Intractable problems in reversible cellular automata

The billiard ball model, a classical mechanical system in which all parameters are real variables, can perform all digital computations. An eight-state, 11-neighbor reversible cellular automaton (an entirely discrete system in which all parameters are integer variables) can simulate this model. One of the natural problems for this system is to determine the shape of a container so that the initial specific distribution of gas molecules eventually leads to a predetermined distribution. This problem is PSPACE-complete. Related intractable and decidable problems are discussed as well.     

On spectral properties of a new operator over sequence spaces c and c0

In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces ?_∞, c${?}_{\infty },\hspace{0.17em}c$ and c₀ according to a new matrix operator W which is obtained by matrix product.     

Cu (II) tyrosinate complexes containing methyl substituted phenanthrolines: Synthesis,X‐ray crystal structures,biomolecular interactions,antioxidant activity,ROS generation and cytotoxicity

In this paper, three new copper (II) complexes, [Cu(4‐mphen)(tyr)(H₂O)]ClO₄ (1) , [Cu(5‐mphen)(tyr)(H₂O)]ClO₄·1.5H₂O (2) and [Cu (tmphen)(tyr)(NO₃)]0.5H₂O (3) (4‐mphen: 4‐methyl‐1,10‐phenanthroline, 5‐mphen: 5‐methyl‐1,10‐phenanthroline, tmphen: 3,4,7,8‐tetramethyl‐1,10‐phenanthroline and tyr: L‐tyrosine), were synthesized and characterized using elemental analyses, FT‐IR, ESI‐MS, cyclic voltammetry and single‐crystal X‐ray diffraction. It was found that the complexes adopt a distorted five‐coordinate square pyramidal geometry. The interaction of the three complexes with calf thymus DNA was also investigated using UV–visible absorption spectra, ethidium bromide and Hoechst 33258 displacement assay and thermal denaturation. The DNA cleavage activity of the complexes, monitored using gel electrophoresis, showed significant damage of the pUC19 plasmid DNA. Binding activity of bovine serum albumin (BSA) reveals that these complexes can strongly quench the fluorescence of BSA through a static quenching mechanism. The results suggested that interaction of the complexes with DNA occurred through a partial intercalation into the minor grooves of DNA. In addition, interaction of the complexes with bovine serum albumin quenched the fluorescence emission of the tryptophan residues of the protein binding constants and thermodynamic parameters were obtained from the fluorescence quenching experiments at different temperatures. Free radical scavenging activities of the complexes were determined by various in vitro assays such as 1,1‐diphenyl‐2‐picryl‐hydrazyl free radicals (DPPH˙) and H₂O₂ scavenging methods. In addition, the cytotoxicity of these complexes in vitro on tumor cell lines (Caco‐2 and MCF‐7) was examined by XTT and showed better antitumor effect on the tested cells. ROS (reactive oxygen species) and comet experiments are consistent with each other and these complexes lead to DNA damage via the production of ROS. The effect of the hydrophobic properties of the synthesized complexes on DNA and BSA binding activities were discussed.     

ON SPECTRAL PROPERTIES OF A NEW OPERATOR OVER SEQUENCE SPACES c AND c0

In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces ?∞, c and c0 according to a new matrix operator W which is obtained by matrix product.     

Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space

We study convergence, rate of convergence and data dependency of normal?S iterative method for a fixed point of a discontinuous operator T on a Banach space. We also prove some Collage type theorems for T. The main aim here is to show that there is a close relationship between the concepts of data dependency of fixed points and the collage theorems and show that the latter provides better estimate. Numerical examples in support of the results obtained are also given.     

Some paranormed Euler sequence spaces of difference sequences of order m

The main purpose of this work is to extend the sequence spaces which are defined in [KARAKAYA, V.—POLAT, H.: Some new paranormed sequence spaces defined by Euler and difference operators, Acta Sci. Math. (Szeged) 76 (2010), 87–100] and [POLAT, H.—BASAR, F.: Some Euler spaces of difference sequences of order m, Acta Math. Sci. Ser. B Engl. Ed. 27 (2007), 254–266] by using difference operator of order m, and to give their alpha, beta and gamma duals. Furthermore, we characterize some classes of the related matrix transformations.     

All linear optical quantum memory based on quantum error correction

When photons are sent through a fiber as part of a quantum communication protocol, the error that is most difficult to correct is photon loss. Here we propose and analyze a two-to-four qubit encoding scheme, which can recover the loss of one qubit in the transmission. This device acts as a repeater, when it is placed in series to cover a distance larger than the attenuation length of the fiber, and it acts as an optical quantum memory, when it is inserted in a fiber loop. We call this dual-purpose device a "quantum transponder."     

SOME GEOMETRIC PROPERTIES OF A NEW DIFFERENCE SEQUENCE SPACE INVOLVING LACUNARY SEQUENCES

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.