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Experiments were carried out in an optical engine, and the effects of hydrogen ratio on the combustion process of diesel/methane/hydrogen triple fuel combustion with 5% diesel fuel ratio were studied. The natural photometric images of the combustion process were recorded by a high-speed camera. Combined with the optical experimental results, the combustion process of methane and hydrogen mixture ignited by trace diesel oil was simulated. The development process of in-cylinder temperature, OH group and combustion components during combustion with different hydrogen ratios was studied. It is found that the increase of hydrogen ratio promoted the combustion, the ignition delay time and combustion duration were significantly reduced, and the heat release stage of combustion was also advanced. When the second derivative of the heat release rate is the largest, a low temperature ignition point is formed at the edge of the cylinder at first, and the flame expands with the increase of temperature in a short time. With the increase of intake pressure, the ignition delay period decreases at the same hydrogen ratio. High hydrogen ratio leads to more NOx emissions due to higher combustion temperature, and CO and CH4 emissions decrease with the increase of hydrogen ratio. • The combustion characteristics of hydrogen, methane and diesel mixture were studied. • The ignition strategy uses 5% trace diesel oil as the ignition fuel. • The combustion data are interpreted by optical visualization. • Higher hydrogen ratio can reduce ignition delay time and combustion duration. • Appropriately increase the proportion of hydrogen to reduce CO and methane emissions. [ABSTRACT FROM AUTHOR]

A novel spectrofluorimetric method has been developed for determination of antazoline (ANT) and tetryzoline (TET) in their pharmaceutical formulation. A combined application of synchronous spectrofluorimetry and second derivative mathematical treatment was developed. The proposed method depends on reacting the cited drugs with dansyl chloride (DNS‐Cl) being a suitable derivatizing agent generating highly fluorescent derivatives measured at emission wavelengths of 703.0 and 642.0 nm after excitation wavelengths of 350.0 and 320.0 nm for ANT and TET, respectively. The joint use of synchronous spectrofluorimetry with second derivative mathematical treatment is for the first time to be developed and optimized in aid of using fluorescence data manager software generating second derivative peak amplitudes at 556.5 nm for ANT and 516.7 nm for TET. Linear responses have been represented over a wide range of concentration (0.5–12.0 μg/mL for ANT and 0.5–10.0 μg/mL for TET). Additionally, statistical comparison of the developed method with the official ones has been carried out where no significant difference was found. Additionally, greenness profile assessment was accomplished by means of four metric tools. Indeed, the method developed is found to be precise, sensitive, and discriminating to assess the cited drugs for regular analysis. [ABSTRACT FROM AUTHOR]

We consider a slightly modified local finite-volume approximation of the Laplacian operator originally proposed by Chandrashekar (Int J Adv Eng Sci Appl Math 8(3):174–193, 2016, ). The goal is to prove consistency and convergence of the approximation on unstructured grids. Consequently, we propose a semi-discrete scheme for the heat equation augmented with Dirichlet, Neumann and Robin boundary conditions. By deriving a priori estimates for the numerical solution, we prove that it converges weakly, and subsequently strongly, to a weak solution of the original problem. A numerical simulation demonstrates that the scheme converges with a second-order rate. [ABSTRACT FROM AUTHOR]

The first partial derivatives of λ with respect to demographic parameters quantify linear responses of population growth to vital rate perturbations, but sensitivity itself is situational and can show non-linear responses. We use the second derivative of λ with respect to the demographic parameters to explore this type of responses in a population of a root hemiparasite (Castilleja tenuiflora). For plants growing with and without hosts, population transition matrices were built for the 2016–2018 period, and sensitivities and elasticities together with pure derivatives of the Hessian matrix were calculated, together with the second derivatives to survival and fecundity. We transformed the Hessian matrix to a logarithmic scale to avoid values with no biological meaning. Germination showed high sensitivity values, while permanence of individuals with dry aerial tissue that re-sprout had the highest elasticity. Negative values on the second derivative and on the logarithmic representation were obtained for germination with and without hosts in both years. Survival and fecundity have a similar behaviour in both conditions and periods, with negative values for survival for the first category and no negative values for fecundity. High negative values of the second derivative of the transition from seed to seedling indicate an evolutionary stable strategy and imply seeds are important to the permanence of C. tenuiflora population. A stochastic analysis of the second derivative of the transition from seed to seedling was performed with a Gamma distribution analysis, and showed negative values in all cases, corroborating this result. [ABSTRACT FROM AUTHOR]

