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Linear Matrix Inequality Representation of SetsJun 11 2003This article concerns the question: which subsets of ${\mathbb R}^m$ can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. ... More

Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and SetsSep 25 2007Dec 07 2008A set $S\subseteq \re^n$ is called to be {\it Semidefinite (SDP)} representable if $S$ equals the projection of a set in higher dimensional space which is describable by some Linear Matrix Inequality (LMI). The contributions of this paper are: (i) For ... More

Semidefinite Representation of Convex SetsMay 28 2007Jul 21 2008Let $S =\{x\in \re^n: g_1(x)\geq 0, ..., g_m(x)\geq 0\}$ be a semialgebraic set defined by multivariate polynomials $g_i(x)$. Assume $S$ is convex, compact and has nonempty interior. Let $S_i =\{x\in \re^n: g_i(x)\geq 0\}$, and $\bdS$ (resp. $\bdS_i$) ... More

Every free basic convex semi-algebraic set has an LMI representationAug 29 2009Aug 30 2011The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and systems engineering. ... More

Free convex sets defined by rational expressions have LMI representationsSep 15 2012Nov 21 2012Suppose p is a symmetric matrix whose entries are polynomials in freely noncommutating variables and p(0) is positive definite. Let D(p) denote the component of zero of the set of those g-tuples X of symmetric matrices (of the same size) such that p(X) ... More

Structured Semidefinite Representation of Some Convex SetsFeb 13 2008Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems are in fact expressible as LMIs. For optimization purposes it can also be ... More

Arveson extreme points span free spectrahedraJun 23 2018Let $ SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices. Given tuples $X=(X_1, \dots, X_g) \in SM_{n_1}(\mathbb{R})^g$ and $Y=(Y_1, \dots, Y_g) \in SM_{n_2}(\mathbb{R})^g$, a matrix convex combination of $X$ and $Y$ is a sum ... More

A Semidefinite Approach for Truncated K-Moment ProblemsMay 02 2011Sep 06 2012A truncated moment sequence (tms) of degree d is a vector indexed by monomials whose degree is at most d. Let K be a semialgebraic set.The truncated K-moment problem (TKMP) is: when does a tms y admit a positive Borel measure supported? This paper proposes ... More

Applications of Realizations (aka Linearizations) to Free ProbabilityNov 17 2015A powerful technique in free probability called ``linearization'' allows one to compute probability distributions of functions $f$ of independent random $N \times N$ matrices as $N \to \infty$. In the free probability context this linearization has been ... More

Non-commutative polynomials with convex level slicesDec 09 2015Jun 20 2017Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric matrices with the result p(A,X) a square matrix. The polynomial p is symmetric ... More

The possible shapes of numerical rangesApr 23 2011Which convex subsets of the complex plane are the numerical range W(A of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that for any A there exists a symmetric matrix B of the same size such that ... More

Determinant Expansions of Signed Matrices and of Certain JacobiansFeb 29 2008This paper treats two topics: matrices with sign patterns and Jacobians of certain mappings. The main topic is counting the number of plus and minus coefficients in the determinant expansion of sign patterns and of these Jacobians. The paper is motivated ... More

Geometry of free loci and factorization of noncommutative polynomialsAug 17 2017Apr 02 2018The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if $Z_n(f)$ is eventually irreducible. ... More

Proper Analytic Free MapsApr 08 2010Dec 01 2010This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free variables. Analytic ... More

The convex Positivstellensatz in a free algebraFeb 23 2011Jun 11 2012Given a monic linear pencil L in g variables let D_L be its positivity domain, i.e., the set of all g-tuples X of symmetric matrices of all sizes making L(X) positive semidefinite. Because L is a monic linear pencil, D_L is convex with interior, and conversely ... More

Sign patterns for chemical reaction networksApr 20 2009Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector consisting of real-valued ... More

