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Szegö's Theorem and its Probabilistic DescendantsAug 01 2011Mar 05 2012The theory of orthogonal polynomials on the unit circle (OPUC) dates back to Szeg\"o's work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his two-volume book [Si4], [Si5], the survey paper (or summary of the ... More

Sects, rooks, pyramids, partitions and paths for type DIII clansJul 20 2019Borel subgroup orbits of the classical symmetric space $SO_{2n}/GL_n$ are parametrized by $(n,n)$-clans of type $DIII$. We describe explicit bijections between such clans, diagonally symmetric rook placements, certain pairs of minimally intersecting set ... More

Multivariate prediction and matrix Szegö theoryMar 05 2012Following the recent survey by the same author of Szeg\"o's theorem and orthogonal polynomials on the unit circle (OPUC) in the scalar case, we survey the corresponding multivariate prediction theory and matrix OPUC (MOPUC).

Voronoi means, moving averages, and power seriesJul 08 2016We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A strong law of ... More

Estimating parameter uncertainty in binding-energy models by the frequency-domain bootstrapMar 26 2017We propose using the frequency-domain bootstrap (FDB) to estimate errors of modeling parameters when the modeling error is itself a major source of uncertainty. Unlike the usual bootstrap or the simple $\chi^2$ analysis, the FDB can take into account ... More

Noncommutative Regularization for the Practical ManAug 08 1999It has been proposed that the noncommutative geometry of the "fuzzy" 2-sphere provides a nonperturbative regularization of scalar field theories. This generalizes to compact Kaehler manifolds where simple field theories are regularized by the geometric ... More

CTRW Pathways to the Fractional Diffusion EquationAug 01 2001The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable probability densities. ... More

Angular size and emission time scales of relativistic fireballsSep 18 1997The detection of delayed X-ray, optical and radio emission, ``afterglow,'' associated with gamma-ray bursts (GRBs) is consistent with models, where the bursts are produced by relativistic expanding blast waves, driven by expanding fireballs at cosmological ... More

Extra galactic sources of high energy neutrinosFeb 08 2005The main goal of the construction of large volume, high energy neutrino telescopes is the detection of extra-Galactic neutrino sources. The existence of such sources is implied by observations of ultra-high energy, >10^{19} eV, cosmic-rays (UHECRs), the ... More

Does the detection of X-ray emission from SN1998bw support its association with GRB980425?Jan 26 2004Mar 04 2004We show that the recent identification of X-ray emission from SN1998bw is naturally explained as synchrotron emission from a shock driven into the wind surrounding the progenitor by a mildly relativistic shell ejected by the supernova, the existence of ... More

Can high energy neutrino annihilation on relic neutrinos generate the observed highest energy cosmic-rays?Apr 02 1998Annihilation of high energy, $\sim 10^{21}$eV, neutrinos on big bang relic neutrinos of $\sim 1$eV mass, clustered in the Galactic halo or in a nearby galaxy cluster halo, has been suggested to generate, through hadronic Z decay, high energy nucleons ... More

Geometric Quantization of Vector BundlesAug 27 1998Dec 16 2000I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection ... More

The Correspondence between Geometric Quantization and Formal Deformation QuantizationNov 08 1998Using the classification of formal deformation quantizations, and the formal, algebraic index theorem, I give a simple proof as to which formal deformation quantization (modulo isomorphism) is derived from a given geometric quantization.

Profinite groups, profinite completions and a conjecture of MooreMay 11 2004Let R be any ring (with 1), \Gamma a group and R\Gamma the corresponding group ring. Let H be a subgroup of \Gamma of finite index. Let M be an R\Gamma -module, whose restriction to RH is projective. Moore's conjecture: Assume for every nontrivial element ... More

The structure of tame minimal dynamical systemsSep 18 2006A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of $\beta \N$, or it is a "tame" topological space whose topology is determined ... More

Dynamic Adaptive Network IntelligenceNov 19 2015Accurate representational learning of both the explicit and implicit relationships within data is critical to the ability of machines to perform more complex and abstract reasoning tasks. We describe the efficient weakly supervised learning of such inferences ... More

Hamiltonian Gravity and Noncommutative GeometryMay 30 1996May 08 1997A version of foliated spacetime is constructed in which the spatial geometry is described as a time dependent noncommutative geometry. The ADM version of the gravitational action is expressed in terms of these variables. It is shown that the vector constraint ... More

