Nonlinear Least-squares Method Research Articles

Selection of spectrum model in estimation of Brillouin frequency shift for distributed optical fiber sensor

To improve real-time performance in distributed optical fiber sensor, the influence of Brillouin spectrum models on performance in estimation of Brillouin frequency shift (BFS) is systematically investigated. First, the related Brillouin spectrum models, objective functions, optimization algorithms and convergence criterion in estimation of BFS are introduced. The BFS estimation algorithms based on the Lorentzian, Gaussian, pseudo-Voigt and Voigt models are written in MATLAB. The algorithms are used to estimate BFS for numerically generated Brillouin spectra with different values of SNR (Signal to Noise Ratio) and measured Brillouin spectra with different values of pulse width and average time. The results reveal that regardless of the simplified Lorentzian and Gaussian models or more accurate pseudo-Voigt and Voigt model-based algorithms used, the estimated BFS between different algorithms is quite similar. However, the fitting error of the simplified model-based algorithms is larger than that of the more accurate model-based algorithms especially for the cases with high value of SNR. The computational burden of the former is less than that of the latter. The Voigt model-based algorithm requires the most computational effort. If the nonlinear least-square fit method is used, the selection of spectrum model has no big influence on the accuracy in the estimated BFS. Therefore, the algorithm based on simplified Lorentzian and Gaussian models should be selected in BFS estimation. Thus, not only high accuracy in BFS estimation is ensured, but also the computation time can, at best, decrease to one-tenth of the maximum value.

An experimental study of CO2 gasification kinetics during activation of a spent tyre pyrolysis char

The reaction kinetics of CO2 gasification during the activation of a spent tyre pyrolysis char was investigated. Activation experiments were conducted under atmospheric pressure to examine the effect of CO2 concentration (33.3% to 66.7vol.% CO2 in CO2/N2 mixture), temperature (750 to 1050°C) and reaction time (1 to 6h) on the fixed carbon conversion. The BET surface area of the activated chars as a function of carbon conversion were also determined. It was confirmed that the CO2 gasification reaction was indeed under kinetic control. Four gasification kinetic models, namely volumetric model, shrinking core model, random pore model, and Dutta model were applied to describe the rate behaviour of the char during activation with CO2. The kinetic parameters (reaction order, activation energy and pre-exponential factor) of each model were determined using the non-linear least-squares method by fitting the experimental data with the models and minimising the sum of square of the error between the experimental data and the predicted results. The volumetric model was found to best describe the experimental data under all conditions. The reaction order, activation energy and pre-exponential factor were found to be 0.7, 112kJmol−1 and 6.24×10−4s−1, respectively.

Role of N-substituents of maleimides on penultimate unit effect for sequence control during radical copolymerization

Radical copolymerization of N-substituted maleimides (RMIs) and olefins provides AAB sequence-controlled copolymers by penultimate unit (PU) control. In this study, we investigated the steric, resonance, and polar effects of N-substituents on sequence control during copolymerization of RMIs as the M2 monomer with diisobutene (DIB) and d-limonene (Lim) as the M1 monomer in chloroform at 60 °C. The monomer reactivity ratios (i.e., r2 (= k22/k21), r12 (= k122/k121), and r22 (= k222/k221)) were determined based on the terminal and PU models using a nonlinear least-squares method. For the copolymerization of RMIs with DIB, the introduction of a bulky N-alkyl group suppressed the PU effect and led to the formation of alternating copolymers. The copolymerization of N-phenylmaleimides with o- and p-substituents was also investigated to reveal the steric, resonance, and polar effects of the substituents. In conclusion, less bulky and more electron-donating substituents effectively induced the PU effect during the radical copolymerization of RMIs and olefins. Radical copolymerization of N-substituted maleimides and olefins provides AAB sequence-controlled copolymers by penultimate unit control. In this study, we investigated the steric, resonance, and polar effects of N-substituents on sequence control during copolymerization of various N-substituted maleimides with diisobutene and limonene in chloroform at 60 °C, and concluded that less bulky and more electron-donating substituents effectively induced the penultimate unit effect. We also demonstrated that 2:1 sequence-controlled maleimide copolymers was efficiently produced during radical copolymerization of limonene and N-phenylmaleimides with an electron-donating substituent.

Comparison and Combination of Techniques for Determining the Parameters of a Magnetic Hysteresis Model

The Jiles-Atherton scalar hysteresis model presents five parameters used to represent the material tested and used to calculate the magnetic losses. This article presents a comparative analysis of the performance of two methods of identifying these parameters. In the first method, the equations of Jiles-Atherton were assembled into a single non-linear ordinary differential equation as a function of the variables of interest. An algebraic system of five equations with five unknowns is obtained by evaluating the non-linear ordinary differential equation in five points belonging to the branch of the experimental hysteresis loop. The parameters are obtained by solving this system of equations using the method of Non-Linear Least Squares (NLLS). In the second method, the inverse model of Jiles-Atherton is used to calculate the magnetic field H from the experimental values of magnetic induction B. Using the method of genetic algorithms (MGA), the objective function given by the sum of the relative error of calculated magnetic field and experimental magnetic field along the hysteresis loop is minimized. To validate methods the experimental curves were compared with calculated ones. When applying the methods, it was verified that NLLS besides providing more accurate results, it is faster when compared to MGA. In the MGA the convergence of the calculated magnitudes to the experimental magnitudes improves when one of the chromosomes of the initial population is the solution obtained applying NLLS.

Influence of molecular structure on the susceptibility of starch to α-amylase

The effect of the molecular structure of sweet potato (SPS), cassava (CAS) and high amylose maize (HAS) starches on the susceptibility to fungal and maltogenic α-amylases was investigated. The logarithm of the slope (LOS) and non-linear least-squares (NLLS) methods were used for fitting hydrolysis kinetics data. The malto-oligosaccharides released during hydrolysis were quantified and the hydrolysis residues were analyzed. The hydrolysis kinetic curves were well fitted to the LOS and NLLS models. SPS, CAS and HAS were hydrolyzed in one single phase by fungal α-amylase while two hydrolysis phases were identified for the root starches and a single phase for HAS, when maltogenic α-amylase was used. The lowest percentage of residual starch was found for CAS, independent of enzyme source, due to the high proportion of amylopectin short chains in this starch. On the other hand, the high proportion of HAS long chains contributed to its increased starch degradation rate coefficient during fungal α-amylase hydrolysis, while the high amylose content favored the endo-action pattern of maltognic α-amylase. Independent of starch source, malto-oligosaccharides of different sizes, especially G2-G5, were released after the fungal α-amylase action which hydrolyzes mainly inner and long amylopectin chains. Mainly maltose was produced in the maltogenic α-amylase hydrolysis which breaks the outer amylopectin chains by exo-action and amylose chains by endo-action. The starch molecular structure strongly interferes in both enzyme susceptibility and the action mechanism, as well as in the distribution and amount of products released.

Reserve of ice in glaciers on the Nordenskiöld Land, Spitsbergen, and their changes over the last decades

Data on thickness and area of 16 glaciers on the Nordenskiöld Land (Svalbard) were obtained in 1999 and 2010–2013. These data were used to determine volume of the glaciers and to establish statistical local relationship between the volume V and the area A (V–A scaling) in the form of the power function V = cAγ, and then to calculate the total ice volume of all 202 glaciers in this area and its changes during the period since 1936 to 2002–2008. The total area of 16 glaciers was 129.9±0.35 km2, 14 of which had areas from 0.2 to 8.1 km2. The two largest ones, the Fridtjof and the West Grenfjord, had the areas 17.5 and 47.3 km2, respectively, and thus occupied about 50% (64.8 km2) of the total area of 16 glaciers. These two glaciers account for 67% of the total measured volume (10,034 km3) of the 16 glaciers. A nonlinear least-squares method was used to estimate ice reserves in all 202 glaciers from data on the volume and area of 16 glaciers. The relation between volume V and area A of the glaciers (V–A scaling) was obtained as the ratio V = 0.03637A1,283 with 95%‑th confidence intervals of the coefficients с and γ, (0.02303–0,4971) and (1.184–1.381), respectively. This made possible to calculate total volume of 202 glaciers as of 2002-2008 state using data from RGI v.6.0, and that prove to be equal to 32.89 (16.75–56.63) km3. To verify this estimation, we applied the bootstrapping method for chosen 43 glaciers and calculated the volume by means of sequential use of data for large and smaller glaciers. According to this estimate, the total volume of 202 glaciers amounted to 30.34 km3 with a 95% confidence interval of 15.42–44.27 km3, that turned out to be slightly smaller than the volume calculated by nonlinear least squares method basing on measurements on 16 glaciers. Despite the large error (on the average, from −49% to +84%) in estimating the total volume of 202 glaciers in the Nordenskiöld Land, the data obtained were used for assessment of relative changes in the total volume of glaciers in this area over different time intervals. During the period from 1936 to1990 (54 years), the total area of all glaciers reduced from 738.1 to 546.7 km2, and the total volume decreased from 49,205 to 34,857 km3. Similar results for the period 1990–2002–2008 (~15 years) are the total area changes from 546.7 to 507.9 km2 and their total volume - from 34.857 to 32.890 km3. The rate of decrease of the volume for the period 1936–1990 was equal to −0.266 km3/year, for the period 1990–2002–2008 – minus 0.131 km3/year, and as a whole for the studied period (since 1936 to 2002–2008) – minus 0.236 km3/year. The average mass balance in the first period was equal to −0.372 m w.e./year, in the second one −0.224 m w.e./year, and for the whole time −0.342 m w.e./year.

