text stringlengths 1 1.19M | meta dict |
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\section{Introduction}
Spallation reactions, i.e. proton-induced reactions on heavy targets at a few hundred MeV, have been the subject of many studies since 1950. They are known to be a valuable tool for the study of the de-excitation of hot nuclei because, contrarily to reactions between heavy ions, they lead to th... | {
"timestamp": "2005-12-09T12:08:54",
"yymm": "0503",
"arxiv_id": "nucl-ex/0503021",
"language": "en",
"url": "https://arxiv.org/abs/nucl-ex/0503021"
} |
\section{Introduction}
The purpose of this paper is to study the structure of the bounded derived
category $\Dbcoh(\boldsymbol{E})$ of coherent sheaves on a singular irreducible
projective curve $\boldsymbol{E}$ of arithmetic genus one.
In the smooth case, such structure results are easily obtained from Atiyah's
des... | {
"timestamp": "2006-02-14T17:10:40",
"yymm": "0503",
"arxiv_id": "math/0503496",
"language": "en",
"url": "https://arxiv.org/abs/math/0503496"
} |
\section{Introduction}
\label{sec:intro}
Kaonic atoms and kaonic nuclei
carry important information concerning the $K^-$-nucleon interaction
in nuclear medium. This information is very important to determine the
constraints on kaon condensation in high density matter. The properties
of kaons in nuclei are strongly... | {
"timestamp": "2005-08-25T03:10:23",
"yymm": "0503",
"arxiv_id": "nucl-th/0503039",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503039"
} |
\section{Introduction}
\label{intro}
There is the evident nigh affinity between the classical probability
function and the Boolean function of the classical propositional logic \cite{LYN66}. These functions are differed by the range of value, only. That is if
the range of values of the Boolean function shall be expande... | {
"timestamp": "2005-05-20T06:21:32",
"yymm": "0503",
"arxiv_id": "math/0503624",
"language": "en",
"url": "https://arxiv.org/abs/math/0503624"
} |
\section{Introduction}
\mlabel{sec:intro}
It is well-known that the natural functor from the category of associative
algebras to that of Lie algebras and the adjoint functor
play a fundamental role in the study of
these algebraic structures and their applications.
This paper establishes a similar relationship between... | {
"timestamp": "2007-05-31T19:49:29",
"yymm": "0503",
"arxiv_id": "math/0503647",
"language": "en",
"url": "https://arxiv.org/abs/math/0503647"
} |
\section{Introduction}
\label{Introduction}
In this article we prove new theorems which are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. In the first section we will give the statements ... | {
"timestamp": "2005-03-30T10:19:28",
"yymm": "0503",
"arxiv_id": "math/0503699",
"language": "en",
"url": "https://arxiv.org/abs/math/0503699"
} |
\section{Introduction}
It is common knowledge that Lifshitz formula \cite{19}
describes the van der Waals and Casimir force acting between
two thick plane parallel material plates separated by a gap
of width $a$. According to this formula, the free energy
of the van der Waals and Casimir interaction can be
represented... | {
"timestamp": "2005-03-06T19:39:25",
"yymm": "0503",
"arxiv_id": "quant-ph/0503064",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503064"
} |
\section{Introduction}
Communities of ecologically similar species that compete with each other solely for resources
are often described by neutral community models (NCM) \cite{Hubbel,Bell,Chave,Norris}. These models proved to be successful and useful in describing many of the basic patterns of biodiversity such as th... | {
"timestamp": "2005-03-17T10:51:17",
"yymm": "0503",
"arxiv_id": "q-bio/0503026",
"language": "en",
"url": "https://arxiv.org/abs/q-bio/0503026"
} |
\section{From ASDYM equations to Einstein--Weyl structures}
\setcounter{equation}{0}
The idea of allowing
infinite--dimensional groups of diffeomorphisms of some manifold $\Sigma$
as gauge groups provides a link between
the Yang--Mills--Higgs theories
on $\mathbb{R}^n$ and conformal gravity theories on
$\mathbb{R... | {
"timestamp": "2005-06-10T19:44:19",
"yymm": "0503",
"arxiv_id": "nlin/0503030",
"language": "en",
"url": "https://arxiv.org/abs/nlin/0503030"
} |
\section{Introduction}
Models of non-linear spatially extended systems exhibit a variety of spatial
and temporal pattern forming phenomena. A subclass of these patterns are
spatially localized structures \cite{rev1} that include pulses, solitons,
fronts, and domain walls. The standard analysis of these localized struc... | {
"timestamp": "2005-08-24T23:54:38",
"yymm": "0503",
"arxiv_id": "nlin/0503039",
"language": "en",
"url": "https://arxiv.org/abs/nlin/0503039"
} |
\section{Introduction}
Let $K,K'$ be closed convex pointed cones with non-empty interior, residing in finite-dimensional real
vector spaces $E,E'$. Then an element $w \in E \otimes E'$ of the tensor product space is called {\sl separable}
if it can be represented as a convex combination of product elements $v \otimes ... | {
"timestamp": "2005-03-24T16:46:37",
"yymm": "0503",
"arxiv_id": "quant-ph/0503194",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503194"
} |
\section{Introdu\c{c}\~ao}
\hspace{.5cm} Nos dias atuais a Teoria Qu\^antica de Campos \'e largamente
empregada em diversas \'areas da f\'{\i}sica, tais como, altas energias,
mec\^anica estat\'{\i}stica, mat\'eria condensada, etc. Sendo a Teoria
Qu\^antica de Campos fundamentalmente de aspectos perturbativos, ela sofr... | {
"timestamp": "2005-03-13T17:39:26",
"yymm": "0503",
"arxiv_id": "physics/0503107",
"language": "pt",
"url": "https://arxiv.org/abs/physics/0503107"
} |
\section{Introduction}
An important part of the theory of vector bundles over homogeneous spaces $G/P$ is
the study of {\em homogeneous} vector bundles. This class of vector bundles has first
been investigated by Kostant and Bott in the 50's, who clarified the relation
between the representation theory of $G$ and homo... | {
"timestamp": "2005-03-23T19:06:05",
"yymm": "0503",
"arxiv_id": "math/0503501",
"language": "en",
"url": "https://arxiv.org/abs/math/0503501"
} |
\section{Introduction}
\label{sec:intro}
Spectral properties of the Laplacian on a compact manifold is a
well-established and still active field of research. Much less is
known on the spectrum of \emph{non-compact} manifolds. We restrict
ourselves here to the class of non-compact \emph{covering} manifolds
$X \to M$ wi... | {
"timestamp": "2007-12-10T16:59:19",
"yymm": "0503",
"arxiv_id": "math-ph/0503005",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503005"
} |
\section{Introduction}
We study the discrete random Schr\"odinger operator
\begin{eqnarray}
H_\omega=\Delta+\lambda V_\omega
\end{eqnarray}
on $\ell^2({\Bbb Z}^2)$,
where $\Delta$ is the (centered) nearest neighbor Laplacian, with
spectrum $[-4,4]$, and $\lambda$ is a small parameter
(the disorder strength).
