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Publisher: Springer-Verlag (Total: 2350 journals)

 Applied Mathematics - A Journal of Chinese Universities   [SJR: 0.275]   [H-I: 8]   [0 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1993-0445 - ISSN (Online) 1005-1031    Published by Springer-Verlag  [2350 journals]
• Sparse recovery in probability via l q -minimization with Weibull random
matrices for 0 < q ≤ 1
• Authors: Yi Gao; Ji-gen Peng; Shi-gang Yue
Pages: 1 - 24
Abstract: Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the l2,q robust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the l2,q robust null space property with high probability. Besides, we prove that Weibull random matrices also possess the l q quotient property with high probability. Finally, with the combination of the above mentioned properties, we give two important approximation characteristics of the solutions to the l q -minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e ∈ ℝ n needs a priori e 2 ≤ є, the other is on the robustness estimate without needing to estimate the bound of e 2. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3430-2
Issue No: Vol. 33, No. 1 (2018)

• Waiting times and stopping probabilities for patterns in Markov chains
• Authors: Min-zhi Zhao; Dong Xu; Hui-zeng Zhang
Pages: 25 - 34
Abstract: Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ ) and the stopping probabilities P(τ = τ A ) with A ∈ C, where τ A is the waiting time until the pattern A appears as a run.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3522-z
Issue No: Vol. 33, No. 1 (2018)

• On the strong convergence properties for weighted sums of negatively
orthant dependent random variables
• Authors: Xin Deng; Xu-fei Tang; Shi-jie Wang; Xue-jun Wang
Pages: 35 - 47
Abstract: In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let {X n , n ≥ 1} be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3423-1
Issue No: Vol. 33, No. 1 (2018)

• Modeling stochastic mortality with O-U type processes
• Authors: Jing Zheng; Chang-qing Tong; Gui-jun Zhang
Pages: 48 - 58
Abstract: Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term. Based on the mortality data of America from Human Mortality database (HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3349-7
Issue No: Vol. 33, No. 1 (2018)

• 2D-3D registration for 3D analysis of lower limb alignment in a
weight-bearing condition
• Authors: Eungjune Shim; Youngjun Kim; Deukhee Lee; Byung Hoon Lee; Sungkyung Woo; Kunwoo Lee
Pages: 59 - 70
Abstract: X-ray imaging is the conventional method for diagnosing the orthopedic condition of a patient. Computerized Tomography(CT) scanning is another diagnostic method that provides patient’s 3D anatomical information. However, both methods have limitations when diagnosing the whole leg; X-ray imaging does not provide 3D information, and normal CT scanning cannot be performed with a standing posture. Obtaining 3D data regarding the whole leg in a standing posture is clinically important because it enables 3D analysis in the weight bearing condition. Based on these clinical needs, a hardware-based bi-plane X-ray imaging system has been developed; it uses two orthogonal X-ray images. However, such methods have not been made available in general clinics because of the hight cost. Therefore, we proposed a widely adaptive method for 2D X-ray image and 3D CT scan data. By this method, it is possible to threedimensionally analyze the whole leg in standing posture. The optimal position that generates the most similar image is the captured X-ray image. The algorithm verifies the similarity using the performance of the proposed method by simulation-based experiments. Then, we analyzed the internal-external rotation angle of the femur using real patient data. Approximately 10.55 degrees of internal rotations were found relative to the defined anterior-posterior direction. In this paper, we present a useful registration method using the conventional X-ray image and 3D CT scan data to analyze the whole leg in the weight-bearing condition.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3459-2
Issue No: Vol. 33, No. 1 (2018)

• Existence and uniqueness results for mild solutions of random impulsive
abstract neutral partial differential equation over real axis
• Authors: P Indhumathi; A Leelamani
Pages: 71 - 87
Abstract: In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3449-4
Issue No: Vol. 33, No. 1 (2018)

• Data driven composite shape descriptor design for shape retrieval with a
VoR-Tree
• Authors: Zi-hao Wang; Hong-wei Lin; Chen-kai Xu
Pages: 88 - 106
Abstract: We develop a data driven method (probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e., retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set. A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3536-6
Issue No: Vol. 33, No. 1 (2018)

