On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.

Interframe Variation Vector:A Novel Feature for Gait Recognition

Gait representation is an important issue in gait recognition. A simple yet efficient approach, called Interframe Variation Vector （IW）, is proposed. IW considers the spatiotemporal motion characteristic of gait, and uses the shape variation information between successive frames to represent gait signature. Different from other features, IVV rather than condenses a gait sequence into single image resulting in spatial sequence lost; it records the whole moving process in an IVV sequence. IVV can encode whole essential features of gait and preserve all the movements of limbs. Experimental results show that the proposed gait representation has a promising recognition performance.

Generalized Bi quasi variational Inequalities in Locally Convex Topological Vector Spaces

In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].

Spatial and Temporal Stress Variations before and after the 2008 Wenchuan M_(w)7.9 Earthquake and its Implications:A Study based on Borehole Stress Data

In situ stress measurement data was analyzed to estimate the temporal and spatial stress variations at shallow depths in the Longmenshan fault zone(LMSF),prior to and following the 2008 Wenchuan earthquake(WCEQ).Analysis of the stress field related to fault strength and behavior is useful for understanding geodynamic processes and conducting hazard assessments.The shallow stress changes after the WCEQ show clear along-strike variations.Degrees of stress orientation rotations have a negative correlation with the horizontal principal stress ratios and the WCEQ apparently reduced the magnitude difference between horizontal principal stresses.Taking stress magnitudes and orientation distribution relative to the fault strike into account,we propose an intermediate-strength of LMSF,with a friction coefficient generally constrained between 0.35 and 0.6.In addition,high-pressure fluids in the fault zone reduce the effective normal stress and to a certain degree weaken the fault strength.The accumulated stress over a certain period following release of the WCEQ indicates the start of another earthquake cycle.The changing crustal stress field makes the LMSF stable or slipping optimally during geodynamic processes.The segmentation feature of the shallow crustal stress field in the LMSF may imply a different tectonic loading and seismic release processes along the fault.The southwestern section to the epicenter of the WCEQ favors the occurrence of future earthquakes,as highμm in a state of critical failure was present in this area,which indicates that the Wenchuan and Lushan earthquakes did not release the accumulated stress to a sufficient extent there.

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems （GVVTIP） are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and general- ized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP axe established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.

MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR MAGNETOELECTROELASTIC BODIES AND STATE-VECTOR EQUATION

Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.

Two properties of sequence of vector measures on effect algebras

Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.

Monitoring models for base flow effect and daily variation of dam seepage elements considering time lag effect

Affected by external environmental factors and evolution of dam performance, dam seepage behavior shows nonlinear time-varying characteristics. In this study, to predict and evaluate the long-term development trend and short-term fluctuation of the dam seepage behavior, two monitoring models were developed, one for the base flow effect and one for daily variation of dam seepage elements. In the first model, to avoid the influence of the time lag effect on the evaluation of seepage variation with the time effect component of seepage elements, the base values of the seepage element and the reservoir water level were extracted using the wavelet multi-resolution analysis method, and the time effect component was separated by the established base flow effect monitoring model. For the development of the daily variation monitoring model for dam seepage elements, all the previous factors, of which the measured time series prior to the dam seepage element monitoring time may have certain influence on the monitored results, were considered. Those factors that were positively correlated with the analyzed seepage element were initially considered to be the support vector machine(SVM) model input factors, and then the SVM kernel function-based sensitivity analysis was performed to optimize the input factor set and establish the optimized daily variation SVM model. The efficiency and rationality of the two models were verified by case studies of the water level of two piezometric tubes buried under the slope of a concrete gravity dam.Sensitivity analysis of the optimized SVM model shows that the influences of the daily variation of the upstream reservoir water level and rainfall on the daily variation of piezometric tube water level are processes subject to normal distribution.

CHARACTERISTICS OF Sq VARIATION OF GEOMAGNETIC FIELD AT THE GREAT WALL STATION, ANTARCTICA IN WINTER

In this paper the characteristics of Sq variation of geomagnetic field in the region of the Chinese Great Wall Station (CGWS), Antarctica, in winter are analyzed from geomagnetic data obtained at the Geomagnetic Observatory of CGWS. The result enables us to reveal the following aspects: (1) The pattern of Sq variation at CGWS in early (Apr.) and Late winter (Sep.) is similar to that at Beijing Geomagnetic Observatory (BJO) at the middle latitude in the Northern Hemisphere. It may be controlled by the midlatitudinal ionospheric dynamo current. Amplitude of Sq variation is very small, and the harmonics in 8 hours or shorter periods in midwinter (June and July) is predominant because of the decreased effect of solar ultraviolet radiation and the dominant geomagnetic disturbance at high latitudes. (2) The vectors of Sq-equivalent current in the daytime are about five times more than that in the night. The direction of the vectors is clockwise in the daytime (08-15h) and counterclockwise in the night in early and late winter. Both of the vectors are very small because of the effect of the current density in the ionosphere is relatively weak in midwinter. The direction of vectors of Sq-equivalent current at CGWS in early and late winter is different from that in midwinter. It may be affected by the ionospheric current and field-aligned current in the polar region.

ITERATIVE ALGORITHMS FOR SYSTEM OF VARIATIONAL INCLUSIONS IN HADAMARD MANIFOLDS

In this paper,we consider system of variational inclusions and its several spacial cases,namely,alternating point problems,system of variational inequalities,etc.,in the setting of Hadamard manifolds.We propose an iterative algorithm for solving system of variational inclusions and study its convergence analysis.Several special cases of the proposed algorithm and convergence result are also presented.We present application to constraints minimization problems for bifunctions in the setting of Hadamard manifolds.At the end,we illustrate proposed algorithms and convergence analysis by a numerical example.The algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to Hadamard manifolds.

SNP site-drug association prediction algorithm based on denoising variational auto-encoder

Single nucletide polymorphism(SNP)is an important factor for the study of genetic variation in human families and animal and plant strains.Therefore,it is widely used in the study of population genetics and disease related gene.In pharmacogenomics research,identifying the association between SNP site and drug is the key to clinical precision medication,therefore,a predictive model of SNP site and drug association based on denoising variational auto-encoder(DVAE-SVM)is proposed.Firstly,k-mer algorithm is used to construct the initial SNP site feature vector,meanwhile,MACCS molecular fingerprint is introduced to generate the feature vector of the drug module.Then,we use the DVAE to extract the effective features of the initial feature vector of the SNP site.Finally,the effective feature vector of the SNP site and the feature vector of the drug module are fused input to the support vector machines(SVM)to predict the relationship of SNP site and drug module.The results of five-fold cross-validation experiments indicate that the proposed algorithm performs better than random forest(RF)and logistic regression(LR)classification.Further experiments show that compared with the feature extraction algorithms of principal component analysis(PCA),denoising auto-encoder(DAE)and variational auto-encode(VAE),the proposed algorithm has better prediction results.

Study of marine geomagnetic diurnal variation correction based on Wavelet Transform

Based on the existing geomagnetic diurnal variation theory and correction method,this paper makes a comprehensive analysis of the international geomagnetic quiet diurnal variation by Fourier Transform and one-dimensional Continuous Wavelet Transform.The frequency band greater than 0.2 Hz is the embodiment of the geomagnetic disturbance field in the frequency domain.Discrete Wavelet Transform is used to separate the variation,thus improving accuracy of the existing geomagnetic diurnal variation correction method.According to the characteristics of variation and Discrete Wavelet Decomposition,Sym8 wavelet is selected as the basic wavelet to decompose the data at 7 layers.The long-term and short-term variation of geomagnetic diurnal variation are effectively separated from the geomagnetic disturbance part under the condition of ensuring the fidelity.Compared with the results of Fourier Series decomposition and low-pass filter,the processing effect of Discrete Wavelet Transform is better.The effective separation and correction of short-term,long-term variation and geomagnetic disturbances can improve the quality of diurnal variation correction in marine geomagnetic measurement,reduce the error accumulation in the process of marine geomagnetic data processing,and improve the scientificity and accuracy of the current diurnal variation correction methods.

Effects of seasonal air temperature variation on airflow and surrounding rock temperature of mines

In underground mines, high air temperatures in the summer months lead to an increase in inlet airflow temperatures. This leads to seasonal thermal pollution in the mines. This paper examines the dynamics and effects of seasonal variation in surface air temperatures and surrounding rock temperatures in deep coal mines. It also examines temperature variations in the main ventilation circuit, working face, and surrounding rock. The study results revealed that airflow temperatures were significantly affected by seasonal air temperature variations. The greater the distance was between the inlet and the wellhead of the ventilation shaft, the less the effect was on temperature. Moreover, slight temperature variations (1.0-3.0 ℃) were observed between various points on the return route during the summer months. Airflow temperatures along the airflow inlet to the return route of the working face first decreased, but then increased. The temperature field of the surrounding rock increased gradually with increased distance between the mine roadway and inlet, with recorded rock temperatures as high as 40.53 ℃. The radius of the heat-adjusting layer was between 28 and 33 m.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes

Let be a fuzzy stochastic process and be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by for each by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind of integral is also measurable, continuous in time t and bounded a.s. under the Hausdorff metric.

Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in t under the Hausdorff metric and L2-bounded.

On Generalized Multivalued Random Variational-Like Inclusions

In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.

Generalized Quasi Variational-Type Inequalities

In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.