Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

The organic geochemistry of crude oil in the Saltpond Basin(Ghana):Organic source input,depositional environment,and thermal maturity

The Saltpond Basin,situated within the South Atlantic margin of Ghana,is a significant area for petro-leum exploration but has received relatively limited research attention.Previous studies have examined source rock com-position,but data on crude oil organic chemistry are lack-ing,hindering understanding of the basin’s petroleum system and evolution.To address this gap,we analyzed biomarkers and stable carbon-isotope ratios in Saltpond Basin crude oil using gas chromatography–mass spectrometry and gas chromatography–isotope ratio mass spectrometry to eluci-date organic matter source,depositional environment,and thermal maturity.Findings were compared with oils from the West African segment of the South Atlantic margin,namely the Tano Basin and the Niger Delta Basin,to iden-tify potential correlations and gain insights into regional variations.Molecular and isotopic results unveiled a sig-nificant prevalence of organic matter derived from lower marine organisms.Patterns of organic matter deposition and preservation in Saltpond oil samples suggested a suboxic marine transitional environment,contradicting conventional understanding of terrestrial dominance in such settings.Moreover,the potential for degradation processes to obscure differentiation between terrestrial and marine organic mat-ter origins underscores the complex nature of organic mat-ter dynamics in transitional marine environments.Analysis of molecular thermal maturity indices suggested Saltpond oils were expelled from source rocks exhibiting thermal maturity at the early maturity stage.Correlation analysis unveiled genetic disparities among crude oils sourced from the Saltpond Basin and those from the Tano and Niger Delta Basin,primarily due to variations in source input and depo-sitional environment conditions.Saltpond oil exhibits lower terrestrial organic input than Tano Basin’s crude oils,which also have less terrestrial input than Niger Delta Basin crude oils.Additionally,its paleodepositional environment nota-bly differs from oils in the Tano Basin(anoxic transitional marine-lacustrine settings)and the Niger Delta Basin(sub-oxic–oxic terrigenous deltaic or marine or lacustrine envi-ronments).Thermal maturity range of Saltpond oil is com-parable to oils in the Tano Basin but lower than oils in the Niger Delta Basin.Thesefindings provide valuable insights into petroleum generation history and unique organic geo-chemical characteristics within the Saltpond Basin,essen-tial for exploration,production,and environmental manage-ment efforts in the region.Furthermore,correlation studies provide evidence that distinct biological,geological,and paleoenvironmental conditions shaped various oil types in the West African segment of the South Atlantic margin.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

Detecting the core of a network by the centralities of the nodes

Many networks exhibit the core/periphery structure.Core/periphery structure is a type of meso-scale structure that consists of densely connected core nodes and sparsely connected peripheral nodes.Core nodes tend to be well-connected,both among themselves and to peripheral nodes,which tend not to be well-connected to other nodes.In this brief report,we propose a new method to detect the core of a network by the centrality of each node.It is discovered that such nodes with non-negative centralities often consist in the core of the networks.The simulation is carried out on different real networks.The results are checked by the objective function.The checked results may show the effectiveness of the simulation results by the centralities of the nodes on the real networks.Furthermore,we discuss the characters of networks with the single core/periphery structure and point out the scope of the application of our method at the end of this paper.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Study on the effective elastic performance of composites containing decagonal symmetric two-dimensional quasicrystal coatings

On account of the Mori-Tanaka approach,the effective elastic performance of composites containing decagonal symmetric two-dimensional(2D)quasicrystal(QC)coatings is studied.Explicit expressions for the effective elastic constants of rare-earth QC reinforced magnesium-based composites are provided.Detailed discussion is presented on the effects of the volume fraction of the inclusions,the aspect ratio of the inclusions,the coating thickness,and the coating material parameters on the effective elastic constants of the composites.The results indicate that considering the coating increases the effective elastic constants of the composites to some extent.

