From lvieira@fe.up.pt Thu Apr 3 05:12:25 2008 Return-Path: X-Original-To: ilas08@star.izt.uam.mx Delivered-To: ilas08@star.izt.uam.mx Received: from smtp2.fe.up.pt (smtp.fe.up.pt [193.136.28.30]) by star.izt.uam.mx (Postfix) with ESMTP id A3B093C98C for ; Thu, 3 Apr 2008 05:12:21 -0500 (CDT) Received: from localhost (localhost [127.0.0.1]) by smtp2.fe.up.pt (Postfix) with ESMTP id D2C0F13F724 for ; Thu, 3 Apr 2008 11:03:19 +0100 (WEST) Received: from smtp2.fe.up.pt ([127.0.0.1]) by localhost (smtp2.fe.up.pt [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id xli-dhp1Fg2E for ; Thu, 3 Apr 2008 11:03:19 +0100 (WEST) Received: from G02CF1402 (G02CF1216.fe.up.pt [192.168.81.122]) by smtp2.fe.up.pt (Postfix) with ESMTP id 8737313F716 for ; Thu, 3 Apr 2008 11:03:19 +0100 (WEST) From: =?iso-8859-1?Q?Lu=EDs_Vieira?= To: Subject: Abstract corrections Date: Thu, 3 Apr 2008 11:04:10 +0100 Message-ID: <000601c89572$0fa28a60$2ee79f20$@up.pt> MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_0007_01C8957A.7166F260" X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: AciVcfoM1UyuNB9bRKiBraRLrixWwA== Content-Language: pt Status: R This is a multipart message in MIME format. ------=_NextPart_000_0007_01C8957A.7166F260 Content-Type: multipart/alternative; boundary="----=_NextPart_001_0008_01C8957A.7166F260" ------=_NextPart_001_0008_01C8957A.7166F260 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear colleague The abstract needs some corrections that I present next =20 Corrections made in the abstract (line i of the body of the abstract) =20 line 3-=20 powers of $A^j$ ----> powers $A^j$ =20 line 4- work ones proves---->exposition one proves =20 line 7 -krein --->Krein =20 line 9 Finally one presents necessary conditions over the parameters and the spectra of the $\tau$ strongly $(n,p;a,c)$ regular graph ---> =20 Finally one presents necessary conditions over the parameters and the spectra of the strongly $(n,p;a,c)$ regular graph $\tau$ MODIFIED ABSTRACT =20 Title ---Euclidean Jordan algebras and inequalities on the parameters = and on the spectra of a strongly regular graph=97 =20 By Luis Vieira =20 \begin{abstract} =20 Let $\tau$ be a strongly $(n,p;a,c)$ regular graph, such that = $0

Dear = colleague

The abstract needs some = corrections that I present next

Corrections made in the abstract = (line i of the body of the abstract)

line 3-

powers of $A^j$ ----> powers = $A^j$

line 4-

=A0work ones = proves---->exposition one proves

line 7

-krein = --->Krein

line 9

Finally one presents necessary = conditions over the parameters and the spectra of the $\tau$ strongly $(n,p;a,c)$ = regular graph

--->

Finally one presents necessary = conditions over the parameters and the spectra of the=A0 strongly $(n,p;a,c)$ = regular graph $\tau$

MODIFIED = ABSTRACT

Title ---Euclidean Jordan = algebras and inequalities on the parameters and on the spectra=A0 of a strongly=A0 = regular graph—

By Luis = Vieira

\begin{abstract}

Let $\tau$ be a strongly = $(n,p;a,c)$ regular=A0=A0 graph, such that $0<c<p<n-1,$ $A$=A0 his matrix = of adjacency and let ${\cal V}_{n}$ be the Euclidean real space spanned by the = powers=A0 $A^j,j\in \mathbb{N}_{0}$=A0 where the scalar product $\bullet|\bullet$ = is defined by $x|y=3D\mbox{trace}(x \cdot y).$ In this exposition one = proves that ${\cal V}_{n}$ is an Euclidean Jordan algebra of rank 3 when one = introduces in ${\cal V}_{n}$ the usual product of matrices.=A0 Working inside the = Euclidean Jordan algebra ${\cal V}_{n}$ with the only complete system of = orthogonal idempotents associated to A=A0 one defines the generalized Krein = parameters of the=A0 strongly $(n,p;a,c)$ regular graph $\tau.$ Finally one presents = necessary conditions over the parameters and the spectra of the=A0 strongly = $(n,p;a,c)$ regular graph $\tau$.

\end{abstract}

{\bf Keywords}: {\it Euclidean = Jordan Algebras; Graph Theory (17C27; 05C50).}

I apologize by these mistakes, I = send to the colleague the winedt and the pdf of the abstract( the modified = abstract) .

My best = regards

Luis = Vieira

My best = regards

------=_NextPart_001_0008_01C8957A.7166F260-- ------=_NextPart_000_0007_01C8957A.7166F260 Content-Type: application/octet-stream; name="congressoilacancun.tex" Content-Transfer-Encoding: quoted-printable Content-Disposition: attachment; filename="congressoilacancun.tex" \documentclass[11pt,a4report]{article} \usepackage{graphicx} \usepackage{amsfonts} \usepackage{a4,amsmath,amssymb,psfig,here,epsf,amsfonts} \usepackage{a4,amsmath,amssymb,psfig,here,epsf,amsfonts} %\usepackage{amsmath,amssymb,psfig,here,epsf,bbold} \newcommand\E{\mathbb E} \newcommand\N{\mathbb N} \newcommand\R{\mathbb R} \newcommand\C{\mathbb C} \newcommand\Z{\mathbb Z} \newcommand\T{\mathbb T} \newcommand\Q{\mathbb Q} \newcommand{\HAT}[1]{\widetilde{#1}} % What to put to denote normalized = fns. \newcommand{\diff}[2]{\frac{\text{d}#1}{\text{d}#2}} % KMB \newcommand\cpp{{C\hspace{-.05em}\raisebox{.4ex}{\tiny\bf ++}}} \newtheorem{definition}{Definition}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{corollary}{Corollary}[section] \newtheorem{corollarydemo}{Corol\'{a}rio}[section] \newtheorem{lemma}{Lemma}[section] \newtheorem{remark}{Remark}[section] \newtheorem{conclusion}{Conclusion}[section] \newenvironment{demo}{\endsloppypar\noindent\bgroup\small {\bf{Proof.} \indent} }{\samepage\null\hfill \mbox{$\rule{2mm}{2mm}$} \quad\endsloppypar\egroup} \title{Euclidean Jordan algebras and inequalities on the parameters and = on the spectra of a strongly regular graph} \author{ Faculty of Engineering\\ Department of Civil Engineering\\ Section of Mathematics and Physics\\ University of Porto\\ S,Roberto Frias 4200-465\\ Portugal \\ Unit-CMUP} \date{ } \begin{document} \maketitle \begin{abstract} Let $\tau$ be a strongly $(n,p;a,c)$ regular graph, such that = $0