Search results for "Applied Mathematic"
showing 10 items of 4398 documents
Humbert surfaces and the Kummer plane
2003
A Humbert surface is a hypersurface of the moduli space A 2 \mathcal A_2 of principally polarized abelian surfaces defined by an equation of the form a z 1 + b z 2 + c z 3 + d ( z 2 2 − z 1 z 3 ) + e = 0 az_1+bz_2+cz_3+d(z_2^2-z_1z_3)+e=0 with integers a , … , e a,\ldots ,e . We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…
On the Neron-Severi group of surfaces with many lines
2008
For a binary quartic form $\phi$ without multiple factors, we classify the quartic K3 surfaces $\phi(x,y)=\phi(z,t)$ whose Neron-Severi group is (rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of prime degree without multiple factors, we prove that the Neron-Severi group of the surface $\phi(x,y)=\psi(z,t)$ is rationally generated by lines.
Seifert manifolds admitting partially hyperbolic diffeomorphisms
2017
We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.
Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate …
2004
We study an analytic Hamiltonian system with two degrees of freedom, having the origin as an elliptic singularity. We assume that the full Birkhoff normal form exists and is divisible by its quadratic part, being indefinite. We show that under the Bruno condition and under the restriction to the zero energy surface, a real analytic transformation into a normal form exists. Such a normal form coincides with the restriction of the Birkhoff normal form to the zero energy surface up to an order as large as we want.
Improving surface detection on nanoindentation of compliant materials
2010
Nanoindentation is a versatile tool for monitoring mechanical properties on a local scale. Accurate knowledge of a contact area, and therefore an initial contact, is however necessary for translating the force curve into sample mechanical properties. It is shown that methods for sensing an initial contact by depth sensing instruments (DSI) may be severely in error for compliant materials. With the hardware adopted in this work, the threshold is determined by the elastic modulus; hence the error potentially increases if the material becomes more compliant. A simple method is therefore suggested to determine with accuracy the initial contact on compliant materials whereby the surface contact …
2021
Abstract We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY ). We say that a metric space (Y, dY ) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY ) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY ) that is quasiconformal in the geometric sense. We show that ϕ has a continuous, monotone, and surjective extension Φ: 𝔻 ̄ → Y ̄. This result is best possible in this generality. In addition, we find a necessary and sufficient condition for Φ to be a quasiconformal homeomorphism. We provide sufficient conditions for the restriction of Φ to 𝕊1 being a quasi…
Closed Form Approximation of Swap Exposures
2013
This paper provides closed form lower and upper bounds for the price of European swaption on cross currency basis swap with the presence of dynamic basis spreads. Cross currency basis spreads are treated as integrals of spot spreads, approach familiar from interest rate models. The spot spread is modelled by two-factor mean reverting Gaussian model that is equivalent to two-factor Hull-White model introduced by [Hull and White(1994)]. This model allows closed form approximations and relatively well fitting and simple calibration to the spread term structure.
Non-volatile memory characteristics of a Ti/HfO2/Pt synaptic device with a crossbar array structure
2022
The resistive switching and synaptic behavior of a fabricated Ti/HfO2/Pt crossbar array device are investigated. The results demonstrated that TiOx layers are created by the movement of oxygen ions during the positive SET process, thereby improving the endurance and multilevel switching behavior of the device. The random properties of SET process were described with the help of stochastic model of memristor based on the length of conductive filament. The analysis of the mean first passage time allows estimating the parameters of the dielectric switching layer such as the activation energy of the diffusive defects, its variation under the influence of the driving voltage and the value of the…
The Regularity of Rhythmic Primes Influences Syntax Processing in Adults
2019
Recent research has shown that auditory rhythmic stimulation improves subsequent syntax processing of speech in children with and without developmental language disorders. Sensitivity to grammatica...