The Tracial Hahn-Banach Theorem, Polar Duals, Matrix Convex Sets, and Projections of Free SpectrahedraJul 30 2014Feb 29 2016This article investigates matrix convex sets and introduces their tracial analogs which we call contractively tracial convex sets. In both contexts completely positive (cp) maps play a central role: unital cp maps in the case of matrix convex sets and ... More

Matrix Convex Hulls of Free Semialgebraic SetsNov 21 2013Dec 29 2013This article resides in the realm of the noncommutative (free) analog of real algebraic geometry - the study of polynomial inequalities and equations over the real numbers - with a focus on matrix convex sets $C$ and their projections $\hat C$. A free ... More

Analytic mappings between noncommutative pencil ballsAug 05 2009Dec 01 2010In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate ... More

Free Convex Algebraic GeometryApr 15 2013This chapter is a tutorial on techniques and results in free convex algebraic geometry and free real algebraic geometry (RAG). The term free refers to the central role played by algebras of noncommutative polynomials R<x> in free (freely noncommuting) ... More

The matricial relaxation of a linear matrix inequalityMar 03 2010Mar 01 2012Given linear matrix inequalities (LMIs) L_1 and L_2, it is natural to ask: (Q1) when does one dominate the other, that is, does L_1(X) PsD imply L_2(X) PsD? (Q2) when do they have the same solution set? Such questions can be NP-hard. This paper describes ... More

Semidefinite programming in matrix unknowns which are dimension freeDec 29 2011One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as variables, and the formulas naturally contain non-commutative polynomials ... More

Non-commutative varieties with curvature having bounded signatureFeb 01 2012The signature(s) of the curvature of the zero set V of a free (non-commutative) polynomial is defined as the number of positive and negative eigenvalues of the non-commutative second fundamental form on V determined by p. With some natural hypotheses, ... More

Non-commutative polynomials with convex level slicesDec 09 2015Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric matrices with the result p(A,X) a square matrix. The polynomial p is symmetric ... More

Free analysis, convexity and LMI domainsJun 11 2012This paper concerns free analytic maps on noncommutative domains. These maps are free analogs of classical holomorphic functions in several complex variables, and are defined in terms of noncommuting variables amongst which there are no relations - they ... More

Homotopy methods for counting reaction network equilibriaNov 09 2007Sep 09 2008Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values ... More

Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraintsMar 17 2007We show that the quadratic matrix equation $VW + \eta (W)W = I$, for given $V$ with positive real part and given analytic mapping $\eta$ with some positivity preserving properties, has exactly one solution $W$ with positive real part. We point out the ... More

Non-Commutative Harmonic and Subharmonic PolynomialsSep 26 2009The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x=(x_1,...,x_g). The Laplacian Lap[p,h] of p is a polynomial in x and in a noncommuting variable h. When all variables commute we have Lap[p,h]=h^2\Delta_x ... More

Bianalytic free maps between spectrahedra and spectraballsApr 25 2018Dec 01 2018Linear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unknowns, called free LMIs, are central to the theories of completely positive ... More

Real Nullstellensatze and *-ideals in *-algebrasFeb 19 2013Feb 20 2013Let F denote either the real or complex field. An ideal I in the free *-algebra F<x,x*> in g freely noncommuting variables and their formal adjoints is a *-ideal if I = I*. When a real *-ideal has finite codimension, it satisfies a strong Nullstellensatz. ... More

Free Semidefinite Representation of Matrix Power FunctionsMay 18 2013Oct 09 2014Consider the matrix power function X^p defined over the cone of positive definite matrices S^{n}_{++}. It is known that X^p is convex over S^{n}_{++} if p is in [-1,0] or [1,2] and X^p is concave over S^{n}_{++} if p is in [0,1]. We show that the hypograph ... More

Free bianalytic maps between spectrahedra and spectraballs in a generic settingNov 26 2017Jan 22 2019Given a tuple $E=(E_1,\dots,E_g)$ of $d\times d$ matrices, the collection of those tuples of matrices $X=(X_1,\dots,X_g)$ (of the same size) such that $\| \sum E_j\otimes X_j\|\le 1$ is called a spectraball $\mathcal B_E$. Likewise, given a tuple $B=(B_1,\dots,B_g)$ ... More

