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CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET
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作者 王晓慧 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期234-246,共13页
This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provi... This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid. 展开更多
关键词 Euler system axisymmetric impinging jet INCOMPRESSIBLE free boundary convexity
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Dynamic behavior of outburst two-phase flow in a coal mine T-shaped roadway:The formation of impact airflow and its disaster-causing effect
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作者 Liang Cheng Jiang Xu +4 位作者 Shoujian Peng Hailin Yang Feng Jiao Bin Zhou Fazhi Yan 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2023年第8期1001-1017,共17页
The study of the dynamic disaster mechanism of coal and gas outburst two-phase flow is crucial for improving disaster reduction and rescue ability of coal mine outburst accidents.An outburst test in a T-shaped roadway... The study of the dynamic disaster mechanism of coal and gas outburst two-phase flow is crucial for improving disaster reduction and rescue ability of coal mine outburst accidents.An outburst test in a T-shaped roadway was conducted using a self-developed large-scale outburst dynamic disaster test system.We investigated the release characteristics of main energy sources in coal seam,and obtained the dynamic characteristics of outburst two-phase flow in a roadway.Additionally,we established a formation model for outburst impact flow and a model for its flow in a bifurcated structure.The results indicate that the outburst process exhibits pulse characteristics,and the rapid destruction process of coal seam and the blocking state of gas flow are the main causes of the pulse phenomenon.The outburst energy is released in stages,and the elastic potential energy is released in the vertical direction before the horizontal direction.In a straight roadway,the impact force oscillates along the roadway.With an increase in the solid–gas ratio,the two-phase flow impact force gradually increases,and the disaster range extends from the middle of the roadway to the coal seam.In the area near the coal seam,the disaster caused by the two-phase flow impact is characterized by intermittent recovery.In a bifurcated roadway,the effect of impact airflow on impact dynamic disaster is much higher than that of two-phase flow,and the impact force tends to weaken with increasing solid-gas ratio.The impact force is asymmetrically distributed;it is higher on the left of the bifurcated roadway.With an increase in the solid-gas ratio,the static pressure rapidly decreases,and the bifurcated structure accelerates the attenuation of static pressure.Moreover,secondary acceleration is observed when the shock wave moves along the T-shaped roadway,indicating that the bifurcated structure increases the shock wave velocity. 展开更多
关键词 Multiphase flow Coal and gas outburst Dynamic disaster Impact airflow t-shaped bifurcated roadway Coal seam
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On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis
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作者 Fangyi Li Dachang Zhu Huimin Shi 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1981-1999,共19页
In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems... In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem. 展开更多
关键词 Mixed uncertainty probability model convex model time-variant reliability analysis
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Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives
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作者 Xuanjie Li Yuedong Xu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第4期459-481,共23页
We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization p... We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios. 展开更多
关键词 Distributed stochastic optimization arbitrary compression fidelity non-strongly convex objective function
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Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach
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作者 Shenquan Wang Wenchengyu Ji +2 位作者 Yulian Jiang Yanzheng Zhu Jian Sun 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期996-1006,共11页
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 i... 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. 展开更多
关键词 Equivalent reciprocal combination technique quadratic function convex approximation approach STABILITY timevarying delay
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Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems
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作者 You Zhao Xing He +1 位作者 Mingliang Zhou Tingwen Huang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1485-1498,共14页
The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on... The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments. 展开更多
关键词 Accelerated projection neurodynamic approach lin-ear and set constraints projection operators smooth and nonsmooth convex optimization time scaling.
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Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods
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作者 Andrés M.Rueda-Ramírez Benjamin Bolm +1 位作者 Dmitri Kuzmin Gregor J.Gassner 《Communications on Applied Mathematics and Computation》 EI 2024年第3期1860-1898,共39页
We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ... We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows. 展开更多
关键词 Structure-preserving schemes Subcellflux limiting Monolithic convex limiting(MCL) Discontinuous Galerkin spectral-element methods(DGSEMS) Legendre-Gauss-Lobatto(LGL)nodes
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Influences of fillet radius and draft angle on local loading process of titanium alloy T-shaped components 被引量:1
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作者 张大伟 杨合 +1 位作者 孙志超 樊晓光 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2011年第12期2693-2704,共12页
In order to study influences of geometric parameters on the T-shaped components local loading process, a new mathematical model considering the fillet radius and draft angle was established by using the slab method. T... In order to study influences of geometric parameters on the T-shaped components local loading process, a new mathematical model considering the fillet radius and draft angle was established by using the slab method. The results obtained by the mathematical model agree with the data form experiment and numerical simulation, and the results are closer to the experimental and simulation results. The influence of draft angle may be neglected under the forming conditions used. The influence of fillet radius is notable, especially in the case that the ratio of fillet radius to rib width is less than 0.75. 展开更多
关键词 fillet radius draft angle t-shaped component local loading slab method
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Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity 被引量:1
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作者 孙清滢 叶留青 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第4期33-37,共5页
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un... Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. 展开更多
关键词 necessary and sufficient conditions generalized convexity nonlinear programming multiobjective programming type functions
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THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS 被引量:13
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作者 褚玉明 孙天川 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1501-1506,共6页
In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequa... In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequalities are established. 展开更多
关键词 symmetric function Schur convex Schur harmonic convex
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MONOTONICITY,CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS 被引量:5
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作者 Miaokun WANG Wen ZHANG Yuming CHU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1440-1450,共11页
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
关键词 Gaussian HYPERGEOMETRIC function generalized ELLIPTIC INTEGRALS convexity inequality
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THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN 被引量:4
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作者 夏卫锋 褚玉明 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1103-1112,共10页
We prove that the Gini mean values S(a,b; x,y) are Schur harmonic convex with respect to (x,y)∈(0,∞)×(0,∞) if and only if (a, b) ∈{(a, b):a≥0,a ≥ b,a+b+1≥0}∪{(a,b):b≥0,b≥a,a+b+1≥0} ... We prove that the Gini mean values S(a,b; x,y) are Schur harmonic convex with respect to (x,y)∈(0,∞)×(0,∞) if and only if (a, b) ∈{(a, b):a≥0,a ≥ b,a+b+1≥0}∪{(a,b):b≥0,b≥a,a+b+1≥0} and Schur harmonic concave with respect to (x,y) ∈ (0,∞)×(0,∞) if and only if (a,b)∈{(a,b):a≤0,b≤0,a|b|1≤0}. 展开更多
关键词 Gini mean values Schur convex Schur harmonic convex
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Performance of a Self-Aligned InP/GaInAs SHBT with a Novel T-Shaped Emitter
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作者 苏树兵 刘训春 +4 位作者 刘新宇 于进勇 王润梅 徐安怀 齐鸣 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2006年第3期434-437,共4页
A self-aligned InP/GalnAs single heterojunction bipolar transistor(HBT) is investigated using a novel T-shaped emitter. A U-shaped emitter layout,selective wet etching,laterally etched undercut, and an air-bridge ar... A self-aligned InP/GalnAs single heterojunction bipolar transistor(HBT) is investigated using a novel T-shaped emitter. A U-shaped emitter layout,selective wet etching,laterally etched undercut, and an air-bridge are applied in this process. The device, which has a 2μm×12μm U-shaped emitter area,demonstrates a common-emitter DC current gain of 170,an offset voltage of 0.2V,a knee voltage of 0.5V, and an open-base breakdown voltage of over 2V. The HBT exhibits good microwave performance with a current gain cutoff frequency of 85GHz and a maximum oscillation frequency of 72GHz, These results indicate that these InP/InGaAs SHBTs are suitable for low-voltage,low-power,and high-frequency applications. 展开更多
关键词 self-alignment emitters InP single heterojunction bipolar transistor t-shaped emitter U-shaped emitter layout
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Improved design of special boundary elements for T-shaped reinforced concrete walls 被引量:9
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作者 Ji Xiaodong Liu Dan Qian Jiaru 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2017年第1期83-95,共13页
This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design metho... This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements ofT-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension. 展开更多
关键词 code comparison displacement-based method seismic design special boundary element t-shaped wall
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NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES 被引量:2
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作者 Ji Gao Satit Saejung 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1035-1040,共6页
We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax(ε) and βx (ε), both related to Gao's modulus of U-convexity of a Banach sp... We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax(ε) and βx (ε), both related to Gao's modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved. 展开更多
关键词 uniform normal structure modulus of convexity ULTRAPOWER
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CERTAIN SUFFICIENT CONDITIONS FOR STARLIKENESS AND CONVEXITY OF MEROMORPHICALLY MULTIVALENT FUNCTIONS 被引量:2
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作者 徐宜会 B.A.FRASIN 刘金林 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1300-1304,共5页
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
关键词 analytic function meromorphically multivalent function starlike function convex function
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APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION 被引量:2
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作者 王根娣 裘松良 +1 位作者 张孝惠 褚玉明 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第2期203-206,共4页
In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa (r) by studying the monotonieity,convexity or concavity of certain composites of μa(r) are ob... In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa (r) by studying the monotonieity,convexity or concavity of certain composites of μa(r) are obtained. 展开更多
关键词 generalized Grotzsch ring function Ramanujan's modular equation convexity concawty.