COSMOLOGICAL GAMMA RAY BURSTS AND THE HIGHEST ENERGY COSMIC RAYSMay 18 1995We discuss a scenario in which the highest energy cosmic rays (CR's) and cosmological $\gamma$-ray bursts (GRB's) have a common origin. This scenario is consistent with the observed CR flux above $10^{20}\text{eV}$, provided that each burst produces similar ... More

Gamma-ray burst after-glow: Confirming the cosmological fireball modelMay 29 1997Sep 22 1997The recent detection of delayed X-ray and optical emission, ``afterglow,'' associated with gamma-ray bursts (GRBs) supports models, where the bursts are produced by relativistic expanding blastwaves, ``fireballs,'' at cosmological distances. The detection ... More

Variational Estimators for Bayesian Optimal Experimental DesignMar 13 2019Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information ... More

Variational Bayesian Optimal Experimental DesignMar 13 2019Jun 03 2019Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019May 17 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

The Role of Dust in Producing the Cosmic Infrared BackgroundMay 21 2001The extragalactic background light (EBL), exclusive of the cosmic microwave background, consists of the cumulative radiative output from all energy sources in the universe since the epoch of recombination. Most of this energy is released at ultraviolet ... More

The Detection of Cold Dust in Cas A: Evidence for the Formation of Metallic Needles in the EjectaJan 07 2004Jan 08 2004Recently, Dunne et al. (2003) obtained 450 and 850 micron SCUBA images of CasA, and reported the detection of 2-4 M_sun of cold, 18K, dust in the remnant. Here we show that their interpretation of the observations faces serious difficulties. Their inferred ... More

The Structure of Noncommutative DeformationsApr 12 2005Jul 13 2006Noncommutatively deformed geometries, such as the noncommutative torus, do not exist generically. I showed in a previous paper that the existence of such a deformation implies compatibility conditions between the classical metric and the Poisson bivector ... More

A Cohomological Perspective on Algebraic Quantum Field TheoryDec 15 2016Dec 18 2017Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

The Evolution of the Elemental Abundances in the Gas and Dust Phases of the GalaxyJul 02 1997Jul 03 1997We present models for the evolution of the elemental abundances in the gas and dust phases of the interstellar medium (ISM) of our Galaxy by generalizing standard models for its dynamical and chemical evolution. In these models, the stellar birthrate ... More

Quantum Gravitational Collapse of a Charged Dust ShellDec 21 1993Dec 22 1993A simple self gravitating system --- a thin spherical shell of charged pressureless matter --- is naively quantized as a test case of quantum gravitational collapse. The model is interpreted in terms of an inner product on the positive energy states. ... More

On cohomology rings of infinite groupsFeb 24 2005Dec 17 2008Let R be any ring (with 1), \Gamma a group and R\Gamma the corresponding group ring. Let Ext_{R\Gamma}^{*}(M,M) be the cohomology ring associated to the R\Gamma-module M. Let H be a subgroup of finite index of \Gamma. The following is a special version ... More

Stable Equilibrium Based on Lévy Statistics: Stochastic Collision Models ApproachOct 22 2003We investigate equilibrium properties of two very different stochastic collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas. For both models the equilibrium velocity distribution is a L\'evy distribution, the Maxwell distribution ... More

On fixed points of self maps of the free ballSep 01 2017Dec 24 2018In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace. We ... More

On Semi-Analytical Integration Specified for Mass Matrix of Finite ElementsJun 06 2015Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix evaluation, ... More

Translation-finite setsNov 02 2011The families of right (left) translation finite subsets of a discrete infinite group $\Gamma$ are defined and shown to be ideals. Their kernels $Z_R$ and $Z_L$ are identified as the closure of the set of products $pq$ ($p\cdot q$) in the \v{C}ech-Stone ... More

A new closed-form model for isotropic elastic sphere including new solutions for the free vibrations problemNov 04 2013We develop a new closed-form model for the dynamics of an elastic and isotropic sphere and use it to derive new closed-form resonant frequencies.

