Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weigh...Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weight, can be folded,twisted, flipped inside-out, or be pasted onto other surfaces of arbitrary shapes. In this paper, an analytical model is presented to study the mechanics of laminated hard-soft structures in flexible electronics under a stickup state. Thirdorder polynomials are used to describe the displacement field,and the principle of virtual work is adopted to derive the governing equations and boundary conditions. The normal strain and the shear stress along the thickness direction in the bimaterial region are obtained analytically, which agree well with the results from finite element analysis. The analytical model can be used to analyze stickup state laminated structures, and can serve as a valuable reference for the failure prediction and optimal design of flexible electronics in the future.展开更多
The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,ratio...The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.展开更多
Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation re...Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation remains a challenge.For example,theoretical research on bistable beams in existing energy-consuming materials has focused mainly on the deformation process of the second-order mode.To address this challenge,the present work establishes an analytical model for the deformation process of a bistable beam from the first-order mode to the third-order mode via the elliptic integral method.Additionally,judgment conditions for identifying the critical points of modal transitions are provided.Second,the analytical model allows for the calculation of the maximum instability force and the unstable equilibrium position when third-order mode deformation occurs in the bistable beam during the snap-through process.The unstable equilibrium position of the bistable beam during third-order mode deformation is significantly lower than the positions of the two fixed ends.The validity of the analytical model was confirmed through experiments and finite element modeling.In the compression experiments of bistable beams with identical dimensional parameters presented in the present work,the work done by the external force during the third-order mode deformation process is 2 times that of the second-order mode deformation process.This will provide a completely new approach for the design of energy-consuming materials based on bistable beams.展开更多
In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in ...In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.展开更多
This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We re...This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We report some novel RW patterns,including nonmultiple root(NMR)-type patterns with distinct shapes such as semicircular sector,acute sector,pseudo-hexagram,and pseudo-rhombus shapes,as well as multiple root(MR)-type patterns characterized by right double-arrow and right arrow shapes.We demonstrate that these RW patterns are intrinsically related to the root structures of a novel class of polynomials,termed generalized mixed Adler-Moser(GMAM)polynomials,which feature multiple arbitrary free parameters.The RW patterns can be interpreted as straightforward expansions and slight shifts of the root structures for the GMAM polynomials to some extent.In the(x,t)-plane,they asymptotically converge to a first-order RW at the location corresponding to each simple root of the polynomials and to a lower-order RW at the location associated with each multiple root.Notably,the position of the lower-order RW within these patterns can be flexibly adjusted to any desired location in the(x,t)-plane by tuning the free parameters of the corresponding GMAM polynomials.展开更多
Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three d...Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin...In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin films of the ionic COF material PySQ-iCOF was successfully fabricated using a solid-liquid interface method,meanwhile the building units extracted to be independent small molecule,1-PySA,were synthesized for comparative studies.Compared to 1-PySA,PySQ-iCOF possesses not only a larger conjugated system but also exhibits enhanced polarization and charge transfer capabilities.The NLO properties of PySQ-iCOF and the small molecule 1-PySA were investigated using Z-scan technique at a wavelength of 532 nm,revealing the PySQ-iCOF thin film exhibits outstanding NLO performance.Specifically,it demonstrates saturable absorption under nanosecond(ns)pulse laser irradiation(β=9.59×10^(-6) m/W),while exhibiting reverse saturable absorption under femtosecond(fs)pulse conditions(β=6.91×10^(-8) m/W).Furthermore,the PySQ-iCOF film exhibits strong negative refractive nonlinearity,−6×10^(-12) m^(2)/W for ns and -3.8×10^(-13) m^(2)/W for fs,respectively.Transient absorption spectroscopy studies indicate that the pulse-width-dependent nonlinear absorption char-acteristics of the PySQ-iCOF film originate from the generation of triplet excited states.Both nonlinear absorption coefficient and nonlinear refractive index of the PySQ-iCOF film surpass those of most reported organic materials measured under comparable conditions,which provides huge potential in all-optical manipulating and switching at the nanoscale as outstanding NLO materials.展开更多
<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style...<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> boundary value problems. </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Third-order</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor </span><span style="font-family:Verdana;">theory, Newtonian fluid mechanics, optimal control, convection</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">diffusion</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> partial differential equation to a first</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">order ordinary differential </span><span style="font-family:Verdana;">equation. Truncation errors are given. The unconditional stability of the method</span> <span style="font-family:Verdana;">is analysed by the Von-Neumann stability analysis. The developed method is </span><span style="font-family:Verdana;">tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and </span><span style="font-family:Verdana;">feasibility of </span><span style="font-family:Verdana;">the presented method. Furthermore, </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">graphical comparison between analyt</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ical and approximate solution</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> is also shown for the illustrated example.</span></span></span>展开更多
