Considerations on the Derivative of the Titration Curve of a Weak Diacid

2019 ◽  
Author(s):  
Marc Blétry
Keyword(s):  
Titration Curve ◽  
First Derivative ◽  
Equivalent Point ◽  
The Difference

We show that the derivative of the titration curve of a diacid can be used to assess the first equivalent as well as the second equivalent point, but also the value for which pH=pKa. This is controlled by the difference between both pKa's of the diacid. A bifurcation is observed for the values of volume of titrant for which the first derivative cancels.<br>

Considerations on the Derivative of the Titration Curve of a Weak Diacid

2019 ◽  
Author(s):  
Marc Blétry
Keyword(s):  
Titration Curve ◽  
First Derivative ◽  
Equivalent Point ◽  
The Difference

We show that the derivative of the titration curve of a diacid can be used to assess the first equivalent as well as the second equivalent point, but also the value for which pH=pKa. This is controlled by the difference between both pKa's of the diacid. A bifurcation is observed for the values of volume of titrant for which the first derivative cancels.<br>

Weibull distribution function for cardiac contraction: integrative analysis

1999 ◽  
Vol 277 (5) ◽  
pp. H1940-H1945 ◽  
Author(s):  
Junichi Araki ◽  
Hiromi Matsubara ◽  
Juichiro Shimizu ◽  
Takeshi Mikane ◽  
Satoshi Mohri ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Systems Engineering ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Cardiac Contraction ◽  
Weibull Function ◽  
Difference Curve ◽  
First Derivative ◽  
The Difference ◽  
Gradual Pressure

The Weibull distribution is widely used to analyze the cumulative loss of performance, i.e., breakdown, of a complex system in systems engineering. We found for the first time that the difference curve of two Weibull distribution functions almost identically fitted the isovolumically contracting left ventricular (LV) pressure-time curve [P( t)] in all 345 beats (3 beats at each of 5 volumes in 23 canine hearts; r = 0.999953 ± 0.000027; mean ± SD). The first derivative of the difference curve also closely fitted the first derivative of the P( t) curve. These results suggest the possibility that the LV isovolumic P( t) curve may be characterized by two counteracting cumulative breakdown systems. Of these, the first breakdown system causes a gradual pressure rise and the second breakdown system causes a gradual pressure fall. This Weibull-function model of the heart seems to give a new systems engineering or integrative physiological view of the logic underlying LV isovolumic pressure generation.

A theoretical evaluation of linearity

1993 ◽  
Vol 39 (3) ◽  
pp. 405-413 ◽  
Author(s):  
M H Kroll ◽  
K Emancipator
Keyword(s):  
Higher Order ◽  
Visual Evaluation ◽  
Theoretical Evaluation ◽  
First Order ◽  
First Derivative ◽  
Lack Of Fit ◽  
Linear Polynomial ◽  
Straight Line ◽  
The Difference ◽  
Major Property

Abstract The measure of linearity is an important part of the evaluation of a method. According to the NCCLS guidelines (Document EP6-P), results of a linearity experiment are fit to a straight line and judged linear either by visual evaluation, which is subjective, or by the lack-of-fit test. This approach depends on the precision of the method, is not necessarily conclusive, and fails to be quantitative. We define linearity as a measure of how well a first-order (linear) polynomial fits the data compared with a higher-order (nonlinear) polynomial. The major property of a linear polynomial is that the first derivative is a constant. The nonlinearity of a method can be measured by the difference between these two polynomials (first-order and higher-order) at specific values or, as an average, the root-mean difference. This approach is independent of the precision of the assay and is conclusive, quantitative, and objective.

scholarly journals Estimating leaf nitrogen concentration based on the combination with fluorescence spectrum and first-derivative

2020 ◽  
Vol 7 (2) ◽  
pp. 191941
Author(s):  
Jian Yang ◽  
Lin Du ◽  
Wei Gong ◽  
Shuo Shi ◽  
Jia Sun
Keyword(s):  
Fluorescence Spectrum ◽  
Nitrogen Concentration ◽  
Principal Component ◽  
Laser Induced Fluorescence ◽  
Leaf Nitrogen ◽  
Leaf Nitrogen Concentration ◽  
Growth Status ◽  
First Derivative ◽  
Fluorescence Characteristics ◽  
The Difference

