High-precision Calculations Research Articles

Extended Higher Order Iterative Method for Nonlinear Equations and its Convergence Analysis in Banach Spaces

In this article, a novel higher order iterative method for solving nonlinear equations is developed. The new iterative method obtained from fifth order Newton-Özban method attains eighth order of convergence by adding a single step with only one additional function evaluation. The method is extended to Banach spaces and its local as well as semi-local convergence analysis is done under generalized continuity conditions. The existence and uniqueness results of solution are also provided along with radii of convergence balls. From the numerical experiments, it can be inferred that the proposed method is more accurate and effective in high precision computations than existing eighth order methods. The computation of error analysis and norm of functions demonstrate that proposed method takes a lead over the considered methods.

Predicting Two-Photon Absorption Spectra of Octupolar Molecules: A Deep-Learning Approach Based Exclusively on Molecular Structures.

Octupolar molecules possessing a strong two-photon response are vital for numerous advanced applications. However, accurately predicting their two-photon absorption (TPA) spectra requires high-precision quantum chemical calculations, which are computationally expensive due to repeated simulations of molecular excited-state properties. To address this challenge, we introduce a deep learning approach capable of rapidly and accurately forecasting TPA spectra for octupolar molecules. By leveraging the geometric structure as an initial descriptor, we employ a graph neural network to predict the maximum two-photon transition wavelength and cross-section. Our model demonstrates a mean absolute percentage error of less than 4% compared to time-dependent density-functional theory calculations, effectively reproducing experimental observations. Notably, this deep learning technique is nearly 100 000 times faster than comparable quantum calculations, making it an efficient and cost-effective tool for simulating TPA properties of octupolar molecules. Furthermore, this method holds great promise for the high-throughput screening of exceptional TPA materials.

Prediction of drilling plug operation parameters based on incremental learning and CNN-LSTM

In order to solve the problems of low prediction accuracy and insufficient use of long time series data, and ensure the safety of drilling plug operation, a method for predicting drilling plug parameters based on incremental learning and the CNN-LSTM model is proposed. By making full use of the measured data of the drilling plug operation and using the sliding window processing method to process the data, then the CNN-LSTM deep learning model is established to predict the downhole parameters, and the reliability and generalization of the model are verified. The results show that the prediction accuracy of the machine learning model is the highest when the fixed width k = 4. According to the error results, it is concluded that CNN-LSTM model has the best processing and forecasting ability for drilling plug operation. By analyzing the prediction results of the whole well data, the validation accuracy of CNN-LSTM model reaches 99.5%, indicating that the model has high accuracy and generalization, and the model has fast calculation speed, providing a prediction method with high precision and fast calculation speed for drilling plug operation.

Syntheses and properties of energetic cyclo-pentazolate cocrystals.

As a new type of polynitrogen species that is stable at room temperature, the pentazolate anion (cyclo-N5-) has attracted much attention in the field of high-energy density materials, but its energy and stability are unbalanced. Cocrystallisation can balance their properties to some extent by forming new chemical compositions from existing cyclo-N5- compounds through non-covalent interactions. This article reviews the research progress of cyclo-N5- cocrystals in recent years, including synthetic methods, cocrystals of metal-N5- compounds, and cocrystals of nonmetallic pentazolate salts. The cocrystals of metal-N5- compounds mainly include metal-N5- solvates, cocrystals composed of metal-N5- compounds and amines/MSM, and metal-containing composite salts. The cocrystals of nonmetallic pentazolate salts include cocrystals composed of cyclo-N5- salts and solvents, cocrystals composed of cyclo-N5- salts and N-heterocyclic molecules, and non-metallic composite salts. The fascinating crystal structures (in some cases topological structures), stable forms, and physicochemical properties of representative cocrystals were highlighted. In addition, the future directions that need to be focused on in this field were pointed out, including the development of more preparation methods, especially those suitable for scaling up; higher precision calculation or testing of enthalpy of formation; improvement of their thermal stabilities; creation of cocrystals of cyclo-N5- salts and high-density, high-oxygen balance, high-energy oxidizers; and exploration of the formation mechanism.