Stable Equilibrium Based on Lévy Statistics: A Linear Boltzmann Equation ApproachMar 13 2003To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with ideal gas particles ... More

High Energy Neutrinos from Gamma-Ray BurstsSep 13 2000Observations suggest that gamma-ray bursts (GRBs) are produced by the dissipation of the kinetic energy of a relativistic fireball. In this talk, recent work on the production of high energy neutrinos by GRB fireballs is reviewed. A significant fraction ... More

Cosmological Origin for Cosmic Rays Above $10^{19}$ eVAug 08 1995The cosmic ray spectrum at $10^{19}{\rm eV}-10^{20}{\rm eV}$, reported by the Fly's Eye and the AGASA experiments, is shown to be consistent with a cosmological distribution of sources of protons, with a power law generation spectrum ${\rm d}\ln N/{\rm ... More

An Obstruction to Quantization of the SphereJun 20 2007Sep 06 2007In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including ... More

Completing Partial Latin Squares - Alternative ProofMay 19 2016The problem of completing a partially specified n by n Latin square is solved by an alternative proof, based on filling the rows (or diagonals) from 1 to n, using an extended form of Hall's marriage theorem.

Finite Type Invariants of Links with Fixed Linking MatrixJun 21 1999In this paper we introduce two theories of finite type invariants for framed links with fixed linking matrix. We show that these thepries are related to the theory of Vassiliev invariants of framed links. We also study the corresponding spaces of ``chord ... More

Consistent mass matrix of ten nodes tetrahedral element based on analytical integrationNov 05 2014Currently, components of consistent mass matrix are computed using various numerical integration schemes, each one alters in number of integration (Gauss) points, requires different amount of computations and possess different level of accuracy. We discuss ... More

Iron: A Key Element for Understanding the Origin and Evolution of Interstellar DustMay 06 2016The origin and depletion of iron differ from all other abundant refractory elements that make up the composition of the interstellar dust. Iron is primarily synthesized in Type Ia supernovae (SNe Ia) and in core collapse supernovae (CCSN), and is present ... More

GRB after-glow: Supporting the cosmological fireball model, constraining parameters, and making predictionsApr 13 1997Cosmological fireball models of gamma-ray bursts (GRBs) predict delayed emission, ``after-glow,'' at longer wavelengths. We present several new results regarding the model predictions, and show that X-ray to optical observations of GRB970228 and GRB970402 ... More

$RP^{[d]}$ is an equivalence relation: An enveloping semigroup proofFeb 13 2014Jan 20 2015We present a purely enveloping semigroup proof of a theorem of Shao and Ye which asserts that for an abelian group $T$, a minimal flow $(X,T)$ and any integer $d \ge 1$, the regional proximal relation of order $d$ is an equivalence relation.

On the codimension growth of G-graded algebrasAug 17 2009Nov 21 2009Let W be an associative PI-affine algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote the codimension growth of W and of the identity component W_e, respectively. We prove: exp(W) ... More

The group $\Aut(μ)$ is Roelcke precompactFeb 22 2009Following a similar result of Uspenskij on the unitary group of a separable Hilbert space we show that with respect to the lower (or Roelcke) uniform structure the Polish group $G= \Aut(\mu)$, of automorphisms of an atomless standard Borel probability ... More

The structure of tame minimal dynamical systems for general groupsJul 01 2017We use the structure theory of minimal dynamical systems to show that, for a general group $\Gamma$, a tame, metric, minimal dynamical system $(X, \Gamma)$ has the following structure: \begin{equation*} \xymatrix {& \tilde{X} \ar[dd]_\pi \ar[dl]_\eta ... More

Short proofs of theorems of Malyutin and MargulisMay 15 2016Jun 03 2016The Ghys-Margulis alternative asserts that a subgroup $G$ of homeomorphisms of the circle which does not contain a free subgroup on two generators must admit an invariant probability measure. Malyutin's theorem classifies minimal actions of $G$. We present ... More

The Cantor set of linear orders on N is the universal minimal S_\infty-systemApr 10 2002Each topological group $G$ admits a unique universal minimal dynamical system $(M(G),G)$. When $G$ is a non-compact locally compact group the phase space $M(G)$ of this universal system is non-metrizable. There are however topological groups for which ... More

Quantization of Multiply Connected ManifoldsApr 17 2003The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the symplectic form ... More

