A general formula of the solutions of the Peterson-Codazzi equations on a hypersphere

1992 ◽  
Vol 59 (2) ◽  
pp. 777-779 ◽  
Author(s):  
V. T. Fomenko
Keyword(s):  
General Formula ◽  
Codazzi Equations

X-ray Structure Refinement and Vibrational Spectroscopy of Ca8Gd2 (PO4)6 O2

2013 ◽  
Vol 12 (10) ◽  
pp. 719-726
Author(s):  
R. Ayadi ◽  
Mohamed Boujelbene ◽  
T. Mhiri
Keyword(s):  
Solid State ◽  
General Formula ◽  
Vibrational Spectroscopy ◽  
Powder Diffraction ◽  
Infrared Spectra ◽  
Solid State Reaction ◽  
Structure Refinement ◽  
Unit Cell ◽  
Cell Group ◽  
X Ray

The present paper is interested in the study of compounds from the apatite family with the general formula Ca10 (PO4)6A2. It particularly brings to light the exploitation of the distinctive stereochemistries of two Ca positions in apatite. In fact, Gd-Bearing oxyapatiteCa8 Gd2 (PO4)6O2 has been synthesized by solid state reaction and characterized by X-ray powder diffraction. The site occupancies of substituents is0.3333 in Gd and 0.3333 for Ca in the Ca(1) position and 0. 5 for Gd in the Ca (2) position.  Besides, the observed frequencies in the Raman and infrared spectra were explained and discussed on the basis of unit-cell group analyses.

Toxicity of Para-Chloro Substituted Benzene Derivatives in the Microtox™ Test

1985 ◽  
Vol 20 (2) ◽  
pp. 36-43 ◽  
Author(s):  
Klaus L.E. Kaiser ◽  
Juan M. Ribo ◽  
Brian M. Zaruk
Keyword(s):  
General Formula ◽  
Functional Group ◽  
Structural Parameters ◽  
Systematic Investigation ◽  
Photobacterium Phosphoreum ◽  
Benzene Derivatives ◽  
Quantitative Structure ◽  
Chlorinated Benzenes ◽  
Chloro Derivatives ◽  
Derivatives Of

Abstract This paper gives the results of part of a systematic investigation into contaminant toxicity to Photobacterium phosphoreum in the Microtox™ test. Reported are the toxicity values for 39 para-chloro substituted benzene derivatives of the general formula l-Cl-C6h4-4-X=CH2CH(NH2)COOH, F, SO2NH2, OCH2COOH, CH2COOH, CONHNH2, NHCOCH3, CONH2, CH=CHCOOH, SeOOH, CH2NH2, CH2CH2NH2, NO2, H, CF3, CHO, CH2OH, OH, CH3, CCl3, COCH3, COOH, NH2, SO2C6H5, Cl, CH2COCH3, COCl, CN, OCH3, NCO, NHCH3, I, COC6H5, CH2Cl, SH, CH2SH, NCS, CH2CN and SO2C6H4Cl. Except for the last compound, whose solubility is below the required concentration, the toxicities increase in the presented order with a total range of more than three orders of magnitude. The data are discussed in terms of quantitative structure-toxicity correlations with compound-specific structural parameters. In combination with a previously developed submodel on chlorinated benzenes, phenols, nitrobenzenes and anilines, the observed relationships allow the prediction of the toxicity of some 780 possible chloro derivatives of the general formula C6H5-nClnX, where n=<5 and X is a functional group as listed above.

Synthesis of isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles)

1990 ◽  
Vol 55 (12) ◽  
pp. 2967-2976 ◽  
Author(s):  
Jan Slouka
Keyword(s):  
General Formula ◽  
Mutual Distance ◽  
Planar Molecules ◽  
Amino Derivatives

The described synthesis of all three isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles) IVa-IVc starts from the respective 1-nitrophenyl-6-azauracil-5-carbonitriles Ia-Ic which were reduced to the corresponding amino derivatives IIa-IIc, diazotized, and coupled with ethyl cyanoacetylcarbamate to give the isomeric hydrazones IIIa-IIIc which were finally cyclized to the title compounds containing two 6-azauracil rings. A general formula is presented for calculation of mutual distance of arbitrary atoms in any planar molecules.

