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In this paper, the graphical method for solving linear programming is extended in fuzzy environment. Here, we dealt with the fully fuzzy linear programming (FFLP) which involves fuzzy constraints and fuzzy objective. Determining and visualizing the fuzzy feasible space in the geometrical space is one of the novel contributions of this study. Defining fuzzy constraints as fuzzy lines and finding the nature of the point of intersection between fuzzy lines are also studied. The fuzzy constraints divide the geometrical into fuzzy half planes. Intersection of such fuzzy half planes yields a fuzzy convex hull. The optimal solution of fuzzy linear programming problem is obtained at an extreme point of this fuzzy convex hull. The results obtained from the proposed method are compared with existing methodologies. [ABSTRACT FROM AUTHOR]

A Mueller matrix covers all the polarization information of the measured sample, however the combination of its 16 elements is sometimes not intuitive enough to describe and identify the key characteristics of polarization changes. Within the Poincaré sphere system, this study achieves a spatial representation of the Mueller matrix: the Global-Polarization Stokes Ellipsoid (GPSE). With the help of Monte Carlo simulations combined with anisotropic tissue models, three basic characteristic parameters of GPSE are proposed and explained, where the V parameter represents polarization maintenance ability, and the E and D† parameters represent the degree of anisotropy. Furthermore, based on GPSE system, a dynamic analysis of skeletal muscle dehydration process demonstrates the monitoring effect of GPSE from an application perspective, while confirming its robustness and accuracy. [ABSTRACT FROM AUTHOR]

We propose a graphical method for classifying phases in gas chromatography using a selectivity map, which is a two-dimensional diagram on the polarity–hydrophilicity coordinates, based on the theoretical description of the selectivity of liquid phases by three-parameter characteristics. The three-parameter characteristic method uses an expression of the intermolecular interaction energy in terms of the contributions of nonpolar, polar, and hydrogen bonds in an asymptotic approximation obtained using the theory of generalized charges and a new quantum-mechanical concept of the energy and probability of hydrogen bond formation. An advantage of the method is that the parameters used in the mathematical expressions have physical meaning, are portable, and can be found without experimentation. Relationships between the characteristics of stationary phases and their structure are revealed. The selectivity map as a classification method enables gas chromatographic liquid stationary phases to be considered in the range from low polarity/low hydrophilic to high polarity/high hydrophilic phases. On the other hand, applying the principle of the similarity of properties in combination with the selectivity map ensures the selection of the most selective phase for the given analytes. This selection can be made a priori, without experimentation. An example is given of choosing a selective stationary phase for separating substances with similar properties using a selectivity map. [ABSTRACT FROM AUTHOR]

Reinforced concrete beams lose resistance at high temperatures and so as to guarantee their good performance, it is mandatory to consider this accidental action in design. As an alternative to the methods proposed by the European and Brazilian standards, above all the tabular method that, despite its simple application, limits calculations to a few pre-defined values, a new tool for fire design of these beams is proposed herein. A graphical method was developed with the Temperature Calculation and Design (TCD) software, which performs transient bi-dimensional thermo-structural analysis using the finite element method. The main variable of this method consists of the resistance to the bending moment of a heated cross-section. For its validation, the moment of four rectangular sections was determined according to four simplified methods. These results were compared among themselves and to those obtained by a more advanced method. They were all verified to lead to similar results. With regard to the TCD, whose results were used for the preparation of the graphical method, the maximum difference compared to a more advanced method was approximately 2.5%. After validation, graphs that associate the ratio between the applied moment in fire and the resistance to bending moment at ambient temperature to the fire resistance for different beams were created. These graphs present design solutions for more than 2300 beam models with T-shaped cross-sections in assorted lengths, heights, covers and reinforcement arrangements, both positive and negative. In the application examples, the results from the graphical method were generally more economic when compared to the tabular method of the fire design standards. [ABSTRACT FROM AUTHOR]

