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Choonkil Park - One of the best experts on this subject based on the ideXlab platform.
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hyers ulam rassias stability of homomorphisms in quasi banach algebras
Banach Journal of Mathematical Analysis, 2007Co-Authors: Choonkil ParkAbstract:Let $q$ be a Positive Rational Number and $n$ be a nonnegative integer. We prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following functional equation: \begin{eqnarray*} \sum_{i=1}^{n} f \left( \sum_{j=1}^{n}q (x_i-x_j) \right) + n f \left(\sum_{i=1}^{n} q x_i \right) = nq \sum_{i=1}^{n} f(x_i) . \end{eqnarray*} This is applied to investigate isomorphisms between quasi-Banach algebras.~The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
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hyers ulam rassias stability of homomorphisms in quasi banach algebras
Banach Journal of Mathematical Analysis, 2007Co-Authors: Choonkil ParkAbstract:Let q be a Positive Rational Number and n be a nonnegative integer. We prove the Hyers–Ulam–Rassias stability of homomorphisms in quasiBanach algebras and of generalized derivations on quasi-Banach algebras for the following functional equation:
Zhiwei Sun - One of the best experts on this subject based on the ideXlab platform.
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each Positive Rational Number has the form φ m2 φ n2
American Mathematical Monthly, 2020Co-Authors: Dmitry Krachun, Zhiwei SunAbstract:In this note, we show that each Positive Rational Number can be written as φ(m2)/φ(n2) , where φ is Euler’s totient function and m and n are Positive integers.
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each Positive Rational Number has the form varphi m 2 varphi n 2
arXiv: History and Overview, 2020Co-Authors: Dmitry Krachun, Zhiwei SunAbstract:In this note, we show that each Positive Rational Number can be written as $\varphi(m^2)/\varphi(n^2)$, where $\varphi$ is Euler's totient function and $m$ and $n$ are Positive integers.
Dmitry Krachun - One of the best experts on this subject based on the ideXlab platform.
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each Positive Rational Number has the form φ m2 φ n2
American Mathematical Monthly, 2020Co-Authors: Dmitry Krachun, Zhiwei SunAbstract:In this note, we show that each Positive Rational Number can be written as φ(m2)/φ(n2) , where φ is Euler’s totient function and m and n are Positive integers.
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each Positive Rational Number has the form varphi m 2 varphi n 2
arXiv: History and Overview, 2020Co-Authors: Dmitry Krachun, Zhiwei SunAbstract:In this note, we show that each Positive Rational Number can be written as $\varphi(m^2)/\varphi(n^2)$, where $\varphi$ is Euler's totient function and $m$ and $n$ are Positive integers.
Sun Zhi-wei - One of the best experts on this subject based on the ideXlab platform.
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Each Positive Rational Number has the form $\varphi(m^2)/\varphi(n^2)$
2020Co-Authors: Krachun Dmitry, Sun Zhi-weiAbstract:In this note, we show that each Positive Rational Number can be written as $\varphi(m^2)/\varphi(n^2)$, where $\varphi$ is Euler's totient function and $m$ and $n$ are Positive integers.Comment: 3 pages, accepted by Amer. Math. Monthl
Bumsig Kim - One of the best experts on this subject based on the ideXlab platform.
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wall crossing in genus zero quasimap theory and mirror maps
Algebraic Geometry, 2014Co-Authors: Ionut Ciocanfontanine, Bumsig KimAbstract:For each Positive Rational Number ", the theory of "-stable quasimaps to certain GIT quotients W==G developed in [CKM14] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory corresponding to " ! 0. For " > 1 one obtains the usual Gromov{Witten theory of W==G, while the other theories are new. However, they are all expected to contain the same information and, in particular, the numerical invariants should be related by wall-crossing formulas. In this paper we analyze the genus zero picture and nd that the wall-crossing in this case signicantly generalizes toric mirror symmetry (the toric cases correspond to abelian groups G). In particular, we give a geometric interpretation of the mirror map as a generating series of quasimap invariants. We prove our wall-crossing formulas for all targets W==G which admit a torus action with isolated xed points, as well as for zero loci of sections of homogeneous vector bundles on such W==G.
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wall crossing in genus zero quasimap theory and mirror maps
arXiv: Algebraic Geometry, 2013Co-Authors: Ionut Ciocanfontanine, Bumsig KimAbstract:For each Positive Rational Number epsilon, the theory of epsilon-stable quasimaps to certain GIT quotients W//G developed in arXiv:1106.3724[math.AG] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory corresponding to epsilon --> 0. For epsilon >1 one obtains the usual Gromov-Witten theory of W//G, while the other theories are new. However, they are all expected to contain the same information and in particular the numerical invariants should be related by wall-crossing formulas. In this paper we analyze the genus zero picture and find that the wall-crossing in this case significantly generalizes toric mirror symmetry (the toric cases correspond to abelian groups G). In particular, we give a geometric interpretation of the mirror map as a generating series of quasimap invariants. We prove our wall-crossing formulas for all targets W//G which admit a torus action with isolated fixed points, as well as for zero loci of sections of homogeneous vector bundles on such W//G.