• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2010.10a
• /
• pp.641-642
• /
• 2010

Trigonometric functions is the study based on the most simple and unique properties of right triangle that if an angular size was settled, the value of the ratio of these sides is constant regardless of the size of the triangle. If it is the angle of right triangle with the length of the lower base and the measured angle of building, the height of the building can be obtained by using trigonometry. it is considered as a good way to gauge the height of the building as the car moves.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.2
• /
• pp.435-440
• /
• 2013

In this paper, we study the Henstock delta integral, which generalizes the Henstock integral. In particular, we study the relation between the Henstock and Henstock delta integrals.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.18 no.2
• /
• pp.4116-4120
• /
• 1976

With the use of many rivers increased nearly to the capacity, the need for information concerning daily quantities of water and the total annual or seasonal runoff has became increased. A systematic record of the flow of a river is commonly made in terms of the mean daily discharge Since. a single observation of stage is converted into discharge by means of rating curve, it is essential that the stage discharge relations shall be accurately established. All rating curves have the looping effect due chiefly to channel storage and variation in surface slope. Loop rating curves are most characteristic on streams with somewhat flatter gradients and more constricted channels. The great majority of gauge readings are taken by unskilled observers once a day without any indication of whether the stage is rising or falling. Therefore, normal rating curves shall show one discharge for one gauge height, regardless of falling or rising stage. The above reasons call for the correction of the discharge measurements taken on either side of flood waves to the theoretical steady-state condition. The correction of the discharge measurement is to consider channel storage and variation in surface slope. (1) Channel storage As the surface elevation of a river rises, water is temporarily stored in the river channel. There fore, the actual discharge at the control section can be attained by substracting the rate of change of storage from the measured discharge. (2) Variation in surface slope From the Manning equation, the steady state discharge Q in a channel of given roughness and cross-section, is given as {{{{Q PROPTO SQRT { 1} }}}} When the slope is not equal, the actual discharge will be {{{{ { Q}_{r CDOT f } PROPTO SQRT { 1 +- TRIANGLE I} CDOT TRIANGLE I }}}} may be expressed in the form of {{{{ TRIANGLE I= { dh/dt} over {c } }}}} and the celerity is approximately equal to 1.3 times the mean watrr velocity. Therefore, The steady-state discharge can be estimated from the following equation. {{{{Q= { { Q}_{r CDOT f } } over { SQRT { (1 +- { A CDOT dh/dt} over {1.3 { Q}_{r CDOT f }I } )} } }}}} If a sufficient number of observations are available, an alternative procedure can be applied. A rating curve may be drawn as a median line through the uncorrected values. The values of {{{{ { 1} over {cI } }}}} can be yielded from the measured quantities of Qr$.$f and dh/dt by use of Eq. (7) and (8). From the 1/cI v. stage relationship, new vlues of 1/cI are obtained and inserted in Eq. (7) and (8) to yield the steady-state discharge Q. The new values of Q are then plotted against stage as the corrected steadystate curve.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.879-885
• /
• 2013

In this paper, we de ne an extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of function $f^*:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale ${\mathbb{T}}$ and prove the convergence theorems for the Henstock delta integral on time scales.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.113-121
• /
• 2014

In this paper, we define an extension $f^*:[a,\;b]{\rightarrow}\mathbb{R}$ of a function $f:[a,\;b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that f is McShane delta integrable on $[a,\;b]_{\mathbb{T}}$ if and only if $f^*$ is McShane integrable on [a, b].

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.625-630
• /
• 2013

In this paper, we define an extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of a function $f^*:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and show that $f$ is Henstock delta integrable on $[a,b]_{\mathbb{T}}$ if and only if $f^*$ is Henstock integrable on $[a, b]$.

• Journal of Periodontal and Implant Science
• /
• v.46 no.4
• /
• pp.277-287
• /
• 2016

Purpose: The purpose of this study was to evaluate the clinical efficacy of enhancing deficient interdental papilla with hyaluronic acid gel injection by assessing the radiographic anatomical factors affecting the reconstruction of the interdental papilla. Methods: Fifty-seven treated sites from 13 patients (6 males and 7 females) were included. Patients had papillary deficiency in the upper anterior area. Prior to treatment, photographic and periapical radiographic standardization devices were designed for each patient. A 30-gauge needle was used with an injection-assistance device to inject a hyaluronic acid gel to the involved papilla. This treatment was repeated up to 5 times every 3 weeks. Patients were followed up for 6 months after the initial gel application. Clinical photographic measurements of the black triangle area (BTA), height (BTH), and width (BTW) and periapical radiographic measurements of the contact point and the bone crest (CP-BC) and the interproximal distance between roots (IDR) were undertaken using computer software. The interdental papilla reconstruction rate (IPRR) was calculated to determine the percentage change of BTA between the initial and final examination and the association between radiographic factors and the reconstruction of the interdental papilla by means of injectable hyaluronic acid gel were evaluated. Results: All sites showed improvement between treatment examinations. Thirty-six sites had complete interdental papilla reconstruction and 21 sites showed improvement ranging from 19% to 96%. The CP-BC correlated with the IPRR. More specifically, when the CP-BC reached 6 mm, virtually complete interdental papilla reconstruction via injectable hyaluronic acid gel was achieved. Conclusions: These results suggest that the CP-BC is closely related to the efficacy of hyaluronic acid gel injection for interdental papilla reconstruction.