Exact Numerical Values Research Articles

Two types of series expansions valid at strong coupling

It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the nth order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n. We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N.

New numerical resolution of the elastic quarter-space, eighth-space and finite-length-space contact problems

In this paper, a new algorithm to solve the elastic quarter-space, the eighth-space and the finite-length-space contact problems is proposed. This corresponds to an extension of the Hertz theory. The theoretical foundations of such a problem are limited, due to the presence of displacements at the free edges- or stresses at the virtual edges — resulting to complex boundary conditions. The new approach presented here is 3D and based on Guilbault’s ingenious fast correction method. In this approach, the edge effects are taken into account by introducing two corrective factors ψ1, ψ2 respectively on the (Ox) and (Oz) axes to replace the mirror pressure iterative process of Hetenyi. The exact numerical values of these two correction factors are derived analytically. The results show that the free edge can substantially increase locally the contact pressure and therefore the stresses and displacement fields if close to the contact area. So the pressure field and the contact zone present an asymmetry which is more pronounced as the free edge is getting closer. This study is carried out on spaces with one, two and four free edges which will be respectively called: quarter-space, eighth-space and finite-length-space. A validation is performed using a Finite Element Method (FEM) analysis. A parametric study is also performed to exhibit the differences with the Hertz solution, including in the situation where one expects the truncation of the contact area when the free edge is virtually located within the Hertz contact area.

User Perceptions of Avatar-Based Patient Monitoring for Intensive Care Units: An International Exploratory Sequential Mixed-Methods Study.

Visual Patient Avatar ICU is an innovative approach to patient monitoring, enhancing the user's situation awareness in intensive care settings. It dynamically displays the patient's current vital signs using changes in color, shape, and animation. The technology can also indicate patient-inserted devices, such as arterial lines, central lines, and urinary catheters, along with their insertion locations. We conducted an international, multi-center study using a sequential qualitative-quantitative design to evaluate users' perception of Visual Patient Avatar ICU among physicians and nurses. Twenty-five nurses and twenty-five physicians from the ICU participated in the structured interviews. Forty of them completed the online survey. Overall, ICU professionals expressed a positive outlook on Visual Patient Avatar ICU. They described Visual Patient Avatar ICU as a simple and intuitive tool that improved information retention and facilitated problem identification. However, a subset of participants expressed concerns about potential information overload and a sense of incompleteness due to missing exact numerical values. These findings provide valuable insights into user perceptions of Visual Patient Avatar ICU and encourage further technology development before clinical implementation.

Fundamental Physical Constants and Primary Physical Parameters

Every four years the Committee on Data for Science and Technology (CODATA) supplies a self-consistent set of values of the basic constants and conversion factors of physics recommended for international use. In 2013, the World-Universe Model (WUM) proposed a principally different depiction of the World as an alternative to the picture of the Big Bang Model. This article: 1) Gives the short history of Classical Physics before Special Relativity; 2) Calculates Fundamental Physical Constants based on experimentally measured Rydberg constant, Electrodynamic constant, Electron Charge-to-Mass Ratio, and Planck constant; 3) Discusses Electrodynamic constant and Speed of Light; 4) Considers Dimensionless Fundamental Parameters (Dirac Large Number Q and Dimensionless Rydberg Constant α); 5) Calculates Newtonian Constant of Gravitation based on the Inter-connectivity of Primary Physical Parameters; 6) Makes a detailed analysis of the Self-consistency of Fundamental Physical Constants and Primary Physical Parameters through the prism of WUM. The performed analysis suggests: 1) Discontinuing using the notion “Vacuum” and its characteristics (Speed of Light in Vacuum, Characteristic Impedance of Vacuum, Vacuum Magnetic Permeability, Vacuum Electric Permittivity); 2) Accepting the exact numerical values of Electrodynamic constant, Planck constant, Elementary charge, and Dimensionless Rydberg Constant α. WUM recommends the predicted value of Newtonian Constant of Gravitation in 2018 to be considered in CODATA Recommend Values of the Fundamental Physical Constants 2022.

