Simple Formula Research Articles

Computing Accurate True Self-Diffusion Coefficients and Shear Viscosities Using the OrthoBoXY Approach.

In a recent paper [Busch, J.; Paschek, D. J. Phys. Chem. B 2023, 127, 7983-7987], we have shown that for molecular dynamics (MD) simulations using orthorhombic periodic boundary conditions with "magic" box length ratios of Lz/Lx = Lz/Ly = 2.7933596497, the self-diffusion coefficients Dx and Dy in x- and y-directions are independent of the system size. They both represent the true self-diffusion coefficient D0 = (Dx + Dy)/2, while the shear viscosity can be calculated from diffusion coefficients in x-, y-, and z-directions, using η = kBT·8.1711245653/[3πLz(Dx + Dy - 2Dz)]. In this contribution, we test this "OrthoBoXY" approach by its application to a variety of different systems: liquid water, dimethyl ether, methanol, triglyme, water/methanol mixtures, water/triglyme mixtures, and imidazolium-based ionic liquids. The chosen systems range from small-sized molecular liquids to complex mixtures and ionic liquids, while spanning a viscosity range of almost 3 orders of magnitude. We assess the efficiency of the method for computing true self-diffusion and viscosity data and provide simple formulas for estimating the required MD simulation lengths and sizes for delivering reliable data with targeted uncertainty levels. Our analysis of the system size dependence of statistical uncertainties for both the viscosity and the self-diffusion coefficient leads us to the conclusion that it is preferable to extend the simulation length instead of increasing the system size. MD simulations consisting of 768 molecules or ion pairs seem to be perfectly adequate.

Fate of false vacuum in non-perturbative regimes

We use some exact results in scalar field theory to revise the analysis by Coleman and Callan about false vacuum decay and propose a simple non-perturbative formalism. We introduce an exact Green’s function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves the Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple λ ϕ 4 theory, and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate in the thin wall approximation, and suggest simple analytic formulae that may be useful for the analysis for the first-order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by making the coupling values very small.

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

In the current study, an ab initio derivation of the neutron self-shielding factor to solve the complex neutron transport problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field having equal flux in all directions. The theory of steady-state neutron transport was employed, starting from Stuart’s formula, to derive simple analytical formulae based on the integral cross-section parameters. The formulae could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interaction probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. The derived analytic formulae agreed greatly with the experimental observations for different elements and geometries.

Sepsis Stewardship: The Puzzle of Antibiotic Therapy in the Context of Individualization of Decision Making.

The main recent change observed in the field of critical patient infection has been universal awareness of the need to make better use of antimicrobials, especially for the most serious cases, beyond the application of simple and effective formulas or rigid protocols. The increase in resistant microorganisms, the quantitative increase in major surgeries and interventional procedures in the highest risk patients, and the appearance of a significant number of new antibiotics in recent years (some very specifically directed against certain mechanisms of resistance and others with a broader spectrum of applications) have led us to shift our questions from "what to deal with" to "how to treat". There has been controversy about how best to approach antibiotic treatment of complex cases of sepsis. The individualized and adjusted dosage, the moment of its administration, the objective, and the selection of the regimen are pointed out as factors of special relevance in a critically ill patient where the frequency of resistant microorganisms, especially among the Enterobacterales group, and the emergence of multiple and diverse antibiotic treatment alternatives have made the appropriate choice of antibiotic treatment more complex, requiring a constant updating of knowledge and the creation of multidisciplinary teams to confront new infections that are difficult to treat. In this article, we have reviewed the phenomenon of the emergence of resistance to antibacterials and we have tried to share some of the ideas, such as stewardship, sparing carbapenems, and organizational, microbiological, pharmacological, and knowledge tools, that we have considered most useful and effective for individualized decision making that takes into account the current context of multidrug resistance. The greatest challenge, therefore, of decision making in this context lies in determining an effective, optimal, and balanced empirical antibiotic treatment.

