Kravchenko probabilityweight functions in problems of radar signals correlation processing

In this report the combined method of correlation radar signal(RS)processing based on the theory of atomic functions(AF)is examined.Examples of using of new Kravchenko probability weight functions(WF)designs are presented.Quality functional to estimate accuracy and efficiency of RS processing for concrete physical models is constructed.It is shown that the proposed approach significantly improves the quality of the coherent analysis of RS.

BUECKNER'S WORK CONJUGATE INTEGRALS AND WEIGHT FUNCTIONS FOR A CRACK IN ANISOTROPIC SOLIDS

The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.

WEIGHT FUNCTIONS FOR INTERFACE CRACKS IN DISSIMILAR ANISOTROPIC MATERIALS

Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.

Adaptive Grid Technique Based on the Variational Principle and Its Weight Functions

Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight func-tions only related to the gradient are unable to enhance the computational accuracy while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Com-pared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.

Temperature and Water Vapor Weighting Functions from Radiative Transfer Equation with Surface Emissivity and Solar Reflectivity

Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.

Commutators of Weighted Lipschitz Functions and Multilinear Singular Integrals with Non-Smooth Kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

Structural failure analysis with CMS-based ground motion selection using innovative cost function and weight factors

The selection and scaling of ground motion records is considered a primary and essential task in performing structural analysis and design.Conventional methods involve using ground motion models and a conditional spectrum to select ground motion records based on the target spectrum.This research demonstrates the influence of adopting different weighted factors for various period ranges during matching selected ground motions with the target hazard spectrum.The event data from the Next Generation Attenuation West 2(NGA-West 2)database is used as the basis for ground motion selection,and hazard de-aggregation is conducted to estimate the event parameters of interest,which are then used to construct the target intensity measure(IM).The target IMs are then used to select ground motion records with different weighted vector-valued objective functions.The weights are altered to account for the relative importance of IM in accordance with the structural analysis application of steel moment resisting frame(SMRF)buildings.Instead of an ordinary objective function for the matching spectrum,a novel model is introduced and compared with the conventional cost function.The results indicate that when applying the new cost function for ground motion selection,it places higher demands on structures compared to the conventional cost function.Moreover,submitting more weights to the first-mode period of structures increases engineering demand parameters.Findings demonstrate that weight factors allocated to different period ranges can successfully account for period elongation and higher mode effects.

An Improved Solov2 Based on Attention Mechanism and Weighted Loss Function for Electrical Equipment Instance Segmentation

The current existing problem of deep learning framework for the detection and segmentation of electrical equipment is dominantly related to low precision.Because of the reliable,safe and easy-to-operate technology provided by deep learning-based video surveillance for unmanned inspection of electrical equipment,this paper uses the bottleneck attention module(BAM)attention mechanism to improve the Solov2 model and proposes a new electrical equipment segmentation mode.Firstly,the BAM attention mechanism is integrated into the feature extraction network to adaptively learn the correlation between feature channels,thereby improving the expression ability of the feature map;secondly,the weighted sum of CrossEntropy Loss and Dice loss is designed as the mask loss to improve the segmentation accuracy and robustness of the model;finally,the non-maximal suppression(NMS)algorithm to better handle the overlap problem in instance segmentation.Experimental results show that the proposed method achieves an average segmentation accuracy of mAP of 80.4% on three types of electrical equipment datasets,including transformers,insulators and voltage transformers,which improve the detection accuracy by more than 5.7% compared with the original Solov2 model.The segmentation model proposed can provide a focusing technical means for the intelligent management of power systems.

Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function

This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).

Prediction of Subcellular Localization of Eukaryotic Proteins Using Position-Specific Profiles and Neural Network with Weighted Inputs

Subcellular location is one of the key biological characteristics of proteins. Position-specific profiles （PSP） have been introduced as important characteristics of proteins in this article. In this study, to obtain position-specific profiles, the Position Specific lterative-Basic Local Alignment Search Tool （PSI-BLAST） has been used to search for protein sequences in a database. Position-specific scoring matrices are extracted from the profiles as one class of characteristics. Four-part amino acid compositions and lst-7th order dipeptide compositions have also been calculated as the other two classes of characteristics. Therefore, twelve characteristic vectors are extracted from each of the protein sequences. Next, the characteristic vectors are weighed by a simple weighing function and inputted into a BP neural network predictor named PSP-Weighted Neural Network （PSP-WNN）. The Levenberg-Marquardt algorithm is employed to adjust the weight matrices and thresholds during the network training instead of the error back propagation algorithm. With a jackknife test on the RH2427 dataset, PSP-WNN has achieved a higher overall prediction accuracy of 88.4% rather than the prediction results by the general BP neural network, Markov model, and fuzzy k-nearest neighbors algorithm on this dataset. In addition, the prediction performance of PSP-WNN has been evaluated with a five-fold cross validation test on the PK7579 dataset and the prediction results have been consistently better than those of the previous method on the basis of several support vector machines, using compositions of both amino acids and amino acid pairs. These results indicate that PSP-WNN is a powerful tool for subcellular localization prediction. At the end of the article, influences on prediction accuracy using different weighting proportions among three characteristic vector categories have been discussed. An appropriate proportion is considered by increasing the prediction accuracy.

Weighted ebyev-Ostrowski type inequalities

In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

CLOSED-FORM WEIGHT FUNCTION FOR EDGE CRACK PROBLEMS

An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency.Examples have been given for problems of edge crack(s)with a number of typical load conditions for illustration.

Method for obtaining high-resolution velocity spectrum based on weighted similarity

Seismic wave velocity is one of the most important processing parameters of seismic data,which also determines the accuracy of imaging.The conventional method of velocity analysis involves scanning through a series of equal intervals of velocity,producing the velocity spectrum by superposing energy or similarity coefficients.In this method,however,the sensitivity of the semblance spectrum to change of velocity is weak,so the resolution is poor.In this paper,to solve the above deficiencies of conventional velocity analysis,a method for obtaining a high-resolution velocity spectrum based on weighted similarity is proposed.By introducing two weighting functions,the resolution of the similarity spectrum in time and velocity is improved.Numerical examples and real seismic data indicate that the proposed method provides a velocity spectrum with higher resolution than conventional methods and can separate cross reflectors which are aliased in conventional semblance spectrums;at the same time,the method shows good noise-resistibility.

APPLICATION OF WAVELET THEORY IN RESEARCHON WEIGHT FUNCTION OF MESHLESS METHOD

Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.

WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES

We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.

V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.