The physical meaning of the derivative and the acceleration term of the proportional-integral-derivative-acceleration (PIDA) controller was analyzed, and a new non-interactive form of the PIDA controller is proposed. Also, a new tuning rule for the PIDA controller was developed by combining the physical meaning of the two derivative terms with the previous integral of the time-weighted absolute value of the error (ITAE) tuning rule for the PID controller. The proposed tuning rule, composed of simple explicit algebraic equations, provides excellent performance for various processes without using any optimization methods and iterative computation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast solver for the linear system-induced from applying the finite difference method. For this purpose, we provide a new decomposition of the matrix consisting of a second-order central finite difference matrix and a small condition number matrix. We analyze the fourth-order finite difference matrix using this decomposition and the good properties of the two decomposed matrices. In addition, we compare the upper bounds of the condition numbers of the three matrices, which are closely related to the number of iterations. In terms of computational cost, we show the superiority of the proposed solver by solving the one-dimensional Poisson's equations. We also demonstrated the efficiency of using the proposed solver by numerically observing the factors, such as condition number and spectral radius. [ABSTRACT FROM AUTHOR]

Aflatoxin M1 (AFM1) is a metabolite of carcinogenic aflatoxin B1 (AFB1) and appears in milk of dairy animals on ingestion of feed contaminated with AFB1. It has been reported to have affinity towards milk proteins, the exact mechanism of which is still unknown. In the present study, ATR-FTIR coupled with chemometrics is utilized to understand AFM1 interaction with milk proteins. The second order derivative spectra of the spectral window 1700–1600 cm−1 confirms the affinity of AFM1 towards milk proteins. The results of principal component analysis suggested that spectral window of 1700–1600 cm−1 is informative and provides an indication of the conformational changes brought by AFM1 in the secondary structure of milk proteins. [ABSTRACT FROM AUTHOR]

An in-silico tool with peak deconvolution for preparative chromatograms was developed for assessing the robustness for peak fluctuations depending on loaded sample quality. The peak positions of high-molecular-weight species (HMWS), target monoclonal antibody (Main), and low-molecular-weight species (LMWS) on a chromatogram of cation-exchange chromatography (CEX) were identified by second derivative processing. The deconvoluted peaks of HWMS, Main, and LMWS were calculated by a fitting algorithm at each identified peak position. The height of deconvolved peaks of each component was varied to mimic the change of loaded sample quality in the chromatogram, and the quality of the pooled fraction obtained from the mimic chromatogram was estimated. In addition, the relationship between the loaded sample quality and the pooled sample quality was shown to evaluate the robustness of chromatographic purification process for peak fluctuations depending on loaded sample quality. A major advantage of this robustness assessment method is to be performed using the results of only a single wet-lab experiment. We considered that it is a useful in-silico tool for rapidly assessing chromatography robustness and also product quality depending on upstream process required to achieve the target quality in the pooled fraction, at the early stage of biological pharmaceutical product development, especially monoclonal antibodies

The estimation of crop yield is a compelling and highly relevant task in the scenario of the challenging climate change we are facing. With this aim, a reinterpretation and a simplification of the Food and Agriculture Organization (FAO) fundamentals are presented to calculate the fresh biomass of forage crops. A normalized difference vegetation index (NDVI) series observed from a multispectral camera on board an unmanned aircraft system (UAS) was the basis for the estimation. Eight fields in Spain of different rainfed intercropping forages were flown over simultaneously, with eight field measurements from February to June 2020. The second derivative applied to the NDVI time series determined the key points of the growing cycle, whereas the NDVI values themselves were integrated and multiplied by a standardized value of the normalized water productivity (WP*). The scalability of the method was tested using two scales of the NDVI values: the point scale (at the precise field measurement location) and the plot scale (mean of 400 m2). The resulting fresh biomass and, therefore, the proposal were validated against a dataset of field-observed benchmarks during the field campaign. The agreement between the estimated and the observed fresh biomass afforded a very good prediction in terms of the determination coefficient (R2, that ranged from 0.17 to 0.85) and the agreement index (AI, that ranged from 0.55 to 0.90), with acceptable estimation errors between 10 and 30%. The best period to estimate fresh biomass was found to be between the second fortnight of April and the first fortnight of May.

