Re: SUO: RE: FW: ONT Re: Manifolds Of Sensuous Impressions (MOSI's)
Hi Graham,
All this info is on the web page at http://suo.ieee.org
Adam
At 02:25 PM 8/7/2001 +1000, Horn, Graham wrote:
>Jim,
> . Thanks for this.
>
> . What are the specifications for the Ontology web address /
>site:
>* scope,
>* purpose,
>* content,
>* etc.?
>
> . Who manages / administers it, and ensures compliance, etc.?
>
> . How does one unsubscribe, should I decide that is the way to
>go?
>
>
>
>Cheers Graham Horn
>National Data Standards Unit
>Australian Institute of Health and Welfare
>================================================
>Phone: 02.6244.1094
>Fax: 02.6244.1199
>Email: Graham.Horn@aihw.gov.au <mailto:graham.horn@aihw.gov.au>
>
>
>-----Original Message-----
>From: jim.s3@juno.com [mailto:jim.s3@juno.com]
>Sent: Tuesday, 7 August 2001 10:12
>To: graham.horn@aihw.gov.au
>Subject: Re: FW: ONT Re: Manifolds Of Sensuous Impressions (MOSI's)
>
>Graham,
>
> I don't subscribe to the Ontology list.
>
> Also, I did not get a copy of this message at my office address,
>so best to send to this address.
>
>Jim
>On Mon, 6 Aug 2001 17:26:15 +1000 "Horn, Graham"
><graham.horn@aihw.gov.au> writes:
> > Jim,
> > . What is the traffic on the Ont address apart from
> > Jon
> > Awbrey?
> >
> >
> >
> > Cheers Graham Horn
> > National Data Standards Unit
> > Australian Institute of Health and Welfare
> > ================================================
> > Phone: 02.6244.1094
> > Fax: 02.6244.1199
> > Email: Graham.Horn@aihw.gov.au
> > <mailto:graham.horn@aihw.gov.au>
> >
> >
> > -----Original Message-----
> > From: Jon Awbrey [SMTP:jawbrey@oakland.edu]
> > <mailto:[SMTP:jawbrey@oakland.edu]>
> > Sent: Saturday, 4 August 2001 1:44
> > To: Arisbe; Generic Ontology Group; Organization Complexity
> > Autonomy
> > Subject: ONT Re: Manifolds Of Sensuous Impressions (MOSI's)
> >
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > Manifold SIG,
> >
> > It will be useful to keep at the ready a compendium
> > of the most essential elements of our subject, and
> > so I will maintain what is needed in a cumulative
> > appendix to these notes.
> >
> > I continue the story with further readings from Lang's DARM,
> > knitting up a
> > few more strands of terminology into our yarn.
> > Recall the definition of an atlas:
> > An "atlas of class C^p (p >= 0)" on a set X is a collection of pairs
> > (U_i,
> > q_i), satisfying the conditions AT 1, AT 2, AT 3, (vide syllabus at
> > end of
> > this note).
> > Naturally enough, however much artifice may have gone into its
> > natural
> > naming, an atlas is conceived and executed all in order to collect a
> > number
> > of charts:
> > | Each pair (U_i, q_i) will be called a "chart" of the atlas.
> > | If a point x of X lies in U_i, then we say that (U_i, q_i)
> > | is a "chart at" x.
> >
> > We find next the need for a notion of "compatibility" among and
> > between
> > different atlases and their charts:
> > | Suppose that we are given an open subset U of X and a topological
> > isomorphism
> > | q : U -> U' onto an open subset of some Banach space E. We shall
> > say that
> > | (U, q) is "compatible" with the atlas {(U_i, q_i)} if each map q_i
> > q^-1
> > | (defined on a suitable intersection as in AT 3) is a
> > C^p-isomorphism.
