A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

On Bounded Variation Functions by General MKZD Operators

In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.

Electromagnetic response function for the semi-annual variations estimated by the single-station method using the night-time values of the geomagnetic fields

The geomagnetic night-time values were used to estimate the electromagnetic response function Q1 for half-year period. If the spatial structure of the source field can be described by the approximation, one can estimate the Q1 value using the single-station Z/H method. This technique enables us to carry out regional deep gcomagnetic sounding by the method. The data used for analyses are geomagnetic night-time values for about, typically, 26 years from 5 good-quality stations and for several years from 34 stations distributed over the globe. The results indicate that the night-time values yield more reliable response estimates for half-year period compared to the usual estimates obtained from daily means. It implies that the approximation for the night-time fields holds good for the half-year period, but the daily means are not suitable for estimating the response function of the semi-annual variations by using the single-station method. Source field analyses for daily means data and night-time means data have also been carried out in this paper.

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.

MNTZ RATIONAL APPROXIMATION FOR SPECIAL FUNCTION CLASSES IN Ba[0,1] SPACES

In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.

HYBRID FEM WITH FUNDAMENTAL SOLUTIONS AS TRIAL FUNCTIONS FOR HEAT CONDUCTION SIMULATION

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.

INFINITELY MANY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH STRONGLY INDEFINITE VARIATIONAL STRUCTURE

Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.

Analysis of the Lost Circulation Problem

The well-known“lost circulation”problem refers to the uncontrolled flow of whole mud into a formation.In order to address the problem related to the paucity of available data,in the present study,a model is introduced for the lost-circulation risk sample profile of a drilled well.The model is built taking into account effective data(the Block L).Then,using a three-dimensional geological modeling software,relying on the variation function and sequential Gaussian simulation method,a three-dimensional block lost-circulation risk model is introduced able to provide relevant information for regional analyses.

Identification of Functional Genetic Variations Underlying Drought Tolerance in Maize Using SNP Markers

Single nucleotide polymorphism （SNP） is a common form of genetic variation and popularly exists in maize genome. An Illumina GoldenGate assay with 1 536 SNP markers was used to genotype maize inbred lines and identified the functional genetic variations underlying drought tolerance by association analysis. Across 80 lines, 1 006 polymorphic SNPs （65.5% of the total） in the assay with good call quality were used to estimate the pattern of genetic diversity, population structure, and familial relatedness. The analysis showed the best number of fixed subgroups was six, which was consistent with their original sources and results using only simple sequence repeat markers. Pairwise linkage disequilibrium （LD） and association mapping with phenotypic traits investigated under water-stressed and well-watered regimes showed rapid LD decline within 100–500 kb along the physical distance of each chromosome, and that 29 SNPs were associated with at least two phenotypic traits in one or more environments, which were related to drought-tolerant or drought-responsive genes. These drought-tolerant SNPs could be converted into functional markers and then used for maize improvement by marker-assisted selection.

Species-specific traits determine shrub-annual interactions during a growing season

Stress gradient hypothesis predicted that facilitative interactions usually increase in intensity and are importance with abiotic stress.By contrast,facilitation may be lost in time,when it involves the growth of benefactors or beneficiaries.Less is known about which response pattern is more common in arid desert.We present an empirical study to explore shrub-annual interactions at the community and individual level along the course of a single growing season in a desert steppe in northwest China.Here the severity of drought stress may increase in time due to uneven precipitation during plant growing season.We assessed growth responses of annuals in understory where two dominant shrubs were removed.Annuals responses showed a switch from weakly positive to more strongly positive beneath Calligonum mongolicum,whereas from positive to negative beneath Nitraria sphaerocarpa during the growing season.Additionally,annual species with contrasting functional traits showed distinct growth responses to canopies removal.There was evidence of an increase in soil moisture below the canopy of shrubs,but a decrease in potential evaporation rate and photosynthetically active radiation,which can partly explain these species-specific responses.We conclude that the balance between competitive and facilitative effects in shrub-annual interactions is not only governed by the severity of stress but also determined by plant traits,such as canopy structure of shrubs and functional traits of their understory annuals.

EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.

Generalized stress field in granular soils heap with RayleigheRitz method

The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.

Research Progress of Genomic Variation in Psoriasis

As a typical representative of global complex diseases,psoriasis has attracted widespread attention because of its high heritability,heterogeneity,and incidence.Environmentally induced activation of the inflammatory-immune axis in patients with psoriasis relies on genetic regulation of genomic variation.The heritability of psoriasis exceeds 80%,and research of genomic variation in psoriasis is of great significance to the interpretation of the biological pathogenesis of the disease.The development of genome-wide association studies(GWASs)has provided a powerful means for the capture of psoriasis susceptibility genes.More than 100 psoriasis susceptibility loci have been captured,enabling humans to gain a breakthrough understanding of the genetics and traits of psoriasis.With the advancement of research methods,increasingly more genetic methodologies are being used to capture the locations and types of variants outside the scope of GWAS scanning,making up for the inclinations and deficiencies of traditional GWAS capture of gene loci in a more detailed manner.This review covers several decades of research on genomic variation in psoriasis,including GWASs in psoriasis,the capture of functional gene variant types,and the translation of genomic variation into precision medicine;summarizes the research progress of genomic variation in psoriasis;and provides a theoretical reference for future genetic-based research of the mechanisms underlying psoriasis.

Space-Time Chaos Filtering for the Incoherent Paradigm for 6G Wireless System Design from Theoretic Perspective

The following material is devoted to the generalization of the chaos modeling to random fields in communication channels and its application on the space-time filtering for the incoherent paradigm;that is the purpose of this research. The approach, presented hereafter, is based on the “Markovian” trend in modeling of random fields, and it is applied for the first time to the chaos field modeling through the well-known concept of the random “treatment” of deterministic dynamic systems, first presented by A. Kolmogorov, M. Born, etc. The material presents the generalized Stratonovich-Kushner Equations (SKE) for the optimum filtering of chaotic models of random fields and its simplified quasi-optimum solutions. In addition to this, the application of the multi-moment algorithms for quasi-optimum solutions is considered and, it is shown, that for scenarios, when the covariation interval of the input random field is less than the distance between the antenna elements, the gain of the space-time algorithms against their “time” analogies is significant. This is the general result presented in the following.

Elliptic Equations with Degenerate Coercivity： Gradient Regularity

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is$ - {\rm div}\left( {a\left( {x,u} \right)Du} \right) = f$ in $D^' \left( \Omega \right),\,\,f \in L^r \left( \Omega \right),\,\,r > 1$where for example, a(x,u)=(1+|u|)^m/ with / ] (0,1). We study the same problem for minima of functionals closely related to the previous equation.

Existence of Solutions for the Critical Elliptic System with Inverse Square Potentials

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s）. Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.

Wave Fans are Special

It is shown that self-similar BV solutions of genuinely nonlinear strictly hyperbolic systems of conservation laws are special functions of bounded variation, with vanishing Cantor part.