May 2003 arXiv papers — page 32

Girish S. Setlur

The degenerate free Fermi gas coupled to a random potential is used to compute a.c. conductivity in various dimensions. We first formally diagonalise the hamiltonian using an appropriate basis that is a functional of the disorder potential. Then we compute the a.c. conductivity at zero temperature using the Kubo formula. This a.c. conductivity is a functiona

Dirk Tasche

As a consequence of the dependence experienced in loan portfolios, the standard binomial test which is based on the assumption of independence does not appear appropriate for validating probabilities of default (PDs). The model underlying the new rules for minimum capital requirements (Basle II) is taken as a point of departure for deriving two parametric te

Magnus Kunow, Andreas Heuer

We formulate a simple harmonic mean-field model with N+1 particles and analyse the relaxation processes following a jump of one of these particles. Either the particle can jump back (single-particle route) or the other N particles adjust themselves (multi-particle route). The dynamics of this model is solved analytically in the linear response regime. Furthe

G. B. Arnold, R. A. Klemm, W. Körner, K. Scharnberg

This comment points out that the recent paper by Maki and Haas [Phys. Rev. B {\bf 67}, 020510 (2003)] is completely wrong.

Keshav N. Shrivastava

Usually the conductivity is quantized as the inverse of the resistivity, ρ=hc/ie^2, σ=ie^2/hc and the velocity versus the electric field is linear, v=μE where μis the mobility of the electrons.However,when the applied electric field exceeds a certain value, microwaves are emitted and the relation v=μE breaks down so that the velocity actually reduces as E in

T. Shimizu, T. Matsumoto, A. Goto, T. V. Chandrasekhar Rao

Evidence for the quasi one-dimensional (1D) antiferromagnetism of CuO is presented in a framework of Heisenberg model. We have obtained an experimental absolute value of the paramagnetic spin susceptibility of CuO by subtracting the orbital susceptibility separately from the total susceptibility through the $^{63}$Cu NMR shift measurement, and compared direc

Wilfried Wunderlich

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the Voronoi construction for calculations of amorphous materials or liquids in comparison to the regular arrangement of atoms in c

Yukitoshi Motome, Nobuo Furukawa

Phase diagram and critical properties are studied for three-dimensional double exchange model with and without quenched disorder. Employing the Monte Carlo method and the systematic analysis on the finite-size effect, we estimate the Curie temperature and the critical exponent as functions of the doping concentration and the strength of the random potential.

V. Schwaemmle, H. Herrmann

Barchan dunes are found where sand availability is low and wind direction quite constant. The two dimensional shear stress of the wind field and the sand movement by saltation and avalanches over a barchan dune are simulated. The resulting final shape is compared to the results of a model with a one dimensional shear stress. A characteristic edge at the cent

S. Saikin, L. Fedichkin

We examine a 31P donor electron spin in a Si crystal to be used for the purposes of quantum computation. The interaction with an uncontrolled system of 29Si nuclear spins influences the electron spin dynamics appreciably. The hyperfine field at the 29Si nuclei positions is non-collinear with the external magnetic field. Quantum operations with the electron w

Robert C. Nichol

I review here past and present research on clusters and groups of galaxies within the Sloan Digital Sky Survey (SDSS). In particular, I discuss the C4 algorithm which is designed to search for clusters within a 7-dimensional data-space, i.e., simultaneous in both color & space. The C4 catalog has a well defined selection function based on mock SDSS galaxy ca

Michael Rowan-Robinson

A sample of local galaxies for which far infrared and uv fluxes are available is used to estimate the characteristic dust extinction in galaxies and to test whether standard dust properties are plausible. Assuming galaxies can be characterized by a single dust optical depth (certainly not valid for galaxies with a dominant starburst component), the infrared

G. V. Vereshchagin

Solutions of gravitational equations of gauge theories of gravity in homogeneous isotropic world with massive scalar field are investigated in the case of flat cosmological models. Special attention is dedicated to general behavior of solutions on contraction stage. It is shown, that on expansion stage inflationary solutions are generic feature of the model.