> > |
> > | Two atlases are said to be "compatible" if each chart of one is
> > compatible
> > with
> > | the other atlas. One verifies immediately that the relation of
> > compatibility
> > | between atlases is an equivalence relation. An equivalence class
> > of
> > atlases
> > | of class C^p on X is said to define a structure of "C^p-manifold"
> > on X.
> > |
> > | If all the vector spaces E_i in some atlas are toplinearly
> > isomorphic,
> > then we can always
> > | find an equivalent atlas for which they are all equal, say to the
> > vector
> > space E. We then
> > | say that X is an "E-manifold" or that X is "modeled" on E.
> > |
> > | Lang, DARM, page 21
> >
> > E-nough For E-nonce,
> > Jon Awbrey
> > ¤~~~~~~~~~¤~~~~~~~~~¤~SYLLABUS~¤~~~~~~~~~¤~~~~~~~~~¤
> > | 2. Manifolds
> > |
> > | 2.1. Atlases, Charts, Morphisms
> > |
> > | Let X be a set. An "atlas of class C^p (p >= 0)" on X is a
> > collection
> > | of pairs (U_i, q_i) (i ranging in some indexing set), satisfying
> > the
> > | following conditions:
> > |
> > | AT 1. Each U_i is a subset of X and the U_i cover X.
> > |
> > | AT 2. Each q_i is a bijection of U_i onto an open subset q_i U_i
> > | of some Banach space E_i and for any i, j, [it holds that]
> > | q_i (U_i |^| U_j) is open in E_i.
> > |
> > | AT 3. The map
> > |
> > | q_j o q_i^-1 : q_i (U_i |^| U_j) --> q_j (U_i |^| U_j)
> > |
> > | is a C^p-isomorphism for each pair of indices i, j.
> > |
> > | Lang, DARM, page 20
> >
> > | o---------------------------------------o
> > o-------------------o
> > | | X | | E_i
> > |
> > | |
> > | |
> > |
> > | | | |
> > o
> > |
> > | | | |
> > / \
> > |
> > | | o | | /
> > \
> > |
> > | | / \ | | /
> > \
> > |
> > | | / \ | | /
> > \
> > |
> > | | / \ q_i | | / q_i
> > U_i \
> > |
> > | | / o---------------------->| o o
> > o
> > |
> > | | / \ | | \ / \
> > /
> > |
> > | | / \ | | \ /
> > \ /
> > |
> > | | / U_i \ | | o
> > o
> > |
> > | | / \ | | \
> > /
> > |
> > | | / \ | | \
> > /
> > |
> > | | o o o | | o
> > |
> > | | \ / \ / | |
> > |
> > | | \ / \ / | |
> > |
> > | | \ / U_i \ / |
> > o---------|---------o
> > | | \ / \ / | |
> > | | o |^| o | q_j o
> > q_i^-1
> > | | / \ / \ | |
> > | | / \ U_j / \ |
> > o---------v---------o
> > | | / \ / \ | | E_j
> > |
> > | | / \ / \ | |
> > |
> > | | o o o | | o
> > |
> > | | \ / | | /
> > \
> > |
> > | | \ / | | /
> > \
> > |
> > | | \ U_j / | | o
> > o
> > |
> > | | \ / | | / \
> > / \
> > |
> > | | \ / | | / \ /
> > \
> > |
> > | | \ o---------------------->| o o
> > o
> > |
> > | | \ / q_j | | \ q_j
> > U_j /
> > |
> > | | \ / | | \
> > /
> > |
> > | | \ / | | \
> > /
> > |
> > | | o | | \
> > /
> > |
> > | | | |
> > \ /
> > |
> > | | | |
> > o
> > |
> > | |
> > | |
> > |
> > | |
> > | |
> > |
> > | o---------------------------------------o
> > o-------------------o
> > |
> > | Figure 1. Manifold Of Coordinated Impressions
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~SUBALLYS~¤~~~~~~~~~¤~~~~~~~~~¤
> >
Adam Pease
Teknowledge
(650) 424-0500 x571