Novelty of Different Distance Approach for Multi-Criteria Decision-Making Challenges Using q-Rung Vague Sets

In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

Effect of long reaction distance on gas composition from organic-rich shale pyrolysis under high-temperature steam environment

When high-temperature steam is used as a medium to pyrolyze organic-rich shale,water steam not only acts as heat transfer but also participates in the chemical reaction of organic matter pyrolysis,thus affecting the generation law and release characteristics of gas products.In this study,based on a long-distance reaction system of organic-rich shale pyrolysis via steam injection,the effects of steam temperature and reaction distance on gas product composition are analyzed in depth and compared with other pyrolysis processes.The advantages of organic-rich shale pyrolysis via steam injection are then evaluated.The volume concentration of hydrogen in the gas product obtained via the steam injection pyrolysis of organic-rich shale is the highest,which is more than 60%.The hydrogen content increases as the reaction distance is extended;however,the rate of increase changes gradually.Increasing the reaction distance from 800 to 4000 mm increases the hydrogen content from 34.91%to 69.68%and from 63.13%to 78.61%when the steam temperature is 500℃ and 555℃,respectively.However,the higher the heat injection temperature,the smaller the reaction distance required to form a high concentration hydrogen pyrolysis environment(hydrogen concentration>60%).When the steam pyrolysis temperature is increased from 500℃ to 555℃,the reaction distance required to form a high concentration of hydrogen is reduced from 3800 to 800 mm.Compared with the direct retorting process,the volume concentration of hydrogen obtained from high-temperature steam pyrolysis of organic-rich shale is 8.82 and 10.72 times that of the commonly used Fushun and Kivite furnaces,respectively.The pyrolysis of organic-rich shale via steam injection is a pyrolysis process in a hydrogen-rich environment.

Responses of soil stoichiometry and soil enzyme activities in the different distance around opencast coal mine of the Hulun Buir Grassland of China

The objectives of this study were to explore the changes in soil stoichiometry and enzyme activities at different distances from an opencast coal mine in the Hulun Buir Grassland of China. Four transects were established on north and east sides of the opencast coal mining area, and samples were collected at 50 m, 550 m, and 1550 m from the pit on each transect. Control samples were collected from a grassland station 8 km from the opencast coal mining area that was not disturbed by mining. Four replicate soil samples were collected at each point on the four transects. Soil physicochemical properties and enzyme activities were determined, and correlations between soil properties and stoichiometric ratios and enzyme activities were explored using redundancy analysis. The increase in distance from mining did not significantly affect soil properties, although soil urease activity was significantly lower than that of the control area. Soil properties 1550 m from the mine pit were similar to those at the grassland control. In addition, soil total nitrogen had the greatest effect on soil stoichiometry, and soil total potassium had the greatest effect on soil enzyme activities. Coal dust from opencast mining might be the main factor affecting soil stoichiometry and enzyme activities. The results of this study provide direction for the next step in studying the influence of mining areas on soil properties and processes.

Leading directions and effective distance of larch offspring dispersal at the upper treeline in the Northern and Polar Urals, Russia

Climate has changed sufficiently over the last 150 years and forced out upper treeline advance at the most studied sites around the world.The rate of advance has been extremely variable–from tens to hundreds meters in altitude.This is because the degree at which tree frontal populations respond to climate change depends on the complex interaction of biological and physical factors.The resulting stand pattern is the consequence of the interaction between dispersal and survival functions.A few publications have addressed the question of how this pattern is generated.In order to understand how the spatial structure of tree stands was formed at the upper limit of their distribution in the Ural Mountains,we assessed the distance and direction of dispersal of offspring from maternal individuals.We found that in frontal Larix sibirica Ledeb.populations,‘effective’dispersal of offspring ranges from 3 to 758 m(with a median of 20–33 m in open forest and 219 m in single-tree tundra in the Polar Urals and 107 m in open forest in the Northern Urals).We revealed that most of the offspring effectively dispersed not only in the direction of the prevailing winds,but also in the opposite direction up the slope,and the distance can reach 500–760 m.The data obtained can be used to develop an individual-based model which is capable of simulating in detail the dynamics of tree stands at the upper limit of their growth and reliably predicting the future position and pattern of treeline ecotone as growth conditions continue to improve in the face of observed climate change.

