Search results for "Mathematical analysis"

Evaluation of time domain electromagnetic fields radiated by constant velocity moving particles traveling along an arbitrarily shaped cross-section w…

2012

[1] A technique for the accurate computation of the time domain electromagnetic fields radiated by a charged distribution traveling along an arbitrarily shaped waveguide region is presented. Based on the transformation (by means of the standard Fourier analysis) of the time-varying current density of the analyzed problem to the frequency domain, the resulting equivalent current is further convolved with the dyadic electric and magnetic Green’s functions. Moreover, we show that only the evaluation of the transverse magnetic modes of the structure is required for the calculation of fields radiated by particles traveling in the axial direction. Finally, frequency domain electric and magnetic f…

Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method

1999

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.

A new mathematical function for describing electrophoretic peaks.

2005

A new model is proposed for characterizing skewed electrophoretic peaks, which is a combination of leading and trailing edge functions, empirically modified to get a rapid recovery of the baseline. The peak model is a sum of square roots and is called thereby "combined square roots (CSR) model". The flexibility of the model was checked on theoretical and experimental peaks with asymmetries in the range of 0-10 (expressed as the ratio of the distance between the center and the trailing edge, and the center and the leading edge of the chromatographic peak, measured at 10% of peak height). Excellent fits were found in all cases. The new model was compared with other three models that have show…

The periods of the generalized Jacobian of a complex elliptic curve

2015

Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.

Optimization of the domain in elliptic variational inequalities

1988

This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.

The Wiener test and potential estimates for quasilinear elliptic equations

1994

On ( p ( x ),  q ( x ))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

2021

In the present work, we consider a (p(x), q(x))-elliptic equation describing the behavior of a double-phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti-Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler-Lagrange functional …

Boundary accessibility and elliptic harmonic measures

1988

Suppose G is a bounded domain in R n such that the complement of G satisfies a capacity dcnsity condition. It is shown that all elliptic measures in G have a support set with Moreover, the capacity density condition cannot be removed. A nonlinear version of the result is also given.

High order normal form construction near the elliptic orbit of the Sitnikov problem

2011

We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.

Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)

2017

Let be a bounded smooth domain in RN. We prove a general existence result of least energy solutions and least energy nodal ones for the problem −u = f(x, u) in u = 0 on ∂ (P) where f is a Carathéodory function. Our result includes some previous results related to special cases of f . Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type f(x, u) = λ|u| s−2u − μ|u| r−2u, with s, r ∈ (1, 2) and λ,μ > 0.