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Numerical investigation of flow pattern and components of three-dimensional velocity around a submerged T-shaped spur dike in a 90° bend 被引量:2
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作者 Mohammad Vaghefi Yaser Safarpoor Maryam Akbari 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第11期2984-2998,共15页
Spur dike is one of the river training structures. This work presented a numerical simulation of flow field and three-dimensional velocity around a T-shaped spur dike located in bend using SSIIM model. The main object... Spur dike is one of the river training structures. This work presented a numerical simulation of flow field and three-dimensional velocity around a T-shaped spur dike located in bend using SSIIM model. The main objective of this work is to investigate the three-dimensional velocities and streamlines at transverse and longitudinal sections and plan views around the T-shaped spur dike in different submergence ratios(0, 5%, 15%, 25% and 50%). It is concluded that by increasing the submergence ratio from 5% to 50%, the maximum of scour is reduced; the maximum of longitudinal velocity increases by 7.7% and occurs at the water surface in spur dike axis. Near the bed, the maximum of vertical velocity occurs at the end of spur wing. By analyzing the streamlines at transverse sections, the followings were deduced for different submergence ratios: different dimensions and different positions of vortices around the spur dike. 展开更多
关键词 t-shaped spur dike flow pattern submergence ratio SSIIM model
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Convexity for New Integral Operator on k-uniformly p-valent a-convex Functions of Complex Order 被引量:1
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作者 LI Shu-hai MA Li-na A O-en 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期88-96,共9页
In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.
关键词 analytic functions p-valently k-uniformly STARLIKE convex integral operator
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Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation 被引量:2
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作者 B.Firouzi M.Zamanian S.A.A.Hosseini 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2016年第6期1104-1122,共19页
In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric vo... In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric voltage between the horizontal part of T-shaped tip mass and an opposite electrode plate. The cantilever microbeam is modeled as an Euler-Bernoulli beam. The T-shaped tip mass is assumed to be a rigid body and the nonlinear effect of electrostatic force is considered. An equation of motion and its associated boundary conditions are derived by the aid of combining the Hamilton principle and Newton’s method. An exact solution is obtained for static deflection and mode shape of vibration around the static position. The differential equation of nonlinear vibration around the static position is discretized using the Galerkin method. The system mode shapes are used as its related comparison functions. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. In addition, effects of mass inertia, mass moment of inertia as well as rotation of the T-shaped mass, which were ignored in previous works, are considered in the analysis. It is shown that by increasing the length of the horizontal part of the T-shaped mass, the amount of static deflection increases, natural frequency decreases and nonlinear shift of the resonance frequency increases. It is concluded that attaching an electrode plate with a T-shaped configuration to the end of the cantilever microbeam results in a configuration with larger pull-in voltage and smaller nonlinear shift of the resonance frequency compared to the configuration in which the electrode plate is directly attached to it. 展开更多
关键词 MEMS ELECTROSTATIC Static deflection Natural frequency Pull-in voltage Perturbation theory t-shaped mass Primary and subharmonic resonances
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