Flood Hazard: A QGIS Plugin for Assessing Flood Consequences

Flash floods cause substantial harm to the social and economic aspects of the affected countries. This is a significant problem in urban areas where drainage systems are inadequate and unable to withstand severe flooding. Understanding the specific regions that are susceptible to flooding is essential to implement strategies aimed at mitigating the risk. Detecting floods in ungauged basins is challenging. The current work aims to establish a practical method for identifying and mapping floodplain areas. We can use several tools, including the FLO-2D integration tool, Flood Risk tool, Geomorphic Flood Area plugin, and Quantum Geographical Information System (QGIS) with Hydrologic Engineering Centre River Analysis System (HEC-RAS) to efficiently and cost-effectively detect flood hazard zones. The QGIS tool, the Geomorphic Flood Index (GFI), is the most valuable tool for identifying flood-prone areas in cases where the areas are extensive and lack sufficient data. This tool offers high data analysis and cost calculation precision while using few resources.

An integrated convolutional neural network-based surrogate model for crashworthiness performance prediction of hot-stamped vehicle panel components

During the structural design of vehicle components, Finite Element (FE) modelling has been extensively used for simulations of physical experiments. A typical design optimisation task requires iterative simulations to identify the optimum design, where FE simulations can be too time-consuming. Surrogate models have been developed to approximate complex simulations, which can reduce computational time and improve the efficiency of the design cycle. This paper presents a novel application of convolutional neural network (CNN) on rapid predictions of crashworthiness performance of vehicle panel components considering manufacturability. The dataset for training the model was generated based on the FE results of hot-stamped ultra-high strength steel (UHSS) B-pillar components. The formed components were analysed with a simplified lateral crash test to evaluate the deformation under impact. The trained model can instantly predict the deformation of the designed component with high accuracy compared to the FE results. Due to its high computational efficiency and precision, the surrogate model enables faster and more extensive design evaluations.

High Precision, Low Complexity, and Fast Calculation Based on Hybrid Recursive DFT and FFT Algorithms for Electrochemical Impedance Spectroscopy System

High Precision, Low Complexity, and Fast Calculation Based on Hybrid Recursive DFT and FFT Algorithms for Electrochemical Impedance Spectroscopy System

A Spectroscopic Investigation of the Lowest Electronic States of the I+ 2 Cation as a Candidate for Detecting the Time Variation of Fundamental Constants

The four lowest Ω substates (X2Π3/2,g, X2Π1/2,g, A2Π3/2,u and A2Π1/2,u) of the I+ 2 cation have been studied by high-precision ab initio calculations in comparison with experimental high-resolution absorption spectra. The potential energy curves were calculated using the multi-reference configuration interaction (MRCI) method and Dirac method, respectively. Rovibrational levels of these electronic states were derived by solving the radial Schrödinger rovibrational equation. Molecular constants were obtained in fitting energy levels to a spectroscopic model. Using the fit spectroscopic constants and newly calculated transition dipole moment matrix elements, line strengths of vibronic bands in the A2Π3/2,u- X2Π3/2,g system, as well as Einstein A coefficients for 45 of these bands with ν′ = 11−19 and ν′′ = 1−5, have been derived. The Einstein A coefficients were used to compute radiative lifetimes of the ν′ = 11−19 vibrational levels of the A2Π3/2,u state. Enhancement factors for detecting the variation of the fine-structure constant (α) and the proton-to-electron mass ratio(µ) using transitions between nearly degenerate rovibronic levels of these low-lying states have been calculated.