Circular Free SpectrahedraApr 19 2016This paper considers matrix convex sets invariant under several types of rotations. It is known that matrix convex sets that are free semialgebraic are solution sets of Linear Matrix Inequalities (LMIs); they are called free spectrahedra. We classify ... More

Non-Commutative Partial Matrix ConvexityApr 03 2008Let $p$ be a polynomial in the non-commuting variables $(a,x)=(a_1,...,a_{g_a},x_1,...,x_{g_x})$. If $p$ is convex in the variables $x$, then $p$ has degree two in $x$ and moreover, $p$ has the form $p = L + \Lambda ^T \Lambda,$ where $L$ has degree at ... More

Bianalytic Maps Between Free SpectrahedraApr 18 2016Dec 06 2018Linear matrix inequalities (LMIs) $I_d + \sum_{j=1}^g A_jx_j + \sum_{j=1}^g A_j^*x_j^*\succeq0$ play a role in many areas of applications and the set of solutions to one is called a spectrahedron. LMIs in (dimension--free) matrix variables model most ... More

Noncommutative polynomials nonnegative on a variety intersect a convex setJul 31 2013Mar 15 2014By a result of Helton and McCullough, open bounded convex free semialgebraic sets are exactly open (matricial) solution sets D_L of a linear matrix inequality (LMI) L(X)>0. This paper gives a precise algebraic certificate for a polynomial being nonnegative ... More

Noncommutative Plurisubharmonic Polynomials Part I: Global AssumptionsDec 30 2010Jan 14 2011We consider symmetric polynomials, p, in the noncommutative free variables (x_1, x_2, ..., x_g). We define the noncommutative complex hessian of p and we call a noncommutative symmetric polynomial noncommutative plurisubharmonic if it has a noncommutative ... More

Measures with zeros in the inverse of their moment matrixFeb 12 2007Aug 27 2008We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure $\mu$ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having ... More

Bianalytic Maps Between Free SpectrahedraApr 18 2016Aug 27 2016Linear matrix inequalities (LMIs) $I_d + \sum_{j=1}^g A_jx_j + \sum_{j=1}^g A_j^*x_j^*\succeq0$ play a role in many areas of applications and the set of solutions to one is called a spectrahedron. LMIs in (dimension--free) matrix variables model most ... More

Noncommutative ball mapsSep 28 2008In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate ... More

Extreme points of matrix convex sets, free spectrahedra and dilation theoryNov 30 2016For matrix convex sets a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of strength, the core notions of "Euclidean" extreme points, "matrix" extreme points, ... More

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta DistributionsDec 03 2014May 07 2016An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V from H to K such that C=V^*TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor $\vartheta(d)$, ... More

The noncommutative Waring problemMar 14 2019This paper poses and treats a noncommutative version of the classical Waring problem for polynomials. That is, for a homogeneous \nc \ polynomial $p$, we find a condition equivalent to $p$ being expressible as sums of powers of homogeneous \nc \ polynomials. ... More

Positive polynomials in scalar and matrix variables, the spectral theorem and optimizationDec 04 2006We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several complex variables ... More

Convex entire noncommutative functions are polynomials of degree two or lessJan 24 2015This paper concerns matrix "convex" functions of (free) noncommuting variables, $x = (x_1, \ldots, x_g)$. Helton and McCullough showed that a polynomial in $x$ which is matrix convex is of degree two or less. We prove a more general result: that a function ... More

Classification of All Noncommutative Polynomials Whose Hessian Has Negative Signature One and A Noncommutative Second Fundamental FormMar 11 2009Every symmetric polynomial p(x)=p(x_1,...,x_g) (with real coefficients) in g noncommuting variables x_1, ..., x_g can be written as a sum and difference of squares of noncommutative polynomials. Let s(p), the negative signature of p, denote the minimum ... More

