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Nonsingle-valley Continuous Solutions of p-order Feigenbaum's Functional Equation 被引量:2
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作者 张爱华 王立娟 宋威 《Northeastern Mathematical Journal》 CSCD 2003年第4期375-380,共6页
The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct... The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given. 展开更多
关键词 functional equation single-valley continuous solution nonsingle-valley continuous solution
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Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations 被引量:3
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作者 李宝麟 吴从炘 《Northeastern Mathematical Journal》 CSCD 2005年第4期421-430,共10页
The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results a... The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations. 展开更多
关键词 Kurzweil equation bounded Φ-variation solution continuous dependence on parameter
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Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems 被引量:2
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作者 马学敏 李宝麟 林长伟 《Chinese Quarterly Journal of Mathematics》 2015年第4期610-619,共10页
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper... The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems. 展开更多
关键词 discontinuous systems Henstock-Kurzweil integral bounded Φ-variation solution continuous dependence
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L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS 被引量:1
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作者 Yajie CHEN Chuanzhi XING Xiao ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1116-1140,共25页
In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the s... In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution. 展开更多
关键词 general mean-field backward stochastic differential equations monotonicity condition continuous condition uniformly continuous condition L^p solution
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CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS II . LATTICE FLUID MODEL
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作者 胡英 英徐根 +1 位作者 D.T.Wu J.M.Prausnitz 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1995年第1期14-25,共12页
Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real po... Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented. 展开更多
关键词 continuous thermodynamics polymer solution polydispersity lattice-fluid model CLOUD-POINT CURVE shadow CURVE SPINODAL upper-critical-solution temperatures lower-critical-solution temperature.
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CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS I.CLOSE-PACKED LATTICE MODEL
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作者 胡英 英徐根 +1 位作者 D.T.Wu J.M.Prausnitz 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1994年第3期4-18,共15页
using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of ... using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are 展开更多
关键词 continuous thermodynamics polymer solution POLYDISPERSITY lattice model CLOUD-POINT CURVE SHADOW CURVE SPINODAL critical point
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EXACT SOLUTION FOR LAMINATED CONTINUOUSOPEN CYLINDRICAL SHELLS
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作者 盛宏玉 范家让 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第11期0-0,0-0+0-0+0-0+0-0+0-0+0-0,共14页
Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. A... Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. An thentical exocl solution is presentedfor the statics of thin. moderately thick and thick laminated continuous openrylindrical shells. Numerical results are obtained and compared with those calculatedusing SAP5. 展开更多
关键词 laminated continuous open cylindrical shell ORTHOTROPY state equation exact solution
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PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS
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作者 刘玉记 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1492-1508,共17页
Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
关键词 singular fractional differential equation impulsive effect piecewise continuous solution fixed point theorem
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HLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS
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作者 Tao TAO Liqun ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2018年第5期1591-1616,共26页
We show the existence of dissipative Hhlder continuous solutions of the Boussi- nesq equations. More precise, for anyβ∈ (0, 1/5), a time interval [0, T] and any given smooth energy profile e : [0, T] → (0, ∞... We show the existence of dissipative Hhlder continuous solutions of the Boussi- nesq equations. More precise, for anyβ∈ (0, 1/5), a time interval [0, T] and any given smooth energy profile e : [0, T] → (0, ∞), there exist a weak solution (v, θ) of the 3d Boussinesq equations such that (v, 8) ∈ Cβ(T3 × [0, T]) with e(t) = ∫T3 |v(x, t)|2dx for all t ∈ [0, T]. This extend the result of [2] about Onsager's conjecture into Boussinesq equation and improve our previous result in [30]. 展开更多
关键词 Boussinesq equations Holder continuous solutions prescribed kinetic energy
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A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations
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作者 Emmanuel Adegbemiro Areo Micheal Temitope Omojola 《American Journal of Computational Mathematics》 2015年第4期447-450,共4页
In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evalua... In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model. 展开更多
关键词 Power Series APPROXIMATE solutions CONSISTENT ZERO Stability continuous BLOCK Method Dynamic Model
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EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM
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作者 林龙威 杨彤 《Acta Mathematica Scientia》 SCIE CSCD 1993年第1期1-12,共12页
In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to t... In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time. 展开更多
关键词 EXISTENCE AND NONEXISTENCE OF GLOBAL continuous solutionS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期1061-1076,共16页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study. 展开更多
关键词 Semigroups Theory Weakly continuous Operators Existence of solution Generalized Schrödinger Equation Distributional Problem Periodic Distributional Space
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Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期919-932,共14页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study. 展开更多
关键词 Groups Theory Weakly continuous Operators Existence of solution Generalized Schrödinger Type Equation Homogeneous Equation Periodic Distributional Space
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Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs
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作者 HAN You-pan CHEN Zhi-ping ZHANG Feng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第1期102-110,共9页
When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Li... When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained. 展开更多
关键词 quadratic program Lipschitz continuity value function feasible solution KKT solution set.
