeg\H{o} function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$ to the exponential ... More

Variants of the Riemann zeta functionAug 08 2017Aug 11 2017We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the family of functions ... More

Comparing two matrices of generalized moments defined by continued fraction expansionsNov 27 2013We study two matrices $N$ and $M$ defined by the parameters of equivalent $S$- and $J$-continued fraction expansions, and compare them by examining the product $N^{-1}M$. Using examples based on the Catalan numbers, the little Schr\"oder numbers and powers ... More

Hecke groups, linear recurrences, and Kepler limitsMar 01 2019We study the linear fractional transformations in the Hecke group $G(\Phi)$ where $\Phi$ is either root of $x^2 - x -1$ (the larger root being the "golden ratio" $\phi = 2 \cos \frac {\pi}5$.) Let $g \in G(\Phi)$ and let $z$ be a generic element of the ... More

The $1/k$-Eulerian Polynomials as Moments, via Exponential Riordan ArraysMar 27 2018Using the theory of exponential Riordan arrays, we show that the $1/k$-Eulerian polynomials are moments for a paramaterized family of orthogonal polynomials. In addition, we show that the related Savage-Viswanathan polynomials are also moments for appropriate ... More

Three Études on a sequence transformation pipelineMar 16 2018We study a sequence transformation pipeline that maps certain sequences with rational generating functions to permutation-based sequence families of combinatorial significance. Many of the number triangles we encounter can be related to simplicial objects ... More

On the $r$-shifted central triangles of a Riordan arrayJun 04 2019Let $A$ be a proper Riordan array with general element $a_{n,k}$. We study the one parameter family of matrices whose general elements are given by $a_{2n+r, n+k+r}$. We show that each such matrix can be factored into a product of a Riordan array and ... More

Graphs of partitions and Ramanujan's tau-functionMay 05 2004May 31 2004The invariant z_{lambda} attached to a partition lambda sits in the denominator of the Girard-Waring solution to Newton's symmetric function relations. We interpret Ramanujan's tau-function in terms of z_lambda, and interpret z_lambda in terms of the ... More

The Classical Moment Problem as a Self-Adjoint Finite Difference OperatorJun 08 1999This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence ... More

Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large DeviationsAug 17 2016Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS Notices

A new approach to inverse spectral theory, I. Fundamental formalismJun 17 1999Nov 01 1999We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\"odinger operator determines the potential. Our approach is an analog ... More

Unitaries Permuting Two Orthogonal ProjectionsMar 16 2017Mar 27 2017Let $P$ and $Q$ be two orthogonal projections on a separable Hilbert space, $\calH$. Wang, Du and Dou proved that there exists a unitary, $U$, with $UPU^{-1} =Q, \quad UQU^{-1} = P$ if and only if $\dim(\ker P \cap \ker(1-Q)) = \dim(\ker Q \cap \ker(1-P))$ ... More

OPUC on One FootFeb 23 2005We present an expository introduction to orthogonal polynomials on the unit circle.

Equilibrium measures and capacities in spectral theoryNov 16 2007This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to ... More

Simple closed form Hankel transforms based on the central coefficients of certain Pascal-like trianglesMay 06 2006We study the Hankel transforms of sequences related to the central coefficients of a family of Pascal-like triangles. The mechanism of Riordan arrays is used to elucidate the structure of these transforms.

Schrodinger Operators with Purely Discrete SpectrumOct 17 2008We prove $-\Delta +V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|\{x\mid V(x)<M\}|<\infty$ and various extensions.

Simplicial isometric embeddings of indefinite metric polyhedraNov 03 2012Aug 05 2015In this paper, isometric embedding results of Greene, Gromov and Rokhlin are extended to what are called "indefinite metric polyhedra". Two definitions for an indefinite metric polyhedron are given, an intuitive definition and a more useful definition. ... More

The $γ$-Vectors of Pascal-like Triangles Defined by Riordan ArraysApr 13 2018We define and characterize the $\gamma$-matrix associated to Pascal-like matrices that are defined by ordinary and exponential Riordan arrays. We also define and characterize the $\gamma$-matrix of the reversions of these triangles, in the case of ordinary ... More

