A general formula for the anisotropic outer Minkowski content of a set

2016 ◽  
Vol 146 (2) ◽  
pp. 393-413 ◽  
Author(s):  
Luca Lussardi ◽  
Elena Villa
Keyword(s):  
General Formula ◽  
Wide Class ◽  
Minkowski Content ◽  
Rectifiable Sets ◽  
Anisotropic Case

We generalize to the anisotropic case some classical and recent results on the (n – 1)-Minkowski content of rectifiable sets in ℝn, and on the outer Minkowski content of subsets of ℝn. In particular, a general formula for the anisotropic outer Minkowski content is provided; it applies to a wide class of sets that are stable under finite unions.

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 Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

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