Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）...Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）^nM（P,1）. In this paper, we obtain certain extensions and refinements of this inequality by in- volving binomial coefficients and some of the coefficients of the polynomial P（z）.展开更多
While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfa...While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfacial evaporation offers sustainable management potential,yet inevitable salt nucleation at evaporation interfaces degrades photothermal conversion and operational stability via light scattering and pathway blockage.Inspired by the mangrove leaf,we propose a photothermal 3D polydopamine and polypyrrole polymerized spacer fabric(PPSF)-based upward hanging model evaporation configuration with a reverse water feeding mechanism.This design enables zero-liquiddischarge(ZLD)desalination through phase-separation crystallization.The interconnected porous architecture and the rough surface of the PPSF enable superior water transport,achieving excellent solar-absorbing efficiency of 97.8%.By adjusting the tilt angle(θ),the evaporator separates the evaporation and salt crystallization zones via controlled capillary-driven brine transport,minimizing heat dissipation from brine discharge.At an optimal tilt angle of 52°,the evaporator reaches an evaporation rate of 2.81 kg m^(−2) h^(−1) with minimal heat loss(0.366 W)under 1-sun illumination while treating a 7 wt%waste brine solution.Furthermore,it sustains an evaporation rate of 2.71 kg m^(−2) h^(−1) over 72 h while ensuring efficient salt recovery.These results highlight a scalable,energy-efficient approach for sustainable ZLD desalination.展开更多
With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT termi...With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT terminals have security risks and vulnerabilities,and limited resources make it impossible to deploy costly security protection methods on the terminal.In order to cope with these problems,this paper proposes a lightweight trust evaluation model TCL,which combines three network models,TCN,CNN,and LSTM,with stronger feature extraction capability and can score the reliability of the device by periodically analyzing the traffic behavior and activity logs generated by the terminal device,and the trust evaluation of the terminal’s continuous behavior can be achieved by combining the scores of different periods.After experiments,it is proved that TCL can effectively use the traffic behaviors and activity logs of terminal devices for trust evaluation and achieves F1-score of 95.763,94.456,99.923,and 99.195 on HDFS,BGL,N-BaIoT,and KDD99 datasets,respectively,and the size of TCL is only 91KB,which can achieve similar or better performance than CNN-LSTM,RobustLog and other methods with less computational resources and storage space.展开更多
The United Nations Sustainable Development Goal(SDG) 2 aims to achieve Zero Hunger by 2030.However,global hunger and food insecurity have continued to rise at an alarming rate(UN 2023).Subtropical regions are home to ...The United Nations Sustainable Development Goal(SDG) 2 aims to achieve Zero Hunger by 2030.However,global hunger and food insecurity have continued to rise at an alarming rate(UN 2023).Subtropical regions are home to more than 30% of the world's population,predominantly in developing countries where per capita farmland and food supply are only 40% of those in developed nations(FAO 2018).Meeting the Zero Hunger target amid ongoing population growth in these regions requires a substantial increase in agricultural production while minimizing soil degradation and adverse ecological impacts.This challenge is shared by many countries across South Asia,Africa,and Central and South America.展开更多
Hainan Province in south China is the country’s second-largest island and the largest free trade port by area.It has entered a historic phase in China’s drive to promote high-level institutional opening up.On 18 Dec...Hainan Province in south China is the country’s second-largest island and the largest free trade port by area.It has entered a historic phase in China’s drive to promote high-level institutional opening up.On 18 December 2025,Hainan officially launched island-wide special customs operations,commonly referred to as“customs closure.”From that date,goods entering or leaving the island,except those traded with the Chinese mainland,are subject to simplified customs procedures and potentially reduced or zero tariffs.展开更多
2026年1月31日-2月4日,美国供热、制冷与空调工程师学会(ASHRAE)2026年冬季会议在美国拉斯维加斯隆重召开。来自全球数十个国家的行业专家、学者及工程师齐聚一堂,共同探讨建筑环境系统与能源工程领域的前沿技术与发展趋势。会议期间,AS...2026年1月31日-2月4日,美国供热、制冷与空调工程师学会(ASHRAE)2026年冬季会议在美国拉斯维加斯隆重召开。来自全球数十个国家的行业专家、学者及工程师齐聚一堂,共同探讨建筑环境系统与能源工程领域的前沿技术与发展趋势。会议期间,ASHRAE学会正式颁发了2026年度“Engineering Global Net Zero”创新奖。“Engineering Global Net Zero”创新奖(Innovation Award 2026)旨在表彰全球范围内在推动建筑环境领域可持续发展与技术创新方面作出卓越贡献的杰出个人,该奖项由美国供热、制冷与空调工程师学会(ASHRAE)组织评议。展开更多
In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the o...In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.展开更多
Suppose that function f（z） is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f（z）f（k）（z） takes any non-zero finite complex nu...Suppose that function f（z） is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f（z）f（k）（z） takes any non-zero finite complex number infinitely times and to consider the normality relation to differential monomials f（z）f（k） （z）.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