A Groupoid Approach to QuantizationDec 13 2006Sep 18 2007Many interesting C*-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I define polarizations for Lie ... More

Beyond Lebesgue and Baire IV: Density topologies and a converse Steinhaus-Weil TheoremJun 30 2016The theme here is category-measure duality, in the context of a topological group. One can often handle the (Baire) category case and the (Lebesgue, or Haar) measure cases together, by working bi-topologically: switching between the original topology ... More

Sequential regular variation: extensions of Kendall's theoremJan 21 2019Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is, with sequential ... More

Set Theory and the AnalystJan 27 2018This survey is motivated by specific questions arising in the similarities and contrasts between (Baire) category and (Lebesgue) measure -- category-measure duality and non-duality, as it were. The bulk of the text is devoted to a summary, intended for ... More

Design of Computer Experiments for Optimization, Estimation of Function Contours, and Related ObjectivesJan 22 2016A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs. For instance, ... More

Uniformity and self-neglecting functions: II. Beurling Regular Variation and the class ΓJul 19 2013Beurling slow variation is generalized to Beurling regular variation. A Uniform Convergence Theorem, not previously known, is proved for those functions of this class that are measurable or have the Baire property. This permits their characterization ... More

The Steinhaus-Weil property: its converse, Solecki amenability and subcontinuityJun 30 2016The Steinhaus-Weil theorem that concerns us here is the `interior points' property -- that in a topological group a non-negligible set S has the identity as an interior point of $SS^{-1}$. There are various converses; the one that mainly concerns us is ... More

New insight into EM radiation from spinning dust and its influence on the Cosmic Microwave BackgroundFeb 01 2019Jun 19 2019Dust is ubiquitous in the Universe and its influence on the observed Electromagnetic (EM) radiation needs to be correctly addressed. In recent years it became clear that scattering of EM radiation from interstellar dust grains could change the local properties ... More

Dimension walks on $\mathbb{S}^d \times \mathbb{R}$Sep 11 2018We verify that the established one- and two-step recurrences for positive definite functions on spheres extend to the spatio-temporal case.

Early emission from type Ia supernovaeAug 29 2011A unique feature of deflagration-to-detonation (DDT) white dwarf explosion models of SNe of type Ia is the presence of a strong shock wave propagating through the outer envelope. We consider the early emission expected in such models, which is produced ... More

Imploding ignition waves: I. one dimensional analysisAug 23 2011Jun 02 2012We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R_c. An approximate analytic expression for R_c is derived ... More

A regional compound Poisson process for hurricane and tropical storm damageFeb 12 2016In light of intense hurricane activity along the U.S. Atlantic coast, attention has turned to understanding both the economic impact and behaviour of these storms. The compound Poisson-lognormal process has been proposed as a model for aggregate storm ... More

New insight into EM radiation from spinning dust and its influence on the Cosmic Microwave BackgroundFeb 01 2019Dust is ubiquitous in the Universe and its influence on the observed Electromagnetic (EM) radiation needs to be correctly addressed. In recent years it became clear that scattering of EM radiation from interstellar dust grains could change the local properties ... More

Gaussian random fields on the sphere and sphere cross lineDec 05 2018Aug 20 2019We review the Dudley integral for the Belyaev dichotomy applied to Gaussian processes on spheres, and discuss the approximate (or restricted) continuity of paths in the discontinuous case. We discuss also the spatio-temporal case, of sphere cross line. ... More

Phonon Random Walks: Predicting Heat Spreading in Many-particle SystemsJun 15 2016Sep 29 2016Inspired by quantum walks (QW), here we propose the concept of classical phonon random walks (PRW), with which we show that, the densities related to ballistic heat transport in many-body Hamiltonian systems with various phonon dispersions can be predicted. ... More

UV/Optical emission from the expanding envelopes of type II supernovaeJul 13 2016The early part of a supernova (SN) light-curve is dominated by radiation escaping from the expanding shock-heated progenitor envelope. For polytropic Hydrogen envelopes, the properties of the emitted radiation are described by simple analytic expressions ... More

Intersection disjunctions for reverse convex setsJan 08 2019Jan 24 2019We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases ... More

A new method for numerical inversion of the Laplace transformJul 28 1998A formula of Doetsch ({\em Math. Zeitschr.} {\bf 42}, 263 (1937)) is generalized and used to numerically invert the one-sided Laplace transform ${\hat C}(\beta)$. The necessary input is only the values of ${\hat C}(\beta)$ on the positive real axis. The ... More