On a transformation of Riordan moment sequencesFeb 09 2018We define a transformation that associates certain exponential moment sequences with ordinary moment sequences in a natural way. The ingredients of this transformation are series reversion, the Sumudu transform (a variant of the Laplace transform), and ... More

On the restricted Chebyshev-Boubaker polynomialsFeb 13 2017Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev-Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and ... More

Eulerian-Dowling Polynomials as Moments, Using Riordan ArraysFeb 13 2017Using the theory of exponential Riordan arrays, we show that the Eulerian-Dowling polynomials are moments for a paramaterized family of orthogonal polynomials. In addition, we show that the related Dowling and the Tanny-Dowling polynomials are also moments ... More

Eulerian polynomials as moments, via exponential Riordan arraysMay 16 2011Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials, which we characterize ... More

Weak convergence of CD kernels and applicationsJul 17 2007We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, ... More

Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequencesJun 14 2019We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships between the moments of these orthogonal polynomials, the moments of the ... More

The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More

Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.

Irreducible polynomials in F_q[x] versus 1 - qz in C[z]Dec 20 2006Dec 21 2006Let q be a prime power and N_n count degree-n monic irreducible polynomials in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small |z|.

Aizenman's Theorem for Orthogonal Polynomials on the Unit CircleNov 17 2004For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if \[ \mathbb{E} \biggl(\int\frac{d\theta}{2\pi} \biggl|\biggl(\frac{\mathcal{C} + e^{i\theta}}{\mathcal{C} ... More

Tosio Kato's Work on Non-Relativistic Quantum Mechanics: An OutlineOct 19 2017Based at a talk given at the Kato Centennial Symposium in Sept. 2017, this article discusses the scientific life and some of the scientific work of T. Kato.

Riordan Pseudo-Involutions, Continued Fractions and Somos $4$ SequencesJul 16 2018Jul 19 2018We define a three parameter family of Bell pseudo-involutions in the Riordan group. The defining sequences have generating functions that are expressible as continued fractions. We indicate that the Hankel transforms of the defining sequences, and of ... More

Sigmoid functions and exponential Riordan arraysFeb 13 2017Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group of exponential ... More

Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circleJun 01 2006We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.

Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicityMar 18 2005We show that the parameters $a_n, b_n$ of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n+1} + O(R^{-2n}) $ where $1 < |\mu_j| < R$ for $j\leq ... More

On a theorem of Kac and GilbertMay 06 2004We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum.

Involutions on tensor products of quaternion algebrasDec 03 2015We study possible decompositions of totally decomposable algebras with involution, that is, tensor products of quaternion algebras with involution. In particular, we are interested in decompositions in which one or several factors are the split quaternion ... More

Riordan arrays, orthogonal polynomials as moments, and Hankel transformsFeb 04 2011Taking the examples of Legendre and Hermite orthogonal polynomials, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials in terms of their associated Riordan arrays. We use these means to calculate ... More

Power series, the Riordan group and Hopf algebrasJun 05 2017The Riordan group, along with its constituent elements, Riordan arrays, has been a tool for combinatorial exploration since its inception in 1991. More recently, this group has made an appearance in the area of mathematical physics, where it can be used ... More

Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGOJul 10 2019This white paper describes the research and development needed over the next decade to realize "Cosmic Explorer," the U.S. node of a future third-generation detector network that will be capable of observing and characterizing compact gravitational-wave ... More

Quantum POMDPsJun 11 2014Oct 01 2014We present quantum observable Markov decision processes (QOMDPs), the quantum analogues of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent's state is represented as a quantum state and the agent can choose a superoperator ... More

Elastic Solver: Balancing Solution Time and Energy ConsumptionMay 23 2016Combinatorial decision problems arise in many different domains such as scheduling, routing, packing, bioinformatics, and many more. Despite recent advances in developing scalable solvers, there are still many problems which are often very hard to solve. ... More

The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problemsApr 03 1999Apr 29 1999In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random impurities, level ... More

Analytical On-shell Calculation of Low Energy Higher Order ScatteringSep 02 2016We demonstrate that the use of analytical on-shell methods involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles (photons or gravitons) can be used to evaluate one-loop contributions ... More

