Pre—Separation Axioms in Fuzzifying Topology

1　 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are …     

Optical absorption of tetraphenylporphyrin thin films in UV-vis-NIR region

The optical absorption of thermally evaporated tetraphenylporphyrin (TPP) in the UV-vis-NIR region have been studied. The absorption spectra recorded in the UV-vis region for the as deposited and annealed films showed different absorption bands, namely the Soret(B) at region 360-490nm, Q-band region consist of four bands in the region 500-720nm and two other bands labeled N and M in UV region. The Soret band always shows its characteristic effect splitting in all the TPP thin films and the effect of annealing on the intensities of these components have been observed. The spectra of the infrared absorption allow characterization of vibrational modes for the powder, as deposited and annealed thin films. Some of the optical absorption parameters, namely molar extinction coefficient, varepsilon, half band width, Deltalambda, electronic dipole strength, q(2) and oscillator strength, f, of the principle optical transitions have also been evaluated.     

Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.     

Soc-Injective Rings and Modules*

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple submodule K of N, any R-homomorphism f : K → M extends to N. In this article, we investigate the notion of soc-injectivity.     

Fourier-transform infrared and optical absorption spectra of 4-tricyanovinyl-N,N-diethylaniline thin films

Thin films of 4-tricyanovinyl-N,N-diethylaniline (TCVA) were prepared for the first time using thermal evaporation technique. The molecular structure and electronic transitions of TCVA films were investigated by Fourier-transform infrared (FTIR) and ultraviolet-visible (UV-vis) spectra. The observed vibrational wavenumbers in FTIR spectra were analysed and assigned to different normal modes of the molecule. UV-vis electronic absorption spectral measurements of TCVA films were analysed to obtain the electronic transitions and optical band gap (E(g)). Other important optical parameters such as molar extinction coefficient (varepsilon(molar)), the oscillator strength (f), and the electric dipole strength (q(2)) were also reported.