Norm Index Research Articles

Predicting Thermal Decomposition Temperature of Binary Imidazolium Ionic Liquid Mixtures from Molecular Structures.

Ionic liquids (ILs) have been regarded as “designer solvents” because of their satisfactory physicochemical properties. The 5% onset decomposition temperature (Td,5%onset) is one of the most conservative but reliable indicators for characterizing the possible fire hazard of engineered ILs. This study is devoted to develop a quantitative structure–property relationship model for predicting the Td,5%onset of binary imidazolium IL mixtures. Both in silico design and data analysis descriptors and norm index were employed to encode the structural characteristics of binary IL mixtures. The subset of optimal descriptors was screened by combining the genetic algorithm with the multiple linear regression method. The resulting optimal prediction model was a four-variable multiple linear equation, with the average absolute error (AAE) for the external test set being 12.673 K. The results of rigorous model validations also demonstrated satisfactory model robustness and predictivity. The present study would provide a new reliable approach for predicting the thermal stability of binary IL mixtures.

Nano-SAR Modeling for Predicting the Cytotoxicity of Metal Oxide Nanoparticles to PaCa2.

Nowadays, the impact of engineered nanoparticles (NPs) on human health and environment has aroused widespread attention. It is essential to assess and predict the biological activity, toxicity, and physicochemical properties of NPs. Computation-based methods have been developed to be efficient alternatives for understanding the negative effects of nanoparticles on the environment and human health. Here, a classification-based structure-activity relationship model for nanoparticles (nano-SAR) was developed to predict the cellular uptake of 109 functionalized magneto-fluorescent nanoparticles to pancreatic cancer cells (PaCa2). The norm index descriptors were employed for describing the structure characteristics of the involved nanoparticles. The Random forest algorithm (RF), combining with the Recursive Feature Elimination (RFE) was employed to develop the nano-SAR model. The resulted model showed satisfactory statistical performance, with the accuracy (ACC) of the test set and the training set of 0.950 and 0.966, respectively, demonstrating that the model had satisfactory classification effect. The model was rigorously verified and further extensively compared with models in the literature. The proposed model could be reasonably expected to predict the cellular uptakes of nanoparticles and provide some guidance for the design and manufacture of safer nanomaterials.

Confirmatory Factor Analysis and Norming of the High School Student’s Entrepreneurial Orientation Scale

Several studies have shown that entrepreneurial orientation in high school students can predict career choices as businessmen in the future. However, not many studies have developed a measurement instrument for entrepreneurial orientation in high school students in one solid variable construct. This study aims to conduct confirmatory factor analysis and norming on a scale that was previously explored. A survey of 646 high school students was conducted in six large cities throughout the provinces on Java Island, Indonesia. The results of this research confirmed that the construct of entrepreneurial orientation in high school students has three dimensions: innovativeness, risky proactiveness and competitiveness. The study also produced a norm index for junior and senior high school students. This scale will be useful in mapping the level of student’s entrepreneurial orientation and assist high school management bodies to prepare programs that are more suitable to developing entrepreneurial behavior in students.

THE PECULIARITIES OF INDUSTRIAL ENTERPRISES’ PROFIT TAXATION IN A DIFFERENTIATED APPROACH

This article studies the problem of improving enterprise profit taxation, the ways to solve it, and one of the main problems of the modern system of the enterprises taxation — how it is connected to the production efficiency. By solving it, we can determine the differentiation of the tax rates to the enterprises’ profit. Within its methodological framework, the author proposes to use the theory of surplus value. In order to spread the global methods for solving the issues of improving the taxation profit of enterprises and ensuring the economic efficiency and growth, the principles of neoclassic marginal theory are used. The system of indicators — signs and criteria — provides evidence for differentiating industrial enterprises into groups for a more optimal taxation of their profits. The author provides suggestions for forming the rate of the profit tax to stimulate the increase of production efficiency and reinvestment of funds for its development. The algorithm for calculating the profit tax rate assumes using the index of the norms of surplus value — profitableness of labor. This article proposes using a matrix for classifying industrial enterprises into groups, defining the level of the tax rates to profit for each of them based on the developed algorithm together with the level of production efficiency for 2018. For industrial enterprises, special industrial level of indicators — the signs differentiation — are considered: the structure of capital, the standard of profit, the profitableness of labor, and the results of their profit taxation using the method of free balance, the normative method, the modern and the proposed tax profit systems. In the case of the industrial enterprises, the relevance of the proposed reforms of the taxation of profit is explained. The results of research constitute the methodological basis of developing a more effective mechanism of taxing enterprises’ profit, which is especially necessary when realizing anti-crisis economic politics.

