Search results for " Algebra"
showing 10 items of 2082 documents
K4-free Graphs as a Free Algebra
2017
International audience; Graphs of treewidth at most two are the ones excluding the clique with four vertices (K4) as a minor, or equivalently, the graphs whose biconnected components are series-parallel. We turn those graphs into a finitely presented free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting these graphs: in addition to parallel composition and series composition, it suffices to consider the neutral elements of those operations and a unary transpose operation. Then we give a finite equational presentation and we prove it complete: two terms from the syntax are congruent if and only if they …
A note on Fréchet and approximate subdifferentials of composite functions
1994
The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.
On the Conditions of Price Consistency in the Input-Output Model
2013
The input-ouput model remains the basis of most SAM or CGE models. It actually uses two periods: the prices indexes solve it with the current period coefficients; the corresponding physical model is monoperiodic: the current prices solve it with the base period coefficients. The Leontief model is not consistent --- both models diverge generally --- unless the interindustry matrix of direct and indirect quantities of labor is stable over time. This implies that the vertically integrated labor coefficients are stable. This assumption is satisfied when the physical production coefficients and the physical labor coefficients are stable over time, two very strong assumptions.
Topology-based goodness-of-fit tests for sliced spatial data
2023
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the test…
Computation of the topological type of a real Riemann surface
2012
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $\mathcal{A}$-cycles are invariant under the anti-holomorphic involution $\tau$.
Multistate active spaces from local CAS-SCF molecular orbitals: the photodissociation of HFCO as an example.
2005
A recently developed algorithm to generate localized molecular orbitals (LMO) is applied to the study of excited states along a photodissociation process. The LMOs allow for the selection of a consistent complete active space (CAS) for the simultaneous description of all the electronic states involved in a multistate process on the basis of simple chemical criteria. The local nature of the orbitals is used to label them in a unique way that does not depend on the molecular geometry. The selection of the electronic configurations of interest for the set of target states on only the basis of the dominant excitations required by the simplest configuration interaction (CI) descriptions for both…
Basis set and correlation effects in the calculation of accurate gas phase dimerization energies of two M+2 to give M2+4 (M = S, Se)
2000
The dimerization energies of two M2+ to give M42+ (M = S, Se) were calcd. They depend strongly on the size of the basis set and the correlation method used (ranging from 217 to 522 kJ/mol, M = S) and, therefore, a systematic study of basis set and correlation effects was performed [MP2, MP3, MP4(SDQ), CCSD, CCSD(T)]. The introduction of a second set of polarizing d-functions caused a significant redn. of the dimerization energies, but neither of the above limits is reached by the MPn (n = 2, 3, 4) theory, even with the largest basis sets [cc-pVQZ]. However, convergence was achieved by CCSD(T), compd. methods or hybrid HF/DFT calcns. employing flexible basis sets [e.g., CCSD(T)/cc-pV5Z, CBS-…
State-specific multireference coupled-cluster theory
2012
The multireference problem is considered one of the great challenges in coupled-cluster (CC) theory. Most recent developments are based on state-specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state-of-the-art methods, including Mukherjee's state-specific multireference coupled-cluster (Mk-MRCC) theory, multireference Brillouin–Wigner coupled-cluster (MR-BWCC) theory, the MRexpT method, and internally contracted multireference coupled-cluster (ic-MRCC) theory. Related methods such as extended single-reference schemes [e.g., the complete active space coupled-cluster (CASCC) theory] and canonical transfo…
Stability and -gain controller design for positive switched systems with mixed time-varying delays
2013
This paper investigates the problems of stability and L"1-gain controller design for positive switched systems with mixed time-varying delays. The mixed time-varying delays are presented in the forms of discrete delay and distributed delay. The purpose of this paper is to design a class of switching signals and a state feedback controller for the considered system such that the resulting closed-loop system is exponentially stable with L"1-gain performance. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and using the average dwell time approach, we propose a sufficient condition to ensure the exponential stability with weighted L"1-gain performance for the sys…
On the preparation of simple and universal buffers including polynuclear species
1986
A simple generalized procedure for the calculation of electrolyte concentrations in pH-buffers is proposed. Mixtures of acid-base systems and formation of polynuclear species at high ionic strengths are considered, and a diagram useful for the study and preparation of the buffers is shown.