Mathematical prognosis of the outcome of the disease of a patient with tuberculosis with HIV infection upon admission to the hospital of the Federal Penitentiary Service

Objective. To identify a mathematical pattern for the subsequent calculation of the prognosis of the outcome of a tuberculosis patient with HIV infection upon admission to the hospital of the Federal Penitentiary Service.Materials and methods. The object of the study was 363 patients with tuberculosis and HIV infection who were admitted for treatment at the hospital of the Federal Penitentiary Service. Discriminant analysis was used to evaluate the features most associated with the discrimination of observations, a priori divided into groups, and reclassify them. As a result, new discriminant axes were obtained, in the space of which the compared groups have the maximum difference.Results and discussion. Formulas were obtained for predicting the outcome of a tuberculosis patient with HIV infection upon admission to a medical institution of the Federal Penitentiary Service: favorable outcome =–91.2138+4.2971×(body mass index)+0.4426×(«experience» of smoking, years)+0.5143×(hemoglobin level, g/l)+0.6158×(stab neutrophils, %)+ 0.4913×(leukocyte T-cell index);unfavorable outcome =–81.8053+3.9467×(body mass index)+0.4071×(«experience» of smoking, years)+0.4724×(hemoglobin level, g/l)+0.6861×(stab neutrophils, %)+0.6630×(leukocyte T-cell index); progression or chronicity =–91.9349+4.2025×(body mass index)+0.5119×(smoking experience, years)+0.5103×(hemoglobin level, g/l)+0.5901×(stab neutrophils, %)+0.5×(leukocyte T-cell index).Conclusion. Simple formulas have been obtained that can be successfully used to calculate the prognosis of the course of the disease upon admission to a hospital in a patient with tuberculosis with concomitant HIV infection.

Scaling Behaviour of dN/dy in High-Energy Collisions

From a recently found family of analytic, finite and accelerating 1+1-dimensional solutions to perfect fluid relativistic hydrodynamics, we derive simple and powerful formulae to describe the rapidity and pseudorapidity density distributions. By introducing a new scaling function, we notice that the rapidity distribution data of the different experiments all collapse into a single curve. This data-collapsing (or -scaling) behaviour in the rapidity distributions suggests that high-energy p+p collisions may be described as collective systems.

Preliminary design and evaluation method for the seismic isolation layer of a shield tunnel

Theoretical analyses and numerical simulations, proposed to increase the efficiency of tunnel seismic isolation measures, are too complex for solving practical problems. Herein, a simplified design method for a tunnel isolation layer is developed for preliminary calculations of the required physical parameters based on the surrounding rock conditions and seismic isolation performance. The internal force response of a shield tunnel in homogeneous ground before and after the installation of a seismic isolation layer is determined using the proposed method, considering the coupled effect of the isolation layer and surrounding rock by calculating the equivalent elastic modulus. The effectiveness of the derived method is verified using wave function expansion and finite element numerical simulation methods. The results obtained using the simplified design formulae are consistent with those obtained using the wave function expansion method. Furthermore, the effects of the seismic wave frequency, surrounding rock type, elastic modulus, and thickness of the seismic isolation layer on the seismic isolation effect are examined via parametric analysis. The proposed method could be applied to preliminary design and evaluation of seismic isolation layers for shield tunnels with different surrounding rock types.

Linear power corrections to top quark pair production in hadron collisions

We compute, in the framework of renormalon calculus, the OΛQCD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\Lambda}_{\ extrm{QCD}}\\right) $$\\end{document} corrections to the production of tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} pairs in hadron collisions under the assumption that qq¯→tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q}\ o t\\overline{t} $$\\end{document} is the dominant partonic channel. This assumption is not applicable to top quark pair production at the LHC but it is valid for the Tevatron where collisions of protons and anti-protons were studied. We show that the linear power correction to the total tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} production cross section vanishes provided one uses a short-distance scheme for the top quark mass. We also derive relatively simple formulas for the power corrections to top quark kinematic distributions. Although small numerically, these power corrections exhibit interesting dependencies on top quark kinematics.