A norm index-based QSPR model to predict the standard absolute entropy of organic compounds in three phase states

The entropy of organics is a fundamental and crucial thermodynamic quantity. In this work, a unified quantitative structure-property relationship (QSPR) model was proposed to predict the standard absolute entropy for 15 kinds of organic compounds in three phase states based on the norm index concept. Three phase states of the standard absolute entropy of organics, namely, the solid state (So(s)), liquid state (So(l)) and gas state (So(g)), were considered in the model. This unified model presented good accuracy and fitting as demonstrated by the R2, F and AARD statistical parameters obtained for 45 So(s) data points, 190 So(l) data points and 174 So(g) data points, respectively. Furthermore, the results of internal and external validation and applicability domain analysis proved that this norm index-based QSPR model was stable and robust and had both statistical quality and predictive ability. The satisfactory obtained results suggested that this unified model can be successfully used to predict the So values of organic compounds in different phase states and that the norm descriptors may be general and universal.

Norm index in QSTR work for predicting toxicity of ionic liquids on Vibrio fischeri

Ionic liquids have been becoming new ‘green solvent’ because of the low saturation vapor pressure, less volatilization and more recycling utilization. Since most ILs are soluble in water, it should be indispensable to evaluate the ecotoxicology effect of ILs on aquatic environment before using them widely. Based on the concept of norm index, a set of norm descriptors were proposed for anions, cations and ILs. The whole IL structure optimization method has been used to build a predictive norm index-based quantitative structure-toxicity relationship model for the toxicity of ILs on Vibrio fischeri. Statistical results indicated that norm descriptors were reliable and robust in expressing the relationship between structural information and toxicity of ILs. Meanwhile, a series of ILs without experimental values were predicted based on this stable QSTR model. The results indicated that for imidazole-based ILs, an increase in the length of substituent in the branch could enhance the toxicity of ILs on Vibrio fischeri, and the branch contains hydroxyl group, double bond or triple bonds might reduce the toxicity of ILs. Results obtained in this present work would be valuable for the molecular design and the toxicity evaluation toward aquatic organism of ILs.

Measuring income inequality based on unequally distributed income

This paper proposes a new framework for measuring income inequality. The framework is based on the unequally distributed (UD) incomes that are obtained by removing the equally distributed parts from incomes. We then derive the normalized norm indexes from the cumulative distribution function and the unscaled Lorenz curve of the UD incomes. The relation between the normalized norm indexes and the popular Gini coefficient and coefficient of variation (CV) shows that the Gini coefficient and CV represent only parts of income inequality. We analyze example income distributions and the Luxembourg Income Study datasets to show that the normalized norm indexes evaluate income inequality appropriately and solve the negative income problem.

Norm index-based QSAR models for acute toxicity of organic compounds toward zebrafish embryo

Zebrafish embryos are highly sensitive to toxicant exposure and have been used to evaluate the potential eco-toxicity caused by organic pollutants in the aquatic environment. This study was to develop four quantitative structure–activity relationship (QSAR) models based on norm descriptors for acute toxicity of different exposure times toward zebrafish embryo of organic compounds with various structures. Norm descriptors were obtained by calculating the norm index of the atomic distribution matrix, which was composed of atomic spatial distribution and atomic properties. These norm index-based QSAR models presented satisfactory results with R2 of 0.8549, 0.9162, 0.8335 and 0.8119 for 48, 96, 120 and 132 h, respectively. Validation results including cross validation, external validation, Y-randomized test and applicability domain analysis indicated that the proposed models were stable, robust and reliable. Accordingly, these norm descriptors might be effective in predicting the acute toxicity of various organics to zebrafish embryos, which might be useful for evaluating the potential hazards of organic pollutants to aquatic environment.