The Coordination Chemistry of Phosphoryl Compounds Containing the — N(CH3)2 Group, Part VIII

1972 ◽  
Vol 27 (7) ◽  
pp. 759-763 ◽  
Author(s):  
M. W. G. De Bolster ◽  
W. L. Groeneveld
Keyword(s):  
Coordination Chemistry ◽  
General Formula ◽  
Ligand Field ◽  
Chemical Analyses ◽  
X Ray ◽  
Physical Measurements ◽  
Ligand Field Spectra ◽  
Chloride Adduct ◽  
Ligand Field Parameters ◽  
Group Part

A number of new solvates and adducts containing bisphenyldimethylaminophosphine oxide is reported. The solvates have the general formula M[(C6H5)2P(O)N(CH3)2]42+(anion-)2, in which M = Mg, Ca, Mn, Fe, Co, Ni, Cu, Zn and Cd, and the anions are ClO4- and BF4-. The adducts have the general formula M[(C6H5)2P(O)N(CH3)2]2Cl2, where M stands for the same series of metals.The compounds are characterized and identified by chemical analyses and physical measurements.Ligand-field and vibrational spectra have been investigated; values for the ligand-field parameters are reported. It is concluded that coordination takes place via the oxygen atom of the ligand.X-ray powder patterns were used in combination with ligand-field spectra to deduce the coordination around the metal ions.The interesting behaviour of the nickel (II) chloride adduct upon heating is discussed and it is shown that both a square pyramidal and a tetrahedral modification exists.

scholarly journals An investigation of polyhedral deformation in two mixed-metal diarsenates: SrZnAs2O7and BaCuAs2O7

2015 ◽  
Vol 71 (4) ◽  
pp. 330-337 ◽  
Author(s):  
Sabina Kovač ◽  
Ljiljana Karanović ◽  
Tamara Đorđević
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
General Formula ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
Hydrothermal Conditions ◽  
X Ray ◽  
Open Framework ◽  
Geometrical Characteristics ◽  
Barium Copper

Two isostructural diarsenates, SrZnAs2O7(strontium zinc diarsenate), (I), and BaCuAs2O7[barium copper(II) diarsenate], (II), have been synthesized under hydrothermal conditions and characterized by single-crystal X-ray diffraction. The three-dimensional open-framework crystal structure consists of corner-sharingM2O5(M2 = Zn or Cu) square pyramids and diarsenate (As2O7) groups. Each As2O7group shares its five corners with five differentM2O5square pyramids. The resulting framework delimits two types of tunnels aligned parallel to the [010] and [100] directions where the large divalent nine-coordinatedM1 (M1 = Sr or Ba) cations are located. The geometrical characteristics of theM1O9,M2O5and As2O7groups of known isostructural diarsenates, adopting the general formulaM1IIM2IIAs2O7(M1II= Sr, Ba, Pb;M2II= Mg, Co, Cu, Zn) and crystallizing in the space groupP21/n, are presented and discussed.

scholarly journals Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 37
Author(s):  
Yan Wang ◽  
Muhammet Cihat Dağli ◽  
Xi-Min Liu ◽  
Feng Qi
Keyword(s):  
General Formula ◽  
Bell Polynomials ◽  
Eulerian Polynomials ◽  
Differentiable Functions ◽  
Faà Di Bruno Formula ◽  
Derivatives Of

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

The effect of terminal N-donor aromatic ligands on sensitization and emission of lanthanide ions in Zn2Ln (Ln = Eu, Tb) complexes with 4-biphenylcarboxylate anions