John Ellis

In the first Lecture, the Big Bang and the Standard Model of particle physics are introduced, as well as the structure of the latter and open issues beyond it. Neutrino physics is discussed in the second Lecture, with emphasis on models for neutrino masses and oscillations. The third Lecture is devoted to supersymmetry, including the prospects for discoverin

T. Banks

This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum theory, which can be gleaned from semiclassical considerations. The constraints of a self-consistent measurement theory in su

Nicholas D. Morgan, Jeffrey A. Snyder, Louis H. Reens

We report that the Sloan Digital Sky Survey quasar SDSS J165043.44+425149.3 is gravitationally lensed into two images, based on observations obtained with the WIYN 3.5 m telescope at the Kitt Peak National Observatory. The lensed quasar, at a redshift of z=1.54, appears as two images separated by 1.2" with B-band magnitudes of 17.8 and 20.0. The lensing

M. Lattanzi, R. Ruffini, G. Vereshchagin

In addition to the problem of galaxy formation, one of the greatest open questions of cosmology is represented by the existence of an asymmetry between matter and antimatter in the baryonic component of the Universe. We believe that a net lepton number for the three neutrino species can be used to understand this asymmetry. This also implies an asymmetry in

Zheng Xiaoping, Yang Shuhua, Li Jiarong

We utilize the bulk viscosity of interacting strange quark matter to reevaluate the damping time scale. The presence of medium effect of bulk viscosity leads to a stronger damping of r-modes, which can be over an order of magnitude for realistic parameters. We find that the r-mode instability window is narrowed due to the medium effect, and hence when a puls

T. Roy Choudhury

In recent years, unprecedented progress in observational cosmology has revealed a great deal of information about the formation and evolution of structures in the universe. This, in turn, has raised many challenging issues for the theorists. In the thesis, we have addressed two such key issues, namely, (a) the formation of baryonic structures and (b) the nat

Joss Bland-Hawthorn, Lucyna Kedziora-Chudczer

The Taurus Tunable Filter (TTF) has now been in regular use for seven years on the Anglo-Australian Telescope. The instrument was also used for three years (1996--1999) on the William Herschel Telescope. We present a brief review of the different applications in order to illustrate the versatility of tunable filters in optical/IR spectrophotometric imaging.

Eric B. Ford, Scott Tremaine

The Space Interferometry Mission (SIM) will make precise astrometric measurements that can be used to detect planets around nearby stars. We have simulated SIM observations and estimated the ability of SIM to detect planets with given masses and orbital periods and measure their orbital elements. We combine these findings with an estimate of the mass and per

John C. Hodge, Michael W. Castelaz

A correlation between (1) the difference between the Tully-Fisher calculated distance and Cepheid calculated distance for a target galaxy and (2) the magnitude and distance of galaxies close to the target galaxy is described. The result is based on a sample of 31 galaxies that have published Cepheid distances with a wide range of characteristics and distance

Ramesh Narayan, Igor V. Igumenshchev, Marek A. Abramowicz

We consider an accretion flow model originally proposed by Bisnovatyi-Kogan & Ruzmaikin (1974), which has been confirmed in recent 3D MHD simulations. In the model, the accreting gas drags in a strong poloidal magnetic field to the center such that the accumulated field disrupts the axisymmetric accretion flow at a relatively large radius. Inside the disrupt

Robert N. Cahn, J. David Jackson

We consider the spectroscopy of heavy-quark light-quark mesons with a simple model based on the non-relativistic reduction of vector and scalar exchange between fermions. Four forces are induced: the spin-orbit forces on the light and heavy quark spins, the tensor force, and a spin-spin force. If the vector force is Coulombic, the spin-spin force is a contac

Eyal Markman

Let S be a K3 surface and Aut D(S) the group of auto-equivalences of the derived category of S. We construct a natural representation of Aut D(S) on the cohomology of all moduli spaces of stable sheaves (with primitive Mukai vectors) on S. The main result of this paper is the precise relation of this action with the monodromy of the Hilbert schemes S^[n] of

William Kung, Randall D. Kamien

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-indu

Andrew R. Frey, Matthew Lippert, Brook Williams

Kachru, Kallosh, Linde, & Trivedi recently constructed a four-dimensional de Sitter compactification of IIB string theory, which they showed to be metastable in agreement with general arguments about de Sitter spacetimes in quantum gravity. In this paper, we describe how discrete flux choices lead to a closely-spaced set of vacua and explore various decay ch

R. Rapp

Realistic vacuum $ππ$ interactions are employed to investigate thermal $π^+π^-$ emission spectra from the late stages of heavy-ion reactions at ultrarelativistic energies. Hadronic in-medium effects, including many-body $ρ$-meson spectral functions used earlier to describe the dilepton excess observed at CERN-SPS energies, are implemented to assess resulting

