Search results for "algebra"
showing 10 items of 4129 documents
STUDY OF THE INTERNAL DYNAMICS OF NON PLANAR PYRAMIDAL MOLECULES IN VIBRATIONALY VERY EXCITED STATES.
2007
From the U (p+1) formalism, we built a Hamiltonian adapted to the stretching modes of nonplanar XY3 molecules having the C3v group of geometrical invariance. This Hamiltonian is then coupled with two possible Hamiltonians describing the bending modes of these molecular system: a) based on the U (p+1) approach, a bending Hamiltonian is developed and the interaction between the bending and the stretching modes is taking into account through adapted 2:1 resonance coupling operator defined as a Us(4) x Ub(4) enveloping algebra operator ; b) based on the standard normal modes formalism, a bending modes Hamiltonian is expanded and the 2:1 interaction is taken into account as a tensorial product o…
Algebraic study of pyramidal molecules in the very excited vibrational states.
2005
In the frame of the algebraic formalism U(p+1), we developed the method to build a vibrational Hamiltonian corresponding to a set of three identical oscillators. In order to test the model, we apply it to the molecules of stibine and arsine. We introduce a supplementary intermediate group K(3) inspired by the similar formalism used in nuclear physics. This group K(3) gives additional labels for classification of the energy levels. The eigenvalues of these invariant operators distinguish the local states of the molecule. Then we study the coupling of the vibrational modes of stretching and bending for the non plane XY3 molecules. We present the construction of an algebraic operator of coupli…
CliffoSor: A Parallel Embedded Architecture for Geometric Algebra and Computer Graphics
2006
Geometric object representation and their transformations are the two key aspects in computer graphics applications. Traditionally, compute-intensive matrix calculations are involved to model and render 3D scenery. Geometric algebra (a.k.a. Clifford algebra) is gaining growing attention for its natural way to model geometric facts coupled with its being a powerful analytical tool for symbolic calculations. In this paper, the architecture of CliffoSor (Clifford Processor) is introduced. ClifforSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on an FPGA board is detailed. Initial test results show more …
cuBool: Bit-Parallel Boolean Matrix Factorization on CUDA-Enabled Accelerators
2018
Boolean Matrix Factorization (BMF) is a commonly used technique in the field of unsupervised data analytics. The goal is to decompose a ground truth matrix C into a product of two matrices A and $B$ being either an exact or approximate rank k factorization of C. Both exact and approximate factorization are time-consuming tasks due to their combinatorial complexity. In this paper, we introduce a massively parallel implementation of BMF - namely cuBool - in order to significantly speed up factorization of huge Boolean matrices. Our approach is based on alternately adjusting rows and columns of A and B using thousands of lightweight CUDA threads. The massively parallel manipulation of entries …
Order-disorder-and order-order-transitions in AB and ABC block copolymers: description by a simple model
1996
Based on the description of AB-block copolymers as micellar structures given by Semenov, the phase diagram of AB-diblock copolymers is calculated taking the homogeneously mixed system as a reference state. The predicted value (χN)c = 10.385 for a symmetric AB-diblock copolymer compares very well to the result of the original Random Phase Approximation theory (10.495). The simplicity of the model allows its extension to predict order-order transitions in ABC-triblock copolymers.
Ergativity and Differential Case Marking
2017
Abstract The present chapter discusses patterns of differential case marking in ergative languages, focusing on differential subject marking, which is more prominent in ergative languages (in contrast to accusative languages, where differential object marking is more prominent). It is argued that patterns of (differential) case marking can be accounted two general constraints related to (role)-indexing, on the one hand, and distinguishability (or markedness) on the other hand. This approach correctly predicts asymmetries between differential object marking (DOM) and differential subject marking (DSM) with regard to animacy, definiteness, as well as discourse features. I also show how this a…
Strengthened splitting methods for computing resolvents
2021
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the notion of the “strengthening” of a set-valued operator, which can be viewed as a type of regularisation that preserves computational tractability. After deriving a number of iterative schemes through this framework, we demonstrate their application to best approximation problems, image denoising and elliptic PDEs. FJAA and RC were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund …
Square of Opposition Under Coherence
2016
Various semantics for studying the square of opposition have been proposed recently. So far, only (Gilio et al., 2016) studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized qu…
Nonlinear Complex PCA for spatio-temporal analysis of global soil moisture
2020
Soil moisture (SM) is a key state variable of the hydrological cycle, needed to monitor the effects of a changing climate on natural resources. Soil moisture is highly variable in space and time, presenting seasonalities, anomalies and long-term trends, but also, and important nonlinear behaviours. Here, we introduce a novel fast and nonlinear complex PCA method to analyze the spatio-temporal patterns of the Earth's surface SM. We use global SM estimates acquired during the period 2010-2017 by ESA's SMOS mission. Our approach unveils both time and space modes, trends and periodicities unlike standard PCA decompositions. Results show the distribution of the total SM variance among its differ…
Inversion of matrix pencils for generalized systems
1993
Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.