Analytic ranks of elliptic curves over number fields

Let $E$ be an elliptic curves over the rational numbers. Let $F$ be a cyclic extension of prime degree $l$. Then, we show that the average of analytic ranks of $E(F)$ over all cyclic extension of prime degree $l$ is at most $2+r_\mathbb{Q}(E)$, where $r_\mathbb{Q}(E)$ is the analytic rank of $E(\mathbb Q)$. This bound is independent of the degree of the cyclic extension. Also, we also obtain some average rank result over $S_d$-fields

Velocity statistics from spectral line data: effects of density-velocity correlations, magnetic field, and shear

In a previous work Lazarian and Pogosyan suggested a technique to extract velocity and density statistics, of interstellar turbulence, by means of analysing statistics of spectral line data cubes. In this paper we test that technique, by studying the effect of correlation between velocity and density fields, providing a systematic analysis of the uncertainties arising from the numerics, and exploring the effect of a linear shear. We make use of both compressible MHD simulations and synthetic data to emulate spectroscopic observations and test the technique. With the same synthetic spectroscopic data, we also studied anisotropies of the two point statistics and related those anisotropies with the magnetic field direction. This presents a new technique for magnetic field studies. The results show that the velocity and density spectral indices measured are consistent with the analytical predictions. We identified the dominant source of error with the limited number of data points along a given line of sight. We decrease this type of noise by increasing the number of points and by introducing Gaussian smoothing. We argue that in real observations the number of emitting elements is essentially infinite and that source of noise vanishes.Comment: 12 pages, 10 figures. Accepted for publication in MNRA

Schwinger Effect in Non-parallel D1-branes: A Path Integral Approach

We study the Schwinger effect in a system of non-parallel D1-branes for the bosonic strings using the path integral formalism. We drive the string pair creation rate by calculating the one loop vacuum amplitude of the setup in presence of the background electric filed defined along one of the D1-branes. We find an angle dependent minimum value for the background field and show that the decaying of vacuum into string pairs takes place for the field above this value. It is shown that in $\theta\rightarrow\frac{\pi}{2}$ limit the vacuum becomes stable and thus no pair creation occurs

Kinetically-controlled thin-film growth of layered β\beta- and γ−\gamma-Nax_{x}CoO2_{2} cobaltate

We report growth characteristics of epitaxial $\beta$-Na$_{0.6}$CoO$_{2}$ and $\gamma$-Na$_{0.7}$CoO$_{2}$ thin films on (001) sapphire substrates grown by pulsed-laser deposition. Reduction of deposition rate could change structure of Na$_{x}$CoO$_{2}$ thin film from $\beta$-phase with island growth mode to $\gamma$-phase with layer-by-layer growth mode. The $\gamma$-Na$_{0.7}$CoO$_{2}$ thin film exhibits spiral surface growth with multiterraced islands and highly crystallized texture compared to that of the $\beta$-Na$_{0.6}$CoO$_{2}$ thin film. This heterogeneous epitaxial film growth can give opportunity of strain effect of physical properties and growth dynamics of Na$_{x}$CoO$_{2}$ as well as subtle nature of structural change.Comment: accepted for publication in Applied Physics Letter

Requirement for Slit-1 and Robo-2 in zonal segregation of olfactory sensory neuron axons in the main olfactory bulb

The formation of precise stereotypic connections in sensory systems is critical for the ability to detect and process signals from the environment. In the olfactory system, olfactory sensory neurons (OSNs) project axons to spatially defined glomeruli within the olfactory bulb (OB). A spatial relationship exists between the location of OSNs within the olfactory epithelium (OE) and their glomerular targets along the dorsoventral axis in the OB. The molecular mechanisms underlying the zonal segregation of OSN axons along the dorsoventral axis of the OB are poorly understood. Using robo-2/ (roundabout) and slit-1/ mice, we examined the role of the Slit family of axon guidance cues in the targeting of OSN axons during development. We show that a subset of OSN axons that normally project to the dorsal region of the OB mistarget and form glomeruli in the ventral region in robo-2/ and slit-1/ mice. In addition, we show that the Slit receptor, Robo-2, is expressed in OSNs in a high dorsomedial to low ventrolateral gradient across the OE and that Slit-1 and Slit-3 are expressed in the ventral region of the OB. These results indicate that the dorsal-to-ventral segregation of OSN axons are not solely defined by the location of OSNs within the OE but also relies on axon guidance cues

Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \textit{Twist}

In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete covariantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the $D=10$ untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the $32$ supersymmetries unbroken.Comment: 1+58 pages, section 4 enhanced, refs added. To appear in JHE