Extended Lorenz majorization and frequencies of distances in an undirected network

Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

Source localization in signed networks with effective distance

While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization in signed network models.Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance,we propose an optimization method for observer selection.Additionally,by using the reverse propagation algorithm we present a method for information source localization in signed networks.Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization,and the higher the ratio of propagation rates between positive and negative edges,the more accurate the source localization becomes.Interestingly,this aligns with our observation that,in reality,the number of friends tends to be greater than the number of adversaries,and the likelihood of information propagation among friends is often higher than among adversaries.In addition,the source located at the periphery of the network is not easy to identify.Furthermore,our proposed observer selection method based on effective distance achieves higher operational efficiency and exhibits higher accuracy in information source localization,compared with three strategies for observer selection based on the classical full-order neighbor coverage.

Robust free-space optical frequency transfer in time-varying link distances conditions

Future inter-satellite clock comparison on high orbit will require optical time and frequency transmission technology between moving objects.Here,we demonstrate robust optical frequency transmission under the condition of variable link distance.This variable link is accomplished by the relative motion of a single telescope fixed on the experimental platform to a corner-cube reflector(CCR)installed on a sliding guide.Two acousto–optic modulators with different frequencies are used to separate forward signal from backward signal.With active phase noise suppression,when the CCR moves back and forth at a constant velocity of 20 cm/s and an acceleration of 20 cm/s^(2),we achieve the best frequency stability of 1.9×10^(-16) at 1 s and 7.9×10^(-19) at 1000 s indoors.This work paves the way for future studying optical frequency transfer between ultra-high-orbit satellites.

Numerical Analysis of the Influence of the Impinging Distance on the Scouring Efficiency of Submerged Jets

Water jet technology is widely used in submerged buried pipes as a non-traditional trenching process,often invol-ving a complex sediment response.An important adjustable and influential engineering variable in this technol-ogy is represented by the impinging distance.In this study,the FLOW-3D software was used to simulate the jet scouring of sand beds in a submerged environment.In particular,four sets of experimental conditions were con-sidered to discern the relationship between the maximum scour depth and mass and the impinging distance.As shown by the results,a critical impinging distance h0 exists by which the static scour depth can be maximized;the scour mass ratio between dynamic and static conditions decreases as the impinging distance increases.Moreover,the profile contours are similar when the erosion parameter Ec is in the range 0.35<Ec<2.Empirical equations applicable for predicting the jet trenching contour under both dynamic and static scour modes are also provided in this study.

The Effect of Lateral Offset Distance on the Aerodynamics and Fuel Economy of Vehicle Queues

The vehicle industry is always in search of breakthrough energy-saving and emission-reduction technologies.In recent years,vehicle intelligence has progressed considerably,and researchers are currently trying to take advantage of these developments.Here we consider the case of many vehicles forming a queue,i.e.,vehicles traveling at a predetermined speed and distance apart.While the majority of existing studies on this subject have focused on the influence of the longitudinal vehicle spacing,vehicle speed,and the number of vehicles on aerodynamic drag and fuel economy,this study considers the lateral offset distance of the vehicle queue.The group fuel consumption savings rate is calculated and analyzed.As also demonstrated by experimental results,some aerodynamic benefits exist.Moreover,the fuel consumption saving rate of the vehicle queue decreases as the lateral offset distance increases.

Efficient ECG classification based on Chi-square distance for arrhythmia detection

This study introduces a new classifier tailored to address the limitations inherent in conventional classifiers such as K-nearest neighbor(KNN),random forest(RF),decision tree(DT),and support vector machine(SVM)for arrhythmia detection.The proposed classifier leverages the Chi-square distance as a primary metric,providing a specialized and original approach for precise arrhythmia detection.To optimize feature selection and refine the classifier’s performance,particle swarm optimization(PSO)is integrated with the Chi-square distance as a fitness function.This synergistic integration enhances the classifier’s capabilities,resulting in a substantial improvement in accuracy for arrhythmia detection.Experimental results demonstrate the efficacy of the proposed method,achieving a noteworthy accuracy rate of 98% with PSO,higher than 89% achieved without any previous optimization.The classifier outperforms machine learning(ML)and deep learning(DL)techniques,underscoring its reliability and superiority in the realm of arrhythmia classification.The promising results render it an effective method to support both academic and medical communities,offering an advanced and precise solution for arrhythmia detection in electrocardiogram(ECG)data.