On real one-sided ideals in a free algebraAug 23 2012Apr 14 2013In classical and real algebraic geometry there are several notions of the radical of an ideal I. There is the vanishing radical defined as the set of all real polynomials vanishing on the real zero set of I, and the real radical defined as the smallest ... More

Algebras, Synchronous Games and Chromatic Numbers of GraphsMar 02 2017We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game, this leads ... More

Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting VariablesDec 04 2012Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non-commutative polynomial p(X,Y) in two k x k matrix variables X and Y. Algorithms ... More

Elemental Abundances in the Ejecta of Old Classical Novae from Late-Epoch Spitzer SpectraJun 18 2012We present Spitzer Space Telescope mid-infrared IRS spectra, supplemented by ground-based optical observations, of the classical novae V1974 Cyg, V382 Vel, and V1494 Aql more than 11, 8, and 4 years after outburst respectively. The spectra are dominated ... More

Searching for Cool Dust: II. Infrared Imaging of the OH/IR Supergiants, NML Cyg, VX Sgr, S Per and the Normal Red Supergiants RS Per and T PerJul 31 2017Apr 04 2018New MMT/MIRAC (9-11 {\mu}m), SOFIA/FORCAST (11-37 {\mu}m), and Herschel/PACS (70 and 160 {\mu}m) infrared (IR) imaging and photometry is presented for three famous OH/IR red supergiants (NML Cyg, VX Sgr, and S Per) and two normal red supergiants (RS Per ... More

Searching for Cool Dust in the Mid-to-Far Infrared: the Mass Loss Histories of The Hypergiants $μ$ Cep, VY CMa, IRC+10420, and $ρ$ CasDec 04 2015Dec 08 2015We present mid- and far- IR imaging of four famous hypergiant stars: the red supergiants $\mu$ Cep and VY CMa, and the warm hypergiants IRC +10420 and $\rho$ Cas. Our 11 to 37 $\mu$m SOFIA/FORCAST imaging probes cool dust not detected in visual and near-IR ... More

Noncommutative polynomials describing convex setsAug 20 2018The free closed semialgebraic set $D_f$ determined by a hermitian noncommutative polynomial $f$ is the closure of the connected component of $\{(X,X^*)\mid f(X,X^*)>0\}$ containing the origin. When $L$ is a hermitian monic linear pencil, the free closed ... More

The 3D Morphology of VY Canis Majoris. I The Kinematics of the EjectaFeb 27 2007Images of the complex circumstellar nebula associated with the famous red supergiant VY CMa show evidence for multiple and asymmetric mass loss events over the past 1000 yrs. Doppler velocities of the arcs and knots in the ejecta showed that they are ... More

Pressure-induced Spin-Peierls to Incommensurate Charge-Density-Wave Transition in the Ground State of TiOClAug 04 2009The ground state of the spin-Peierls system TiOCl was probed using synchrotron x-ray diffraction on a single-crystal sample at T = 6 K. We tracked the evolution of the structural superlattice peaks associated with the dimerized ground state as a function ... More

The Early Spectrophotometric Evolution of V1186 Scorpii (Nova Scorpii 2004 #1)May 04 2007We report optical photometry and optical through mid-infrared spectroscopy of the classical nova V1186 Sco. This slowly developing nova had an complex light curve with multiple secondary peaks similar to those seen in PW Vul. The time to decline 2 magnitudes, ... More

Massive Star Formation in the LMC. I. N159 and N160 ComplexesNov 23 2016We present images and spectral energy distributions (SEDs) of massive young stellar objects (YSOs) in three star-forming H II regions of the Large Magellanic Cloud: N159A, N159 Papillon, and N160. We use photometry from SOFIA/FORCAST at 25.3--37.1 um ... More

Analysis of Rapidity Gap Cuts in Diffractive DISMay 31 1999The requirement of a large pseudo-rapidity gap to select diffractive DIS events at HERA restricts the kinematically accessible region of phase space for a significant range of $Q^2$, $\beta$ and $\xpom$. Consequences of this include a breakdown of $\xpom$-factorization ... More