Leaf nitrogen concentration (LNC) is a major indicator in the estimation of the crop growth status which has been diffusely applied in remote sensing. Thus, it is important to accurately obtain LNC by using passive or active technology. Laser-induced fluorescence can be applied to monitor LNC in crops through analysing the changing of fluorescence spectral information. Thus, the performance of fluorescence spectrum (FS) and first-derivative fluorescence spectrum (FDFS) for paddy rice (Yangliangyou 6 and Manly Indica) LNC estimation was discussed, and then the proposed FS + FDFS was used to monitor LNC by multivariate analysis. The results showed that the difference between FS ( R 2 = 0.781, s.d. = 0.078) and FDFS ( R 2 = 0.779, s.d. = 0.097) for LNC estimation by using the artificial neural network is not obvious. The proposed FS + FDFS can improved the accuracy of LNC estimation to some extent ( R 2 = 0.813, s.d. = 0.051). Then, principal component analysis was used in FS and FDFS, and extracted the main fluorescence characteristics. The results indicated that the proposed FS + FDFS exhibited higher robustness and stability for LNC estimation ( R 2 = 0.851, s.d. = 0.032) than that only using FS ( R 2 = 0.815, s.d. = 0.059) or FDFS ( R 2 = 0.801, s.d. = 0.065).

scholarly journals UV Spectrophotometric Methods to Quantify Alogliptin Benzoate and Pioglitazone Hydrochloride

2021 ◽  
pp. 31-41
Author(s):  
Dhanya B. Sen ◽  
Ashim K. Sen ◽  
Aarti S. Zanwar ◽  
Harshita Pandey ◽  
Rajesh A. Maheshwari
Keyword(s):  
Limit Of Detection ◽  
Spectroscopic Method ◽  
Simultaneous Estimation ◽  
Control Analysis ◽  
Limit Of Quantification ◽  
Spectrophotometric Methods ◽  
First Derivative ◽  
Ich Guidelines ◽  
The Difference ◽  
Tablet Dosage

Three new, precise, accurate and sensitive UV-Spectrophotometric methods namely Ratio Difference Spectroscopic Method (RDSM), First Derivative of Ratio Spectra Method (DR1) and Area Under Curve Method (AUC) were developed and validated for simultaneous assessment of alogliptin benzoate (ALO) and pioglitazone hydrochloride (PIO) in tablet dosage form. In RDSM, ratio spectra of both the drugs were recorded by dividing the mixtures using interfering drug as divisor. Then the difference between the amplitudes of obtained ratio spectra was measured at 288 and 291 nm for ALO and 236 and 245 nm for PIO. The second method DR1, where the first derivative of ratio spectra of both the drugs were recorded and the first derivative signal was measured at 290 nm for ALO and 276.8 nm for PIO. The scaling factor was fixed as 1 and wavelength interval (Δλ) as 2 for recording the first derivative of ratio spectra.  In the third method (AUC), peak area of recorded zero order spectra was measured at 276 ± 10 nm for ALO and 267.8 ± 10 nm for PIO. All three proposed methods were validated according to “International Conference on Harmonization” (ICH) guidelines parameters. For all three methods, ALO and PIO obeyed Beer’s law in the range of 0.5-5 & 1.8-18 µg/ml, respectively. The % RSD of repeatability of measurement, intra-day and inter-day precision were found to be less than 2 for all three methods. Limit of detection (LOD) and Limit of quantification (LOQ) of the drugs were calculated which proved the sensitivity of the methods. The accuracy ranged between 98-101% for all three methods. No interference from pharmaceutical excipients present in the formulation was observed.  These proposed methods were found to be simple, sensitive, accurate and precise and can be applied to the simultaneous estimation of ALO and PIO in combined tablet formulation and also appropriate for routine quality control analysis.

scholarly journals STABILITY-INDICATING METHODS FOR THE DERTERMINATION OF GEMIFLOXACIN IN PRESENCE OF ITS ACID DEGRADATION PRODUCT(S)

2015 ◽  
Vol 11 (6) ◽  
pp. 3698-3708
Author(s):  
Fatma Alamin ◽  
Ezzat Abdel Moety ◽  
Amr Badawey ◽  
Heba Hefne
Keyword(s):  
Degradation Products ◽  
Zero Crossing ◽  
Stability Indicating ◽  
Acid Degradation ◽  
First Derivative ◽  
Wide Range ◽  
Intact Drug ◽  
Minimal Data ◽  
The Difference

