• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.31-38
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• 1999

This paper focuses on extracting formants from transfer function, derived from linear prediction analysis of speech signal. The second derivative of the log magnitude spectrum of the transfer function, the first and third derivatives of the phase spectrum of the transfer function in the z-plane are discussed. Their resolutions of detecting formants are analyzed and some comparisons are given. Theoretical analyses and experimental results show that the third derivative of the phase spectrum decays more rapidly around the formant locations than the first derivative of the phase spectrum and the second derivative of the log magnitude spectrum. Compared with the second derivative of the log spectrum and the first derivative of the phase spectrum, the third derivative of the phase spectrum has higher resolution in frequency domain and provides more accurate formant extraction.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.21-29
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• 2006

The method to construct a surface from point data are widely known. But the way to make a surface from derivative data is not usually used since derivative data in engineering appears very often. In this paper, if more than one types of data among three possible data such as point data, first derivative data, second derivative data are given, we can construct a surface. If only first derivative data are given, we add a function value at the one point. If only second derivative data are given, we add a linear function.

• East Asian mathematical journal
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• v.18 no.2
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• pp.163-173
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• 2002

In this paper an inequality of Ostrowski type in terms of the lower and upper bounds of the first derivative is found.

• Bulletin of the Korean Chemical Society
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• v.24 no.12
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• pp.1731-1736
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• 2003

The reaction of ${\alpha}$-Benzilmonoxime with palladium(II) produces a green complex in triton X-100 micellar media. Palladium has been determined using zero and first derivative spectrophotometric methods. The absorbances of Pd(II)- ${\alpha}$--benzilmonoxime complex at 441.8 and 677.0 nm in 0.10 M perchloric acid solution were monitored and linear working ranges of 0.3-12.0 and 0.7-20 ${\mu}$g mL$^{-1}$ with detection limits of 0.07 and 0.10 ${\mu}$g $mL^-1$ were obtained, respectively. Also, recoveries in the range of 92.8 to 100.1% and relative standard deviations in the range of 0.4 to 7.1% were obtained. First derivative spectrophotometry has also been applied for palladium determination under the optimum condition. The linear dynamic range of 0.2-24.0 ${\mu}$g $mL^{-1}$ palladium with relative standard deviations of 0.6-6.9% and recoveries in the range of 94.9-102.5% has been obtained by first derivative spectrophotometry. The method shows high selectivity because of the high concentration of acid used, which prevents formation of complexes of ${\alpha}$--benzilmonoxime with the other cations. The palladium complex formed was stable at least one day. The method was successfully applied to the determination of palladium in some synthetic palladium alloys and palladium-charcoal powder.

• Archives of Pharmacal Research
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• v.13 no.3
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• pp.215-220
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• 1990

Two different, derivative spectrophotometric and gas-liquid chromatographic, procedures for direct quantitation of caffeine and some commonly dispensed antihistaminics in bulk forms, in their laboratory prepared mmixtures and in dosage formulations, have been investigated. The limit, sensitivity reproducibility and accuracy of each method were studied for each individual drug substance and in some usual pharmaceutical formulations.

• Bulletin of the Korean Chemical Society
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• v.25 no.8
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• pp.1137-1142
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• 2004

A spectrophotometric and first derivative spectrophotometric method was developed in aquatic Tween 80 micellar solutions for selective determination of nickel without using any pre-separation step. 1-(2-Pyridylazo)-2-naphthol (PAN), as a sensitive chromogenic complexing agent formed a red-colored Ni(II)-PAN complex in Tween 80 media with satisfactory solubility and stability. Conditions such as pH, PAN concentration, type and concentration of micellizing agent were optimized. Molar absorptivity of Ni-PAN complex was found $4.62\;{\times}\;10^4L\;cm^{?1}\;mol^{?1}$ at 569 nm, under the optimum condition. Calibration graphs were derived by zero, first and second derivative spectrophotometry at maximum wavelengths of 569, 578 and 571 nm with linear ranges of 30-1800, 20-2500 and 30-2000 ng $mL^{?1}$ , respectively. Precision as standard deviation as well as accuracy as recovery percent were in the range of 1-20 ng $mL^{?1}$, and 93.3-103.3%, respectively, for the entire of the linear ranges. Spectrophotometric detection limit was 3 ng $mL^{?1}$ and effects of diverse ions on the first derivative determination of nickel were studied to investigate selectivity of the method. Interferences of cobalt and copper on the nickel determination were prevented using o-phenanthroline as masking agent. The recommended procedures were applied to the various synthetic and stainless steel alloys, tea leaves and human hair, with satisfactory results.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.11
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• pp.251-253
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• 1996

Noninvasive monitoring of total Hemoglobin value is feasible with the use of spectroscopic measurements. As a step toward tile final goal of the development of a noninvasive monitor, the spectra$(400{\sim}800mm)$of EDTA whole blood were obtained along with reference total Hemoglobin values. Under the same condition water spectrum was generated. It was subtracted from each blood sample, and then tile first derivative of each subtracted data was taken by 'approximated first derivative algorithm' with gap (1,6,10,20nm). The correlation was obtained between total Hemoglobin and first valley wavelength of first derivative spectrum (sample number: 93).

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.147-154
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• 2009

Tamanoi proposed higher Schwarzian operators which include the classical Schwarzian derivative as the first nontrivial operator. In view of the relations between the classical Schwarzian derivative and the analogous differential operator defined in terms of Peschl's differential operators, we define the generating function of our generalized higher operators in terms of Peschl's differential operators and obtain recursion formulas for them. Our generalized higher operators include the analogous differential operator to the classical Schwarzian derivative. A special case of our generalized higher Schwarzian operators turns out to be the Tamanoi's operators as expected.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Bulletin of the Korean Chemical Society
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• v.25 no.12
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• pp.1764-1768
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• 2004

The present work reports on the investigations based on the interaction of sodium hydroxide with catechol derivatives. The first derivative spectra allowed the simultaneous determination of levodopa and carbidopa. The calibration graph was constructed from the first derivative signals by measuring $^1D$ at 350 nm for standard samples containing between 3 and 30 mg $L^{-1}$ of levodopa and at 305 nm for standard samples containing between 3 and 80 mg $L^{-1}$ of carbidopa. This method offers the advantages of simplicity, rapidity, selectivity and higher sensitivity than most of the existing spectophotometric methods.