Search results for "algebra"
showing 10 items of 4129 documents
Transition Dipole Orientation of Linear Polyenes: Semiempirical Models and Extrapolation to the Infinite Chain Limit
1999
Linear conjugated polyenes have an electronic transition dipole moment for the strongly allowed 1Ag to 1Bu electronic excitation that is not oriented along the major axis of the polyene chain. In this paper, the experimental values of this off-axis angle are compared to semiempirical and ab initio theoretical predictions. The semiempirical computations are shown to be reliable and are extended to long chains (n = 20). The results are then extrapolated to the infinite chain limit. A nonzero value of 6°−11° for the infinite polyene is suggested by this extrapolation but state of the art ab initio results for a series of small polyenes yield a zero asymptotic value.
The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations
2003
The vertical electronic spectrum of formaldehyde has been studied by means of (SC)2-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchan, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the 2B2 state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)2 dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is s…
The expansion $\star$ mod $\bar{o}(\hbar^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization
2019
The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 w…
The homotopy Leray spectral sequence
2018
In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations necessary to build the spectral sequence and give a convenient description of its $E_2$-page. Our description of the $E_2$-page is in terms of homology of the local system of fibers, which is given using a theory similar to Rost's cycle modules. We close by providing some sample applications of the spectral sequence and some hints at future work.
From top-down urban planning to culturally sensitive planning? Urban renewal and artistic activism in a neo-bohemian district in Barcelona
2020
The city of Barcelona in general and its historic center in particular have undergone a sea change from an industrial city to a global tourism and service center. Some authors argue that urban rene...
An Observation Framework for Multi-agent Systems
2009
Existing middleware platforms for multi-agent systems (MAS) do not provide general support for observation. On the other hand, observation is considered to be an important mechanism needed for realizing effective and efficient coordination of agents. This paper describes a framework called Agent Observable Environment (AOE) for observation-based interaction in MAS. The framework provides 1) possibility to model MAS components with RDF-based observable soft-bodies, 2) support for both query and publish/subscribe style ontology-driven observation, and 3) ability to restrict the visibility of observable information using observation rules. Additionally, we report on an implementation of the fr…
Towards Concrete Syntax Based Find for Graphical Domain Specific Languages
2019
One of the main reasons why Model-Driven Engineering (MDE) technologies including Domain-specific modelling languages (DSML) have not reached the expected acceptance in the industry is a poor tool support. One of the features with a limited support even in commercial modelling tools is search (find). Typically, MDE tools support only a simple keyword-based textual search functionality. The same is true for the tools built using Domain-specific language (DSL) tool definition frameworks. It is proposed to provide the concrete syntax-based find functionality as a service of a DSL tool definition framework. The find diagrams are defined in a concrete syntax of a DSL. A definition of a DSL is us…
Multiobjective service restoration in distribution networks using an evolutionary approach and fuzzy sets
2000
Abstract In this article, the service restoration (SR) problem in electrical distribution networks is dealt with using an evolutionary strategy (ES) with a fuzzy definition of the conflicting objectives. The normal operation status allows the remote control of tie-switches, of capacitor banks and load connection. When a permanent fault occurs, the same remote control actions can be performed with the aim of restoring the service in the concerned areas. The status of these remotely controllable elements is the boolean optimisation variables for the SR problem. Besides this, here the SR problem is dealt with in a multiple objectives (MO) formulation. Indeed, the power losses’ term is consider…
Generalized Rough Sets in Contextual Spaces
1997
This paper presents a generalization of Pawlak’s conception of rough sets [6] and [7]. It is more general than Pawlak’s solution of the problem of the definability of sets, the knowledge of which is incomplete and vague. The authors’ conception is based on conception of contextual space [4], which was inspired by Ziarko’s approach [12] to rough sets. Rough sets introduced by Pawlak [6] are particular cases of contextual rough sets defined in the contextual approximation space. This space is defined axiomatically by means of so called context relations. Every contextual rough set determined by set X can be determined by the union of the lower approximation of X and a subset of the boundary o…