Abstract Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon.

Background: Controlling the coronavirus disease 2019 (COVID-19) epidemic requires information beyond new and cumulative cases. This study aims to conduct an in-depth analysis by geographic strata: Wuhan City (hereafter referred to as Wuhan) only, Hubei Province (hereafter referred to as Hubei) excluding Wuhan, and China excluding Hubei. Methods: Daily cumulative confirmed COVID-19 cases between December 8, 2019 (the date of symptom onset based on patients’ recall during the investigation), and March 1, 2020, from official sources and published studies were analyzed. The second derivative model was used for information extraction. Data analysis was conducted separately for the three strata. Results: A total of 80 026 diagnosed COVID-19 cases were reported during the first 85 days of the epidemic, with 49 315 cases from Wuhan, 17 788 from Hubei excluding Wuhan, and 12 923 from China excluding Hubei. Analytical results indicate that the COVID-19 epidemic consists of an Acceleration, a Deceleration, and a Stabilization Phase in all three geographic strata, plus a Silent Attack Phase for Wuhan only. Given the reported incubation period of 14 days, effects of the massive anti-epidemic actions were revealed by both the Acceleration and Deceleration Phases. The Acceleration Phase signaled the effect of the intervention to detect the infected; the Deceleration Phase signaled the declines in new infections after the infected were detected, treated and quarantined. Conclusion: Findings of the study provide new evidence to better monitor the epidemic, evaluate its response to intervention, and predict the trend long. In addition to re-evaluating the control of the COVID-19 epidemic in China, this study provided a model for monitoring outbreaks of COVID-19 in different countries across the world.

Due to some limitations, such as picking errors for traveltimes from the seismic logging data, the conventional seismic logging will produce some false stratigraphic boundaries, and the results are difficult to meet the needs of geophysical exploration. Based on the seismic logging data excited at the surface and received in the well, and this paper proposed a new method, which uses the characteristics of the second derivative of seismic traveltimes and the “threshold C” indicating the velocity contrast between the upper and current layer, to determine the velocity discontinuities. The results from theoretical data and observed seismic logging data shown that consistent with the theoretical model basically. The maximum error of the depth is 0. 5 m, and the maximum error of the layer velocity is 14. 22 m / s. After adding 5% random disturbance in the theoretical traveltime data, it is still possible to invert the good velocity structural characteristics in the well. This method is simple, fast, and can produce a very well velocity structure for seismic logging accurately. [ABSTRACT FROM AUTHOR]

Background: Spatio-temporal variations of structural components of the POM–DOM fractions exhibit in urban rivers, which is valuable information to reveal dynamic migration and transformation within and between the organic matter pools, also provide important support for river water quality improvement and management measures. Second derivative UV–visible spectroscopy (SDUVS) was applied to simultaneously characterize structural components and spatial variations of dissolved (DOM: Diameter < 0.2 μm) and particulate (POM1: 0.2 < diameter < 0.7 μm; POM2: diameter > 0.7 μm) organic matters in an urbanized river of northeast China. Results: Thirty-six water samples were collected from mainstream and tributaries along a human impact gradient, i.e., rural, town and urban regions. The DOM was a representative fraction for the natural organic matter pool, which was mostly derived from allochthonous and terrestrial sources. Four components C1 to C4 were identified from the POM–DOM fractions by the SDUVS. The C1 associated with phenolic groups and the C2 related to carboxylic groups were dominant for the organic matter pool. The C3 was composed of the primary humificated materials, and the %C3 was kept relatively consistent in the organic matter pool. The C4 presented deeply humificated organic matter with the increase of aromatic and alkyl structures. The average %C4 of the POM pool was higher than that of the DOM pool, indicating that the humification degree of the POM fractions was higher than that of the DOM fraction. Conclusions: Moreover, the tributaries had a higher average %C4 within the DOM than the mainstream, and trends of the POM pool were similar to the DOM pool. The trophic level of the river water decreased in the order of urban region > town region > rural region, while the molecular sizes of the POM–DOM decreased in the order of rural region > town region > urban region. [ABSTRACT FROM AUTHOR]

A novel spectrofluorimetric method has been developed for determination of antazoline (ANT) and tetryzoline (TET) in their pharmaceutical formulation. A combined application of synchronous spectrofluorimetry and second derivative mathematical treatment was developed. The proposed method depends on reacting the cited drugs with dansyl chloride (DNS-Cl) being a suitable derivatizing agent generating highly fluorescent derivatives measured at emission wavelengths of 703.0 and 642.0 nm after excitation wavelengths of 350.0 and 320.0 nm for ANT and TET, respectively. The joint use of synchronous spectrofluorimetry with second derivative mathematical treatment is for the first time to be developed and optimized in aid of using fluorescence data manager software generating second derivative peak amplitudes at 556.5 nm for ANT and 516.7 nm for TET. Linear responses have been represented over a wide range of concentration (0.5-12.0 μg/mL for ANT and 0.5-10.0 μg/mL for TET). Additionally, statistical comparison of the developed method with the official ones has been carried out where no significant difference was found. Additionally, greenness profile assessment was accomplished by means of four metric tools. Indeed, the method developed is found to be precise, sensitive, and discriminating to assess the cited drugs for regular analysis., (© 2024 John Wiley & Sons Ltd.)

Background and Objectives: Previously, the diastolic section of the pulse wave was most often analyzed as the result of reflection of a direct wave from the elements of peripheral vessels. However, measurements of the negative linear velocity of blood flow using ultrasound dopplerograms clearly indicate the presence of reverse blood flow in the arteries. The aim of the work was to establish the relationship of the second derivative of the pulse pressure wave with the value of the reverse blood flow in the arterial bed. Materials and Methods: The shape of the pressure pulse wave was calculated based on the two-element windkessel model. The calculation of the second derivative of the pulse pressure wave was performed taking into account the direct and reverse blood flow occurring in the arteries at different values of the reverse blood flow. Results: The linear dependence of the second derivative of the pulse wave on the value of the blood volume of the reverse wave on the diastole is obtained. Conclusions: It is concluded that the second derivative of the pulse pressure wave can be used to estimate the value of the reverse blood flow in the artery, which depends on the state of the peripheral vascular system.

In this note we propose a calculus for piece-wise linear functions, in order to obtain derivatives and second derivatives at points where the function is not differentiable. Such derivatives can be used to calculate coefficients of risk aversion at initial wealth for piece-wise linear utility functions for gains, which display loss aversion-and hence non differentiability at zero gains. [ABSTRACT FROM AUTHOR]

Abstract Background Similar to outbreaks of many other infectious diseases, success in controlling the novel 2019 coronavirus infection requires a timely and accurate monitoring of the epidemic, particularly during its early period with rather limited data while the need for information increases explosively. Methods In this study, we used a second derivative model to characterize the coronavirus epidemic in China with cumulatively diagnosed cases during the first 2 months. The analysis was further enhanced by an exponential model with a close-population assumption. This model was built with the data and used to assess the detection rate during the study period, considering the differences between the true infections, detectable and detected cases. Results Results from the second derivative modeling suggest the coronavirus epidemic as nonlinear and chaotic in nature. Although it emerged gradually, the epidemic was highly responsive to massive interventions initiated on January 21, 2020, as indicated by results from both second derivative and exponential modeling analyses. The epidemic started to decelerate immediately after the massive actions. The results derived from our analysis signaled the decline of the epidemic 14 days before it eventually occurred on February 4, 2020. Study findings further signaled an accelerated decline in the epidemic starting in 14 days on February 18, 2020. Conclusions The coronavirus epidemic appeared to be nonlinear and chaotic, and was responsive to effective interventions. The methods used in this study can be applied in surveillance to inform and encourage the general public, public health professionals, clinicians and decision-makers to take coordinative and collaborative efforts to control the epidemic.

