Search results for "Arity"
showing 10 items of 2893 documents
p −1-Linear Maps in Algebra and Geometry
2012
At least since Habousch’s proof of Kempf’s vanishing theorem, Frobenius splitting techniques have played a crucial role in geometric representation theory and algebraic geometry over a field of positive characteristic. In this article we survey some recent developments which grew out of the confluence of Frobenius splitting techniques and tight closure theory and which provide a framework for higher dimension geometry in positive characteristic. We focus on local properties, i.e. singularities, test ideals, and local cohomology on the one hand and global geometric applicatioms to vanishing theorems and lifting of sections on the other.
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Polarity conversion of GaN nanowires grown by plasma-assisted molecular beam epitaxy
2019
International audience; It is demonstrated that the N-polarity of GaN nanowires (NWs) spontaneously nucleated on Si (111) by molecular beam epitaxy can be reversed by intercalation of an Al-or Ga-oxynitride thin layer. The polarity change has been assessed by a combination of chemical etching, Kelvin probe force microscopy, cathodo-and photoluminescence spectroscopy and transmission electron microscopy experiments. Cathodoluminescence of the Ga-polar NW section exhibits a higher intensity in the band edge region, consistent with a reduced incorporation of chemical impurities. The polarity reversal method we propose opens the path to the integration of optimized metal-polar NW devices on any…
Investigation on partial discharges in HVDC cables after polarity reversal events
2020
Due to the accumulation of space charge inside the insulating layer of HVDC cables, the electric field under load conditions may be altered compared to what is established in HVAC cables. For example, a high thermal gradient leads to the inversion of the electric field pattern until the maximum value is reached in proximity of the dielectric-semicon interfaces. These maximum values can be further increased due to transient overvoltages and polarity reversal events until reaching electric field values higher than the rated ones. The main goal of this research is to investigate the possibility that, during these transient phenomena, conditions are created that favor the occurrence of partial …
Effect of Polarity Reversal on the Partial Discharge Phenomena
2020
In the field of High Voltage Direct Current (HVDC) transmission, the space charge accumulation phenomenon and the Partial Discharges (PD) phenomena are considered the main causes of dielectric ageing. During the years, the degradation effect of both phenomena under constant DC stress has been widely studied by several researchers. In case of polarity reversal, typically carried out to control bi-directional power flow between interconnected High Voltage transmission systems, the space charge movement may not synchronously follow the electric field polarity. This could make the moment of reversing polarity a very critical one, where space charge injected during preceding polarity produces hi…
Polarity reversal in HVDC joints - The effect of the axial thermal conduction
2020
It has been shown that the establishment of a thermal gradient over the radius of HVDC cables involves the accumulation of space charge within the dielectric layer. High thermal gradients over the insulation thickness of loaded cables can lead to the inversion of the radial electric field pattern. In this scenarios, transient overvoltages and polarity reversal can lead to local and transitory peaks of electric field. Since the temperature distribution plays an important role in reaching critical values of the electric field, it has been considered interesting to have a more in-depth view of the thermal behavior of HVDC systems close the discontinuities of the geometry along the cable axis. …
Enhanced alignment and orientation of polar molecules by vibrational resonant adiabatic passage
2007
The authors show that polar molecules can be adiabatically aligned and oriented by laser pulses more efficiently when the laser frequencies are vibrationally resonant. The aligned molecules are found in a superposition of vibrational pendular states, each associated with the alignment of the rotor in one vibrational state. The authors construct the dressed potential associated with this mechanism. Values of detunings and field amplitudes are given to optimize the degree of alignment and orientation for the CO molecule.
A Rotational Thermalization Model for the Calculation of Collisionally Narrowed Isotropic Raman-Scattering Spectra - Application to the Srs-N2 Q-Bran…
1986
Abstract A model for the calculation of collisionally narrowed isotropic. Raman scattering spectra is proposed. In this model, the rotational transition probabilities are calculated within the strong collision approximation, allowing the rotational energy transfer rates to be expressed in terms of the sole individual Q( J ) line broadening coefficients. These transfer rates satisfy both detailed balance principle and unitarity of the scattering matrix in contrast with most of the previous approaches. Under further approximation concerning the rotational distribution of the collisional frequency, simpler expressions for transfer rates are deduced, which do not satisfy necessarily both unitar…
Electrostatic complementarity in pseudoreceptor modeling based on drug molecule crystal structures: the case of loxistatin acid (E64c)
2015
After a long history of use as a prototype cysteine protease inhibitor, the crystal structure of loxistatin acid (E64c) is finally determined experimentally using intense synchrotron radiation, providing insight into how the inherent electronic nature of this protease inhibitor molecule determines its biochemical activity. Based on the striking similarity of its intermolecular interactions with those observed in a biological environment, the electrostatic potential of crystalline E64c is used to map the characteristics of a pseudo-enzyme pocket.