İzotropik 3‐Uzayda Yüzeyler Üzerine Sınıflandırma Sonuçları

İzotropik 3‐uzay ?? Cayley‐Klein uzaylarından biridir ve Öklidyen uzayda standart Öklidyen uzaklık ile

Anahtar Kelimeler:

İzotropik uzay, Helikoidal yüzey, İzotropik ortalama eğrilik, Relatif eğrilik, Jeodezik, Asimptotik eğri.

Synthesis, Characterization of Chalcone Containing Methacrylate Polymers: Investigation of Fluorescence, Thermal and Dielectric Properties

In this study, the (1‐benzofurane‐2‐yl)‐3‐oxo‐prop‐1‐en‐1‐yl]‐2‐methoxyphenyl 2‐methyl acrylate monomer were synthesized from the acylation reaction of this compound with methacryloyl chloride that commercially purchased. Free radicalic or atom transfer radical polymerization methods were used for preparation of copolymers. FT‐IR, 1H and 13C‐NMR techniques were used for structure characterization of polymers. The thermal behaviors of polymers were relatively investigated by DSC and TGA, and the results were compared with each other. The dielectric behaviors of polymers were investigated as a function of temperature and frequency. The results obtained were associated with their the structures. The spectroscopic properties of the polymers were investigated by UV‐Vis and fluorescence spectroscopies. Effects of the solvent polarity on emission measurement were investigated with fluorescence spectroscopy. Under cover of dimerization property of chalcone, the chalcone ended polymer was photodimerizatied.

Keywords:

Thermal properties, Dielectric Properties, Chalcone, Photodimerization, Fluorescence,

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Arvanitoyeorgos, A., Kaimakamis, G., 2010. Helicoidal surfaces in the Heisenberg 3‐space. JP Geometry and Topology, 10(1), 1‐10.
Aydin, M.E., 2015. A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom., DOI 10.1007/s00022‐015‐0292‐0.
Aydin, M.E., Mihai, I., 2016. On surfaces in the isotropic 4‐space, Math. Commun. to appear. Aydin, M.E., Ogrenmis A.O., 2016. Homothetical and translation surfaces with constant curvature in the isotropic space, BSG proceedings, 23, 1‐10.
Baba‐Hamed, C.H., Bekkar, M., 2009. Helicoidal surfaces in the three‐dimensional Lorentz‐Minkowski space satisfying , i i i  r   r Int. J. Contemp. Math. Sciences 4(7), 311‐327.
Baikoussis, C., Koufogioros, T., 1998. Helicoidal surface with prescribed mean or Gauss curvature, J. Geom. 63, 25‐29.
Beneki, Ch.C., Kaimakamis, G., Papantoniou, B.J., 2002. Helicoidal surface in three dimensional Minkowski space, J. Math. Anal. Appl. 275, 586‐614.
Chen, B.‐Y., Decu, S., Verstraelen, L., 2014. Notes on isotropic geometry of production models, Kragujevac J. Math. 37(2), 217‐‐220.
Choi, M., Yoon, D.W., 2015. Helicoidal surfaces of the third fundamental form in Minkowski 3‐space, Bull. Korean Math. Soc. 52(5), 1569‐‐1578.
Choi, M., Kim, Y.H., Liu, H., Yoon, D.W., 2010. Helicoidal surfaces and their Gauss map in Minkowski 3‐space, Bull. Korean Math. Soc. 47(4), 859‐‐881.
Decu, S., Verstraelen, L., 2013. A note on the isotropical geometry of production surfaces, Kragujevac J. Math. 38(1), 23‐‐33.
Delaunay, G., 1841. Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pures Appl. Series 6(1), 309‐320.
Divjak, B., Milin Sipus, Z., 2008. Some special surfaces in the pseudo‐Galilean space, Acta Math. Hungar., 118(3), 209‐226.
Do Carmo, M.P., Dajczer, M., 1982. Helicoidal surfaces with constant mean curvature, Tohoku Math. J. 34, 425‐435.
Do Carmo, M.P., 1976. Differential geometry of curves and surfaces, Prentice Hall: Englewood Cliffs, NJ. Erjavec, Z., Divjak, B., Horvat, D., 2011. The general solutions of Frenet's system in the equiform geometry of the Galilean, pseudo‐Galilean, simple isotropic and double isotropic space, Int. Math. Forum 6(17), 837‐856.
Gray, A., 2005. Modern differential geometry of curves and surfaces with mathematica. CRC Press LLC. Ji, F., Hou, Z.H., 2005. A kind of helicoidal surfaces in 3‐ dimensional Minkowski space, J. Math. Anal. Appl. 275, 632‐643.
Hou, Z.H., Ji, F., 2007. Helicoidal surfaces with H 2  K in Minkowski 3‐space, J. Math. Anal. Appl. 325, 101‐113.
Kamenarovic, I., 1982. On line complexes in the isotropic space , ) 1(3 I Glasnik Matematicki 17(37), 321‐329.
Kamenarovic, I., 1994. Associated curves on ruled surfaces in the isotropic space , ) 1(3 I Glasnik Matematicki 29(49), 363‐370.
Kenmotsu, K., Surfaces of revolution with prescribed mean curvature, Tohoku Math. J. 32, 147‐153.
Kim, Y.H., Turgay, N.C., 2013. Classifications of helicoidal surfaces with  1 L pointwise 1‐type Gauss map, Bull. Korean Math. Soc. 50(4), 1345‐1356.
Kim, Y.H., Koh, S.‐E., Shin, H., Yang, S.‐D., 2012. Helicoidal minimal surfaces in H2 R, B. Aust. Math Soc. 86(1), 135‐149.
Lopez, R., Demir, E., 2014. Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature, Cent. Eur. J. Math. 12(9), 1349‐1361.
Milin Sipus, Z., 2014. Translation surfaces of constant curvatures in a simply isotropic space, Period. Math. Hung. 68, 160‐‐175
Milin Sipus, Z., Divjak, B., 1998. Curves in n‐dimensional k‐isotropic space, Glasnik Matematicki 33(53), 267‐ 286.
Palman, D., 1979. Spharische quartiken auf dem torus im einfach isotropen raum, Glasnik Matematicki 14(34), 345‐357.
Pavkovic, B., 1980. An interpretation of the relative curvatures for surfaces in the isotropic space, Glasnik Matematicki 15(35) (1980), 149‐152.
Sachs, H., 1990a. Ebene Isotrope Geometrie, Vieweg‐ Verlag, Braunschweig, Wiesbaden. Sachs, H., 1990b. Isotrope Geometrie des Raumes, Vieweg Verlag, Braunschweig. Sachs, H., 1978. Zur Geometrie der Hyperspharen in ndimensionalen einfach isotropen Raum, Jour. f. d. reine u. angew. Math. 298, 199‐217.
Senoussi, B., Bekkar, M., 2015. Helicoidal surfaces with J r  Ar in 3‐dimensional Euclidean space, Stud. Univ. Babes‐Bolyai Math. 60(3), 437‐448. Strubecker, K., 1942. Differentialgeometrie des isotropen Raumes III, Flachentheorie, Math. Zeitsch. 48, 369‐427.