Prediction of the thermal decomposition temperatures of imidazolium ILs based on norm indexes

Thermal decomposition temperature (Td) is a vital feature to assess the thermal hazard of ionic liquids (ILs). In this approach, a statistically significant quantitative structure-property relationship (QSPR) model was developed to forecast the Td of imidazolium ILs merely derived from their molecular structures. The new proposed norm indexes were employed to characterize not only the structural characteristics of anions and cations but also the interaction between anions and cations. The genetic algorithm-based multiple linear regression (GA-MLR) method was adopted to choose the best set of norm indexes that oblige a prominent contribution to the Td of imidazolium ILs. The results prediction model was obtained from a multilinear equation with thirteen variables, as consisting of three cationic descriptors, seven anionic descriptors, and three interaction descriptors. The squared correlation coefficients (R2) and the root-mean-squared error (RMSE) of the resulting model are 0.895 and 21.626, respectively. The developed model was then rigorously verified by various validation methods, and thoroughly extensively compared with formerly circulated published models. The results showed satisfactory sturdiness and accountability of the model, which would be considered to be able to forecast the Td of imidazolium ILs and provide some guidelines for designing as well manufacturing safer ILs with better thermal stability.

On the numerical index of absolute symmetric norms on the plane

ABSTRACT We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real -space for .

Optimal Sensor Placement Method Considering the Importance of Structural Performance Degradation for the Allowable Loadings for Damage Identification

Considering the importance of damage for the structural performance and for decreasing the identification error, this paper proposes an optimal sensor placement method based on a weighted standard deviation norm (WSDN) index. The standard deviation of the identified damage parameters is solved using the series expansion theory and probabilistic method to quantify the effect of a measurement error on damage identification. The damage estimation weight (DEW) index, which can reflect the importance of each element in the structural capabilities, is established based on a performance-damage curve. A significant DEW for a specified element indicates that the element is important for the structure and that its identification error should be small. The WSDN index is obtained from the Hadamard product of the standard deviations (SDs) and DEWs. Thus, the identification error of the entire structure is measured using the weighting coefficient. The optimal sensor placement (OSP) procedure is performed by minimizing the WSDN index. The proposed method can clearly decrease the uncertainties of the identification results for the important elements. Other OSP criteria, including the condition number, information entropy, and standard deviation norm, which aim to decrease the identification error, are discussed in this paper for comparison with the proposed method. Two numerical examples and an experiment, which pertain to the deformation performance, buckling features, and dynamic characteristics, are discussed to verify the advantages of the proposed method.

Norm Index-Based QSAR Model for Acute Toxicity of Pesticides Toward Rainbow Trout.

The aquatic ecological environment is being threatened from overuse of pesticides, and the aquatic toxicity toward rainbow trout (Oncorhynchus mykiss) plays a significant role in environmental risk assessment of agrochemicals. In the present study, 2 norm index formulas were developed, from which several norm descriptors were derived. A quantitative structure-activity relationship (QSAR) model was established for the prediction of acute toxicity (median lethal concentration) toward rainbow trout of various pesticides. Results indicated that the present QSAR model presented an R2 of 0.8053. Meanwhile, internal validation (QLOO2 = 0.7606), external validation (Rtraining2 = 0.8011, Rtesting2 = 0.8108), Y-randomization test, and applicability domain analysis further demonstrated the stability, reliability, and wide application domain of the present QSAR model. Accordingly, these norm descriptors might be applicable to the structures of pesticides for predicting the acute toxicity to aquatic organism. Environ Toxicol Chem 2020;39:352-358. © 2019 SETAC.

