The classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.Comment: 9 page

mtDNA lineage analysis of mouse L-cell lines reveals the accumulation of multiple mtDNA mutants and intermolecular recombination

The role of mitochondrial DNA (mtDNA) mutations and mtDNA recombination in cancer cell proliferation and developmental biology remains controversial. While analyzing the mtDNAs of several mouse L cell lines, we discovered that every cell line harbored multiple mtDNA mutants. These included four missense mutations, two frameshift mutations, and one tRNA homopolymer expansion. The LA9 cell lines lacked wild-type mtDNAs but harbored a heteroplasmic mixture of mtDNAs, each with a different combination of these variants. We isolated each of the mtDNAs in a separate cybrid cell line. This permitted determination of the linkage phase of each mtDNA and its physiological characteristics. All of the polypeptide mutations inhibited their oxidative phosphorylation (OXPHOS) complexes. However, they also increased mitochondrial reactive oxygen species (ROS) production, and the level of ROS production was proportional to the cellular proliferation rate. By comparing the mtDNA haplotypes of the different cell lines, we were able to reconstruct the mtDNA mutational history of the L-L929 cell line. This revealed that every heteroplasmic L-cell line harbored a mtDNA that had been generated by intracellular mtDNA homologous recombination. Therefore, deleterious mtDNA mutations that increase ROS production can provide a proliferative advantage to cancer or stem cells, and optimal combinations of mutant loci can be generated through recombination

Optimal approximate fixed point results in locally convex spaces

Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate fixed point net. Next, it is shown that if $C$ is bounded but not totally bounded, then there is a uniformly continuous map $f\colon C\to C$ without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, it is constructed a affine sequentially continuous map from a compact convex set into itself without fixed points.Comment: 12 page

Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.Comment: 62 page

Diffusion as mixing mechanism in granular materials

We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the grains by adding a random force. Starting with a segregated system, we show that uniform agitation (heating) leads to a uniform mixture of grains of different sizes. We define a characteristic mixing time, $\tau_{mix}$, and study theoretically and numerically its dependence on other parameters like the density. We examine a model for bidisperse systems for which we can calculate some physical quantities. We also examine the effect of a temperature gradient and demonstrate the appearance of an expected segregation.Comment: 15 eps figures, include

The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal $K$-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.Comment: 21 page

The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun

The dynamics of horizontal plasma flows during the first hours of the emergence of active region magnetic flux in the solar photosphere have been analyzed using SOHO/MDI data. Four active regions emerging near the solar limb have been considered. It has been found that extended regions of Doppler velocities with different signs are formed in the first hours of the magnetic flux emergence in the horizontal velocity field. The flows observed are directly connected with the emerging magnetic flux; they form at the beginning of the emergence of active regions and are present for a few hours. The Doppler velocities of flows observed increase gradually and reach their peak values 4-12 hours after the start of the magnetic flux emergence. The peak values of the mean (inside the +/-500 m/s isolines) and maximum Doppler velocities are 800-970 m/s and 1410-1700 m/s, respectively. The Doppler velocities observed substantially exceed the separation velocities of the photospheric magnetic flux outer boundaries. The asymmetry was detected between velocity structures of leading and following polarities. Doppler velocity structures located in a region of leading magnetic polarity are more powerful and exist longer than those in regions of following polarity. The Doppler velocity asymmetry between the velocity structures of opposite sign reaches its peak values soon after the emergence begins and then gradually drops within 7-12 hours. The peak values of asymmetry for the mean and maximal Doppler velocities reach 240-460 m/s and 710-940 m/s, respectively. An interpretation of the observable flow of photospheric plasma is given.Comment: 20 pages, 10 figures, 3 tables. The results of article were presented at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102, P.4.12, http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf

Rms-flux relation in the optical fast variability data of BL Lacertae object S5 0716+714

The possibility that BL Lac S5 0716+714 exhibits a linear root mean square (rms)-flux relation in its IntraDay Variability (IDV) is analysed. The results may be used as an argument in the existing debate regarding the source of optical IDV in Active Galactic Nuclei. 63 time series in different optical bands were used. A linear rms-flux relation at a confidence level higher than 65% was recovered for less than 8% of the cases. We were able to check if the magnitude is log-normally distributed for eight timeseries and found, with a confidence > 95%, that this is not the case.Comment: Accepted by Astrophysics and Space Scienc

The Method of Approximate Particular Solutions for Solving Elliptic Problems with Variable Coefficients

A new version of the method of approximate particular solutions (MAPSs) using radial basis functions (RBFs) has been proposed for solving a general class of elliptic partial differential equations. In the solution process, the Laplacian is kept on the left-hand side as a main differential operator. The other terms are moved to the right-hand side and treated as part of the forcing term. In this way, the close-form particular solution is easy to obtain using various RBFs. The numerical scheme of the new MAPSs is simple to implement and yet very accurate. Three numerical examples are given and the results are compared to Kansa\u27s method and the method of fundamental solutions

Supermassive Black Hole Binaries: The Search Continues

Gravitationally bound supermassive black hole binaries (SBHBs) are thought to be a natural product of galactic mergers and growth of the large scale structure in the universe. They however remain observationally elusive, thus raising a question about characteristic observational signatures associated with these systems. In this conference proceeding I discuss current theoretical understanding and latest advances and prospects in observational searches for SBHBs.Comment: 17 pages, 4 figures. To appear in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag