Search results for "second order"
showing 10 items of 33 documents
Branches of index-preserving solutions to systems of second order ODEs
2009
We investigate the existence of a continuum of index-preserving solutions to a Dirichlet problem associated with a parameter-dependent system of second order ordinary differential equations, developing a detailed analysis on the behaviour of the branches of nontrivial solutions. Our approach is based on the Rabinowitz global bifurcation Theorem combined with the notion of index and nullity of suitable linear boundary value problems. An application of the result to the study of branches of odd, periodic solutions for suitable systems of two linearly coupled pendulums of lenghts variables is also analyzed.
Some properties of local weighted second-order statistics for spatio-temporal point processes
2019
Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the…
Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2
2009
AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.
Spatio-temporal log-Gaussian Cox processes on eartquake events
2017
In this paper we aim at studying some extensions of complex space-time models, useful for the description of earthquake data. In particular we want to focus on the Log-Gaussian Cox Process (LGCP) model estimation approach, with some results on global informal diagnostics. Indeed, in our opinion the use of Cox processes that are natural models for point process phenomena that are environmentally driven could be a new approach for the description of seismic events. These models can be useful in estimating the intensity surface of a spatio-temporal point process, in constructing spatially continuous maps of earthquake risk from spatially discrete data, and in real-time seismic activity surveil…
Lyapunov Functions for Second-Order Differential Inclusions: A Viability Approach
2001
AbstractIn this paper the existence of Lyapunov functions for second-order differential inclusions is analyzed by using the methodology of the Viability Theory. A necessary assumption on the initial states and sufficient conditions for the existence of local and global Lyapunov functions are obtained. An application is also provided.
Donor and acceptor substituted triphenylamines exhibiting bipolar charge-transporting and NLO properties
2017
Donor-acceptor type triphenylamine-based malonodinitriles were synthesized and their thermal, optical, photophysical, electrochemical and nonlinear optical properties were studied. The synthesized compounds formed glasses with the glass transition temperatures ranging from 38 to 107 °C. The ionization potentials of the samples of the compounds established by cyclic voltammetry were found to be in the range of 5.50–5.57 eV, while those estimated by photoelectron emission spectrometry ranged from 5.36 to 5.74 eV. The electron affinity values of the compounds were found to be in the range of −3.41–−3.05 eV. The ambipolar charge-transporting properties were observed for the layers of triphenyla…
Infinitely many periodic solutions for a second-order nonautonomous system
2003
The existence of infinitely many solutions for a second-order nonautonoumous system was investigated. Some multiplicity results for problem (P) under very different assumptions on the potential G were established. It was shown that infinitely many solutions follow from a variational principle by B. Ricceri.
Numerical simulation of Kerr nonlinear systems : analyzing non-classical dynamics
2019
Abstract We simulate coherent driven free dissipative Kerr nonlinear system numerically using Euler’s method by solving Heisenberg equation of motion and time evolving block decimation (TEBD) algorithm, and demonstrate how the numerical results are analogous to classical bistability. The comparison with analytics show that the TEBD numerics follow the quantum mechanical exact solution obtained by mapping the equation of motion of the density matrix of the system to a Fokker-Plank equation . Comparing between two different numerical techniques, we see that the semi-classical Euler’s method gives the dynamics of the system field of one among two coherent branches, whereas TEBD numerics genera…
AC Stark shift of the ground state of atomic hydrogen
2004
An analytical expression for the second-order AC Stark shift of the ground state of atomic hydrogen is derived, which is convergent for negative as well as for positive energies of intermediate states except for the resonances. To clarify the applicability of the second-order perturbation theory, we compared results with those which are obtained by us and other authors using nonperturbative methods. It appears that values obtained for the AC Stark shift using our simple formula agree on average with Floquet-method calculations up to the field strength F=0.12 (a.u.), which corresponds to I=1015 W/cm2.
Elementary hypergeometric functions, Heun functions, and moments of MKZ operators
2019
We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.