An iterative solution to the generalized Towers of Hanoi problem

An iterative solution to the generalized Towers of Hanoi problem, and its derivation are presented. In this generalization, one or more towers, consisting of a total ofn discs, are given as an initial legal configuration, and the task is to move them to a specified peg under the usual restrictions. An analysis of the iterative algorithm is also discussed.     

The fabrication of superhydrophobic copper films by a low-pressure-oxidation method

The lotus-leaf-like superhydrophobic copper was fabricated by a facile two-step method without the chemical modification, on which the water contact angle can reach 158° and the water-sliding angle is less than 10°. Reversible superhydrophobicity to superhydrophilicity transition was observed and controlled by alternation of UV irradiation and dark storage. More interestingly, the superhydrophobic surface exhibits superoleophilicity and all those properties can be well used in reversible switch, separating the water and oil and so on.     

The Poincaré Series of Relative Invariants of Finite Pseudo-Reflection Groups

Let F be a field with characteristic 0,V=F~n the n-dimensional vector space over F and let G be a finite pseudo-reflection group which acts on V.Let χ:G→F~* be a 1-dimensional representation of G.In this article we show that X(g)=(detg)~α(0≤α≤r-1),where g∈G and r is the order of g.In addition,we characterize the relation between the relative invariants and the invariants of the group G,and then we use Molien's Theorem of invariants to compute the Poincaré series of relative invariants.     

He's homotopy perturbation method for solving the shock wave equation

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.     

Lifting Modules with Indecomposable Decompositions

A module M is called a “lifting module” if, any submodule A of M contains a direct summand B of M such that A/B is small in M/B. This is a generalization of projective modules over perfect rings as well as the dual of extending modules. It is well known that an extending module with ascending chain condition (a.c.c.) on the annihilators of its elements is a direct sum of indecomposable modules. If and when a lifting module has such a decomposition is not known in general. In this article, among other results, we prove that a lifting module M is a direct sum of indecomposable modules if (i) rad(M ^(I)) is small in M ^(I) for every index set I, or, (ii) M has a.c.c. on the annihilators of (certain) elements, and rad(M) is small in M.     

Infinite Direct Sums of Lifting Modules

A module M over a ring R is called a lifting module if every submodule A of M contains a direct summand K of M such that A/K is a small submodule of M/K (e.g., local modules are lifting). It is known that a (finite) direct sum of lifting modules need not be lifting. We prove that R is right Noetherian and indecomposable injective right R-modules are hollow if and only if every injective right R-module is a direct sum of lifting modules. We also discuss the case when an infinite direct sum of finitely generated modules containing its radical as a small submodule is lifting.     

Anticancer Photodynamic Therapy Properties of Sulfur‐Doped Graphene Quantum Dot and Methylene Blue Preparations in MCF‐7 Breast Cancer Cell Culture

Photodynamic therapy (PDT) is a field with many applications including chemotherapy. Graphene quantum dots (GQDs) exhibit a variety of unique properties and can be used in PDT to generate singlet oxygen that destroys pathogenic bacteria and cancer cells. The PDT agent, methylene blue (MB), like GQDs, has been successfully exploited to destroy bacteria and cancer cells by increasing reactive oxygen species generation. Recently, combinations of GQDs and MB have been shown to destroy pathogenic bacteria via increased singlet oxygen generation. Here, we performed a spectrophotometric assay to detect and measure the uptake of GQDs, MB and several GQD‐MB combinations in MCF‐7 breast cancer cells. Then, we used a cell counting method to evaluate the cytotoxicity of GQDs, MB and a 1:1 GQD:MB preparation. Singlet oxygen generation in cells was then detected and measured using singlet oxygen sensor green. The dye, H₂DCFDA, was used to measure reactive oxygen species production. We found that GQD and MB uptake into MCF‐7 cells occurred, but that MB, followed by 1:1 GQD:MB, caused superior cytotoxicity and singlet oxygen and reactive oxygen species generation. Our results suggest that methylene blue's effect against MCF‐7 cells is not potentiated by GQDs, either in light or dark conditions.     

Ni(II), Cu(II), and Zn(II) complexes of tetradentate schiff base containing two thiadiazoles units: Structural,spectroscopic, magnetic properties,and molecular modeling studies

Four new mononuclear metal complexes with a mononucleating Schiff base ligand containing two thiadiazoles units have been synthesized. The ligand and metal complexes were characterized by elemental analyses, IR, ¹H, and ¹³C NMR, UV–vis, ESR, electrospray ionization mass spectra, and magnetic susceptibility measurements. Electronic spectra, magnetic susceptibility measurement, and molecular modeling studies support octahedral geometry around the Ni(II), Cu(II), and Zn(II) ions. The magnetic properties were investigated, and ferromagnetic coupling is observed in Cu(II) and Ni(II) complexes. In addition, total energy and heat of formation calculated for conformers of the Schiff base ligand by the semiempirical AM1 calculations have shown that E,Z‐isomer of the ligand is more stable (about 5.3 kcal/mol) than E,E‐ and Z,Z‐isomers. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:700–712, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20496     

Accurate,sensitive determination of omega-6 and omega-3 polyunsaturated fatty acids in human plasma,urine samples

Quantitative determination of omega-6 and omega-3 polyunsaturated fatty acids in human plasma and urine with high accuracy and precision provides significant information to monitor the underlying etiology of several diseases. In this regard, liquid chromatography-mass spectrometry is a good choice owing to its great selectivity and sensitivity. Additionally, the hybrid quadrupole–time of flight–mass spectrometer systems provides easy identification of target compounds with superior mass measurements. In this study, an analytical method has been developed for simple, accurate and simultaneous determination of linoleic acid, arachidonic acid, docosahexaenoic acid and eicosapentaenoic acid in a short chromatographic analysis period. The developed method is suitable for the quantitative detection of these four compounds with detection limits ranging between 1.1–3.0 ng ml⁻¹ and its applicability was assessed in human urine and plasma samples. As a result, acceptable accuracy (between 83 and 111%) and good precision (<6%) were obtained for target compounds using matrix matching calibration strategy.