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Some Global Estimates for the Jacobians of Quasiregular Mappings
Gao, Hongya,Ren, Suna,Sun, Lanxiang Department of Mathematics 2011 Kyungpook mathematical journal Vol.51 No.1
Some global estimates for the Jacobians of quasiregular mappings f = ($f^1$, $f^2$, ${\cdots}$, $f^n$) of the Sobolev class $W^{1,n}$(${\Omega}$, $R^n$) in $L^{\varphi}({\mu})$-domains and John domains are established.
New Two-Weight Imbedding Inequalities for A-Harmonic Tensors
GAO, HONGYA,CHEN, YANMIN,CHU, YUMING 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.1
In this paper, we first define a new kind of two-weight-A_(r)^(λ_(3))(λ_(1), λ_(2), Ω)-weight, and then prove the imbedding inequalities for A-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space L^(P)(D, ∧^(l)) to the Sobolev space W^(1, p)(D, ∧^(l-l), l= 1, 2, · · , n, and to establish the basic weighted L^(P)-estimates for A-harmonic tensors.
$\bar{WT}$-Classes of Differential Forms on Riemannian Manifolds
Hongya, Gao,Zhihua, Gu,Yuming, Chu Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.1
The purpose of this paper is to study the relations between quasilinear elliptic equations on Riemannian manifolds and differential forms. Two classes of differential forms are introduced and it is shown that some differential expressions are connected in a natural way to quasilinear elliptic equations.
Some Optimal Convex Combination Bounds for Arithmetic Mean
Hongya, Gao,Ruihong, Xue Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.4
In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.
Degenerate Weakly (k<sub>1</sub>, k<sub>2</sub>)-Quasiregular Mappings
Gao, Hongya,Tian, Dazeng,Sun, Lanxiang,Chu, Yuming Department of Mathematics 2011 Kyungpook mathematical journal Vol.51 No.1
In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$\"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n \atop l})^{3/2}n^{l/2}\;{\times}\;2^{n+1}l\;{\times}\;100^{n^2}\;\[2^l(2^{n+3l}+1)\]\;(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${\in}$ $W_{loc}^{1,q_1}$ (${\Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${\Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.
Three Characteristic Beltrami System in Even Dimensions (I): p-Harmonic Equation
Gao, Hongya,Chu, Yuming,Sun, Lanxiang Department of Mathematics 2007 Kyungpook mathematical journal Vol.47 No.3
This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.
Caccioppoli Type Inequality for Weak Solutions of A-harmonic Equation and Its Applications
Hongya Gao,Yinzhu Chen 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.3
In this paper, we use a sufficient and necessary condition of weak solutions of A-harmonic equation to obtain the Caccioppoli type inequality and reverse Hőlder inequality. As some applications of the above results, we derive the Lp-integrability, Hőlder continuity and almost everywhere differentiability for weak solutions of A-harmonic equation. The same results were given for the component functions of quasi regular mappings.
Hei, Hongya,Gao, Jianjun,Dong, Jibin,Tao, Jie,Tian, Lulu,Pan, Wanma,Wang, Hongyu,Zhang, Xuemei Korean Society for Molecular and Cellular Biology 2016 Molecules and cells Vol.39 No.7
Large conductance calcium-activated potassium (BK) channels participate in many important physiological functions in excitable tissues such as neurons, cardiac and smooth muscles, whereas the knowledge of BK channels in bone tissues and osteoblasts remains elusive. To investigate the role of BK channels in osteoblasts, we used transcription activator-like effector nuclease (TALEN) to establish a BK knockout cell line on rat ROS17/2.8 osteoblast, and detected the proliferation and mineralization of the BK-knockout cells. Our study found that the BKknockout cells significantly decreased the ability of proliferation and mineralization as osteoblasts, compared to the wild type cells. The overall expression of osteoblast differentiation marker genes in the BK-knockout cells was significantly lower than that in wild type osteoblast cells. The BK-knockout osteoblast cell line in our study displays a phenotype decrease in osteoblast function which can mimic the pathological state of osteoblast and thus provide a working cell line as a tool for study of osteoblast function and bone related diseases.
MAXIMUM PRINCIPLE, CONVERGENCE OF SEQUENCES AND ANGULAR LIMITS FOR HARMONIC BLOCH MAPPINGS
Qiao, Jinjing,Gao, Hongya Korean Mathematical Society 2014 대한수학회보 Vol.51 No.6
In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.
Maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings
Jinjing Qiao,Hongya Gao 대한수학회 2014 대한수학회보 Vol.51 No.6
In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.