• East Asian mathematical journal
• /
• 제29권1호
• /
• pp.91-99
• /
• 2013

In this paper, we prove that the BMO norm and the Garsia norm are equivalent on a bounded domain in $\mathbb{R}^N$. Also, we investigate the equivalent relation between the Lipschitz norm and the Garsia-type norm for harmonic functions.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제13권4호
• /
• pp.2028-2041
• /
• 2019

Compressed sensing (CS) is a new theory. With regard to the sparse signal, an exact reconstruction can be obtained with sufficient CS measurements. Nevertheless, in practical applications, the transform coefficients of many signals usually have weak sparsity and suffer from a variety of noise disturbances. What's worse, most existing classical algorithms are not able to effectively solve this issue. So we proposed an efficient algorithm based on smoothed ${\ell}_0$ norm for sparse signal reconstruction. The direct ${\ell}_0$ norm problem is NP hard, but it is unrealistic to directly solve the ${\ell}_0$ norm problem for the reconstruction of the sparse signal. To select a suitable sequence of smoothed function and solve the ${\ell}_0$ norm optimization problem effectively, we come up with a generalized approximate function model as the objective function to calculate the original signal. The proposed model preserves sharper edges, which is better than any other existing norm based algorithm. As a result, following this model, extensive simulations show that the proposed algorithm is superior to the similar algorithms used for solving the same problem.

• 한국지구물리탐사학회:학술대회논문집
• /
• 한국지구물리탐사학회 2007년도 공동학술대회 논문집
• /
• pp.124-129
• /
• 2007

For seismic imaging and inversion, the inverted image depends on how we define the objective function. ${\ell}^1$-norm is more robust than ${\ell}^2$-norm. However, it is difficult to apply the Newton-type algorithm directly because the partial derivative for ${\ell^1$-norm has a singularity. In our paper, to overcome the difficulties of singularities, Huber function given by hybrid ${\ell}^1/{\ell}^2$-norm is used. We tested the robustness of our new object function with several noisy data set. Numerical results show that the new objective function is more robust to band limited spiky noise than the conventional object function.

• 전기전자학회논문지
• /
• 제20권2호
• /
• pp.136-142
• /
• 2016

본 논문에서는 혼합 norm을 이용한 가중치 함수 기반의 비국부 평균 노이즈 제거 방식을 제안한다. 비국부 평균 노이즈 제거 방식에서 중심 패치와 참조 패치의 오차에 대한 신뢰도는 노이즈 양 및 국부 활동성에 의존적인 특성을 갖고 있다. 본 논문에서는 혼합 norm 기반의 새로운 가중치 함수를 제안하고, 혼합 norm의 차수를 노이즈 정도 및 중심 패치의 국부 활동성에 의해 적응적으로 결정하여 비국부 평균 노이즈 제거 방식의 성능을 개선하고자 하였다. 실험 결과를 통해 기존의 비국부 평균 노이즈 제거 방식과 비교하여 제안 방식의 정량적 및 정성적 성능의 우수성을 확인할 수 있었다. 더불어, 제안 방식은 표준 유클리드 norm 기반의 다른 형태의 비국부 평균 노이즈 방식의 성능을 개선할 수 있는 능력이 있음을 확인할 수 있었다.

• 대한수학회지
• /
• 제59권5호
• /
• pp.927-944
• /
• 2022

Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.

• Journal of applied mathematics & informatics
• /
• 제7권1호
• /
• pp.61-82
• /
• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• 충청수학회지
• /
• 제24권4호
• /
• pp.713-724
• /
• 2011

We investigate the irreducibility of iterate and composite polynomials. For this purpose discriminant and resultant are computed by means of the norm function.

• 대한화학회지
• /
• 제32권2호
• /
• pp.94-102
• /
• 1988

principle of least motion의 정량적 표현을 제시하였다. potential energy surface상의 주어진 반응 경로에 대하여 전자 위치 변수의 함수, 그 함수의 norm과 반응 경로 평균 에너지를 일의적으로 정의하였고, 그들의 성질을 검토하였다. 함수의 norm과 평균 에너지를, 일분자 이성질체화 반응의 허용된 경로를 판별하는 척도로 사용할 수 있음을 제안하였다. 대칭성을 가진 분자에 대해서 계산하지 않고 허용된 경로를 판별하였으며 Woodward-Hoffmann 규칙의 적용과 같은 결과를 얻었다

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.2246-2251
• /
• 2003

This paper proposes shape design of frame structures for vibration suppression and weight reduction. The $H_{\infty}$ norm of the transfer function from disturbance sources to the output points where vibration should be suppressed, is adopted as the performance index to represent the magnitude of vibration transfer. The design parameters are the node positions of the frame structure, on which constraints are imposed so that the structure achieves given tasks. For computation of Pareto optimal solutions to the two-objective design problem, a number of linear combinations of the $H_{\infty}$ norm and the total weight of the structure are considered and minimized. For minimization of the scalared objective function, a Lagrange function is defined by the objective function and the imposed constraints on the design parameters. The solution for which the Lagrange function satisfies the Karush-Kuhn-Tucker condition, is searched by the sequential quadratic programming (SQP) method. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

• 호남수학학술지
• /
• 제24권1호
• /
• pp.9-23
• /
• 2002

For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.