A new theorem is applied to the Kuramoto-Sivashinsky equation with L-periodic boundary conditions, proving the existence of an asymptotically complete inertial manifold attracting all initial data. Combining this result with a new estimate of the size of the globally absorbing set yields an improved estimate of the dimension, N ∼ L.

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

We study a linear fractional differential equation with a periodic boundary condition and give the explicit form of the solution and the corresponding Green’s function. Using some properties of the Green’s function we present some new comparison results.

The nonlinear eigenvalue problem of the differential equation ( |x′|p−2 x′ )′ + (λ+ c(t)) |x|p−2 x = 0, p > 1, with respect to the periodic boundary conditions: x(0) = x(T ), x′(0) = x′(T ), or to the antiperiodic boundary conditions: x(0) = −x(T ), x′(0) = −x′(T ) are considered. Various results on the set of eigenvalues concerning both problems are presented. Some estimates are given for the ...

We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of Þxed or free boundary curves in R, S and H. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem fo...

Under two boundary conditions: the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary.

We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary in...

This paper discusses about the detection of clause boundaries using a hybrid approach. The Conditional Random fields (CRFs), which have linguistic rules as features, identifies the boundaries initially. The boundary marked is checked for false boundary marking using Error Pattern Analyser. The false boundary markings are re-analysed using linguistic rules. The experiments done with our approach...

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Hölder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetr...