1,135 research outputs found
A Note on Computations of D-brane Superpotential
We develop some computational methods for the integrals over the 3-chains on
the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of
the topological B-model in the context of the open mirror symmetry. We discuss
such 3-chain integrals in two approaches. In the first approach, we provide a
systematic algorithm to obtain the inhomogeneous Picard-Fuchs equations. In the
second approach, we discuss the analytic continuation of the period integral to
compute the 3-chain integral directly. The latter direct integration method is
applicable for both on-shell and off-shell formalisms.Comment: 61 pages, 5 figures; v2: typos corrected, minor changes, references
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Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
In this paper, we generalize Walcher's computation of the open Gromov-Witten
invariants of the quintic hypersurface to Fano and Calabi-Yau projective
hypersurfaces. Our main tool is the open virtual structure constants. We also
propose the generalized mirror transformation for the open Gromov-Witten
invariants, some parts of which are proven explicitly. We also discuss possible
modification of the multiple covering formula for the case of higher
dimensional Calabi-Yau manifolds. The generalized disk invariants for some
Calabi-Yau and Fano manifolds are shown and they are certainly integers after
re-summation by the modified multiple covering formula. This paper also
contains the direct integration method of the period integrals for higher
dimensional Calabi-Yau hypersurfaces in the appendix.Comment: 24pages, 5figure
Accelerating the calibration of stochastic volatility models
This paper compares the performance of three methods for pricing vanilla options in models with known characteristic function: (1) Direct integration, (2) Fast Fourier Transform (FFT), (3) Fractional FFT. The most important application of this comparison is the choice of the fastest method for the calibration of stochastic volatility models, e.g. Heston, Bates, Barndor®-Nielsen-Shephard models or Levy models with stochastic time. We show that using additional cache technique makes the calibration with the direct integration method at least seven times faster than the calibration with the fractional FFT method.Stochastic Volatility Models; Calibration; Numerical Integration; Fast Fourier Transform
Accelerating the calibration of stochastic volatility models
This paper compares the performance of three methods for pricing vanilla options in models with known characteristic function: (1) Direct integration, (2) Fast Fourier Transform (FFT), (3) Fractional FFT. The most important application of this comparison is the choice of the fastest method for the calibration of stochastic volatility models, e.g. Heston, Bates, Barndorff-Nielsen-Shephard models or Levy models with stochastic time. We show that using additional cache technique makes the calibration with the direct integration method at least seven times faster than the calibration with the fractional FFT method. --Stochastic Volatility Models,Calibration,Numerical Integration,Fast Fourier Transform
Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
We investigate the open mirror symmetry of certain non-complete intersection
Calabi- Yau 3-folds, so called pfaffian Calabi-Yau. We perform the prediction
of the number of disk invariants of several examples by using the direct
integration method proposed recently and the open mirror symmetry. We treat
several pfaffian Calabi-Yau 3-folds in and branes with two
discrete vacua. Some models have the two special points in its moduli space,
around both of which we can consider different A-model mirror partners. We
compute disc invariants for both cases. This study is the first application of
the open mirror symmetry to the compact non-complete intersections in toric
variety.Comment: 64 pages; v2: typos corrected, minor changes, references added; v3:
published version, minor corrections and improvement
Computing eigenvalues of periodic Sturm-Liouville problems using shooting technique and direct integration method
This paper deals with computing eigenvalues of periodic Sturm-Liouville (SL) problem by direct integration (DI) method using shooting technique without reducing to the system of first order ODEs. Floquet theory is applied to find a non-trivial solution of SL problems and the eigenvalues are approximated by the application of shooting techniques. Computational advantages are presented comparing the results obtained by the DI method with that of reducing to the system of first order ODEs
Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models
Gravitational lensing of distant objects caused by gravitational tidal forces
from inhomogeneities in the universe is weak in most cases, but it is noticed
that it gives a great deal of information about the universe, especially
regarding the distribution of dark matter. The statistical values of optical
quantities such as convergence, amplification and shear have been derived by
many people using various approaches, which include the linear perturbational
treatment in the weak limit and the nonlinear treatment considering small-scale
matter distribution.
In this review paper we compare the following three main approaches: (a) the
approach in the multi-lens-plane theory; (b) the approach due to the direct
integration method; and (c) the perturbational approach.
In the former two approaches inhomogeneous matter distributions are produced
in the CDM model using -body simulations (the PM code and the tree-code,
respectively). In (c) the power spectrum corresponding to the CDM model is used
for the large-scale matter distribution.Comment: 30 pages, 13 figure
Application of the direct integration method to analysis of elasticity and thermoelasticity problems for inhomogeneous solids
The application of the direct integration method for finding the solutions of 2D elasticity and thermoelasticity problems for the radially inhomogeneous ring and for the strip inhomogeneous with respect to width is presented. The main feature of this approach is the integration of the equilibrium equations, which do not depend on material properties. This gives the possibility to express all the stresses in terms of a governing one, as well as to deduce the integral equilibrium conditions for all of the stress tensor components. In such way, the original problem can be reduced to finding the governing stress from compatibility equation. The governing equation is reduced to the Volterra type integral equation and it can be solved by simple iterations
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