序Banach空间中带⊕算子的广义混合序变分不等式组

在序Banach空间中,引入和研究了带算子的广义混合序变分不等式组.应用序Banach空间理论和矩阵分析方法,给出了其不等式组解的存在性定理,并基于序B-限制增生映象,给出了求解不等式组的迭代算法,迭代序列的收敛性和逼近解.

关于Szász-Mirakjan算子的一个定理的证明

本文指出了《数学杂志》1984年第2期中《关于Szász-Mirakjan算子》一文中其主要定理证明的不妥之处,并给出了新的证明.

Deep learning model based on PET/CT and combination with Cox proportional hazard model for predicting progression of lung invasive adenocarcinoma after surgery

Objective To observe the efficacy of deep learning(DL)model based on PET/CT and its combination with Cox proportional hazard model for predicting progressive disease(PD)of lung invasive adenocarcinoma within 5 years after surgery.Methods The clinical,PET/CT and 5-year follow-up data of 250 patients with lung invasive adenocarcinoma were retrospectively analyzed.According to PD or not,the patients were divided into the PD group(n=71)and non-PD group(n=179).The basic data and PET/CT findings were compared between groups,among which the quantitative variables being significant different between groups were transformed to categorical variables using receiver operating characteristic(ROC)curve and corresponding cut-off value.Multivariant Cox proportional hazard model was used to select independent predicting factors of PD of lung invasive adenocarcinoma within 5 years after surgery.The patients were divided into training,validation and test sets at the ratio of 6∶2∶2,and PET/CT data in training set and validation set were used to train model and tuning parameters to build the PET/CT DL model,and the combination model was built in serial connection of DL model and the predictive factors.In test set,the efficacy of each model for predicting PD of lung invasive adenocarcinoma within 5 years after surgery was assessed and compared using the area under the curve(AUC).Results Patients'gender and smoking status,as well as the long diameter,SUV max and SUV mean of lesions measured on PET images,the long diameter,short diameter and type of lesions showed on CT were statistically different between groups(all P<0.05).Smoking(HR=1.787[1.053,3.031],P=0.031)and lesion SUV max>4.15(HR=5.249[1.062,25.945],P=0.042)were both predictors of PD of lung invasive adenocarcinoma within 5 years after surgery.In test set,the AUC of PET/CT DL model for predicting PD was 0.847,of the combination model was 0.890,of the latter was higher than of the former(P=0.036).Conclusion DL model based on PET/CT had high efficacy for predicting PD of lung invasive adenocarcinoma within 5 years after surgery.Combining with Cox proportional hazard model could further improve its predicting efficacy.

PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

High-order generalized screen propagator migration based on particle swarm optimization

Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unresolved. To describe the seismic wave propagation in media with lateral velocity variations and to image high-angle structures, we propose the generalized screen propagator based on particle swarm optimization （PSO-GSP）, for the precise fitting of the single-square-root operator. We use the 2D SEG/EAGE salt model to test the proposed PSO-GSP migration method to image the faults beneath the salt dome and compare the results to those of the conventional high-order generalized screen propagator （GSP） migration and split-step Fourier （SSF） migration. Moreover, we use 2D marine data from the South China Sea to show that the PSO-GSP migration can better image strong reflectors than conventional imaging methods.

Hybrid aggregation operator and its application to multiple attribute decision making problems

By combining the advantages of the additive weighted mean (AWM) operator and the ordered weighted averaging (OWA) operator, this paper first presents a hybrid operator for aggregating data information, and then proposes a hybrid aggregation (HA) operator-based method for multiple attribute decision making (MADM) problems. The theoretical analyses and the numerical results show that the HA operator generalizes both the AWM and OWA operators, and reflects the importance of both the given argument and the ordered position of the argument. Thus, the HA operator can reflect better real situations in practical applications. Finally, an illustrative example is given.

