Search results for "π"
showing 10 items of 67 documents
On Extensional Fuzzy Sets Generated by Factoraggregation
2014
We develop the concept of a general factoraggregation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. We show how the generalized factoraggregation can be used for construction of extensional fuzzy sets and consider approximations of arbitrary fuzzy sets by extensional ones.
Experimental investigation of anion-π interactions : Applications and biochemical relevance
2015
Chemical communications 52(9), 1778 - 1795(2016). doi:10.1039/C5CC09072E
Comparative Study of the a Posteriori Error Estimators for the Stokes Problem
2007
The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods. We show that functional type a posteriori error estimators are applicable to various types of approximations (including non-Galerkin ones) and robust with respect to the mesh structure, type of the finite element and computational procedure used. This allows the construction of effective mesh adaptation procedures in all cases considered. Numerical tests justify the approach suggested.
Reliable polygonal approximations of imaged real objects through dominant point detection
1998
Abstract The problem of dominant point detection is posed, taking into account what usually happens in practice. The algorithms found in the literature often prove their performance with laboratory contours, but the shapes in real images present noise, quantization, and high inter and intra-shape variability. These effects are analyzed and solutions to them are proposed. We will also focus on the conditions for an efficient (few points) and precise (low error) dominant point extraction that preserves the original shape. A measurement of the committed error (optimization error, E 0 ) that takes into account both aspects is defined for studying this feature.
Host-guest complexes of conformationally flexible
2018
Host–guest complexes of C-hexyl-2-bromoresorcinarene (BrC6) with twelve potential aromatic N-oxide guests were studied using single crystal X-ray diffraction analysis and 1H NMR spectroscopy. In the solid state, of the nine obtained X-ray crystal structures, eight were consistent with the formation of BrC6-N-oxide endo complexes. The lone exception was from the association between 4-phenylpyridine N-oxide and BrC6, in that case the host forms a self-inclusion complex. BrC6, as opposed to more rigid previously studied C-ethyl-2-bromoresorcinarene and C-propyl-2-bromoresorcinarene, undergoes remarkable cavity conformational changes to host different N-oxide guests through C–H···π(host) intera…
A Characterization of Bispecial Sturmian Words
2012
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian wo…
A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
Bridging vs. chelating coordination modes of vinylsilanes in CuI π-Complexes: Structure and stability
2014
Two new copper(I) olefin complexes, [Cu6Cl6(MTrVS)2] (1) and [Cu2Cl2(DMVSP)2] (2), of tridentate bridging methyltrivinylsilane (MTrVS) and bidentate chelating 2-[dimethyl(vinyl)silyl]pyridine (DMVSP) have been synthesized and characterized by single-crystal X-ray structure analysis, IR and 1H NMR spectroscopy. It has been shown that using the alkenylsilanes with required electronic properties, molecular symmetry and conformational flexibility, it is possible to control the formation of optimal copper(I) halide oligomers. The obtained results, together with relevant literature data, also illustrate how the coordination mode of vinylsilanes is related to Cu–(C=C) bond strengthening and, conse…
An Open-Shell Coronoid with Hybrid Chichibabin-Schlenk Conjugation.
2021
A hexaradicaloid molecule with alternating Kekule and non-Kekule connectivities between adjacent spin centers was obtained by fusing two conjugation motifs in Chichibabin and Schlenk hydrocarbons into a coronoid structure. 1 H NMR, ESR, and SQUID experiments and computational analyses show that the system has a singlet ground state with a significant hexaradicaloid character (γ0 =0.826, γ1 =γ2 =0.773). It has multiple thermally accessible high-spin states (up to the septet), with uniform energy gaps of ca 1.0 kcal mol-1 between consecutive multiplicities. In line with its open-shell character, the coronoid has a small electronic band gap (ca. 0.8 eV) and undergoes two consecutive one-electr…