Search results for " symmetry"
showing 10 items of 701 documents
Generalized Symmetry Models for Hypercubic Concordance Tables
2000
Summary Frequency data obtained classifying a sample of 'units' by the same categorical variable repeatedly over 'components', can be arranged in a hypercubic concordance table (h.c.t.). This kind of data naturally arises in a number of different areas such as longitudinal studies, studies using matched and clustered data, item-response analysis, agreement analysis. In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a h.c.t. can all be analyzed via models of symmetry and quasi-symmetry, which exploit the special structure of the h.c.t. The paper extends the definition of such models to any dimension, introducing the class of generalized symmetry…
Stepping molecular motor amid Lévy white noise
2015
We consider a model of a stepping molecular motor consisting of two connected heads. Directional motion of the stepper takes place along a one-dimensional track. Each head is subject to a periodic potential without spatial reflection symmetry. When the potential for one head is switched on, it is switched off for the other head. Additionally, the system is subject to the influence of symmetric, white Lévy noise that mimics the action of external random forcing. The stepper exhibits motion with a preferred direction which is examined by analyzing the median of the displacement of a midpoint between the positions of the two heads. We study the modified dynamics of the stepper by numerical sim…
Tetra-p-tolyl-verbindungen p-Tol4Si und p-Tol4Ge: Ein beitrag zur konfiguration der tetraaryl-methan-analoga Ar4M (M = C, Si, Ge, Sn, Pb)
1992
Abstract p-Tol4Si and p-Tol4Ge have been obtained from the reaction of p-TolLi with SiCl4 and of p-TolMgBr with GeCl4, respectively. The crystal structures have been determined and compared with those of the homologous compounds p-Tol4Sn and p-Tol4Pb. The latter two molecules (space group I 4 ) exhibit a S4 axis running between the aromatic groups and are shortened along this axis: all four p-Tol groups are closer together than in an undistorted tetrahedron. In the cases of the silane and germane (space group Pc), the tetrahedron is lengthened along one of the bond axes CM: only three of the four p-Tol groups are closer together, and the set up of a special molecular symmetry is blocked. A…
Chemistry of density : extension and structural origin of Carnelley's rule in chloroethanes
2012
Low-density liquids and solids, with all intermolecular contacts longer than the sum of van der Waals radii, are formed by all ethanes chlorinated at one locant: CH2ClCH3, CHCl2CH3 and CCl3CH3. The concepts of molecular symmetry described by Carnelley and that of point groups have been compared. Carnelley's rule, when applied to liquid and solid chloroethanes clearly reveals the density dependence on the presence of intermolecular Cl⋯Cl and H⋯Cl short contacts, or their absence due to steric hindrances of overcrowded substituents. At 2.62 GPa, CH2ClCH3 freezes directly into phase II, with molecules arranged into layers with short Cl⋯Cl, H⋯Cl and H⋯H contacts. Only for CH2ClCH3, both the low…
Icosahedral carboranes as scaffolds for congested regioselective polyaryl compounds: the distinct distance tuning of C–C and its antipodal B–B
2019
Four-fold aryl substituted o-carborane derivatives with defined patterns of substitution at the antipodal region of the cluster carbon atoms have been achieved. It is proven that this region is congested but lacks steric hindrance. Also, the two antipodal sites Cc–Cc and B9–B12 are affected very distinctly by electron donor substituents.
Halogen...halogen interactions in pressure-frozen ortho- and meta-dichlorobenzene isomers.
2007
Isomers 1,2-dichlorobenzene (o-DCB) and 1,3-dichlorobenzene (m-DCB) were high-pressure frozen in-situ in a Merrill–Bassett diamond–anvil cell and their structures determined at room temperature and at 0.18 (5) GPa for o-DCB, and 0.17 (5) GPa for m-DCB by single-crystal X-ray diffraction. The patterns of halogen...halogen intermolecular interactions in these structures can be considered to be the main cohesive forces responsible for the molecular arrangements in these crystals. The molecular packing of dichlorobenzene isomers, including three polymorphs of 1,4-dichlorobenzene (p-DCB), have been compared and relations between their molecular symmetry, packing arrangements, intermolecular inte…
Bond-based 3D-chiral linear indices: Theory and QSAR applications to central chirality codification
2008
The recently introduced non-stochastic and stochastic bond-based linear indices are been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These improved modified descriptors are applied to several well-known data sets to validate each one of them. Particularly, Cramer's steroid data set has become a benchmark for the assessment of novel quantitative structure activity relationship methods. This data set has been used by several researchers using 3D-QSAR approaches such as Comparative Molecular Field Analysis, Molecular Quantum Similarity Measures, Comparative Molecular Moment Analysis, E-state, Mapping Prope…
Tendencies in ABO3 Perovskite and SrF2, BaF2 and CaF2 Bulk and Surface F-Center Ab Initio Computations at High Symmetry Cubic Structure
2021
This research was partly funded by the Latvian Council of Science project No. LZP‐ 2020/2‐0009 (for R. Eglitis), as well as the ERAF Project No. 1.1.1.1/18/A/073. We express our gratitude for the financial support from Latvian–Ukraine cooperation Project No. Latvia–Ukraine LV‐ UA/2021/5. The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence has received funding from the European Unions Horizon 2020 Framework Pro‐ gramme H2020‐WIDESPREAD01‐2016‐2017‐Teaming Phase2 under Grant Agreement No. 739508, project CAMART2.
Shell structure in large nonspherical metal clusters.
1992
Electronic shell structure of icosahedral and cuboctahedral sodium clusters with 300 to 1500 atoms has been studied using a potential-well approximation for the effective one-electron potential. The results show that icosahedral clusters yield the same shell structure as spherical clusters up to the cluster size of about 500 atoms and that similarities persist until the cluster has about 1000 atoms. The shell structure of a cuboctahedral geometry begins to deviate from that of a sphere when the cluster size is about 100. A study on quadrupole deformations of large clusters shows that surface fluctuations in liquid clusters cannot destroy the shell structure even in the largest clusters.
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…