Garry Bowen, Stefano Mancini

In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted c

Daniel Z. Freedman, Umut Gursoy

Non-degenerate perturbation theory, which was used to calculate the scale dimension of operators on the gauge theory side of the correspondence, breaks down when effects of triple trace operators are included. We interpret this as an instability of excited single-string states in the dual string theory for decay into the continuum of degenerate 3-string stat

Mark Wyman, David Chernoff, Ira Wasserman

We study explosions of stars using a one-dimensional Lagrangian hydrodynamics code. We calculate how much mass is liberated as a function of the energy of explosion for a variety of pre-explosion stellar structures and for equations of state with a range of radiation-to-gas pressure ratios. The results show that simple assumptions about the amount of mass lo

I. Coddington, P. Engels, V. Schweikhard, E. A. Cornell

We directly image Tkachenko waves in a vortex lattice in a dilute-gas Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a consequence of the small but nonvanishing elastic shear modulus of the vortex-filled superfluid. The frequencies are measured for rotation rates as high as 98% of the centrifugal limit for the harmonically confined gas.

P. H. Rivera, P. A. Schulz

Recent results on magnetoresistance in a two dimensional electron gas under crossed magnetic and microwave fields show a new class of oscillations, suggesting a new kind of zero-resistance states. A complete understanding of the effect is still lacking. We consider the problem from the point of view of the electronic structure dressed by photons due to a in

Bo Feng, Xinmin Zhang

Recent released WMAP data show a low value of quadrupole in the CMB temperature fluctuations, which confirms the early observations by COBE. In this paper we consider a model of two inflatons with different masses, $V(ϕ_1,ϕ_2)={1\over 2}m_1^2ϕ_1^2 + {1 \over 2} m_2^2 ϕ_2^2$, $m_1>m_2$ and study its effects on CMB of suppressing the primordial power spectrum

Satoshi Yamaguchi

We investigate an AdS_4 x L_2 D5-brane in AdS_5 x X_5 space-time, in the context of AdS/dCFT correspondence. Here, X_5 is a Sasaki-Einstein manifold and L_2 is a submanifold of X_5. This brane has the same supersymmetry as the 3-dimensional N=1 superconformal symmetry if L_2 is a special Legendrian submanifold in X_5. In this case, this brane is supposed to

M. Derouich, S. Sahal-Brechot, P. S. Barklem

The theory of collisional depolarization of spectral lines by atomic hydrogen (Derouich et al. \cite{derouich1}) is extended to $d$ $(l$=2) atomic levels. Depolarization rates, polarization and population transfer rates are calculated and results are given as a function of the temperature. Cross sections as a function of the effective quantum number for a re

A. D. Barbour, B. Granovsky

This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges at the radius of convergence; here, this property is expressed in terms of the expectations of {\it independent} random

Rasulkhozha S. Sharafiddinov

The idea has been spoken that any of Dirac and Pauli form factors of leptonic current includes both normal and anomalous components. From this point of view, the dependence of independent parts of charge and magnetic moment is established with the use of cross sections of elastic scattering of unpolarized and longitudinal polarized electrons and their neutri

W. Mao, P. Coleman, C. Hooley, D. Langreth

Using the Majorana fermion representation of spin-1/2 local moments, we show how it is possible to directly read off the dynamic spin correlation and susceptibility from the one-particle propagator of the Majorana fermion. We illustrate our method by applying it to the spin dynamics of a non-equilibrium quantum dot, computing the voltage-dependent spin relax

S. Sharma, C. Ambrosch-Draxl

We present a full formalism for the calculation of the linear and second-order optical response for semiconductors and insulators. The expressions for the optical susceptibilities are derived within perturbation theory. As a starting point a brief background of the single and many particle Hamiltonians and operators is provided. As an example we report calcu

Adam Lewandowski, Michele Redi

We develop a renormalization group formalism for the compactified Randall-Sundrum scenario wherein the extra-dimensional radius serves as the scaling parameter. Couplings on the hidden brane scale as we move within local effective field theories with varying size of the warped extra dimension. We consider this RG approach applied to U(1) gauge theories and g

H. Jeong, M. Paternostro, M. S. Kim

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters and photodetectors. Our model enables us to simulate a quantum random walk with use of the wave nature of classical light fields. Furthermore, the proposed set-up allows the analysis of the effects of decoherence. The transition from a pu

Ulf Leonhardt

Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes.