Modeling hydrogen solubility in water: Comparison of adaptive boosting support vector regression, gene expression programming, and cubic equations of state

Predicting the solubility of hydrogen (H2) in aqueous solutions is crucial for studying reactions of hydrogen in the formation, which also affects the security and optimal design of hydrogen storage. In this research, five robust machine learning (ML) algorithms, namely adaptive boosting decision tree (AdaBoost-DT), adaptive boosting support vector regression (AdaBoost-SVR), gradient boosting decision tree (GB-DT), gradient boosting support vector regression (GB-SVR), and k-nearest neighbors (KNN) and three powerful white-box techniques, namely gene expression programming (GEP), genetic programming (GP), and group method of data handling (GMDH) were developed to accurately predict H2 solubility in pure and saline water systems. To this aim, a widespread databank containing 427 experimental data points was collected, and temperature, pressure, and salt concentration (mSalt) were considered as input variables. The validity and precision of the developed models were assessed utilizing several statistical and graphical tests. Results demonstrate that the AdaBoost-SVR smart model could obtain a superior performance and provides precise predictions with root mean square error (RMSE) of 0.000115 and determination coefficient (R2) of 0.9973. Among the white-box models, the GEP provided the best results with an RMSE of 0.000362 and an R2 of 0.9542. Although the accuracy of GEP is slightly lower than that of AdaBoost-SVR, it offers explicit and simple mathematical formula for calculating H2 solubility, which is the main advantage of white box models. The results also demonstrated that AdaBoost-SVR outperforms cubic equations of state (EOSs) such as Peng-Robinson (PR), Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), and Zudkevitch-Joffe (ZJ). Besides, trend analysis showed that AdaBoost-SVR model could match actual trends of H2 solubility change versus temperature and pressure. Finally, outlier detection analysis using the Leverage technique indicated that the majority of data points used for modeling (nearly 94 %) are reliable and placed in the valid zone.

Coupon Collector Problem with Reset Button

We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection that has already been drawn. For the case where standard coupons have unequal probabilities of being drawn, we obtain the distribution of the waiting time until the end of the collection process. For the case where standard coupons have equal probabilities, we derive a simple formula for the expected waiting time in terms of the beta function, and discuss the asymptotic properties of this expected waiting time, when the number of standard coupons tends toward infinity.

Statistical model of electronic structure in InAs, InP, GaSb, and Si quantum dots with surface roughness

Simulations based on the sp 3 d 5 s * empirical tight-binding method were performed to provide a statistical understanding of the electronic structures and bandgap distributions of III–V (InAs, InP, GaSb) and IV (Si) semiconductor quantum dots (QDs) with surface roughness. The electronic states and wavefunctions of QDs with surface roughness of different sizes, shapes, and materials were computed. The effects of surface roughness on the electronic structures and the bandgap distributions of QDs were investigated. The results show that the bandgaps of QDs of considered materials/sizes/shapes increase on average when introducing surface roughness. It is shown that the simulated bandgap distributions of QDs with surface roughness can be reproduced by a simple model formula, which can be applied to different materials, sizes, and shapes. The model formula was derived by assuming that removing and adding of one atom procedures are independent random processes.

Lagrange-enhanced GRA framework for probabilistic simplified neutrosophic multiple-attributes decision-making and applications to painting teaching quality evaluation

Universities are important talent training bases in China and the main driving force for achieving the strategic layout of “revitalizing the country through science and education” and “strengthening the country through talent". Oil painting is a global art with rich humanistic and artistic value. Most art colleges in China have set up oil painting courses. Analyze the current situation and value of oil painting course teaching in local art (teacher training) majors, and leverage the educational role of oil painting courses by enriching course offerings, emphasizing the integration of humanistic innovation, improving teacher literacy, and striving to further improve the quality and efficiency of oil painting course teaching. The quality evaluation of oil painting teaching in universities is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of oil painting teaching in universities. In this paper, in order to obtain the weight information, an optimization model implemented to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) technique is implemented for MADM to rank the alternatives. Finally, a numerical example for quality evaluation of oil painting teaching in universities is used to verify the practicability of the PSNN-GRA technique and compares it with other techniques.