In the automotive engineering community, the modified maximum force criterion proposed by Hora and co-workers is considered acceptable for theoretically estimating the forming limit curve (FLC) of sheet metals. Based on this criterion, a graphical method is proposed to simplify evaluation of the FLC. This paper investigates the proposed graphical method in a special case by using a power-hardening law and the Mises yield function, which leads to an explicit expression of the critical strains according the strain paths. The FLC of a DP590 sheet estimated using the proposed method is compared with that estimated using existing analytical methods. The proposed method provides the best prediction of the FLC of the tested material. For verification, the calculated FLC is then adopted into the finite-element method to predict the punch stroke at fracture of several notched specimens subjected to Nakazima tests. The good agreement between the predicted and experimentally determined values of the punch strokes verifies the ability and potential of the proposed method in industrial engineering. [ABSTRACT FROM AUTHOR]

This paper introduces a more streamlined and convenient graphical approach to investigate the stability of fractional-order dynamical systems comprehensively. In particular, we focus on the utilization of Kharitonov theorem, renowned for robust stability analysis of incommensurate fractional-order systems in the presence of uncertainty. A novel graphical framework is illustrated, promising to streamline the stability analysis of such systems, which leads to reducing the computational burden. Using the proposed method, we can achieve the least possible Kharitonov polynomials among the existing methods to analyze the robust stability of the incommensurate fractional-order systems. To validate our approach, we perform numerical simulations on four illustrative examples, demonstrating its effectiveness. Simulation results underscore the real-world utility of our methodology, emphasizing its potential significance in fractional-order system analysis. [ABSTRACT FROM AUTHOR]

It is known that the one-dimensional (1D) compression behavior is commonly represented by the e-logp' curve, which is obtained from the oedometer test. Five numbers of mathematical models were adopted to best fit the experimental data from the consolidation test. It is observed that Fredlund and Xing (1994)'s (FX) model, which is commonly used for the representation of the soil–water characteristic curve (SWCC), gives the best performance in best fitting the experimental data of e-logp' curves. Subsequently, the graphical method is adopted to determine the pre-consolidation pressure (Pc) by adopting FX model. Consequently, the equations are proposed for the determination of the Pc of the soil from the fitting parameters in FX model. The proposed method provides an alternative method for the determination of the Pc. [ABSTRACT FROM AUTHOR]

Issues are examined in the calculation of the secondary currents of an arc in the implementation of single-phase auto-reclosing (SPAR) for elimination of unstable single-phase faults of 500 and 750-kV ultra-high-voltage lines. Dependences are shown for the backfeed arc extinguishment time, and the SPAR currentless pause recommended in the references, on the amplitude of the forced component of the secondary arc current. A graphical method is proposed for the calculation of secondary arc currents in ultra-high-voltage lines under the condition of SPAR currentless pause. The adequacy of the modeling of a backfeed arc was confirmed by a comparison of the calculated and experimental data from a 750-kV 525-km line. Examples are presented of the application of the graphical method proposed in this article for calculation of secondary backfeed arc currents in 500 kV lines of various length. The features of the implementation of SPAR in 300 and 1000 km lines are noted, and in particular, the effect of zero-power reactors connected to the neutral of the shunt reactors. An example of the implementation of SPAR using automatic phase shunting (APS) in a 500 km line is also examined. [ABSTRACT FROM AUTHOR]

This paper presents a new and computationally efficient load-flow algorithm for ac distribution systems using graphical search technique along with matrix algebra. The proposed algorithm is equally applicable to balanced, unbalanced and meshed distribution systems. In contrast with traditional load-flow methods, the developed technique does not require any LU decomposition or bus admittance matrix. The significant feature of the algorithm lies in the formulation of path impedance matrix and loads beyond branch matrix; once formulated, it will remain unaltered for the entire operation. The reconfiguration of these matrices takes place automatically in accordance with the change in input data. Moreover, by storing all the system data in array/matrix form it hoards enormous computer memory. Because of the aforementioned reasons, the developed technique is computationally potent when applied on large-sized distribution systems. The efficacy of the proposed methodology is tested on various standard test systems. It is evident from the test results that the proposed algorithm is robust and time efficient for any size of distribution network when compared with several other existing load-flow methods. [ABSTRACT FROM AUTHOR]

