在全平面上解析的Laplace-Stieltjes变换的正规增长性

本文研究了应用Knopp-Kojima的方法得到的Dirichlet级数正规增长性.利用Dirichlet级数和Laplace-Stieltjes变换的关系,得到了Laplace-Stieltjes变换在全平面上的正规增长级的等价条件.     

A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location

The primary objective of this work is a detailed theoretical and computational study of the elasticity imaging inverse problem for tumor identification within the human body. Apart from this inverse problem's important and interesting application, it also poses noteworthy mathematical challenges since the underlying mathematical model is a system of elasticity involving incompressibility. This gives rise to the “locking” effect and special treatment is necessary for both the direct and inverse problems. To study the inverse problem in an optimization framework, we introduce a general computational scheme for handling parameter identification in saddle point problems along with the introduction and analysis of a new energy output least-squares objective functionals. We also present a treatment of the identification of discontinuous elasticity coefficients using the total variation regularization method. General formulas for the computation of the coefficient-to-solution map and a complete convergence analysis are given for the continuous problem as well as for its discrete analogue. Discrete formulas and implementation issues are discussed in detail and numerical examples for smooth and discontinuous coefficients are given.     

Equivalent definitions of BV space and of total variation on metric measure spaces

In this paper we introduce a new definition of BV   based on measure upper gradients and prove the equivalence of this definition, and the coincidence of the corresponding notions of total variation, with the definitions based on relaxation of L¹$L^1$ norm of the slope of Lipschitz functions or upper gradients. As in the previous work by the first author with Gigli and Savaré in the Sobolev case, the proof requires neither local compactness nor doubling and Poincaré.     

A fast alternating minimization algorithm for total variation deblurring without boundary artifacts

Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang (2008) [32]. The method in a nutshell consists of a discrete Fourier transform-based alternating minimization algorithm with periodic boundary conditions and in which two fast Fourier transforms (FFTs) are required per iteration. In this paper, we propose an alternating minimization algorithm for the continuous version of the total variation image deblurring problem. We establish convergence of the proposed continuous alternating minimization algorithm. The continuous setting is very useful to have a unifying representation of the algorithm, independently of the discrete approximation of the deconvolution problem, in particular concerning the strategies for dealing with boundary artifacts. Indeed, an accurate restoration of blurred and noisy images requires a proper treatment of the boundary. A discrete version of our continuous alternating minimization algorithm is obtained following two different strategies: the imposition of appropriate boundary conditions and the enlargement of the domain. The first one is computationally useful in the case of a symmetric blur, while the second one can be efficiently applied for a nonsymmetric blur. Numerical tests show that our algorithm generates higher quality images in comparable running times with respect to the Fast Total Variation deconvolution algorithm.     

The Radon‐Nikodym property,generalized bounded variation and the average range

A generalized bounded variation characterization of Banach spaces possessing the Radon‐Nikodym property is given in terms of the average range. We prove that a Banach space X has the Radon‐Nikodym property if and only if for each function of generalized bounded variation on [0, 1], the average range is a nonempty set at almost all .     

Deformation investigation on iPP/SiO2 composites: Influence of stretching temperature and particle size on morphology evolution and crystalline structure of thin films

 In the present work, structure changes during stretching of isotactic polypropylene (emPP) and emPP/silicon dioxide (SiO₂) composites have been investigated systematically. The α-form crystal structure of both iPP and emPP/SiO₂ composites is destroyed and transforms into the mesophase as the samples are stretched at a low temperature (35℃), while stretching at high temperatures (90℃ and 120℃) can restrain the appearance of defects and keep the perfection of crystal structure. FTIR results reveal that the stretching temperatures show no obvious difference of the effect on the orientation of pure iPP, however, the orientation of emPP/SiO₂ composites is greatly changed by the tensile temperature. In the case of micron-sized SiO₂ particles (average particle diameter d>1 μm), the orientation of the composites is lower than that of pure iPP at all stretching temperatures. The above results suggest that the stretching temperature and the SiO₂ particle size have great influence on the structure variation and orientation behavior of emPP/SiO₂ composites.     

Selective and sensitive homogenous assay of serum albumin with 1-anilinonaphthalene-8-sulphonate as a biosensor

Homogenous selective assay of albumin (ALB) in clinical sera was tested with 1-anilinonaphthalene-8-sulphonate (ANS) as Förster-resonance-energy-transfer (FRET) acceptor of tryptophan residues and biosensor of ALB. Between the excitation at 280 and 350 nm, the ratio of the fluorescence at 470 nm of free ANS in ethanol was about 1.9 while that of the complexes of ALB and ANS was about 3.9, supporting FRET in complexes of ANS and ALB. ANS below 1.0 mM saturated one site of ALB with K_d of about 0.13 μM in 20 mM sodium phosphate buffer at pH 7.0. For selective assay of ALB, 0.30 μM ANS was used to quantify fluorescence of the complexes at 470 nm under the excitation at 280 nm. ALB from 1.8 to 25 nM was quantified, whose lower limit was below 1% than that by bromocresol green assay while one-third than that by immunoturbidimetric assay. Globular proteins at comparable levels gave negligible signals. This new method showed reasonable resistance to other interfering substances in clinical sera. Quantities of ALB in clinical sera by this method were consistent with those by bromocresol green assay and immunoturbidimetric assay. Hence, homogenous assay of ALB with ANS as FRET biosensor was effective.     

Discriminative detection of low‐abundance point mutations using a PCR/ligase detection reaction/capillary gel electrophoresis method and fluorescence dual‐channel monitoring

We applied a facile LIF dual‐channel monitoring system recently developed and reported by our group to the polymerase chain reaction/ligase detection reaction/CGE method for detecting low‐abundance point mutations present in a wild‐type sequence‐dominated population. Mutation discrimination limits and signaling fidelity of the analytical system were evaluated using three mutant variations in codon 12 of the K‐ras oncogene that have high diagnostic value for colorectal cancer. We demonstrated the high sensitivity of the present method by detecting rare mutations present among an excess of wild‐type alleles (one mutation among ～100 normal sequences). This method also simultaneously interrogated the allelic compositions of the test samples with high specificity through spectral discrimination of the dye‐tagged ligase detection reaction products using the dual‐channel monitoring system.     

Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization

We concern with fast domain decomposition methods for solving the total variation minimization problems in image processing. By decomposing the image domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and subdomain problems are uniformly convex, we can apply the acceleration method to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing methods are discussed, which not only demonstrate the advantages of our method but also support the theoretical convergence rate.