• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.453-463
• /
• 2021

In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.

• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.279-290
• /
• 2024

In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.

• Honam Mathematical Journal
• /
• v.45 no.4
• /
• pp.668-677
• /
• 2023

In this study, we bring forth a new general formula for inextensible flows of Euclidean curves as regards modified orthogonal frame (MOF) in E³. For an inextensible curve flow, we provide the necessary and sufficient conditions, which are denoted by a partial differential equality containing the curvatures and torsion.

• Journal of Biomedical Engineering Research
• /
• v.24 no.3
• /
• pp.217-231
• /
• 2003

Coded excitation with complementary Golay sequences is an effective means to increase the SNR and penetration of ultrasound imaging. in which the two complementary binary codes are transmitted successively along each scan-line, reducing the imaging frame rate by half. This method suffers from low frame rate particularly when multiple transmit focusing is employed, since the frame rate will be further reduced in proportion to the number of focal zones. In this paper. a new ultrasound imaging technique based on simultaneous multiple transmit focusing using modified orthogonal Golay codes is proposed to improve lateral resolution with no accompanying decrease in the imaging frame rate, in which a pair of orthogonal Golay codes focused at two different focal depths are transmitted simultaneously. On receive, these modified orthogonal Golay codes are separately compressed into two short pulses and individually focused. These two focused beams are combined to form a frame of image with improved lateral resolution. The Golay codes were modified to improve the transmit power efficiency (TPE) for practical imaging. Computer simulations and experimental results show that the proposed method improves significantly the lateral resolution and penetration of ultrasound imaging compared with the conventional method.

• Proceedings of the KIEE Conference
• /
• 2001.11c
• /
• pp.187-190
• /
• 2001

A new ultrasound imaging technique based on simultaneous multiple transmit focusing using orthogonal modified Golay codes is presented. modified Golay codes are used to increase signal-to-noise-ratio(SNR) and maximize the transmit power efficiency(TPE). Conventional Golay codes consist of a pair of complementary codes with same length and can be compressed into a delta-like signal due to their complementary property. In the present work, two modified Golay codes focused at different depths are transmitted at the same time, which are mutually orthogonal. On receive, these orthogonal modified Golay codes are separately compressed into two short pulses and individually focused. These two focused beam are combined to form a frame of image with improved lateral resolution. Computer simulations are performed to verity the proposed method improves the lateral resolution of image compared with the conventional echo system.