Heavy quark drag and diffusion coefficients in the prehydrodynamic QCD plasma

Kinetic and chemical equilibrations play important roles in the formation of the quark-gluon plasma (QGP) in relativistic heavy-ion collisions (HICs). These processes further influence the production of hard and electromagnetic probes in HICs, in particular, the thermalization of heavy quarks, which are produced at an extremely early time before the formation of the QGP. I calculate the drag and diffusion coefficients of heavy quarks in the prehydrodynamic quantum chromodynamic (QCD) plasma with the state-of-the-art QCD effective kinetic theory (EKT) solver. The time, momentum, and angular dependencies of these coefficients for gluon and quark contributions are presented separately, showing the effects of isotropization and chemical equilibration from the QCD plasma. I also provide a simple formula to estimate the heavy quark drag and diffusion coefficients, as well as its energy loss, within the prehydrodynamic plasma at different coupling strengths based on the attractor theory. Finally, I discuss the validity of these estimations with leading-order calculations and leading-logarithmic rescaling factors. Published by the American Physical Society 2024

On correlation functions in models related to the Temperley-Lieb algebra

We deal with quantum spin chains whose Hamiltonian arises from a representation of the Temperley-Lieb algebra, and we consider the mean values of those local operators which are generated by the Temperley-Lieb algebra. We present two key conjectures which relate these mean values to existing literature about factorized correlation functions in the XXZ spin chain. The first conjecture states that the finite volume mean values of the current and generalized current operators are given by the same simple formulas as in the case of the XXZ chain. The second conjecture states that the mean values of products of Temperley-Lieb generators can be factorized: they can expressed as sums of products of current mean values, such that the coefficients in the factorization depend neither on the eigenstate in question, nor on the selected representation of the algebra. The coefficients can be extracted from existing work on factorized correlation functions in the XXZ model. The conjectures should hold for all eigenstates that are non-degenerate with respect to the local charges of the models. We consider concrete representations, where we check the conjectures: the so-called golden chain, the QQ-state Potts model, and the trace representation. We also explain how to derive the generalized current operators from concrete expressions for the local charges.

On the temperature dependence of transition intensities of rare-earth ions: A modified Judd-Ofelt theory

We report on a modification of the Judd-Ofelt theory accounting for thermal populations of Stark sub-levels of the multiplets involved in transitions in absorption and emission. The calculations require the data on the crystal-field splitting, the irreducible representations of Stark sub-levels and the selection rules for electric-dipole transitions. Simple formulas for absorption oscillator strengths and probabilities of radiative spontaneous transitions are obtained. The application of the proposed model allowed us to remove the contradiction between the transition intensities in absorption and emission (3H6 ↔ 3F4) for Tm3+-doped crystals. It was also used to explain the experimental temperature dependences of luminescence lifetimes of the 3F4 Tm3+ manifold in two widely used laser crystals, LiYF4 and Y3Al5O12. The case of Yb3+ ions featuring a small number of crystal-field sub-levels is also considered.

Discussion of So-Called “Architectural Heritage DNA” via a Case Study of the Conservation of the Nara Palace Site, Japan

This study introduces a brief history of the discovery of and conservation efforts to preserve the Nara Palace Site in Japan, which brought about the recognition of this heritage site as a World Cultural Heritage location by UNESCO in 1996. Accordingly, the 1994 Nara Document on Authenticity plays an important role in contributing to Japanese cultural heritage conservation achievements, with the expansion of cultural diversity and heritage diversity and the concepts of values and authenticity, which proposed a new orientation in terms of awareness and openness to develop a broader vision when identifying architectural heritage values. Against this background, we first discuss the newly proposed concept of so-called “architectural heritage DNA” and its potential structure, providing a simple formula for appraising the authentic values of architectural heritage conservation works. Working within conservation theory, besides the doctrinal study of the 1994 Nara Document on Authenticity, this study also focuses on other important international conventions, such as the 1964 Venice Charter and the 1999 Burra Charter, to clarify the concepts of conservation, restoration, and reconstruction, adding the concept of inheritance between conservation and development, which addresses the lack of international conventions regarding cultural heritage conservation. The viewpoints expressed in this paper are based on the most common concepts of these international conventions but are interpreted in a novel, understandable, practical, and highly applicable approach suited to both the current socio-political situation and future scenarios.

