Search results for "Matrix"
showing 10 items of 3205 documents
Symplectic Applicability of Lagrangian Surfaces
2009
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equa- tions. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…
Weyl symbols and boundedness of Toeplitz operators
2019
International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.
Weyl-Type Theorems on Banach Spaces Under Compact Perturbations
2018
In this paper, we study Browder-type and Weyl-type theorems for operators $$T+K$$ defined on a Banach space X, where K is (a non necessarily commuting) compact operator on X. In the last part, the theory is exemplified in the case of isometries, analytic Toeplitz operators, semi-shift operators, and weighted right shifts.
Some Remarks on the Spectral Properties of Toeplitz Operators
2019
In this paper, we study some local spectral properties of Toeplitz operators $$T_\phi $$ defined on Hardy spaces, as the localized single-valued extension property and the property of being hereditarily polaroid.
Contractions yielding new supersymmetric extensions of the poincaré algebra
1991
Two new Poincare superalgebras are analysed. They are obtained by the Wigner-Inonu contraction from two real forms of the superalgebra OSp(2;4;C) - one describing the N = 2 anti-de-Sitter superalgebra with a non-compact internal symmetry SO(1, 1) and the other corresponding to the de-Sitter superalgebra with internal symmetry SO(2). Both are 19-dimensional self-conjugate extensions of the Konopel'chenko superalgebra. They contain 10 Poincare generators and one generator of internal symmetry in addition to 8 odd generators half of which, however, do not commute with translations.
Application of the H-point standard additions method by using absorbance increment values as analytical signals
1991
Abstract This paper demonstrates how the absorbance increment (ΔA) between two wavelengths selected according to the fundamental criteria for application of the H-Point standard additions method (HPSAM) are only related to the analyte concentration. A procedure for calculation of the unknown analyte concentration with no bias error by applying HPSAM to ΔA values in much the same way as the method of standard additions (MOSA), is reported. The method was also applied to a calibration with a single standard. The results obtained on 6 samples with maximal separations between 65 and 0 nm are reported. Finally, the proposed method was applied to the resolution of different phenol-o-cresol mixtur…
Smart Sorption Materials in Green Analytical Chemistry
2019
The use of smart materials as alternative sorption materials for their use in greening sample preparation has been reviewed. It has been taking into consideration recent advances on the use of natural products, without any modification or purification, for making analyte extraction and pre-concentration and the use of specific materials in solid-phase extraction (SPE) and solid-phase microextraction (SPME) approaches. Inorganic materials, such as metal oxides, alumina-based, silica-based, and carbon-based materials together with biomimetic sorbents such as classical immunosorbents, aptamers, and molecularly imprinted polymers, have been reviewed as examples of these materials, stressing the…
Analyte estimation using the generalized H-point standard additions method and a new methodology for locating linear spectral intervals for unknown i…
1998
An improvement in the way to locate linear spectral intervals for unknown interferents which overlap the analyte signal in UV–visible spectrophotometry is offered as an alternative to the method previously described by Campins-Falco et al. (Anal. Chim. Acta, 302, 323 (1995)). In that report, quotients of the second-derivative spectra of the sample and analyte were used. The new method improves on the old one by using first- instead of second-derivative data, thus eliminating the possible divisions by zero (inflection points for the analyte) obtained in the previous procedure. The linear intervals are now obtained by plotting for each wavelength the differences in first-derivative data betwe…
Evaluation of a Multidimensional Solid-Phase Extraction Platform for Highly Selective On-Line Cleanup and High-Throughput LC−MS Analysis of Triazines…
2001
A novel highly selective sample cleanup procedure based on the use of molecularly imprinted polymers (MIPs) as solid-phase extraction materials has been evaluated with respect to its applicability and routine use in environmental analysis. The method comprises the combination of a restricted access material (RAM) and a MIP allowing a selective sample preparation to be achieved in the online mode. This combination is called the size-selective sample separation and solvent switch (six-SPE). The RAM column combines size exclusion and adsorption chromatography, reducing the concentration of matrix molecules by a cutoff of 15 kDa. The MIP column selectively retains the triazine analytes whereas …