Analysis of optical axis deviation caused by structural stiffness in equatorial telescopes

The impact of structural stiffness on optical axis deviation poses a significant challenge in the design of equatorial telescope structures.A comprehensive analysis during the design process can reduce the reliance of a telescope on advanced control technologies,thereby improving its economic feasibility.Although full-system finite element analyses are reliable,they are encumbered by significant time requirements and limitations in covering all possible telescope orientations.Therefore,we propose an efficient and comprehensive analytical method to evaluate the optical axis deviation of equatorial telescopes across a full range of angles.To address the challenge of ensuring that the analysis covers all possible positions of an equatorial telescope,based on a model from SiTian project,we analyze the optical axis deviations caused by the fork arm at 25 different angles and then use fitting methods to obtain results for all angles.Based on the analysis results of the optical axis deviation caused by the stiffness of the optical tube in the horizontal position,we derive the results for the tube at any position using geometric relationships.Finally,we calculate the coupling factors and combine these impacts.Furthermore,we identify six discrete feature points to reflect possible telescope orientations and conduct comprehensive finite element analyses.The results are in alignment with those acquired through a comprehensive computational approach.

Joint Predictive Control of Power and Rate for Wireless Networks

为了在分布式的无线网络，预兆的力量和率控制计划减轻循环延期，为系统模型被建议也说明拥挤层次和输入延期而不是在一个网络推迟状态。有输入延期的一个测量反馈控制问题被最小化之间的差别的精力提出实际并且控制的需要的 signal-to-interference-plus-noise 比率(SNR ) 层次，以及精力定序。解决这个问题，我们在场为控制的二个 Riccati 方程和在时间的评价推迟系统。一个完全的分析最佳的控制器被使用分离原则并且解决二个 Riccati 方程获得，在一个人是为随机的线性二次的规定的向后的方程，其它是标准过滤 Riccati 方程的地方。模拟结果说明建议力量和率控制计划的表演。

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.

F-generation law and recognition of system law

If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.

Vertex-distinguishing VE-total Colorings of Cycles and Complete Graphs

Let G be a simple graph of order at least 2.A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints.Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u.If C(u)=C(v) for any two vertices u and v of V (G),then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short.The minimum number of colors required for a VDVET coloring of G is denoted by χ ve vt (G) and it is called the VDVET chromatic number of G.In this paper we get cycle C n,path P n and complete graph K n of their VDVET chromatic numbers and propose a related conjecture.

Conservation Laws and Symmetries of the Levi Equation

The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.

The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order

In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.

THE BOREL DIRECTIONS OF ALGEBROIDAL FUNCTION AND ITS COEFFICIENT FUNCTIONS

In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

Reduction and New Explicit Solutions of （2＋1）-Dimensional Breaking Soliton Equation

Abstract By applying the Lie group method, the （2＋l）-dimensional soliton equation is reduced to some （1＋1）-dimensional nonlinear equations. Based upon some new explicit solutions of the （2＋1）-dimensional breaking soliton equation are obtained.

Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials

This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition.A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is proposed.In the statistical multiscale formulations,a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations,which are our main contributions.Besides,a numerical algorithm based on the statistical multiscale method is given in details.Numerical results prove the accuracy and efficiency of our method for multiscale simulation of transient nonlinear conduction and radiation heat transfer problem in random porous materials.

THE METRIC GENERALIZED INVERSE AND ITS SINGLE-VALUE SELECTION IN THE PRICING OF CONTINGENT CLAIMS IN AN INCOMPLETE FINANCIAL MARKET

This article continues to study the research suggestions in depth made by M.Z.Nashed and G.F.Votruba in the journal"Bull.Amer.Math.Soc."in 1974.Concerned with the pricing of non-reachable"contingent claims"in an incomplete financial market,when constructing a specific bounded linear operator A:l_(1)^(n)→l_(2) from a non-reflexive Banach space l_(1)^(n) to a Hilbert space l_(2),the problem of non-reachable"contingent claims"pricing is reduced to researching the(single-valued)selection of the(set-valued)metric generalized inverse A■ of the operator A.In this paper,by using the Banach space structure theory and the generalized inverse method of operators,we obtain a bounded linear single-valued selection A^(σ)=A+of A■.