... | {
"timestamp": "2005-10-26T19:55:58",
"yymm": "0503",
"arxiv_id": "math-ph/0503064",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503064"
} |
\section*{Introduction}
An operator $A:\mathbb R^d\rightarrow\mathbb R^d$ is called additively homogeneous if it satisfies $A(x+a\textbf{1})=A(x)+a\textbf{1}$ for all $x\in\mathbb R^d$ and $a\in\mathbb R$, where $\textbf{1}$ is the vector $(1,\cdots,1)'$ in $\mathbb R^d$. It is called isotone if $x\le y$ implies $A(x)\... | {
"timestamp": "2007-01-08T14:52:18",
"yymm": "0503",
"arxiv_id": "math/0503634",
"language": "en",
"url": "https://arxiv.org/abs/math/0503634"
} |
\section{Introduction}
In \cite{Wer1}, we introduced a theory of {\it contractive Markov
systems (CMS)} which provides a unifying framework in so-called
'fractal' geometry. It extends the known theory of {\it iterated
function systems (IFS) with place dependent probabilities}, which
are contractive on average, \cite... | {
"timestamp": "2005-08-18T12:13:14",
"yymm": "0503",
"arxiv_id": "math/0503633",
"language": "en",
"url": "https://arxiv.org/abs/math/0503633"
} |
\section{Introduction}
Whether or not quantum information processing and quantum computing
\cite{QCcomp} become practical technologies crucially depends on the
ability to implement high-fidelity quantum logic gates in a scalable way
\cite{diVinc}. Among alternative routes to this challenging goal, are of
particula... | {
"timestamp": "2005-03-07T16:59:02",
"yymm": "0503",
"arxiv_id": "quant-ph/0503071",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503071"
} |
\section{Introduction}
\label{sec:intro}
We consider a family of generalized nonlinear Schr\"odinger and
Hartree equations with a focusing nonlinearity. These equations have
solitary wave solutions, and, in this paper, we study the effective
dynamics of such solitary waves. The equations have the form:
\begin{equatio... | {
"timestamp": "2005-03-07T01:01:06",
"yymm": "0503",
"arxiv_id": "math-ph/0503009",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503009"
} |
\section{Introduction}
In our previous papers [1-6] published recently, a
time-independent novel perturbation theory has been developed in
the bound state domain, which is non-perturbative, self-consistent
and systematically improvable, and used to treat successfully
significant problems in different fields of physic... | {
"timestamp": "2005-03-21T13:21:05",
"yymm": "0503",
"arxiv_id": "nucl-th/0503055",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503055"
} |
\section{Introduction} \label{Sec:Introduction}
Homotopy continuation methods provide reliable and efficient numerical
algorithms to compute accurate approximations to all isolated solutions
of polynomial systems, see e.g.~\cite{Li03} for a recent survey.
As proposed in~\cite{SW}, we can approximate a positive dimensi... | {
"timestamp": "2005-03-29T18:46:35",
"yymm": "0503",
"arxiv_id": "math/0503688",
"language": "en",
"url": "https://arxiv.org/abs/math/0503688"
} |
\section{Introduction}
Quantum computation and quantum information are subjects
of much continuing interest and study. An initial impetus
for this work was the realization that as computers became
smaller, quantum effects would become more important.
Additional interes... | {
"timestamp": "2005-06-20T21:21:04",
"yymm": "0503",
"arxiv_id": "quant-ph/0503154",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503154"
} |
\section{Introduction}
\indent \indent In complex dynamics there exists an extensive
study of polynomials as dynamical systems acting on ${\mathbb C}$. The
orbit of a point $z_0\in{\mathbb C}$ under a polynomial $f \in {\mathbb C}[z]$ is
the sequence $z_0,z_1,z_2,\ldots$ defined by
$$z_n =f^n(z_0).$$
\hspace{0pt} Sub... | {
"timestamp": "2005-03-30T23:37:03",
"yymm": "0503",
"arxiv_id": "math/0503720",
"language": "en",
"url": "https://arxiv.org/abs/math/0503720"
} |
\section{Introduction}
\label{Sect:1}
It has long been recognised that the ultimate accuracy of optical measurements
is set by the quantum nature of light. Indeed the desire to approach these
quantum limits was a strong motivation for the study of nonclassical and
particularly squeezed states of light \cite{LoudonKn... | {
"timestamp": "2005-03-30T02:50:23",
"yymm": "0503",
"arxiv_id": "quant-ph/0503224",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503224"
} |
\section{Introduction}
Low-energy ${\bar K}N$ and ${\bar K}A$
interactions have gained substantial interest during the last
two decades. It is known from the time-honored Martin analysis~\cite{Martin}
that the isoscalar $s$-wave $K^-N$ scattering length is large and repulsive,
Re$a_0{=}{-}1.7$~fm, while
the isovecto... | {
"timestamp": "2005-03-30T08:42:06",
"yymm": "0503",
"arxiv_id": "nucl-th/0503076",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503076"
} |
\section{Quantum catastrophe models}
We begin by constructing the quantum catastrophe models and first consider
those derived from catastrophes occurring in a single variable,
such as the cusp.