Pressure-dependent rate rules for intramolecular H-migration reactions of normal-alkyl cyclohexylperoxy radicals

For hydrocarbon fuels, reliable chemical mechanisms play an essential role towards improving the simulations of combustion process. However, in most of the previous modeling studies for alkylcycloalkanes combustion, the kinetic parameters are taken from acyclic alkanes based on the similarities between the reaction classes of alkylcycloalkanes and acyclic alkanes. Among the reaction families for alkylcycloalkanes, the intramolecular H-migration reactions of normal-alkyl cyclohexylperoxy radicals are one of the most important reaction families in the low temperature oxidation mechanisms. High-pressure limit rate rules and pressure-dependent rate rules for this reaction family have been developed based on quantum chemical computations at the CBS-QB3 level in combination with the transition state theory (TST) and Rice–Ramsberger–Kassel–Marcus/Master-Equation (RRKM/ME) theory. The reactions in this family involve a bicyclic transition state and can be divided into classes depending upon the cycle size of the newly formed cycle in the transition states and the types of the carbons from which the H atoms are migrated and if the H-migration occurs on the alkyl side chain, or on the cycle, or from the side chain to the cycle, or from the cycle to the side chain. For each reaction class, a representative set of reactions are chosen from methylcyclohexane to n-butylcyclohexane and the energy barriers of all chosen reactions are calculated and the average value for each class is obtained and compared with the value of the similar reaction class in alkanes. The high-pressure limit rate constants and the pressure-dependent rate constants of all reactions at pressures varying from 0.01 to 100 atm are calculated and the high-pressure limit rate rules and pressure-dependent rate rules for each class are derived from the average rate constants of reactions within each class. All calculated rate constants are fitted by a nonlinear least-squares method to the form of a modified Arrhenius rate expression.It is shown that there are large differences of the rate constants between alkylcycloalkanes and alkanes no matter if the H-migration occurs on the alkyl side chain, on the cycle or between the side chain and the cycle. Therefore, the construction of rate rules for alkylcycloalkanes, instead of taking values from similar reactions in alkanes, is necessary and significant to the low-temperature combustion modeling of alkylcyclohexanes.

Nonlinear Estimation of Variables for Heat Release Calculation Using a Gradient Method

Advanced combustion such as the partially premixed combustion (PPC) is characterized by high energy efficiency. However, they are sensitive to the inlet condition and injection of a combustion engine. Therefore, it is essential to use combustion feedback. The accuracy of the feedback variables, derived from the cylinder pressure signal, is crucial for effective combustion feedback control. This paper proposes a nonlinear least-squares regression method to estimate the pressure offsets and variable polytropic exponent in heat release calculation automatically. The combustion feedback variables derived from the auto-tuned heat-release rate were applied to a heavy-duty compression ignition (CI) engine burning with gasoline fuel.