Brilliant, valid and simple five UV spectrophotometric stability indicating techniques are adopted for the determination of Gemifloxacin (GEM) in presence of its acid degradation products over a concentration range of 2-12 μg mL-1. The first method is an application of the first derivative (1D) spectrophotometry, that allows the determination of GEM without interference of its acid degradation products at zero crossing wavelength (254.6 nm). The second method depends on the first-derivative of the ratio spectra spectrophotometry (1DD) for determination of GEM in presence of its acid degradation products at a maximum of 273.0 nm and a minimum of 284.0 nm, While the third dual wavelength method offers a superior stability indicating procedures for the determination of GEM in the zero order spectra at the wavelength pair of 271.8 nm and 325.0 nm. The fourth method is the ratio difference one, with the advantages of minimal data processing and wide range of application. It is applied for the analysis of intact drug in presence of its acid degradation products by measuring the difference in the peak amplitude at the ratio spectra at 355.0 nm and 270.0 nm. The last method is based on the quantification of GEM through the bivariate calibration at 255.0 nm and 277.0 nm by adopting simple mathematic algorithm that provides simplicity and rapidity.

scholarly journals The titration curve of insulin in the presence of various bivalent metal ions

1968 ◽  
Vol 106 (4) ◽  
pp. 777-781 ◽  
Author(s):  
John Graae
Keyword(s):  
Metal Ions ◽  
Titration Curve ◽  
Amino Groups ◽  
Dilute Solutions ◽  
Bivalent Metal ◽  
Titration Curves ◽  
Bivalent Metal Ions ◽  
Presence And Absence ◽  
The Difference

1. Titration curves of insulin in the presence and absence of various metal ions are reported. 2. The difference in base consumption with and without the metal ions is compared with calculated curves. 3. These experiments suggest that in dilute solutions Zn2+ and Cu2+ ions are bound to α-amino groups.

Compact differences of composition operators on weighted Dirichlet spaces

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Robert Allen ◽  
Katherine Heller ◽  
Matthew Pons
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Complex Interpolation ◽  
Dirichlet Spaces ◽  
Space Of Analytic Functions ◽  
First Derivative ◽  
Weighted Dirichlet Spaces ◽  
The Difference

AbstractHere we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

On the variation of Teichmüller's metric

1980 ◽  
Vol 85 (1-2) ◽  
pp. 143-152 ◽  
Author(s):  
Frederick P. Gardiner
Keyword(s):  
Second Derivative ◽  
Difference Quotient ◽  
First Derivative ◽  
The Difference

SynopsisThe main result of this article is the calculation of the first derivative of Teichmüller's metric from an inequality of Reich and Strebel. Furthermore, from the same inequality one is able to calculate information about the difference quotient for the second derivative. From the techniques used here it does not seem possible to determine whether the metric isC2.

scholarly journals Development and Validation for Simultaneous Estimation of Sofosbuvir and Daclatasvir Dihydrochloride in Pharmaceutical Dosage form by Ratio Derivative and Dual Wavelength Methods

2020 ◽  
Vol 11 (01) ◽  
pp. 25-31
Author(s):  
Sapna M. Rathod ◽  
Paresh U. Patel
Keyword(s):  
Dosage Form ◽  
Dual Wavelength ◽  
Simultaneous Estimation ◽  
Pharmaceutical Dosage Form ◽  
First Derivative ◽  
Absorbance Difference ◽  
The Difference ◽  
Development And Validation ◽  
Selection Of

Development and validation of new simple, sensitive, accurate and precise spectrophotometric method involving ratio derivative and dual-wavelength method, was done as per ICH Q2 (R1) for simultaneous estimation of Sofosbuvir (SOFO) and daclatasvir dihydrochloride (DACLA) in a combined dosage form. The overlapping in the spectra of both drugs was the reason for the selection of both methods. The absorbance difference (ΔA) value between 235.8 nm and 270.6 nm was selected for the quantitative determination of SOFO, where DACLA gives equal absorbance at the selected wavelength in the dual-wavelength method (Method A). The determination of DACLA is done quantitatively by measuring the difference in absorbance value at 249 nm and 268.6 nm where SOFO gives equal absorbance at a selected wavelength. Ratio spectra method (Method B) was based on dividing the spectra of a mixture with standard spectra of one of the analytes, and the first derivative spectra was recorded with Δλ = 8 nm and scaling factor 1. The amount of SOFO and DACLA was estimated in the binary mixtures by computing the first derivative signal at 247.0 nm and 341.0 nm, respectively. The calibration curve was linear in the concentration range of 10–90 μg/mL for SOFO and 4–20 μg/mL for DACLA for both the methods. The methods were successfully applied for the simultaneous determination of these drugs in combined dosage form with acceptable recoveries.

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