• Journal of Industrial Technology
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• v.2
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• pp.45-51
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• 1982

Schwartz-Christofel transformation has been widely used to solve engineering problems. In this paper, this transformation is used to calculate topographic problems. Any two points of z-plane are transformed into ${\xi}$-plane by Schwartz-Christofel transformation using calculator.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.179-186
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• 2009

Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz distribution and prove that every approximately convex Schwartz distribution is an approximately convex function.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.483-493
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• 1999

We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of n of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.7-16
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• 2001

We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.17-25
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• 1999

In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability v on (H, C) can be extend as a finitely additive probability measure $\hat{v}$ on a field $\hat{C}{\;}{\supset}{\;}C$ which is equivalent to the Dunford-Schwartz integral on ($H,{\;}\hat{C},{\;}\hat{v}$).

• ETRI Journal
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• v.33 no.3
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• pp.401-406
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• 2011

This paper presents a fast block-matching algorithm based on the normalized cross-correlation, where the elimination order is determined based on the gradient magnitudes of subblocks in the current macroblock. Multilevel Cauchy-Schwartz inequality is derived to skip unnecessary block-matching calculations in the proposed algorithm. Also, additional complexity reduction is achieved re-using the normalized cross correlation values for the spatially neighboring macroblock because the search areas of adjacent macroblocks are overlapped. Simulation results show that the proposed algorithm can improve the speed-up ratio up to about 3 times in comparison with the existing algorithm.

• Clinical and Experimental Pediatrics
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• v.52 no.9
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• pp.999-1004
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• 2009

Purpose : Glomerular filtration rate (GFR) is a fundamental parameter in assessing renal function and predicting the progression of chronic renal disease. Because the use of serum creatinine has several disadvantages, many studies have investigated the use of cystatin C for estimating GFR. We compared creatinine clearance and GFR with formulas using serum creatinine and cystatin C. Methods : We retrospectively analyzed 211 patients with various renal diseases and classified them into two groups according to creatinine clearance (Group 1: CrCl >$90mL/min/1.73m^2$, Group 2: CrCl <$90mL/min/1.73m^2$). We measured serum creatinine, cystatin C, and creatinine clearance. We calculated GFR using the Schwartz, Counahan, Filler and Lepage, Bokencamp et al, and Grubb et al formulas. Results : GFR determined by the Schwartz formula had the highest correlation to creatinine clearance (r=0.415, P=0.00). GFR determined by various formulas using cystatin C had lower correlation to creatinine clearance (r=0.187, r=0.187, r=0.291). The Schwartz and Counahan formulas showed greater diagnostic accuracy in detecting decreased GFR than cystatin C in group 2 (areas under the curve: Schwartz, 0.596; Counahan, 0.572; Filler, 0.512; Bokencamp, 0.508; and Grubb, 0.514). Conclusion : GFR determined by the Schwartz and Counahan formulas using serum creatinine showed higher correlation coefficient than that determined by formulas using cystatin C. The formulas using cystatin C were not superior to those using serum creatinine in detecting decreased GFR. Cystatin C measurement was not satisfactory for assessing GFR in patients whose renal function was not severely decreased.

• Investigative Magnetic Resonance Imaging
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• v.18 no.2
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• pp.87-106
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• 2014

Purpose : To describe how a robust implementation of a radial 3D gradient-echo sequence with stack-of-stars sampling can be achieved, to review the imaging properties of radial acquisitions, and to share the experience from more than 5000 clinical patient scans. Materials and Methods: A radial stack-of-stars sequence was implemented and installed on 9 clinical MR systems operating at 1.5 and 3 Tesla. Protocols were designed for various applications in which motion artifacts frequently pose a problem with conventional Cartesian techniques. Radial scans were added to routine examinations without selection of specific patient cohorts. Results: Radial acquisitions show significantly lower sensitivity to motion and allow examinations during free breathing. Elimination of breath-holding reduces failure rates for non-compliant patients and enables imaging at higher resolution. Residual artifacts appear as streaks, which are easy to identify and rarely obscure diagnostic information. The improved robustness comes at the expense of longer scan durations, the requirement for fat suppression, and the nonexistence of a time-to-center value. Care needs to be taken during the configuration of receive coils. Conclusion: Routine clinical use of radial stack-of-stars sequences is feasible with current MR systems and may serve as substitute for conventional fat-suppressed T1-weighted protocols in applications where motion is likely to degrade the image quality.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.391-404
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• 2010

The well-known characterizations of the Schwartz space of rapidly decreasing functions is extended to new algebras of rapidly decreasing generalized functions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.