In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus ...on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.
The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these ...definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of fuzzy soft set, intervalvalued fuzzy soft set, hesitant fuzzy soft set and intuitionistic soft set are also discussed. We also suggest an approach to unify the definitions of soft point which is more applicable than the existing notions.
Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These materials are ...promising for applications as inexpensive “designer” solvents exhibiting a host of tunable physicochemical properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure–property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their melting point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.
Physiochemical properties of pure components serve as the basis for the design and simulation of chemical products and processes. Models based on the molecular structural information of chemicals for ...the following 25 pure component properties are presented in this work: (critical‐) temperature, pressure, volume, acentric factor; (normal‐) boiling point, melting point, auto‐ignition temperature; flash point; (standard‐) enthalpy of formation, Gibbs energy of formation, enthalpy of fusion, enthalpy of vaporization, liquid molar volume; (environmental‐) (lethal dose‐) LC50 and LD50, photo‐chemical oxidation potential, bioconcentration factor, permissible exposure limit; (physicochemical‐) acid dissociation constant, water‐solubility, octanol–water partition coefficient, Hildebrandt solubility parameter, Hansen solubility parameters. Utilizing functional groups for molecular representation, two parallel property estimation models where the group contributions for each property are regressed through traditional regression techniques and machine learning techniques are presented. Both techniques use an a priori data analysis before regression of model parameters. A dataset with more than 24,000 chemicals for the 25 pure component properties has been utilized for the development of the two sets of property models. The efficacy of the developed models and their use are highlighted together with a discussion on the overall performance, application range, and predictive capabilities with implications to product and/or process engineering problem solutions.
The contour feature points of object point cloud are the main features of human perception on target, and play an important role in many fields such as indoor model reconstruction, object detection ...and location. In this paper, we present a new method to extract the contour feature points of point cloud, which mainly includes two main contents: (1) The conspicuous and inconspicuous boundary points are extracted according to the characteristics of distribution of the azimuth between adjacent vectors in two-dimentional view. (2) According to the direction of main feature vector, a two-dimensional projection plane of adjacent points in the bounding sphere is constructed, and the crease points are extracted according to the constraint parameters model of distribution mechanism of adjacent points in the two-dimensional view. We evaluate the performance of the proposed method using objects of different sizes in real world scenarios. Simultaneously, the extraction effect of contour feature points is compared with other methods, and the results show that the extraction and anti-noise performance of the proposed method is superior to the other methods. Simultaneously, it is suitable not only for regular flat-shaped buildings but also for objects with irregular curvilinear architecture. Moreover, the proposed method involves only one parameter that needs to be tuned, and the parameter can be quickly obtained based on the distance resolution.
Machine learning has proven to be a powerful tool for accelerating biofuel development. Although numerous models are available to predict a range of properties using chemical descriptors, there is a ...trade-off between interpretability and performance. Neural networks provide predictive models with high accuracy at the expense of some interpretability, while simpler models such as linear regression often lack in accuracy. In addition to model architecture, feature selection is also critical for developing interpretable and accurate predictive models. We present a method for systematically selecting molecular descriptor features and developing interpretable machine learning models without sacrificing accuracy. Our method simplifies the process of selecting features by reducing feature multicollinearity and enables discoveries of new relationships between global properties and molecular descriptors. To demonstrate our approach, we developed models for predicting melting point, boiling point, flash point, yield sooting index, and net heat of combustion with the help of the Tree-based Pipeline Optimization Tool (TPOT). For training, we used publicly available experimental data for up to 8351 molecules. Our models accurately predict various molecular properties for organic molecules (mean absolute percent error (MAPE) ranges from 3.3% to 10.5%) and provide a set of features that are well-correlated to the property. This method enables researchers to explore sets of features that significantly contribute to the prediction of the property, offering new scientific insights. To help accelerate early stage biofuel research and development, we also integrated the data and models into a open-source, interactive web tool.
•Developed method for selecting chemical descriptors and minimizing collinearity•Trained five property prediction models using diverse data sets•Models are interpretable and yield excellent peformance•Feature importances are consistent and agree with previous research•Webtool available at feedstock-to-function.lbl.gov
Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the ...Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes N below the correlation volume Nξ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length ξ ∼ ln Nξ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast “diffusion,” which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance Σ2 (ω) crossing over, with increasing frequency ω, from ergodic behavior Σ2 = (2/π2) ln ω/Δ to Σ2 ∝ ω2 at ωc ∼ (N Nξ) −1/2 and finally to Poissonian behavior Σ2 = ω/Δ at ωξ ∼ N−1ξ. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate d → ∞ limit of the Anderson model in d spatial dimensions.
A solution-phase synthesis of colloidally stable A2BF6 nanocrystals is reported for the first time, focusing on A+ = Cs+, NH4+ and B4+ = Zr4+. Handling hypertoxic HF is avoided by using NH4F and a ...low-boiling-point alcohol, representing the first synthesis of any A2BF6 nanocrystals without HF addition. The chemical incompatability of Zr4+ with other common fluoride sources is discussed.
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