Search results for "Linear Algebra."
showing 10 items of 552 documents
One-particle Green's function
2013
In this chapter we get acquainted with the one-particle Green's function G , or simply the Green's function. The chapter is divided in three parts. In the first part (Section 6.1) we illustrate what kind of physical information can be extracted from the different Keldysh components of G . The aim of this first part is to introduce some general concepts without being too formal. In the second part (Section 6.2) we calculate the noninteracting Green's function. Finally in the third part (Sections 6.3 and 6.4) we consider the interacting Green's function and derive several exact properties. We also discuss other physical (and measurable) quantities that can be calculated from G and that are re…
Accurate Nonlinear Optical Properties for Small Molecules
2006
During the last decade it became possible to calculate by quantum chemical ab initio methods not only static but also frequency-dependent properties with high accuracy. Today, the most important tools for such calculations are coupled cluster response methods in combination with systematic hierarchies of correlation consistent basis sets. Coupled cluster response methods combine a computationally efficient treatment of electron correlation with a qualitatively correct pole structure and frequency dispersion of the response functions. Both are improved systematically within a hierarchy of coupled cluster models. The present contribution reviews recent advances in the highly accurate calculat…
Tunneling-charging Hamiltonian of a Cooper-pair pump
2001
General properties of the tunneling-charging Hamiltonian of a Cooper pair pump are examined with emphasis on the symmetries of the model. An efficient block-diagonalization scheme and a compatible Fourier expansion of the eigenstates is constructed and applied in order to gather information on important observables. Systematics of the adiabatic pumping with respect to all of the model parameters are obtained and the link to the geometrical Berry's phase is identified.
Architectural Scenes Reconstruction from Uncalibrated Photos and Map Based Model Knowledge
2001
In this paper we consider the problem of reconstructing architectural scenes from multiple photographs taken from arbitrarily viewpoints. The original contribution of this work is the use of a map as a source of a priori knowledge and geometric constraints in order to obtain in a fast and simple way a detailed model of a scene. We suppose images are uncalibrated and have at least one planar structure as a facade for exploiting the planar homography induced between world plane and image to calculate a first estimation of the projection matrix. Estimations are improved by using correspondences between images and map. We show how these simple constraints can be used to calibrate the cameras, t…
Defining relations of the noncommutative trace algebra of two 3×3 matrices
2006
The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have found explicitly such a subalgebra $S$ and a set of free generators of the $S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an algebra and a Groebner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit prese…
Correcting AVHRR Long Term Data Record V3 estimated LST from orbital drift effects
2012
Abstract NOAA (National Oceanic and Atmospheric Administration) satellite series is known to suffer from what is known as the orbital drift effect. The Long Term Data Record (LTDR [Pedelty et al., 2007]), which provides AVHRR (Advanced Very High Resolution Radiometer) data from these satellites for the 80s and the 90s, is also affected by this orbital drift. To correct this effect on Land Surface Temperature (LST) time series, a novel method is presented here, which consists in adjusting retrieved LST time series on the basis of statistical information extracted from the time series themselves. This method is as simple and straightforward as possible, in order to be implemented easily for s…
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
A new constructive method using the theory of invariants to obtain material behavior laws
2006
International audience; The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.
A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates
2019
Abstract In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer C z 0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C z 1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are consider…
Matroid optimization problems with monotone monomials in the objective
2022
Abstract In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present a complete description of this polytope. Apart from linearization constraints one needs appropriately strengthened rank inequalities. The separation problem for these inequalities reduces to a submodular function minimization problem. These polyhedral results give rise to a new hiera…