2021 ◽  
Author(s):  
Stanislav N. Melnikov ◽  
Igor Evstifeev ◽  
Stanislav A. Nikolaevskii ◽  
Ivan V. Ananyev ◽  
Evgenia Varaksina ◽  
...  
Keyword(s):  
General Formula ◽  
Molecular Complexes ◽  
Lanthanide Ions ◽  
Biphenylcarboxylic Acid

The systematical series of Zn-Ln trinuclear carboxylate molecular complexes with general formula [Zn2Ln(NO3)(phbz)6(L)2] (Ln = Eu, Gd, Tb; phbz is anion of 4-biphenylcarboxylic acid; L is pyridine, 2,3-lutidine or 2,2’-bipyridine)...

scholarly journals Influence of Copper(I) Halides on the Reactivity of Aliphatic Carbodiimides

2020 ◽  
Vol 3 (1) ◽  
pp. 20
Author(s):  
Valentina Ferraro ◽  
Marco Bortoluzzi
Keyword(s):  
Density Functional Theory ◽  
Electronic Structure ◽  
General Formula ◽  
Electron Density ◽  
Density Functional ◽  
Functional Theory ◽  
Fukui Functions ◽  
Bond Lengths ◽  
Linear Complexes ◽  
Nitrogen Bond

The influence of copper(I) halides CuX (X = Cl, Br, I) on the electronic structure of N,N′-diisopropylcarbodiimide (DICDI) and N,N′-dicyclohexylcarbodiimide (DCC) was investigated by means of computational DFT (density functional theory) methods. The coordination of the considered carbodiimides occurs by one of the nitrogen atoms, with the formation of linear complexes having a general formula of [CuX(carbodiimide)]. Besides varying the carbon–nitrogen bond lengths, the thermodynamically favourable interaction with Cu(I) reduces the electron density on the carbodiimides and alters the energies of the (NCN)-centred, unoccupied orbitals. A small dependence of these effects on the choice of the halide was observable. The computed Fukui functions suggested negligible interaction of Cu(I) with incoming nucleophiles, and the reactivity of carbodiimides was altered by coordination mainly because of the increased electrophilicity of the {NCN} fragments.

scholarly journals A theorized new class of polyhedral hydrocarbons of molecular formula CnHn and their bottom-up scaffold expansions into hyperstructures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Camila M. B. Machado ◽  
Nathalia B. D. Lima ◽  
Sóstenes L. S. Lins ◽  
Alfredo M. Simas
Keyword(s):  
General Formula ◽  
Chemical Structure ◽  
Molecular Formula ◽  
Fusion Reactions ◽  
3D Scaffold ◽  
3D Scaffolds ◽  
Bottom Up ◽  
New Class ◽  
Euler’S Theorem ◽  
2D And 3D

AbstractWe address the use of Euler's theorem and topological algorithms to design 18 polyhedral hydrocarbons of general formula CnHn that exist up to 28 vertexes containing four- and six-membered rings only; compounds we call “nuggets”. Subsequently, we evaluated their energies to verify the likelihood of their chemical existence. Among these compounds, 13 are novel systems, of which 3 exhibit chirality. Further, the ability of all nuggets to perform fusion reactions either through their square faces, or through their hexagonal faces was evaluated. Indeed, they are potentially able to form bottom-up derived molecular hyperstructures with great potential for several applications. By considering these fusion abilities, the growth of the nuggets into 1D, 2D, and 3D-scaffolds was studied. The results indicate that nugget24a (C24H24) is predicted to be capable of carrying out fusion reactions. From nugget24a, we then designed 1D, 2D, and 3D-scaffolds that are predicted to be formed by favorable fusion reactions. Finally, a 3D-scaffold generated from nugget24a exhibited potential to be employed as a voxel with a chemical structure remarkably similar to that of MOF ZIF-8. And, such a voxel, could in principle be employed to generate any 3D sculpture with nugget24a as its level of finest granularity.

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