The optimal dimensional relations in machining the cap of the rotary mechanism in an Acros 585 combine may be calculated by a graphical method. That clearly shows the dimensional chains and their relationships; permits formalized calculation of the dimensions, margins, and tolerances; and permits selection of appropriate basing and coordination options. In addition, the best sequence of surface machining may be identified, and the optimal technological process may be established. [ABSTRACT FROM AUTHOR]

Proposed was a graphical method to solve decomposable problems of combinatorial optimization with the of use the Bellman optimality principle. In distinction to the dynamic programming algorithms based on the same principle, the graphical algorithm considers all possible system states by groups and not separately. This becomes possible if one takes into account the analytical form of the objective function, that is, handles the function 'graph' and transforms it analytically at each stage. The graphical method enables one to reduce running time of solution of some problems and construct efficient approximation schemes. The results of numerical experiments corroborate efficiency of the of the graphical method. [ABSTRACT FROM AUTHOR]

The detection of community structures within network data is a type of graph analysis with increasing interest across a broad range of disciplines. In a network, communities represent clusters of nodes that exhibit strong intra-connections or relationships among nodes in the cluster. Current methodology for community detection often involves an algorithmic approach, and commonly partitions a graph into node clusters in an iterative manner before some stopping criterion is met. Other statistical approaches for community detection often require model choices and prior selection in Bayesian analyses, which are difficult without some amount of data inspection and pre-processing. Because communities are often fuzzily-defined human concepts, an alternative approach is to leverage human vision to identify communities. The work presents a tool for community detection in form of a web application, called gravicom, which facilitates the detection of community structures through visualization and direct user interaction. In the process of detecting communities, the gravicom application can serve as a standalone tool or as a step to potentially initialize (and/or post-process) another community detection algorithm. In this paper we discuss the design of gravicom and demonstrate its use for community detection with several network data sets. An 'Appendix' describes details in the technical formulation of this web application built on the R package Shiny and the JavaScript library D3. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method based on the surfaces enveloping theory developed as a vertical application in the CATIA graphical design environment. This method is created for profiling tools intended to generate cylindrical helical surfaces with constant pitch. The devised method is applicable for the profiling of disc tools which are bounded by a primary peripheral surface of revolution. A few examples for the determination of the tool's 3D primary peripheral surface are presented such as helical flutes of cutting tools, worms with wide pitches, and gear involute flanks. The results are presented in both graphical and tabular form for completeness. Screen snapshots of the CATIA-based vertical application are also shown. [ABSTRACT FROM AUTHOR]

This paper attempts to expand the graphical analysis concept proposed by Chen and Abousleiman (Géotechnique, 2022. https://doi.org/10.1680/jgeot.21.00172) to deduce the undrained expansion solution of a cylindrical cavity in shear strain-hardening Drucker–Prager frictional soil. Based on the geometrical representation of the stress state/path and strain increments in the deviatoric planes, it is shown that the deviatoric stress-Lode angle stress path can be desirably determined by solving a first-order differential equation for the stress ratio (deviatoric stress over mean effective stress) in term of the Lode angle. The essential cavity expansion curve may also be readily constructed by calculating the internal cavity pressure and the corresponding expanded cavity radius, respectively, through simple numerical integrations with respect to the same variable of stress ratio. In particular, the ultimate cavity pressure can be easily evaluated by directly integrating the expression for cavity pressure with the stress ratio up to its limiting value. Some numerical results obtained from the proposed graphical method are presented to illustrate the impacts on the cavity responses of the earth pressure coefficient at rest, K 0 , and the key plasticity hardening parameters, which have also been compared with alternative solutions that require dealing with a system of coupled differential equations involving three principal effective stress components. [ABSTRACT FROM AUTHOR]

