In this paper, we develop third-order conservative sign-preserving and steady-state-preserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows. In this problem, the density and pressure are nonnegative, and the mass fraction for the ith species, denoted as zi, 1<=i<=M, should be between 0 and 1, where M is the total number of species. There are four main difficulties in constructing high-order bound-preserving techniques for multispecies and multireaction detonations. First of all, most of the bound-preserving techniques available are based on Euler forward time integration. Therefore, for problems with stiff source, the time step will be significantly limited. Secondly, the mass fraction does not satisfy a maximum-principle and hence it is not easy to preserve the upper bound 1. Thirdly, in most of the previous works for gaseous denotation, the algorithm relies on second-order Strang splitting methods where the ux and stiff source terms can be solved separately, and the extension to high-order time discretization seems to be complicated. Finally, most of the previous ODE solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time. In this paper, we will construct third-order conservative sign-preserving Rugne-Kutta and multistep methods to overcome all these difficulties. The time integrations do not depend on the Strang splitting, i.e. we do not split the flux and the stiff source terms. Moreover, the time discretization can handle the stiff source with large time step and preserves the steady-state. Numerical experiments will be given to demonstrate the good performance of the bound-preserving technique and the stability of the scheme for problems with stiff source terms.

Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel It diffusion process based on the approximate factor models and call it a factor GARCH-It model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-It model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed

Texture mapping and texture synthesis are two popular methods for the decoration of surfaces with visual detail. Here, an existing challenge is to preserve, or at least balance, two competing metrics: scale and angle. In this paper we present two methods for this, both based on global conformal parameterization. First, we describe a texture synthesis algorithm for surfaces with arbitrary topology. By using the conformal parameterization, the 3D surface texture synthesis problem can be converted to a 2D image synthesis problem, which is more intuitive, easier, and conceptually simpler. While the conformality of the parameterization naturally preserves the angles of the texture, in this paper we provide a multi-scale technique to also maintain a more uniform area scaling factor. A second novel contribution is to employ the global parameterization to simultaneously preserve orthogonality and size in texture

Theorem 1. Let D be an irreducible bounded symmetric domain in C', n&gt;= 2. Let F be a (nonuniform) lattice in Aut (D), ie a discrete subgroup of Aut (D) for which N:= D/F (is noncompact and) has. finite volume (wrt the locally symmetric metric induced from D). Suppose that a group F isomorphic to F (as an abstract group) acts as a discrete automorphism group on a contractible K (ihler manifold tVI. Assume that lQ/f has a finite singularity free cover M (ie M is a manifold) which is quasiprojective ie admits a compactification as a projective variety IVI and that~ I\M is of codimension at least three in~ l. Then] Q is biholomorphically equivalent to D, and f is conjugate to F in Aut (D).

The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to nd the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant negative Gauss curvature surfaces (pseudospherical surfaces) in Euclidean 3-space, and for timelike constant non-zero mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. We prove that there is a unique solution if the prescribed curve is noncharacteristic, and for characteristic initial curves (asymptotic curves for pseudospherical surfaces and null curves for timelike CMC) it is necessary and sucient for similar data to be prescribed along an additional characteristic curve that intersects the rst. The proofs also give a means of constructing all solutions using loop group techniques. The method used is the innite dimensional d'Alembert type representation for surfaces associated with Lorentzian harmonic maps (1-1 wave maps) into symmetric spaces, developed since the 1990's. Explicit formulae for the potentials in terms of the prescribed data are given, and some applications are considered.