First principles investigation of binary intermetallics in Mg-Al-Ca-Sn alloy:Stability,electronic structures,elastic properties and thermodynamic properties

The structural stability, electronic structures, elastic properties and thermodynamic properties of the main binary phases Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca in Mg-Al-Ca-Sn alloy were determined from the first-principles calculation. The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Al_2Ca has the strongest alloying ability and structural stability. The densities of states（DOS）, Mulliken electron occupation number, metallicity and charge density difference of these compounds are given. The elastic constants of Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca phases are calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio are derived. The calculations of thermodynamic properties show that the Gibbs free energies of Al_2Ca and Mg_2 Sn are lower than that of Mg_（17）Al_（12）, which indicates that Al_2Ca and Mg_2 Sn are more stable than Mg_（17）Al_（12） phase. Hence, the heat resistance of Mg-Al-based alloys can be improved by adding Ca and Sn additions.

Linguistic approaches to multiple attribute decision making in uncertain linguistic setting

We studied multiple attribute decision-making problems with uncertain linguistic information, in which the preference values took the form of uncertain linguistic variables. We introduced some operational laws of uncertain linguistic variables and a formula for the comparison between two uncertain linguistic variables. We proposed two new aggregation operators called extended uncertain linguistic aggregation (EULA) operator and interval linguistic aggregation (ILA) operator, and then develop an EULA operator-based linguistic approach and an ILA operator-based linguistic approach, respectively, to multiple attribute decision making in uncertain linguistic setting. The approaches were straightforward and do not produce any loss of information. Finally, an illustrative example was given to verify the developed approaches and to demonstrate their practicality and effectiveness.

AN ALGORITHM OF EDGE DETECTION BASED ON ENTROPY OPERATOR

This paper presents an algorithm of edge detection in image processing. A new entropy operator and threshold estimation technique are effectively proposed. The algorithm overcomes some drawbacks of Shiozaki operator. It not only has higher speed but also can extract the edge better. Finally, an example of 2D image is given to demonstrate the usefulness and advantages of the algorithm.

Method based on fuzzy linguistic scale and FIOWGA operator for decision-making problems

In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.

Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

A first-principles study on electronic structure and elastic properties of Al_4Sr, Mg_2Sr and Mg_(23)Sr_6 phases

The electronic structures and mechanical properties of Al4Sr, Mg2Sr and Mg23Sr6 phases were determined by the use of first-principles calculations. The calculated heat of formation and cohesive energy indicate that Al4Sr has the strongest alloying ability as well as the highest structural stability. The elastic parameters were calculated, and then the bulk modulus, shear modulus, elastic modulus and Poisson ratio were derived. The ductility and plasticity were discussed. The results show that Al4Sr and Mg2Sr phases both are ductile, on the contrary, Mg23Sr6 is brittle, and among the three phases, Mg2Sr is a phase with the best plasticity.

Three methods for generating monotonic OWA operator weights with given orness level

Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples.

Dynamic compensation for sensors based on particle swarm optimization and realization on LabVIEW

In shock wave＇s pressure testing,a dynamic compensation digital filter is designed based on particle swarm optimization （PSO） algorithm.Dynamic calibration experiment and simulation are conducted for the pressure sensor.PSO algorithm is applied on Matlab platform to achieve optimization according to input and output data of the sensor as well as the reference model,and the global optimal values got by optimization become the parameters of the compensator.Finally,the dynamic compensation filter is established on LabVIEW platform.The experimental results show that the data after processing with the compensation filter truly reflects the input signal.

IMPROVEMENT OF MATRIX REPRESENTATION METHOD IN NORMAL FORM THEORY

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.

The Multiplier Algebra of a Ternary Algebra

In this article, we have given the definition of the relative double multiplier (quasi-multiplier) on a ternary algebra,and studied the isomorphic problem of the multiplier algebra M(A,e) of a ternary algerbra A.

Research on Rice Panicle L-system Model Based on Substructure Algorithm

In order to decrease model complexity of rice panicle for its complicated morphological structure,an interactive L-system based on substructure algorithm was proposed to model rice panicle in this study.Through the analysis of panicle morphology,the geometrical structure models of panicle spikelet,axis and branch were constructed firstly.Based on that,an interactive panicle L-system model was developed by using substructure algorithm to optimize panicle geometrical models with the similar structure.Simulation results showed that the interactive L-system panicle model based on substructure algorithm could fast construct panicle morphological structure in reality.In addition,this method had the well reference value for other plants model research.

The Existence of Generalized Solutions for a Nonhomogeneous Boundary Value Problem

Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions