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Mahsa Fatehi,Mahmood Haji Shaabani 대한수학회 2017 대한수학회지 Vol.54 No.2
If $\psi$ is analytic on the open unit disk $\mathbb{D}$ and $\varphi$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{\psi,\varphi}$ is defined by $C_{\psi,\varphi}f(z)=\psi(z)f (\varphi (z))$, when $f$ is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^{2}(\beta)$, we prove that if $C_{\psi,\varphi}$ is cohyponormal on $H^{2}(\beta)$, then $\psi$ never vanishes on $\mathbb{D}$ and $\varphi$ is univalent, when $\psi \not \equiv 0$ and $\varphi$ is not a constant function. Moreover, for $\psi=K_{a}$, where $|a| < 1$, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{\psi,\varphi}$. After that, for $\varphi $ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{\psi,\varphi}$, when $\psi \not \equiv 0$ and $\psi$ is analytic on $\overline{\mathbb{D}}$. Finally, we find all normal weighted composition operators which are bounded below.
On a subclass of certain convex harmonic functions
S\.{i}bel Yal\c{c}in,Met\.in \ 대한수학회 2006 대한수학회지 Vol.43 No.4
We define and investigate a subclass of complex valued harmonicconvex functions that are univalent and sense preserving in theopen unit disk. We obtain coefficient conditions, extreme points,distortion bounds, convolution conditions for the above family of
Non-triviality of two homotopy elements in $\pi_{\ast}S$
Xiugui Liu 대한수학회 2006 대한수학회지 Vol.43 No.4
Let A be the mod p Steenrod algebra for p an arbitrary oddprime and S the sphere spectrum localized at p. In this paper,some useful propositions about the May spectral sequence are firstgiven, and then, two new nontrivial homotopy elements alpha_1jxi_n (pgeq 5,ngeq 3) and gamma_salpha_1 jxi_n(pgeq 7, ngeq 4) are detected in the stable homotopy groupsof spheres, where xi_nin pi_{p^nq+pq-2}M is obtained in [2].The new ones are of degree 2(p-1)(p^n+p+1)-4 and2(p-1)(p^n+sp^2+sp+(s-1))-7 and are represented up to nonzeroscalar by b_0h_0h_n, b_0 h_0 h_n tilde{gamma}_{s}not=0inoperatorname{Ext}_A^{ast,ast}(Z_p,Z_p) in the Adams spectralsequence respectively, where 3leq s<p-2.
Slant Submanifolds of an Almost Product Riemannian Manifold
Bayram Sahin 대한수학회 2006 대한수학회지 Vol.43 No.4
In this paper, we study both slant and semi-slant submanifolds ofan almost product Riemannian manifold. We give characterizationtheorems for slant and semi-slant submanifolds and investigatespecial class of slant submanifolds which are product version ofKaehlerian slant submanifold. We also obtain integrabilityconditions for the distributions which are involved in thedefinition of a semi-slant submanifold. Finally, we prove atheorem on the geometry of leaves of distributions under acondition.
Weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings
David F. Anderson,Ayman Badawi,Brahim Fahid 대한수학회 2018 대한수학회지 Vol.55 No.5
Let $R$ be a commutative ring with $ 1 \neq 0$, $I$ a proper ideal of $R$, and $m$ and $n$ positive integers. In this paper, we define $I$ to be a weakly $(m,n)$-closed ideal if $ 0\neq x^{m}\in I$ for $x \in R$ implies $x^{n} \in I$, and $R$ to be an $(m,n)$-von Neumann regular ring if for every $x \in R$, there is an $r \in R$ such that $x^mr = x^n$. A number of results concerning weakly $(m, n)$-closed ideals and $(m,n)$-von Neumann regular rings are given.
Nuclearity properties and C*-envelopes of operator system inductive limits
Ajay Kumar,Preeti Luthra 대한수학회 2018 대한수학회지 Vol.55 No.5
We investigate the relationship between $C^*$-envelopes and inductive limit of operator systems. Various operator system nuclearity properties of inductive limit for a sequence of operator systems are also discussed.
이승원,고성은 대한수학회 1998 대한수학회논문집 Vol.13 No.3
쌍곡공간$^3$에 들어있는 닫힌 곡면의 주곡률함수가 특별한 함수 관계를 만족시킨다면 그 곡면은 둥근공임을 보였다. 이 결과를 이용하여 Gauss-Kronecker 곡률이 상수인 닫힌 곡면은 둥근공 뿐이 없음도 보였다.