Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff-Young inequality

We establish the existence of Salem sets in the ring of integers of any local field and study the Fourier restriction phenomenon on such sets. Optimal extension of the Hausdorff-Young inequality, initially attained for the torus by G. Mockenhaupt and W. Ricker, is also established in the local field setting.     

Recognition of gas–liquid two-phase flow patterns based on improved local binary pattern operator

A new method to pattern recognition of gas–liquid two-phase flow regimes based on improved local binary pattern (LBP) operator is proposed in this paper. Five statistic features are computed using the texture pattern matrix obtained from the improved LBP. The support vector machine and back-propagation neural network are trained to flow pattern recognition of five typical gas–liquid flow regimes. Experimental results demonstrate that the proposed method has achieved better recognition accuracy rates than others. It can provide reliable reference for other indirect measurement used to analyze flow patterns by its physical objectivity.     

Localization Results for the Meyer-König and Zeller Max-Product Operator

In this article, we investigate the local approximation and shape preserving properties in subintervals for the Meyer-König and Zeller max-product operators. The results obtained put in evidence that in the class of strictly positive continuous functions, the local properties of the nonlinear Meyer-König and Zeller max-product operators are much stronger and more general than those in the case of their linear counterparts.     

A compatible and conservative spectral element method on unstructured grids

We derive a formulation of the spectral element method which is compatible on very general unstructured three-dimensional grids. Here compatible means that the method retains discrete analogs of several key properties of the divergence, gradient and curl operators: the divergence and gradient are anti-adjoints (the negative transpose) of each other, the curl is self-adjoint and annihilates the gradient operator, and the divergence annihilates the curl. The adjoint relations hold globally, and at the element level with the inclusion of a natural discrete element boundary flux term.     

A smoothing-type algorithm for solving system of inequalities

In this paper we consider system of inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A Newton-type algorithm is applied to solve iteratively the smooth equations so that a solution of the problem concerned is found. We show that the algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results are reported.     

The Rees Valuations of Complete Ideals in a Regular Local Ring

Let I be a complete m-primary ideal of a regular local ring (R, m) of dimension d ≥ 2. In the case of dimension two, the beautiful theory developed by Zariski implies that I factors uniquely as a product of powers of simple complete ideals and each of the simple complete factors of I has a unique Rees valuation. In the higher dimensional case, a simple complete ideal of R often has more than one Rees valuation, and a complete m-primary ideal I may have finitely many or infinitely many base points. For the ideals having finitely many base points Lipman proves a unique factorization involving special *-simple complete ideals and possibly negative exponents of the factors. Let T be an infinitely near point to R with dim R = dim T and R/m = T/m _T . We prove that the special *-simple complete ideal P _RT has a unique Rees valuation if and only if either dim R = 2 or there is no change of direction in the unique finite sequence of local quadratic transformations from R to T. We also examine conditions for a complete ideal to be projectively full.     

Stability and Hopf bifurcation in a predator–prey model with stage structure for the predator

A predator–prey system with stage structure for the predator and time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and two boundary equilibria of the system is discussed, respectively. Further, the existence of a Hopf bifurcation at the positive equilibrium is also studied. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and one of the boundary equilibria of the proposed system. As a result, the threshold is obtained for the permanence and extinction of the system. Numerical simulations are carried out to illustrate the main results.     

Prediction of index futures returns and the analysis of financial spillovers—A comparison between GARCH and the grey theorem

This paper adopts the GM(1, 1) model to predict the rates of return of nine major index futures in the American and Eurasian markets. In a further step, by means of local grey relational analysis and by employing the GM(1, N) model for the first time, the variation relatedness and the main influencing factor among the above mentioned targeted markets is determined. Then, a comparison between GARCH/TGARCH and the grey theory with regard to predictive power is conducted. The findings reveal that the GARCH/TGARCH model performs better than the GM(1, 1), including the optimal α method, in terms of forecasting capabilities. Meanwhile, it is also found that GARCH and spillover effects indeed exist. Moreover, GM(1, N) also reveals that the daily rate of return of the Dow Jones index futures has the most influence on the rates of return of the other index futures.     

Comparison of presmoothing methods in kernel density estimation under censoring

The behavior of the presmoothed density estimator is studied when different ways to estimate the conditional probability of uncensoring are used. The Nadaraya–Watson, local linear and local logistic approach are compared via simulations with the classical Kaplan–Meier estimator. While the local logistic presmoothing estimator presents the best performance, the relative benefits of the local linear versus the Nadaraya–Watson estimator depend very much on the shape of some underlying functions.     

Projection-Based Partitioning for Large,High-Dimensional Datasets

Recent work in the field of cluster analysis has focused on designing algorithms that address the issue of ever growing datasets and provide meaningful solutions for data with high cardinality and/or dimensionality, under the natural restriction of limited resources. Within this line of research, we propose a method drawing on the principles of projection pursuit and grid partitioning, which focuses on reducing computational requirements for large datasets without loss of performance. To achieve that, we rely on procedures such as sampling of objects, feature selection, and quick density estimation using histograms. The present algorithm searches for low-density points in potentially favorable one-dimensional projections, and partitions the data by a hyperplane passing through the best split point found. Tests on synthetic and reference data indicate that our method can quickly and efficiently recover clusters that are distinguishable from the remaining objects on at least one direction; linearly nonseparable clusters are usually subdivided. The solution is robust in the presence of noise in moderate levels, and when the clusters are partially overlapping. An implementation of the algorithm is available online, as supplemental material.