Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.     

Experimental high-gain quantum-injected optical parametric amplification and multiphoton phase-covariant cloning

We investigate multiphoton states generated by high-gain optical parametric amplification of a single injected photon—polarization encoded as a qubit. The experimental configuration exploits the optimal phase-covariant cloning. The output state of the apparatus is found to exhibit the quantum superposition property of mesoscopic multiphoton assemblies involving about 300 photons. This work represents an experimental advance toward the test of several fundamental quantum processes in mesoscopic or macroscopic frameworks.     

Wavelet and harmonic filtering for distortion-invariant volume holographic correlation

The wavelet and harmonic filtering method suggested by Zalevsky and Ouzieli is introduced in this paper and adopted in our volume holographic image recognition system. This composite filter combines several scaled versions of the cascaded wavelet and harmonic filter, obtaining high discrimination ability and wide dynamic range of rotation and scale deformations. Optical experiments are conducted to demonstrate the validity and practicability of the algorithm. To the best of our knowledge, this is the first report of using this algorithm in a volume holographic system. Moreover, the separate correlation approach proposed in this paper greatly simplifies the manufacturing process and reduces the cost of the system.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

Effect of stoichiometry on liquid crystalline supramolecular polymers formed with complementary nucleobase pair interactions

We report herein studies on the liquid crystalline behavior of a series of supramolecular materials that contain different ratios of two complementary symmetrically-substituted alkoxy-bis(phenylethynyl)benzene AA- and BB-type monomers. One monomer has thymine units placed at either end of the rigid mesogenic core, while the other has N⁶-(4-methoxybenzoyl)-adenine units placed on the ends. Differential scanning calorimetric and polarized optical microscopy studies have been carried out on these systems. These studies show that the material's behavior is strongly dependent on its thermal history. As a result, the materials can exhibit, on heating, either a liquid crystalline phase, a crystalline phase, or the coexistence of crystalline and liquid crystalline regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5049–5059, 2006     

Ethylene polymerization by novel Ziegler–Natta‐type catalysts obtained in situ by the oxidative addition of 8‐hydroxyquinoline‐based ligands to bis(1,5‐cyclooctadiene)nickel(0) and methylaluminoxane

Novel catalytic systems, prepared in situ by the oxidative addition of 8‐hydroxyquinoline ligands to bis(1,5‐cyclooctadiene)nickel(0) and activated by methylaluminoxane, were studied in ethylene polymerization. When 8‐hydroxyquinoline was employed, only oligomeric products were obtained. On the contrary, 5,7‐dinitro‐8‐hydroxyquinoline gave linear polyethylene (PE), but with a modest activity. For the catalyst based on 5‐nitro‐8‐hydroxyquinoline, the productivity was largely dependent on the content of free trimethylaluminum (TMA) present in the commercial aluminoxane. The progressive optimization of the TMA/oligomeric methylaluminoxane ratio increased the productivity, which reached 700 kg of PE/(mol of Ni × h), by an order of magnitude. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 200–206, 2006     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Stable hysteretic reflection of light at a nonlinear interface

We have observed a hysteretic (bistable) reflection of a Gaussian laser beam at the interface between glass and a liquid solution of polystyrene microspheres as nonlinear medium with both branches of the hysteretic curve being stable, in contrast to the results of previous experiments.     

Decomposition theorems in orthomodular posets: the problem of uniqueness

We provide some conditions which are equivalent to the uniqueness of Hewitt-Yosida-type decomposition and Lebesgue-type decomposition for real valued additive functions defined on orthomodular posets.