Применение модели Хассела для прогнозирования плотности популяции золотистой картофельной нематоды после выращивания глободероустойчивого сорта картофеля

The purpose of the research is evaluation the possibility of application the Hassell model for prediction the dynamics of population density of golden nematode of potato in the ground after growing Globodera resistant variety of potato in the single-crop. Materials and methods . For the research database of population density of golden nematode of potato (amount of ootids and larvae) was used on the three plots where amenable varieties of potato were grown and one plot where Globodera resistant variety of potato Kardinal was grown in the Kaluga Region within 14 years (1979–1993). Non-linear least-squares method which is the version of least-squares method for non-linear systems was used as the method for evaluation the model parameters. Toolset of search for solution in the program Excel was used for analysis. Results and discussion . Hassell model for prediction the dynamics of population density of golden nematode of potato in the ground after growing Globodera resistant variety of potato in the single-crop demonstrated high confidence. (R 2 = 0.94). Based on the Hassell model for development golden nematode of potato population in plot soil with growing nematode resistant variety modeling of introduction of Globodera resistant variety was conducted for different initial amount of golden nematode of potato and different levels of fertility of soil: low, average, high. Hassell model has confirmed that it is the most multifunctional in the category of discrete one-period models for prediction dynamics of population density of golden nematode of potato in the ground and permits to predict the amount of golden nematode of potato for agrobiocenosis with single-crop of potato of amenable and Globodera resistant varieties.

Novel method for sphere target detection and center estimation from mobile terrestrial laser scanner data

Sphere targets have been widely used in mobile terrestrial laser scanner (MTLS) registration, using their center coordinates the multiple viewpoints clouds data can be transformed into a unified coordinate system. However, in practice, the task of sphere target detection and center estimation is still a labor intensive and time consuming for large surveying and mapping projects. For this reason, a novel method of fusion adaptive dynamic random sample consensus (AD-RANSAC) and nonlinear least squares (NLS) is proposed to automatically detect and optimally estimate center of sphere target. The basic procedure of the proposed method is that, firstly, a newly AD-RANSAC algorithm is developed to automatically and rapidly detect the sphere targets from MTLS point clouds data, which extends the traditional RANSAC algorithm to detect the sphere targets in dynamic states and recursively update the state estimations using sequential measurements, also improves the accuracy and speed of detection of sphere target. Secondly, the sphere target center coordinate is determined through the NLS optimal estimation algorithm, which has regions mathematical calculation and minimizes the errors in estimation of sphere targets center. Finally, twenty pre-surveyed sphere targets distributed in indoor field were conducted to check the validity of proposed method, experimental results are presented that validate this method and demonstrate our proposed method can automatically detect the sphere targets in more than 1 million points data within 1 min, the accuracy of the sphere center coordinate estimation is less than 2 cm.

Statistical characteristics of raindrop size distribution in south China summer based on the vertical structure derived from VPR-CFMCW

The raindrop size distribution (DSD) characteristics during the precipitation season are analyzed using data collected by an OTT Particle Size Velocity (Parsivel) disdrometer and a Vertical Pointing Radar with C-band Frequency Modulation Continuous Wave (VPR-CFMCW) technology. The two datasets were collected at the same site in Longmen, Guangdong Province, which is the precipitation center of south China, from June to July in 2016 and 2017. We evaluate different fitting methods for the gamma model function and choose a nonlinear least-squares method to fit DSD. Based on the radar reflectance obtained by VPR-CFMCW, the precipitating clouds that occur during the summer precipitation season in south China are classified into four types (i.e., convective, stratiform, mixture, and shallow). The characteristic parameters and the gamma model parameters of different precipitation types are compared. Avoiding the limitations of rainfall classification at the surface, the new classification quantifies the characteristics of mixture and shallow precipitation. The results show that the stratiform precipitation makes up 43.1% of the summer precipitation process in south China, and the contribution of convective precipitation to total rainfall is 62.7%. The precipitation parameters of the four types of precipitation, such as the rain rate (R), the mass-weighted mean diameter (Dm), the radar reflectance (Z), and the liquid water content (LWC), follow the pattern: convective > mixture > stratiform > shallow. The DSD characteristics of the four precipitating cloud types are investigated. For the DSD of convective and mixture precipitation, the spectra width is similar but the rain drop concentration of the mixture is smaller. For the DSD of stratiform and shallow clouds, the rain drop concentrations are similar, but the spectra width of the shallow clouds are smaller. In addition, the relationships between μ-Λ, Dm-Nw, Dm-R, and Z-R are obtained. These new relationships will help improve the accuracy of precipitation estimation and deepen the understanding of the characteristics of surface precipitation microphysical parameters for different types of precipitating clouds in south China.