J. E. Dubicki, C. D. Froggatt

The possibility of incorporating a chiral fourth generation into a SUSY-GUT is investigated. Precision fits to electroweak observables require us to introduce light supersymmetric particles, with masses less than mZ. These particles might also provide decay channels for fourth generation quarks of mass ~ 100 GeV. We also require tan(beta) to lie in the range

Ashoke Sen

The tachyon effective field theory describing the dynamics of a non-BPS D-$p$-brane has electric flux tube solutions where the electric field is at its critical value and the tachyon is at its vacuum. It has been suggested that these solutions have the interpretation of fundamental strings. We show that in order that an electric flux tube can `end' on a

G. A. Kozlov, A. N. Sissakian, J. I. Khubua, G. Arabidze

Based on the two Higgs doublet model, we study the effect of Higgs-boson exchange on the (super)heavy quarkonium \bar QQ, which induces a strong attractive force between a (super)heavy quark Q and an antiquark \bar Q. An interesting application is the decay of (super)heavy quarkonia \bar QQ into a Higgs boson associated with gauge bosons. The criterion for m

Lisa M. H. Hall, Ian G. Moss, Arjun Berera

We present a numerical integration of the cosmological scalar perturbation equations in warm inflation. The initial conditions are provided by a discussion of the thermal fluctuations of an inflaton field and thermal radiation using a combination of thermal field theory and thermodynamics. The perturbation equations include the effects of a damping coefficie

Kazuo Fujikawa, Hiroshi Suzuki

We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spur

N. Bray-Ali, J. E. Moore

The reduction of 2D superconducting or antiferromagnetic order by random dilution is studied as a model for the 2D diluted Heisenberg antiferromagnet (DHAF) La$_2$Cu$_{1-p}$(Zn,Mg)$_p$O$_4$ and randomly inhomogeneous 2D suerconductors. We show in simplified models that long-range order can persist at the percolation threshold despite the presence of disorder

A. I. Titov, T. -S. H. Lee

The diffractive $ϕ$-meson photoproduction amplitude is dominated by the Pomeron exchange process and contains the terms that govern the spin-spin and spin-orbital interactions. We show that these terms are responsible for the spin-flip transitions at forward photoproduction angles and appear in the angular distributions of $ϕ\to K^+K^-$ -decay in reactions w

C. A. Bertulani, A. E. Stuchbery, T. J. Mertzimekis, A. D. Davies

The effects of retardation in the Coulomb excitation of radioactive nuclei in intermediate energy collisions (Elab ~100 MeV/nucleon) are investigated. We show that the excitation cross sections of low-lying states in 11Be, {38,40,42}S and {44,46}Ar projectiles incident on gold and lead targets are modified by as much as 20% due to these effects. The angular

A. Saichev, A. Helmstetter, D. Sornette

We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the

Kang-Sin Choi, Jihn E. Kim

A $Z_3$ orbifold compactification of $E_8\times E_8^\prime$ heterotic string is considered toward a trinification $SU(3)^3$ with three light families. The GUT scale VEV's of the $SU(2)_W\times U(1)_Y\times SU(3)_c$ singlet chiral fields in two sets of the trinification spectrum allow an acceptable symmetry breaking pattern toward MSSM. We show that a dou

Philip G. Calabrese

The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or conditional propositions). This system of ordered pairs (A|B) of events A, B, can express all of the non-Boolean aspects of

Gediminas Juzeliunas, Luciana Davila Romero, David L. Andrews

By means of a canonical transformation it is shown how it is possible to recast the equations for molecular nonlinear optics to completely eliminate ground-state static dipole coupling terms. Such dipoles can certainly play a highly important role in nonlinear optical response - but equations derived by standard methods, in which these dipoles emerge only as

Kil-Chan Ha, Seung-Hyeok Kye, Young Sung Park

We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way, and show that they generate extreme rays in the cone of all positive semi-definite matrices with positive partial transpos

Holger F. Hofmann

As a consequence of having a positive partial transpose, bound entangled states lack many of the properties otherwise associated with entanglement. It is therefore interesting to identify properties that distinguish bound entangled states from separable states. In this paper, it is shown that some bound entangled states violate a non-symmetric class of local

Holger F. Hofmann, Shigeki Takeuchi

The efficient experimental verification of entanglement requires an identification of the essential physical properties that distinguish entangled states from non-entangled states. Since the most characteristic feature of entanglement is the extreme precision of correlations between spatially separated systems, we propose a quantitative criterion based on lo

Mark A. Rubin

The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous

M Yudin

The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering of the events in the system is not automatically implied based on the values of time, but must be specified explicitly.