• Nichols algebras over weak Hopf algebras
• Authors: Zhi-xiang Wu
Pages: 107 - 126
Abstract: In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra ℍ. Although the category of all left ℍ-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra ℍ, and a series of weak Hopf algebras. Some results of [8] are generalized.
PubDate: 2018-03-01
DOI: 10.1007/s11766-018-3327-0
Issue No: Vol. 33, No. 1 (2018)

• Feature selection of ultrahigh-dimensional covariates with survival
outcomes: a selective review
• Authors: Hyokyoung Grace Hong; Yi Li
Pages: 379 - 396
Abstract: Many modern biomedical studies have yielded survival data with high-throughput predictors. The goals of scientific research often lie in identifying predictive biomarkers, understanding biological mechanisms and making accurate and precise predictions. Variable screening is a crucial first step in achieving these goals. This work conducts a selective review of feature screening procedures for survival data with ultrahigh dimensional covariates. We present the main methodologies, along with the key conditions that ensure sure screening properties. The practical utility of these methods is examined via extensive simulations. We conclude the review with some future opportunities in this field.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3547-8
Issue No: Vol. 32, No. 4 (2017)

• The convergence ball and error analysis of the two-step Secant method
• Authors: Rong-fei Lin; Qing-biao Wu; Min-hong Chen; Yasir Khan; Lu Liu
Pages: 397 - 406
Abstract: Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order, we obtain an estimate of the radius of the convergence ball for the two-step secant method. Moreover, we also provide an error estimate that matches the convergence order of the two-step secant method. At last, we give an application of the proposed theorem.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3487-3
Issue No: Vol. 32, No. 4 (2017)

• New normalized nonlocal hybrid level set method for image segmentation
• Authors: Qiong Lou; Jia-lin Peng; De-xing Kong; Chun-lin Wang
Pages: 407 - 421
Abstract: This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3345-3
Issue No: Vol. 32, No. 4 (2017)

• Image segmentation by level set evolution with region consistency
constraint
• Authors: Li Zhong; Yuan-feng Zhou; Xiao-feng Zhang; Qiang Guo; Cai-ming Zhang
Pages: 422 - 442
Abstract: Image segmentation is a key and fundamental problem in image processing, computer graphics, and computer vision. Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation. However, poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation. In this paper, we present a region consistency constraint term to measure the regional consistency on both sides of the boundary, this term defines the boundary of the image within a range, and hence increases the stability of the level set model. The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary. Furthermore, this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour. The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3534-0
Issue No: Vol. 32, No. 4 (2017)

• Derivatives and differentials for multiplicative intuitionistic fuzzy
information
• Authors: Shan Yu; Ze-shui Xu; Shou-sheng Liu
Pages: 443 - 461
Abstract: By using the unsymmetrical scale instead of the symmetrical scale, the multiplicative intuitionistic fuzzy sets (MIFSs) reflect our intuition more objectively. Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number (MIFN) and is based on the unbalanced scale (i.e., Saaty’s 1-9 scale). In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively, in this paper, we firstly propose two new basic operational laws for MIFNs, which are the subtraction law and the division law. Secondly, we describe the change values of MIFNs when considering them as variables, classify these change values based on the basic operational laws for MIFNs, and depict the convergences of sequences of MIFNs by the subtraction and division laws. Finally, we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities, derivatives and differentials, and also give their application in selecting the configuration of a computer.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3479-3
Issue No: Vol. 32, No. 4 (2017)