Analisis Kesalahan Simple Past Tense pada Latihan Menulis Recount Text pada Materi Kuliah Bahasa Inggris Dasar (Studi Kasus pada Kelas 63.1C.25 Jurusan Akuntansi Fakultas Ekonomi & Bisnis 2022/2023 UBSI)

This study investigated the misapplication of the simple past tense formula by 43 students who attended the Basic English course at the Department of Accounting, Faculty of Economics and Business, Bina Sarana Informatics University. The research data was obtained from the analysis of participants' recount text writing exercises to evaluate their ability to understand the formula. The research method applied is qualitative descriptive. Research findings show one common mistake that often arises, namely in the use of sentence elements that do not conform to the simple past tense formula. The error comes from students' negligence and lack of accuracy when completing assignments, as well as the tendency to mix past tense formulas with other tenses. Data collection is carried out through direct observation of student activities. The purpose of this study is to gain a deeper understanding of common mistakes in the application of simple past tense formulas, especially in the context of teaching basic English in a university environment.

Experimental and theoretical investigation on residual bearing capacity of CFDST-T joints after lateral impact

This study investigates the residual performance of concrete-filled double-skin steel tubular (CFDST) T-joints after lateral impact. One hollow T-joint and five CFDST-T joints with various steel tube thickness and hollow rate were first tested by a pendulum machine. The axial compression test was subsequently performed to explore the residual performance in terms of failure mode, residual bearing capacity, ductility, energy dissipation, and strain evolution. Results indicated that the failure modes of the CFDST-T joint and hollow T-joint were characterized by global bending and severe local indentation, respectively. Besides, the CFDST-T joints exhibited the strongest residual bearing capacity with a hollow rate of 0.52 and the greatest ductility of 0.63. Moreover, increasing the outer tube thickness improved the residual bearing capacity and simultaneously reduced the ductility coefficient while the inner tube exerted little effect on residual performance. Simplified calculation formulas were finally derived to predict the impact residual deflection and residual bearing capacity of the CFDST-T joint based on parametric analysis. This study will provide a reference for future research to contribute to the design of more reasonable CFDST-T joints and promote their application.

System Size Dependence of the Diffusion Coefficients in MD Simulations: A Simple Correction Formula for Pure Dense Fluids.

A practical correction formula relating the self-diffusion coefficient of dense liquids from molecular dynamics (MD) simulations with periodic boundary conditions to the self-diffusion coefficient in the thermodynamic limit is discussed. This formula applies to pure dense fluids and has a very simple form D = D0(1 - γN-1/3), where D0 is the self-diffusion coefficient in the thermodynamic limit and N is the number of particles in the simulation. The numerical factor γ is dependent on the geometry of the simulation cell. Remarkably, γ ≃ 1.0 is the most popular cubic geometry. The success of this formula is supported by results from MD simulations, including very recent simulations with a "magic" simulation geometry.

Simple method for optical characterization of surface agents on conjugated silver nanoparticles

In this study, a simple formula has been proposed to calculate the refractive index of surface agents of silver nanoparticles (Ag NPs) by using the plasmonic peak of the absorption spectra of dispersed Ag nano-colloids. The basis of the study is the shift in the localized surface plasmon resonance (LSPR) of Ag NPs upon alteration of surface agents. The color changes in a typical metal nano-colloid are mainly due to the shift in the LSPR, which is caused because of electrical interactions of surface agents on the particles. There are some theoretical models to simulate the absorption spectrum, but using these methods to evaluate the plasmonic peak is not facile for a wide range of users. Here, the required simulations were performed for different values of the refractive index of surface agents and particle sizes, and the absorption spectrum and dispersive curves were accordingly plotted. A simple formula was obtained between the wavelength of the plasmonic peak, the refractive index of the shell of surface agents, and the ratio of the hydrodynamic diameter to Feret size of the particles (R0). The refractive index of the surface agents can be calculated by n2=λmax−(202.3R02−748.6R0+947.4)−152.2R02+561.3R0−405.1, where λmax (in nanometer) is the wavelength of the absorption peak due to LSPR. This method can pave the way for experimenters to obtain the refractive index and consequently the type of surface agents around Ag NPs without the need for numerical or mathematical operations. It can also be useful in analyzing the spectral diagnosis of biological agents such as viral antibodies and antigens.