This paper approaches the issue of profiling gear hob bounded by a cylindrical helical surface with constant pitch, reciprocally enveloping with an ordered surfaces curl. The process kinematics of generation reproduces the 3D gear between the worm and the wheel. This gear has crossing axes and it is used for the profiling of the primary peripheral surface of the gear hub in the intermediary surface method (the common rack-gear of the surfaces curl to be generated and the primary peripheral surface of the gear hob). An algorithm in the CATIA design environment is presented, based onto an original method for the determination of the reference rack-gear form—the rack-gear reciprocally enveloping with the surfaces curl, using the principle of the cylindrical helical motion decomposition in translation and rotation motions. Graphical and analytical profiling examples are presented for the gear hob for generation of a parallel spline shaft and for the generation of a toothed wheel with involute teeth. Solutions for the interference problems, problems due to the singular points onto the profiles, are presented. [ABSTRACT FROM AUTHOR]

The article reports a graphical method of dating chicks using bivariate body measurements. It obtains fiducial limits for dates by evaluating whether pairs of measurements fall within confidence ellipses in the predicted morphologcial spaces of chicks of given ages. It concludes that the precision of date estimates obtained using wing lengths alone were similar to those using both body measures.

Abstract  This article presents a graphical method to calculate reflection corrections for radiation thermometry. The method is based on the observation that the measured radiance of a target is a linear combination of radiances dependent on the emissivity of the target. The method is most easily implemented as a nomogram, enabling thermometer users to estimate reflection corrections immediately when measurements are taken. The nomogram also provides a visual means of explaining the impact of reflection errors on measurements and for explaining the impact of measurement uncertainties on temperature measurements corrected for reflections. [ABSTRACT FROM AUTHOR]

Comparing the differences in outcomes (that is, in "dependent variables") between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to "independent variables." The independent variables are generally known as "scores," as in propensity scores for matching or as in the probabilities predicted by statistical or machine-learned models, for example. If the outcomes are discrete, then some averaging is necessary to reduce the noise arising from the outcomes varying randomly over those discrete values in the observed data. The traditional method of averaging is to bin the data according to the scores and plot the average outcome in each bin against the average score in the bin. However, such binning can be rather arbitrary and yet greatly impacts the interpretation of displayed deviation between the subpopulations and assessment of its statistical significance. Fortunately, such binning is entirely unnecessary in plots of cumulative differences and in the associated scalar summary metrics that are analogous to the workhorse statistics of comparing probability distributions—those due to Kolmogorov and Smirnov and their refinements due to Kuiper. The present paper develops such cumulative methods for the common case in which no score of any member of the subpopulations being compared is exactly equal to the score of any other member of either subpopulation. [ABSTRACT FROM AUTHOR]

The problem of describing the behavior of a highly filled polymeric material under compression, which was preceded by preliminary compression and unloading, is considered. The peculiarity of the compression diagrams obtained in the experiment is the downward convexity of the curves of the stress modulus versus time. To solve this problem, a variant of the non-linear endochronic theory of aging viscoelastic materials with several aging and viscosity functions and a numerical-graphical method for identifying the properties of viscoelasticmaterials proposed by the authors earlier, suggesting comparison of the deformation diagrams of intact samples and those that received preliminary damage, are used. [ABSTRACT FROM AUTHOR]

Continuous variable dichotomization is a popular technique used in the estimation of the effect of risk factors on health outcomes in multivariate regression settings. Researchers follow this practice in order to simplify data analysis, which it unquestionably does. However thresholds used to dichotomize those variables are usually ad-hoc, based on expert opinions, or mean, median or quantile splits and can add bias to the effect of the risk factors on specific outcomes and underestimate such effect. In this paper, we suggest the use of a semi-parametric method and visualization for improvement of the threshold selection in variable dichotomization while accounting for mixture distributions in the outcome of interest and adjusting for covariates. For clinicians, these empirically based thresholds of risk factors, if they exist, could be informative in terms of the highest or lowest point of a risk factor beyond which no additional impact on the outcome should be expected. [ABSTRACT FROM AUTHOR]