GDH2000 Convenor's Report: Spin PolarizabilitiesOct 10 2000The subject of low energy polarized Compton scattering from the proton, which is characterized by phenomenological spin-polarizabilities, is introduced and connection is made to new theoretical and experimental developments which were reported to this ... More

Low Energy Compton Scattering and Nucleon StructureJun 12 1998The low energy virtual Compton scattering process $eN\to e'N\gamma$ offers a new and potentially high resolution window on nucleon sturcture via measurement of so-called generalized polarizabilities (GPs). We present calculations of GPs within heavy baryon ... More

Is SU(3) Chiral Perturbation Theory an Effective Field Theory?Jun 12 1998We argue that the difficulties associated with the convergence properties of conventional SU(3) chiral perturbation theory can be ameliorated by use of a cutoff, which suppresses the model-dependent short distance effects in such calculations.

Low Energy Tests of Chiral SymmetryJun 04 1996The present status of low energy test of chiral invariance via chiral perturbation theory is reviewed, both in the meson and baryon sectors, and future prospects are discussed.

Chiral Anomaly and $γ3π$Dec 18 1995Measurement of the $\gamma 3\pi$ process has revealed a possible conflict with what should be a solid prediction generated by the chiral anomaly. We show that inclusion of appropirate energy-momentum dependence in the matrix element reduces the discrepancy. ... More

Dynamic DNA Processing: A Microcode Model of Cell DifferentiationDec 17 2013A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a unique set of allowed ... More

Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phasesFeb 13 2015Apr 09 2015We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to ... More

Quantum measurement, detection and localityJun 27 2007According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the interaction between ... More

Nearly Ordinary Galois Deformations over Arbitrary Number FieldsAug 17 2007Jan 16 2008Let K be an arbitrary number field, and let rho: Gal(Kbar/K) -> GL_2(E) be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of rho. When K is totally real and rho is modular, results ... More

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetimeOct 28 2016If a small "particle" of mass $\mu M$ (with $\mu \ll 1$) orbits a black hole of mass $M$, the leading-order radiation-reaction effect is an $\mathcal{O}(\mu^2)$ "self-force" acting on the particle, with a corresponding $\mathcal{O}(\mu)$ "self-acceleration" ... More

Viscoelastic response of quantum Hall fluids in a tilted fieldNov 20 2018Jan 17 2019In this paper, we examine the viscoelastic properties of integer quantum Hall (IQH) states in a tilted magnetic field. In particular, we explore to what extent the tilted-field system behaves like a two-dimensional electron gas with anisotropic mass in ... More

GALEX: Galaxy Evolution ExplorerMar 25 2005We review recent scientific results from the Galaxy Evolution Explorer with special emphasis on star formation in nearby resolved galaxies.

Reducing quadratic forms by kneading sequencesAug 20 2014Dec 08 2014We introduce an invertible operation on finite sequences of positive integers and call it "kneading". Kneading preserves three invariants of sequences -- the parity of the length, the sum of the entries, and one we call the "alternant". We provide a bijection ... More

End-symmetric continued fractions and quadratic congruencesJun 30 2014Dec 08 2014We show that for a fixed integer $n \neq \pm2$, the congruence $x^2 + nx \pm 1 \equiv 0 \pmod{\alpha}$ has the solution $\beta$ with $0 < \beta < \alpha$ if and only if $\alpha/\beta$ has a continued fraction expansion with sequence of quotients having ... More

Free Torus Actions and Two-Stage SpacesSep 26 2003We prove the toral rank conjecture of Halperin in some new cases. Our results apply to certain elliptic spaces that have a two-stage Sullivan minimal model, and are obtained by combining new lower bounds for the dimension of the cohomology and new upper ... More

Refined class number formulas and Kolyvagin systemsSep 22 2009We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime $p$, each side of Darmon's conjectured formula (indexed by positive integers $n$) is "almost" a $p$-adic Kolyvagin ... More

Orientations and p-Adic AnalysisApr 30 2009May 04 2009Matthew Ando produced power operations in the Lubin-Tate cohomology theories and was able to classify which complex orientations were compatible with these operations. The methods used by Ando, Hopkins and Rezk to classify orientations of topological ... More