We take as our model a system of two interacting bosonic modes. Let
($x_1$, $p_{x_1}$) and ($x_2$, $p_{x_2}$) be the (abst... | {
"timestamp": "2005-03-17T18:39:50",
"yymm": "0503",
"arxiv_id": "quant-ph/0503160",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503160"
} |
\section{Introduction}
\label{1}
A comprehensive understanding of Hamiltonian dynamics is a long outstanding
problem in nonlinear and statistical physics, which has important applications
in various other areas of physics. Typical Hamiltonian systems are
nonhyperbolic as they exhibit mixed phase space with coexisting... | {
"timestamp": "2005-03-29T02:56:47",
"yymm": "0503",
"arxiv_id": "nlin/0503060",
"language": "en",
"url": "https://arxiv.org/abs/nlin/0503060"
} |
\section{}
\section{Introduction}
As a century old theory, quantum mechanics has provided the most
effective description of the physical world. Recently, new
discoveries were found for its applications to information and
computation science \cite{Nielsen}, \textit{e.g.}, the efficient
prime factorization of larger num... | {
"timestamp": "2006-07-03T20:48:46",
"yymm": "0503",
"arxiv_id": "quant-ph/0503168",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503168"
} |
\section{Introduction\label{introsec}}
A collection of journal papers is a database of papers that
comprehensively samples the journal literature of a scientific
specialty. As such, the social and epistemological processes of the
specialty are manifested in the complex network of linkages among
entities within the coll... | {
"timestamp": "2005-03-08T18:48:08",
"yymm": "0503",
"arxiv_id": "physics/0503061",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503061"
} |
\section*{Introduction.}
Let $(M^n,g)$ be a Riemannian manifold and $(TM^n,g_s)$ its
tangent bundle equipped with the Sasaki metric \cite{Sk}. Let
$\xi$ be a given smooth vector field on $M^n$. Then $\xi$
naturally defines a mapping $\xi:M^n\to TM^n$ such that the
submanifold $\xi(M^n)\subset TM^n$ is transverse to th... | {
"timestamp": "2005-03-24T21:52:54",
"yymm": "0503",
"arxiv_id": "math/0503561",
"language": "en",
"url": "https://arxiv.org/abs/math/0503561"
} |
\section{INTRODUCTION}
Due to the fundamental importance of the waves and instabilities
in plasma and hydrodynamics investigations, computational
researchers have devoted great efforts in developing appropriate
tools. One of the main challenges after developing numerically
stable algorithms in fluid models has been ge... | {
"timestamp": "2005-03-05T14:09:47",
"yymm": "0503",
"arxiv_id": "physics/0503043",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503043"
} |
\section{Introduction}
The characterization and elimination of decoherence and other
noise sources has emerged as one of the major challenges
confronting the coherent experimental control of increasingly
large multi-body quantum systems. Decoherence arising from
undesired interactions with background (or environment) ... | {
"timestamp": "2005-12-16T02:56:07",
"yymm": "0503",
"arxiv_id": "quant-ph/0503243",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503243"
} |
\section{Introduction}
\setcounter{equation}{0}
Let $\lambda_1 ,\lambda_2 ,\lambda_2, \lambda_4 >0$ be given.
We consider the following system for $(u, \eta )$ in $\Bbb R^2$.
\begin{eqnarray}
\label{11}
\Delta u&=&-\lambda_1 e^{\eta} -\lambda_2 e^{u}+4\pi \sum_{j=1} ^{N} \delta (z-z_{j} ),\\
\label{12}
\Delta ... | {
"timestamp": "2005-03-23T15:47:36",
"yymm": "0503",
"arxiv_id": "math/0503493",
"language": "en",
"url": "https://arxiv.org/abs/math/0503493"
} |
\section*{Introduction}
Let $(M,g)$ be an $n+1$ -- dimensional Riemannian manifold with
metric $g$. A vector field $\xi$ on it is called {\it holonomic}
if $\xi$ is a field of normals of some family of regular
hypersurfaces in $M$ and {\it non-holonomic} otherwise. The
foundation of the classical ... | {
"timestamp": "2005-03-24T22:24:41",
"yymm": "0503",
"arxiv_id": "math/0503567",
"language": "en",
"url": "https://arxiv.org/abs/math/0503567"
} |
\section{Introduction}
Very much physics is sometimes contained in simple and basic results
of optics and electromagnetics. In this paper I shall focus on the
character of electromagnetic waves reflected from a planar surface. As
is well known, many everyday light phenomena that we can observe with
plain eyes \cite{Mi... | {
"timestamp": "2005-03-29T12:50:47",
"yymm": "0503",
"arxiv_id": "physics/0503216",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503216"
} |
\section{Introduction}
Given a graph $G$ with $m$ edges, the Max-Cut problem is to determine
(the size of) the maximum cut in
$G$. For complete graphs, the largest cut has size $m/2+o(m)$.
On the other hand, it is well known that a cut of
size at least $m/2$ in a graph $G$ can be found using the natural greedy
algori... | {
"timestamp": "2005-03-21T15:25:40",
"yymm": "0503",
"arxiv_id": "math/0503403",
"language": "en",
"url": "https://arxiv.org/abs/math/0503403"
} |
\section{Introduction}
One of the key features of a physical system for quantum information
processing (QIP) is quantum entanglement. The problem of entanglement
of multipartite systems is far from being completely understood, and
it has numerous interesting aspects.