Modification of native ecosystems through land use can affect the biophysical functioning of agroecosystems, with spatial arrangement (configuration) through time often determining the degree to which landscapes experience dysfunctional states. An improved understanding is needed of how spatial and temporal patterns in land use affect ecohydrological dysfunctions, such as how landscapes leak or fail to retain water and soil, at scales relevant to farm management. We develop and apply a Graphical LAndscape Map Survey method, or ‘GLAMS’, for measuring changes in landscape function based upon a 3D graphic of a hypothetical sub-catchment. GLAMS was applied within four Landcare Groups comprised of farmers from the Western Catchments of Southeast Queensland, Australia. The aim was to capture the behaviors of farmers who manage land use under natural variations in precipitation, especially extended dry periods, and with the associated risks from ecohydrologically dysfunctional or ‘leaky’ landscapes. GLAMS provided variable spatial and temporal resolution which allowed quantification of the land use responses for three different property sizes: (1) small, less than 100 ha; (2) medium, 100–500 ha; and (3) large, larger than 500 ha. Responses were quantified using Bayesian Belief Networks to provide probability estimates of the likelihood of a given action, taking place within a particular part of the landscape, considering both climatic and ecohydrological risks. The findings indicated that GLAMS was more intuitive to farmers than traditional question-based surveys, resulting in a low cost technique that is rapid to implement while providing spatially explicit information relevant to farm and catchment management. [ABSTRACT FROM AUTHOR]

introduces a method of aggregating intra-subject behavioral data strings into behavior-specific domains that, when pooled across subjects, can quantify complex interoorganism processes. Representation of the aggregation by a coordination index expressed as either interactant disparity or coherence.

Investigates two methods of sequential analysis which were applied to hypothetical observational data. What the two methods were; Indepth look at both of the methods; Discussion on the findings.

Based on the nonlinear algorithmic theory, the R-SVM water source discrimination model and prediction method were established by using the piper qualitatively to compare the differences between the ionic components and R-type factor approximation indicator input dimensions. Taking the mine water samples of Zhaogezhuang Coal Mine as an example, according to the chemical composition analysis of the water samples from different monitoring points, six indexes of Na+, Ca2+, Mg2+, Cl–, SO42– and HCO3– were selected as the discrimination factors. According to the water characteristics of each aquifer and the actual needs of discrimination, the water inrush sources in the mining area were divided into four categories: The goaf water is class I, Ordovician carbonate is class II, Sandstone fracture water from the 13 coal system is class III, and Sandstone fracture water from the 12 coal system is class IV. Taking 56 typical water inrush samples as training samples, 11 groups for prediction samples, establish the input index as typical ion content, output as water source type, using SPSS statistics and MATLAB to realize the R-SVM water source discriminant analysis model, automatically establishing the mapping relationship between the water quality indexes and the evaluation standards, which can achieve the purpose of rapid and accurate discrimination of the water sample data. The results showed that the accuracy of the R-SVM model classification was 90.90% in the verification of the water source discrimination example of Zhaogezhuang mine and the coupled model has high accuracy, good applicability and discriminant ability, and has certain guiding significance for the prevention and control of water damage and the related field work. [ABSTRACT FROM AUTHOR]

Flood routing in natural channels is essential to predict the location and the physical properties of the flood waves, which is very important for the design of hydraulic structures and flood control processes and strategies. For example, the flood routing gives accurate information on flood peak and the period of water level rise. In this context, this study employed Muskingum's graphical method along with other numerical methods [least interpolation, nonlinear regression, classical fourth-order Runge–Kutta, and improved bat algorithm (IBA)] to conduct a flood routing in the Euphrates River at Husaybah region (near the Iraqi-Syrian borders). The IBA, which is based on the chaotic search tool and it improves the population homogeneity and periodicity, was employed in this study to optimize the estimated values of the Muskingum model. The flood routing in this study was developed using a big enough hydrological data (from 1993 to 2017) from the records of the Euphrates River. The collected data were processed and analyzed using the MATLAB software (version 9.6). The results of the analysis indicated that all the numerical methods can acceptably estimate the parameters of the Muskingum's graphical method, but the IBA was the best method as it fits the data with the minimum errors. In terms of the sum of squared differences between the observed and expected discharges (SSQ) were as follows (in a descending order): Nonlinear regression (2.46), Runge–kutta method (2.38), Least squares method (2.28), Graphical method (2.21), IBA (1.36). [ABSTRACT FROM AUTHOR]

