Search results for " Order"

Periodic solutions for a class of second-order Hamiltonian systems

2005

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.© 2005 Texas State University - San Marcos.

Indefinite integrals from Wronskians and related linear second-order differential equations

2021

Many indefinite integrals are derived for Bessel functions and associated Legendre functions from particular transformations of their differential equations which are closely linked to Wronskians. A large portion of the results for Bessel functions is known, but all the results for associated Legendre functions appear to be new. The method can be applied to many other special functions. All results have been checked by differentiation using Mathematica.

On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels

2014

Moment Generating Functions and Central Moments

2018

This section deals with the moment generating functions (m.g.f.) up to sixth order of some discretely defined operators. We mention the m.g.f. and express them in expanded form to obtain moments, which are important in the theory of approximation relevant to problems of convergence.

A sequence of positive solutions for sixth-order ordinary nonlinear differential problems

2021

Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.

A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates

2019

Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…

Words and Patterns

2002

In this paper some new ideas, problems and results on patterns are proposed. In particular, motivated by questions concerning avoidability, we first study the set of binary patterns that can occur in one infinite binary word, comparing it with the set of factors of the word. This suggests a classification of infinite words in terms of the "difference" between the set of its patterns and the set of its factors. The fact that each factor in an infinite word can give rise to several distinct patterns leads to study the set of patterns of a single finite word. This set, endowed with a natural order relation, defines a poset: we investigate the relationships between the structure of such a poset…

Existence of a traveling wave solution in a free interface problem with fractional order kinetics

2021

Abstract In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 α 1 . We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincare-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is fin…

Angular harmonic dependence from a 3D-H2+ Molecular Ion

2012

The time-dependent Schroedinger equation of a H2+ molecular ion in the presence of a linearly polarized laser field is numerically solved by means of a split-operator parallel code. The electron, driven by the laser electric field, emits electromagnetic radiation whose HHG spectrum (shown in Figure 1) can be finely controlled by changing the angle between the laser electric field and the molecular axis. The numerical results confirm that the structure of the spectra strongly depends on this angle. In particular the correlation between the laser orientation (with respect to the molecular axis) and the intensity of various harmonic peaks are displayed in Figure 2.

Laser induced ultrafast H2+ dinamic and attosecond generation

2012

We examine the possibility that a H2+ molecular ion driven by a linearly polarized laser field can be considered as a source of attosecond pulses. The emisseion is investigated taking into account the role of the internuclear distance and by changing the angle between the laser field and the molecular axis. We find that the attosecond pulses emission happens when the electron cloud is over one nucleus; on the contrary, when the elctron is travelling between the two nuclei the attosecond emission do not take place.