Abstract : In this paper, we introduce the notion of {\it semi-symmetric structure Jacobi operator } for Hopf real hypersufaces in the complex quad\-ric $Q^m = SO_{m+2}/SO_mSO_2$. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric $Q^m$ with either symmetric (parallel), or recurrent structure Jacobi operator.
Abstract : Let $n\geqslant 2$ be an integer, we denote the smallest integer $b$ such that $\gcd\qty{\binom nk: b<k<n-b}>1$ as $b(n)$. For any prime $p$, we denote the highest exponent $\alpha$ such that $p^\alpha\mid n$ as $v_p(n)$. In this paper, we partially answer a question asked by Hong in 2016. For a composite number $n$ and a prime number $p$ with $p\mid n$, let $n=a_mp^m+r$, $0\leqslant r<p^m$, $0<a_m<p$. Then we have\\ \resizebox{\linewidth}{4.5mm}{ $\displaystyle v_p\qty(\gcd\qty{\binom nk: b(n)<k<n-b(n),\ (n,k)>1})= \begin{cases} 1,&a_m=1\text{ and }r=b(n), \\ 0,&\text{otherwise}. \end{cases} $}
Abstract : A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.
Abstract : In this paper, we study products of composition, multiplication and differentiation acting on the fractional Cauchy spaces and mapping into the Zygmund space. Characterizations are provided for boundedness and compactness of these operators.
Abstract : Let ${\mathcal A}=(A_n)_{n\geq 0}$ be an increasing sequence of rings. We say that ${\mathcal I}=(I_n)_{n\geq 0}$ is an associated sequence of ideals of ${\mathcal A}$ if $I_0=A_0$ and for each $n\geq 1$, $I_n$ is an ideal of $A_n$ contained in $I_{n+1}$. We define the polynomial ring and the power series ring as follows: ${\mathcal I}[X]=\lbrace f={\sum_{i=0}^n}a_iX^i\in {\mathcal A}[X]: n\in \mathbb{N}, a_i\in I_i\rbrace$ and ${\mathcal I}[[X]]=\lbrace f={\sum_{i=0}^{+\infty}}a_iX^i\in {\mathcal A}[[X]]: a_i\in I_i\rbrace$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.
Abstract : Let $\{T_t\}_{t\in \Delta}$ be the translation semigroup with a sector $\Delta\subset \mathbb{C}$ as index set. The recurrent hypercyclicity criterion (RHCC) for the $C_0$-semigroup $\{T_t\}_{t\in \Delta}$ is established, and then the equivalent conditions ensuring $\{T_t\}_{t\in \Delta}$ satisfying the RHCC on weighted spaces of $p$-integrable and of continuous functions are presented. Especially, every chaotic semigroup $\{T_t\}_{t\in \Delta}$ satisfies the RHCC.
Abstract : In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.
Abstract : This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.
Abstract : In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\mathbf{P}^{n}(\mathbf{C})$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.
Abstract : Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers and let $P(A)=\left\{\sum \varepsilon_ia_i: a_i\in A, \varepsilon_i=0\text{ or }1, \sum \varepsilon_i<\infty\right\}$. Burr posed the following question: Determine conditions on integers sequence $B$ that imply either the existence or the non-existence of $A$ for which $P(A)$ is the set of all non-negative integers not in $B$. In this paper, we focus on some problems of subset sum related to Burr's question.
Imsoon Jeong, Gyu Jong Kim, Changhwa Woo
Bull. Korean Math. Soc. 2023; 60(4): 849-861
https://doi.org/10.4134/BKMS.b220152
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368
Rita Hibschweiler
Bull. Korean Math. Soc. 2023; 60(4): 1061-1070
https://doi.org/10.4134/BKMS.b220471
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166
Imsoon Jeong, Gyu Jong Kim, Changhwa Woo
Bull. Korean Math. Soc. 2023; 60(4): 849-861
https://doi.org/10.4134/BKMS.b220152
Rita Hibschweiler
Bull. Korean Math. Soc. 2023; 60(4): 1061-1070
https://doi.org/10.4134/BKMS.b220471
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