A norm indexes-based QSPR model for predicting the standard vaporization enthalpy and formation enthalpy of organic compounds

As important thermodynamic properties, vaporization enthalpy and formation enthalpy were extensively utilized in the chemical industry process and chemical engineering design, environment and agriculture. Based on the concept of norm index proposed by our group previously, a unified QSPR model was built for predicting four properties endpoints for 14 families of organic compounds. Four thermodynamic properties endpoints, including standard vaporization enthalpy (ΔHv0), standard formation enthalpy in gas state (ΔHf0(g)), standard formation enthalpy in solid state (ΔHf0(s)) and standard formation enthalpy in liquid state (ΔHf0(l)), were involved in the same modelling work. This model has satisfactory fitting effect for four properties endpoints with R2 of 0.967 for ΔHv0, R2 of 0.990 for ΔHf0(g), R2 of 0.989 for ΔHf0(s) and R2 of 0.987 for ΔHf0(l), respectively. Moreover, the results of internal validation, external validation and applicability domain analysis indicated the good stability and robustness of this model. This work not only calculated vaporization enthalpy and formation enthalpy with the same formula, but also covered gas, solid and liquid phases for formation enthalpy. Satisfying results obtained in the present work suggest that this model and norm indexes have good reliability and generalization.

Norm index for predicting the rate constants of organic contaminants oxygenated with sulfate radical.

The degradation of organic contaminants in aquatic systems has raised immense attention worldwide, and the second-order rate constant ([Formula: see text]) of water pollutants oxidized by sulfate radical anion is an important index for assessing the degradation efficiency of organics. Herein, a new norm mathematical formula is defined. Based on this, four new descriptors are proposed and a QSPR model is developed for predicting [Formula: see text] using 30 families of emerging organic pollutants in water. The statistical results fully prove that this model has good fitting effect and stability with R2 of 0.8862, Q2LOO of 0.8466, and Q25-fold of 0.8329, respectively. The validation results including cross validation, applicability domain analysis, and model comparison show that this model has good robustness, predictive performance, and reliability. These decent results indicate that the new norm mathematical formula is effective in calculating descriptors and the norm indexes have a great application for evaluating the transformation fate of organic pollutants by sulfate radical in aquatic systems.

Differential principal factors and Pólya property of pure metacyclic fields

Barrucand and Cohn’s theory of principal factorizations in pure cubic fields [Formula: see text] and their Galois closures [Formula: see text] with [Formula: see text] types is generalized to pure quintic fields [Formula: see text] and pure metacyclic fields [Formula: see text] with [Formula: see text] possible types. The classification is based on the Galois cohomology of the unit group [Formula: see text], viewed as a module over the automorphism group [Formula: see text] of [Formula: see text] over the cyclotomic field [Formula: see text], by making use of theorems by Hasse and Iwasawa on the Herbrand quotient of the unit norm index [Formula: see text] by the number [Formula: see text] of primitive ambiguous principal ideals, which can be interpreted as principal factors of the different [Formula: see text]. The precise structure of the group of differential principal factors is determined with the aid of kernels of norm homomorphisms and central orthogonal idempotents. A connection with integral representation theory is established via class number relations by Parry and Walter involving the index of subfield units [Formula: see text]. Generalizing criteria for the Pólya property of Galois closures [Formula: see text] of pure cubic fields [Formula: see text] by Leriche and Zantema, we prove that pure metacyclic fields [Formula: see text] of only one type cannot be Pólya fields. All theoretical results are underpinned by extensive numerical verifications of the [Formula: see text] possible types and their statistical distribution in the range [Formula: see text] of [Formula: see text] normalized radicands.

