The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for ana...The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions.In the second approach,some approximations to(un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method.In the third approach,He’s frequency-amplitude principle is applied for deriving some approximations to the(un)damped PPO.In the forth approach,He’s homotopy technique is employed for analyzing the forced(un)damped PPO numerically.In the fifth approach,the p-solution Method,which is constructed based on Krylov–Bogoliúbov Mitropolsky method,is introduced for deriving an approximation to the forced damped PPO.In the final approach,the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically.All proposed techniques are compared to the fourth-order Runge–Kutta(RK4)numerical solution.Moreover,the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations.The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science,e.g.waves and oscillations in plasma physics.展开更多
The triangular zone cracks in 2101 duplex stainless steel produced by the vertical continuous caster have troubled company A for a long time. To simulate the temperature and thermal stress distributions in the solidif...The triangular zone cracks in 2101 duplex stainless steel produced by the vertical continuous caster have troubled company A for a long time. To simulate the temperature and thermal stress distributions in the solidification process of 2101 duplex stainless steel produced by the vertical continuous caster, a two-dimensional viscoelastic-plastic thermomechanically coupled finite element model was established by the secondary development of the commercial nonlinear finite element analysis software MSC Marc. The results show that the thermal stress on the surface reaches a maximum at the exit of the mould, and the highest thermal stresses at the centre of the wide face and the narrow face are 75 and 115 MPa, respectively. Meanwhile, the internal temperature of slab is still higher than the solidus temperature, resulting in no thermal stress. The slab shows different high-temperature strengths and suffers from different stresses at different positions; thus, the risk of cracking also varies. At a location of 6-8 m from the meniscus, the temperature of the triangular zone is 1270-1360℃ and the corresponding permissible high-temperature strength is about 10-30 MPa, while the thermal stress at this time is 60 MPa, which is higher than the high-temperature strength. As a result, triangular zone cracks form easily.展开更多
In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, th...In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticles and microorganisms are reduced to a set of fully coupled nonlinear differential equations. The homotopy analysis method （HAM）-finite difference method （FDM） technique is used to obtain exact solutions. The effect of various physical parameters on distribution of the motile microorganisms and the important physical quantities of practical interests are presented and discussed.展开更多
This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on t...This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.展开更多
We give some new characterizations of strongly one-sided(b,c)-invertibility of elements in rings,and establish the relations between one-sided(b,c)-inverses and strongly one-sided(b,c)-inverses.When b=c,Kaplansky'...We give some new characterizations of strongly one-sided(b,c)-invertibility of elements in rings,and establish the relations between one-sided(b,c)-inverses and strongly one-sided(b,c)-inverses.When b=c,Kaplansky's theorem on the number of one-sided inverses is generalized to the case of strongly one-sided(b,c)-inverses.Moreover,we give some new characterizations of Dedekind-finite rings from the viewpoint of(b,c)-finiteness,and thus answer a question in[L.Wang,D.Mosic,The one-sided inverse along two elements in rings,Linear Multilinear Algebra 69(13)(2021)2410-2422].展开更多
Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, so...The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, some properties of ＊τx are proved. Finally, the approach theorem is easily obtained.展开更多
A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twis...A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(Δ)- finite M-twisted double incidence algebras is given in case the posets are linearly ordered.展开更多
This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
基金The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project (Grant No. PNURSP2022R17)Taif University Researchers supporting project number (TURSP2020/275), Taif University, Taif, Saudi Arabia。
文摘The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions.In the second approach,some approximations to(un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method.In the third approach,He’s frequency-amplitude principle is applied for deriving some approximations to the(un)damped PPO.In the forth approach,He’s homotopy technique is employed for analyzing the forced(un)damped PPO numerically.In the fifth approach,the p-solution Method,which is constructed based on Krylov–Bogoliúbov Mitropolsky method,is introduced for deriving an approximation to the forced damped PPO.In the final approach,the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically.All proposed techniques are compared to the fourth-order Runge–Kutta(RK4)numerical solution.Moreover,the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations.The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science,e.g.waves and oscillations in plasma physics.
文摘The triangular zone cracks in 2101 duplex stainless steel produced by the vertical continuous caster have troubled company A for a long time. To simulate the temperature and thermal stress distributions in the solidification process of 2101 duplex stainless steel produced by the vertical continuous caster, a two-dimensional viscoelastic-plastic thermomechanically coupled finite element model was established by the secondary development of the commercial nonlinear finite element analysis software MSC Marc. The results show that the thermal stress on the surface reaches a maximum at the exit of the mould, and the highest thermal stresses at the centre of the wide face and the narrow face are 75 and 115 MPa, respectively. Meanwhile, the internal temperature of slab is still higher than the solidus temperature, resulting in no thermal stress. The slab shows different high-temperature strengths and suffers from different stresses at different positions; thus, the risk of cracking also varies. At a location of 6-8 m from the meniscus, the temperature of the triangular zone is 1270-1360℃ and the corresponding permissible high-temperature strength is about 10-30 MPa, while the thermal stress at this time is 60 MPa, which is higher than the high-temperature strength. As a result, triangular zone cracks form easily.
基金supported by the Program for New Century Excellent Talents in University of China(No.NCET-12-0347)
文摘In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticles and microorganisms are reduced to a set of fully coupled nonlinear differential equations. The homotopy analysis method （HAM）-finite difference method （FDM） technique is used to obtain exact solutions. The effect of various physical parameters on distribution of the motile microorganisms and the important physical quantities of practical interests are presented and discussed.
基金supported by the National Natural Science Foundation of China (10771134).
文摘This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.
基金National Natural Science Foundation of China(Nos.12171083,11871145 and 12071070)Qing Lan Project of Jiangsu Province,and the Postgraduate Research and Practice Innovation Program of Jiangsu Province(No.KYCX21_0078).
文摘We give some new characterizations of strongly one-sided(b,c)-invertibility of elements in rings,and establish the relations between one-sided(b,c)-inverses and strongly one-sided(b,c)-inverses.When b=c,Kaplansky's theorem on the number of one-sided inverses is generalized to the case of strongly one-sided(b,c)-inverses.Moreover,we give some new characterizations of Dedekind-finite rings from the viewpoint of(b,c)-finiteness,and thus answer a question in[L.Wang,D.Mosic,The one-sided inverse along two elements in rings,Linear Multilinear Algebra 69(13)(2021)2410-2422].
基金National Natural Science Foundation of China(10171082)by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE.
文摘Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
基金Foundation item:the Natural Science Foundation of Shaanxi Province(2007A12)the Basic Research Foundation of Xi'an Arch.&Tech.University(JC0620)the Youth Science Technology of Xi'an Arch.&Tech.University (QN0736)
文摘The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, some properties of ＊τx are proved. Finally, the approach theorem is easily obtained.
文摘A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(Δ)- finite M-twisted double incidence algebras is given in case the posets are linearly ordered.
文摘This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