C. Y. Chen

Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples and direct analyses, involved paradoxes manifest themselves.

Clifford M. Krowne

Guided wave propagation through a left-handed medium has been studied, and new physics discovered. The results are based upon ab initio Green's function calculations. Numerically generated dispersion diagrams and field distribution plots are provided.

Y. Zhang, P. E. Mueller

At the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory (ORNL), molecular ions extracted from a positive ion source and subsequently broken up in a charge exchange cell produce Radioactive Ion Beams (RIBs) with several hundred eV energy spread, preventing effective magnetic isobar separation. In order to perform magnetic isoba

David L. Andrews, Luciana C. Davila Romero, Mohamed Babiker

Optical beams with a new and distinctive type of helicity have become the subject of much recent interest. While circularly polarised light comprises photons with spin angular momentum, these optically engineered 'twisted beams' (optical vortices) are endowed with orbital angular momentum. Here, the wave- front surface of the electromagnetic fields a

J. D. Harrop, S. N. Taraskin, S. R. Elliott

Typographical corrections to the original paper, intended for publication in Physical Review E.

Felix Otto

Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We give a simple example from micromagnetics. In soft ferromagnetic films, the geometric character of a wall separating two m

Joseph H. Silverman

Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).

Radford M. Neal

I describe a new Markov chain method for sampling from the distribution of the state sequences in a non-linear state space model, given the observation sequence. This method updates all states in the sequence simultaneously using an embedded Hidden Markov model (HMM). An update begins with the creation of a ``pool'' of K states at each time, by apply

Martin Klazar

We introduce a containment relation of hypergraphs which respects linear orderings of vertices and investigate associated extremal functions. We extend, by means of a more generally applicable theorem, the n.log n upper bound on the ordered graph extremal function of F=({1,3}, {1,5}, {2,3}, {2,4}) due to Z. Furedi to the n.(log n)^2.(loglog n)^3 upper bound

Arnold W. Miller

Define z to be the smallest cardinality of a function f:X->Y with X and Y sets of reals such that there is no Borel function g extending f. In this paper we prove that it is relatively consistent with ZFC to have b<z where b is, as usual, smallest cardinality of an unbounded family in w^w. This answers a question raised by Zapletal. We also show that it is r

Edith Adan-Bante

Let G be a finite p-group, where p is a prime number, and $χ$ and $ψ$ be faithful complex irreducible characters of G. We study the relation between the number $η(χ,ψ)$ of distinct irreducible constituents of the product $χψ$ and p.

W. B. Vasantha Kandasamy

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our every day&#

S. Satheesh

Continuing the study reported in Satheesh (2001),(arXiv:math.PR/0304499 dated 01May2003) here we study certain aspects of randomization in infinitely divisible (ID) and max-infinitely divisible (MID) laws. They generalize ID and MID laws. In particular we study mixtures of ID & MID laws, its relation to random sums & random maximums, corresponding stationary

Daniel Daigle

We classify weighted forests up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.

Joseph H. Silverman

Let E --> C be an elliptic surface defined over a number field K. For each finite covering C&#39; --> C defined over K, let E&#39; --> C&#39; be the pullback. We give a strong upper bound for the rank of E&#39;(C&#39;/K) in the case that C&#39; --> C is an unramified abelian covering and under the assumption that the Tate conjecture is true for the surface E

Kyeonghee Jo

In this article, we study convex affine domains which can cover a compact affine manifold. For this purpose, we first show that every strictly convex quasi-homogeneous projective domain has at least $C^1$ boundary and it is an ellipsoid if its boundary is twice differentiable. And then we show that an n-dimensional paraboloid is the only strictly convex quas

Anjing Qu

The first approach to the history of mathematics in China led by Li Yan (1892--1963) and Qian Baocong (1892--1974) featured discovering {\it what} mathematics had been done in China&#39;s past. From the 1970s on, Wu Wen-tsun and others shifted this research paradigm to one of recovering {\it how} mathematics was done in ancient China. Both approaches, howeve