Qualitative reasoning in a two-layered framework

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events.The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a unary belief modality B that connects the inner layer to the outer one where the reasoning is formalised by means of Gödel logic. We design their Hilbert-style axiomatisations and prove their completeness. In the second part, we discuss the paraconsistent generalisations of the logics for qualitative uncertainty that take into account the case of the available information being contradictory or inconclusive.

Newly observed exotic doubly charmed meson [formula omitted

In this work, we treat the newly observed doubly charmed four-quark state Tcc+ as an axial-vector tetraquark with content ccu‾d‾, and calculate its spectroscopic parameters and width. The mass and current coupling of the tetraquark Tcc+ are found by means of the QCD two-point sum rule method by taking into account quark, gluon and mixed condensates up to dimension 10. The width of the Tcc+ is evaluated using partial widths of decay processes Tcc+→T˜π0 and Tcc+→Tcc;u‾u‾0π+, where T˜=ccu‾d‾ and Tcc;u‾u‾0 are scalar tetraquarks. To compute the partial width of the first process, we apply the QCD three-point sum rule approach and exact numerical value of the strong coupling g that corresponds to the vertex Tcc+T˜π0. The width of the second decay is estimated using isospin symmetry and the prediction obtained for the first channel. Our results for the mass m=(3868±124)MeV and width Γ=(489±92)keV of the tetraquark Tcc+ are in a nice agreement with recent measurements of the LHCb collaboration.

New Product Design Using Chebyshev’s Inequality Based Interval-Valued Intuitionistic Z-Fuzzy QFD Method

In Quality function deployment (QFD) approach, customers tend to express their needs in linguistic terms rather than exact numerical values and these needs generally contain vague and imprecise information. To overcome this challenge and to use the method more effectively for complex customer-oriented design problems, this paper introduces a novel intuitionistic Z-fuzzy QFD method based on Chebyshev’s inequality (CI) and applies it for a new product design. CI provides the assignment of a more objective reliability function. The reliability value is based on the maximum probability obtained from CI. Then, the expected values of lower and upper bounds of interval-valued intuitionistic fuzzy (IVIF) numbers are determined. A competitive analysis among our firm and competitor firms and an integrative analysis for the different functions of QFD is presented. The proposed Z-fuzzy QFD method is applied to the design and development of a hand sanitizer for struggling with COVID-19.

EVALUATION OF RECONNECTION PARAMETERS FOR COLLISIONLESS DISPENSATION IN SOLAR CORONA

In the present paper, we have obtained an analytical solution for the thickness of current sheet in the dissipation region of the solar corona, reconnection time and reconnection rate for collisionless magnetic reconnection occuring in the solar corona. For our analysis we have used the length scale of the electron dissipation region based on field reversals. The reconnection electric field and component of the electron pressure tensor used in the Sweet-Parker model have been utilised to finally determine the exact numerical value of the thickness of current sheet, reconnection time and reconnection rate. It is shown that the thickness of the current sheet in the collisionless reconnection model is directly proportional to the electron mass and inversely proportional to the length scale of the electron dissipation region. Also, it is shown that the reconnection time is inversely proportional to the cube of the magnetic field and directly proportional to length scale, whereas reconnection rate is inversely proportional to the length scale of the electron dissipation region.

A Novel spherical fuzzy CRITIC method and its application to prioritization of supplier selection criteria

Linguistic terms are quite suitable to make evaluations in multiple criteria decision making problems since humans prefer them rather than sharp evaluations. When linguistic evaluations are used in the decision matrix instead of exact numerical values, fuzzy set theory can capture the vagueness in the linguistic evaluations. Ordinary fuzzy sets have been extended to many new types of fuzzy sets such as intuitionistic fuzzy sets, neutrosophic sets, spherical fuzzy sets and picture fuzzy sets. Spherical fuzzy sets are an extension of picture fuzzy sets whose squared sum of their parameters is at most equal to one. This paper develops a novel spherical fuzzy CRiteria Importance Through Intercriteria Correlation (CRITIC) method and applies it for prioritizing supplier selection criteria. Supplier selection is one of the most critical aspects of any organization since any mistake in this process may cause poor supplier performance and inefficiencies in the business processes. Supplier selection is a multi-criteria decision making problem involving several conflicting criteria and alternatives. A numerical illustration of the proposed method is also given for this problem.