High-precision electron structure calculation of CaSH molecules and theoretical analysis of its application to laser-cooled target molecules

The CaSH molecule is an important target in the field of laser cooling non-linear polyatomic molecules. Successful cooling of such molecules marks a breakthrough of the technical limitations of laser cooling diatomic and linear triatomic molecules. To identify the possible optical cycle in cooling CaSH, precise geometries of the CaSH ground state and the three lowest excited states, along with their excitation energy, are determined by utilizing the EA-EOM-CCSD (electron attachment equation-of-motion coupled cluster singles and doubles) method, in combination with energy extrapolation using cc-pV<i>X</i>Z/cc-pCV<i>X</i>Z (<i>X</i> = T, Q ) serial basis sets. Geometric parameters of the ground state <inline-formula><tex-math id="M10">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M10.png"/></alternatives></inline-formula> are found to be <i>R</i><sub>CaS</sub>= 2.564 Å, <i>R</i><sub>SH</sub>= 1.357 Å, and<i>∠</i>CaSH= 91.0°. Additionally, the equilibrium geometries of three excited states are also obtained. The <inline-formula><tex-math id="M11">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M11.png"/></alternatives></inline-formula> state has a similar equilibrium structure to the ground state, while the <inline-formula><tex-math id="M12">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M12.png"/></alternatives></inline-formula>and <inline-formula><tex-math id="M13">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M13.png"/></alternatives></inline-formula> states exhibit significant conformer distortions. Specifically, the CaS bond of the <inline-formula><tex-math id="M14">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M14.png"/></alternatives></inline-formula> state and <inline-formula><tex-math id="M15">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M15.png"/></alternatives></inline-formula> state tend to contract, and the CaSH angel bends by 5° relative to the ground state. The vertical excitation energy from the ground state to <inline-formula><tex-math id="M16">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M16.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M17">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M17.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M18">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M18.png"/></alternatives></inline-formula> are of 1.898, 1.945 and 1.966 eV, respectively, which are in good agreement with the previous experimental results. Moreover, the potential energy surfaces of the four lowest electronic states of CaSH are calculated by EA-EOM-CCSD with 3ζ level of basis sets. The nuclear equations of motion are solved to obtain the vibrational frequencies of the CaS bond stretching and CaSH bending. The vibrational frequencies of the (0,1,0) mode and the CaS stretching frequency of four states are 316 cm<sup>–1</sup>, 315 cm<sup>–1</sup>, 331 cm<sup>–1</sup> and 325 cm<sup>–1</sup>, which are in close agreement with the available experimental results. The frequencies of the CaSH bending mode are presented for the first time, with the values of 357 cm<sup>–1</sup>, 396 cm<sup>–1</sup>, 384 cm<sup>–1</sup>, 411 cm<sup>–1</sup> for the <inline-formula><tex-math id="M19">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M19.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M20">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M20.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M21">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M21.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M22">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M22.png"/></alternatives></inline-formula> states, respectively. Theoretical calculations give the Frank-Condon factors of 0.9268, 0.9958 and 0.9248 for the <inline-formula><tex-math id="M23">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M23.png"/></alternatives></inline-formula> to <inline-formula><tex-math id="M24">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M24.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M25">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M25.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M26">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M26.png"/></alternatives></inline-formula> transitions. All three excited states are the bright states with considerable oscillator strength relative to the ground state. Based on the Frank-Condon factor and lifetime of excited states, the <inline-formula><tex-math id="M27">\begin{document}$ {{\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0)\to \tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M27.png"/></alternatives></inline-formula> transition is regarded as the main cooling cycle for the CaSH molecule. The corresponding pump light wavelength is 678 nm. By exciting the vibrational excited states (0,1,0) and (0,0,1) of the <inline-formula><tex-math id="M28">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M28.png"/></alternatives></inline-formula> state to <inline-formula><tex-math id="M29">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M29.png"/></alternatives></inline-formula> using lasers at 666 nm and 668 nm, respectively, the optical cooling branch ratio of CaSH is expected to exceed 0.9998.

Statistical match reports of the 2022 volleyball World Championship in the context of network analysis with Gephi