This paper deals with the construction of a functionally fitted method for solving first-order differential systems whose solutions present an oscillatory behaviour. The method incorporates the second derivative to obtain better accuracies and is developed on the basis that it provides no errors when the true solution is a linear combination of some trigonometric and exponential functions containing a parameter. The main properties of the method are presented, showing a fourth-order convergence. Some numerical experiments are included to show the good performance of the proposed method. [ABSTRACT FROM AUTHOR]

Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon. [ABSTRACT FROM AUTHOR]

This paper presents a method for compensating the load cell’s nonlinear error based on neural network with the second derivative constraints. In this method, for improving the ability of the neural network in the case of lack of samples, the prior knowledge of load cell, i.e., the second derivative of the load cell’s input-output function is less than zero, is used to construct the constraint of neural network. The augmented performance index of training neural network with penalty function method is founded, and its detailed training algorithm is given. In addition, the performance of neural network affected by the punishing factor is discussed. This proposed method can reduce the NN’s generalization error when the training samples are insufficient. The experimental results show that the generalization ability of this proposed neural network is better than that of the conventional data inducing neural network (DINN, i.e. training neural network by only using data samples and not any constraints), and the nonlinear error of load cell with this proposed method is far less than that of DINN. [ABSTRACT FROM AUTHOR]

The structural changes and the degree of maturity of three Colombian coals from the Santander and Antioquia provinces were studied using a simple and fast curve fitting method of the RBS parameters (the distance between band G and band D), FWHM - G (total width at half the maximum of the G band) and AR (area of the Raman spectrum), obtained by deconvolution and band resolution of the Micro-Raman spectra. The results were compared by morphological and chemical analysis using a SEM scanning electron microscope coupled with a solid state X - ray EDS detector. A percentage of vitrinite reflectance (% Ro) of 4.3 %, 3.8 % and 0.07 % was obtained, a percentage of carbon by EDS analysis of 91.47 %, 87.78 %, 73.4 %, a morphological description by SEM analysis presenting smooth, rough surfaces and rough-lumpy and pore size between 0.7 µm - 0.8 µm, 1.3 µm - 1.5 µm and 0.2 µm - 0.7 µm for the anthracite, semi-anthracite and bituminous samples, respectively. The results showed that based on this method, it was possible to obtain a model that allows to rapidly analyze and characterize the coal. The results compare very well to those of Colombian coals normalized by other methods to improve the precision of the measurement. The modified method, however, did not offer an appropriate fit for the lower range coal and produced extremely low reflectance values. This effect is possibly related with the molecular structure of organic matter in coal or the presence of fluorescence interference.

Onset potential defined as the point where the change in current starts to accelerate or when it is at its maximum can be easily obtained using a new and simple mathematical procedure (SODDM) For proper and fair comparison of the performance of Oxygen reduction reaction (ORR) electrocatalysts an un-biased method to determine an onset potential value is needed. Here we report an easy mathematical approach based on the second derivative of linear sweep voltammetry curves, referred to as a second order discrete differentiation method (SODDM) that allows to accurately provide the onset potential. Analysis of the published results showed that the reported values might be affected by an intrinsic human error associated with the application of the most common approaches addressed as a tangent method or those relaying on a visual estimation of the onset potential based on the shape of a linear scan voltammetry (LSV) curve. We have also demonstrated that by using SODDM, electrochemical data collected on different instruments by different researchers leads to comparable results in terms of the ORR onset potential values. [ABSTRACT FROM AUTHOR]

In this work, a one-step L-stable Block Hybrid Multistep Method (BHMM) of order five was developed. The method is constructed for solving first order Ordinary Differential Equations with given initial conditions. Interpolation and collocation techniques, with power series as a basis function, are employed for the derivation of the continuous form of the hybrid methods. The discrete scheme and its second derivative are derived by evaluating at the specific grid and off-grid points to form the main and additional methods respectively. Both hybrid methods generated are composed in matrix form and implemented as a block method. The stability and convergence properties of BHMM are discussed and presented. The numerical results of BHMM have proven its efficiency when compared to some existing methods.