Failure analysis of CNC machines due to human errors: An integrated IT2F-MCDM-based FMEA approach

Computer numerical control (CNC) machining has become one of the salient transformative technologies due to its ability to manufacture precise components, scalable production, constant uptime, uniformity and repeatability. Despite the claim of minimum human intervention during CNC machining operation, operators’ involvement leading to CNC machine failures cannot be totally neglected. In this paper, a modified failure modes and effects analysis (FMEA)-based risk analysis approach is presented to identify the major human errors, their causes and effects during CNC machining operation based on the participation of a team of cross-functional experts. An integrated interval type-2 fuzzy sets (IT2FSs)-based multi-criteria decision making (MCDM) framework is subsequently developed for prioritizing the risks associated with each identified human error with respect to four pertinent risk factors, i.e. safety, economic consequences, occurrence and detection. However, due to lack of exact numerical values, the errors are linguistically assessed by the experts. To deal with subjective uncertainties, IT2FSs are chosen as a viable alternative due to their numerous superiorities over the traditional type-1 fuzzy sets (T1FSs). The IT2F-analytic hierarchy process (IT2F-AHP) is adopted to calculate weights of the risk factors, and IT2F-decision making trial and evaluation laboratory (IT2F-DEMATEL) is employed to model the causal interactions among different errors. For risk ranking, the traditional measurement of alternatives and ranking according to compromise solution (MARCOS) method is extended in IT2F-domain (IT2F-MARCOS). Finally, the computed risk ranking results are contrasted with other popular IT2FSs and T1FSs-based MCDM methods to validate feasibility of the proposed approach. This integrated framework comprising IT2F-AHP, IT2F-DEMATEL and IT2F-MARCOS is novel with respect to its development as well as application context and would surely be an interesting tool helping the entire decision making community.

SI-2019 and prospects for improving the accuracy of electrical measurements

Increasing requirements for the accuracy of measurements have led to the need to revise the existing International System of Units (SI). The important element of the SI-2019 reform is “the establishment of the SI base units through seven defining constants, the numerical values of which are fixed”.
 The approach to the establishment of the measurement units has fundamentally changed. If earlier a definition was given of how the unit is realized, now only the exact numerical values of the fundamental constants are fixed, and their values are expressed in the corresponding SI units. Measurement units are determined on the basis of known physical laws, which include certain fundamental constants.
 The article analyzes the changes in SI-2019 related to electrical measurements, and also discusses the prospects for the development of accurate electrical measurements.

The mixed integer robust maximum expert consensus models for large-scale GDM under uncertainty circumstances

Consensus commonly improves the efficiency of subsequent implementation of the solution in large-scale group decision making (LSGDM). The maximum expert consensus model (MECM) is a significance decision method for consensus reaching processes. In the MECM, the unit adjustment cost of each decision maker and a consensus budget are assumed to be deterministic. Within real-world decision environment, however, it is scarcely possible to obtain an exact numerical value of them. To solve this problem, novel MECMs are constructed on the basis of robust optimization under uncertainty circumstances. Considering the uncertainty of costs, we propose three mixed integer robust maximum expert consensus models (MIR-MECMs) by introducing uncertain box, ellipsoid and polyhedron sets, respectively. Further, we take the aggregation operators into these proposed models. Additionally, to comprehensively analyze the impact of the uncertain parameters in MECM, we develop two models under indeterminacy of the costs and a consensus budget. Finally, an improved genetic algorithm is provided to solve the proposed models in large-scale GDM. Numerical example is used to demonstrate that the solution of the deterministic MECM is too optimistic and the solution of the proposed models are more robust under the uncertainty circumstances. A simulation analysis shows that the ordered weighed averaging (OWA) operator is more stable performance with parameters perturbation.

