Search results for "Linear Algebra."
showing 10 items of 552 documents
Fast evaluation of a linear number of local exchange matrices
2002
A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.
Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
2020
Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non trace-preserving character of the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we sh…
Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
1999
This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems:
An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach
2009
A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model
2002
The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.
About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO
2006
Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…
Critical analysis of the spin-rotation constants of CF2 and CCl2: A theoretical investigation
2005
Quantum chemical ab initio calculations for the spin-rotation constants of difluorocarbene (CF2) and dichlorocarbene (CCl2) were carried out using coupled-cluster techniques with sequences of correlation-consistent basis sets. Theoretical best estimates were obtained using extrapolation to the complete basis-set limit and taking into account corrections for core correlation, additional diffuse functions and zero-point vibrational effects. It is demonstrated that such accurate theoretical estimates can be used either to support or to challenge the analysis of the experimental spectra and the reliability of the resulting data. 2005 Elsevier B.V. All rights reserved.
New Theoretical Solution of Stage-Discharge Relationship for Slit Weirs
2018
In this paper, the flow-process of a slit weir was analyzed on the basis of a theorem of dimensional analysis and incomplete selfsimilarity theory. The theoretically deduced stage-discharge formula then was calibrated using experimental data obtained for a ratio between the weir and the channel width, ranging from 0.05 to 0.25. The deduced stage-discharge relationship allowed measuring discharge values characterized by errors that, for 98% of the measured values, were less than or equal to 5%. The performance of the proposed theoreticalstage-discharge formula also was improved by introducing the Reynolds number (for 98.5% of the measured values the error was less than or equal to 5%, and th…
Aggregation of Risk Level Assessments Based on Fuzzy Equivalence Relation
2017
The paper deals with the problem of aggregation of risk level assessments. We describe the technique of a risk level evaluation taking into account values of the risk level obtained for objects which are in some sense equivalent. For this purpose we propose to use the construction of a general aggregation operator based on the corresponding fuzzy equivalence relation. Numerical example of the investment risk level aggregation using an equivalence relation obtained on the basis of different macroeconomic factors for countries of one region is considered.
On complete set of solutions for polynomial matrix equations
1990
Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.