Universal rates for reactive ultracold polar molecules in reduced dimensions

Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.Comment: 4 pages, 3 figure

Schr\"{o}dinger operator with a complex steplike potential

The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this operator is trivial if and only if the imaginary part of the potential is constant. As a by-product, a new method to obtain a sharp resolvent estimate is developed, answering a concern of Henry and Krej\v{c}i\v{r}\'{i}k, and a way to construct an optimal pseudomode is discovered, answering a concern of Krej\v{c}i\v{r}\'{i}k and Siegl. The spectrum and the norm of the resolvent of the complex point interaction of the operator is also studied carefully in this article.Comment: 43 pages, 6 figure

The multicolored Asian lady beetle : Harmonia axyridis (Pallas, 1773) (Coleoptera: Coccinellidae) ; a not so new invasive insect in Colombia and South America

The first reports of the multicolored Asian lady beetle Harmonia axyridis (Pallas, 1773) (Coleoptera: Coccinellidae) in Colombia appeared in 2011. However, based on museum insect specimens, the introduction of H. axyridis in Colombia occurred in 1989 or earlier, making it the second oldest record of the species in South America after the deliberate releases of the species in Argentina in 1986. Currently in Colombia, H. axyridis is well established and is here recorded from the States of Antioquia, Caldas, Cauca, Cundinamarca, Nariño, Tolima and Valle del Cauca.Los primeros reportes de la mariquita multicolor asiática Harmonia axyridis (Pallas, 1773) (Coleoptera: Coccinellidae) aparecieron en el 2011. Sin embargo, con base en colecciones de insectos en museos, la introducción de H. axyridis en Colombia ocurrió en 1989 o antes, haciendo que este sea el segundo registro más antiguo de esta especie en Sur América, después de las liberaciones intencionales de la especie en Argentina en 1986. Actualmente en Colombia, H. axyridis está bien establecida y aquí se reporta en los departamentos de Antioquia, Caldas, Cauca, Cundinamarca, Nariño, Tolima y el Valle del Cauca

Some analytical properties of the multidimensional continuous Mróz model of plasticity

We study the geometrical structure of memory induced by the continuous multidimensional Mr'oz model of plasticity. The results are used for proving the thermodynamic consistency of the model and composition and inversion formulas for input - memory state - output operators. We also show an example of nonuniqueness of solutions to a simple initial value problem involving the Mr'oz operator

Terguride stimulates locomotor activity at 2 months but not 10 months after 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine treatment of common marmosets

The mixed dopamine (DA) agonist/antagonist terguride acts as a DA antagonist on normosensitive receptors but shows DA agonistic properties at supersensitive DA receptors. Such a compound could offer an alternative to the treatment of Parkinson's disease with indirect or direct DA agonists. The present study compares the actions of terguride, 4-12 mg/kg i.p., in naive common marmosets with its effects in animals rendered parkinsonian by administration of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), 2 months or 10 months previously, in order to test its antiparkinsonian efficacy. Terguride reduced locomotor activity in naive common marmosets, similar to its effects in rodents and in line with the DA antagonistic activity of the compound. In marmosets treated with MPTP 2 months previously and exhibiting pronounced behavioural motor deficits, terguride stimulated locomotor activity, showing DA agonistic properties under these conditions. In contrast, the locomotor activity of animals that had recovered from MPTP treatment 10 months previously was not altered by terguride. It is concluded that terguride has anti-akinetic efficacy in this primate model of Parkinson's disease. In addition, terguride offers a unique opportunity to differentiate, pharmacologically, the extent of dopaminergic recovery from MPTP treatment in this primate species

Infinite networks and variation of conductance functions in discrete Laplacians

For a given infinite connected graph $G=(V,E)$ and an arbitrary but fixed conductance function $c$, we study an associated graph Laplacian $\Delta_{c}$; it is a generalized difference operator where the differences are measured across the edges $E$ in $G$; and the conductance function $c$ represents the corresponding coefficients. The graph Laplacian (a key tool in the study of infinite networks) acts in an energy Hilbert space $\mathscr{H}_{E}$ computed from $c$. Using a certain Parseval frame, we study the spectral theoretic properties of graph Laplacians. In fact, for fixed $c$, there are two versions of the graph Laplacian, one defined naturally in the $l^{2}$ space of $V$, and the other in $\mathscr{H}_{E}$. The first is automatically selfadjoint, but the second involves a Krein extension. We prove that, as sets, the two spectra are the same, aside from the point 0. The point zero may be in the spectrum of the second, but not the first. We further study the fine structure of the respective spectra as the conductance function varies; showing now how the spectrum changes subject to variations in the function $c$.Comment: 32 pages, 3 figure