Discrete element modelling for wheel-soil interaction and the analysis of the effect of gravity

The discrete element method (DEM) is widely seen as one of the more accurate, albeit more computationally demanding approaches for terramechanics modelling. Part of its appeal is its explicit consideration of gravity in the formulation, making it easily applicable to the study of soil in reduced gravity environments. The parallel particles (P2) approach to terramechanics modelling is an alternate approach to traditional DEM that is computationally more efficient at the cost of some assumptions. Thus far, this method has mostly been applied to soil excavation maneuvers. The goal of this work is to implement and validate the P2 approach on a single wheel driving over soil in order to evaluate the applicability of the method to the study of wheel-soil interaction. In particular, the work studies how well the method captures the effect of gravity on wheel-soil behaviour. This was done by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency required for stable simulation behaviour and then tuning the physical simulation parameters to obtain physically accurate results. The former were tuned via the convergence of particle settling energy plots for various frequencies. The latter were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed with a martian soil simulant in a reduced gravity environment. Sensitivity of the simulation to model parameters was also analyzed. Simulations produced promising data when compared to experiments as far as predicting experimentally observable trends in drawbar pull and sinkage, but also showed limitations in predicting the exact numerical values of the measured forces.

Application of Fuzzy AHP on Determining the Dewatering Main Criteria Weights in Egypt

selecting an appropriate dewatering system is a key for successful completion of a project. The selection process depends mainly upon the subjective opinion of construction practitioners. Therefore, this experience has to be documented and stored in the company database for usage in future projects. However, such an evaluation involves a complex decision-making process associated with numerous uncertainty factors, imprecise information and judgments. The Analytical Hierarchy Process (AHP) has been widely applied to evaluate alternatives related to multiple decision criteria. Nevertheless, the AHP is incapable of dealing with the inherent subjectivity and ambiguity existing in the mapping of the decision-maker judgment to exact numerical values. This paper introduces an attempt to store the experts’ subjective experience using a fuzzy AHP approach in an attempt to determine the dewatering main criteria weights. The approach employs triangular fuzzy numbers and the α-cut concept to better represent the degrees of uncertainty held by the decision-maker.

The extention rank ordering criteria weighting methods in fuzzy enviroment

Weight elicitation is an important part of multi-criteria decision analysis. In real-life decision-making problems precise information is seldom available, and providing weights is often cognitively demanding as well as very time- and effort-consuming. The judgment of decision-makers (DMs) de-pends on their knowledge, skills, experience, personality, and available information. One of the weights determination approaches is ranking the criteria and converting the resulting ranking into numerical values. The best known and most widely used are rank sum, rank reciprocal and centroid weights techniques. The goal of this paper is to extend rank ordering criteria weighting methods for imprecise data, especially fuzzy data. Since human judgments, including preferences, are often vague and cannot be expressed by exact numerical values, the application of fuzzy concepts in elicitation weights is deemed relevant. The methods built on the ideas of rank order techniques take into account imprecise information about rank. The fuzzy rank sum, fuzzy rank reciprocal, and fuzzy centroid weights techniques are proposed. The weights obtained for each criterion are triangular fuzzy numbers. The proposed fuzzy rank ordering criteria weighting methods can be easily implemented into decision support systems. Numerical examples are provided to illustrate the practicality and validity of the proposed methods.

A novel spherical fuzzy QFD method and its application to the linear delta robot technology development

Extensions of ordinary fuzzy sets have been put forward one after the other in the literature. The latest extension is spherical fuzzy sets theory proposed by Kutlu Gündoğdu and Kahraman (2019a), which is based on three independent membership parameters defined on a unit sphere with a constraint related to their squared summation. This new extension presenting larger domains for each parameter is employed for production design in this paper. Quality Function Deployment (QFD) is a structured approach for defining customer needs or requirements, which translates them into the final product in order to satisfy these needs. Spherical fuzzy QFD (SF-QFD) under impreciness and vagueness involving linguistic evaluations rather than exact numerical values is proposed in this paper. The importance ratings and global weights of customer requirements (CR) and improvement directions of design requirements (DR) are successfully represented by using spherical fuzzy sets. Judgments of multi-customers/experts are aggregated by spherical fuzzy aggregation operators. A comparative analysis using SF-TOPSIS is applied for competitive firms. A linear delta robot technology design and evaluation is performed by the proposed SF-QFD and a competitive analysis is presented.