Background and Study Aim. Modern volleyball teams participating in tournaments provide extensive statistical data about their actions. These data are available for analysis and represent a valuable source for assessing the potential and future success of both individual athletes and teams as a whole. In this context, tools such as Gephi become particularly valuable for visualizing and analyzing events at high-level tournaments. Our study aims to create and analyze network models of interaction among men's volleyball teams during the qualifying matches of the 2022 World Championship using the Gephi software.
 Materials and Methods. For the research, data were obtained from a volleyball statistics website renowned for its extensive database. The study centered on Group C, comprising the teams: Poland, USA, Mexico, and Bulgaria. Data from six matches were extracted into Microsoft Excel tables and then converted into CSV format. The data from these tables were processed using the PyCharm programming environment and Python code. Visualization and analysis of the data were conducted using Gephi.
 Results. The results of the data processing highlight the professional expertise of the teams. The average values for all primary metrics underscore the teams' proficiency in executing fundamental actions at an elevated level. Eigenvector centrality helps determine the significance of nodes in the graph. The graph's density is 0.601, suggesting a relatively dense network of connections within the team. This indicates that volleyball players frequently engage with one another and share information on the court. Such extensive interaction can lead to enhanced coordination and efficiency in team actions. The parameter ε has a value of 1.0E-4, denoting high computational precision. The average interaction degree among volleyball players stands at 46.244. This measure denotes the interaction intensity among team members, hinting at the overall court activity. The modularity measure is 0.483, which signals the structural organization of the graph rooted in modularity. The graph comprises 5 modular communities, hinting at shared characteristics and cohesion among players within these groups. The HITS (Hyperlink-Induced Topic Search) metric assesses the node significance in the graph in terms of hubs and authorities. High HITS values pinpoint pivotal players acting as hubs, signifying their numerous connections with fellow teammates. Such players are crucial for facilitating information flow and coordination within the squad.
 Conclusions. Utilizing statistical match reports in volleyball, combined with the Gephi software, offers a deeper insight into the dynamics of player interactions. This aids in pinpointing key players, refining team strategies, and enhancing court coordination. Coaches are advised to leverage these tools for an in-depth evaluation of gameplay instances and to make informed decisions. Network analysis methodologies might soon be indispensable tools in the contemporary coaching toolkit.

A Fast Fixed-Point Logarithmic Functions Based on ARM Microprocessor

The fixed-point mathematical library refers to a highly optimized collection of high-precision mathematical functions primarily used for fast and high-precision real-time calculations. It can execute equivalent code written in the C language with floating-point format faster, while maintaining considerable accuracy. Current mainstream fixed-point mathematical libraries face issues such as being non-open source, having unknown models, incomplete basic mathematical operation functions, and insufficient precision. Therefore, designing an open-source, fast, more optimized, and high-precision fixed-point mathematical library will have a groundbreaking impact. It can not only play a crucial role in industrial control algorithms but also eliminate the dependency of domestic fixed-point MCUs on foreign library functions. This paper conducts research on fixed-point arithmetic for logarithmic functions, designs, and improves the implementation of fast logarithmic functions.Taking Q12 as an example, Simulation experiments and MCU experiments show that, in the Q12 format, the highest precision that can be represented by a 32-bit fixed-point number is 0.000244141. From the test results, it can be observed that for 98.15% of the test data, the computational errors of the two mathematical libraries are both smaller than the highest precision value. Both two logarithmic function computations can maintain good computational accuracy within the ARM microprocessor. In terms of computational speeds, the average computation cycle of the fixed-point logarithmic function designed in this paper is reduced by 31.88% compared to the counterpart. This substantial improvement in computational speed, while ensuring computational accuracy, enhances the performance of fixed-point logarithmic operations based on ARM microprocessors.

Explicitly correlated Gaussians for high-precision variational calculations of S^{e},P^{e}, and D^{e} states of quantum systems: An efficient algorithm.

In this work we consider an efficient algorithm for variational calculations of quantum few-particle systems in S,P, and D states of the even parity using all-particle explicitly correlated Gaussian (ECG) basis sets. We primarily focus on the description of states where the dominant configuration contains either two particles in p states or a single particle in a d state (all other particles are in s states). The basis functions we consider are products of spherically symmetric ECGs and bipolar harmonics. We introduced a scheme for deriving expressions for matrix elements of the overlap, kinetic and potential energy, as well as their derivatives with respect to the nonlinear parameters of the Gaussians. This allowed us to improve the efficiency of numerical calculations of the matrix elements (which is the most critical part of any code that uses ECGs) by one to two orders of magnitude compared to previous implementations. We provide a complete set of formulas for all basic matrix elements using the formalism of matrix differential calculus and discuss some technical details relevant to their efficient implementation. Lastly, we report a few example calculations of the ^{2}D^{e} states of the Li atom, ^{4}P^{e} and ^{2}D^{e} states of the B atom, and ^{3}P^{e} states of the C atom.

