Linear complementarity problems on extended second order cones

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg-Marquardt algorithm. Finally, we present some numerical examples

Occurrence of Grey Mould on Bucida buceras, a Tree of Subtropical Origin, under Indoor Conditions - A Disease Note

In December 2012 then in the following winter season, the occurrence of whitish mycelial coat was observed on the collar of 3- to 6-m high Bucida buceras trees grown in hydrocultures to decorate a spacious indoor community space in Vienna. (This plant [shown in Fig. 1] belongs to Combretaceae, Myrtales and commonly named black olive tree, bullet tree, gregorywood and oxhorn bucida.) The mycelium-infested area of the bark appeared to be water-soaked. Near the surface of the potting mix (earth ball embedded in clay pebbles), the roots were also covered with whitish mycelia (Fig. 2). Over the winter season when the indoor temperature increased from 20 °C to 25 °C, these symptoms were unnoticeable. Regardless of the season, the rhizosphere contained numbers of sclerotia, dark-grey, globose and 8–12 mm in diameter that occasionally developed rhizomorph-like mycelial cords. Direct plating of mycelium fragments from the bark and sclerotia from the rhizosphere onto potato dextrose agar amended with ampicillin (500 mg/l) eventually yielded pure fungal cultures of similar characteristics. Cultures routinely incubated in the dark developed white and submerged colonies with sparse aerial mycelia. The fungus grew well between 10 °C and 25 °C, and failed to grow at either 5 °C or 32 °C. The optimal growth was measured at 20 °C with an average radial growth rate of 11 mm per day. After 10 to 12 days, a ring of sclerotia begun to develop near the edge of the colonies; they turned dark grey and sized 3–8 mm. Rather misleadingly, neither conidia, nor sexual spores were observed in these cultures. However, when the fungus was cultured in natural light under laboratory conditions at 25 °C, a completely different colony pattern was observed; it was cottony, greyish then dark grey, and produced abundant hyaline conidia borne on grey, branching tree-like conidiophores. Conidia were one-celled and egg-shaped, and their dimensions fell in the range of 9.89–14.63 (11.48±0.31) µm×7.05–10.05 (8.31±0.20) µm. These features concurred with those characterising the polyphagous grey mould fungus Botryotinia fuckeliana (anamorph: Botrytis cinerea) (Elad et al., 2007). The ITS1/ITS2 including the 5.8S subunit of rDNA of one of the isolates were amplified with primers ITS1-F/ITS4, then the PCR products were sequenced. The ITS sequence determined in this way was identical to known sequences of B. fuckeliana strains, e.g. that of CBS 131.28 (GenBank accession number: KF859918), the type material of Botrytis cinerea f. lini, DAOM 231372 (GenBank accession number: KF859924) and so on. Pathogenicity tests resulted in rapidly (within 2 weeks) developing disease symptoms around the site of wound inoculation with a 5-mm-diametre mycelial agar plug: fruit rot on apple and lemon in the laboratory, and sunken lesions on stems of hydrocultured ornamental plants such as the herbaceous Monstera deliciosa and the woody Dracena marginata. To fulfill Koch’s postulates, the fungus was re-isolated from symptomatic apple fruit, and was found to exhibit the afore-mentioned morpho-physiological characteristics. Inoculation test on Bucida was not performed because of the costly risk i.e., the sale price of the trees is € 3 to 10 thousand. Consequently, the actual sensitivity of Bucida to grey mould remains uncertain, so much the more because this plant species has not been recorded as a host of the pathogen or other important parasitic fungi in natural (subtropical) environment (e.g. Whelburg et al., 1975). To our knowledge, this report is the first description of Botryotinia fuckeliana on Bucida buceras. In addition to the fact that periodic emergence of fungal mycelia on the trunk impairs the tree’s aesthetic appearance, the sclerotia resting in the potting mix may cause more serious problems in the long term. However, it cannot be precluded that the elevated indoor temperature reduces disease progression and thus the economic importance of the pathogen on this plant

Possible observation of phase coexistence of the ν=1/3\nu=1/3 fractional quantum Hall liquid and a solid

We have measured the magnetoresistance of a very low density and an extremely high quality two-dimensional hole system. With increasing magnetic field applied perpendicularly to the sample we observe the sequence of insulating, $\nu=1/3$ fractional quantum Hall liquid, and insulating phases. In both of the insulating phases in the vicinity of the $\nu=1/3$ filling the magnetoresistance has an unexpected oscillatory behavior with the magnetic field. These oscillations are not of the Shubnikov-de Haas type and cannot be explained by spin effects. They are most likely the consequence of the formation of a new electronic phase which is intermediate between the correlated Hall liquid and a disorder pinned solid.Comment: 5 pages, 4 figure

