Coefficient bounds for biholomorphic mappings which have a parametric representation

The main purpose of this paper is to prove a collection of new fixed point theorems for so-called weakly F-contractive mappings. By analogy, we introduce also a class of strongly F-expansive mappings and we prove fixed point theorems for such mappings. We provide a few examples, which illustrate these results and, as an application, we prove an existence and uniqueness theorem for the generalized Fredholm integral equation of the second kind. Finally, in Appendix A, we apply the Mönch fixed point theorem to prove two results on the existence of approximate fixed points of some continuous mappings.     

Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios

We derive in closed form distribution free lower bounds and optimal subreplicating strategies for spread options in a one-period static arbitrage setting. In the case of a continuum of strikes, we complement the optimal lower bound for spread options obtained in [Rapuch, G., Roncalli, T., 2002. Pricing multiasset options and credit derivatives with copula, Credit Lyonnais, Working Papers] by describing its corresponding subreplicating strategy. This result is explored numerically in a Black-Scholes and in a CEV setting. In the case of discrete strikes, we solve in closed form the optimization problem in which, for each asset S₁ and S₂, forward prices and the price of one option are used as constraints on the marginal distributions of each asset. We provide a partial solution in the case where the marginal distributions are constrained by two strikes per asset. Numerical results on real NYMEX (New York Mercantile Exchange) crack spread option data show that the one discrete lower bound can be far and also very close to the traded price. In addition, the one strike closed form solution is very close to the two strike.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer

The objective of this paper is to construct and analyze a fitted operator finite difference method (FOFDM) for the family of time‐dependent singularly perturbed parabolic convection–diffusion problems. The solution to the problems we consider exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then, we discretize the time variable using the classical Euler method. This results in a system of singularly perturbed interior layer two‐point boundary value problems. We propose a FOFDM to solve the system above. Through a rigorous error analysis, we show that the scheme is uniformly convergent of order one with respect to both time and space variables. Moreover, we apply Richardson extrapolation to enhance the accuracy and the order of convergence of the proposed scheme. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme.     

直流磁控溅射Au膜的微观应变研究

采用直流磁控溅射技术在室温下制备了厚度为108.4和215.6 nm的Au膜,膜厚由椭偏仪测定.利用常规CBD扫描模式对Au膜微结构进行分析,并采用剖面分析直接法测定Au膜的微观应变.X射线衍射(XRD)分析表明,Au膜在平行于基片表面沿<111>方向择优生长;衍射线剖面的宽化主要由晶格畸变所致.厚度为215.6 nm Au膜的微观应变量为0.065,比108.4 nm Au膜(0.055)略大.     

Tuning the optical properties of ZnTPP using carbonyl ring fusion

Zinc meso-tetraphenylporphyrin (ZnTPP) was modified in such a way to allow the effect of an asymmetric structural distortion on its optical properties to be investigated. This involved the fusion of a phenyl group to an adjacent pyrrole ring via a carbonyl bridge. With the aid of Density Functional Theory (DFT) and time-dependent DFT (TD-DFT) calculations it was found that the asymmetric distortion away from planarity induced by the carbonyl fusion resulted in a loss of degeneracy in the two lowest unoccupied molecular orbitals (LUMOs). The effect was a red shift of the electronic absorbance bands, an increased Q:B ratio from 0.046 in ZnTPP to 0.096 in the fused derivative, and the appearance of additional UV–vis peaks. This study therefore suggests that structural distortions, as well as electronic substituents may be used to alter absorbance spectra, a technique which is of interest in the design of light-harvesting dyes.     

双圆性质曲线和拟共形映射

设 f : R²→R² 是一同胚, f (∝)=∝. 该文证明了f 是拟共形映射的充要条件是f 保持曲线的双圆性质不变.     

Lower bounds in communication complexity based on factorization norms

We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access to several powerful tools from this area such as normed spaces duality and Grothendiek's inequality. This extends the arsenal of methods for deriving lower bounds in communication complexity. As we show, our method subsumes most of the previously known general approaches to lower bounds on communication complexity. Moreover, we extend all (but one) of these lower bounds to the realm of quantum communication complexity with entanglement. Our results also shed some light on the question how much communication can be saved by using entanglement. It is known that entanglement can save one of every two qubits, and examples for which this is tight are also known. It follows from our results that this bound on the saving in communication is tight almost always. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

On convergent numerical algorithms for unsymmetric collocation

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified Kansa’s method converges faster than the interpolant to the solution; that is, exponential convergence for the multiquadric and Gaussian radial basis functions (RBFs). Some numerical algorithms are proposed for efficiency and accuracy in practical applications of Kansa’s method. In double–precision, even for very large RBF shape parameters, we show that the modified Kansa’s method, through a subspace selection using a greedy algorithm, can produce acceptable approximate solutions. A benchmark algorithm is used to verify the optimality of the selection process.     

Distortion theorem for Bloch mappings on the unit ball <Emphasis Type="Italic">ℬ</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.