One of the possible approaches to multipartite ent... | {
"timestamp": "2005-03-15T10:31:08",
"yymm": "0503",
"arxiv_id": "quant-ph/0503133",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503133"
} |
\section{Introduction}
In this paper we prove a slight variant of the hypergraph removal lemma established recently and independently by Gowers \cite{gowers}
and Nagle, R\"odl, Schacht and Skokan \cite{nrs}, \cite{rodl}, \cite{rodl2}. To motivate this lemma, let us first recall the more well-known triangle removal le... | {
"timestamp": "2005-11-16T18:07:49",
"yymm": "0503",
"arxiv_id": "math/0503572",
"language": "en",
"url": "https://arxiv.org/abs/math/0503572"
} |
\section{\label{sec:level1}First-level heading:\protect\\ The line
Implementing atom-optical devices often requires a strong confinement for all except one
degree of freedom~\cite[and Refs therein]{intro}. Examples of physical situations where a
strong confinement is needed are guided matter-wave interferometers~\ci... | {
"timestamp": "2005-06-24T15:05:21",
"yymm": "0503",
"arxiv_id": "quant-ph/0503196",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503196"
} |
\section{Introduction}
\label{sec:intro}
The multivector fields on a smooth manifold $M$ can be seen as
multidifferential operators on the algebra $\mathcal{C}^\infty(M)$ of smooth
functions on $M$. This assignment is a particular case of the following
general construction: given a graded associative and commutativ... | {
"timestamp": "2006-01-12T13:17:51",
"yymm": "0503",
"arxiv_id": "math/0503380",
"language": "en",
"url": "https://arxiv.org/abs/math/0503380"
} |
\section{Introduction}
The parallelogram law states that $\|x+y\|^2+\|x-y\|^2=2(\|x\|^2 +
\|y\|^2)$ holds for all vectors $x$ and $y$ in a Hilbert space.
This law implies that the so-called parallelogram inequality
$\|x+y\|^2\leq 2(\|x\|^2 + \|y\|^2)$ trivially holds. S. Saitoh
\cite{SAI} noted the inequality $\|x+y\|... | {
"timestamp": "2005-12-23T11:29:41",
"yymm": "0503",
"arxiv_id": "math/0503616",
"language": "en",
"url": "https://arxiv.org/abs/math/0503616"
} |
\section{Introduction}
This paper summarizes some results of work originally initiated by
Peter Carr. It supposes to investigate various numerical and
analytical methods of option pricing using VG model in order to find
out which algorithm is most efficient.
Let us first give a brief overview of the VG model. The Vari... | {
"timestamp": "2010-01-15T20:29:12",
"yymm": "0503",
"arxiv_id": "physics/0503137",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503137"
} |
\section{Introduction}
A classical problem in geometry is to determine whether a Riemannian
manifold ${\mathcal V}$ can be isometrically immersed in another Riemaniann
manifold $\bar{\mathcal V}$. We will restrict ourselves to the case of codimension $1$
immersions, i.e., ${\mathcal V}$ has dimension $n$ and $\bar{\ma... | {
"timestamp": "2005-03-23T18:45:51",
"yymm": "0503",
"arxiv_id": "math/0503500",
"language": "en",
"url": "https://arxiv.org/abs/math/0503500"
} |
\section{The Hidden Subgroup Problem}
One of the principal quantum algorithmic paradigms is the use of the abelian
Fourier transform to discover a function's hidden periodicities. In the
examples relevant to quantum computing, an oracle function $f$ defined on an
abelian group $G$ has ``hidden periodicity'' if the... | {
"timestamp": "2005-03-09T20:06:26",
"yymm": "0503",
"arxiv_id": "quant-ph/0503095",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503095"
} |
\section{Introduction and summary \label{sec:intro}}
One of the most intriguing {experimental} puzzles encountered in
contemporary physics is the evident absence of SUSY partners of
elementary particles in nature. In the context of {field theory}
this means that SUSY, if it exists, must be spontaneously broken.
Witte... | {
"timestamp": "2005-03-03T13:59:17",
"yymm": "0503",
"arxiv_id": "quant-ph/0503035",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503035"
} |
\section{Introduction}
The quantum walk (QW) is an interesting quantum process that is attracting
much attention from the algorithmic point of view \cite{Ambainis04}, but
also because of its intrinsic interest \cite{Kempe03} through its connection
with quantum cellular automata \cite{Meyer96}, and with the physics of ... | {
"timestamp": "2005-03-07T16:18:33",
"yymm": "0503",
"arxiv_id": "quant-ph/0503069",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503069"
} |
\section{Introduction}
Optical, non imaging detectors are widely used for the detection of weakly
interacting particles. At present the main focus of observation is on
neutrinos and antineutrinos from various sources, but there are also plans to
construct large optical detectors to search for as yet undiscovered part... | {
"timestamp": "2005-03-23T21:46:18",
"yymm": "0503",
"arxiv_id": "physics/0503185",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503185"
} |
\section{Introduction}
Let us recall the notion of a \emph{Poincar\'e embedding}:
\begin{defin}[\rm({Levitt \cite{Levitt}, and \cite[Section 5]{Klein} for a modern exposition})]
\label{def-Pemb}
Let $W$ be a Poincar\'e duality space of dimension $n$ and let
$P$ be a finite CW-complex of dimension $m$.
A \emph{Poincar\... | {
"timestamp": "2005-03-25T16:47:01",
"yymm": "0503",
"arxiv_id": "math/0503605",
"language": "en",
"url": "https://arxiv.org/abs/math/0503605"
} |
\section*{Introduction}
Let $M$ be a complex manifold, and $T^*M$ its cotangent bundle endowed with
the canonical symplectic structure. Let $\mathcal{W}_M$ be the sheaf of rings of WKB
operators, that is, microdifferential operators with an extra central
parameter $\tau$. This ring provides a of $T^*M$.
Recall th... | {
"timestamp": "2005-12-21T18:37:22",
"yymm": "0503",
"arxiv_id": "math/0503400",
"language": "en",
"url": "https://arxiv.org/abs/math/0503400"
} |
\section{Definitions and Notations}
We briefly recall some well known notions of $CR$ geometry that
will be used in the paper.
