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.     

Global Optimal Image Reconstruction from Blurred Noisy Data by a Bayesian Approach

In this paper, a procedure is presented which allows the optimal reconstruction of images from blurred noisy data. The procedure relies on a general Bayesian approach, which makes proper use of all the available information. Special attention is devoted to the informative content of the edges; thus, a preprocessing phase is included, with the aim of estimating the jump sizes in the gray level. The optimization phase follows; existence and uniqueness of the solution is secured. The procedure is tested against simple simulated data and real data.     

Testing Extreme Value Conditions

A test statistic is developed that checks the validity of the extreme value conditions without specifiying the shape parameter of the limiting extreme value distribution.     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

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