Reflection Groups and Polytopes over Finite Fields, IIIJul 26 2007When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often be the automorphism ... More

On a Question of Glasby, Praeger, and Xia in Characteristic $2$Mar 14 2014Recently, Glasby, Praeger, and Xia asked for necessary and sufficient conditions for the `Jordan partition' $\lambda(m,n,p)$ to be standard. Previously we gave such conditions when $p$ is any odd prime. Here we give such conditions when $p=2$. Our main ... More

Generators for Decompositions of Tensor Products of Modules associated with standard Jordan partitionsAug 07 2015If $K$ is a field of finite characteristic $p$, $G$ is a cyclic group of order $q=p^\alpha$, $U$ and $W$ are indecomposable $KG$-modules with $\dim U=m$ and $\dim W=n$, and $\lambda(m,n,p)$ is a standard Jordan partition of $ m n$, we describe how to ... More

Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operatorsJul 28 1999Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators

How Large is the "Natural" Magnetic Moment?Jul 17 2006The "natural" magntic moment of a particle of spin S is generally assumed to be that given by the Belinfante conjecture and has the value g=1/S for its gyromagnetic ratio. Thus, for the spin 1/2 electron we find the Dirac value $g_e=2$. However, in the ... More

Hadronic Parity Violation: an Analytic ApproachJul 18 2006Using a recent reformulation of the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT), we show how predictions for parity-violating observables in low-energy light hadronic systems can be understood in an analytic ... More

Quantum Corrections to the Reissner-Nordstrom and Kerr-Newman Metrics: Spin 1Jul 12 2006A previous evaluation of one-photon loop corrections to the energy-momentum tensor has been extended to particles with unit spin and speculations are presented concerning general properties of such forms.

Hyperon Physics-a Personal OverviewOct 16 1999A range of issues in the field of hyperon physics is presented, together with an assessment of where important challenges remain.

Majorization: Here, There and EverywhereJan 28 2008The appearance of Marshall and Olkin's 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years this continues ... More

Low-energy effective theory in the bulk for transport in a topological phaseJul 10 2014Feb 15 2015We construct a low-energy effective action for a two-dimensional non-relativistic topological (i.e.\ gapped) phase of matter in a continuum, which completely describes all of its bulk electrical, thermal, and stress-related properties in the limit of ... More

Evolutions, Symbolic Squares, and Fitting IdealsNov 15 1995Given a reduced local algebra $T$ over a suitable ring or field $k$ we study the question of whether there are nontrivial algebra surjections $R\to T$ which induce isomorphisms $\Omega_{R/k}\otimes T \to \Omega_{T/k}$. Such maps, called evolutions, arise ... More

Observation of the Halo of NGC 3077 Near the "Garland" Region Using the Hubble Space TelescopeMar 07 2001We report the detection of upper main sequence stars and red giant branch stars in the halo of an amorphous galaxy, NGC3077. The observations were made using Wide Field Planetary Camera~2 on board the Hubble Space Telescope. The red giant branch luminosity ... More

Deviations from tribimaximal mixing due to the vacuum expectation value misalignment in A_4 modelsMar 11 2010Jun 10 2010The addition of an A_4 family symmetry and extended Higgs sector to the Standard Model can generate the tribimaximal mixing pattern for leptons, assuming the correct vacuum expectation value alignment of the Higgs scalars. Deviating this alignment affects ... More

Neutrino Mass Sum-rules in Flavor Symmetry ModelsJul 29 2010Sep 27 2010Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be probed in three ... More

Who Gets the Job and How are They Paid? Machine Learning Application on H-1B Case DataApr 24 2019In this paper, we use machine learning techniques to explore the H-1B application dataset disclosed by the Department of Labor (DOL), from 2008 to 2018, in order to provide more stylized facts of the international workers in US labor market. We train ... More

Unveiling the Sigma-Discrepancy in IR-Luminous Mergers I: Dust & DynamicsJan 08 2010Jan 13 2010Mergers in the local universe present a unique opportunity for studying the transformations of galaxies in detail. Presented here are recent results, based on multi-wavelength, high-resolution imaging and medium resolution spectroscopy, which demonstrate ... More