Let $N\subset{\mathbb C}} \def\l{\lambda^n$ be a smooth connected real submanifold, and let
$p\in N$. We denote by $T_p(N)$ the tangent space of $N$ at the
point $p$, and by $H_p(N)$ the... | {
"timestamp": "2006-07-28T17:00:11",
"yymm": "0503",
"arxiv_id": "math/0503430",
"language": "en",
"url": "https://arxiv.org/abs/math/0503430"
} |
\section{Collecting the relevant $K$- and $L$-theory.}
\setcounter{altel}{0}
\pagenumbering{arabic}
The material in this first section related to quadratic forms
and L-groups has primarily been extracted from \cite{Giffen;k2} and
\cite{Wall;lfound}, while the facts concerning the algebraic $K$-groups
$K_0$, $K_1$ an... | {
"timestamp": "2005-03-24T14:18:00",
"yymm": "0503",
"arxiv_id": "math/0503538",
"language": "en",
"url": "https://arxiv.org/abs/math/0503538"
} |
\section{Introduction.}\nin
Let $X$ be a (connected and reduced) complex space. We
recall that $X$ is said to be {\it strongly} $q$-{\it pseudoconvex} in the sense of
Andreotti-Grauert~\cite{AG} if there exists a compact subset $K$ and a smooth function
$\varphi:X\to{\mathbb {R}}} \def\a {\alpha} \def\b {\beta}\def\g... | {
"timestamp": "2005-03-23T14:12:59",
"yymm": "0503",
"arxiv_id": "math/0503490",
"language": "en",
"url": "https://arxiv.org/abs/math/0503490"
} |
\section*{Introduction}
Throughout the paper $k$ is a fixed algebraically closed field.
All considered categories are additive $k$-categories and all
functors are $k$-functors.
One of the aims of the representation theory of finite-dimensional
algebras is a description of indecomposable modules and
homomorphism space... | {
"timestamp": "2005-08-02T10:23:19",
"yymm": "0503",
"arxiv_id": "math/0503513",
"language": "en",
"url": "https://arxiv.org/abs/math/0503513"
} |
\section{Introduction}
\label{sec:intro}
The known meson spectrum contains three pseudoscalars [$I^G (J^{PC}) = 1^- (0^{-+}) $], all with masses below $2\,$GeV \cite{pdg}: $\pi(140)$; $\pi(1300)$; and $\pi(1800)$. The lightest of these, the pion [$\pi(140)$], is much studied and well understood as QCD's Goldstone mode... | {
"timestamp": "2005-03-16T01:27:42",
"yymm": "0503",
"arxiv_id": "nucl-th/0503043",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503043"
} |
\section{Main Theorem}
\label{intro}
Vector bundles over the projective space
${\mathbf{P}}}% \P == \mathbb{P^n_{\mathbb{K}}}% \P == \mathbb{P$ are one of the main subjects in both (algebraic) geometry
and commutative algebra. The most fundamental result in this area is
the theorem due to Grothendieck which asserts ... | {
"timestamp": "2005-03-30T16:08:12",
"yymm": "0503",
"arxiv_id": "math/0503710",
"language": "en",
"url": "https://arxiv.org/abs/math/0503710"
} |
\section{Introduction}
The geometric approach to the theory of linear
dynamical systems has provided deep insights
and elegant solutions to many control problems,
such as the disturbance decoupling problem, the block
decoupling problem, and the model matching problem
(see~\cite{wonham} and the references therein)... | {
"timestamp": "2007-04-06T21:04:51",
"yymm": "0503",
"arxiv_id": "math/0503448",
"language": "en",
"url": "https://arxiv.org/abs/math/0503448"
} |
\section{Introduction}
In a typical Bell experiment, two or more entangled particles are distributed to separate observers. Each observer measures on his particle one from a set of possible observables and obtains some outcome. One of the most striking features of quantum mechanics is that the resulting joint outcome ... | {
"timestamp": "2005-06-18T04:21:07",
"yymm": "0503",
"arxiv_id": "quant-ph/0503179",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503179"
} |
\section{Introduction}
\indent\indent We study the long time behaviour of solutions to a
class Korteweg-de Vries-type equations, with an additional term
$b(t,x)u$. These equations, from now on called the bKdV, are of
the form
\begin{align}
\partial_t u=-\partial_x\left(\partial_x^2 u+f(u)-b(t,x)u\right),
\label{Eqn:K... | {
"timestamp": "2005-03-08T18:12:31",
"yymm": "0503",
"arxiv_id": "math-ph/0503016",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503016"
} |
\section{Introduction}
Human altruistic behavior is a long-standing problem in
evolutionary theory, as first realized by Darwin himself:
\begin{quotation}
He who was ready to sacrifice his life (\dots) rather than betray his comrades,
would often leave no offspring to inherit his noble nature\dots Therefore,
it seems... | {
"timestamp": "2005-03-16T20:03:02",
"yymm": "0503",
"arxiv_id": "q-bio/0503024",
"language": "en",
"url": "https://arxiv.org/abs/q-bio/0503024"
} |
\section{#1}}
\newcommand{\newsubsection}[1]{\setcounter{equation}{0}
\setcounter{dfn}{0}
\subsection{#1}}
\renewcommand{\theequation}{\thesection.\arabic{equation}}
\newtheorem{dfn}{Definition}[section]
\newtheorem{thm}[dfn]{Theorem}
\newtheorem{lmma}[dfn]{Lemma}
\newtheorem{ppsn}[dfn]{Proposition}
\newtheorem{crlre... | {
"timestamp": "2005-04-21T17:52:13",
"yymm": "0503",
"arxiv_id": "math/0503689",
"language": "en",
"url": "https://arxiv.org/abs/math/0503689"
} |
\section{Introduction}
The Heider balance \cite{h46,hei2,hara,dor1,wt} is a final state of personal relations
between members of a society, reached when these relations evolve according to
some dynamical rules. The relations are assumed to be symmetric, and they can be friendly
or hostile. The underlying psycho-so... | {
"timestamp": "2005-03-11T17:49:04",
"yymm": "0503",
"arxiv_id": "physics/0503085",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503085"
} |
\section{Introduction \label{In}}
\bigskip
Although there is a long history of theoretical work on the solution of
the Coulomb problem in three-particle scattering
\cite{alt:78a,berthold:90a,kievsky:96a,kievsky:01a,chen:01a,alt:02a,
suslov:04a}, the work of Refs.~\cite{kievsky:96a,kievsky:01a}
pioneered the effort ... | {
"timestamp": "2005-03-04T18:22:53",
"yymm": "0503",
"arxiv_id": "nucl-th/0503015",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503015"
} |
\section{Introduction}
\label{sec:introduction}
Half wave plate (HWP) retarders are used extensively for polarimetric
measurements. The technique is used across a broad range of
electro-magnetic frequencies because it provides an effective way to
discriminate against systematic errors. The modulation efficiency of
a ... | {
"timestamp": "2005-03-15T09:30:31",
"yymm": "0503",
"arxiv_id": "physics/0503122",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503122"
} |
\section{Introduction}
The Casimir effect concerns the Lamb shifts in the frequency of radiation
modes due to the interaction between photon modes and electrical currents.