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material. [ABSTRACT FROM AUTHOR]

Objective: [[Formula: see text]] N-isopropyl-p-iodoamphetamine ([Formula: see text]-IMP) is an ideal perfusion tracer for single photon emission computed tomography, which shows good linearity between cerebral blood flow (CBF) and accumulation. However, quantification of CBF using [Formula: see text]-IMP without arterial blood sampling has been challenging, with previous methods requiring empirically obtained regression formulae to estimate CBF. Furthermore, the CBF value obtained via some of the previous methods would be affected by the clearance rate of [Formula: see text]-IMP from the lungs. This paper introduces a new non-invasive quantification method for CBF using [Formula: see text]-IMP and dynamic planar images.Methods: We have developed a theory based on Microsphere model. This method does not involve regression formulae for estimation and allows for direct measurement of CBF, considering the clearance rate of [Formula: see text]-IMP from the lungs. The study method is executed as easily as conventional Graph-Plot method. We compared the CBF values obtained by our study method and the established autoradiograph (ARG) method.Results: CBF values obtained using the new method demonstrated significant correlation with values determined using ARG method.Conclusions: The novel method described presents a reliable and more simple way of determining CBF when compared to current methods. [ABSTRACT FROM AUTHOR]

A graphical method for the analysis of relaxation data is presented. It allows a fast estimation of the range of values of the components of the axially symmetric rotational diffusion tensor that are compatible with the experimental relaxation data. The graphical method clearly shows the contribution of different experimental relaxation parameters to the measured anisotropy. In particular, for proteins with moderate anisotropy, data from at least two N-H bonds forming angles close to 0° and 90° with respect to the principal axis of the rotational diffusional tensor are needed. For very anisotropic systems, combination of different relaxation parameters from a single residue is enough to characterize the local anisotropy. [ABSTRACT FROM AUTHOR]

A graphical method for the evaluation of vacuum expectation values of products of creation and annihilation operators, is presented. This method is an adaptation of Danos' switchyard technique to the particular case of strings of only creation and annihilation operators and is easier to use and more transparent than Wick's theorem. [ABSTRACT FROM AUTHOR]

The fundamental equation of the theory of multiple fixations without interaction (MFWI) is where r is the number of saturated sites, m the maximal number of such sites, K the association constant and A the activity of the univalent fixing elements. When m is large, the determination of 1/ m as the intercept in a plot of 1/ r versus 1/ A is impracticable. It can be shown that, given three half-rays OA, OB and OC respectively defined by the polar angles O, π/3 and 2π/3, the relation holds for any straight line ABC crossing the axes. Such a graph can be used to represent the fundamental equation of the theory of MFWI: a set of straight lines corresponds to a set of points ( r,A) and these lines converge on the axis OC. This graphical method has been used to test Wurmser's theory of isohemagglutination; the results are aberrant. It is concluded that either the theory is wrong, or the experimental errors are considerable. The findings closely agree with the views of E. A. Kabat. [ABSTRACT FROM AUTHOR]

We introduce a novel approach to compute Compton amplitudes involving a fermion pair inspired by Hopf algebra amplitude constructions. This approach features a recursive relation employing quasi-shuffle sets, directly verifiable by massive factorization properties. We derive results for minimal gauge invariant color-kinematic numerators with physical massive poles using this method. We have also deduced a graphical method for deriving numerators that simplifies the numerator generation and eliminates redundancies, thus providing several computational advantages. [ABSTRACT FROM AUTHOR]

