Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Va...

A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth order Runge–Kutta method, instead of the finite difference method, the resulting system of ordinary...

a r t i c l e i n f o a b s t r a c t In this paper we use a numerical relaxation algorithm to improve and generalize the obtainment of the perturbation eigenstates of nonlinear systems. As a model problem we consider the linear stability analysis of the vortex eigenstates of the cubic–quintic nonlinear Schrödinger equation. It is shown by numerical calculations that the relaxation algorithm pe...

The left hand side (or A–side) of this identity was a generating series for the numbers n(d) of rational curves of various degrees d lying on a smooth quintic hypersurface in P. The right hand side (B–side) was a certain hypergeometric function. The Mirror Identity states that the two functions become identical after an explicit change of variables which is defined as a quotient of two hypergeo...

The problem of interpolating scattered 3D data by a geometrically smooth surface is considered. A completely local method is proposed, based on employing degenerate triangular Bernstein{B ezier patches. An analysis of these patches is given and some numerical experiments with quartic and quintic patches are presented. Supported by the Netherlands Foundation of Mathematics (SMC) and the Netherla...

In this paper, numerical solutions of the nonlinear Burgers_ equation are obtained by a method based on collocation of quintic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by one test problem. The numerical results are found to be in good agreement with...

In contrast to an infinite degree of nonlocality, we demonstrate that vortex solitons in nonlinear media under competing self-focusing cubic and self-defocusing quintic nonlocal nonlinearities can be stabilized with a finite degree of nonlocality. Stable vortex solitons in the upper branch, bifurcated from the competing cubic-quintic nonlinearities, are found to be supported when the original d...

The appropriateness of various numerical procedures for obtaining valid time-derivative data recently reported in the literature (Zernicke et a/., 1976: McLaughlin er al., 1977; Pezzack et u/., 1977) is discussed. A case for the use of quintic natural splines is presented. based on the smoothness of higher derivatives and flexibility in application. \‘ES; /\ . _J”P JGTc, SE=5 :;yz,s’sy = z7 ___...

The quintic B-spline collocation method is developed to solve the fourth-order parabolic partial differential equation. This kind of problem arises in the field of transverse vibration of the uniform flexible beam. Stability analysis of the method has also been proven. Two examples have been considered to illustrate the efficiency of the method developed. It has been observed that the numerical...