Finite-aperture effects for Fourier transform systems with convergent illumination. Part I: 2-D system analysis

The Optical Fourier Transform (OFT) is one of the most fundamental operations in analogue Optical Signal Processing (OSP). There are many optical arrangements for implementing the OFT, however one which is particularly popular is the Scaled Optical Fourier Transform (SOFT) because it offers the user the ability to scale the output Fourier distribution. In this paper we study some of the practical limits introduced by using a converging spherical lens of finite aperture to produce the illuminating field in the implementation of the SOFT. By deriving simple rules of thumb, based on examining phase and intensity deviations from the ideal unapertured case, we define an area inside the geometric shadow, which we refer to as a sub-geometric shadow. Inside this sub-geometric shadow we show that the worst-case errors in the resulting SOFT, arising due to diffraction, can be quantified and avoided.     

Withanolides from Withania adpressa

From the leaves of Withania adpressa, a plant endemic to Sahara of Morocco and Algeria, the novel steroidal lactone (22R)‐14α,15α,17β,20β‐tetrahydroxy‐1‐oxowitha‐2,5,24‐trien‐26,22‐olide (= (15S,17S)‐14,15,17,20‐tetrahydroxy‐22,26‐epoxyergosta‐2,5,24‐triene‐1,26‐dione; 1 ), was isolated, along with three known compounds, withanolides F ( 2 ), J ( 3 ), and oleanolic acid. Their structures were mainly solved by in‐depth 1D‐ and 2D‐NMR (including ADEQUATE) experiments, as well as by HR‐MS analyses and chemical evidence.     

Symplectic hypersurfaces in the complement of an isotropic submanifold

Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity results in the K?hler case and various applications. Received: 9 January 2001 / Published online: 19 October 2001     

Magnetic properties of neptunium diarsenide

The magnetic properties of a collection of single crystals of NpAs₂ have been investigated in the temperature range 4.2-300 K and in applied fields up to 100 kOe. For small magnetic fields (3 kOe), NpAs₂ is ferromagnetic up to T_IC=18 K, antiferromagnetic from 28 K to T_N=52 K, then paramagnetic. Both transitions are first order. When the applied field increases T_IC is shifted towards T_N. The antiferromagnetic phase disappears for H#62;30 kOe. The ferromagnetic range is characterized by a very large anisotropy. In the paramagnetic state, NpAs₂ has an effective moment 1.88 μ_B.     

Synthesis of multi-1,10-phenanthroline ligands with 1,3-phenylene linkers and their lithium complexes

The synthesis of two multisite ligands containing four and five 1,10-phenanthroline (phen) chelates in line, respectively, is presented. The connectors are 1,3-phenylene linkers. The two ligands were prepared following multistep procedures, the two key reactions being the Suzuki coupling reaction between aromatic nuclei and the nucleophilic addition of aryllithium derivatives onto a phen fragment. The coordination chemistry of both ligands with Li+ ions was very clean and selective, whereas their reaction with copper(I) led to intractable mixtures of insoluble complexes. The tetraphen and the pentaphen compounds afforded almost quantitatively the four- and five-lithium double-stranded helical complexes, respectively. The helical systems are probably highly wound, as indicated by NMR measurements. The pronounced strain of the 5-Li+ complex is reflected by the easy loss of a lithium cation, as shown by electrospray mass spectrometry.     

An uncountable family of nonorbit equivalent actions of

For each , we construct an uncountable family of free ergodic measure preserving actions of the free group on the standard probability space such that any two are nonorbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid' (in the sense of Popa), with the IIfactors mutually nonisomorphic (even nonstably isomorphic) and in the class

     

Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy

In combination of direct phase retrieval of coherent x-ray diffraction patterns with a novel tomographic reconstruction algorithm, we, for the first time, carried out quantitative 3D imaging of a heat-treated GaN particle with each voxel corresponding to 17 x 17 x 17 nm3. We observed the platelet structure of GaN and the formation of small islands on the surface of the platelets, and successfully captured the internal GaN-Ga2O3 core shell structure in three dimensions. This work opens the door for nondestructive and quantitative imaging of 3D morphology and 3D internal structure of a wide range of materials at the nanometer scale resolution that are amorphous or possess only short-range atomic organization.