The chemical composition of propolis is complex and varies according to location, seasonality, and vegetation where the hives are located. Raw and macerated propolis produced in different regions of Brazil were assessed and produced iPLS models from FTNIR combined to multivariate calibration to determine total phenolic content (TPC). The spectra of raw propolis were obtained analyzing samples directly, without treatment or processing, while macerated propolis was submitted to the milling process using liquid nitrogen. Concerning the results, the TPC ranged from 3.61 to 90.4 mg GAE g‐1, which indicates a significant difference among samples. It was possible to conclude that macerated propolis presented the best multivariate calibration obtained from the second derivative and SNV pre‐processing. The error values RMSECV and RMSEP were 3.79 and 6.17 mg GAE g‐1 respectively, while the determination coefficients in the calibration, cross‐validation, and external validation were 0.97, 0.87, and 0.82, respectively. [ABSTRACT FROM AUTHOR]

Boundary-optimized summation-by-parts (SBP) finite difference operators for second derivatives with variable coefficients are presented. The operators achieve increased accuracy by utilizing non-equispaced grid points close to the boundaries of the grid. Using the optimized operators we formulate SBP schemes for the acoustic and elastic operators defined directly on curvilinear multiblock domains. Numerical studies of the acoustic and elastic wave equations demonstrate that, compared to traditional SBP difference operators, the new operators provide increased accuracy for surface waves as well as block interfaces in multiblock grids. For instance, simulations of Rayleigh waves demonstrate that the boundary-optimized operators more than halve the runtime required for a given error tolerance. • SBP difference operators for variable-coefficient second derivatives are presented. • Operator accuracy is increased using non-equispaced grid points close to boundaries. • Provides full compatibility with existing boundary-optimized SBP first derivatives. • Simulations of acoustic and elastic wave equations demonstrate increased accuracy. • Simulations of Rayleigh waves demonstrate increased efficiency. [ABSTRACT FROM AUTHOR]

[Display omitted] • Sunset yellow (SSY) and sodium tetradecyl sulphate (STS) interaction has been studied. • The synergistic effect of SSY on STS CMC was influenced by NaCMC. • The binding efficiency of SSY in STS micelle was increased in NaCMC media. • The UV absorbance method was used to calculate the SSY occupancy (i 0) of STS micelles. The textile, pharmaceutical, and coloring industries can all benefit from a better understanding of the process by which dyes and surfactants interact to develop better formulas and techniques for dye separation. UV–vis spectroscopy was widely used to investigate interactions between the anionic food colour sunset yellow (SSY) and the anionic surfactant sodium tetradecyl sulphate (STS) in the absence and presence of sodium carboxymethyl cellulose (NaCMC) in various concentrations at 25 °C. The critical micelle concentration (CMC) of STS was lowered in both aqueous and NaCMC solutions when SSY was present. NaCMC prevented STS from becoming micellized when the amount was increased in the micellar medium. The CMC values obtained using the "second-derivative" method were consistent with those discovered using UV absorbance techniques. The binding capabilities of SSY with STS micelles in the presence of NaCMC were evaluated using a UV absorbance study at 25 °C. The outcomes demonstrated that hydrophobic interaction influenced SSY binding. The occupancy of SSY molecules was projected to rise with an increase in NaCMC in the STS micellar solution based on the quantity of SSY molecules (i 0). Finally, when NaCMC was present, the presence of SSY was used as a counterion to enhance the micellization of STS. This formulation would be necessary for both medicinal and textile applications. [ABSTRACT FROM AUTHOR]

