• Kyungpook Mathematical Journal
• /
• v.64 no.1
• /
• pp.31-46
• /
• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• Journal of Internet Computing and Services
• /
• v.10 no.4
• /
• pp.1-11
• /
• 2009

Recently there has arisen concern in both the database community and the graphics society about data retrieval from large motion databases because the high dimensionality of motion data implies high costs. In this circumstance, finding an effective distance measure and an efficient query processing method for such data is a challenging problem. This paper presents an elaborate motion query processing system, SMoFinder (Similar Motion Finder), which incorporates a novel kinematic distance measure and an efficient indexing strategy via adaptive frame segmentation. To this end, we regard human motions as multi-linkage kinematics and propose the weighted Minkowski distance metric. For efficient indexing, we devise a new adaptive segmentation method that chooses representative frames among similar frames and stores chosen frames instead of all frames. For efficient search, we propose a new search method that processes k-nearest neighbors queries over only representative frames. Our experimental results show that the size of motion databases is reduced greatly (${\times}1/25$) but the search capability of SMoFinder is equal to or superior to that of other systems.

• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.117-124
• /
• 2021

We obtain a new matrix generalization result dealing with weighted mean summability of infinite series by using a new general class of power increasing sequences obtained by Sulaiman [9]. This theorem also includes some new and known results dealing with some basic summability methods.

• Journal of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1359-1380
• /
• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.