Essential proteins identification method based on four-order distances and subcellular localization information

Essential proteins are inseparable in cell growth and survival. The study of essential proteins is important for understanding cellular functions and biological mechanisms. Therefore, various computable methods have been proposed to identify essential proteins. Unfortunately, most methods based on network topology only consider the interactions between a protein and its neighboring proteins, and not the interactions with its higher-order distance proteins. In this paper, we propose the DSEP algorithm in which we integrated network topology properties and subcellular localization information in protein–protein interaction(PPI) networks based on four-order distances, and then used random walks to identify the essential proteins. We also propose a method to calculate the finite-order distance of the network, which can greatly reduce the time complexity of our algorithm. We conducted a comprehensive comparison of the DSEP algorithm with 11 existing classical algorithms to identify essential proteins with multiple evaluation methods. The results show that DSEP is superior to these 11 methods.

Reciprocal Distance Laplacian Eigenvalue Distribution Based on Graph Parameters

Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.

Relationship between Inter Canine Width and Inter Alar Width, Inter Commissural Width, and Inter Canthal Distance: A Pilot Study

The aim of this study was to determine the relationship between inter canine width (ICW) and inter alar width (IAW), inter commissural width (ICoW), and inter canthal distance (ICaD) in Bantu population. Materials and Methods: It was a pilot study included all participants who were aged at least 18 years, without a history of orthodontics treatment from Prosthodontics Department, Faculty of Dental Medicine, University of Kinshasa. The Ethics committee of the National Center of Research for Dental Sciences in DR Congo approved the study protocol (CNRSB 1504.218). The participants medical records were obtained from the interview and dental examination. Nature of the study was explained with participant information sheet, and an informed consent of all participants was obtained. The inclusion criteria were no missing maxillary and mandibular teeth, no diastema, and no anterior restorations, 18 years old before enrollment in the study. The exclusion criteria were inability to meet the above requirements, pregnancy, and refusal to participate in the study. The inter-canine width (ICW), inter alar width (IAW), inter canthal distance (ICaD) and inter-commissural width (ICoW) of each participant were measured with a digital Vernier caliper (Mitutoyo, UK Ltd.,) (0.01 mm) three times and the average value was recorded. The inter canthal distance (ICaD) was measured without applying pressure by bringing the recording parts of the caliper just in contact with the medial angle. The inter alar width (IAW) was marked with a fine marked pencil on the widest outer surface of the alae of the nose on either side or width. Those two points were measured without applying pressure by bringing the recording parts of the caliper just in contact with the outer surface. The participant was told to stop breathing shortly to avoid any change in shape of the nose. The inter-commissural width (ICoW) was determined by measuring the maxillary lip vermilion from commissure to commissure without the application of pressure on the tissue in the relaxed state. The inter-canine width (ICW) was measured indirectly using a dental floss. A dental floss was marked on one end prior to placement in the mouth. Using that point as reference, the dental floss was circumference along the curvature of the anterior dentition such that it passed along the contact point of all the teeth. The distal end of the canine teeth on both sides was then marked on the floss while it was stretched in the patients mouth. Floss was marked on both sides with the marker pencil. The distance between the two proximal contact points was measured and recorded. Data, analysis and validation were performed by the SPSS software (version 22.0, IBM SPSS Statistics, Chicago, IL, USA). Unpaired t-test was used, of Kolmogorov-Smirnov test. Analysis of variance (ANOVA) test was used to test for comparability between socio-demographic characteristics dental measurements. Pearsons correlation coefficients test was calculated to determine the relationship between facial and dental parameters. Significance was set at P 0.01. Results: Of 314 participants enrolled, 202 were included. The age ranged from 18 to 68 years, with a mean age of 40.62 12.99 years. Although the Pearsons correlation coefficients were negative. Ninety-three participants (46%) were men and one hundred and nine (54%) were women. The overall mean age was 40.62 12.99 years. Facial and dental measurements were greater in women than men with significant differences for ICW (p = 0.04). However, no significant difference was seen between men and women for IAW, ICaD and ICoW (p = 0.44, p = 0.23, p = 0.31 respectively). The correlation including Pearsons correlation coefficient and P-values for all participants is not demonstrated. Conclusion: Within the limitations of this study, the results suggest that IAW, ICaD and ICoW cannot be used as a preliminary method for determining the width of the maxillary for anterior teeth for edentulous patients.

