Applied Mathematics-a Journal Of Chinese Universities Series B最新文献

In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable.

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the results for many dependent structures, such as END, ϱ*-mixing, ϱ⁻-mixing and φ-mixing, etc.

Fractal interpolation is a modern technique to fit and analyze scientific data. We develop a new class of fractal interpolation functions which converge to a data generating (original) function for any choice of the scaling factors. Consequently, our method offers an alternative to the existing fractal interpolation functions (FIFs). We construct a sequence of α-FIFs using a suitable sequence of iterated function systems (IFSs). Without imposing any condition on the scaling vector, we establish constrained interpolation by using fractal functions. In particular, the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data. The existence of ({{cal C}^r} - alpha - {rm{FIFs}}) is investigated. We identify suitable conditions on the associated scaling factors so that α-FIFs preserve r-convexity in addition to the ({{cal C}^r} - {rm{smoothness}}) of original function.

Multiplicative calculus (MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC. Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization (CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization (MGNM) method along with its convergence properties. The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.

In this note, we show a sharp lower bound of (min left{{sumnolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} ldots {u_k}}} right.) is a path of (2-)connected G on its order such that (k-1)-iterated line graphs L^k−1(G) are hamiltonian.

In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces L^p(ℝⁿ), Hardy spaces H^p(ℝⁿ) and general mixed norm spaces, which implies almost everywhere convergence of such operator. In this paper, we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces.

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming. Ranked set sampling (RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3, 385–390] as an effective way to estimate the pasture mean. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the best linear unbiased estimators(BLUEs) for the simple linear regression model. The BLUEs for this model under MERSS are derived. The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.

Automatic segmentation of the liver and hepatic lesions from abdominal 3D computed tomography (CT) images is fundamental tasks in computer-assisted liver surgery planning. However, due to complex backgrounds, ambiguous boundaries, heterogeneous appearances and highly varied shapes of the liver, accurate liver segmentation and tumor detection are still challenging problems. To address these difficulties, we propose an automatic segmentation framework based on 3D U-net with dense connections and globally optimized refinement. Firstly, a deep U-net architecture with dense connections is trained to learn the probability map of the liver. Then the probability map goes into the following refinement step as the initial surface and prior shape. The segmentation of liver tumor is based on the similar network architecture with the help of segmentation results of liver. In order to reduce the influence of the surrounding tissues with the similar intensity and texture behavior with the tumor region, during the training procedure, I × liver_label is the input of the network for the segmentation of liver tumor. By doing this, the accuracy of segmentation can be improved. The proposed method is fully automatic without any user interaction. Both qualitative and quantitative results reveal that the proposed approach is efficient and accurate for liver volume estimation in clinical application. The high correlation between the automatic and manual references shows that the proposed method can be good enough to replace the time-consuming and non-reproducible manual segmentation method.

Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemannian manifolds. We give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sobolev inequality is true and obtain a new estimate on the entropy.

In this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.