On the degeneracy of <Emphasis Type="Italic">SU</Emphasis>(3)<Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> topological phases

The ground state degeneracy of an SU(N) _k topological phase with n quasiparticle excitations is a relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any N >2. Here we present the problem in an explicit combinatorial way and analyze the case N = 3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.     

Nanoemulsions of Jasminum humile L. and Jasminum grandiflorum L. Essential Oils: An Approach to Enhance Their Cytotoxic and Antiviral Effects

Unprecedented nanoemulsion formulations (NE) of Jasminum humile and Jasminum grandiflorum essential oils (EO) were prepared, and examined for their cytotoxic and antiviral activities. NE characterization and stability examination tests were performed to ensure formula stability. The antiviral activity was determined against hepatitis A (HAV) and herpes simplex type-1 (HSV-1) viruses using MTT assay, while the cytotoxic potential was determined against liver (HepG-2), breast (MCF-7), leukemia (THP-1) cancer cell lines and normal Vero cells. Statistical significance was determined in comparison with doxorubicin as cytotoxic and acyclovir as antiviral standard drugs. GC-MS analysis indicated twenty four compounds in the EO of J. humile and seventeen compounds in the EO of J. grandiflorum. Biological investigations of pure EOs revealed weak cytotoxic and antiviral effects. Nevertheless, their NE formulations exhibited high biological value as cytotoxic and antiviral agents. NE formulations also showed feasible selectivity index for the viral-infected and cancer cells (especially HepG-2) than normal Vero cells. Both nanoemulsions showed lower IC₅₀ than standard doxorubicin against HepG-2 (26.65 and 22.58 vs. 33.96 μg/mL) and MCF-7 (36.09 and 36.19 vs. 52.73 μg/mL), respectively. The study results showed the dramatic effect of nanoemulsion preparation on the biological activity of EOs and other liposoluble phytopharmaceuticals.     

Potential Anticancer Activities and Catalytic Oxidation Efficiency of Platinum(IV) Complex

The treatment of an aqueous acetonitrile solution of chloroplatinic acid hydrate H₂PtCl₆.xH₂O and pyridine-2-carbaldehyde-oxime (paOH) in the presence of potassium thiocyanate at room temperature (25°) led to the formation of a new Pt(IV) complex with the formula [Pt(SCN)₂(paO)₂], (1). Complex 1 was fully characterized by FT-IR, UV-vis and NMR spectroscopic techniques as well as elemental analysis. The crystallographic structure of complex 1 was obtained by single-crystal X-ray diffraction. The structure of complex 1 consists of a distorted octahedral geometrical environment around the platinum center in which the coordination sites are occupied by two terminal thiocyanate ligands in trans arrangement and two bidentate paO ligands through four nitrogen atoms. In addition, the in vitro evaluation of the cytotoxicity of platinum complex 1 against four different cancer cell lines was performed. The IC₅₀ values for colon (HCT116), liver (HepG2), breast (MCF-7) and erythroid (JK-1) treated with complex 1 are 19 ± 6, 21 ± 5, 22 ± 6, and 13 ± 3 μM, respectively. In HCT116 cells treated with the IC50 dose of our title compound, apoptosis and necrosis were increased by 34% and 27.8%, respectively. Cells halted in the proliferative phase (S phase) to 21.7 % and 29.8% in HCT116 and HepG2 cells treated with complex 1 have anti-proliferative actions. Furthermore, the catalytic activity of synthesized complex 1 was examined in the oxidation reaction of benzyl alcohols in the presence of an oxidant. Finally, the luminescence behavior of complex 1 was investigated.