Search results for "Partition"

Surface free energy of the open XXZ spin-1/2 chain

2012

We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representati…

Riemann-Type Definition of the Improper Integrals

2004

Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane's definition of the Lebesgue integral by imposing a Kurzweil-Henstock's condition on McShane's partitions.

New complex polycyclic compounds: Synthesis, antiproliferative activity and mechanism of action

2020

Abstract Polycyclic or O-glycoconiugate polycyclic compounds 1a-g were previously tested for their in vitro antiproliferative activity. In this series of compounds, activity increases as log P decreases. Specifically, compounds 1d and 1g showed lower log P values together with the best antiproliferative profiles. With the aim of extending our understanding of the structure–activity relationship (SAR) of this class of compounds, we prepared new polycyclic derivatives 2a-c, which bear on each of the two phenyl rings hydrophilic substituents (OH, SO2NH2 or NHCOCH3). These substituents are able to form hydrogen bonds and to decrease the partition coefficient value as compared with compound 1d. …

Polymetamorphism and ductile deformation of staurolite-cordierite schist of the Bossost Dome: indication for Variscan extension in the Axial Zone of …

2003

The Bossòst dome is an E–W-trending elongated structural and metamorphic dome developed in Cambro-Ordovician metasedimentary rocks in the Variscan Axial Zone of the central Pyrenees. A steep fault separates a northern half-dome, cored by massif granite, from an E–W-trending doubly plunging antiform with granitic sills and dykes in the core to the south. The main foliation is a flat-lying S1/2 schistosity that grades into a steeper-dipping slaty cleavage at the dome margins. Three major deformational and two metamorphic phases can be differentiated. S1/2 schistosity is an axial planar cleavage to W-vergent recumbent folding that probably occurred in mid-Westphalian time. Peak regional metamo…

1980

A phenomenological theory of the Phase Distribution Chromatography (PDC)-separation effect is outlined and a theoretical equation for the measured PDC-calibration curves is given. Assuming a reversible-thermodynamical equilibrium in the polystyrene-PDC-column, only a relatively small part of the measured PDC-calibration curves could be explained: namely those running below their tangents. In order to explain the whole sigmoidal shape of the experimental curves, a theory of steady state in the system sol/gel was developed assuming deformation of the polymer coil near the gel front due to the stress related to the velocity gradient. The resulting dynamical flow-equilibrium differs highly from…

Controls on strontium and barium incorporation into freshwater bivalve shells ( Corbicula fluminea )

2017

Abstract Trace elements of bivalve shells can potentially serve as proxies of environmental change. However, to reconstruct past environments using the geochemical properties of the shells and determine the degree to which the element levels are biologically influenced, it is essential to experimentally determine the relationship between environmental variables and the element composition of the shells. To disentangle possible controls on the incorporation of strontium and barium into freshwater bivalve shells, we conducted controlled laboratory experiments using the extremely salinity and temperature tolerant Asian clam, Corbicula fluminea as a model species. Bivalves were reared for five …

Large‐scale set partitioning problems: Some real‐world instances hide a beneficial structure

2006

In this paper we consider large‐scale set partitioning problems. Our main purpose is to show that real‐world set partitioning problems originating from the container‐trucking industry are easier to tackle in respect to general ones. We show such different behavior through computational experiments: in particular, we have applied both a heuristic algorithm and some exact solution approaches to real‐world instances as well as to benchmark instances from Beasley OR‐library. Moreover, in order to gain an insight into the structure of the real‐world instances, we have performed and evaluated various instance perturbations. Didelės matematinės aibės dalijimo problemų sprendimas, nagrinėjant reali…

Influence of the composition and the structure of different media on the release of aroma compounds

2004

International audience; The release of 2-nonanone and hexenol (hex-4-en-3-ol) was studied in model media with different structures and compositions: water, a gel of $\beta$-lactoglobulin, gelified or non-gelified emulsions (5.0% Miglyol, 6.9% $\beta$-lactoglobulin; the gelation was realized by heating) and milk. The aroma compounds were analyzed by gas chromatography. A strong influence of the nature of the volatile compound on its behavior towards the food matrix was observed: in the case of 2-nonanone, a hydrophobic compound (log P = 2.9) with a relatively high vapor-water partition coefficient (Kmol = 33.6), the release was greatly influenced by the composition and the structure of the m…

Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling

2017

Intrinsic and extrinsic stability of the (Mg, Fe) O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth's mantle is investigated by the combination of quantum mechanical calculations (Hartree-26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg, Fe) O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23-42 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg, Fe) O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanit…

Space partitioning of exchange-correlation functionals with the projector augmented-wave method

2018

We implement a Becke fuzzy cells type space partitioning scheme for the purposes of exchange-correlation within the GPAW projector augmented-wave method based density functional theory code. Space partitioning is needed in the situation where one needs to treat different parts of a combined system with different exchange-correlation functionals. For example, bulk and surface regions of a system could be treated with functionals that are specifically designed to capture the distinct physics of those regions. Here, we use the space partitioning scheme to implement the quasi-nonuniform exchange-correlation scheme, which is a useful practical approach for calculating metallic alloys on the gene…