Search results for "Formula"
showing 10 items of 755 documents
A Unifying Framework for Perturbative Exponential Factorizations
2021
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of theWilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.
Electronic structure and transport properties of the Heusler compound Co2TiAl
2009
The properties of the Heusler compound Co2TiAl were investigated in detail by experimental techniques and theoretical methods. X-ray diffraction measurements indicate that as-cast samples of the compound exhibit the L21 structure with a small amount of B2-type disorder. This leads to a reduced saturation magnetization per formula unit of 0.747 μB. The Curie temperature is approximately 120 K. The transport properties are influenced by the change in the electronic structure at the Curie temperature, as revealed experimentally by conductivity, thermal transport and specific heat measurements. Different theoretical models based on ab initio calculations of the electronic structure are used to …
New rotational levels in $^{186}$Re nucleus
2020
International audience; Excited levels of 186 Re have been studied using results of the single γ -ray spectra measurements following the thermal neutron capture reaction. Energies and intensities of more than 500 γ -transitions have been obtained with the high-resolution crystal diffraction spectrometer GAMS5 of ILL. Most of the obtained intense γ -transitions have been placed in the 186 Re level scheme. A number of new levels, as well as the depopulation for levels observed earlier in the 187 Re (p,d)186 Re reaction measurements have been proposed. Structure of 186 Re levels is interpreted in terms of two-quasiparticle plus rotor coupling model and compared with that of the neighbouring do…
Three-dimensional behavior of apodized nontelecentric focusing systems.
2002
The scalar field in the focal volume of nontelecentric apodized focusing systems cannot be accurately described by the Debye integral representation. By use of the Fresnel–Kirchhoff diffraction formula it is found that, if the aperture stop is axially displaced, the focal-volume structure is tuned. We analyze the influence of the apodizing function and find that, whereas axially superresolving pupil filters are highly sensitive to the focal-volume reshaping effect, axially apodizing filters are more inclined to the focal-shift effect.
Corrected whole blood biomarkers : the equation of Dill and Costill revisited
2018
An exercise bout or a dehydration often causes a reduction in plasma volume, which should be acknowledged when considering the change in biomarkers before and after the plasma changing event. The classic equation from Dill and Costill (1974, J. Appl. Physiol., 37, 247–248) for plasma volume shift is usually utilized in such a case. Although this works well with plasma and serum biomarkers, we argue in this note that this traditional approach gives misleading results in the context of whole blood biomarkers, such as lactate, white cells, and thrombocytes. In this study, we demonstrate that to calculate the change in the total amount of circulating whole blood biomarker, one should utilize a …
Analytical prediction of ultimate moment and curvature of RC rectangular sections in compression
2013
This paper presents closed form expressions linking the ultimate bearing capacity to the ultimate curvature of rectangular RC sections subjected to axial load and bending moment acting in one of the two symmetry planes of the section. With respect to possible simplified formulations the following effects are also considered: confinement of the concrete, hardening of the longitudinal reinforcement, and presence of reinforcing bars distributed orthogonally to the neutral axis. The formulation is proposed in dimensional terms after a preliminary definition of the geometrical and mechanical parameters governing the structural response of the class of sections considered. The analytical expressi…
A remark on absolutely continuous functions in ℝ n
2006
We introduce the notion ofα, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that eachα, λ-absolutely continuous function isn, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets
2013
We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed
A new Euler–Mahonian constructive bijection
2011
AbstractUsing generating functions, MacMahon proved in 1916 the remarkable fact that the major index has the same distribution as the inversion number for multiset permutations, and in 1968 Foata gave a constructive bijection proving MacMahon’s result. Since then, many refinements have been derived, consisting of adding new constraints or new statistics.Here we give a new simple constructive bijection between the set of permutations with a given number of inversions and those with a given major index. We introduce a new statistic, mix, related to the Lehmer code, and using our new bijection we show that the bistatistic (mix,INV) is Euler–Mahonian. Finally, we introduce the McMahon code for …