Analysis for Effects of Temperature Rise of PV Modules upon Driving Distance of Vehicle Integrated Photovoltaic Electric Vehicles

The development of vehicle integrated photovoltaics-powered electric vehicles (VIPV-EV) significantly reduces CO2 emissions from the transport sector to realize a decarbonized society. Although long-distance driving of VIPV-EV without electricity charging is expected in sunny regions, driving distance of VIPV-EV is affected by climate conditions such as solar irradiation and temperature rise of PV modules. In this paper, detailed analytical results for effects of climate conditions such as solar irradiation and temperature rise of PV modules upon driving distance of the VIPV-EV were presented by using test data for Toyota Prius and Nissan Van demonstration cars installed with high-efficiency InGaP/GaAs/InGaAs 3-junction solar cell modules with a module efficiency of more than 30%. The temperature rise of some PV modules studied in this study was shown to be expressed by some coefficients related to solar irradiation, wind speed and radiative cooling. The potential of VIPV-EV to be deployed in 10 major cities was also analyzed. Although sunshine cities such as Phoenix show the high reduction ratio of driving range with 17% due to temperature rise of VIPV modules, populous cities such as Tokyo show low reduction ratio of 9%. It was also shown in this paper that the difference between the driving distance of VIPV-EV driving in the morning and the afternoon is due to PV modules’ radiative cooling. In addition, the importance of heat dissipation of PV modules and the development of high-efficiency PV modules with better temperature coefficients was suggested in order to expand driving range of VIPV-EV. The effects of air-conditioner usage and partial shading in addition to the effects of temperature rise of VIPV modules were suggested as the other power losses of VIPV-EV.

Interrelationships between Length of the Day, Moon Distance, Phanerozoic Geodynamic Cycles, Tidal Dissipation and Earth’s Core: Review and Analysis

The rotation of the Earth and the related length of the day (LOD) are predominantly affected by tidal dissipation through the Moon and the growth of the Earth’s core. Due to the increased concentration of mass around the rotation axis of the spinning Earth during the growth of the core the rotation should have been accelerated. Controversially the tidal dissipation by the Moon, which is mainly dependent on the availability of open shallow seas and the kind of Moon escape from a nearby position, acts towards a deceleration of the rotating Earth. Measurements of LOD for Phanerozoic and Precambrian times open ways to solve questions concerning the geodynamical history of the Earth. These measurements encompass investigations of growth patterns in fossils and depositional patterns in sediments (Cyclostratigraphy, Tidalites, Stromatolites, Rhythmites). These patterns contain information on the LOD and on the changing distance between Earth and Moon and can be used as well for a discussion about the growth of the Earth’s core. By updating an older paper with its simple approach as well as incorporating newly published results provided by the geoscientific community, a moderate to fast growth of the core in a hot early Earth will be favored controversially to the assumption of a delayed development of the core in an originally cold Earth. Core development with acceleration of Earth’s rotation and the contemporaneous slowing down due to tidal dissipation during the filling of the ocean may significantly interrelate.

Study on Fatigue Life Prediction of TC4-DT Structural Simulants by Using Critical Distance Theory

In the actual engineering of the structure, mechanical notch is inevitable, which will significantly reduce the fatigue life of the structure. In order to ensure the application of notch structures in engineering, the accurate evaluation of the impact of notch on fatigue life has become the basis of fatigue reliability design of structures. To investigate the influence of the concave structure on the overall fatigue life in practical engineering, three different sizes of V-notch parts and concave structure simulation parts were designed, and the life prediction was carried out by using the critical distance method. The results show that the stress gradient of the concave structure with the same stress concentration coefficient is much greater than that of the V-notch structure. Considering the notch effect, the S-T model in the critical distance method is modified by the stress concentration coefficient and stress gradient, and it is found that the life prediction accuracy reaches the ideal.

UOUU:User-Object Distance and User-User Distance Combined Method for Collaboration Task

Augmented reality superimposes digital information onto objects in the physical world and enables multi-user collaboration.Despite that previous proxemic interaction research has explored many applications of user-object distance and user-user distance in an augmented reality context,respectively,and combining both types of distance can improve the efficiency of users’perception and interaction with task objects and collaborators by providing userswith insight into spatial relations of user-task object and user-user,less is concerned about howthe two types of distances can be simultaneously adopted to assist collaboration tasks acrossmulti-users.To fulfill the gap,we present UOUU,the user-object distance and user-user distance combined method for dynamically assigning tasks across users.We conducted empirical studies to investigate how the method affected user collaboration tasks in terms of collaboration occurrence and overall task efficiency.The results show that the method significantly improves the speed and accuracy of the collaboration tasks as well as the frequencies of collaboration occurrences.The study also confirms the method’s effects on stimulating collaboration activities,as the UOUU method has effectively reduced the participants’perceived workload and the overall moving distances during the tasks.Implications for generalising the use of the method are discussed.

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.

CONSTANT DISTANCE BOUNDARIES OF THE t-QUASICIRCLE AND THE KOCH SNOWFLAKE CURVE

LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.