Applications of fractional transforms to object reconstruction from in-line holograms

We propose a method for the digital reconstruction of an object whose diffraction pattern has been recorded on a hologram. The fractional Fourier transform is used for the object reconstruction. To determine the position of the object, the fractional order is scanned. The fractional cosine and fractional Hartley transforms are also employed for object reconstruction. These two transforms are real valued and allow the reconstruction to be done with lower computing complexity. Simulations and experimental results are presented.     

Use of ultrafast-laser-driven microexplosional for fabricating three-dimensional void-based diamond-lattice photonic crystals in a solid polymer material

Micro-sized void spheres are successfully generated in a solid polymer by use of a tightly focused femtosecond laser beam from a high-repetition-rate laser oscillator. Confocal reflection images show that the void spheres are longitudinal rotational symmetric ellipsoids with a ratio of long to short axes of approximately 1.5. Layers of void spheres are then stacked to create three-dimensional diamond-lattice photonic crystals. Three gaps are observed in the [100] direction with a suppression rate of the second gap of up to approximately 75% for a 32-layer structure. The observed first- and second-order gaps shift to longer and shorter wavelengths, respectively, as the angle of incidence increases.     

Widely tunable continuous-wave diode-pumped 2-microm Tm-Ho:KYF4 laser

Continuous-wave laser action at approximately 2 microm is demonstrated in a Tm-Ho:KYF4 single crystal at room temperature. Crystal growth, spectroscopic measurements, and laser results are presented. An output power in excess of 250 mW is obtained with a tuning range of 99 nm, the largest ever published, to our knowledge, for Tm-Ho in any crystalline host.     

Aziridines as a protecting and directing group. Stereoselective synthesis of (+)-bromoxone

[reaction: see text] The directing ability of an aziridine group for the epoxidation of adjacent double bonds is demonstrated. The aziridine group is also used to effectively protect a double bond in a cycloenone system for a short synthesis of the title compound.     

An efficient palladium-catalyzed synthesis of cinnamaldehydes from acrolein diethyl acetal and aryl iodides and bromides

The reaction of aryl iodides and bromides with acrolein diethyl acetal in the presence of Pd(OAc)(2), (n)()Bu(4)NOAc, K(2)CO(3), KCl, and DMF, at 90 degrees C until the disappearance of the acetal followed by the addition of 2 N HCl to the crude reaction mixture, affords cinnamaldehydes in good to high yields. A variety of functional groups are tolerated in the aryl halides, including ether, aldehyde, ketone, ester, dialkylamino, nitrile, and nitro groups. The presence of substituents close to the oxidative addition site does not hamper the reaction.     

Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57