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Finsler's Lemma for Matrix PolynomialsJun 28 2014Finsler's Lemma charactrizes all pairs of symmetric $n \times n$ real matrices $A$ and $B$ which satisfy the property that $v^T A v>0$ for every nonzero $v \in \mathbb{R}^n$ such that $v^T B v=0$. We extend this characterization to all symmetric matrices ... More

Noncommutative Positivstellensätze for pairs representation-vectorNov 22 2010Jul 07 2013We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first consider the ... More

A nullstellensatz for partial differential equations with polynomial coefficientsAug 13 2016In this paper an equation means a homogeneous linear partial differential equation in $n$ unknown functions of $m$ variables which has real or complex polynomial coefficients. The solution set consists of all $n$-tuples of real or complex analytic functions ... More

Archimedean operator-theoretic PositivstellensätzeNov 22 2010Feb 02 2011We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz Theorem of Dritschel-Rovnyak and positivstellens\"atze of Ambrozie-Vasilescu and Scherer-Hol. We also obtain ... More

A Real Nullstellensatz for Free ModulesFeb 10 2013Jul 07 2013Let $A$ be the algebra of all $n \times n$ matrices with entries from $\RR[x_1,\ldots,x_d]$ and let $G_1,\ldots,G_m,F \in A$. We will show that $F(a)v=0$ for every $a \in \RR^d$ and $v \in \RR^n$ such that $G_i(a)v=0$ for all $i$ if and only if $F$ belongs ... More

Archimedean classes of matrices over ordered fieldsMar 14 2015Sep 03 2015Let $(F,\le)$ be an ordered field and let $A,B$ be square matrices over $F$ of the same size. We say that $A$ and $B$ belong to the same archimedean class if there exists an integer $r$ such that the matrices $r A^T A-B^T B$ and $r B^T B-A^T A$ are positive ... More

Real algebraic geometry for matrices over commutative ringsJun 26 2011Apr 29 2012We define and study preorderings and orderings on rings of the form $M_n(R)$ where $R$ is a commutative unital ring. We extend the Artin-Lang theorem and Krivine-Stengle Stellens\"atze (both abstract and geometric) from $R$ to $M_n(R)$. While the orderings ... More

A representation theorem for archimedean quadratic modules on *-ringsJul 31 2008We present a new approach to noncommutative real algebraic geometry based on the representation theory of $C^\ast$-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules ... More

Maximal quadratic modules on *-ringsJul 31 2008We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example ... More

Local linear dependence of linear partial differential operatorsNov 13 2017Jan 02 2018We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such operators is equal ... More

Strict Positivstellensätze for matrix polynomials with scalar constraintsNov 22 2010Nov 26 2010We extend Krivine's strict positivstellensatz for usual (real multivariate) polynomials to symmetric matrix polynomials with scalar constraints. The proof is an elementary computation with Schur complements. Analogous extensions of Schm\" udgen's and ... More

Formally real involutions on central simple algebrasJul 31 2008An involution $#$ on an associative ring $R$ is \textit{formally real} if a sum of nonzero elements of the form $r^# r$ where $r \in R$ is nonzero. Suppose that $R$ is a central simple algebra (i.e. $R=M_n(D)$ for some integer $n$ and central division ... More

A nullstellensatz for linear partial differential equations with polynomial coefficientsAug 13 2016Jul 14 2017In this paper an equation means a homogeneous linear partial differential equation in $n$ unknown functions of $m$ variables which has real or complex polynomial coefficients. The solution set consists of all $n$-tuples of real or complex analytic functions ... More

CW type of inverse limits and function spacesAug 21 2007Given CW complexes X and Y, let map(X,Y) denote the space of continuous functions from X to Y with the compact open topology. The space map(X,Y) need not have the homotopy type of a CW complex. Here the results of an extensive investigation of various ... More

Homotopy characterization of ANR mapping spacesAug 27 2007Aug 29 2007Let Y be an absolute neighborhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let map(X,Y) denote the space of continuous maps from X to Y with the compact open topology. It is shown that if X is a CW complex then map(X,Y) ... More

A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programmingJun 11 2009Jul 07 2013A method for computing global minima of real multivariate polynomials based on semidefinite programming was developed by N. Z. Shor, J. B. Lasserre and P. A. Parrilo. The aim of this article is to extend a variant of their method to noncommutative symmetric ... More

Cesium bright matter-wave solitons and soliton trainsFeb 08 2019A setup for studying bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is studied. Formation of soliton ... More

Output stages inside a negative feedback loop: application to a low-voltage three-phase DC-AC converter for educational purposesNov 18 2013The circuit presented in this paper aims at providing three 40 Vpp 50Hz AC voltages sources with 120-degree phase separation between them. This is a fully analogue circuit that uses standard, low-cost electronic components without resorting to a microcontroller ... More

Induced quadratic modules in $*$-algebrasJan 06 2012Jun 28 2014Positivity in $\ast$-algebras can be defined either algebraically, by quadratic modules, or analytically, by $\ast$-representations. By the induction procedure for $\ast$-representations we can lift the analytical notion of positivity from a $\ast$-subalgebra ... More

Theoretical analysis of the performance of a diffraction grating back- reflector in infrared-sensitive solar cellsNov 19 2008The increase of cell efficiency resulting from using a diffraction grating as a back reflector is investigated. An enhancement coefficient is introduced as a figure of merit that accounts for the ability of the rear grating to increase the generation ... More

LC sine-wave oscillators using general-purpose voltage operational-amplifiersJul 18 2005It has been found that some text-books show LC-oscillators that may not work as assumed. Thus, the typical example showing a LC-oscillator driven by a voltage operational-amplifier is simply wrong. The difficulty stems from the fact that such oscillators ... More

Light trapping within the grooves of 1D diffraction gratings under monochromatic and sunlight illuminationMar 31 2011Apr 01 2011The Rayleigh-Modal method is used to calculate the electromagnetic field within the grooves of a perfectly conducting, rectangular-shaped 1D diffraction grating. An \emph{enhancement coefficient} ($\eta$) is introduced in order to quantify such an energy ... More

On the Real Multidimensional Rational K-Moment ProblemJul 12 2008Oct 19 2009We present a solution to the real multidimensional rational K-moment problem, where K is defined by finitely many polynomial inequalities. More precisely, let S be a finite set of real polynomials in X=(X_1,...,X_n) such that the corresponding basic closed ... More

Hardware In The Loop Simulator in UAV Rapid Development Life CycleApr 24 2008Field trial is very critical and high risk in autonomous UAV development life cycle. Hardware in the loop (HIL) simulation is a computer simulation that has the ability to simulate UAV flight characteristic, sensor modeling and actuator modeling while ... More

On $q$-normal operators and quantum complex planeJan 15 2011Jan 20 2011For $q>0$ let $\cA$ denote the unital $\ast$-algebra with generator $x$ and defining relation $xx^\ast=qxx^\ast$. Based on this algebra we study $q$-normal operators, the complex $q$-moment problem, positive elements and sums of squares.

On the Hodge conjecture for $q$-complete manifoldsApr 08 2014Jul 04 2014We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$ of any complex ... More

Algorithms of the LDA model [REPORT]Jul 01 2013We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm -- Collapsed ... More

Closures of quadratic modulesApr 09 2009We consider the problem of determining the closure of a quadratic module M in a commutative R-algebra with respect to the finest locally convex topology. This is of interest in deciding when the moment problem is solvable and in analyzing algorithms for ... More

Positivity in power series ringsJul 31 2008We extend and generalize the results of Scheiderer (2006) on the representation of polynomials nonnegative on two-dimensional basic closed semialgebraic sets. Our extension covers some situations where the defining polynomials do not satisfy the transversality ... More

Sums of squares and moment problems in equivariant situationsAug 01 2008We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group $G$ over $\R$ acting on an affine $\R$-variety $V$, we consider the induced dual action on the coordinate ring $\R[V]$ and on the linear dual ... More

Unmanned Aerial Vehicle Instrumentation for Rapid Aerial Photo SystemApr 24 2008This research will proposed a new kind of relatively low cost autonomous UAV that will enable farmers to make just in time mosaics of aerial photo of their crop. These mosaics of aerial photo should be able to be produced with relatively low cost and ... More

Automated Flight Test and System Identification for Rotary Wing Small Aerial Platform using Frequency Responses AnalysisApr 24 2008This paper proposes an autopilot system that can be used to control the small scale rotorcraft during the flight test for linear-frequency-domain system identification. The input frequency swept is generated automatically as part of the autopilot control ... More

On the minimum value of sum-Balaban indexJan 10 2017We consider extremal values of sum-Balaban index among graphs on $n$ vertices. We determine that the upper bound for the minimum value of the sum-Balaban index is at most $4.47934$ when $n$ goes to infinity. For small values of $n$ we determine the extremal ... More

A Fluid Dynamics Calculation of Sputtering from a Cylindrical Thermal SpikeSep 13 2001The sputtering yield, Y, from a cylindrical thermal spike is calculated using a two dimensional fluid dynamics model which includes the transport of energy, momentum and mass. The results show that the high pressure built-up within the spike causes the ... More

Electron swaps and the stopping of protons by hydrogenAug 20 2009The relevance of the electronic swap in the stopping process of proton by hydrogen is investigated. To this end, the Classical Trajectory Monte-Carlo method is used to calculate the k-stopping cross-section, i.e. the stopping cross-section given the occurrence ... More

A Non-commutative Real Nullstellensatz Corresponds to a Non-commutative Real Ideal; AlgorithmsMay 20 2011Feb 11 2012This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes related to our ... More

Ultrafast jamming of electrons into an amorphous entangled stateMar 01 2018New emergent states of matter in quantum systems may be created under non-equilibrium conditions if - through many body interactions - its constituents order on a timescale which is shorter than the time required for the system to reach thermal equilibrium. ... More

Theoretical Modeling of the Non-equilibrium Amorphous State in 1T-TaS$_2$Jan 21 2019Jan 30 20191T-TaS$_2$ is known for it's remarkably complex phase diagram and it's unique long-lived metastable hidden (H) state. Recently, a novel metastable state has been discovered using higher fluences for photoexcitation than in the case of the H state. The ... More

Correlated Configurational States and a Quantum Charge Liquid in Layered Metallic DichalcogenidesJan 08 2019Two-dimensional metallic dichalcogenides display diverse charge ordering phenomena, but the mechanisms for the formation of low-temperature commensurate order have proven surprisingly controversial. Fermi surface instabilities, the electron-phonon interaction, ... More