The photon mode Lagrangian is discussed in Sec.\ref{LCMD}. Mode
frequency shifts induce changes in the free energy which in the zero
temperature li... | {
"timestamp": "2005-03-01T19:02:52",
"yymm": "0503",
"arxiv_id": "quant-ph/0503016",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503016"
} |
\section{Introduction}
In this note, we study graphs without cycles of prescribed even
lengths. For a finite or infinite set ${\cal C}$ of cycles, define
$\mbox{ex}(n,{\cal C})$ to be the maximum possible number of edges
in an $n$-vertex graph which does not contain any of the cycles in
${\cal C}$. The asymptotic behav... | {
"timestamp": "2005-03-28T02:39:06",
"yymm": "0503",
"arxiv_id": "math/0503623",
"language": "en",
"url": "https://arxiv.org/abs/math/0503623"
} |
\section{Introduction}
Many aspects of life as a responsible citizen in society
involve having an understanding of the probability
of one type of event in comparison to others. Yet event probabilities are
often expressed using unfamiliar or varied terminology (\textit{i.e.,}
negative exponents, such as $10^{-4}$ or $... | {
"timestamp": "2005-04-01T01:56:05",
"yymm": "0503",
"arxiv_id": "physics/0503229",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503229"
} |
\section{Motivation}
Short-term financial data usually exhibit similar properties called `stylized facts' like, e.g., leptokurtosis,
dependence of simultaneous extremes, radial asymmetry, vola\-tility clustering, etc., especially if the
log-price changes (called the `log-returns') of stocks, stock indices, and foreign... | {
"timestamp": "2005-03-01T11:59:44",
"yymm": "0503",
"arxiv_id": "physics/0503007",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503007"
} |
\section{Introduction}
Quantum states which differ only by a overall phase cannot be distinguished by measurements
in quantum mechanics. Hence phases were thought to be unimportant
until Berry made an important and interesting observation regarding the behavior of pure quantum
systems in a slowly changing environmen... | {
"timestamp": "2005-03-03T07:41:01",
"yymm": "0503",
"arxiv_id": "quant-ph/0503032",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503032"
} |
\section{Introduction, Notations}
\medskip
As is well known, the CSM converts the description of resonances by
non-integrable Gamow states into one by square integrable states while
leaving the discrete spectrum unchanged \cite{ABC}. Cuts describing the
continuum are rotated, however, but this may be advantageous, ... | {
"timestamp": "2005-03-17T18:30:57",
"yymm": "0503",
"arxiv_id": "nucl-th/0503049",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503049"
} |
\section{Introduction}\label{s:intro}
Analysis of complex high dimensional data is an exploding area of
research, with applications in diverse fields, such as machine
learning, statistical data analysis, bio-informatics, meteorology,
chemistry and physics. In the first three application fields, the
underlying assumpti... | {
"timestamp": "2005-03-22T07:46:24",
"yymm": "0503",
"arxiv_id": "math/0503445",
"language": "en",
"url": "https://arxiv.org/abs/math/0503445"
} |
\section{Introduction}
The use and development of ion trapping techniques, which started
about 50 years ago \cite{cite1}, have led to a broad range of
discoveries and new experiments in physics and chemistry. In
particular, one can cite high precision spectroscopy, mass
measurements, particle dynamics, nuclear and ato... | {
"timestamp": "2005-03-14T21:35:30",
"yymm": "0503",
"arxiv_id": "physics/0503117",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503117"
} |
\section{Introduction}
\subsection{Harmonic analysis of boolean functions}
\label{sec:intro} The motivation for this paper is the study of
\emph{boolean functions} $f : \{-1,1\}^n \to \{-1,1\}$, where $\{-1,1\}^n$
is equipped with the uniform probability measure. This topic is of
significant interest in theoretical c... | {
"timestamp": "2005-05-24T01:54:02",
"yymm": "0503",
"arxiv_id": "math/0503503",
"language": "en",
"url": "https://arxiv.org/abs/math/0503503"
} |
\section{\label{Intro}Introduction}
Entanglement is a property of correlated quantum systems that cannot
be accounted for classically. Entangled states of distinct (possibly
interacting) quantum systems, which are those that cannot be
factorized into product states of the subsystems, are of fundamental
interest in qua... | {
"timestamp": "2006-09-04T17:15:28",
"yymm": "0503",
"arxiv_id": "quant-ph/0503116",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503116"
} |
\section{Introduction}
\indent Ebola hemorrhagic fever is a highly infectious and lethal disease named after a
river in the Democratic Republic of the Congo (formerly Zaire) where it
was first identified in 1976 \cite{CDC1}. Twelve outbreaks of Ebola
have been reported in Congo, Sudan, Gabon, and Uganda as of Septemb... | {
"timestamp": "2005-03-02T00:52:48",
"yymm": "0503",
"arxiv_id": "q-bio/0503006",
"language": "en",
"url": "https://arxiv.org/abs/q-bio/0503006"
} |
\section{introduction}
One of the major problems in mathematical physics is concerned
with the geometrical information stored in the spectrum of the Laplace
Beltrami operator
\begin{equation}
-\triangle\psi_j({\bf r}) = E_j\psi_j({\bf r}); \;\; {\bf r}
\in \Omega(\alpha) \ .
