Möbius Polynomials of Face Posets of Convex Polytopes

The Möbius polynomial is an invariant of ranked posets, closely related to the Möbius function. In this paper, we study the Möbius polynomial of face posets of convex polytopes. We present formulas for computing the Möbius polynomial of the face poset of a pyramid or a prism over an existing polytope, or of the gluing of two or more polytopes in terms of the Möbius polynomials of the original polytopes. We also present general formulas for calculating Möbius polynomials of face posets of simplicial polytopes and of Eulerian posets in terms of their f-vectors and some additional constraints.     

Effects of hydroxyapatite nanoparticles on proliferation and apoptosis of human breast cancer cells (MCF-7)

The study aimed to correlate cell proliferation inhibition with oxidative stress and p53 protein expression in cancerous cells. Hydroxyapatite (HAP) (Ca₁₀(PO₄)₆(OH)₂) is the essential component of inorganic composition in human bone. It has been found to have obvious inhibitory function on growth of many kinds of tumor cells and its nanoparticle has stronger anti-cancerous effect than macromolecule microparticles. Human breast cancer cells (MCF-7) were cultured and treated with HAP nanoparticles at various concentrations. Cells viability was detected with MTT colorimetric assay. The morphology of the cancerous cells was performed by transmission electron microscopy and the expression of a cell apoptosis related gene (p53) was determined by ELISA assay and flow cytometry (FCM). The intracellular reactive oxygen species (ROS) level in HAP exposed cells was measured by H₂DCFDA staining. DNA damage was measured by single-cell gel electrophoresis assay. The statistical analysis was done by one way ANOVA. The cellular proliferation inhibition rate was significantly (p < 0.05) increasing in a dose-dependent manner of HAP nanoparticles. Cell apoptotic characters were observed after MCF-7 cells were treated by HAP nanoparticles for 48 h. Moreover, ELISA assay and FCM shows a dose-dependent activation of p53 in MCF-7 cells treated with nanoHAP. These causative factors of the above results may be justified by an overproduction of ROS. In this study, a significant (p < 0.05) increase in the level of intracellular ROS in HAP-treated cells was observed. This study shows that HAP inhibits the growth of human breast cancer MCF-7 cells as well as induces cell apoptosis. This study shows that HAP NPs Induce the production of intracellular reactive oxygen species and activate p53, which may be responsible for DNA damage and cell apoptosis.     

Synthesis of 5,6-dihydrobenz[c]acridines: a comparative study

5,6-Dihydrobenz[c]acridines were synthesized by the reaction of 1-chloro-3,4-dihydro-2-naphthaldehyde with aromatic amines under three different conditions:

a.

Thermolysis of 1-chlorovinyl-(N-aryl)imines prepared from 1-chloro-3,4-dihydro-2-naphthaldehyde.

b.

Acid catalyzed cyclization of 1-(N-aryl)amino-3,4-dihydro-2-naphthaldehydes.

c.

Thermolysis of N-arylenaminoimine hydrochlorides derived from 1-chloro-3,4-dihydro-2-naphthaldehyde in DMF medium.

All the three approaches exclusively yielded only 5,6-dihydrobenz[c]acridines and not the isomeric 7,8-dihydrobenzo[k]phenanthridines.The structures of these products have been unambiguously established by detailed NMR spectral study and by independent synthesis as well as by single crystal XRD study.     

Catalyst‐free one‐pot regioselective synthesis of benzo[d]imidazo[2,1‐b]thiazoles by heating or grinding

Eco‐friendly, efficient, and simple one‐pot catalyst‐free new procedures have been reported for the synthesis of benzo[d]imidazo[2,1‐b]thiazoles by condensation of phenylglyoxal, cyclic enolizable carbonyl compounds, and 2‐aminobenzothiazole at 80°C or by grinding the components at room temperature in glycerol. Cyclic enolizable carbonyl compounds employed in the protocol include dimedone, cyclohexa‐1,3‐dione, cyclopenta‐1,3‐dione, 5‐methylcyclohexa‐1,3‐dione, and 4‐hydroxy‐6‐methyl‐2‐pyrone. All the reactions were complete in ~30 min. The structures of all the products were confirmed by spectral data. The structures of compounds IVl and IVe have also been confirmed by X‐ray crystallographic studies. This protocol offers advantages such as short reaction time, easy workup, high yields and an environmentally benign methodology.     

Microwave Activated Solid Support Synthesis of New Antibacterial Quinolones

Summary.  A novel synthesis of 6-fluoro-7-(5-aryl-1,3,4-thiadiazol/oxadiazol-2-yl-sulfanyl)-4-quinolone-3-carboxylic acids from 7-chloro-6-fluoro-4-quinolone-3-carboxylic acid and 5-substituted 1,3,4-thiadiazoles/oxadiazoles on basic alumina under microwave activation is described. All compounds were screened for their in vitro antibacterial activity against B. lichenformis, 2689, K. aerogens 2281, S. typhimurium 2501, E. herbicola 2491, and P. vulgaris 2027 and found to possess activities comparable to that of the standard drug norfloxacin. Received May 2, 2000. Accepted (revised) June 13, 2000     

Parameterizing above Guaranteed Values: MaxSat and MaxCut

In this paper we investigate the parameterized complexity of the problems MaxSat and MaxCut using the framework developed by Downey and Fellows. LetGbe an arbitrary graph havingnvertices andmedges, and letfbe an arbitrary CNF formula withmclauses onnvariables. We improve Cai and Chen'sO(2^2ckcm) time algorithm for determining if at leastkclauses of ac-CNF formulafcan be satisfied; our algorithm runs inO(|f| + k²φ^k) time for arbitrary formulae and inO(cm + ckφ^k) time forc-CNF formulae, where φ is the golden ratio . We also give an algorithm for finding a cut of size at leastk; our algorithm runs inO(m + n + k4^k) time. We then argue that the standard parameterization of these problems is unsuitable, because nontrivial situations arise only for large parameter values (k ≥ m/2), in which range the fixed-parameter tractable algorithms are infeasible. A more meaningful question in the parameterized setting is to ask whether m/2 + kclauses can be satisfied, or m/2 + kedges can be placed in a cut. We show that these problems remain fixed-parameter tractable even under this parameterization. Furthermore, for up to logarithmic values of the parameter, our algorithms for these versions also run in polynomial time.     

Superconducting linear accelerator system for NSC

This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed sufficiently. Details of the entire accelerator system including the cryogenics facility, RF electronics development, facilities for fabricating niobium resonators indigenously, and present status of the project are presented.     

Development and validation of a reversed-phase liquid chromatographic method for separation and simultaneous determination of COX-2 inhibitors in pharmaceuticals and its application to biological fluids

An isocratic reversed-phase high-performance liquid chromatographic method has been developed for separation and simultaneous determination of COX-2 inhibitors, viz., celecoxib, rofecoxib, valdecoxib, nimesulide and nabumetone, using 4-chloro-2-nitroaniline as internal standard. Good chromatographic separation was achieved using a reversed-phase Inertsil C(18) column with mobile phase consisting of methanol and 0.05% aqueous glacial acetic acid (68:32 v/v) using photodiode array (PDA) detector at 230 nm. It was validated with respect to accuracy, precision, linearity, limit of detection and quantification. The linearity range was found to be 1.0--20 microg/mL and the percentage recoveries were between 97.55 and 100.14. The method is suitable not only for the estimation of active ingredients in pharmaceutical dosage forms but also in vitro estimations in human plasma. It is simple, rapid, selective and capable of detecting and determining COX-2 inhibitors with a detection limit of 0.127--1.040 microg/mL simultaneously.