Image restoration is a common problem in visual process. In this paper, a modified minimization model is presented, which combines the L1 and L2 fidelity terms with a combined quadratic L2 and TV regularizer just as the regularizer of Cai et al. (2013). The combined regularizer has the priorities of preserving desirable edges and ensuring several kinds of noises can be removed clearly. Split-Bregman algorithm is effi- ciently employed to solve this model and convergence analysis is also discussed. Moreover, we extend the proposed model and algorithm for image restoration involving blurry images and color images. Experimental results show that our proposed model and algorithm have good performance both in visual and ISNR values for different kinds of blurs and noises including mixed noise.

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrdinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

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Let$F$be a family of meromorphic functions on the unit disc Δ and let$a$and$b$be distinct values. If for every$f$∈$F$,$f$and$f′$share$a$and$b$on Δ, then$F$is normal on Δ.

Let$D$be a relatively compact domain in$C$^{2}with smooth connected boundary ∂$D$. A compact set$K⊂∂D$is called removable if any continuous CR function defined on ∂$D/K$admits a holomorphic extension to$D$. If$D$is strictly pseudoconvex, a theorem of B. Jöricke states that any compact$K$contained in a smooth totally real disc$S⊂∂D$is removable. In the present article we show that this theorem is true without any assumption on pseudoconvexity.