In modern shape analysis, deformation is quantified in different ways depending on the algorithms used and on the scale at which it is evaluated. While global affine and non-affine deformation components can be decoupled and computed using a variety of methods, the very local deformation can be considered, infinitesimally, as an affine deformation. The deformation gradient tensor F can be computed locally using a direct calculation by exploiting triangulation or tetrahedralization structures or by locally evaluating the first derivative of an appropriate interpolation function mapping the global deformation from the undeformed to the deformed state. A suitable function is represented by the thin plate spline (TPS) that separates affine from non-affine deformation components. F, also known as Jacobian matrix, encodes both the locally affine deformation and local rotation. This implies that it should be used for visualizing primary strain directions (PSDs) and deformation ellipses and ellipsoids on the target configuration. Using C = FTF allows, instead, one to compute PSD and to visualize them on the source configuration. Moreover, C allows the computation of the strain energy that can be evaluated and mapped locally at any point of a body using an interpolation function. In addition, it is possible, by exploiting the second-order Jacobian, to calculate the amount of the non-affine deformation in the neighborhood of the evaluation point by computing the body bending energy density encoded in the deformation. In this contribution, we present (i) the main computational methods for evaluating local deformation metrics, (ii) a number of different strategies to visualize them on both undeformed and deformed configurations, and (iii) the potential pitfalls in ignoring the actual three-dimensional nature of F when it is evaluated along a surface identified by a triangulation in three dimensions.

The reanalysis method to obtain the second derivatives of static displacement is innovatively proposed in this paper. This method is based on the combined approximations method. The reanalysis formulations of the second derivative of static displacement are derived to provide a programmatic procedure of formulations construction. Besides, the normalized error and the number of algebraic operations are considered to evaluate the accuracy and efficiency, respectively. Finally, three typical numerical results verify the accuracy and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper provides an approach to monitor oscillation status in tunnel diode measurement circuits-by,measuring the second derivative of the current-voltage (I-V) characteristic curve while doing I-V curve measurement. The method of using the second derivative to detect oscillations works even when the oscillation frequency is ultrahigh or the oscillation amplitude is very small, e.g., below 10 mV. In this paper, the experimental principle of the tunneling spectroscopy was extended to measurement circuits with the presence of internal oscillations, in contrast to the conventional tunneling spectroscopy, which normally does not deal with internal oscillation. The numerical relationships between the measured average values of transient derivatives and the derivatives of the average current are derived: The average values of the transient first and second derivatives are shown to equal the derivatives of the average current. These relationships serve as the foundation for the authors' experiments. The typical oscillation characteristics in the curves of the first and the second derivatives are used to detect the presence of oscillations and the bias voltage range of oscillation in the I-V curve. The monitor of oscillation status during measurements provides the tester the confidence in the measurement data and whether it is necessary to improve the test circuit further. Finally, benefited from free-of-oscillation, the indirect tunneling current contributions arising by 121-mV (TO + 0) two-phonon combination, 144-mV (TA + 0 + 0) and 181-mV (TO + 0 + 0) three-phonon combinations at the negative differential resistance region are observed from a silicon Esaki tunnel diode at 4.2 K.

In this paper, a novel frequency estimation algorithm based on discrete Fourier transform (DFT) and second derivative is proposed. The proposed algorithm consists of three stages, namely, DFT, second derivative, and frequency estimation. First, the input signal is decomposed using DFT into two orthogonal components, the real and imaginary parts. In other words, the signal is filtered with cosine and sine filters. Secondly, the second derivatives of the two orthogonal components are obtained by numerical approximation. Because this step can cause an error, the central difference approximation for five-point second derivative is used for error reduction. Finally, the two orthogonal components and their second derivatives are combined to estimate the power frequency considering a zero-crossing problem and the gains of finite impulse response (FIR) filters. The performance of the proposed algorithm is evaluated considering frequency changes when generating the test signals. Besides, a dynamic condition which is simulated in a 5-bus transmission system modelled by PSCAD/EMTDC is also considered. The performance evaluations show that the proposed algorithm is an effective method.

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Copyright of Revista Facultad de Ingeniería - UPTC is the property of Universidad Pedagogica y Tecnologica de Colombia, Facultad de Ingenieria and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)