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