Digital Version of Green`s Theorem and its Application to The Coverage Problem in Formal VerificationSep 07 2003We present a novel scheme to the coverage problem, introducing a quantitative way to estimate the interaction between a block and its enviroment.This is achieved by setting a discrete version of Green`s theorem, specially adapted for Model Checking based ... More

HAMR Thermal Reliability via Inverse Electromagnetic DesignJul 12 2014Heat-Assisted Magnetic Recording (HAMR) has promise to allow for data writing in hard disks of beyond 1 Tb/in2 areal density, by temporarily heating the area of a single datum to its Curie temperature while simultaneously applying a magnetic field from ... More

The Cumulative Bakground of High-Energy Neutrinos from Starburst GalaxiesJan 30 2006Apr 21 2006We show that starburst galaxies convert efficiently cosmic-rays into pions, which in turn decay into high-energy neutrinos and photons. The cumulative background of GeV neutrinos is 10^{-7}GeV/cm^2/s/sr. Its extrapolation to higher neutrino energies depends ... More

Asymptotic self-similar solutions with a characteristic time-scaleFeb 20 2010Aug 18 2010For a wide variety of initial and boundary conditions, adiabatic one dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, $R$, diverges or tends to zero. It is commonly ... More

The early UV/Optical emission from core-collapse supernovaeFeb 18 2010Apr 13 2013We derive a simple approximate model describing the early, hours to days, UV/optical supernova emission, which is produced by the expansion of the outer <~0.01 solar mass part of the shock-heated envelope, and precedes the optical emission driven by radioactive ... More

Constraints on the Local Sources of Ultra High-Energy Cosmic RaysSep 22 2008Ultra high-energy cosmic rays (UHECRs) are believed to be protons accelerated in magnetized plasma outflows of extra-Galactic sources. The acceleration of protons to ~10^{20} eV requires a source power L>10^{47} erg/s. The absence of steady sources of ... More

Prompt optical emission from residual collisions in GRB outflowsNov 15 2007Jan 03 2008The prompt gamma-ray emission in gamma-ray bursts is believed to be produced by internal shocks within a relativistic unsteady outflow. The recent detection of prompt optical emission accompanying the prompt gamma-ray emission appears to be inconsistent ... More

Distribution of Time-Averaged Observables for Weak Ergodicity BreakingJul 26 2007We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, ... More

Simple G-graded algebras and their polynomial identitiesJul 23 2011Nov 15 2011Let G be any group and F an algebraically closed field of characteristic zero. We show that any G-graded finite dimensional associative G-simple algebra over F is determined up to a G-graded isomorphism by its G-graded polynomial identities. This result ... More

On regular G-gradingDec 03 2012Mar 08 2013Let A be an associative algebra over an algebraically closed field F of characteristic zero and let G be a finite abelian group. Regev and Seeman introduced the notion of a regular G-grading on A, namely a grading A= {\Sigma}_{g in G} A_g that satisfies ... More

Circular orders, ultrahomogeneity and topological groupsMar 17 2018Jan 23 2019We study topological groups $G$ for which the universal minimal $G$-system $M(G)$, or the universal irreducible affine $G$-system $IA(G)$ are tame. We call such groups intrinsically tame and convexly intrinsically tame. These notions are generalized versions ... More

On doubly minimal systems and a question regarding product recurrenceAug 12 2015We show that a doubly minimal system $X$ has the property that for every minimal system $Y$ the orbit closure of any pair $(y,x) \in Y \times X$ is either $Y \times X$ or it has the form $\Gamma_\pi = \{(\pi(x),x) : x \in X\}$ for some factor map $\pi: ... More

On fixed point theorems and nonsensitivityJul 29 2010Nov 02 2010Sensitivity is a prominent aspect of chaotic behavior of a dynamical system. We study the relevance of nonsensitivity to fixed point theory in affine dynamical systems. We prove a fixed point theorem which extends Ryll-Nardzewski's theorem and some of ... More

Isomorphic extensions and applicationsFeb 24 2015If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ is also a measure-theoretic isomorphism. We consider the case when the systems ... More

