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Korean Mathematical Society
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ISSN(Online) 2234-3016
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2022-11-30
Some remarks on problems of subset sum
Min Tang, Hongwei XuAbstract : 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.
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2024-03-31
Sharp bounds of fifth coefficient and Hermitian-Toeplitz determinants for Sakaguchi classes
SURYA GIRI, S. SIVAPRASAD KUMARAbstract : For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{2 z {f}'(z)}{f(z) - f(-z)} \prec \varphi(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec \varphi(z) , $$ denoted by $\mathcal{S}^*_s(\varphi)$ and $\mathcal{C}_s(\varphi)$, respectively, the sharp bound of the $n^{th}$ Taylor coefficients are known for $n=2$, $3$ and $4$. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.
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2024-01-31
A function-field analogue of the Goldbach counting function and the associated Dirichlet series
Shigeki Egami, Kohji MatsumotoAbstract : We consider a function-field analogue of Dirichlet series associated with the Goldbach counting function, and prove that it can, or cannot, be continued meromorphically to the whole plane. When it cannot, we further prove the existence of the natural boundary of it.
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2023-03-31
$\Delta$-transitivity for semigroup actions
Tiaoying ZengAbstract : In this paper, we study $\Delta$-transitivity, $\Delta$-weak mixing and $\Delta$-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.
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2023-09-30
Betchov-Da Rios equation by null Cartan, pseudo null and partially null curve in Minkowski spacetime
Melek Erdoğdu, Yanlin Li, Ayşe YavuzAbstract : The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of $s$ parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of $s$ parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan $s$ parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null $s$ parameter curve.
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2023-01-31
A note on the properties of pseudo-weighted Browder spectrum
Preeti Dharmarha, Sarita KumariAbstract : The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of $\alpha$-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.
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2023-03-31
Hankel determinants for starlike functions with respect to symmetrical points
Nak Eun Cho, Young Jae Sim, Derek K. ThomasAbstract : We prove sharp bounds for Hankel determinants for starlike functions $f$ with respect to symmetrical points, i.e., $f$ given by $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ for $z\in \mathbb{D}$ satisfying $$ Re\dfrac{zf'(z)}{f(z)-f(-z)}>0, \quad z\in \mathbb{D}. $$ We also give sharp upper and lower bounds when the coefficients of $f$ are real.
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2023-03-31
Rings and modules which are stable under nilpotents of their injective hulls
Nguyen Thi Thu HaAbstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
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2022-09-30
On transcendental meromorphic solutions of certain types of differential equations
Abhijit Banerjee, Tania Biswas, Sayantan MaityAbstract : In this paper, for a transcendental meromorphic function $f$ and $a\in \mathbb{C}$, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: \[f^n+af^{n-2}f'+ P_d(z,f) = \sum_{i=1}^{k}p_i(z)e^{\alpha_i(z)}, \] where $P_d(z,f)$ is a differential polynomial of $f$, $p_i$'s and $\alpha_{i}$'s are non-vanishing rational functions and non-constant polynomials, respectively. When $a=0$, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case $a\neq 0$ has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.
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2022-07-31
$P$-extremal functions and Bernstein-Markov properties associated to compact sets in $\mathbb R^d$
Hoang Thieu Anh, Kieu Phuong Chi, Nguyen Quang Dieu, Tang Van LongAbstract : Given a compact subset $P \subset (\mathbb R^+)^d$ and a compact set $K$ in $\mathbb C^d$. We concern with the Bernstein-Markov properties of the triple $(P,K,\mu)$ where $\mu$ is a finite positive Borel measure with compact support $K$. Our approach uses (global) $P$-extremal functions which is inspired by the classical case (when $P=\Sigma$ the unit simplex) in [7].
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On Chowla's hypothesis implying that $L(s,\chi)>0$ for $s>0$ for real characters $\chi$
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The nilpotency of the prime radical of a Goldie module
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Constructions of regular sparse anti-magic squares
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, Wen Li, Bangying Xin, Ming ZhongBull. Korean Math. Soc. 2022; 59(3): 617-642
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Spin structures on complex projective spaces and circle actions
Donghoon Jang
Bull. Korean Math. Soc. 2023; 60(5): 1295-1298
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Partial sums and inclusion relations for starlike functions associated with an evolute of a nephroid curve
Gurpreet Kaur, Sumit Nagpal
Bull. Korean Math. Soc. 2023; 60(6): 1477-1496
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Canal hypersurfaces generated by non-null curves in Lorentz-Minkowski 4-space
Mustafa Altın, Ahmet Kazan, Dae Won Yoon
Bull. Korean Math. Soc. 2023; 60(5): 1299-1320
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MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon Hyun
Bull. Korean Math. Soc. 2023; 60(3): 561-574
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