\end{equation}
\noindent The spectrum is or... | {
"timestamp": "2005-03-03T12:54:32",
"yymm": "0503",
"arxiv_id": "nlin/0503002",
"language": "en",
"url": "https://arxiv.org/abs/nlin/0503002"
} |
\section{Introduction}
Let $\left( \Omega ,\mathcal{F},\left( \mathcal{F}_{t}\right) _{t\geq 0},%
\mathbf{P}\right) $ be a filtered probability space satisfying the
usual hypotheses (right continuous and complete). Given the end $L$\
of an $\left(
\mathcal{F}_{t}\right) $\ predictable set $\Gamma $, i.e\textbf{\ }%
\b... | {
"timestamp": "2007-08-02T23:45:56",
"yymm": "0503",
"arxiv_id": "math/0503386",
"language": "en",
"url": "https://arxiv.org/abs/math/0503386"
} |
\section{\label{intro}Introduction}
Let $X$ be a finite set. A (symmetric) {\it association scheme} with $d$ classes on $X$ is a partition of
$X\times X$ into sets $R_0$, $R_1, \ldots , R_d$ (called {\it associate classes} or {\it relations}) such that
\begin{enumerate}
\item $R_0=\{(x,x) \mid x\in X\}$ (the diagonal... | {
"timestamp": "2005-03-24T23:34:25",
"yymm": "0503",
"arxiv_id": "math/0503570",
"language": "en",
"url": "https://arxiv.org/abs/math/0503570"
} |
\section{Introduction}
\label{intro}
Donald Coxeter's work on regular polytopes and groups of reflexions is often viewed as his most important contribution. At its heart lies a dialogue between geometry and algebra which was so characteristic for his mathematics (see, for example, \cite{c_rp,c_rcp,cm}). This paper ... | {
"timestamp": "2005-03-18T20:24:09",
"yymm": "0503",
"arxiv_id": "math/0503389",
"language": "en",
"url": "https://arxiv.org/abs/math/0503389"
} |
\section{Introduction}
\lbl{sec.intro}
\subsection{The volume conjecture for small angles}
\lbl{sub.volume}
In an earlier publication, the authors stated and proved the {\em Volume
Conjecture}
for small purely imaginary angles; see \cite{GL2}. More precisely, the authors
proved that for every knot $K$ in $S^3$ the... | {
"timestamp": "2005-04-04T16:14:11",
"yymm": "0503",
"arxiv_id": "math/0503641",
"language": "en",
"url": "https://arxiv.org/abs/math/0503641"
} |
\section{Introduction}
Alternative models for quantum computation based on projective measurements \cite{Raussen01, Nielsen01, Leung03} have recently attracted much attention. A common concept of these models is the simulation of individual quantum circuit operations and how simulations can be composed together \cite{... | {
"timestamp": "2006-03-27T21:52:23",
"yymm": "0503",
"arxiv_id": "quant-ph/0503130",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503130"
} |
\section{Introduction}
Consider a region ${\mathcal D}$ in ${\mathbb R}^2$ with piecewise smooth boundary and finite area. The {\em billiard flow} on the unit cotangent bundle of ${\mathcal D}$ is defined as the motion along straight lines with specular reflections at its boundary $\partial{\mathcal D}$. The quantum s... | {
"timestamp": "2005-03-28T16:58:14",
"yymm": "0503",
"arxiv_id": "math-ph/0503066",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503066"
} |
\section{Introduction}
Systems made up of entities that interact pairwise can be modeled as
networks. To comprehend the emergent properties of such systems---the
objective of the study of complex systems and systems biology---one
approach is to investigate the global properties of the corresponding
networks \cite{mejn... | {
"timestamp": "2005-03-06T19:52:49",
"yymm": "0503",
"arxiv_id": "q-bio/0503010",
"language": "en",
"url": "https://arxiv.org/abs/q-bio/0503010"
} |
\section{Introduction}
The general structures ruling the evolution of classical and quantum
systems are not essentially different. For instance both systems are
Hamiltonian vector fields and both are derivations on the Lie
algebra of observables with respect to the Poisson bracket and the
commutator bracket respectivel... | {
"timestamp": "2005-03-15T17:04:05",
"yymm": "0503",
"arxiv_id": "math-ph/0503040",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503040"
} |
\section{Introduction}
The Galton board is an upright board with evenly
spaced nails driven into its upper half. The
nails are arranged in staggered order. The lower half of the board is
divided with vertical slats into a number of narrow rectangular
slots. From the front, the whole installation is covered with a
glas... | {
"timestamp": "2005-03-10T14:51:54",
"yymm": "0503",
"arxiv_id": "nlin/0503024",
"language": "en",
"url": "https://arxiv.org/abs/nlin/0503024"
} |
\section{Introduction}
This work is motivated by the problem of multi-vehicle formation
(or swarm) control, e.g., for meter-scale UAVs (unmanned aerial
vehicles), and builds on our earlier work on planar formation
control laws \cite{scltechrep,scl02,cdc03} by extending the key
results to the three-dimensional setting.... | {
"timestamp": "2005-03-18T22:37:41",
"yymm": "0503",
"arxiv_id": "math/0503390",
"language": "en",
"url": "https://arxiv.org/abs/math/0503390"
} |
\section{Introduction}
In a preceding article \cite{FHPR02} {\it
coherence in a relative sense}, i. e., understood
as a relation between a given observable and a
given quantum state, was postulated to be {\it
identical with incompatibility} between
observable and state as far as its {\it quantity}
$I_C$ is concerned. ... | {
"timestamp": "2005-03-08T10:22:35",
"yymm": "0503",
"arxiv_id": "quant-ph/0503077",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503077"
} |
\section{Introduction}
Generalizations $\Gamma_n$ of Hermite polynomials $H_n$ were recently
\cite{GiMeWe} proposed to describe, for instance, density perturbations
constrained by a condition of matter conservation. Because of the constraint,
such polynomials cannot form a complete set, but span a subspace well sui... | {
"timestamp": "2005-03-25T15:10:30",
"yymm": "0503",
"arxiv_id": "math-ph/0503060",
"language": "en",
"url": "https://arxiv.org/abs/math-ph/0503060"
} |
\section{Introduction}\label{s:1}
Nonlocality, {\em i.e.} the existence of correlations which cannot
be explained by any local hidden variable model, is perhaps