Norm formulas for finite groups and induction from elementary abelian subgroupsFeb 09 2004Apr 21 2005It is known that the norm map N_G for a finite group G acting on a ring R is surjective if and only if for every elementary abelian subgroup E of G the norm map N_E for E is surjective. Equivalently, there exists an element x_G in R with N_G(x_G) = 1 ... More

Signed partitions - A balls into urns approachMar 07 2019Using Reiner's definition of Stirling numbers of type B of the second kind, we provide a 'balls into urns' approach for proving a generalization of a well-known identity concerning the classical Stirling numbers of the second kind: $x^n=\sum\limits_{k=0}^n{S(n,k)[x]_k}.$ ... More

Minimal hyperspace actions of homeomorphism groups of h-homogeneous spacesJul 07 2011May 07 2012Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysis of what we call stable collections of subsets of a finite set, ... More

Constraining High-Energy Cosmic Neutrino Sources: Implications and ProspectsJul 06 2016We consider limits on the local ($z=0$) density ($n_0$) of extragalactic neutrino sources set by the nondetection of steady high-energy neutrino sources producing $\gtrsim30$ TeV muon multiplets in the present IceCube data, taking into account the redshift ... More

An Investigation of the Chung-Feller TheoremOct 05 2004In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.

High Energy Astrophysical Neutrinos: the Upper Bound is RobustFeb 18 1999Dec 02 2000We elucidate the physical basis for the upper bound on high energy neutrino fluxes implied by the observed cosmic ray flux. We stress that the bound is valid for neutrinos produced either by p,gamma reactions or by p-p(n) reactions in sources which are ... More

A Sub-Relativistic Shock Model for the Radio Emission of SN1998bwAug 13 1998SN1998bw is the most luminous radio supernova ever observed. Previous discussions argued that its exceptional radio luminosity, 4e38 erg/s, must originate from a highly relativistic shock which is fully decoupled from the supernova ejecta. Here we present ... More

Shock breakout theoryJul 05 2016Apr 24 2017The earliest supernova (SN) emission is produced when the optical depth of the plasma lying ahead of the shock, which ejects the envelope, drops below c/v, where v is the shock velocity. This "breakout" may occur when the shock reaches the edge of the ... More

The upstream magnetic field of GRB shocksMar 16 2006Jul 02 2006Gamma-ray burst (GRB) afterglow emission is believed to be produced by synchrotron emission of electrons accelerated to high energy by a relativistic collisionless shock propagating into a weakly magnetized plasma. Afterglow observations have been used ... More

Fluctuations in the Radio Background from Intergalactic Synchrotron EmissionJul 05 2000The shocks produced in the intergalactic medium during large-scale structure formation accelerate a population of highly relativistic electrons which emit synchrotron radiation due to intergalactic magnetic fields. In a previous paper (Loeb & Waxman 2000) ... More

Nonthermal emission from clusters of galaxiesMar 12 2009Feb 22 2010We show that the spectral and radial distribution of the nonthermal emission of massive, M>10^{14.5}M_sun, galaxy clusters (GCs) may be approximately described by simple analytic expressions, which depend on the GC thermal X-ray properties and on two ... More

Time averaged Einstein relation and fluctuating diffusivities for the Lévy walkNov 07 2012Feb 17 2013The L\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\bar{\delta^2}$ often used to analyze single particle tracking experiments. ... More

Pronounced Effect of pn-Junction Dimensionality on Tunnel Switch Threshold ShapeSep 01 2011Oct 30 2014Designing tunneling junctions with abrupt on-off characteristics and high current densities is critical for many different devices including backward diodes and tunneling field effect transistors (TFETs). It is possible to get a sharp, high conductance ... More

Weakly non-ergodic Statistical PhysicsMar 16 2008We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the ... More

Occupation times on a comb with ramified teethFeb 02 2014We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows Lamperti's distribution, ... More

Uniformly recurrent subgroupsFeb 20 2014We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in a work of M. Abert, Y. Glasner and B. Virag. Our main results are as follows. (i) It was ... More

Circularly ordered dynamical systemsAug 17 2016Aug 30 2016We study topological properties of circularly ordered dynamical systems and prove that every such system is representable on a Rosenthal Banach space, hence, is also tame. We derive some consequences for topological groups. We show that several Sturmian ... More