Comparative assessment of linear least-squares, nonlinear least-squares, and Patlak graphical method for regional and local quantitative tracer kinetic modeling in cerebral dynamic 18 F-FDG PET.

Dynamic 18 F-FDG PET allows quantitative estimation of cerebral glucose metabolism both at the regional and local (voxel) level. Although sensitive to noise and highly computationally expensive, nonlinear least-squares (NLS) optimization stands as the reference approach for the estimation of the kinetic model parameters. Nevertheless, faster techniques, including linear least-squares (LLS) and Patlak graphical method, have been proposed to deal with high resolution noisy data, representing a more adaptable solution for routine clinical implementation. Former research investigating the relative performance of the available algorithms lack precise evaluation of kinetic parameter estimates under realistic acquisition conditions. The present study aims at the systematic comparison of the feasibility and pertinence of kinetic modeling of dynamic cerebral 18 F-FDG PET using NLS, LLS, and Patlak method, based on numerical simulations and patient data. Numerical simulations were used to study the bias and variance of K1 and Ki parameters estimation under representative noise levels. Patient data allowed to assess the concordance between the three methods at the regional and voxel scale, and to evaluate the robustness of the estimations with respect to patient head motion. Our findings indicate that at the regional level NLS and LLS provide kinetic parameter estimates (K1 and Ki ) with similar bias and variance characteristics (K1 bias±relative standard deviation [RSD] 0.0±5.1% and 0.1%±4.9% for NLS and LLS respectively, Ki bias±RSD 0.1%±4.5% and -0.7%±4.4% for NLS and LLS respectively). NLS estimates appear, however, to be slightly less sensitive to patient motion. At the voxel level, provided that patient motion is negligible or corrected, LLS offers an appealing alternative solution for local K1 mapping. It yields K1 estimates that are highly correlated, with high correlation with NLS values (Pearson's r=0.95 on actual data) within computations times less than two orders of magnitude lower. Last, Patlak method appears as the most robust and accurate technique for the estimation of Ki values at the regional and voxel scale, with or without head motion. It provides low bias/low variance Ki quantification (bias±RSD -1.5±9.5% and -4.1±19.7% for Patlak and NLS respectively) as well as smooth parametric images suitable for visual assessment.

Application of a power-exponential function-based model to mortality rates forecasting

There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.

A Novel Doppler Rate Estimator Based on Fractional Fourier Transform for High-Dynamic GNSS Signal

When the fractional Fourier transform (FRFT) is introduced into the weak and high-dynamic global navigation satellite system (GNSS) signal acquisition, the 2-D search cell will be transferred to a 3-D one with respect to the code chip, the Doppler shift, and the Doppler rate. The proper determinations of the code bin and Doppler shift bin in the acquisition process have already been covered in the previous researches. The aim of this paper is to provide an exhaustive analysis of the approach to specify an optimal FRFT order bin, in terms of the Doppler shift rate. The lower and upper bound of FRFT order ranges is determined by the incoming signal dynamics. Then, we propose a precise model to yield an optimal FRFT order bin. Besides, a novel and fast Doppler estimator based on the non-linear least square (NLS) method is presented to improve the performance of the digital FRFT implementation. Finally, an alternate search procedure is proposed to reduce the singular estimations of the NLS method. The simulating examples demonstrate the performance of the proposed algorithms. It has been verified that the computation efficiency and the estimation accuracy have been significantly improved by proposed techniques.

Measurement of middle infrared spectroscopic parameters of carbon disulfide based on tunable diode laser absorption spectroscopy

