A CLASS OF MIXED-TYPE FUNDAMENTAL PROBLEMS ON ELASTIC HALF-PLANE

The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integrals by reducing them to Riemann boundary value problems. The analytic expressions of the solutions are obtained in cases of uniform loads. In particular, the solution is written in detail for the important case when uniform pressure is given on a single interval or two equal intervals.

EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.

MCBC-SMOTE:A Majority Clustering Model for Classification of Imbalanced Data

Datasets with the imbalanced class distribution are difficult to handle with the standard classification algorithms.In supervised learning,dealing with the problem of class imbalance is still considered to be a challenging research problem.Various machine learning techniques are designed to operate on balanced datasets;therefore,the state of the art,different undersampling,over-sampling and hybrid strategies have been proposed to deal with the problem of imbalanced datasets,but highly skewed datasets still pose the problem of generalization and noise generation during resampling.To overcome these problems,this paper proposes amajority clusteringmodel for classification of imbalanced datasets known as MCBC-SMOTE(Majority Clustering for balanced Classification-SMOTE).The model provides a method to convert the problem of binary classification into a multi-class problem.In the proposed algorithm,the number of clusters for themajority class is calculated using the elbow method and the minority class is over-sampled as an average of clustered majority classes to generate a symmetrical class distribution.The proposed technique is cost-effective,reduces the problem of noise generation and successfully disables the imbalances present in between and within classes.The results of the evaluations on diverse real datasets proved to provide better classification results as compared to state of the art existing methodologies based on several performance metrics.

Dealing with the Class Imbalance Problem in the Detection of Fake Job Descriptions

In recent years,the detection of fake job descriptions has become increasingly necessary because social networking has changed the way people access burgeoning information in the internet age.Identifying fraud in job descriptions can help jobseekers to avoid many of the risks of job hunting.However,the problem of detecting fake job descriptions comes up against the problem of class imbalance when the number of genuine jobs exceeds the number of fake jobs.This causes a reduction in the predictability and performance of traditional machine learning models.We therefore present an efficient framework that uses an oversampling technique called FJD-OT(Fake Job Description Detection Using Oversampling Techniques)to improve the predictability of detecting fake job descriptions.In the proposed framework,we apply several techniques including the removal of stop words and the use of a tokenizer to preprocess the text data in the first module.We then use a bag of words in combination with the term frequency-inverse document frequency(TF-IDF)approach to extract the features from the text data to create the feature dataset in the second module.Next,our framework applies k-fold cross-validation,a commonly used technique to test the effectiveness of machine learning models,that splits the experimental dataset[the Employment Scam Aegean(ESA)dataset in our study]into training and test sets for evaluation.The training set is passed through the third module,an oversampling module in which the SVMSMOTE method is used to balance data before training the classifiers in the last module.The experimental results indicate that the proposed approach significantly improves the predictability of fake job description detection on the ESA dataset based on several popular performance metrics.

Teaching Strategies for Large English Classes

In China, College English classes are usually large. Nowadays, most College English language teachers are confronting the challenge of teaching larger classes than before. This paper analyzes some problems caused by large English classes and suggests some teaching strategies to deal with such problems.

A CLASS OF VARIATIONAL DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM

In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element method. Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation. The schemes studied in refs. [1], [3], [4] and [51 belong to the cllass.

A MODIFIED PROJECTION AND CONTRACTION METHOD FOR A CLASS OF LINEAR COMPLEMENTARITY PROBLEMS

Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.

Optimized Stacked Autoencoder for IoT Enabled Financial Crisis Prediction Model

Recently,Financial Technology(FinTech)has received more attention among financial sectors and researchers to derive effective solutions for any financial institution or firm.Financial crisis prediction(FCP)is an essential topic in business sector that finds it useful to identify the financial condition of a financial institution.At the same time,the development of the internet of things(IoT)has altered the mode of human interaction with the physical world.The IoT can be combined with the FCP model to examine the financial data from the users and perform decision making process.This paper presents a novel multi-objective squirrel search optimization algorithm with stacked autoencoder(MOSSA-SAE)model for FCP in IoT environment.The MOSSA-SAE model encompasses different subprocesses namely preprocessing,class imbalance handling,parameter tuning,and classification.Primarily,the MOSSA-SAE model allows the IoT devices such as smartphones,laptops,etc.,to collect the financial details of the users which are then transmitted to the cloud for further analysis.In addition,SMOTE technique is employed to handle class imbalance problems.The goal of MOSSA in SMOTE is to determine the oversampling rate and area of nearest neighbors of SMOTE.Besides,SAE model is utilized as a classification technique to determine the class label of the financial data.At the same time,the MOSSA is applied to appropriately select the‘weights’and‘bias’values of the SAE.An extensive experimental validation process is performed on the benchmark financial dataset and the results are examined under distinct aspects.The experimental values ensured the superior performance of the MOSSA-SAE model on the applied dataset.

