518 research outputs found
2,4-Bis(2-fluorophenyl)-3-azabicyclo[3.3.1]nonan-9-one
The title compound, C20H19F2NO, exists in a twin-chair conformation with an equatorial orientation of the two 2-fluorophenyl groups on both sides of the secondary amine group. The benzene rings are orientated at an angle of 25.68 (4)° with respect to one another and the F atoms point upwards (towards the carbonyl group). The crystal is stabilized by an intermolecular N—H⋯π interaction
2,6-Bis(4-methoxyphenyl)-1,3-dimethylpiperidin-4-one O-benzyloxime
The central ring of the title compound, C28H32N2O3, exists in a chair conformation with an equatorial disposition of all the alkyl and aryl groups on the heterocycle. The para-anisyl groups on both sides of the secondary amino group are oriented at an angle of 54.75 (4)° with respect to each other. The oxime derivative exists as an E isomer with the methyl substitution on one of the active methylene centers of the molecule. The crystal packing features weak C—H⋯O interactions
2,6-Bis(4-chlorophenyl)-1,3-dimethylpiperidin-4-one O-benzyloxime
The piperidin-4-one ring in the title compound, C26H26Cl2N2O, exists in a chair conformation with equatorial orientations of the methyl and 4-chlorophenyl groups. The C atom bonded to the oxime group is statistically planar (bond-angle sum = 360.0°) although the C—C=N bond angles are very different [117.83 (15) and 127.59 (15)°]. The dihedral angle between the chlorophenyl rings is 54.75 (4)°. In the crystal, molecules interact via van der Waals forces
2,4-Bis(3-methoxyphenyl)-3-azabicyclo[3.3.1]nonan-9-one
In the crystal structure, the title compound, C22H25NO3, exists in a twin-chair conformation with equatorial orientations of the meta-methoxyphenyl groups on both sides of the secondary amino group. The title compound is a positional isomer of 2,4-bis(2-methoxyphenyl)-3-azabicyclo[3.3.1]nonan-9-one and 2,4-bis(4-methoxyphenyl)-3-azabicyclo[3.3.1]nonan-9-one, which both also exhibit twin-chair conformations with equatorial dispositions of the anisyl rings on both sides of the secondary amino group. In the title compound, the meta-methoxyphenyl rings are orientated at an angle of 25.02 (3)° with respect to each other, whereas in the ortho and para isomers, the anisyl rings are orientated at dihedral angles of 33.86 (3) and 37.43 (4)°, respectively. The crystal packing is dominated by van der Waals interactions and by an intermolecular N—H⋯O hydrogen bond, whereas in the ortho isomer, an intermolecular N—H⋯π interaction (H⋯Cg = 2.75 Å) is found
2,4-Bis(4-bromophenyl)-3-azabicyclo[3.3.1]nonan-9-one
The title compound, C20H19Br2NO, shows a chair–chair conformation for the azabicycle with an equatorial disposition of the 4-bromophenyl groups [dihedral angle between the aromatic rings = 16.48 (3)°]. In the crystal, a short Br⋯Br contact [3.520 (4) Å] occurs and the structure is further stabilized by N—H⋯O hydrogen bonds and C—H⋯O interactions
2,4-Bis(4-chlorophenyl)-3-azabicyclo[3.3.1]nonan-9-one
In the molecular structure of the title compound, C20H19Cl2NO, the molecule exists in a twin-chair conformation with equatorial dispositions of the 4-chlorophenyl groups on both sides of the secondary amino group; the dihedral angle between the aromatic ring planes is 31.33 (3)°. The crystal structure is stabilized by N—H⋯O interactions, leading to chains of molecules
2,4,6,8-Tetrakis(4-chlorophenyl)-3,7-diazabicyclo[3.3.1]nonan-9-one O-benzyloxime acetone monosolvate
In the title compound, C38H31Cl4N3O·C3H6O, the 3,7-diaza-bicycle exists in a chair–boat conformation. The 4-chlorophenyl groups attached to the chair form are equatorially oriented at an angle of 18.15 (3)° with respect to each other, whereas the 4-chlorophenyl groups attached to the boat form are oriented at an angle of 32.64 (3)°. In the crystal, molecules are linked by N—H⋯π and C—H⋯O interactions
2,4-Bis(2-ethoxyphenyl)-7-methyl-3-azabicyclo[3.3.1]nonan-9-one
The crystal structure of the title compound, C25H31NO3, exists in a twin-chair conformation with an equatorial orientation of the ortho-ethoxyphenyl groups. According to Cremer and Pople [Cremer & Pople (1975 ▶), J. Am. Chem. Soc. 97, 1354–1358], both the piperidone and cyclohexanone rings are significantly puckered with total puckering amplitutdes Q
T of 0.5889 (18) and 0.554 (2) Å, respectively. The ortho-ethoxyphenyl groups are located on either side of the secondary amino group and make a dihedral angle of 12.41 (4)° with respect to each other. The methyl group on the cyclohexanone part occupies an exocyclic equatorial disposition. The crystal packing is stabilized by weak van der Waals interactions
A Comparative Study of Chi-Square Goodness-of-Fit Under Fuzzy Environments
Testing goodness-of-fit plays a vital role in data analysis. This problem seems to be much more complicated in the presence of vague data. In this paper, the chi-square goodness-of-fit under trapezoidal fuzzy numbers (tfns.) is proposed using alpha cut interval method. And the ranking grades of tfns. are also used to compute the chi-square test statistic. The proposed technique is illustrated with two different numerical examples along with different methods of ranking grades for a concrete comparative study. Keywords: Chi-square Test, Fuzzy Sets, Trapezoidal Fuzzy Numbers, Alpha Cut, Ranking Function, Graded Mean Integration Representation
A Comparative Study of Latin Square Design Under Fuzzy Environments Using Trapezoidal Fuzzy Numbers
This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbers (Tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study. Keywords: LSD, Trapezoidal Fuzzy Numbers, Alpha Cut, Membership Function, Ranking Function, Total Integral Value, Graded Mean Integration Representation. AMS Mathematics Subject Classification (2010): 62A86, 62F03, 97K8
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