The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while ther...The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all...Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.展开更多
Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient esti...Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient estimates for the polynomials with positive real part in the unit disk are established in this paper.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f（z）f（z ...We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f（z）f（z ＋ c）.展开更多
Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z...Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z）｜≤1/2{（｜R^n＋β（R＋1/2）^n｜＋｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜ -（｜R^n＋β（R＋1/2）^n｜-｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜}.In this paper we generalize the above inequality for polynomials having no zeros in }z} 〈 k, k ≤ 1. Our results generalize certain well-known polynomial inequalities.展开更多
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential p...We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.展开更多
This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists ...This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients展开更多
In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are of...In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11572022 and 11172022)
文摘Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weight, can be folded,twisted, flipped inside-out, or be pasted onto other surfaces of arbitrary shapes. In this paper, an analytical model is presented to study the mechanics of laminated hard-soft structures in flexible electronics under a stickup state. Thirdorder polynomials are used to describe the displacement field,and the principle of virtual work is adopted to derive the governing equations and boundary conditions. The normal strain and the shear stress along the thickness direction in the bimaterial region are obtained analytically, which agree well with the results from finite element analysis. The analytical model can be used to analyze stickup state laminated structures, and can serve as a valuable reference for the failure prediction and optimal design of flexible electronics in the future.
基金Project supported by the National Natural Science Foundation of China(Grant No.12201329)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY24A010002)the Natural Science Foundation of Ningbo(Grant No.2023J126)。
文摘The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.
基金supported by the Guangdong Province Basic and Applied Basic Research Fund(Grant No.2025A1515011975)the research project of Guangdong University of Technology(Grant No.2023SDKYA010)for their funding.
文摘Bistable beams,with their characteristic recoverable elastic large deformations,are widely utilized in reversible deformation designs.However,analytical modeling of bistable beams under third-order mode deformation remains a challenge.For example,theoretical research on bistable beams in existing energy-consuming materials has focused mainly on the deformation process of the second-order mode.To address this challenge,the present work establishes an analytical model for the deformation process of a bistable beam from the first-order mode to the third-order mode via the elliptic integral method.Additionally,judgment conditions for identifying the critical points of modal transitions are provided.Second,the analytical model allows for the calculation of the maximum instability force and the unstable equilibrium position when third-order mode deformation occurs in the bistable beam during the snap-through process.The unstable equilibrium position of the bistable beam during third-order mode deformation is significantly lower than the positions of the two fixed ends.The validity of the analytical model was confirmed through experiments and finite element modeling.In the compression experiments of bistable beams with identical dimensional parameters presented in the present work,the work done by the external force during the third-order mode deformation process is 2 times that of the second-order mode deformation process.This will provide a completely new approach for the design of energy-consuming materials based on bistable beams.
基金supported by the National Natural Science Foundation of China(No.12271527)。
文摘In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.
基金supported by the NSFC(12471236)the Guangzhou Municipal Science and Technology Project(Guangzhou Science and Technology Plan,No.2024A04J6245)Guangdong Natural Science Foundation(2025A1515011868)。
文摘This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We report some novel RW patterns,including nonmultiple root(NMR)-type patterns with distinct shapes such as semicircular sector,acute sector,pseudo-hexagram,and pseudo-rhombus shapes,as well as multiple root(MR)-type patterns characterized by right double-arrow and right arrow shapes.We demonstrate that these RW patterns are intrinsically related to the root structures of a novel class of polynomials,termed generalized mixed Adler-Moser(GMAM)polynomials,which feature multiple arbitrary free parameters.The RW patterns can be interpreted as straightforward expansions and slight shifts of the root structures for the GMAM polynomials to some extent.In the(x,t)-plane,they asymptotically converge to a first-order RW at the location corresponding to each simple root of the polynomials and to a lower-order RW at the location associated with each multiple root.Notably,the position of the lower-order RW within these patterns can be flexibly adjusted to any desired location in the(x,t)-plane by tuning the free parameters of the corresponding GMAM polynomials.