Ground state of a partially melted Wigner molecule

We consider three spinless fermions free to move on 2d square lattice with periodic boundary conditions and interacting via a U/r Coulomb repulsion. When the Coulomb energy to kinetic energy ratio r_s is large, a rigid Wigner molecule is formed. As r_s decreases, we show that melting proceeds via an intermediate regime where a floppy two particle molecule coexists with a partially delocalized particle. A simple ansatz is given to describe the ground state of this mesoscopic solid-liquid regime.Comment: to appear in Europhysics Letter

Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents

For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one gets identical results when the inter-electron spacing to the Bohr radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three criteria giving similar r_s^* are proposed and checked using square lattices.Comment: 7 pages, 5 postscript figure

Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder

Using the persistent current I induced by an Aharonov-Bohm flux in square lattices with random potentials, we study the interplay between electronic correlations and disorder upon the ground state (GS) of a few polarized electrons (spinless fermions) with Coulomb repulsion. K being the total momentum, we show that I is proportional to K in the continuum limit. We use this relation to distinguish between the continuum regimes, where the lattice GS behaves as in the continuum limit and I is independent of the interaction strength U when K is conserved, and the lattice regimes where I decays as U increases. Changing the disorder strength W and U, we obtain many regimes which we study using the map of local currents carried by three spinless fermions

Disappearing scales in carps: Re-visiting Kirpichnikov's model on the genetics of scale pattern formation

The body of most fishes is fully covered by scales that typically form tight, partially overlapping rows. While some of the genes controlling the formation and growth of fish scales have been studied, very little is known about the genetic mechanisms regulating scale pattern formation. Although the existence of two genes with two pairs of alleles (S&s and N&n) regulating scale coverage in cyprinids has been predicted by Kirpichnikov and colleagues nearly eighty years ago, their identity was unknown until recently. In 2009, the ‘S’ gene was found to be a paralog of fibroblast growth factor receptor 1, fgfr1a1, while the second gene called ‘N’ has not yet been identified. We re-visited the original model of Kirpichnikov that proposed four major scale pattern types and observed a high degree of variation within the so-called scattered phenotype due to which this group was divided into two sub-types: classical mirror and irregular. We also analyzed the survival rates of offspring groups and found a distinct difference between Asian and European crosses. Whereas nude × nude crosses involving at least one parent of Asian origin or hybrid with Asian parent(s) showed the 25% early lethality predicted by Kirpichnikov (due to the lethality of the NN genotype), those with two Hungarian nude parents did not. We further extended Kirpichnikov's work by correlating changes in phenotype (scale-pattern) to the deformations of fins and losses of pharyngeal teeth. We observed phenotypic changes which were not restricted to nudes, as described by Kirpichnikov, but were also present in mirrors (and presumably in linears as well; not analyzed in detail here). We propose that the gradation of phenotypes observed within the scattered group is caused by a gradually decreasing level of signaling (a dose-dependent effect) probably due to a concerted action of multiple pathways involved in scale formation

PtOx-SnOx-TiO2 catalyst system for methanol photocatalytic reforming: Influence of cocatalysts on the hydrogen production

Effects of modification of PtOx-TiO2 photocatalysts by tin were elucidated by exploring relationships between the structural properties of variously prepared tin-loaded catalysts and their catalytic activity in methanol photocatalytic reforming. Tin free and amorphous tin-oxide decorated TiO2 samples were prepared by sol-gel method from titanium-isopropoxide. In other approach, Sn was loaded onto the sol-gel prepared TiO2 by impregnation followed by calcination. Pt was introduced by impregnation followed by either reduction in H2 at 400 °C or calcination at 300 °C. TEM, XRD and Raman spectroscopic measurements proved that TiO2 existed in the form of aggregates of polycrystalline anatase with primary particle size of 15–20 nm in all samples. Photocatalytic hydrogen production was influenced by the combined effect of many parameters. Both the presence of Sn and the way of Pt co-catalyst formation played important role in the activity of these photocatalysts. The Sn introduction by both sol-gel method and impregnation clearly enhanced the photocatalytic activity. 1H MAS NMR measurements revealed that the Sn introduction reduced the amount of the terminal Ti-OH groups of relatively basic character considered to be unfavorable for the photocatalytic reaction. Presence of SnOx decreased the signal of the undesirable vacancies observed by ESR. Furthermore surface SnOx enhanced the dispersion of Pt. Formation of the Pt co-catalyst by calcination was more favorable than by H2 treatment. In case of the calcined samples in situ reduction of the Pt nanoparticles at the beginning of the photocatalytic reaction was found to be favorable for the hydrogen production. The relatively modest photocatalytical activity obtained after high temperature H2 treatment could be related to at least two processes in this system: (i) creation of unfavorable oxygen vacancies and (ii) segregation of SnOx to the surface of the Pt cocatalyst as the result of the air exposure of the alloy type Pt-Sn nanoparticles formed during the H2 treatment, resulting in a decreased number of active sites for reduction of H+