Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i...Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i1∧i2) =i1∧i2;(4) (i1∨i2) = i1∨i2, for arbitrary algebra a∈A and any i1,i2∈La,where j denotes the ideal of a uniquely determined by R(a/j) = j/j?展开更多
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give ...In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.展开更多
In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the correspon...In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. （Yuan W J, Xiao B, Zhang J J. The general theorem of Gol＇dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58：1788 1791）. Meanwhile, we also take some examples to show that our estimate is sharp.展开更多
In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theore...In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.展开更多
Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three addit...Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica. For a comprehensive understanding, the frequency of the normal mode is used for a visual animation;an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.展开更多
Puczylowski established the general theory of radicals of the class of objects called algebras. In this paper, we make use of the method of lattice theory to characterize the general hereditary radicals and general st...Puczylowski established the general theory of radicals of the class of objects called algebras. In this paper, we make use of the method of lattice theory to characterize the general hereditary radicals and general strongly semisimple radicals and investigate some properties of them in normal classes of algebras. This extends some known studies on the theory of radicals of various algebraic strutures.展开更多
基金The NSF (2024201051) of Liaoning Education Department.
文摘Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i1∧i2) =i1∧i2;(4) (i1∨i2) = i1∨i2, for arbitrary algebra a∈A and any i1,i2∈La,where j denotes the ideal of a uniquely determined by R(a/j) = j/j?
基金Supported by the Natural Science Foundation of Guangdong Province（04010474） Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University（2011SQRL172）
文摘This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
基金supported by the NNSF of China(11101048)supported by the Tianyuan Youth Fund of the NNSF of China(11326083)+4 种基金the Shanghai University Young Teacher Training Program(ZZSDJ12020)the Innovation Program of Shanghai Municipal Education Commission(14YZ164)the Projects(13XKJC01)from the Leading Academic Discipline Project of Shanghai Dianji Universitysupported by the NNSF of China(11271090)the NSF of Guangdong Province(S2012010010121)
文摘In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.
基金The NSF(10471065)of Chinathe Foundation(2011SQRL172)of the Education Department of Anhui Province for Outstanding Young Teachers in Universitythe Foundation(2012xq26)of the Huaibei Normal University for Young Teachers
文摘In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. （Yuan W J, Xiao B, Zhang J J. The general theorem of Gol＇dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58：1788 1791）. Meanwhile, we also take some examples to show that our estimate is sharp.
基金supported by the National Natural Science Foundation of China(No.11361064)the project No.174024 of the Ministry of Education,Science and Technological Department of the Republic of Serbia
文摘In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.
文摘Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica. For a comprehensive understanding, the frequency of the normal mode is used for a visual animation;an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.
文摘Puczylowski established the general theory of radicals of the class of objects called algebras. In this paper, we make use of the method of lattice theory to characterize the general hereditary radicals and general strongly semisimple radicals and investigate some properties of them in normal classes of algebras. This extends some known studies on the theory of radicals of various algebraic strutures.
