Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Butterfly taxonomic and functional diversity in the urban green spaces of Hefei city

Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.

Gamma Approximation Based Multi-Antenna Covert Communication Detection

Covert communication technology makes wireless communication more secure,but it also provides more opportunities for illegal users to transmit harmful information.In order to detect the illegal covert communication of the lawbreakers in real time for subsequent processing,this paper proposes a Gamma approximation-based detection method for multi-antenna covert communication systems.Specifically,the Gamma approximation property is used to calculate the miss detection rate and false alarm rate of the monitor firstly.Then the optimization problem to minimize the sum of the missed detection rate and the false alarm rate is proposed.The optimal detection threshold and the minimum error detection probability are solved according to the properties of the Lambert W function.Finally,simulation results are given to demonstrate the effectiveness of the proposed method.

Integrity and Size of Green Spaces Are Critical for the Functional Di-versity of Birds:Evidence from the Eastern and Northwestern Regions of China

Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and func-tional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern re-gion but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant posit-ive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that pre-serving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.

Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

QSPR modeling of azeotropic temperatures and compositions for binary azeotropes containing lower alcohols using a genetic function approximation

Binary azeotropes, which contain two chemicals with a relative volatility of 1, are very common in the chemical industry. Understanding azeotropes is essential for effectively separating binary azeotropes containing lower alcohols. Experimental techniques and ab initio approaches can produce accurate results;however, these two processes are time consuming and labor intensive. Although thermodynamic equations such as UNIFAC are widely used, experimental values are required, and it is difficult to choose the best groups to represent a complex system. Because of their high efficiency and fast calculation speed, quantitative structure–property relationship(QSPR) tools were used in this work to predict the azeotropic temperatures and compositions of binary azeotropes containing lower alcohols. The QSPR models for 64 binary azeotropes based on centroid approximation and weighted-contribution-factor approximation were established using the genetic function approximation(GFA) procedure in Materials Studio software, and a leave-one-out cross-validation procedure was conducted.External tests of an additional 16 azeotropes were also investigated, and high determination coefficient values were obtained. The best QSPR models were explained in terms of the molecular structure of the azeotropes,and good predictive ability was obtained within acceptable prediction error levels.

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.

APPROXIMATION ANALYSES FOR FUZZY VALUED FUNCTIONS IN L_1(μ)-NORM BY REGULAR FUZZY NEURAL NETWORKS

By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.

Weighted approximation of functions with singularities by Bernstein operators

As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.

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.

Constructive Approximation by Superposition of Sigmoidal Functions

In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.

约束Green函数与非线性地基梁模态分析

在生物和医学领域,微机电系统(MEMS)中的微梁结构在植入人体的使用时,由于体内的细胞环境类似于水凝胶,在这种环境下工作,设备和仪器的精度和稳定性很大程度上受到细胞弹性的影响.为了分析此类地基梁的动力学问题,本文建立了非线性基础上的梁振动模型,研究了任意位置弹簧和非线性弹簧基础上的梁模态.通过Laplace变换和线性叠加原理,得到了一种约束Green函数,利用数值计算验证方案的有效性,并研究了各种重要物理参数的影响,发现弹簧位置向跨中移动时,模态对称性被打破,弹簧刚度增加,模态阶数改变.

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

The Approximation of the Exponential Weibull Renewal Function

The analytical renewal function(RF) is not tractable of the exponential Weibull(EW) distribution. In the proposed model, the n-fold convolution of the EW cumulative distribution function(CDF) is approximated by a n-fold convolutions of Gamma and normal CDFs. We obtain the EW RF by a series approximation model. The method is very simple in the computation. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via some numerical experiments.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.