Applied Mathematics-A Journal of Chinese Universities Series B最新文献

In this paper, we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity. As applications of the above result, we shall prove the existence of one-sign solutions to the following problem

where λ ≠ 0 is a parameter, R is a positive constant and B_R(0) = {x ∈ ℝ^N: ∣x∣ < R} is the standard open ball in the Euclidean space ℝ^N (N ≥ 1) which is centered at the origin and has radius R. v⁺ = max{v, 0},v⁻ = − min{v, 0}, (a(x) in C(overline {{B_R}(0)} ), a(x), α(x) and β(x) are radially symmetric with respect to x; f ∈ C(ℝ, ℝ), sf(s) > 0 for s ≠ 0, and f₀ ∈ [0, ∞], where f₀ = lim_∣s∣→0f(s)/s. We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results. We also study the asymptotic behaviors of positive radial solutions as λ → +∞.

The purpose of this paper is to define the notions of convergence, Cauchy st—convergence, st—Cauchy, I—convergence and I—Cauchy for double sequences in 2—fuzzy n—normed spaces with respect to α—n—norms and study certain classical and standard properties related to these notions.

In this article, the zero-inflated non-central negative binomial (ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.

Learning disentangled representation of data is a key problem in deep learning. Specifically, disentangling 2D facial landmarks into different factors (e.g., identity and expression) is widely used in the applications of face reconstruction, face reenactment and talking head et al.. However, due to the sparsity of landmarks and the lack of accurate labels for the factors, it is hard to learn the disentangled representation of landmarks. To address these problem, we propose a simple and effective model named FLD-VAE to disentangle arbitrary facial landmarks into identity and expression latent representations, which is based on a Variational Autoencoder framework. Besides, we propose three invariant loss functions in both latent and data levels to constrain the invariance of representations during training stage. Moreover, we implement an identity preservation loss to further enhance the representation ability of identity factor. To the best of our knowledge, this is the first work to end-to-end disentangle identity and expression factors simultaneously from one single facial landmark.

This paper presents an optimization method to compute the rotary axes of a 5-axis FDM printer whose A- and C-axes have large deviations relative to the x- and z-directions. The optimization model is designed according to the kinematic model in which a point rotates around a spatial line in the machine coordinate system of the printer. The model considers the A- and C-axes as two spatial lines. It is a two-object optimization model including two aspects. One is that the sum of deviations between the measured and computed points should be small; the other is that the deviations should be uniformly distributed for every measured point. A comparison of the new optimization method with conventional error-compensation methods reveals that the former has higher location accuracy. Using the optimized AC axes, 5-axis 3D printing paths are planned for some complex workpieces. Data analysis and printing samples show that the optimized AC axes satisfy 5-axes FDM printing requirements for nozzles with a diameter of 1.0 mm.

In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use linear transformation to make the interval into a fixed interval [−1, 1]. Then we use the Gauss quadrature formula to approximate the solution. With the help of lemmas, we get the result that the numerical error decay exponentially in the infinity norm and the Chebyshev weighted Hilbert space norm. Some numerical experiments are given to confirm our theoretical prediction.

Petri net (PN) is one of the promising computational and mathematical formalisms used to represent and study the behavior of complex metabolic networks. The various available analysis techniques of PN could be used to validate and analyze the network in different scenarios. Plasmodium falciparum is one of the threatening parasites which causes malaria, a deadly disease affecting a large number of today’s world population. The development of antimalarial drug resistance is an emerging global threat, highlighting the need to discover novel antimalarial targets. The fatty acid biosynthesis of malarial parasite is one of the essential metabolic pathways required for its growth and is present in apicoplast, a non-photosynthetic plastid. The malarial parasite obtains fatty acids by using type two fatty acid synthase (FAS II) enzyme, which is different from type one enzyme used by human host, making it an ideal drug target. This article proposes and studies the PN model of the parasite’s FAS II pathway to analyze the mechanism of potential drug targets in this pathway. The proposed PN model can serve as a base for further findings in the field of antimalarial drug targets to decrease the malaria mortality rate.

Accurate pancreas segmentation is critical for the diagnosis and management of diseases of the pancreas. It is challenging to precisely delineate pancreas due to the highly variations in volume, shape and location. In recent years, coarse-to-fine methods have been widely used to alleviate class imbalance issue and improve pancreas segmentation accuracy. However, cascaded methods could be computationally intensive and the refined results are significantly dependent on the performance of its coarse segmentation results. To balance the segmentation accuracy and computational efficiency, we propose a Discriminative Feature Attention Network for pancreas segmentation, to effectively highlight pancreas features and improve segmentation accuracy without explicit pancreas location. The final segmentation is obtained by applying a simple yet effective post-processing step. Two experiments on both public NIH pancreas CT dataset and abdominal BTCV multi-organ dataset are individually conducted to show the effectiveness of our method for 2D pancreas segmentation. We obtained average Dice Similarity Coefficient (DSC) of 82.82±6.09%, average Jaccard Index (JI) of 71.13± 8.30% and average Symmetric Average Surface Distance (ASD) of 1.69 ± 0.83 mm on the NIH dataset. Compared to the existing deep learning-based pancreas segmentation methods, our experimental results achieve the best average DSC and JI value.

The era of big data brings opportunities and challenges to developing new statistical methods and models to evaluate social programs or economic policies or interventions. This paper provides a comprehensive review on some recent advances in statistical methodologies and models to evaluate programs with high-dimensional data. In particular, four kinds of methods for making valid statistical inferences for treatment effects in high dimensions are addressed. The first one is the so-called doubly robust type estimation, which models the outcome regression and propensity score functions simultaneously. The second one is the covariate balance method to construct the treatment effect estimators. The third one is the sufficient dimension reduction approach for causal inferences. The last one is the machine learning procedure directly or indirectly to make statistical inferences to treatment effect. In such a way, some of these methods and models are closely related to the de-biased Lasso type methods for the regression model with high dimensions in the statistical literature. Finally, some future research topics are also discussed.

In this paper, we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems. By virtue of this method, we investigate the qualitative properties of positive solutions for the following Schrödinger system with fractional p-Laplacian

where 0 < s, t < 1 and 2 < p < ∞. We obtain the radial symmetry in the unit ball or the whole space ℝ^N (N ≥ 2), the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g, respectively.