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AUTOMATIC CONTINUITY OF ALMOST MULTIPLICATIVE LINEAR FUNCTIONALS ON FRÉCHET ALGEBRAS
Honary, Taher Ghasemi,Omidi, Mashaallah,Sanatpour, Amir Hossein Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3
A linear functional T on a $Fr{\acute{e}}echet$ algebra (A, (pn)) is called almost multiplicative with respect to the sequence ($p_n$), if there exists ${\varepsilon}{\geq}0$ such that ${\mid}Tab-TaTb{\mid}{\leq}{\varepsilon}p_n(a)p_n(b)$ for all $n{\in}\mathbb{N}$ and for every $a,b{\in}A$. We show that an almost multiplicative linear functional on a $Fr{\acute{e}}echet$ algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous $Fr{\acute{e}}echet$ algebra is continuous.
APPROXIMATION IN LIPSCHITZ ALGEBRAS OF INFINITELY DIFFERENTIABLE FUNCTIONS
Honary, T.G.,Mahyar, H. Korean Mathematical Society 1999 대한수학회보 Vol.36 No.4
We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.
Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity
Honary, Bahman,Bahabadi, Alireza Zamani Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).
Honary, Bahman,Bahabadi, Alireza Zamani Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.
Bahman Honary,Alireza Zamani Bahabadi 대한수학회 2008 대한수학회보 Vol.45 No.4
Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W. Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.
Automatic continuity of almost multiplicative linear functionals on Fréchet algebras
Taher Ghasemi Honary,Mashaallah Omidi,Amir Hossein Sanatpour 대한수학회 2016 대한수학회보 Vol.53 No.3
A linear functional $T$ on a Fr$\acute{\mathbf{\text{e}}}$chet algebra $(A, (p_n))$ is called \textit{almost multiplicative} with respect to the sequence $(p_n)$, if there exists $\varepsilon\geq0$ such that $|Tab - Ta Tb|\leq \varepsilon p_n(a) p_n(b)$ for all $n \in \mathbb{N}$ and for every $a, b \in A$. We show that an almost multiplicative linear functional on a Fr$\acute{\mathbf{\text{e}}}$chet algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous Fr$\acute{\mathbf{\text{e}}}$chet algebra is continuous.
Pooyan, Honari,Ahmad, Ebrahimi,Azadeh, Rakhshan Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.15
Background: Glioblastoma is a highly aggressive and malignant brain tumor. Risk factors are largely unknown however, although several biomarkers have been identified which may support development, angiogenesis and invasion of tumor cells. One of these biomarkers is PAI-1.4G/5G and A-844G are two common polymorphisms in the gene promotor of PAI 1 that may be related to high transcription and expression of this gene. Studies have shown that the prevalence of the 4G and 844G allele is significantly higher in patients with some cancers and genetic disorders. Materials and Methods: We here assessed the association of 4G/5G and A-844G polymorphisms with glioblastoma cancer risk in Iranians in a case-control study. All 71 patients with clinically confirmed and 140 volunteers with no history and symptoms of glioblastoma as control group were screened for 4G/5G and A-844G polymorphisms of PAI-1, using ARMS-PCR. Genotype and allele frequencies of case and control groups were analyzed using the DeFinetti program. Results: Our results showed significant associations between 4G/5G (p=0.01824) and A-844G (p = 0.02012) polymorphisms of the PAI-1 gene with glioblastoma cancer risk in our Iranian population. Conclusions: The results of this study supporting an association of the PAI-1 4G/5G (p=0.01824) and A-844G (p = 0.02012) polymorphisms with increasing glioblastoma cancer risk in Iranian patients.
Chatroudi, Mahla Honari,Khalili, Mohammad Ali,Ashourzadeh, Sareh,Anbari, Fatemeh,Shahedi, Abbas,Safari, Somayyeh The Korean Society for Reproductive Medicine 2019 Clinical and Experimental Reproductive Medicine Vol.46 No.4
Objective: In vitro maturation (IVM) of immature oocytes can be useful for some infertile patients. In IVM programs, the rates of embryo formation and pregnancy are low. Therefore, it is essential to recognize the main factors involved in regulating oocyte maturation in vitro. The purpose of this study was to investigate the effects of growth differentiation factor 9 (GDF9) and cumulus cell (CC) supplementation in IVM medium on the rates of embryo formation and viability of human blastocysts. Methods: A total of 80 germinal vesicle oocytes from stimulated cycles underwent an IVM program. The oocytes were divided into four groups, where group I consisted of IVM media only and served as the control, group II consisted of IVM+CCs, group III consisted of IVM+GDF9 (200 ng/mL), and group IV consisted of IVM+CCs+GDF9 (200 ng/mL). Intracytoplasmic sperm injection was performed on the IVM oocytes, and the cleavage embryos that were generated were vitrified. Following thawing, the embryos were cultured for 3 additional days, and the viability rates of the developed blastocysts were determined. Results: The maturation rate of the oocytes did not differ significantly across the four groups. The fertilization rate in group II was significantly higher than that in the control group (76.5% vs. 46.2%). Embryo formation was significantly more frequent in all experimental groups than in the control group, while blastocyst formation did not show significant differences in the three experimental groups compared to the control. The mean viability rates in groups II, III, and IV were 58.16%, 55.91%, and 55.95%, respectively, versus 37.78% in the control group (p< 0.05). Conclusion: Supplementation of IVM culture media with GDF9 and CCs enhanced the fertilization, embryo formation, and viability rates of blastocysts generated from vitrified cleavage embryos.