Search results for "Asymptotic"
showing 10 items of 230 documents
Inflection points and topology of surfaces in 4-space
2000
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
ASYMPTOTIC CURVES ON SURFACES IN ℝ5
2008
We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.
MUSIC-characterization of small scatterers for normal measurement data
2009
We investigate the reconstruction of the positions of a collection of small metallic objects buried beneath the ground from measurements of the vertical component of scattered fields corresponding to vertically polarized dipole excitations on a horizontal two-dimensional measurement device above the surface of the ground. A MUSIC reconstruction method for this problem has recently been proposed by Iakovleva et al (2007 IEEE Trans. Antennas Propag. 55 2598). In this paper, we give a rigorous theoretical justification of this method. To that end we prove a characterization of the positions of the scatterers in terms of the measurement data, applying an asymptotic analysis of the scattered fie…
Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases
2022
We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.
Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations
2008
In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of…
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
2015
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.
Air Traffic, Boarding and Scaling Exponents
2014
The air traffic is a very important part of the global transportation network. In distinction from vehicular traffic, the boarding of an airplane is a significant part of the whole transportation process. Here we study an airplane boarding model, introduced in 2012 by Frette and Hemmer, with the aim to determine precisely the asymptotic power–law scaling behavior of the mean boarding time 〈t b 〉 and other related quantities for large number of passengers N. Our analysis is based on an exact enumeration for small system sizes N ≤ 14 and Monte Carlo simulation data for very large system sizes up to \(N = 2^{16} = 65,536\). It shows that the asymptotic power–law scaling 〈t b 〉 ∝ N α holds with…
The warping torsion as a sequence of infinite bending problems
2014
[EN] In the present article, a methodology for teaching modeling problem of mixed torsion for thin-walled open sections. The mathematical analogy of warped twist as a problem of Euler-Bernoulli beams is exploited. In fact, the paper proposes to represent the warped torsion differential equation as a perturbation of the pure torsion or also called the Saint-Venant theory. Thus, it is demonstrated that under certain conditions related to the value of the torsional slenderness the response of a beam is the addition of infinite pure warped problems, that is, infinite bending problems, according to the analogy. We call this the asymptotic torsion analogy.
ÉQUATIONS DIFFÉRENTIELLES À COEFFICIENTS DANS DES CORPS DE SÉRIES GÉNÉRALISÉES.
2007
We express the connection between the support of some equations and those of generalized series solutions. On the one hand we prove that any real power series solution of a sub-analytic differential equation belong to a lattice (i.e. an additive sub semi-group of positive reals). On the other hand we consider the field Mr of series with well-ordered support included in the Hahn product Hr with finite rank r (i.e. the lexicographic product of r copies of the reals). We equip Mr with a "Hardy type" derivation and define some well-ordered sets T1, ..., Tr such that : for all equation F(y,...,y(n))=0 with F in Mr[[Y0,...,Yn]] and whose support Supp F is a well-ordered subset of Hr, and for all …
Unfolding of saddle-nodes and their Dulac time
2016
Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a b…