A CLASS OF FACTORIZED QUASI-NEWTON METHODS FOR NONLINEAR LEAST SQUARES PROBLEMS

This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.

A CLASS OF BOUNDARY PROBLEMS FOR SOME HYPERBOLIC EQUATIONS

A boundary problem for the Klein-Gordon equation in the strip O≤t≤T is considered with the boundary condition:the initial state at t=O and the final state at t=T.It is proven that the problem admits of an infinite number of solutions.The same result holds for a generic 2nd order hyperbolic equation in 2-variables.Using the result for the wave operator in 3-space dimensions we give a method to reconstruct functions whose integral on all unit spheres in R~3 is a given function.

一类三维趋化–斯托克斯方程组正则化问题解的先验估计

本文研究了一类带流体耦合的三维趋化–斯托克斯方程,该模型刻画了流体环境中的生物趋化现象。大量的生物实验观测表明,在趋化流体模型中,重力对细胞运动的影响和趋化本身对流体的交互作用都应该放在方程中同时考虑。本文将在 的条件下利用权函数的方法建立正则化问题解的先验估计,为进一步研究解的定性理论做好准备。

Evolutionary under-sampling based bagging ensemble method for imbalanced data classification

In the class imbalanced learning scenario, traditional machine learning algorithms focusing on optimizing the overall accuracy tend to achieve poor classification performance especially for the minority class in which we are most interested. To solve this problem, many effective approaches have been proposed. Among them, the bagging ensemble methods with integration of the under-sampling techniques have demonstrated better performance than some other ones including the bagging ensemble methods integrated with the over-sampling techniques, the cost-sensitive methods, etc. Although these under-sampling techniques promote the diversity among the generated base classifiers with the help of random partition or sampling for the majority class, they do not take any measure to ensure the individual classification performance, consequently affecting the achievability of better ensemble performance. On the other hand, evolutionary under-sampling EUS as a novel under- sampling technique has been successfully applied in searching for the best majority class subset for training a good- performance nearest neighbor classifier. Inspired by EUS, in this paper, we try to introduce it into the under-sampling bagging framework and propose an EUS based bagging ensemble method EUS-Bag by designing a new fitness function considering three factors to make EUS better suited to the framework. With our fitness function, EUS-Bag could generate a set of accurate and diverse base classifiers. To verify the effectiveness of EUS-Bag, we conduct a series of comparison experiments on 22 two-class imbalanced classification problems. Experimental results measured using recall, geometric mean and AUC all demonstrate its superior performance.

SUBSPACE SEARCH METHOD FOR A CLASS OF LEAST SQUARES PROBLEM

Presents information on a study which described a subspace search method for solving a class of least squares problem. Derivation of the algorithm; Convergence results; Modification of algorithm and applications.

Dirichlet problem related to a class of superprocesses

ASSUME that ξ = （ξt, Ⅱx） is a right Markov process in Rd. Let φ（x, z） = a（x）z+b（x）z2+integral from n=0 to ∞ (e-uz-1+uz)nx（du）, x∈ Rd, z∈R+. （1）Consider the following Dirichlet problem:

INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS

The existence of global weak solutions to the periodic boundary problem or the initial value problem for the nonlinear Pseudo-hyperbolic equation u_(tt)-[a_1+a_2(u_x)^(2m)]u_(xx)-a_3u_(xxt)=f(x,t,u,u_x) is proved by the method of the vanishing of the additional diffusion terms, Leray-Schauder's fixedpoint argument and Sobolev's estimates,where m≥1 is a natural number and a_i>0(i=1,2,3)are constants.