pinecone/core-2020-05-10-deduplication huggingface dataset:
Scratchpad's view of algebra I: Basic commutative algebra

While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency
Photochemistry of Transition Metal Complexes Induced by Outer-Sphere Charge Transfer Excitation

The intermolecular (outer sphere, OS) interaction of a reducing and an oxidizing metal complex generates a new optical transition involving charge transfer (CT) from the electron donor to the acceptor. OS CT transitions are classified according to the redox site (metal or ligand). Generally, the interaction between donor and acceptor is facilitated by ion pairs consisting of an oxidizing complex cation and a reducing complex anion. There are also ion pairs which are composed of a metal complex and an organic counter ion as electron donor or acceptor. In addition, the review includes examples of OS CT interaction which do not involve ion pairs at all. — A short introduction into the theory is followed by the discussion of the spectroscopy of OS CT of transition metal complexes. Finally, photoreactions induced by OS CT transitions are reviewed. The optical transfer is frequently followed by a rapid back electron transfer which regenerates the starting complexes. In many cases the primary products are kinetically labile and substitution reactions compete successfully with back electron transfer. As a result stable redox products may be formed. As an alternative, the substitution can be followed by back electron transfer. Product formation appears then as a substitution of the starting complexes. The various possibilities are illustrated by appropriate examples
Quantum Limits of Measurements and Uncertainty Principle

In this paper, we show how the Robertson uncertainty relation gives certain
intrinsic quantum limits of measurements in the most general and rigorous
mathematical treatment. A general lower bound for the product of the
root-mean-square measurement errors arising in joint measurements of
noncommuting observables is established. We give a rigorous condition for
holding of the standard quantum limit (SQL) for repeated measurements, and
prove that if a measuring instrument has no larger root-mean-square
preparational error than the root-mean-square measurement errors then it obeys
the SQL. As shown previously, we can even construct many linear models of
position measurement which circumvent this condition for the SQL.Comment: 15 pages, presented at the International Workshop on Quantum Aspects
  of Optical Communications, C.N.R.S. Paris, France, November 26-28, 199
Continuous Non-Demolition Observation, Quantum Filtering and Optimal
  Estimation

A quantum stochastic model for an open dynamical system (quantum receiver)
and output multi-channel of observation with an additive nonvacuum quantum
noise is given. A quantum stochastic Master equation for the corresponding
instrument is derived and quantum stochastic filtering equations both for the
Heisenberg operators and the reduced density matrix of the system under the
nondemolition observation are found. Thus the dynamical problem of quantum
filtering is generalized for a noncommutative output process, and a quantum
stochastic model and optimal filtering equation for the dynamical estimation of
an input Markovian process is found. The results are illustrated on an example
of optimal estimation of an input Gaussian diffusion signal, an unknown
gravitational force say in a quantum optical or Weber's antenna for detection
and filtering a gravitational waves.Comment: A revised version of the paper published in the Proceedings of the
  1st QCMC conference, Paris 199
Propagation - a new operation in a framework for abstract interpretation of logic programs

Most frameworks for abstract interpretation of logic programs provide abstract operations which safely approximate their concrete counterpart. That means, given a concrete state S described by an abstract state AS and a concrete operation O producing O(S), the corresponding abstract operation AO produces AO(AS) which must describe O(S). We sketch a framework which relaxes this condition and requires that the safe approximation condition is only reached after a propagation step which reexecutes - at the abstract level - all operations leading to O(S) until a stable abstract state is reached. We illustrate the novel framework with a mode analysis which, notwithstanding a very simple abstract domain, reaches on several examples similar precision as mode analysis systems using much complexer abstract domains.status: publishe
Towards Intelligent Databases

This article is a presentation of the objectives and techniques
of deductive databases. The deductive approach to databases aims at extending
with intensional definitions other database paradigms that describe
applications extensionaUy. We first show how constructive specifications can
be expressed with deduction rules, and how normative conditions can be defined
using integrity constraints. We outline the principles of bottom-up and
top-down query answering procedures and present the techniques used for
integrity checking. We then argue that it is often desirable to manage with
a database system not only database applications, but also specifications of
system components. We present such meta-level specifications and discuss
their advantages over conventional approaches.
A storage and access architecture for efficient query processing in spatial database systems