The paper gives two estimates of the distance between adjacent zeros of solutions of the first\|order delay differential equation x′(t)+p(t)x(t-τ) =0 in the case when p(t)≥0 and ∫ t t-τ p(s)d s-1e ...The paper gives two estimates of the distance between adjacent zeros of solutions of the first\|order delay differential equation x′(t)+p(t)x(t-τ) =0 in the case when p(t)≥0 and ∫ t t-τ p(s)d s-1e oscillates or p(t) itself oscillates.展开更多
We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus ...We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C(-2, 2, ···,(-1)r2) by the recursive form and discuss the distribution of their zeros.展开更多
In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak-1 is the dominant coefficient, then every transcen...In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak-1 is the dominant coefficient, then every transcendental solution f（z） of equation……satisfies ）λ（f） =∞, where A（f） denotes the exponent of convergence of zeros of the meromor- phic function f（z）.展开更多
Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of o...Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.展开更多
The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =αnZn+...+α1Z+α0satisfying the r...In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =αnZn+...+α1Z+α0satisfying the restriction αn≥αn-1≥...≥α1≥α0≥0 lie in the closed unit disk.展开更多
In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant ...In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.展开更多
In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the l...In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.展开更多
In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally converge...In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadratic polynomials.展开更多
Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in...Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in Hausdorff topology for λ∈R.展开更多
By studying the distribution of zeros of combinations of a Dirichlet L-function and its first-order derivative,we prove that every Dirichlet L-function has more than 66.7934%distinct zeros.
文摘Let P（z） be a polynomial of degree n which does not vanish in ｜z｜ 〈k, k≥ 1. It is known that for each 0 〈 s 〈 n and 1 ≤ R ≤ k,M（P（s）,R）≤（1/（R^s＋k^s）[{d（s）/dx（s）（1＋x^n）}x=1]（（R＋k）/（1＋k）^nM（P,1）. In this paper, we obtain certain extensions and refinements of this inequality by in- volving binomial coefficients and some of the coefficients of the polynomial P（z）.
基金supported by National Key Research and Development Program of China(2022YFB3804902,2022YFB3804900)the National Natural Science Foundation of China(52203226,52161145406,42376045)the Fundamental Research Funds for the Central Universities(2232024Y-01,2232025D-02).
文摘While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfacial evaporation offers sustainable management potential,yet inevitable salt nucleation at evaporation interfaces degrades photothermal conversion and operational stability via light scattering and pathway blockage.Inspired by the mangrove leaf,we propose a photothermal 3D polydopamine and polypyrrole polymerized spacer fabric(PPSF)-based upward hanging model evaporation configuration with a reverse water feeding mechanism.This design enables zero-liquiddischarge(ZLD)desalination through phase-separation crystallization.The interconnected porous architecture and the rough surface of the PPSF enable superior water transport,achieving excellent solar-absorbing efficiency of 97.8%.By adjusting the tilt angle(θ),the evaporator separates the evaporation and salt crystallization zones via controlled capillary-driven brine transport,minimizing heat dissipation from brine discharge.At an optimal tilt angle of 52°,the evaporator reaches an evaporation rate of 2.81 kg m^(−2) h^(−1) with minimal heat loss(0.366 W)under 1-sun illumination while treating a 7 wt%waste brine solution.Furthermore,it sustains an evaporation rate of 2.71 kg m^(−2) h^(−1) over 72 h while ensuring efficient salt recovery.These results highlight a scalable,energy-efficient approach for sustainable ZLD desalination.
基金supported by National Key R&D Program of China(No.2022YFB3105101).
文摘With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT terminals have security risks and vulnerabilities,and limited resources make it impossible to deploy costly security protection methods on the terminal.In order to cope with these problems,this paper proposes a lightweight trust evaluation model TCL,which combines three network models,TCN,CNN,and LSTM,with stronger feature extraction capability and can score the reliability of the device by periodically analyzing the traffic behavior and activity logs generated by the terminal device,and the trust evaluation of the terminal’s continuous behavior can be achieved by combining the scores of different periods.After experiments,it is proved that TCL can effectively use the traffic behaviors and activity logs of terminal devices for trust evaluation and achieves F1-score of 95.763,94.456,99.923,and 99.195 on HDFS,BGL,N-BaIoT,and KDD99 datasets,respectively,and the size of TCL is only 91KB,which can achieve similar or better performance than CNN-LSTM,RobustLog and other methods with less computational resources and storage space.