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Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion
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作者 Tianwen Luo Tao Tao Liqun Zhang 《Science China Mathematics》 SCIE CSCD 2024年第8期1777-1806,共30页
We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0... We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1]. 展开更多
关键词 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy
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THE CONTINUAL DIFFERENTIABLE PEAK-UNIMODAL SOLUTIONS OF FEIGENBAUM’S FUNCTIONAL EQUATIONS
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作者 程宝龙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第5期419-426,共8页
For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on ... For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions. 展开更多
关键词 THE continuAL DIFFERENTIABLE PEAK-UNIMODAL solutionS OF FEIGENBAUM S FUNCTIONAL EQUATIONS
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Solute redistribution and macrosegregation in continuous casting slab of carbon steel during solidification process
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作者 WEN Hongquan WU Cunyou ZHOU Yueming 《Baosteel Technical Research》 CAS 2020年第4期33-39,共7页
Based on the modified Scheil model of solute redistribution,the effects of solidification rate,molten steel flow,and alloy composition on solute macrosegregation during the solidification of carbon steel continuous ca... Based on the modified Scheil model of solute redistribution,the effects of solidification rate,molten steel flow,and alloy composition on solute macrosegregation during the solidification of carbon steel continuous casting billet are calculated and analyzed. The formation mechanism of "white band "segregation under the condition of electromagnetic stirring is also involved,and some practical countermeasures to restrain the central segregation are suggested. The results show that the modified Scheil model can be applied to predict and analyze the macrosegregation of casting slab effectively. The ratio vx/R of the flow velocity of molten steel to solidification rate has decisive formations of segregation such as linear,V,and "white band"types. It is an effective way to select sufficient terminal cooling and reasonable electromagnetic stirring in order to decrease macrosegregation in the slab. The concept of the characteristic distance of solute enrichment layer can drastically simplify the calculation of solute redistribution at the solid/liquid interface of various elements in carbon steel. 展开更多
关键词 central segregation solute redistribution Scheil model continuous casting
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Hlder continuity for solutions of elltptic equations involving measures
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作者 LiangXiting LuYouwen 《怀化师专学报》 1996年第5期34-43,共10页
The Hoider continuity is proved to bounded solutions of degenerate elliptic e-quations involving measures. The structural conditions of the equation are more general and therestrictions on the structural coofficients ... The Hoider continuity is proved to bounded solutions of degenerate elliptic e-quations involving measures. The structural conditions of the equation are more general and therestrictions on the structural coofficients are weaker. 展开更多
关键词 包含测度 椭圆型方程解 Hoolder连续性 结构系数
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THE HOLDER CONTINUITY OF GENERALIZED SOLUTIONS OF A CLASS QUASILINEAR PARABOLIC EQUATIONS
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作者 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第6期573-583,共11页
Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del... Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del u) + B(x, t, U, del u) = 0. 展开更多
关键词 parabolic equation natural growth condition generalized solution local Holder continuity
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