Synthesis,characterization and antioxidant,antibacterial activity Zn2+, Cu2+, Ni2+ and Co2+, complexes of ligand [2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole]

New metal complexes of (Zn(II), Co(II), Ni(II) and Cu(II)) based on the ligand 2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole] were synthesized, whose structures were determined with the different spectroscopic techniques ¹H NMR,¹³C NMR, FT-IR, UV–Visible and by mass spectrometry. The thermal analysis was performed by TG-DTA. The antioxidant activity of the ligand and its complexes was evaluated by DPPH (2,2-diphenyl-1-picrylhydrazyl) method, in comparison with the synthetic antioxidant, ascorbic acid. The results obtained showed that the antioxidant activity of the ligand and its complexes is moderate and that the copper complex has a high activity that exceeds that of ascorbic acid. Antimicrobial activity of the ligand and its metal complexes was studied against two Gram-positive bacteria: Bacillus subtilis ILP1428B, Staphylococcus aureus CIP543154 and two Gram-negative bacteria: Pseudomonas aeruginosa ATCC27653, Escherichia coli CIP5412 (American Type Culture Collection)the activity data show that the metal complexes are more potent than the free ligand.     

Cell scale self-organisation in the OFC model for earthquake dynamics

We examine the cell scale self organising mechanisms in the Olami Feder Christensen (OFC) model that have the potential to generate critical behaviour. In particular we demonstrate how spatial organisation and quantisation of strain distributions occurs, why temporal strain fluctuations are minimised as the local strain conservation factor, β → 1.0, and how the strain distributions are dependent upon the lattice geometry employed. The origin of the self-organising behaviour can be divided into two regimes; at low β where no re-rupturing of cells occurs and for higher β where the probability of re-rupturing becomes increasingly significant. The presence or absence of the re-rupturing mechanism leads to different system optimisations, tending from spatially well ordered strain domains at intermediate β to a spatially rough strain field but a temporally stationary, memory less strain distribution at β = 1. The construction of the Markov chain demonstrates that degeneracy of the transitions is a primary control on transition probabilities at β = 1. The stationary state occupation is controlled by transition degeneracy, local correlations and mean residence times.     

An O(n log n) algorithm for finding all repetitions in a string

Any nonempty string of the form xx is called a repetition. An O(n log n) algorithm is presented to find all repetitions in a string of lenght n. The algorithm is based on a linear algorithm to find all the new repetitions formed when two strings are concatenated. This linear algorithm is possible because new repetitions of equal length must occur in blocks with consecutive starting positions. The linear algorithm uses a variation of the Knuth-Morris-Pratt algorithm to find all partial occurrences of a pattern within a text string. It is also shown that no algorithm based on comparisons of symbols can improve O(n log n). Finally, some open problems and applications are suggested.     

Secondary ion mass spectra of alkali halides

Mass spectra of positive and negative secondary ions from various alkali halides have been measured in the Manitoba time-of-flight mass spectrometer. The ions were produced by Cs⁺ and K⁺ bombardment at primary ion energies of 3 to 19 keV for the positive spectra, and 11 to 28 keV for the negative spectra. The ions measured were those emitted within a time interval ～ 20 ns after the primary ion impact. The secondary ion yields are strongly dependent on the sample composition and treatment; prior irradiation may change the yield by an order of magnitude or more. The secondary ion yields also depend strongly on the energy loss of the primary ion, but the ratio of yields of different cluster ions from a given target is almost independent of this parameter. The results appear to be consistent with models in which the clusters are ejected directly from the target, but do not determine whether or not they possess the original surface structure. The results may also be described by a recombination model if the recombination is essentially complete.     

? expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

We extend a theory of first order ? corrections to Gutzwiller’s trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_4v-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the ? expansion method.