Search results for "funktio"
showing 10 items of 319 documents
Synthesis of Enaminones-Based Benzo[d]imidazole Scaffold: Characterization and Molecular Insight Structure
2020
(E)-1-(1H-Benzo[d]imidazol-2-yl)-3-(dimethylamino)prop-2-en-1-one 2 was synthesized by one-pot synthesis protocol of 2-acetyl benzo[d]imidazole with dimethylformamide dimethylacetal (DMF-DMA) in xylene at 140 °
Synthesis, X-ray Structure, Conformational Analysis, and DFT Studies of a Giant s-Triazine bis-Schiff Base
2021
The current work involves the synthesis of 2,2′-(6-(piperidin-1-yl)-1,3,5-triazine-2,4-diyl)bis(hydrazin-2-yl-1-ylidene))bis(methanylylidene))diphenol 4, characterization, and the DFT studies of the reported compound. The crystal unit cell parameters of 4 are a = 8.1139(2) Å, b = 11.2637(2) Å, c = 45.7836(8) Å. The unit cell volume is 4184.28(15) Å3 and Z = 4. It crystallized in the orthorhombic crystal system and Pbca space group. The O…H, N…H, C…H, H…H and C…C intermolecular contacts which affect the crystal stability were quantitatively analyzed using Hirshfeld calculations. Their percentages were calculated to be 9.8, 15.8, 23.7, 46.4, and 1.6% from the whole contacts occurred in the cr…
Synthesis and X-ray Crystal Structure of New Substituted 3-4′-Bipyrazole Derivatives. Hirshfeld Analysis, DFT and NBO Studies
2021
A new compounds named 3-4′-bipyrazoles 2 and 3 were synthesized in high chemical yield from a reaction of pyran-2,4-diketone 1 with aryl hydrazines under thermal conditions in MeOH. Compound 2 was unambiguously confirmed by single-crystal X-ray analysis. It crystalizes in a triclinic crystal system and space group P-1. Its crystal structure was found to be in good agreement with the spectral characterizations. With the aid of Hirshfeld calculations, the H…H (54.8–55.3%) and H…C (28.3–29.2%) intermolecular contacts are the most dominant, while the O…H (5.8–6.5%), N…H (3.8–4.6%) and C…C (3.0–4.9%) are less dominant. The compound has a polar nature with a net dipole moment of 6.388 Debye. The …
Reciprocal lower bound on modulus of curve families in metric surfaces
2019
We prove that any metric space $X$ homeomorphic to $\mathbb{R}^2$ with locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on modulus of curve families associated to a quadrilateral. More precisely, let $Q \subset X$ be a topological quadrilateral with boundary edges (in cyclic order) denoted by $\zeta_1, \zeta_2, \zeta_3, \zeta_4$ and let $\Gamma(\zeta_i, \zeta_j; Q)$ denote the family of curves in $Q$ connecting $\zeta_i$ and $\zeta_j$; then $\text{mod} \Gamma(\zeta_1, \zeta_3; Q) \text{mod} \Gamma(\zeta_2, \zeta_4; Q) \geq 1/\kappa$ for $\kappa = 2000^2\cdot (4/\pi)^2$. This answers a question concerning minimal hypotheses under which a metric space admits a quasiconfor…
Accessible parts of boundary for simply connected domains
2018
For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with a suitable John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obta…
Removable singularities for div v=f in weighted Lebesgue spaces
2018
International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.
Mappings of Finite Distortion : Compactness of the Branch Set
2017
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed
Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
2018
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $\Omega [\mathbf{G}]$ regarded as variational functional of the Green's function $G$ based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger-Ward form. By restricting the input Green's function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To establish the one-to-one mapping we use that, at any finite temperature and for a given 1RDM $\…
Luftverschmutzung als wichtiger Kofaktor bei COVID-19-Sterbefällen
2021
Zusammenfassung Hintergrund Die Sterblichkeit bei COVID-19 ist in Anwesenheit kardiopulmonaler Komorbiditäten erhöht. Luftverschmutzung ist ebenfalls mit einer erhöhten Sterblichkeit assoziiert, v. a. vermittelt durch kardiopulmonale Erkrankungen. Beobachtungen zu Beginn der COVID-19-Pandemie zeigten, dass die Sterblichkeit bei COVID-19 v. a. in Regionen mit stärkerer Luftverschmutzung erhöht ist. Ungeklärt ist der Einfluss von Luftverschmutzung für den Krankheitsverlauf bei COVID-19. Methode Es wurde eine selektive Literaturrecherche von Studien bis Anfang April 2021 in PubMed zum Zusammenhang von Luftverschmutzung und der COVID-19-Mortalität mit den Suchbegriffen „air pollution AND/OR COV…