60 research outputs found
The Advantage of a Multi-User Mode
The purpose of this very short note, which maybe considered as a comment on
"hep-th/9401067", is to prove the following proposition. PROPOSITION. There
exist certain models of Mobilevision, in which interpretational figures are
observable only in a multi--user mode in contrast to single--user ones. This
result maybe interesting as for applications as for the understanding of
theoretical foundations of quantum interactive processes (hep-th/9403015).Comment: 2 pages AMSTE
Octonions and Binocular Mobilevision
This paper is devoted to an interaction of 2 objects: the 1st of them is
octonions, the classical structure of pure mathematics, the 2nd one is
Mobilevision, the recently developped technique of computer graphics. Namely,
it is shown that the binocular Mobilevision maybe elaborated by use of the
octonionic colour space - the 7-dimensional extension of the classical one,
which includes a strange overcolour besides two triples of ordinary ones
(blue,green, red for left and right eyes).
Contents.
I. Interpretational geometry, anomalous virtual realities, quantum projective
field theory and Mobilevision:(1.1. Interpretational geometry; 1.2. Anomalous
virtual realities; 1.3. Colours in anomalous virtual realities; 1.4. Quantum
projective field theory; 1.5. Mobilevision).
II. Quantum conformal and q_R-conformal field theories, an infinite
dimensional quantum group and quantum field analogs of Euler-Arnold top:(2.1.
Quantum conformal field theory; 2.2. Lobachevskii algebra, the quantization of
the Lobachevskii plane; 2.3. Quantum q_R-conformal field theory; 2.4. An
infinite dimensional quantum group; 2.5. Quantum-field Euler-Arnold top and
Virasoro master equation).
III. Octonionic colour space and binocular Mobilevision:(3.1. Quaternionic
description of ordinary colour space; 3.2. Octonionic colour space and
binocular Mobilevision).Comment: 9p AMSTEX, (revised version: printing formats are changed,
typographi- cal errors are excluded
Belavkin-Kolkoltsov watch-dog effects in interactively controlled stochastic computer-graphic dynamic systems. A mathematical study
Stochastic properties of the long-time behaviour of a continuously observed
(and interactively controlled) quantum-field top are investigated
mathematically. Applications to interactively controlled stochastic
computer-graphic dynamic systems are discussed.Comment: an essentially completed version of chao-dyn/940601
On the nonhamiltonian interaction of two rotators. II. Unraveling the algebraic structure
This note being is devoted to the unraveling of the algebraic structure,
which governs the quadratic nonhamiltonian interaction of two rotators
described in the first part. It should be considered in the context of a
general ideology of the inverse problem of representation theory (see
mp_arc/96-477). The resulted objects are formalized as Lie algebras with
operators (Lie algebras with additional unary operations).Comment: AMSTEX. Part I: dg-ga/940900
Topics in Hidden Symmetries
These three topics are an attempt to explicate some curiosities of the
inverse problem of representation theory (i.e. having a set of operators to
describe the "correct" algebraic object, which is represented by them) on
simple examples related to the Lie algebra sl(2,C). Such consideration maybe
regarded as toy one for analogous infinite dimensional problems in the modern
quantum field theory (conformal field theory, integrable models, field theory
in non-trivial backgrounds). Some constructions inspired by these topics and
related to infinite dimensional hidden symmetries, which are produced by vertex
operator fields, will be discussed in the forthcoming article.Comment: 11 pages AMSTEX, amsppt styl
Experimental detection of interactive phenomena and their analysis
The article is devoted to mathematical methods of experimental detection of
interactive phenomena in complex systems and their analysis
Belavkin-Kolokoltsov watch-dog effects in interactively controlled stochastic computer-graphic dynamic systems
Stochastic properties of the long time behavior of a continuously observed
(and interactively controlled) quantum--field top are investigated
mathematically. Applications to interactively controlled stochastic
computerographical dynamic systems are discussed.Comment: A mathematical study. 11pp, amstex [revised: 8.X.94]., (e mail:
[email protected]
Topics in hidden symmetries. V
This note being devoted to some aspects of the inverse problem of
representation theory contains a new insight into it illustrated by two topics.
The attention is concentrated on the manner of representation of abstract
objects by the concrete ones as well as on the abstract objects themselves. The
results of researches allow to state that the actual richness and
attractiveness of the inverse problem of representation theory are based not
only on a large scope of various interesting abstract algebraic structures,
which may be concretely represented and somehow unravelled, but also on the
diversity of the manners of representation, which may produce very intriguing
unexpected and nontrivial effects under the intent look even in the simple and
almost hackneyed situations.Comment: small correction - one remark is excluded; Parts.I-IV,VI:
hep-th/9405050, q-alg/9610026, q-alg/9611003, q-alg/9622019, q-alg/970802
On the dynamics of noncanonically coupled oscillators and its hidden superstructure
The classical and quantum dynamics of the noncanonically coupled oscillators
is considered. It is shown that though the classical dynamics is well--defined
for both harmonic and anharmonic oscillators, the quantum one is well--defined
in the harmonic case, admits a hidden (super)Hamiltonian formulation, and thus,
preserves the initial operator relations, whereas a na\"\i ve quantization of
the anharmonic case meets with principal difficulties.Comment: revised version -- refs are update
Droems: experimental mathematics, informatics and infinite dimensional geometry
The article is devoted to a problem of elaboration of the real-time
interactive videosystems for accelerated nonverbal cognitive computer and
telecommunications. The proposed approach is based on the using of droems
(dynamically reconstructed objects of experimental mathematics) and
interpretational figures as pointers to them. Four paragraphs of the article
are devoted to (1) an exposition of basic notions of the interpretational
geometry, (2) the operator methods in the theory of interactive dynamical
videosystems, (3) the general concept of organization of the integrated
interactive real-time videocognitive systems, (4) the droems and processes of
their dynamical reconstruction, where the general notions are illustrated by a
concrete example related to the infinite dimensional geometry. The exposition
is presumably heuristic and conceptual (the first and the third paragraphs)
though some particular aspects such as content of the second and the fourth
paragraphs, which allow deeper formalization and detailing in present, are
exposed on the mathematical level of rigor.Comment: bilingual version [English translation+Russian original]: 43 pages,
AMSTE
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