A very luminous, highly extinguished, very fast nova - V1721 AquilaeApr 15 2011Fast novae are primarily located within the plane of the Galaxy, slow novae are found within its bulge. Because of high interstellar extinction along the line of sight many novae lying close to the plane are missed and only the brightest seen. One nova ... More

Log-symmetric regression models for correlated errors with an application to mortality dataOct 18 2018Log-symmetric regression models are particularly useful when the response variable is continuous, strictly positive and asymmetric. In this paper, we proposed a class of log-symmetric regression models in the context of correlated errors. The proposed ... More

Polarized neutron scattering studies of the kagome lattice antiferromagnet KFe3(OH)6(SO4)2Aug 19 2009We report polarized neutron scattering studies of spin-wave excitations and spin fluctuations in the S=5/2 kagome lattice antiferromagnet KFe3(OH)6(SO4)2 (jarosite). Inelastic polarized neutron scattering measurements at 10 K on a single crystal sample ... More

Evolution of the commensurate and incommensurate magnetic phases of the S = 3/2 kagome staircase Co3V2O8 in an applied fieldJul 25 2011Nov 30 2011Single crystal neutron diffraction studies have been performed on the S = 3/2 kagome staircase compound Co3V2O8 with a magnetic field applied along the magnetization easy-axis (H || a). Previous zero field measurements [Y. Chen, et al., Phys. Rev. B 74, ... More

High-flux beam source for cold, slow atoms or moleculesAug 15 2005Aug 15 2005We demonstrate and characterize a high-flux beam source for cold, slow atoms or molecules. The desired species is vaporized using laser ablation, then cooled by thermalization in a cryogenic cell of buffer gas. The beam is formed by particles exiting ... More

Spin Correlations in the Geometrically Frustrated Pyrochlore Tb2Mo2O7Jul 14 2008We report neutron scattering studies of the spin correlations of the geometrically frustrated pyrochlore Tb2Mo2O7 using single crystal samples. This material undergoes a spin-freezing transition below Tg~24 K, similar to Y2Mo2O7, and has little apparent ... More

The Unexpected Spectrum of the Innermost Ejecta of the Red Hypergiant VY CMaMar 20 2019HST/STIS spectra of the small clumps and filaments closest to the central star in VY CMa reveal that the very strong K I emission and TiO and VO molecular emission, long thought to form in a dusty circumstellar shell, actually originate in a few small ... More

CK Vul: a smorgasbord of hydrocarbons rules out a 1670 nova (and much else besides)Dec 07 2015We present observations of CK Vul obtained with the Spitzer Space Telescope. The infrared spectrum reveals a warm dust continuum with nebular, molecular hydrogen and HCN lines superimposed, together with the "Unidentified Infrared" (UIR) features. The ... More

Magnetic transitions in the topological magnon insulator Cu(1,3-bdc)Mar 02 2016Jun 02 2016Topological magnon insulators are a new class of magnetic materials that possess topologically nontrivial magnon bands. As a result, magnons in these materials display properties analogous to those of electrons in topological insulators. Here, we present ... More

Absence of a static in-plane magnetic moment in the "hidden-order" phase of URu$_2$Si$_2$Mar 18 2013Aug 07 2013We have carried out a careful magnetic neutron scattering study of the heavy fermion compound \URuSi\ to probe the possible existence of a small magnetic moment parallel to tetragonal basal plane in the "hidden-order" phase. This small in-plane component ... More

Correlated impurities and intrinsic spin liquid physics in the kagome material HerbertsmithiteDec 21 2015Low energy inelastic neutron scattering on single crystals of the kagome spin liquid compound ZnCu3(OD)6Cl2 (Herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers E < 0.8 meV (~J/20). The momentum dependence ... More

Using radiative energy losses to constrain the magnetisation and magnetic reconnection rate at the base of black hole jetsOct 26 2016We calculate the severe radiative energy losses which occur at the base of black hole jets using a relativistic fluid jet model, including in-situ acceleration of non-thermal leptons by magnetic reconnection. Our results demonstrate that including a self-consistent ... More

