Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-01-31
Some results related to differential-difference counterpart of the Br\"{u}ck conjecture
Md. Adud, BIKASH CHAKRABORTYAbstract : In this paper, our focus is on exploring value sharing \linebreak problems related to a transcendental entire function $f$ and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Br\"{u}ck conjecture.
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2024-01-31
Intrinsic theory of $C^v$-reducibility in Finsler Geometry
Salah Gomaa Elgendi, Amr SoleimanAbstract : In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the $C^v$-reducible and generalized $C^v$-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is $C^v$-reducible if and only if it is $C$-reducible and satisfies the $\mathbb{T}$-condition. We study the generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$. We show that a Finsler manifold $(M,L)$ is generalized $C^v$-reducible with $\mathbb{A}$ if and only if it is $C$-reducible and $\mathbb{T}=\mathbb{A}$. Moreover, we prove that a Landsberg generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$ is Berwaldian. Finally, we consider a special $C^v$-reducible Finsler manifold and conclude that a Finsler manifold is a special $C^v$-reducible if and only if it is special semi-$C$-reducible with vanishing $\mathbb{T}$-tensor.
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2023-07-31
Coloring links by the symmetric group of degree three
Kazuhiro Ichihara, Eri MatsudoAbstract : We consider the number of colors for colorings of links by the symmetric group $S_3$ of degree $3$. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by $S_3$ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by $S_3$ with 5 colors, then the link also admits such a coloring with only 4 colors.
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2023-10-31
Geometry of generalized Berger-type deformed metric on $B$-manifold
ABDERRAHIM ZAGANEAbstract : Let $(M^{2m},\varphi,g)$ be a $B$-manifold. In this paper, we introduce a new class of metric on $(M^{2m},\varphi,g)$, obtained by a non-conformal deformation of the metric $g$, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on $M$ with respect to a generalized Berger-type deformed metric.
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2024-04-30
Geometric properties of starlikeness involving hyperbolic cosine function
Om P. Ahuja, Asena Çetinkaya, Sushil KumarAbstract : In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.
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2024-04-30
A weaker notion of the finite factorization property
Henry Jiang, Shihan Kanungo, Hwisoo KimAbstract : An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid $M$ is a length-finite factorization monoid if each $b \in M$ has only finitely many factorizations of any prescribed length. An additive submonoid of $\mathbb{R}_{\ge 0}$ is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.
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2023-10-31
Generalized Fourier--Feynman transforms and convolutions for exponential type functions of generalized Brownian motion paths
Jae Gil ChoiAbstract : Let $C_{a,b}[0,T]$ denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier--Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space $C_{a,b}[0,T]$. For our purpose, we use the exponential type functions on the general Wiener space $C_{a,b}[0,T]$. The class of all exponential type functions is a fundamental set in \linebreak $L_2(C_{a,b}[0,T])$.
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2024-01-31
An example for the non-stability of multi-additive-quadratic-cubic mappings
Abasalt BodaghiAbstract : In this paper, we improve Corollary 1 of \cite{bras} and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.
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2023-01-31
Detectable means and applications
Mustapha Ra\"{\i}ssouliAbstract : In this paper, we introduce a new concept for bivariate means and we study its properties. Application of this concept for mean-inequal\-ities is also discussed. Open problems are derived as well.
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2023-10-31
Geometry of a semi-symmetric recurrent metric connection
Jaeman KimAbstract : In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.
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Riemannian submersions whose total space is endowed with a torse-forming vector field
\c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}
Commun. Korean Math. Soc. 2022; 37(4): 1199-1207
https://doi.org/10.4134/CKMS.c210336 -
The dimension of the maximal spectrum of some ring extensions
Rachida EL KHALFAOUI, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 983-992
https://doi.org/10.4134/CKMS.c220332 -
Circle approximation using parametric polynomial curves of high degree in explicit form
Young Joon Ahn
Commun. Korean Math. Soc. 2022; 37(4): 1259-1267
https://doi.org/10.4134/CKMS.c210333 -
Numerical method for a system of Caputo fractional differential equations with non-local boundary conditions
S. Joe Christin Mary, Ayyadurai Tamilselvan
Commun. Korean Math. Soc. 2023; 38(1): 281-298
https://doi.org/10.4134/CKMS.c210252
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Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold
Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2023; 38(3): 893-900
https://doi.org/10.4134/CKMS.c220287 -
Estimates for certain shifted convolution sums involving Hecke eigenvalues
Guodong Hua
Commun. Korean Math. Soc. 2023; 38(2): 319-330
https://doi.org/10.4134/CKMS.c210366 -
Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the torus
Ioannis Diamantis
Commun. Korean Math. Soc. 2022; 37(4): 1221-1248
https://doi.org/10.4134/CKMS.c210169 -
Pascal's hexagon theorem reproved by elementary tools only
Insong Choe
Commun. Korean Math. Soc. 2022; 37(4): 989-993
https://doi.org/10.4134/CKMS.c210397
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