Moritz Epple

After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th century debates on physical space this speculation gave rise to the problem of classifying spaces of constant curvature from a

Umberto Bottazzini

In the 1850s Weierstrass succeeded in solving the Jacobi inversion problem for the hyper-elliptic case, and claimed he was able to solve the general problem. At about the same time Riemann successfully applied the geometric methods that he set up in his thesis (1851) to the study of Abelian integrals, and the solution of Jacobi inversion problem. In response

Deborah Loewenberg Ball, Celia Hoyles, Hans Niels Jahnke, Nitsa Movshovitz-Hadar

This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present results of studies that explore the challenges for teachers in helping students learn to reason in disciplined ways about ma

Shutie Xiao

This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)&#39;&#39; in 1995, supported by the National Ministry of Education. There are thirteen universities participated in this project. The Report not only reflects results of our participants, bu

Vagn Lundsgaard Hansen

It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we point to some possible topics for general mathematical conversation.

Jean-Luc Dorier

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a synthetic overview of the main results of these works focusing o

Jia-An Yan

In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete markets in terms of martingale deflators, present a recent result of Kramkov and Schachermayer (1999, 2001) on portfolio opti

Zhouping Xin

Studies on singular flows in which either the velocity fields or the vorticity fields change dramatically on small regions are of considerable interests in both the mathematical theory and applications. Important examples of such flows include supersonic shock waves, boundary layers, and motions of vortex sheets, whose studies pose many outstanding challenge

Alfio Quarteroni

In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.

Alexander Mielke

We consider rate-independent models which are defined via two functionals: the time-dependent energy-storage functional $\calI:[0,T]\ti X\to [0,\infty]$ and the dissipation distance $\calD:X\ti X\to[0,\infty]$. A function $z:[0,T]\to X$ is called a solution of the {energetic model}, if for all $0\leq s<t\leq T$ we have stability: $\mathcal I(t,z(t)) \leq \ma

Nancy Kopell

The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms to perform functionally important tasks. To address those questions, it is first useful to understood in a mechanistic w

Thomas C. Hales

The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than $π/\sqrt{18}$. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical introduction to the problem. It describes the procedure that converts this problem into an optimization problem in a finite

Lei Guo

Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory is to understand the maximum capability and potential limits of the feedback mechanism. This paper gives a survey of som

Nicole El Karoui

Financial markets have developed a lot of strategies to control risks induced by market fluctuations. Mathematics has emerged as the leading discipline to address fundamental questions in finance as asset pricing model and hedging strategies. History began with the paradigm of zero-risk introduced by Black & Scholes stating that any random amount to be paid

Yann Brenier

We discuss several geometric PDEs and their relationship with Hydrodynamics and classical Electrodynamics. We start from the Euler equations of ideal incompressible fluids that, geometrically speaking, describe geodesics on groups of measure preserving maps with respect to the $L^2$ metric. Then, we introduce a geometric approximation of the Euler equation,

Eitan Tadmor

A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution computations. We overview recent developments of modern computational methods for the approximate solution of such problems

Christoph Schwab

Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and of the length scale. Problems with stochastic input data are reformulated as high dimensional deterministic problems fo

Rolf Rannacher

The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of nonlinear problems. Employing duality techniques as used in optimal control theory the error in the target quantities is estim

Mitchell Luskin

Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary forces, or external magnetic field changes. We have developed a numerical analysis of microstructure and used this theory to

James Demmel

Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational expressions as entries. More precisely, {\em accuracy} means the relative error in the output must be less than one (no matter ho

Sonia Martinez, Jorge Cortes, Francesco Bullo

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We present a catalog of solutions for all underactuated systems on $\SE{2}$, $\SO{3}$ and $\SE{2}\times\real$ classified acc

James T. Wheeler

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton&#39;s law with the simplest measurement theory leads to Lagra

Paul Mansfield, David Nolland, Tatsuya Ueno

Using Supergravity on $AdS_7\times S^4$ we calculate the bulk one-loop contribution to the conformal anomaly of the (2,0) theory describing $N$ coincident M5 branes. When this is added to the tree-level result, and an additional subleading order contribution calculated by Tseytlin, it gives an expression for the anomaly that interpolates correctly between th