Generalised unitarity for dimensionally regulated amplitudes within FDFJan 21 2016We review the Four-Dimensional-Formulation variant of the Four-Dimensional-Helicity scheme, by showing two applications of this regularisation scheme. The first one is the computation of one-loop helicity amplitudes, for which we present preliminary results ... More

What does photon energy tell us about cellphone safety?Apr 26 2011It has been argued that cellphones are safe because a single microwave photon does not have enough energy to break a chemical bond. We show that cellphone technology operates in the classical wave limit, not the single photon limit. Based on energy densities ... More

Simple MaxEnt Models for Food Web Degree DistributionsJan 08 2009Degree distributions have been widely used to characterize biological networks including food webs, and play a vital role in recent models of food web structure. While food webs degree distributions have been suggested to follow various functional forms, ... More

Muonium Lifetime and Heavy Quark DecaysMar 05 2004Environmental effects on the muon lifetime are described. A general theorem on the cancellation of bound state phase space suppression and final state interaction enhancement is illustrated for muonium and muonic atoms. Lessons from those bound muon examples ... More

Transverse Momentum Structure of Diffractive DIS ModelsOct 13 1999The transverse momentum distribution of the diffractive final state provides an interesting test of models of diffractive deep-inelastic scattering at HERA. We present a comparison of several colour-singlet exchange models with thrust transverse momentum ... More

Proof of Xiong's conjectured refinement of Euler's partition theoremAug 11 2016In a recent preprint, Xinhua Xiong conjectured a refinement of Euler's partition theorem that partitions with distinct parts are equinumerous with those into odd parts. His conjecture applies to all moduli and generalizes a result of Pak and Postnikov ... More

High Performance Algorithms for Quantum Gravity and CosmologyMay 11 2018Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or graphs. After ... More

Differential forms canonically associated to even-dimensional compact conformal manifoldsNov 15 2002Feb 27 2003On a 6-dimensional, conformal, oriented, compact manifold $M$ without boundary, we compute a whole family of differential forms $\Omega_6(f,h)$ of order 6, with $f,h \in C^\infty(M).$ Each of these forms will be symmetric on $f,$ and $h,$ conformally ... More

The Structure of Models of Second-order Set TheoriesApr 25 2018This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories. The main results ... More

Families of major index distributions: closed forms and unimodalityAug 03 2018Closed forms for $f_{\lambda,i} (q) := \sum_{\tau \in SYT(\lambda) : des(\tau) = i} q^{maj(\tau)}$, the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a large collection ... More

SN2010U -- a Luminous Nova in NGC 4214May 24 2010The luminosity, light curve, post--maximum spectrum, and lack of a progenitor on deep pre-outburst images suggest that SN 2010U was a luminous, fast nova. Its outburst magnitude is consistent with that for a fast nova using the Maximum Magnitude-Rate ... More

Future prospects for inference on solar-type starsSep 28 2011We discuss prospects for asteroseismic inference on solar-type stars, in particular opportunities that are being made possible by the large ensemble of exquisite-quality Kepler data.

Precise Determination of |V{us}| from Lattice Calculations of Pseudoscalar Decay ConstantsFeb 27 2004Combining the ratio of experimental kaon and pion decay widths, Gamma(K to mu antineutrino{mu} (gamma)) / Gamma(pi to mu \antineutrino (gamma)), with a recent lattice gauge theory calculation of f{K}/f{pi} provides a precise value for the CKM quark mixing ... More

KAON 99 - Summary and PerspectiveNov 16 1999An overview of KAON 99 with commentary is presented. Emphasis is placed on the state of CKM mixing and CP violation. The Jarlskog invariant, J_{CP}, is shown to provide a useful quantitative comparison of K and B phenomenology. The potential of future ... More