Advancements in number representation for high-precision computing

Efficient representation of data is a fundamental prerequisite for addressing computational problems effectively using computers. The continual improvement in methods for representing numbers in computers serves as a critical step in expanding the scope and capabilities of computing systems. In this research, we conduct a comprehensive review of both fundamental and advanced techniques for representing numbers in computers. Additionally, we propose a novel model capable of representing rational numbers with absolute precision, catering to specific high precision applications. Specifically, we adopt fractional positional notation coupled with explicit codification of the periodic parts, thereby accommodating the entire rational number set without any loss of accuracy. We elucidate the properties and hardware representation of this proposed format and provide the results of extensive experiments to demonstrate its expressiveness and minimal codification error when compared to other real number representation formats. This research contributes to the advancement of numerical representation in computer systems, empowering them to handle complex computations with heightened accuracy, making them more reliable and versatile in a wide range of applications.

An enhanced accuracy method for monitoring formation water salinity utilizing elemental spectroscopy logging

The accurate determination of formation water salinity is crucial for petroleum exploration and development, as it plays a significant role in determining reservoir parameters. The salinity of formation water affects physical parameters such as resistivity and Sigma, which are essential in calculating reservoir oil saturation. Therefore, this paper proposes an effective calculation method of formation water salinity based on elemental spectroscopy logging technology. The method starts by accurately calculating the formation chlorine (Cl) content through a combination of inelastic and capture energy spectrum analyses. Subsequently, a high-precision calculation model of formation water salinity is constructed by utilizing formation density and porosity information. Compared to the traditional oxide closure model, the joint bispectral method improves the calculation accuracy of Cl content by an order of magnitude and keeps the calculation error of formation water salinity within 2 g/L. The field logging example further demonstrates the high agreement between the calculated results of formation water salinity and laboratory analysis results, validating the accuracy of the joint bispectral method. This method is not affected by the mineral composition of the formation, making it suitable for a wide range of applications and highly versatile, which provides valuable technical support for the exploration and development of oil and gas in saltwater-bearing reservoirs.

Numerical Approximations of the Riemann–Liouville and Riesz Fractional Integrals

In this paper, the numerical algorithms for calculating the values of the left- and right-sided Riemann–Liouville fractional integrals and the Riesz fractional integral using spline interpolation techniques are derived. The linear, quadratic and three variants of cubic splines are taken into account. The estimation of errors using analytical methods are derived. We show four examples of numerical evaluation of the mentioned fractional integrals and determine the experimental rate of convergence for each derived algorithm. The high-precision calculations are executed using the 128-bit floating-point numbers and arithmetic routines.

High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies.

Thermodynamic stability assessment of nanocrystal systems requires precise free energy calculations. This study highlights the importance of meticulous control over various factors, including the thermostat, time step, potential cutoff, initial configuration, sampling method, and overall simulation duration. Free energy computations in dry (solvent-free) systems are on the order of several hundred kBT but can be obtained with consistent accuracy. However, calculation of internal energies becomes challenging, as they are typically much larger in magnitude than free energies and exhibit significant noise and reduced reliability. To address this limitation, we propose a new internal energy estimate that drastically reduces the noise. We also present formulas that enable the optimization of the parameters of the harmonic bias potential for optimal convergence. Finally, we discuss the implications of these findings for the computation of free energies in nanocrystal clusters and superlattices.