Carbon disulfide (CS<sub>2</sub>) is a toxic volatile sulfur compound with flammability and harmfulness, which can seriously harm the human health and threaten the industrial production safety. Therefore, it is of high importance for monitoring CS<sub>2</sub> concentration in the air. Tunable diode laser absorption spectroscopy is very suitable for the detection of trace gas for it possesses high sensitivity and fast response. And the precise knowledge of spectroscopic parameters is essential for deducing the CS<sub>2</sub> concentration. However, primary database including HITRAN and GEISA lacks spectroscopic parameters of CS<sub>2</sub>. Thus, to address this issue, a measurement system of absorption spectrum is built for determining spectroscopic parameters by using a quantum cascade laser with narrow linewidth and high output power operating near 4.6 um as a light source. In this paper, direct absorption spectroscopy is used to measure the CS<sub>2</sub> absorption spectra under different sample pressures and the environment temperature is controlled at 296 K, which is adjusted by an air conditioner. We intensively study the absorption spectra of CS<sub>2</sub> in a range between 2178.99 and 2180.79 cm<sup>–1</sup>.According to the relevant reports and the need of actual measurement, four absorption lines are mainly measured in a range of 2180.5−2180.74 cm<sup>–1</sup>. Combining with the multiple linear regression algorithm based on the nonlinear least-square method and Beer-Lambert law, the integrated area and Lorentz line width of measured CS<sub>2</sub> absorption spectrum can be determined. Then the spectroscopic parameters including absorption line intensity and air broadening coefficient are precisely obtained by linearly fitting the integrated areas and Lorentz line widths of CS<sub>2</sub> absorption spectra at different pressures. Moreover, nitrous oxide (N<sub>2</sub>O) absorption spectrum with high spectral resolution is measured to calibrate the central position of carbon disulfide absorption line according to its known line position extracted from HITRAN database and the results obtained by etalon. The calculated results show that the uncertainty of line intensity and air broadening coefficient are less than 5% and 15%, respectively. It demonstrates that the measured spectroscopic parameters of four absorption lines for this study can be recorded in the database of HITRAN, which is very important for trace gas sensing of CS<sub>2</sub>. In the future, we will further improve the system for measuring CS<sub>2</sub> absorption line parameters to fill in the gaps in their spectral parameters in HITRAN and GEISA databases.

Synthesis and homopolymerization kinetics of 7-(methacroyloxy)-2-oxo-heptylphosphonic acid and its copolymerization with methyl methacrylate

ABSTRACTThe synthesis of polymerizable 7-(methacroyloxy)-2-oxo-heptylphosphonic acid M1 destined for self-etch adhesives is described. M1 is characterized by 1H, 13C and 31P-NMR spectroscopy. Its homopolymerization and copolymerization reactivity in the solvents methanol and dioxane between 45 and 70°C in the presence of azobisisobutyronitrile (AIBN) are examined. Polymerization proceeds readily through a thermal free radical initiation. The intensity exponents for the monomer and initiator are only slightly over 1 and approximately 0.5, respectively. This is in accordance with the results typically observed for an ideal free radical polymerization with termination mainly by disproportionation, which is typical for methyl methacrylate (MMA) homopolymerization. The kinetics of copolymerization with MMA are monitored by online 1H-NMR spectroscopy. Two copolymerization reactions for each pair of co-monomers are sufficient to evaluate the copolymerization parameters using the Jaacks method, the Fineman–Ross method and the nonlinear least-squares method. All three methods give similar results for particular monomer M1/MMA couple.

The numerical method for predicting failure in single point incremental forming using a new anisotropic ductile fracture model

Abstract Although single point incremental forming (SPIF) possesses various advantages such as great simplicity and high flexibility, the major limitation is failure and fracture that result from extreme thinning along the thickness direction for complex sheet metal parts. So it is necessary and important on investigating the deformation modes and predicting failure and fracture. In this study, the Hu-Chen ductile fracture criterion (DFC) is modified by tensor transformation, then a new anisotropic ductile fracture criterion is proposed. And the new anisotropic ductile fracture criterion is implemented into Abaqus/Explicit by a user subroutine VUSDFLD. Based on the fracture strain measured from experiments, the parameters of anisotropic DFC can be determined by minimizing the system of nonlinear functions using the nonlinear least-square method, so that the calibrated anisotropic ductile fracture model can be applied into finite element simulations of SPIF. The stress and strain states of the deformation field in FE simulations of SPIF are comprehensively analysed. The new anisotropic ductile fracture model on predicting failure behaviours in SPIF is assessed by the comparisons between simulations and experiments for the parts.

