Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel nor...Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.展开更多
From the results of researches of active faults in resent years, a correlation analysis between segments of the faults according to surface ruptures in nine historical strong earthquakes occurring in downfaulted syste...From the results of researches of active faults in resent years, a correlation analysis between segments of the faults according to surface ruptures in nine historical strong earthquakes occurring in downfaulted system and active structures around Ordos block is conducted in paper. The result shows that there is a good correlation between them, except few individual data that have more uncertain parameters. It shows that intensity and segments of surface ruptures in these strong earthquakes are intrinsically related with the active structures. These strong earthquakes produced stable and unstable rupture boundaries of characteristic-earthquake type and successive occurrence of strong earthquakes on the different boundary faults in the same tectonic unit.展开更多
In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection be...In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.展开更多
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introduci...The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.展开更多
Strong differential subordination and superordination properties are determined for Phi-like functions in the open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwi...Strong differential subordination and superordination properties are determined for Phi-like functions in the open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.展开更多
LetΩbe a domain of Rn with n≥2 and p(·)be a local Lipschitz funcion inΩwith 1<p(x)<∞inΩ.We build up an interior quantitative second order Sobolev regularity for the normalized p(·)-Laplace equati...LetΩbe a domain of Rn with n≥2 and p(·)be a local Lipschitz funcion inΩwith 1<p(x)<∞inΩ.We build up an interior quantitative second order Sobolev regularity for the normalized p(·)-Laplace equation−Δ_(p)^(N)(·)u=0 inΩas well as the corresponding inhomogeneous equation−Δ_(p)^(N)(·)u=f inΩwith f∈C^(0)(Ω).In particular,given any viscosity solution u to−Δ_( p(·))^(N)u=0 inΩ,we prove the following:(i)in dimension n=2,for any subdomain U■Ωand anyβ≥0,one has|Du|^(β)Du∈L_(loc)^(2+δ)(U)with a quantitative upper bound,and moreover,the map(x_(1),x_(2))→|Du|^(β)(u_(x1),−u_(x2))is quasiregular in U in the sense that|D[|Du|^(β)Du]|^(2)≤−C detD[|Du|^(β)Du]a.e.inU.(ii)in dimension n≥3,for any subdomain U■Ωwith infU p(x)>1 and supU p(x)<3+2/(n−2),one has D^(2)u∈L_(loc)^(2+δ)(U)with a quantitative upper bound,and also with a pointwise upper bound|D^(2)u|^(2)≤−CΣ_(1≤i<j≤n)[u_(x_(i)x_(j))u_(x_(j)x_(i))−u_(x_(i)x_(i))u_(x_(j)x_(j))]a.e.inU.Here constantsδ>0 and C≥1 are independent of u.These extend the related results obtaind by Adamowicz-H¨ast¨o[Mappings of finite distortion and PDE with nonstandard growth.Int.Math.Res.Not.IMRN,10,1940-1965(2010)]when n=2 andβ=0.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
文摘Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.
基金Chinese Joint Seismological Science Foundation.Contribution! No. 2000A005Institute of Crustal Dynamics, China Seismological
文摘From the results of researches of active faults in resent years, a correlation analysis between segments of the faults according to surface ruptures in nine historical strong earthquakes occurring in downfaulted system and active structures around Ordos block is conducted in paper. The result shows that there is a good correlation between them, except few individual data that have more uncertain parameters. It shows that intensity and segments of surface ruptures in these strong earthquakes are intrinsically related with the active structures. These strong earthquakes produced stable and unstable rupture boundaries of characteristic-earthquake type and successive occurrence of strong earthquakes on the different boundary faults in the same tectonic unit.
基金the Science Research Foundation of Qingdao Technological University(C2002-214)
文摘In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.
基金Project supported by the National Natural Science Foundation of China (Grant No 10872141)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20060056005)
文摘The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
基金Supported by UGC New Delhi(Grant No.MRP-5591/15(SERO/UGC))
文摘Strong differential subordination and superordination properties are determined for Phi-like functions in the open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12025102,12071098,11871088)。
文摘LetΩbe a domain of Rn with n≥2 and p(·)be a local Lipschitz funcion inΩwith 1<p(x)<∞inΩ.We build up an interior quantitative second order Sobolev regularity for the normalized p(·)-Laplace equation−Δ_(p)^(N)(·)u=0 inΩas well as the corresponding inhomogeneous equation−Δ_(p)^(N)(·)u=f inΩwith f∈C^(0)(Ω).In particular,given any viscosity solution u to−Δ_( p(·))^(N)u=0 inΩ,we prove the following:(i)in dimension n=2,for any subdomain U■Ωand anyβ≥0,one has|Du|^(β)Du∈L_(loc)^(2+δ)(U)with a quantitative upper bound,and moreover,the map(x_(1),x_(2))→|Du|^(β)(u_(x1),−u_(x2))is quasiregular in U in the sense that|D[|Du|^(β)Du]|^(2)≤−C detD[|Du|^(β)Du]a.e.inU.(ii)in dimension n≥3,for any subdomain U■Ωwith infU p(x)>1 and supU p(x)<3+2/(n−2),one has D^(2)u∈L_(loc)^(2+δ)(U)with a quantitative upper bound,and also with a pointwise upper bound|D^(2)u|^(2)≤−CΣ_(1≤i<j≤n)[u_(x_(i)x_(j))u_(x_(j)x_(i))−u_(x_(i)x_(i))u_(x_(j)x_(j))]a.e.inU.Here constantsδ>0 and C≥1 are independent of u.These extend the related results obtaind by Adamowicz-H¨ast¨o[Mappings of finite distortion and PDE with nonstandard growth.Int.Math.Res.Not.IMRN,10,1940-1965(2010)]when n=2 andβ=0.
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.