Norm descriptors for predicting the hydrophile-lipophile balance (HLB) and critical micelle concentration (CMC) of anionic surfactants

The hydrophile-lipophile balance (HLB) and critical micelle concentration (CMC) are vitally important indexes to measure the performance of surfactants quantitatively. Herein, based on the concept of norm index, new norm descriptors were proposed for describing the HLB and CMC of anionic surfactants, and two QSPR models were built to calculate the two values. Results showed that the norm descriptors-based models could give satisfactory prediction effect for the HLB and CMC of anionic surfactants with the R2 of 0.9983 for HLB and R2 of 0.9130 for CMC. The satisfactory results of several validations demonstrated that these models were stable, reliable and had a very good predictive ability. Moreover, for anionic surfactants without experimental values, the predicted HLB of 19 anionic surfactants and predicted CMC of 101 anionic surfactants were respectively calculated using the proposed models. The above results indicated that the norm index was suitable for evaluating the HLB and CMC.

Prediction of ionic liquids heat capacity at variable temperatures based on the norm indexes

The heat capacity of ILs is essential in the chemical engineering and design applications. In this study, the dataset consisting of 5964 heat capacity data points within a wide temperature range (191.13–550.00 K) of 185 ILs was collated. Based on the concept of norm index, a serial of norm indexes were derived and adopted to develop the QSPR model. Here, the temperature parameters were adjusted on the basis of the molecular structure information. The linear model is precise for estimating heat capacity of ILs at variable temperatures with square of correlation coefficient R2 = 0.996, average absolute relative deviation AARD = 2.49% and the root mean square error RMSE = 19.43. Besides, the good results of multiple verification methods further illustrate the stability and reliability of this work. Consequently, this norm-index based work could provide a correlation method to describe the heat capacity of different structures ILs at variable temperatures.

Norm indexes for predicting enthalpy of vaporization of organic compounds at the boiling point

Enthalpy of vaporization (∆Hv) is an important physicochemical property and has been widely used in chemical industry and process design. In this work, based on the concept of norm index proposed by our group, a QSPR model was developed to predict ∆Hv at the boiling point for 13 kinds of organic compounds including chain and cyclic hydrocarbons, alcohols, ketones, carboxylic acids and amines etc. The results showed that this model had satisfactory predictive performance with the squared correlation coefficient R2 of 0.9503, the Fisher's criterion F of 378.84 and the average absolute relative deviation of 3.17%. The internal validation, external validation and applicability domain analysis results indicated the robustness and reliability of this model. Moreover, comparison results demonstrated that this model performed well both in accuracy and stability. The satisfactory results further suggested that the norm index can be applied to the calculation of ∆Hv for organic compounds.

Oracle inequalities and adaptive estimation in the convolution structure density model

We study the problem of nonparametric estimation under $\mathbb{L}_{p}$-loss, $p\in[1,\infty)$, in the framework of the convolution structure density model on $\mathbb{R}^{d}$. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. The original pointwise selection rule from a family of “kernel-type” estimators is proposed. For the selected estimator, we prove an $\mathbb{L}_{p}$-norm oracle inequality and several of its consequences. Next, the problem of adaptive minimax estimation under $\mathbb{L}_{p}$-loss over the scale of anisotropic Nikol’skii classes is addressed. We fully characterize the behavior of the minimax risk for different relationships between regularity parameters and norm indexes in the definitions of the functional class and of the risk. We prove that the proposed selection rule leads to the construction of an optimally or nearly optimally (up to logarithmic factors) adaptive estimator.

Multiple toxicity endpoint–structure relationships for substituted phenols and anilines

Quantitative structure–toxicity relationship (QSTR) models with the same mathematical structure were proposed for predicting the multiple toxicity endpoints of substituted phenols and anilines towards Chlorella vulgaris (C. vulgaris) based on the norm indexes. Four aquatic toxicity endpoints including growth inhibition concentrations of IC50, IC20, LOEC and NOEC towards C. vulgaris were involved in the modeling work. The results indicated that the developed models could produce satisfactory predictive results for the four different toxicity endpoints with high squared correlation coefficients (R2). Leave-one-out cross validation, Y-randomized validation and application domain analysis demonstrated the accuracy, robustness and reliability of these models. Accordingly, the results obtained in this work suggested that it might be possible to develop QSTR models with the same mathematical structure for predicting multiple toxicity endpoints successfully via norm index descriptors.