Search results for "Matrix"

A closed formula for the evaluation of foams

2020

International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homology categorifying the sl(N) link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.

Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model

2020

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…

On the representation of integers by indefinite binary Hermitian forms

2011

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.

THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

2013

Unicity of biproportion

1994

International audience; The biproportion of S on margins of M is called the intern composition law, K: (S,M) -> X = K(S,M) / X = A S B. A and B are diagonal matrices, algorithmically computed, providing the respect of margins of M. Biproportion is an empirical concept. In this paper, the author shows that any algorithm used to compute a biproportion leads to the me result. Then the concept is unique and no longer empirical. Some special properties are also indicated.

QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms

2018

[EN] Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of 106 equations). In CT, the Feldkamp, Davis, and Kress back projection algorithm (FDK) and iterative methods like conjugate gradient (CG) are the standard methods used for image reconstruction. As the image reconstruction problem can be modeled by a large linear system of equations, QR-factorization of the system matrix could be used to solve this system. Current advances in computer science enable the use of direct methods for…

The M4 transitions of isomeric states

2015

Tässä pro gradu -tutkielmassa tutkitaan isomeeristen tilojen magneettisten M4-gammasiirtymien redusoituja matriisielementtejä. Tutkittavat siirtymät ovat venyneitä M4-siirtymiä kaksoisbeetahajoamisten massa-alueilla A=85-115 ja A=135-143. Tutkielman tarkoituksena on verrata kokeellisia ydinmatriisielementtejä kvasihiukkasmatriisielementteihin ja MQPM-teorian avulla laskettuihin matriisielementteihin. Kokeelliset matriisielementi lasketaan kokeellisesti määritettyjen arvojen avulla ja kvasihiukkas- sekä MQPM-matriisielementit määritetään tietokoneohjelmien avulla. Kokeellisten ja kvasihiukkasmatriisielementtien välinen suhde osoittautui olevan noin 0,29 ja kokeellisten ja MQPM-matriisielemen…

Analysis of mycotoxins in barley using ultra high liquid chromatography high resolution mass spectrometry: comparison of efficiency and efficacy of d…

2012

The effectiveness of four extraction methods (modified QuEChERS, matrix solid-phase dispersion (MSPD), solid-liquid extraction (SLE) and solid-phase extraction (SPE) clean-up) were evaluated for simultaneous determination of 32 mycotoxins produced by the genus Fusarium, Claviceps, Aspergillus, Penicillium and Alternaria in barley by ultra high pressure liquid chromatography coupled to ultra-high resolution mass spectrometry (UHPLC-Orbitrap(®) MS). The efficiency and efficacy of extraction methods were evaluated and compared in number of extracted mycotoxins and obtained recoveries. From the one point of view, QuEChERS procedure was fast and easy, as well as it was able to successfully extra…

On the accurate determination of nonisolated solutions of nonlinear equations

1981

A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.

Structure and Matrix Isolation Infrared Spectrum of Formyl Fluoride Dimer:  Blue-Shift of the C−H Stretching Frequency

2006

Infrared spectroscopy (IR) of formyl fluoride (HCOF) dimer is studied in low-temperature argon and krypton matrixes. New IR absorptions, ca. 17 cm(-1) blue shifted from the monomer C-H stretching fundamental, are assigned to the HCOF dimer. The MP2/6-311++G calculations were utilized to define structures and harmonic frequencies of various HCOF dimers. Among the four optimized structures, the dimer having two C-H...O hydrogen bonds possesses strongest intermolecular bonding. The calculated harmonic frequencies of this dimer structure are shifted from the monomer similarly as observed in the experiment. Thus, we suggest that the experimentally observed blue shifted C-H bands belong to the di…