POLYROTAXANE WITH π-CONJUGATED PORPHYRIN AND POLYAZOMETHINE SYSTEMS PREPARED FROM A TYPE OF PORPHYRIN-DIALDEHYDE AND COMPLEX OF β-CYCLODEXTRIN WITH 1,4-PHENYLENEDIAMINE

The synthesis of 5,15-bis[4-(methoxycarbonyl)phenyl]-10,20-diphenylporphyrin (2) and its reduction to 5,15-bis[4-(hydroxymethyl)phenyl]-10,20-diphenylporphyrin (3), and so its oxidation to provide 5,15-bis(4-formylphenyl)-10,20-diphenylporphyrin (4) are reported. The copolymer possessing β-cyclodextrin (β-CD), π-conjugated porphyrin and polyazomethine systems was synthesized by the polycondensation of porphyrin-dialdehyde monomer (4) and β-cyclodextrin/1,4-phenylenediamine complex (5). The monomers and the copolymer were characterized by UV-Vis, 1H-NMR and IR spectra. Furthermore, 1H-NMR and FT-IR spectra confirmed locating the aromatic ring of 1,4-phenylenediamine molecule in the center of β-cyclodextrin cavity.     

Synthesis and investigation of nonlinear optical properties of semiconductor ZnS nanoparticles

ZnS nanoparticles were prepared by a simple chemical method and using PVP (poly vinylpyrrolidone) as capping agent. The sample was characterized by UV-vis spectrophotometer, X-ray diffraction (XRD) and Z-scan technique. XRD pattern showed that the ZnS nanoparticles had zinc blende structure with an average size of about 2.18 nm. The value of band gap of these nanoparticles was measured to be 4.20 eV. The nonlinear optical properties of ZnS nanoparticles in aqueous solution were studied by Z-scan technique using CW He-Ne laser at 632.8 nm. The nonlinear absorption coefficient (β) was estimated to be as high as 3.2×10⁻³ cm/W and the nonlinear refractive index (n₂) was in order of 10⁻⁸ cm²/W. The sign of the nonlinear refractive index obtained negative that indicated this material exhibits self-defocusing optical nonlinearity.     

Cluster decay half-lives using asymmetry dependent densities

By adopting different neutron and proton density distributions, cluster decay half-lives were investigated using double-folding potentials with constant and nuclear asymmetry dependent sets of nuclear density parameters. Two adopted asymmetry dependent sets of parameters were fitted based on microscopic calculations, and they were calculated based on the neutron skin/halo-type nuclei assumption and by employing experimental rms charge radii. A bulk agreement between theory and experiment was obtained for all sets of parameters using a calculated cluster preformation probability. Few differences were observed between the skin and halo-type assumptions. However, the notable role of the asymmetry parameter was observed in the relatively large differences between the skin and skin-type with zero thickness.     

When Essential Extensions of Finitely Generated Modules are Finitely Generated

For certain classes 𝒞 of R-modules, including singular modules or modules with locally Krull dimensions, it is investigated when every module in 𝒞 with a finitely generated essential submodule is finitely generated. In case 𝒞 = Mod-R, this means E(M)/M is Noetherian for any finitely generated module M_R. Rings R with latter property are studied and shown that they form a class 𝒬 properly between the class of pure semisimple rings and the class of certain max rings. Duo rings in 𝒬 are precisely Artinian rings. If R is a quasi continuous ring in 𝒬 then R ? A ⊕ T where A is a semisimple Artinian ring and T ∈ 𝒬 with Z(T_T) ≤_ess T_T.     

Rationalizing chain microstructure in the polyα-olefins synthesized by cationic AlCl3/H2O catalytic system

In this study, three middle range α-olefin monomers including 1-hexene, 1-octene, and 1-decene were oligomerized using conventional AlCl₃/H₂O catalytic system. Molecular weight and microstructure of the oligomers were analyzed by GPC and ¹HNMR, respectively. By ¹HNMR spectra, both internal (CHR=CHR′ and CHR=CR′R′′) and external (CH₂=CR′R′′) olefins containing di and tri-substituted C=C bonds were detected. After successful oligomerization, synthesized polyα-olefins underwent hydrogenation process using Pd(0)-Hal catalyst to yield synthetic oils of PHex, POct, and PDec, respectively and then completion of the hydrogenation was confirmed by ¹HNMR spectroscopy. The microstructure of the synthesized oligomers was rationalized using the ratio under the peak of CH?+?CH₂/CH₃ hydrogens (S1/S2) in ¹HNMR spectra and the degree of oligomerization obtained from M_n. According to the results, the best match between theoretical and real S1/S2 is obtained when considering double bond isomerization in the synthesized PAOs. By knowing PAO molecular weight, a relationship between monomer type and S1/S2 in the PAO homopolymers was detected. Our suggested methodology can be generalized to the unknown PAO homopolymers to unravel their monomer type by simple ¹HNMR and GPC analyses.     

Thermal Entanglement Between Two Two-Level Atoms in a Two-Photon Jaynes-Cummings Model with an Added Kerr Medium

In this paper, we consider a Hamiltonian model that includes interaction of two coupled two-level atoms with a single-mode quantized electromagnetic field in a cavity via the degenerate two-photon transition. The cavity is filled with a Kerr-like medium and is held at a temperature T. The free field Hamiltonian possesses the su(1,1) symmetry which realized by either even or odd photon-number states. The total number of excitation as a constant of motion, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a results, the representation of the Hamiltonian becomes block-diagonal matrix with three blocks. After diagonalizing each block, we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. Finally, the effect of temperature, atom-atom and Kerr-type couplings on the degree of thermal entanglement between the atoms are investigated. Our results show that within the single-excitation subspace spanned with odd photon-number states, the entanglement between the atoms is thermally robust.     

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.