• Boundedness of Hausdorff operators on the power weighted Hardy spaces
• Authors: Jie-cheng Chen; Shao-yong He; Xiang-rong Zhu
Pages: 462 - 476
Abstract: In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space $$H_{{{\left X \right }^\alpha }}^1({R^2})( - 1 \leqslant \alpha \leqslant 0)$$ , defined by $${H_{\Phi ,A}}f(x) = \int {_{{R^2}}} \Phi (u)f(A(u)x)du,$$ , where Φ ∈ L loc 1(R 2), A(u) = (a ij (u)) i,j=1 2 is a 2 × 2 matrix, and each a i,j is a measurable function. We obtain that H Φ,A is bounded from $$H_{{{\left X \right }^\alpha }}^1({R^2})( - 1 \leqslant \alpha \leqslant 0)$$ to itself, if $$\int {_{{R^2}}} \left {\Phi (u)} \right \left {\det \;{A^{ - 1}}(u)} \right {\left\ {A(u)} \right\ ^{ - \alpha }}\;\ln \;(1 + \frac{{{{\left\ {{A^{ - 1}}(u)} \right\ }^2}}}{{\left {\det \;{A^{ - 1}}(u)} \right }})du < \infty .$$ . This result improves some known theorems, and in some sense it is sharp.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3523-3
Issue No: Vol. 32, No. 4 (2017)

• When q theory meets large losses risks and agency conflicts
• Authors: Ying Wang; Wen-li Huang; Sheng-hong Li
Pages: 477 - 492
Abstract: We incorporate large losses risks into the DeMarzo et al.(2012) model of dynamic agency and the q theory of investment. The large losses risks induce losses costs and losses arising from agency conflicts during the large losses prevention process. Both of them reduce firm’s value, distort investment policy and generate a deeper wedge between the marginal and average q. In addition, we study the implementation of the contract to enhance the practical utility of our model. The agent optimally manages the firm’s cash flow and treats the cash reservation and credit line as the firm’s financial slack, and hedges the productivity shocks and large losses shocks via futures and insurance contracts, respectively.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3509-1
Issue No: Vol. 32, No. 4 (2017)

• Competitive analysis of price online inventory problem with cost function
• Authors: Shu-guang Han; Jiu-ling Guo; Lu-ping Zhang; Jue-liang Hu
Pages: 493 - 502
Abstract: In this paper, a new price is given to the online decision maker at the beginning of each day. The trader must decide how many items to purchase according to the current price. We present three variants and an online algorithm based on cost function. The competitive ratio of the online algorithm is given for each variant, which is a performance measure of an online algorithm. More importantly, we show that the online algorithm is optimal.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3280-3
Issue No: Vol. 32, No. 4 (2017)

• Bounds on partial derivatives of NURBS surfaces
• Authors: Guo-jin Wang; Hui-xia Xu; Qian-qian Hu
Pages: 281 - 293
Abstract: In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3429-0
Issue No: Vol. 32, No. 3 (2017)

• A novel enhancement method for low illumination images based on microarray
camera
• Authors: Jian-cheng Zou; Wen-qi Zheng; Zhi-hui Yang
Pages: 313 - 322
Abstract: It is difficult but important to get clear information from the low illumination images. In recent years the research of the low illumination image enhancement has become a hot topic in image processing and computer vision. The Retinex algorithm is one of the most popular methods in the field and uniform illumination is necessary to enhance low illumination image quality by using this algorithm. However, for the different areas of an image with contrast brightness differences, the illumination image is not smooth and causes halo artifacts so that it cannot retain the detail information of the original images. To solve the problem, we generalize the multi-scale Retinex algorithm and propose a new enhancement method for the low illumination images based on the microarray camera. The proposed method can well make up for the deficiency of imbalanced illumination and significantly inhibit the halo artifacts as well. Experimental results show that the proposed method can get better image enhancement effect compared to the multi-scale Retinex algorithm of a single image enhancement. Advantages of the method also include that it can significantly inhibit the halo artifacts and thus retain the details of the original images, it can improve the brightness and contrast of the image as well. The newly developed method in this paper has application potential to the images captured by pad and cell phone in the low illumination environment.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3458-8
Issue No: Vol. 32, No. 3 (2017)

• On vector variational-like inequalities and vector optimization problems
with ( G , α )-invexity
• Authors: Anurag Jayswal; Sarita Choudhury
Pages: 323 - 338
Abstract: The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3339-1
Issue No: Vol. 32, No. 3 (2017)

• On fundamental solution for powers of the sub-Laplacian on the Heisenberg
group
• Authors: Hai-meng Wang; Qing-yan Wu
Pages: 365 - 378
Abstract: We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3506-4
Issue No: Vol. 32, No. 3 (2017)

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