An 8.8 TFLOPS/W Floating-Point RRAM-Based Compute-in-Memory Macro Using Low Latency Triangle-Style Mantissa Multiplication

High-precision computation with low latency and high energy efficiency is required for AI-driven application and scientific computing. Emerging compute-in-memory (CIM) technology shows a great potential to accelerate multiplication and accumulation (MAC) operations which are frequently executed in such scenarios. Resistive RAM (RRAM) is highly suitable for CIM due to its excellent features such as nonvolatility, small cell size and MAC-friendly structure. However, the existing RRAM CIMs focus on the acceleration of fixed-point/integer operations. Several works adopt the logic-CIM structure to support high-precision Floating-point (FP) calculations, but they require lots of cycles and area to perform a FP operation. To meet the need of low latency and high energy efficiency of widely used FP calculation, we propose an accelerated FP-MAC architecture, based on 40nm RRAM CIM array. A full-parallel data input scheme and triangle weights arrangement is proposed for low latency multi-bits multiplication. A non-uniformly grouped sense amplifiers (NUGSAs) array is adopted for energy and area saving. Experiments show that the proposed FP-MAC design achieves an energy efficiency of up to 8.8 TFLOPS/W at FP8 mode and 3.3 TFLOPS/W at bFP16 mode, and the computing latency is 3.34ns.

Hückel Molecular Orbital Analysis for Stability and Instability of Stacked Aromatic and Stacked Antiaromatic Systems.

Face-to-face stacking of aromatic compounds leads to stacked antiaromaticity, while that of antiaromatic compounds leads to stacked aromaticity. This is a prediction with a long history; in the late 2000s, the prediction was confirmed by high-precision quantum chemical calculations, and finally, in 2016, a π-conjugated system with stacked aromaticity was synthesized. Several variations have since been reported, but essentially, they are all the same molecule. To realize stacked aromaticity in a completely new and different molecular system and to trigger an extension of the concept of stacked aromaticity, it is important to understand the origin of stacked aromaticity. The Hückel method, which has been successful in giving qualitatively correct results for π-conjugated systems despite its bold assumptions, is well suited for the analysis of stacked aromaticity. We use this method to model the face-to-face stacking systems of benzene and cyclobutadiene molecules and discuss their stacked antiaromaticity and stacked aromaticity on the basis of their π-electron energies. By further developing the discussion, we search for clues to realize stacked aromaticity in synthesizable molecular systems.

A novel method for solving hydration heat release based on equivalent heat release theory

Current hydration heat release rate algorithms that consider the temperature history are based on the Arrhenius law and other hypothetical conditions. Nevertheless, reported research results have shown controversy regarding the values of Arrhenius law and other model parameters, potentially introducing errors in calculated results. Some studies have shown that adiabatic temperature rises at different placement temperatures can be expressed by a mathematical expression; thus, this study establishes a relational model for the hydration temperature rise rate of concrete structures under any temperature history. This study uses the hydration temperature rise rate of the adiabatic temperature rise test under equivalent conditions to directly obtain the hydration temperature rise rate for any temperature history. Except for special cases, the proposed algorithm does not rely on the Arrhenius law and other hypothetical conditions, thus avoiding errors caused by the associated assumptions. Additionally, this study utilizes an integration method to solve a problem in which a small calculation time step is required to guarantee the accuracy of the solution under the conventional finite element framework. Furthermore, an iterative algorithm is proposed to solve the problem in which the temperature at the end of the calculation time step must be used when the temperature history is considered. Examples show that the proposed method exhibits a high calculation precision and improves efficiency; and the maximum temperature difference between the calculated and measured values is only 0.085 °C.

Self-aware face emotion accelerated recognition algorithm: a novel neural network acceleration algorithm of emotion recognition for international students.

With an increasing number of human-computer interaction application scenarios, researchers are looking for computers to recognize human emotions more accurately and efficiently. Such applications are desperately needed at universities, where people want to understand the students' psychology in real time to avoid catastrophes. This research proposed a self-aware face emotion accelerated recognition algorithm (SFEARA) that improves the efficiency of convolutional neural networks (CNNs) in the recognition of facial emotions. SFEARA will recognize that critical and non-critical regions of input data perform high-precision computation and convolutive low-precision computation during the inference process, and finally combine the results, which can help us get the emotional recognition model for international students. Based on a comparison of experimental data, the SFEARA algorithm has 1.3× to 1.6× higher computational efficiency and 30% to 40% lower energy consumption than conventional CNNs in emotion recognition applications, is better suited to the real-time scenario with more background information.