Due to the high complexity of objects and queries and also due to extremely
large data volumes, geographic database systems impose stringent requirements on their
storage and access architecture with respect to efficient query processing. Performance
improving concepts such as spatial storage and access structures, approximations, object
decompositions and multi-phase query processing have been suggested and analyzed as
single building blocks. In this paper, we describe a storage and access architecture which
is composed from the above building blocks in a modular fashion. Additionally, we incorporate
into our architecture a new ingredient, the scene organization, for efficiently
supporting set-oriented access of large-area region queries. An experimental performance
comparison demonstrates that the concept of scene organization leads to considerable
performance improvements for large-area region queries by a factor of up to 150.
Query processing of spatial objects: Complexity versus Redundancy

The management of complex spatial objects in applications, such as geography and cartography,
imposes stringent new requirements on spatial database systems, in particular on efficient
query processing. As shown before, the performance of spatial query processing can be improved
by decomposing complex spatial objects into simple components. Up to now, only decomposition
techniques generating a linear number of very simple components, e.g. triangles or trapezoids, have
been considered. In this paper, we will investigate the natural trade-off between the complexity of
the components and the redundancy, i.e. the number of components, with respect to its effect on
efficient query processing. In particular, we present two new decomposition methods generating
a better balance between the complexity and the number of components than previously known
techniques. We compare these new decomposition methods to the traditional undecomposed representation
as well as to the well-known decomposition into convex polygons with respect to their
performance in spatial query processing. This comparison points out that for a wide range of query
selectivity the new decomposition techniques clearly outperform both the undecomposed representation
and the convex decomposition method. More important than the absolute gain in performance
by a factor of up to an order of magnitude is the robust performance of our new decomposition
techniques over the whole range of query selectivity.
Object-oriented querying of existing relational databases

In this paper, we present algorithms which allow an object-oriented
querying of existing relational databases. Our goal is to provide an improved query
interface for relational systems with better query facilities than SQL. This
seems to be very important since, in real world applications, relational systems
are most commonly used and their dominance will remain in the near future. To
overcome the drawbacks of relational systems, especially the poor query facilities
of SQL, we propose a schema transformation and a query translation algorithm.
The schema transformation algorithm uses additional semantic information to enhance
the relational schema and transform it into a corresponding object-oriented
schema. If the additional semantic information can be deducted from an underlying
entity-relationship design schema, the schema transformation may be done
fully automatically. To query the created object-oriented schema, we use the
Structured Object Query Language (SOQL) which provides declarative query facilities
on objects. SOQL queries using the created object-oriented schema are
much shorter, easier to write and understand and more intuitive than corresponding
S Q L queries leading to an enhanced usability and an improved querying of
the database. The query translation algorithm automatically translates SOQL queries
into equivalent SQL queries for the original relational schema.
Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating
factor in CAD/CAM applications has necessitated the development of database
systems with appropriate modelling and retrieval capabilities. One essential
problem is the treatment of geometric data which has led to the development of
spatial databases. Unfortunately, most proposals only deal with simple geometric
objects like multidimensional points and rectangles. On the other hand, there has
been a rapid development in the field of representing geometric objects with free
form curves or surfaces, initiated by engineering applications such as mechanical
engineering, aviation or astronautics. Therefore, we propose a concept for the realization
of spatial retrieval operations on geometric objects with free form
boundaries, such as B-spline or Bezier curves, which can easily be integrated in
a database management system. The key concept is the encapsulation of geometric
operations in a so-called query processor. First, this enables the definition of
an interface allowing the integration into the data model and the definition of the
query language of a database system for complex objects. Second, the approach
allows the use of an arbitrary representation of the geometric objects. After a
short description of the query processor, we propose some representations for free
form objects determined by B-spline or Bezier curves. The goal of efficient query
processing in a database environment is achieved using a combination of decomposition
techniques and spatial access methods. Finally, we present some experimental
results indicating that the performance of decomposition techniques is
clearly superior to traditional query processing strategies for geometric objects
with free form boundaries.
Timewise Refinement for Communicating Processes.

A theory of timewise refinement is presented. This allows the translation of specifications and proofs of correctness between semantic models, permitting each stage in the verification of a system to take place at the appropriate level of abstraction. The theory is presented within the context of CSP. A denotational characterisation is given in terms of relations between behaviours at different levels of abstraction, and various properties for the preservation of refinement through parallel composition are discussed. An operational characterisation is also given in terms of timed and untimed tests, and observed to coincide with the denotational characterisation
Prima Facie Questions in Quantum Gravity

The long history of the study of quantum gravity has thrown up a complex web
of ideas and approaches. The aim of this article is to unravel this web a
little by analysing some of the {\em prima facie\/} questions that can be asked
of almost any approach to quantum gravity and whose answers assist in
classifying the different schemes. Particular emphasis is placed on (i) the
role of background conceptual and technical structure; (ii) the role of
spacetime diffeomorphisms; and (iii) the problem of time.Comment: 20,IC/TP/0
The semiclassical approximation to quantum gravity

A detailed review is given of the semiclassical approximation to quantum
gravity in the canonical framework. This includes in particular the derivation
of the functional Schr\"odinger equation and a discussion of semiclassical time
as well as the derivation of quantum gravitational correction terms to the
Schr\"odinger equation. These terms are used to calculate energy shifts for
fields in De~Sitter space and non-unitary contributions in black hole
evaporation. Emphasis is also put on the relevance of decoherence and
correlations in semiclassical gravity. The back reaction of non-gravitational
quantum fields onto the semiclassical background and the emergence of a Berry
connection on superspace is also discussed in this framework.Comment: LATEX, 47 pages, report Freiburg THEP-93/27, to appear in ``Canonical
  gravity -- from classical to quantum", edited by J. Ehlers and H. Friedrich
  (Springer, Berlin, 1994
Reduced models for quantum gravity

The preceding talks given at this conference have dealt mainly with general
ideas for, main problems of and techniques for the task of quantizing gravity
canonically. Since one of the major motivations to arrange for this meeting was
that it should serve as a beginner's introduction to canonical quantum gravity,
we regard it as important to demonstrate the usefulness of the formalism by
means of applying it to simplified models of quantum gravity, here formulated
in terms of Ashtekar's new variables. From the various, completely solvable,
models that have been discussed in the literature we choose those that we
consider as most suitable for our pedagogical reasons, namely 2+1 gravity and
the spherically symmetric model. The former model arises from a dimensional,
the latter from a Killing reduction of full 3+1 gravity. While 2+1 gravity is
usually treated in terms of closed topologies without boundary of the initial
data hypersurface, the toplogy for the spherically symmetric system is chosen
to be asymptotically flat. Finally, 2+1 gravity is more suitably quantized
using the loop representation while spherically symmetric gravity is easier to
quantize via the self-dual representation. Accordingly, both types of
reductions, both types of topologies and both types of representations that are
mainly employed in the literature in the context of the new variables come into
practice. What makes the discussion especially clear is the fact that for both
models the reduced phase space turns out to be finitely dimensional.Comment: 27p, LATE
String theory and classical integrable systems

We discuss different formulations and approaches to string theory and $ 2d$
quantum gravity. The generic idea to get a unique description of {\it many}
different string vacua altogether is demonstrated on the examples in $ 2d$
conformal, topological and matrix formulations. The last one naturally brings
us to the appearance of classical integrable systems in string theory. Physical
meaning of the appearing structures is discussed and some attempts to find
directions of possible generalizations to ``higher-dimensional" models are
made. We also speculate on the possible appearence of quantum integrable
structures in string theory.Comment: lecture given at III Baltic Rim student seminar, Helsinki, September
  1993} 33pp, late
Lectures on Mirror Symmetry

We give an introduction to mirror symmetry of strings on Calabi-Yau manifolds
with an emphasis on its applications e.g. for the computation of Yukawa
couplings. We introduce all necessary concepts and tools such as the basics of
toric geometry, resolution of singularities, construction of mirror pairs,
Picard-Fuchs equations, etc. and illustrate all of this on a non-trivial
example. Extended version of a lecture given at the Third Baltic Student
Seminar, Helsinki September 1993Comment: LMU-TPW-94-02, 45 pages, harvma
Baxterization, dynamical systems, and the symmetries of integrability

We resolve the `baxterization' problem with the help of the automorphism
group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations.
This infinite group of symmetries is realized as a non-linear (birational)
Coxeter group acting on matrices, and exists as such, {\em beyond the narrow
context of strict integrability}. It yields among other things an unexpected
elliptic parametrization of the non-integrable sixteen-vertex model. It
provides us with a class of discrete dynamical systems, and we address some
related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are
  BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to
  viallet@lpthe.jussieu.fr and give your postal mail addres
A lecture on the Calogero-Sutherland models

In these lectures, I review some recent results on the Calogero-Sutherland
model and the Haldane Shastry-chain. The list of topics I cover are the
following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics.
The form factor of the density operator. 2) The Dunkl operators and their
relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The
Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at
a specific coupling constant.Comment: (2 references added, small modifications
Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems
  on the Cylinder

Pure gravity and gauge theories in two dimensions are shown to be special
cases of a much more general class of field theories each of which is
characterized by a Poisson structure on a finite dimensional target space. A
general scheme for the quantization of these theories is formulated. Explicit
examples are studied in some detail. In particular gravity and gauge theories
with equivalent actions are compared. Big gauge transformations as well as the
condition of metric nondegeneracy in gravity turn out to cause significant
differences in the structure of the corresponding reduced phase spaces and the
quantum spectra of Dirac observables. For $R^2$ gravity coupled to SU(2) Yang
Mills the question of quantum dynamics (`problem of time') is addressed. [This
article is a contribution to the proceedings (to appear in LNP) of the 3rd
Baltic RIM Student Seminar (1993). Importance is attached to concrete examples.
A more abstract presentation of the ideas underlying this article (including
new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-
Wodzicki residue and anomalies of current algebras

The commutator anomalies (Schwinger terms) of current algebras in $3+1$
dimensions are computed in terms of the Wodzicki residue of pseudodifferential
operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie
algebra of PSDO's. The construction of the (second quantized) current algebra
is closely related to a geometric renormalization of the interaction
Hamiltonian $H_I=j_{\mu} A^{\mu}$ in gauge theory.Comment: 15 pages, updated version of a talk at the Baltic School in Field
  Theory, September 199
Genetic lander: An experiment in accurate neuro-genetic control

International audienceThe control problem of soft-landing a toy lunar module sim-ulation is investigated in the context of neural nets. While traditional supervised back-propagation training is inappropriate for lack of train-ing exemplars, genetic algorithms allow a controller to be evolved with-out diiculty: Evolution is a form of unsupervised learning. A novelty introduced in this paper is the presentation of additional renormalized inputs to the net; experiments indicate that the presence of such inputs allows precision of control to be attained faster, when learning time is measured by the number of generations for which the GA must run to attain a certain mean performance
Superstrings: the view from below

review the Standard Model in a form conducive to formulating its possible short distance extensions. This depends on the value of the Higgs mass, the only unknown parameter of the model. We suggest methods to reproduce many of the small numbers in the model in terms of scale ratios, applying see-saw like ideas to the breaking of chiral symmetries. We then investigate how the N=1 Standard Model extrapolated to or near the Planck scale can fit superstring models, emphasizing the use of some non-renormalizable operators generic to superstrings
Non-Standard Fermion Propagators from Conformal Field Theory

It is shown that Weyl spinors in 4D Minkowski space are composed of primary
fields of half-integer conformal weights. This yields representations of
fermionic 2-point functions in terms of correlators of primary fields with a
factorized transformation behavior under the Lorentz group. I employ this
observation to determine the general structure of the corresponding Lorentz
covariant correlators by methods similar to the methods employed in conformal
field theory to determine 2- and 3-point functions of primary fields. In
particular, the chiral symmetry breaking terms resemble fermionic 2-point
functions of 2D CFT up to a function of the product of momenta. The
construction also permits for the formulation of covariant meromorphy
constraints on spinors in 3+1 dimensions.Comment: 15 pages, Latex, LMU-TPW 94-1
Symmetry Principles for String Theory

The gauge symmetries that underlie string theory arise from inner
automorphisms of the algebra of observables of the associated conformal field
theory. In this way it is possible to study broken and unbroken symmetries on
the same footing, and exhibit an infinite-dimensional supersymmetry algebra
that includes space-time diffeomorphisms and an infinite number of
spontaneously broken level-mixing symmetries. We review progress in this area,
culminating in the identification of a weighted tensor algebra as a subalgebra
of the full symmetry. We also briefly describe outstanding problems. Talk
presented at the Gursey memorial conference, Istanbul, Turkey, June, 1994.Comment: 5 pages, Plain TeX, no figure
Spatial Geometry and the Wu-Yang Ambiguity

We display continuous families of SU(2) vector potentials $A_i^a(x)$ in 3
space dimensions which generate the same magnetic field $B^{ai}(x)$ (with det
$B\neq 0$). These Wu-Yang families are obtained from the Einstein equation
$R_{ij}=-2G_{ij}$ derived recently via a local map of the gauge field system
into a spatial geometry with $2$-tensor $G_{ij}=B^a{}_i B^a{}_j\det B$ and
connection $\Gamma_{jk}^i$ with torsion defined from gauge covariant
derivatives of $B$.Comment: Based on talks given by R. Khuri at PASCOS-94, Syracuse University,
  May 1994 and at Gursey Memorial Conference I, Istanbul, June 1994, 7 pages,
  TeX (typo in first Author's name is corrected.