Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

A new definition for the symmetries of Itô and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Itô andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofItô dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.     

Triiron and Triruthenium Carbonyl Clusters Bearing Bridging Long Chain Diphosphine and Capping Chalcogenido Ligands

Treatment of Ru₃(CO)₁₂ with dpphSe₂ (dpph = 1,6-bis(diphenylphosphino)hexane) in refluxing toluene in the presence of Me₃NO afforded two new compounds, Ru₃(CO)₇(-CO)(₃-Se)(-dpph) (1) and Ru₃(CO)₇(₃-Se)₂(-dpph) (2). A similar reaction of Ru₃(CO)₁₂ with dpppeSe₂ (dpppe = 1,5-bis(diphenylphosphino)pentane) gave exclusively Ru₃(CO)₇(₃-Se)₂(-dpppe) (3). Treatment of Ru₃(CO)₁₂ with dpphS₂ and dpppeS₂ at 110°C in the presence of Me₃NO afforded Ru₃(CO)₇(₃-S)₂(-dpph) (4) and Ru₃(CO)₇(₃-S)₂(-dpppe) (5), respectively. Reactions of Fe₃(CO)₁₂ with dpphSe₂ and dpppeSe₂, under identical conditions, afforded Fe₃(CO)₇(₃-Se)₂(-dpph) (6) and Fe₃(CO)₇(₃-Se)₂(-dpppe) (7), respectively. Compounds 1–7 were characterized spectroscopically and the molecular structures of compounds 1–4 were determined by single crystal X-ray crystallography. The core of 1 contains an equilateral triangle of ruthenium atoms with one capping selenium, one bridging dpph, one doubly bridging carbonyl and seven terminal carbonyl ligands. Complexes 2–4 have a square-pyramidal structure with two metal and two chalcogenide atoms alternating in the basal plane and the third metal atom at the apex of the pyramid, and belong to the family of well-known nido clusters with seven skeletal electron pairs.     

Synthesis, structures and reactivity of triosmium clusters containing terminal pyrazines, bridging hydroxy and methoxycarbonyl ligands

Four triosmium carbonyl clusters bearing terminal pyrazines, bridging hydroxy and methoxycarbonyl ligands of general formula [Os₃(CO)₉(μ-OH)(μ-OMeCO)L] (1, L = pyrazine; 2, L = 2-methylpyrazine; 3, L = 2,3-dimethylpyrazine; 4, L = 2,3,5-trimethylpyrazine) were synthesized by the reactions of [Os₃(CO)₁₂] with the corresponding pyrazine derivatives and water in the presence of a methanolic solution of Me₃NO in moderate yields. Compounds [Os₃(CO)₉(μ-OH)(μ-OMeCO)L] react with a series of two electron donor ligands, L′ at ambient temperature to give [Os₃(CO)₉(μ-OH)(μ-OMeCO)L′] (5, L′ = PPh₃; 6, L′ = P(OMe)₃; 7, L′ = ^tBuNC; 8, L′ = C₅H₅N) in good yields by the displacement of the pyrazine ligands. This implies that the pyrazine ligands in 1–4 are relatively labile. Compounds 2, 3, 4, and 8 were characterized by single crystal X-ray diffraction analyses. All the four compounds possess two metal–metal bonds and a non-bonded separation of two osmium atoms defined by Os(1)Os(3), which are simultaneously bridged by OH and MeOCO ligands and a heterocyclic ligand is terminally coordinated to one of the two non-bonded osmium atoms.     

Selective LC Determination of Cabergoline in the Bulk Drug and in Tablets: In Vitro Dissolution Studies

Cabergoline (CAB) is an ergot alkaloid derivative with dopamine agonist activity. A novel, simple, and rapid stability-indicating high-performance liquid chromatographic (HPLC) method for assay of CAB in tablets has been developed and validated. Chromatography was performed on a 4.6 mm i.d. × 250 mm, 5 μm particle, cyano column with acetonitrile–10 mM phosphoric acid, 35:65 (v/v), containing 0.04% triethylamine, as mobile phase, at a flow rate of 1.0 mL min^?1, and UV detection at 280 nm. Response was a linear function of concentration in the range 0.1–4 μg mL^?1 (r ² = 0.9999). The recovery of the method was good (99.45%) and RSD values for intra-day and inter-day precision were 0.24–0.88% and 0.66–1.19%, respectively. The method can be used for quality-control assay of CAB in tablets, for stability studies, and for in vitro dissolution studies.     

Thiosemicarbazide-Substituted Coumarins as Selective Inhibitors of the Tumor Associated Human Carbonic Anhydrases IX and XII

A novel series of thiosemicarbazide-substituted coumarins was synthesized and the inhibitory effects against four physiologically relevant carbonic anhydrase isoforms I, II, IX and XII showed selective activities on the tumor-associated IX and XII isozymes. Molecular modeling studies on selected compounds 14a and 22a were performed. The binding modes of such compounds were determined assuming their enzymatically active structures (i.e., cinnamic acid) in the thermodynamically favored, and not previously explored, E geometry. Molecular modelling suggests multiple interactions within the enzymatic cavity and may explain the high potency and selectivity reported for the hCAs IX and XII.     

A new agent for sentinel lymph node detection: preliminary results

Sentinel lymph node detection is widely used to identify lymph nodes that receive lymphatic drainage from a primary tumor. ^99mTc labeled iron oxide nanoparticles were prepared to invent a new colorful radioactive agent for sentinel lymph node detection. Iron oxide nanoparticles were produced by co-precipitation of FeCl₃ and FeCl₂ in the presence of NaOH. Then iron oxide nanoparticles were labeled with ^99mTc. ^99mTc labeled nanoparticles (7.4 MBq/0.1 mL) were intradermally injected in the distal hind limb of 16 rabbits. Dynamic and static lymphoscintigraphic images were taken for 24 h. Labeling efficiencies of ^99mTc-iron oxide nanoparticles were over 99%. Their sizes are between 50 and 60 nm. ^99mTc-iron oxide nanoparticles were accumulated in the popliteal lymph node in 11 of 16 rabbits (69%). Retention of nanoparticles in the popliteal lymph node was obvious at from 2nd through 24th hours. The radioactive lymph node was identified easily by gamma probe. The popliteal lymph node was excised and established for radioactivity and black dye. These black and radioactive nanoparticles may be potential agent successfully used for sentinel lymph node detection.     

Microcalorimetric investigation of water vapor adsorption on silica gel

In this study, the activities of four ginsenosides Rc, Re, Rd, and Rf on splenic lymphocytes growth were studied by microcalorimetry. Some qualitative and quantitative information, such as the metabolic power–time curves, growth rate constant k, maximum heat-output power of the exponential phase P _max and the corresponding appearance peak time t _max, total heat output Q _t, and promotion rate R _p of splenic lymphocytes growth affected by the four ginsenosides were calculated. In accordance with thermo-kinetic model, the corresponding quantitative relationships of k, P _max, t _max, Q _t, R _p, and c were established, . Also, the median effective concentration (EC₅₀) was obtained by quantitative analysis. Based on both the quantitative quantity–activity relationships (QQAR) and EC₅₀, the sequence of promotion activity was Rc > Re > Rd > Rf. The analysis of structure–activity relationships showed that the number, type, and position of sugar moieties on the gonane steroid nucleus had important influences on the promotion activity of Rc, Re, Rd, and Rf on splenic lymphocytes growth. Microcalorimetry can be used as a useful tool for determining the activity and studying the quantity–activity relationship of drugs on cell.