Copolymers of sodium 4-styrene sulphonate and vinyl derivatives of nitrogen-containing heterocycles

The formation of ion-exchange composite materials based on high molecular weight precursors appears to be an intensively developing area in the synthesis of proton-conducting membranes for fuel cells. In such membranes, proton transfer is often provided by functional polymers simultaneously containing sulphonic acid groups in their composition units along with fragments of vinyl derivatives of nitrogen-containing heterocyclic bases. Proton exchange activity in the latter is determined by the possibility of doping with inorganic acids. In the framework of this study, for the further formation of hybrid composite membranes under conditions of radical initiation, copolymers of sodium 4-styrene sulphonate (SSt) with 4-vinylpyridine (VP) and 1-vinylimidazole (VIM) were obtained. The monomodal nature of the turbidimetric titration curves for solutions of copolymerisation reaction products indicates the presence of true copolymers during the process of formation. The composition and structure of the copolymers were characterised using data from elemental analysis, as well as from IR and 13 C NMR spectroscopy. Constants of the relative activity for the monomers and the microstructure parameters of the polymer chains are calculated according to the non-linear leastsquares method using the MathCAD package. The calculated copolymerisation constant values indicate a greater reactivity of SSt in comparison with nitrogen-containing monomers. The lengths of the monomer unit blocks depend on the composition of the initial mixture and vary over a wide range from 1 to 18. The possibility of varying the length of the unit blocks in the composition of the copolymers will affect the ion-conducting properties of hybrid composites formed on their basis. The stability of the copolymers to thermal oxidative degradation by heating in air was studied using the differential scanning calorimetry (DSC) method. The copolymers demonstrated significant thermo-oxidative stability. Decomposition temperatures were 350 °С and 400 °С for SSt-VIM and SSt-VP copolymers, respectively.

METHOD OF DETERMINING THE ACCURACY CHARACTERISTICS OF THE SATELLITE NAVIGATION SYSTEM

The key actions for the implementation of the global navigation satellite systems are described in this article. At the testing stage, the conformity of the system with the operating standards is established, its accuracy characteristics are proved, the temperature of the control bodies and the units are measured, in addition, the composition of the aircraft explores the electromagnetic compatibility of the navigation satellite systems with the equipment of the aircraft.Failure to recognize the deficiencies at the testing stage will lead to significant economic losses in the implementation and refinement of already certified fleet of aircrafts, and worsening of safety flights. Therefore, it is very important to consider all the factors that may affect the work of the system, such as: the temperature of the outside air, the position of the aircraft in space, the connection of the navigation satellite systems with the equipment of the aircraft with partial and complete failure of this equipment, etc. The main but not the only parameter of the navigation satellite systems is precision characteristics, which together with the precise characteristics of manual or automatic control of the aircraft, allow us to meet the requirements of the concept of zonal navigation, which greatly expands the technical capabilities of the aircraft. Therefore, the article pays special attention to the precision characteristics of the navigation satellite systems, methods for increasing the accuracy of statistical analysis of data by: 1) the method of maximum likelihood or nonlinear least squares; 2) the method of simultaneous determination of state variables and Kalman filtration parameters and nonlinear estimation.

Fourier-transform spectroscopy, direct potential fit, and electronic structure calculations on the entirely perturbed (4)1Πstate of RbCs

We perform a high-resolution Fourier-transform spectroscopic study of the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state of the RbCs molecule by applying two-step $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\leftarrow}A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\sim}b{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}\ensuremath{\leftarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ optical excitation followed by observation of the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ laser-induced fluorescence (LIF) spectra. In many LIF progressions the collision-induced satellite rotational lines are observed, thus increasing the amount of term values and allowing us to estimate the $\mathrm{\ensuremath{\Lambda}}$-doubling effect in the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state. The direct potential fit (DPF) of experimental term values of 777 rovibronic levels of both $^{85}\mathrm{RbCs}$ and $^{87}\mathrm{RbCs}$ isotopologues is performed by means of the robust weighted nonlinear least-squares method. The DPF analysis based on the adiabatic approximation and analytical expanded Morse oscillator potential reveals numerous regular shifts in the measured level positions. The spectroscopic studies of the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state are supported by the electronic structure calculations including the potential energy curves of the singlet- and triplet-state manifold and spin-allowed transition dipole moments. The subsequent estimates of radiative lifetimes and corresponding vibronic branching ratios elucidate a dominant contribution of the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\rightarrow}A\ensuremath{\sim}b$ channel into the total radiative decay of the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state. The relative intensity distributions simulated for $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ LIF progressions agree well with their observed counterparts even for the profoundly shifted levels of the entirely perturbed $(4){\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state. To get insight into the origin of the intramolecular perturbations, the relevant spin-orbit- and $L$-uncoupling electronic matrix elements are evaluated.