the most debated implication of quantum mechanics. During the last
decade other aspects of nonlocality, in addition to
generating nonlocal correlations, hav... | {
"timestamp": "2005-03-10T14:51:39",
"yymm": "0503",
"arxiv_id": "quant-ph/0503104",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503104"
} |
\section{Introduction}
In Newton's conception, there was an absolute background space. While matter, forces, energy and the like were actors acting out in time. So also the law of gravitation was an action at a distance theory. Every material particle exerted the force of gravitation instantly on every other material p... | {
"timestamp": "2005-03-29T14:59:39",
"yymm": "0503",
"arxiv_id": "physics/0503220",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503220"
} |
\section{Introduction}
\subsection{Reminder on Moyal product.}\label{reminder} Let $V$ be a finite
dimensional vector space equipped with a nondegenerate
bivector $\pi\in\wedge^2V$. Associated with $\pi$ is
a Poisson bracket $f,g\mapsto \{f,g\}:=\langle df\wedge dg,\pi\rangle$
on $\mathbf{k}[V],$ the polynomial algebra... | {
"timestamp": "2005-03-20T23:52:15",
"yymm": "0503",
"arxiv_id": "math/0503405",
"language": "en",
"url": "https://arxiv.org/abs/math/0503405"
} |
\section{Introduction}
\setcounter{equation}{0}
Let $M$ be a connected complex manifold and $\hbox{Aut}(M)$ the group of holomorphic automorphisms of $M$. If $M$ is Kobayashi-hyperbolic, $\hbox{Aut}(M)$ is a Lie group in the compact-open topology \cite{Ko}, \cite{Ka}. Let $d(M):=\hbox{dim}\,\hbox{Aut}(M)$. It is well-... | {
"timestamp": "2005-09-22T02:04:09",
"yymm": "0503",
"arxiv_id": "math/0503471",
"language": "en",
"url": "https://arxiv.org/abs/math/0503471"
} |
\section{\label{}Introduction}
In the last years a widespread attention has been devoted to the role
played by the isospin degree of freedom in the heavy--ion reaction
physics. The interest on this subject is twofold: the knowledge
of the symmetry term in the Equation of State (EOS) of
asymmetric nuclear matter, w... | {
"timestamp": "2005-03-08T19:37:21",
"yymm": "0503",
"arxiv_id": "nucl-th/0503018",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503018"
} |
\section{Introduction}
There is a well known similarity between the two-dimensional models of the
planetary atmosphere and the magnetized plasma. In the absence of
dissipation the models can be reduced to differential equations having the
same structure: the Charney equation for the nonlinear Rossby waves , in the
phy... | {
"timestamp": "2005-03-31T04:34:52",
"yymm": "0503",
"arxiv_id": "physics/0503155",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503155"
} |
\section{Introduction}
In [\ref{C}], the author studied the problem of finding ``almost squares" in short intervals, namely:
\begin{question}
\label{old}
For $0 \leq \theta < 1/2$, what is the least $f(\theta)$ such
that, for some $c_1, c_2 > 0$, any interval $[x - c_1 x^{f(\theta)}, x
+ c_1 x^{f(\theta)}]$ contains an... | {
"timestamp": "2005-03-24T18:42:42",
"yymm": "0503",
"arxiv_id": "math/0503438",
"language": "en",
"url": "https://arxiv.org/abs/math/0503438"
} |
\section{introduction}
In relativistic heavy ion collisions a localized high energy density
domain, a fireball, is created. The study of the properties of this
hot and dense matter is the main objective of the experiments being
conducted at RHIC and as of 2007 at LHC.
Event-by-event particle fluctuations are the obser... | {
"timestamp": "2006-04-29T17:03:29",
"yymm": "0503",
"arxiv_id": "nucl-th/0503026",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503026"
} |
\section{INTRODUCTION}
\label{sectoin1}
The proton separation energies of nuclei lying in the domain beyond the proton drip line are negative. Consequently these proton rich nuclei have positive $Q$ values for proton emissions with a natural tendency to shed off excess protons and are spontaneous proton emitters... | {
"timestamp": "2005-11-17T07:06:55",
"yymm": "0503",
"arxiv_id": "nucl-th/0503007",
"language": "en",
"url": "https://arxiv.org/abs/nucl-th/0503007"
} |
\section{Introduction}
\indent \hspace{7mm}
Random variables having orders-of-magnitude large values, but with
correspondingly orders-of-magnitude small probabilities for their
occurrence, are known to give non-Gaussian statistics for their
fluctuations - the L\'{e}vy statistics \cite{Paul}. For
these {\it larger-than-... | {
"timestamp": "2005-03-08T12:47:39",
"yymm": "0503",
"arxiv_id": "physics/0503059",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503059"
} |
\section{Introduction}
A nearest particle system
on $S= \{1,2,\cdots,N\}$ is a continuous time Markov chain with
the state space $\{ A : A \subset S \}$. The jump rates are
specified as follows:
$$
\begin{array}{ll}
q (A, A \setminus \{x\}) = 1 & {\rm if} \ x \in A; \\
q(A, A \cup \{x\}) = \beta(l_x(A), r_x(A)) & {\... | {
"timestamp": "2005-03-21T05:48:36",
"yymm": "0503",
"arxiv_id": "math/0503409",
"language": "en",
"url": "https://arxiv.org/abs/math/0503409"
} |
\section{Introduction}
During the past 20 years a number of methods has been devised for
state selective preparation and manipulation of discrete-level
quantum systems
\cite{paramonov1983,chelkowski1990,kaluza1993,bergmann1998,rabitz2003}.
However, simple population oscillations, induced by a resonant
driving pulse ha... | {
"timestamp": "2005-03-25T00:19:11",
"yymm": "0503",
"arxiv_id": "quant-ph/0503197",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0503197"
} |
\section{Introduction}
The century old Riemann hypothesis \cite{WaWh} states that the only nontrivial zeros of the
zeta function,
\begin{eqnarray}
\zeta(s) = \sum_{n=1}^\infty {1\over n^s} = \prod (1-p^{-s})^{-1} \ ,
\end{eqnarray}
are on the set of points $s={1\over 2}+it$. Tremendous numerical computations ... | {
"timestamp": "2005-03-16T21:21:47",
"yymm": "0503",
"arxiv_id": "physics/0503141",
"language": "en",
"url": "https://arxiv.org/abs/physics/0503141"
} |
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