Precision Electroweak Measurements and ``New Physics''Feb 12 1999The status of several precisely measured electroweak parameters is reviewed. Natural relations among them are shown to constrain the Higgs mass, m_H, as well as various ``New Physics'' effects. Indications of an anomalous Zb anti-b coupling are discussed. ... More

Determination of the QCD color factor ratio CA/CF from the scale dependence of multiplicity in three jet eventsNov 09 1999Nov 14 1999I examine the determination of the QCD color factor ratio CA/CF from the scale evolution of particle multiplicity in e+e- three jet events. I fit an analytic expression for the multiplicity in three jet events to event samples generated with QCD multihadronic ... More

CP Violation in Charged Higgs ProductionMay 13 2005I present a study estimating the amount of CP violation present in the production of charged Higgs bosons due to the presence of complex trilinear scalar couplings. I compare the results of my study with previous results for the decay. I briefly comment ... More

Optimal conditions for observing Josephson oscillations in a double-well Bose-gas condensateFeb 08 2001The Josephson oscillations between condensates in a double-well trap are known theoretically to be strongly effected by the mean field interaction in dilute atomic gases. The most important effect is that the amplitude of oscillation in the relative population ... More

The Hill and Eshelby tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostaticsJul 26 2015In 1957 Eshelby showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in a homogeneous isotropic host would feel uniform strains and stresses when uniform strains or stresses are applied in the far-field. Of specific importance is the ... More

Numerical estimation of the escaping flux of massless particles created in collisions around a Kerr black holeJan 25 2011Jun 21 2011The geodesics of massless particles produced in collisions near a rotating black hole are solved numerically and a Monte Carlo integration of the momentum distribution of the massless particles is performed to calculate the fraction that escape the black ... More

Explaining the Fermi Galactic Centre Excess in the CMSSMOct 02 2015We present an analysis of the compatibility between the Galactic Centre Excess (GCE) and the Constrained MSSM (CMSSM). We perform a global fit to the relevant experimental data including the GCE taking into account the systematic uncertainties. We find ... More

The 2-adic valuation of plane partitions and totally symmetric partitionsMar 02 2011This paper confirms a conjecture of Amdeberhan and Moll that the power of 2 dividing the number of plane partitions in an n-cube is greater than the power of 2 dividing the number of totally symmetric plane partitions in the same cube when n is even, ... More

Tunneling Through the Math Barrier: The Fledgling Physics Student's Field Guide to Essential MathematicsMay 28 2018[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe and understand ... More

One Repeat Point Gives a Closed, Unbounded Ultrafilter on {ω_1}Mar 19 2014It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.

I[omega_2] can be the nonstationary ideal on Cof(omega_1)Jul 13 2004Apr 30 2007We answer a question of Shelah by showing that it is consistent that every set of ordinals of cofinality omega_1 in I[omega_2] is nonstationary if and only if it is consistent that that there is a kappa^+ Mahlo cardinal kappa.

The part-frequency matrices of a partitionJan 05 2016A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a simple tool, ... More

Modelling the spectral energy distribution of the red giant in RS Ophiuchi: evidence for irradiationOct 30 2015We present an analysis of optical and infrared spectra of the recurrent nova RS Oph obtained during between 2006 and 2009. The best fit to the optical spectrum for 2006 September 28 gives effective temperature Tef = 3900~K for log g = 2.0, while for log ... More

Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet HerbertsmithiteFeb 04 2010Apr 06 2010The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both ... More

Recent QCD Results from LEP-1 and LEP-2Mar 12 1999A summary is given of some recent QCD results from LEP. For LEP-2, the topics include event shape measurements, determinations of the strong coupling constant, and measurements of the charged particle multiplicity distribution at the recently completed ... More

The Loop-Gas Approach to Bose-Einstein Condensation for Trapped ParticlesJun 11 1999We examine Bose-Einstein condensation (BEC) for particles trapped in a harmonic potential by considering it as a transition in the length of permutation cycles that arise from wave-function symmetry. This ``loop-gas'' approach was originally developed ... More