On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Solenoidal versus compressive turbulence forcing

We analyze the statistics and star formation rate obtained in high-resolution numerical experiments of forced supersonic turbulence, and compare with observations. We concentrate on a systematic comparison of solenoidal (divergence-free) and compressive (curl-free) forcing, which are two limiting cases of turbulence driving. Our results show that for the same RMS Mach number, compressive forcing produces a three times larger standard deviation of the density probability distribution. When self-gravity is included in the models, the star formation rate is more than one order of magnitude higher for compressive forcing than for solenoidal forcing.Comment: 1 page, to appear in the proceedings of the IAU General Assembly Joint Discussion 14 "FIR2009: The ISM of Galaxies in the Far-Infrared and Sub-Millimetre", ed. M. Cunningha

Cuts and flows of cell complexes

We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory of cuts and flows in graphs, most notably the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and give sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.Comment: 30 pages. Final version, to appear in Journal of Algebraic Combinatoric

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

Paradoxical effects of the topoisomerase inhibitor, ethoxidine, in the cellular processes leading to angiogenesis on EaHy.926 endothelial cells

Topoisomerase I generates transient single-stranded breaks in DNA and have the capacity to fragment the genome. Thus, this enzyme is the target for some of the most successful anticancer drugs. Ethoxidine, a benzo[c]phenanthridines derivative, was identified as a potent inhibitor of topoisomerase I. As angiogenesis is a critical step in tumorigenesis, this study was designed to test the potential effect of ethoxidine on different processes leading to neovascularisation on EaHy endothelial cells including adhesion, migration and proliferation. Ethoxidine was tested at two concentrations, 100 μM and 10 μM . VEGF (20 ng/mL) was used as control. Adherent cells were evaluated using crystal violet staining, migration using a model of wound healing. Proliferation was analyzed using CyQUANT Cell Proliferation Assay Kit. Both O2- and NO productions were assessed using electronic paramagnetic resonance technique. All the effects of ethoxidine were evaluated at 24 h treatment. Low concentration of ethoxidine promoted migration to the same extent as that produced by VEGF whereas high concentration inhibited this process. Ethoxidine significantly enhanced adhesion at similar level than VEGF at low concentration. It was without effect at high concentration. Although ethoxidine had no effect at low concentration, it significantly reduced cell proliferation at high concentration. At any concentration tested, ethoxidine did not modify basal O2- production. Interestingly, ethoxidine significantly increase NO production at low concentration but it was without effect at high concentration. As control experiment, VEGF enhanced Eahy cells NO production under the same experimental conditions. Altogether, the present study highlights paradoxical effects of ethoxidine depending on the concentration used. At low concentration, it promotes both Eahy cells migration and adhesion without any effect on proliferation. Importantly, these effects were associated with an increase of NO production. In contrast at high concentration, ethoxidine reduced Eahy cells migration and proliferation but had no effect neither on adhesion nor NO release. Of note is the fact that ethoxidine did not alter endothelial cells oxidative stress at any concentration tested. Thus, these data underscore the potential anti-tumoral property of ethoxidine at high concentration and endothelial cells in the present study. The property of ethoxidine in inhibiting proliferation in both cell type probably account for its high antitumor activity

The non-linear Schr\"odinger equation and the conformal properties of non-relativistic space-time

The cubic non-linear Schr\"odinger equation where the coefficient of the nonlinear term is a function $F(t,x)$ only passes the Painlev\'e test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.Comment: Thoroughly revised version, in the light of new interest in non-relativistic conformal tranformation, with a new reference list. 8 pages, LaTex, no figures. To be published in Int. J. Theor. Phy

Spinor vortices in non-relativistic Chern-Simons theory

The non-relativistic `Dirac' equation of L\'evy-Leblond is used to describe a spin {\small 1/2} particle interacting with a Chern-Simons gauge field. Static, purely magnetic, self-dual spinor vortices are constructed. The solution can be `exported' to a uniform magnetic background field.Comment: 7 pages, Plain Te

Effect of Supplementary Cementitious Materials on the Compressive Strength and Durability of Short-Term Cured Concrete

This research focuses on studying the effect different supplementary cementitious materials (silica fume, fly ash, slag, and their combinations) on strength and durability of concrete cured for a short period of time—14 days. This work primarily deals with the characteristics of these materials, including strength, durability, and resistance to wet and dry and freeze and thaw environments. Over 16 mixes were made and compared to the control mix. Each of these mixes was either differing in the percentages of the additives or was combinations of two or more additives. All specimens were moist cured for 14 days before testing or subjected to environmental exposure. The freeze–thaw and wet–dry specimens were also compared to the control mix. Results show that at 14 days of curing, the use of supplementary cementitious materials reduced both strength and freeze–thaw durability of concrete. The combination of 10% silica fume, 25% slag, and 15% fly ash produced high strength and high resistance to freeze–thaw and wet–dry exposures as compared to other mixes. This study showed that it is imperative to cure the concrete for an extended period of time, especially those with fly ash and slag, to obtain good strength and durability. Literature review on the use of different supplementary cementitious materials in concrete to enhance strength and durability was also reported