基金Supported by the National Natural Science Foundation of China (Grant No.12161074)the Talent Introduction Research Foundation of Suqian University (Grant No.106-CK00042/028)+1 种基金Suqian Sci&Tech Program (Grant No.M202206)Sponsored by Qing Lan Project of Jiangsu Province and Suqian Talent Xiongying Plan of Suqian。
文摘Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.
基金the National Natural Science Foundation of China(22171076)Jing Li at the Technical Institute of Physics and Chemistry,Chinese Academy of Sciences(CAS),for his measurement of dynamic processes.
文摘In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin films of the ionic COF material PySQ-iCOF was successfully fabricated using a solid-liquid interface method,meanwhile the building units extracted to be independent small molecule,1-PySA,were synthesized for comparative studies.Compared to 1-PySA,PySQ-iCOF possesses not only a larger conjugated system but also exhibits enhanced polarization and charge transfer capabilities.The NLO properties of PySQ-iCOF and the small molecule 1-PySA were investigated using Z-scan technique at a wavelength of 532 nm,revealing the PySQ-iCOF thin film exhibits outstanding NLO performance.Specifically,it demonstrates saturable absorption under nanosecond(ns)pulse laser irradiation(β=9.59×10^(-6) m/W),while exhibiting reverse saturable absorption under femtosecond(fs)pulse conditions(β=6.91×10^(-8) m/W).Furthermore,the PySQ-iCOF film exhibits strong negative refractive nonlinearity,−6×10^(-12) m^(2)/W for ns and -3.8×10^(-13) m^(2)/W for fs,respectively.Transient absorption spectroscopy studies indicate that the pulse-width-dependent nonlinear absorption char-acteristics of the PySQ-iCOF film originate from the generation of triplet excited states.Both nonlinear absorption coefficient and nonlinear refractive index of the PySQ-iCOF film surpass those of most reported organic materials measured under comparable conditions,which provides huge potential in all-optical manipulating and switching at the nanoscale as outstanding NLO materials.
文摘<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> boundary value problems. </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Third-order</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor </span><span style="font-family:Verdana;">theory, Newtonian fluid mechanics, optimal control, convection</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">diffusion</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> partial differential equation to a first</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">order ordinary differential </span><span style="font-family:Verdana;">equation. Truncation errors are given. The unconditional stability of the method</span> <span style="font-family:Verdana;">is analysed by the Von-Neumann stability analysis. The developed method is </span><span style="font-family:Verdana;">tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and </span><span style="font-family:Verdana;">feasibility of </span><span style="font-family:Verdana;">the presented method. Furthermore, </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">graphical comparison between analyt</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ical and approximate solution</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> is also shown for the illustrated example.</span></span></span>
基金the UGC,New Delhi,India for financial assistance via the UGC-Junior Research Fellowship(CSIR-UGC NET JULY 2024)(Student ID:241610090610)。
文摘The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
文摘Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.
文摘Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient estimates for the polynomials with positive real part in the unit disk are established in this paper.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金supported by the National Natural Science Foundation of China (10871076)
文摘We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f（z）f（z ＋ c）.
文摘Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z）｜≤1/2{（｜R^n＋β（R＋1/2）^n｜＋｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜ -（｜R^n＋β（R＋1/2）^n｜-｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜}.In this paper we generalize the above inequality for polynomials having no zeros in }z} 〈 k, k ≤ 1. Our results generalize certain well-known polynomial inequalities.
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
基金supported by the NSFC(11026110,11101201)the NSF of Jiangxi(2010GQS0144)
文摘We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.
基金Supported by Inner Mongolia Natural Science Foundations of China (200408020108).
文摘This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients
文摘In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.