An extended TOPSIS method based on ordered fuzzy numbers for group decision making

Multiple criteria decision making methods have become very popular in recent years and are frequently applied in many real-life situations. One of the most commonly used is the Technique for Order Preference by Similarity to Ideal Solution. Its original version is based on the information provided by the decision maker as exact numerical values. However, in some real-life situations, the decision maker may not be able to precisely express the value of the ratings of alternatives with respect to criteria or else he/she uses linguistic expressions. In such situations he/she may use other data formats, such as: interval numbers, fuzzy numbers, ordered fuzzy numbers, hesitant fuzzy sets, intuitionistic fuzzy sets and other. On the other hand, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. The aim of this paper and its main contribution is to present a new approach for ranking of alternatives for group decision making using the Technique for Order Preference by Similarity to Ideal Solution method based on ordered fuzzy numbers. This is an alternative to methods that use different forms of averages for the aggregation of the individual matrices into a collective matrix. In the proposed approach aggregation is not needed and all individual decision information of decision makers is taken into account in determining the ranking of alternatives and the selecting the best one. The key stage of this method is the transformation of the decision matrices provided by the decision makers into matrices of alternatives. A matrix corresponding to an alternative is composed of its assessments with respect to all criteria, performed by all the decision makers. A numerical example illustrates the proposed approach.

Risk Assessment of Water Penetration for Shield Tunnel Construction in Coastal Area

In the process of assessing the risk of flooding during the construction of shield tunnel in coastal area, the basic probability of accidents is often difficult to be expressed by an exact numerical value due to the fact that the actual statistical data of accidents are too few or missing. In order to solve this problem, this paper, with the factors by combining the fuzzy Bayesian network inference advantages and the advantages of the fuzzy set theory to deal with fuzzy information, using a risk assessment method based on fuzzy Bayesian network method, established the waterfront subway shield tunnel construction risk decision model and predicted the subway shield tunnel flooded the area of probability; at the same time, the sensitivity of each basic event was calculated according to the fuzzy significance to identify the key risk factors, and the applicability and accuracy of this method were verified by combining with the regional engineering of Hujing station ∼ Wanshou station of Fuzhou Metro Line 6.

Fuzzy logic-based moving obstacle avoidance method

In this study, a fuzzy logic-based collision avoidance method is studied. Mobile robots operating in a dynamic environment may encounter moving obstacles. The distance from the obstacles to the robot is provided as a control input. The change of distance is provided as the secondary input. The output speed value is expressed as ‘stop’, ‘very slow’, ‘slow’, ‘medium’ and ‘fast’, respectively. Each of these expressions has an exact numerical value, but it depends on the inputs and the rule base, and therefore the numerical values belong to the variable ratios. The input parameters do not have an exact value and they are assigned to different numerical ranges at different ratios. The input membership functions defined in this study are defined as triangular functions. The defuzzification process of the output parameter is performed by the weighted average method. Keywords: fuzzy; logic-based; mobile; avoidance method

COMPARISON OF MATHEMATICAL MODELS FOR THE USE OF ENROFLOXACIN IN DOGS

This article analyzes the process of changing the concentration of enrofloxacin in blood plasma in dogs after a single intravenous injection of the substance. Three mathematical models are proposed - algebraic and two models, based on a differential equation of first and second order. Identification of their parameters has been performed. Based on Akaike information criterion corrected as the best model was chosen the represented by a second-order differential equation. Three equations are identified and the exact numerical values of their parameters are obtained. For the evaluation and comparison of the three models, Akaike information criterion was used. The best results showed the second-order differential model. It will be used in future developments.