用次微分表达的对偶问题

本利用次微分建立了多目标规划的一个新的对偶问题，并给出其弱、强和逆对偶性，得到了一个新的次梯度的定义，并用其建立了一个新的对偶问题。     

A total variation based approach to correcting surface coil magnetic resonance images

Magnetic resonance images which are corrupted by noise and by smooth modulations are corrected using a variational formulation incorporating a total variation like penalty for the image and a high order penalty for the modulation. The optimality system is derived and numerically discretized. The cost functional used is non-convex, but it possesses a bilinear structure which allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing the maximum value of the modulation. Since the cost is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the cost is minimized with respect to one variable after the other using an inner generalized Newton iteration. Favorable computational results are shown for artificial phantoms as well as for realistic magnetic resonance images. Reported computational times demonstrate the feasibility of the approach in practice.     

On simultaneous weakly-Chebyshev subspaces

In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev (and weakly-Chebyshev) subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.     

Synthesis of NMP/RAFT inifers and preparation of block copolymers

Two different initiator/transfer agents (inifers) containing an alkoxyamine and a dithiobenzoate were synthetized and used to trigger out either reversible addition‐fragmentation chain transfer (RAFT) polymerization or nitroxide‐mediated polymerization (NMP). α‐Dithiobenzoate‐ω‐alkoxyamine‐difunctional polymers were produced in both cases which were subsequently used as precursors in the formation of block copolymers. This synthetic approach was applied to N‐isopropylacrylamide (NIPAM) or polyethylene oxide methacrylate (EOMA) to form α,ω‐heterodifunctional homopolymers via RAFT at 60°C which were chain extended with styrene by activating the alkoxyamine moiety at 120°C. Under such temperature conditions, it is proposed that a tandem NMP/RAFT polymerization is initiated producing a simultaneous growth of polystyrene blocks at both chain‐ends. Self‐assembled nanostructures of these amphiphilic block copolymers were evidenced by scanning electron microscopy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

On approximation of dual spaces and dual operators

We study the connection between equations which approximate an initial abstract linear equation and the adjoint one. We prove that the operator which is adjoint to the approximating one approximates the adjoint operator. As examples we consider adjoint linear integral equations and mutually dual linear programming problems.     

Analysis of flow between a wafer and pad during CMP processes

In this paper, we summarize the development of a numerical model for the chemical mechanical planarization (CMP) process and experimentally investigate the effects of pad conditioning on slurry transport and mixing. A simplified two-dimensional numerical model of slurry flow beneath a stationary wafer was developed to determine the pressure and shear stress beneath a wafer. The initial results indicate that in the hydrodynamic regime a positive upward pressure is exerted on the wafer. We also examined three cases to study pad effects on slurry transport; polishing with an Embossed Politex pad, an unconditioned IC1000 pad, and a conditioned IC1000 pad. Cab-O-Sperse SC1 slurry was used in a 1:1.5 dilution with water. Mixing data show that conditioning has a negligible effect on the rate of slurry entrainment and mixing; however, conditioning has a large effect on the thickness of the slurry layer between the wafer and pad. Conditioning was found to increase the slurry thickness by a factor of two. In addition the gradients in slurry age beneath the wafer were compared among the three cases. The IC1000 pads supported a gradient in the inner third of the wafer only, while the Embossed Politex pad showed a linear gradient across the wafer implying it retains pockets of unmixed slurry in the embossed topography.     

双模手机的发展、技术与机遇

移动通信从2G发展到3G,由于标准众多,不同标准的网络产生了不同制式的移动终端。用同一个手机实现在不同的网络漫游切换的想法由来已久,基于此双模手机的概念也越来越多地被人提及,文章讨论了双模手机产生的背景、双模手机系统的网络结构和软件无线电在其中的应用,并根据当前双模手机的发展状况进一步阐述了双模手机的发展趋势。     

A remark on full rank perfect codes

Any full rank perfect 1-error correcting binary code of length n=2^k-1 and with a kernel of dimension n-log(n+1)-m, where m is sufficiently large, may be used to construct a full rank perfect 1-error correcting binary code of length 2^m-1 and with a kernel of dimension n-log(n+1)-k. Especially we may construct full rank perfect 1-error correcting binary codes of length n=2^m-1 and with a kernel of dimension n-log(n+1)-4 for m=6,7,…,10.This result extends known results on the possibilities for the size of a kernel of a full rank perfect code.     

On the Duals of Segre Varieties

The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M.M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree?