• 대한수학회논문집
• /
• 제37권3호
• /
• pp.719-722
• /
• 2022

In this paper, we present some estimates for the norm of a multilinear form T ∈ 𝓛(^m𝑙ⁿ_p) for 1 ≤ p ≤ ∞ and n, m ≥ 2.

• 호남수학학술지
• /
• 제42권3호
• /
• pp.569-576
• /
• 2020

An element x ∈ E is called a norming point of P ∈ P(ⁿE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(ⁿE), we define Norm(P) = {x ∈ E : x is a norming point of P}. Norm(P) is called the norming set of P. We classify Norm(P) for P ∈ 𝒫(²𝑙²_∞).

• East Asian mathematical journal
• /
• 제24권3호
• /
• pp.275-287
• /
• 2008

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

• Journal of Applied and Pure Mathematics
• /
• 제6권1_2호
• /
• pp.71-96
• /
• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• 대한수학회보
• /
• 제60권1호
• /
• pp.171-184
• /
• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• Nuclear Engineering and Technology
• /
• 제55권5호
• /
• pp.1757-1762
• /
• 2023

Radiological hazards from external exposure of naturally occurring radioactive materials (NORM) scales residues, generated during the extraction process of oil and gas production in southern Algeria, are evaluated. The activity concentrations of ²²⁶Ra, ²³²Th, and ⁴⁰K were measured using high-purity gamma-ray spectrometry (GeHP). Mean activity concentration of ²²⁶Ra, ²³²Th and ⁴⁰K, found in scale samples are 4082 ± 41, 1060 ± 38 and 568 ± 36 Bq kg^-1, respectively. Radiological hazard parameters, such as radium equivalent (Ra_eq), external and internal hazard indices (H_ex, H_in), and gamma index (I_γ) are also evaluated. All hazard parameter values were greater than the permissible and recommended limits and the average annual effective dose value exceeded the dose constraint (0.3 mSv y^-1). However, for occasionally exposed workers, the dose rate of 0.65 ± 0.02 mSv y^-1 is lower than recommended limit of 1 mSv y^-1 for public.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1769-1784
• /
• 2008

The group Hameo (M, $\omega$) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, $\omega$) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the $L^{(1,{\infty})}$-Hofer norm (and not the $L^{\infty}$-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the $L^{\infty}$-case. In view of the fact that the Hofer norm on the group Ham (M, $\omega$) of Hamiltonian diffeomorphisms does not depend on the choice of the $L^{(1,{\infty})}$-norm vs. the $L^{\infty}$-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.

• 대한수학회지
• /
• 제48권5호
• /
• pp.1043-1052
• /
• 2011

We introduce a new norm, called the $N^p$-norm (1 $\leq$ p < ${\infty}$ on the space $N^p$(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space $N^p$(V,W), we also discover that if W is complete, then the space $N^p$(V,W) is also a Banach space with respect to this norm for 1 $\leq$ p < ${\infty}$.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1567-1605
• /
• 2023

Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a^*, ∞), the fractional Schrödinger operator 𝓛_a is defined by 𝓛_a := (-Δ)^α/2 + a|x|^-α, where $a^*:={\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}(d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with 𝓛_a and two-weight norm estimates for several square functions associated with 𝓛_a.

• Kyungpook Mathematical Journal
• /
• 제48권3호
• /
• pp.387-393
• /
• 2008

In this note, we present some inequalities for the norm and numerical radius of 2-homogeneous polynomials from the 2-dimensional real space $l_p^2$, (1 < p < $\infty$) to itself in terms of their coefficients. We also give an upper bound for n^{(k)}(l_p^2), (k = 2, 3, $\cdots$).