• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.477-484
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• 2020

For a non-zero complex number b and for m and n in 𝒩₀ = {0, 1, 2, …} let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dⁿ f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a₃ - 𝜇a²₂| are obtained.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.797-811
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• 2024

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A_E(M). The vertex set of A_E(M) is the set of equivalence classes {[x] | x ∈ T(M)^*}, where two torsion elements x, y ∈ T(M)^* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A_E(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A_E(M) has degree two if and only if it is an associated prime of M.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.943-956
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• 2023

Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D_𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial $$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z₀, |z₀| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D_𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• Proceedings of the Membrane Society of Korea Conference
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• 2002.11a
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• pp.170-173
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• 2002

• Journal of the Korean Magnetics Society
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• v.17 no.1
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• pp.14-17
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• 2007

Magnetic properties of transition metal doped $La_{0.5}Ca_{0.5}(Mn_{0.98}TM_{0.02})O_3$(TM=Cr and Ti) are studied. The samples are synthesized by the conventional solid-state method. Using vibrating sample magnetometer magnetization-temperature measurement were carried out with zero field cooling and field cooling at 50 Oe. Cr-doped sample shows cluster or spin glass like behavior while Ti doped does not. Curie temperature obtained were decreased from that of LCMO(245.5 K). Curie temperatures of Cr-doped and Ti-doped samples are 235.5 K and 232.7 K, respectively. The temperature-dependent coercivity $H_c(T)$ was also measured. The coercive force continuously decreases with the substitution of Cr and Ti, The result can be understood in terms of the interaction between defect and domain wall.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.4
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• pp.308-313
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• 2002

Samples with the norminal composition, $Bi_{2-x}Au_xSr_2CaCu_2O_{8+\delta}$ (x = 0, 0.05. 0.1, 0.15) were prepared by the solid-state reaction method. The superconducting properties, x-ray powder diffraction patterns, critical temperature and microstructure of surface were measured the samples. x-ray patterns show the single phase(2212) nature of the samples. But, the peaks of 2201 at $2\theta=30^{\circ}$ and Au peak at $2\theta=38.31^{\circ}$ are observed in the Au additive samples. The grain sire are enlarged with the increase of x. As the result of enlargement the grain size, the onset and offset critical temperature($T_c^{on}$,$T_c^{zero}$) increased with increase of x.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.447-460
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• 2022

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space A^α,m_q (ℂ) of q-analytic functions with the weight ϕ(z) = -α log |z|²+|z|^2m for any positive integer m. We obtain the corresponding reproducing kernel K^ℂ_α,q,m(z, w) using the weighted Laguerre polynomials and the Mittag-Leffler functions. Finally, we investigate the necessary and sufficient condition on (α, q, m) such that K^ℂ_α,q,m(z, w) is zero-free.