文摘The United Nations Sustainable Development Goal(SDG) 2 aims to achieve Zero Hunger by 2030.However,global hunger and food insecurity have continued to rise at an alarming rate(UN 2023).Subtropical regions are home to more than 30% of the world's population,predominantly in developing countries where per capita farmland and food supply are only 40% of those in developed nations(FAO 2018).Meeting the Zero Hunger target amid ongoing population growth in these regions requires a substantial increase in agricultural production while minimizing soil degradation and adverse ecological impacts.This challenge is shared by many countries across South Asia,Africa,and Central and South America.
文摘Hainan Province in south China is the country’s second-largest island and the largest free trade port by area.It has entered a historic phase in China’s drive to promote high-level institutional opening up.On 18 December 2025,Hainan officially launched island-wide special customs operations,commonly referred to as“customs closure.”From that date,goods entering or leaving the island,except those traded with the Chinese mainland,are subject to simplified customs procedures and potentially reduced or zero tariffs.
文摘2026年1月31日-2月4日,美国供热、制冷与空调工程师学会(ASHRAE)2026年冬季会议在美国拉斯维加斯隆重召开。来自全球数十个国家的行业专家、学者及工程师齐聚一堂,共同探讨建筑环境系统与能源工程领域的前沿技术与发展趋势。会议期间,ASHRAE学会正式颁发了2026年度“Engineering Global Net Zero”创新奖。“Engineering Global Net Zero”创新奖(Innovation Award 2026)旨在表彰全球范围内在推动建筑环境领域可持续发展与技术创新方面作出卓越贡献的杰出个人,该奖项由美国供热、制冷与空调工程师学会(ASHRAE)组织评议。
基金supported by the National Natural Science Foundation of China (11171119 and 10871076)
文摘In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.
基金Foundation item： Supported by the National Natural Science Foundation of Education Department of Sichuan Province（2002A031） Supported by the ＂11.5＂ Research and Study Programs of SWUST（06zx2116） Supported by the National Natural Science Foundation of China（10271122）
文摘Suppose that function f（z） is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f（z）f（k）（z） takes any non-zero finite complex number infinitely times and to consider the normality relation to differential monomials f（z）f（k） （z）.
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.
文摘The paper gives two estimates of the distance between adjacent zeros of solutions of the first\|order delay differential equation x′(t)+p(t)x(t-τ) =0 in the case when p(t)≥0 and ∫ t t-τ p(s)d s-1e oscillates or p(t) itself oscillates.
基金Supported by the National Science Foundation of China（11471151） Supported by Program for Liaoning Excellent Talents in University（LR2011031）
Acknowledgment The authors would like to thank the referees for kind suggestions and many useful comments
文摘We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C(-2, 2, ···,(-1)r2) by the recursive form and discuss the distribution of their zeros.
基金supported by the National Natura Science Foundation of China (11171119)Funding of Tianyuan (11226090)
文摘In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak-1 is the dominant coefficient, then every transcendental solution f（z） of equation……satisfies ）λ（f） =∞, where A（f） denotes the exponent of convergence of zeros of the meromor- phic function f（z）.
基金supported by the NSF of Shandong Province, China (ZR2010AM030)the NNSF of China (11171013 & 11041005)
文摘Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.
基金supported by the National Natural Science Foundation of China(11201395)supported by the Science Foundation of Educational Commission of Hubei Province(Q20132801)
文摘The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
文摘In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =αnZn+...+α1Z+α0satisfying the restriction αn≥αn-1≥...≥α1≥α0≥0 lie in the closed unit disk.
文摘In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.
文摘In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.
基金The Project is supported by the National Natural Science Foundation of China and by Natural Science Foundation of Zhejiang Province.
文摘In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadratic polynomials.
基金supported by National Natural Science Foundation of China (10625107)Program for New Century Excellent Talents in University (04-0490)
文摘Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in Hausdorff topology for λ∈R.
基金This work was supported in part by NSFC(11871187)the Fundamental Research Funds for the Central Universities of China。
文摘By studying the distribution of zeros of combinations of a Dirichlet L-function and its first-order derivative,we prove that every Dirichlet L-function has more than 66.7934%distinct zeros.