The in-plane shear and compressive properties of unidirectional (UD) HTS40/977-2 carbon fibre-toughened resin (CF/TR) laminates are investigated. Scanning Electron microscopy (SEM) and optical microscopy are used to reveal the failure mechanisms developed during compression. It is found that damage initiates by fibre microbuckling (a fibre instability failure mode) which then is followed by yielding of the matrix to form a fibre kink band zone that leads to final fracture. Analytical models are briefly reviewed and a graphical method, based on the shear response of the composite system, is described in order to estimate the UD compressive strength. Predictions for the HTS40/977-2 system are compared to experimental measurements and to data of five other unidirectional carbon fibre reinforced polymer (CFRP) composites that are currently used in aerospace and other structural applications. It is shown that the estimated values are in a good agreement with the measured results. [ABSTRACT FROM AUTHOR]

Abstract  We discuss the use of the Schmidt graphical method to calculate the time required to heat a polychlorinated biphenyl (PCB)-contaminated capacitor in the vacuum thermal recycling process to the processing temperature of 400°C, and we evaluate the results of the heating time calculation by comparing the calculated values with the corresponding experimental values. The thermal conductivity and specific heat of the insulating paper and the carbonized paper in the capacitor were unknown, so we determined their values from experimental data obtained during the vacuum thermal recycling process. The capacitor element is a multilamination of aluminum foil and insulating paper, so we used an equation for a multilayer plane wall to calculate the value of the thermal conductivity. For the thermal conductivity and specific heat of the insulating paper impregnated with PCBs, we used values calculated from the mass ratios and thermal conductivities and specific heats of the individual materials. In addition, the physical properties vary according to the treatment because of the evaporation of PCBs and the carbonization of the insulating paper, so we modified the values of the thermal conductivity, specific heat, and density at the boiling point of the PCB and the carbonization point of the insulating paper before performing the calculations. Our calculated heating times were almost the same as, or were above, the experimental values, so we concluded that our method can be used as a simple calculation of the heating time. [ABSTRACT FROM AUTHOR]

We describe a novel graphical method which, in conjunction with the previously proposed graphical determination of monomer shift, dimer shift, and dimerization constant for self-association, allows us to determine the complex shift and equilibrium constant for a hetero-association, A + B ⇌ AB, accompanying self-associations, A + A ⇌ A2, and B + B ⇌ B2. The merit of the new method includes the removal of the restrictions imposed on the conventional Benesi-Hildebrand (B-H) plot: (1) that the concentration of one component must be much less than that of the other; (2) that there be no accompanying self-association. The simultaneous equilibrium of the self-association of 2-pyrrolidone (A) and that of 4-methyl-α-pyrrolidone (B) and the hetero-association between A and B in acetonitrile-d3 at 25‡C is studied. The inappropriateness of the B-H plot in dealing with this case is also pointed out. [ABSTRACT FROM AUTHOR]

The Bayesian approach is applied to estimation of the Weibull-power law process (WPLP) parameters as an alternative to the maximum likelihood (ML) method in the case when the number of events is small. For the process model considered we propose to apply the independent Jeffreys prior distribution and we argue that this is a useful choice. Comparisons were also made between the accuracy of the estimators obtained and those obtained by using other priors—informative and weakly informative. The investigations show that the Bayesian approach in many cases of a fairly broad collection of WPLP models can lead to the Bayes estimators that are more accurate than the corresponding ML ones, when the number of events is small. The problem of fitting the WPLP models, based on ML and Bayes estimators, to some real data is also considered. It is shown that the TTT-concept, used in the reliability theory, is not fully useful for the WPLP models, and it may be so for some other trend-renewal processes. In order to assess the accuracy of the fitting to the real data considered, two other graphical methods are introduced. [ABSTRACT FROM AUTHOR]

Analysis of five-axis transformations permits the development of a method of adjusting multifunctional equipment for five-coordinate machining. The adjustment precision of the 500V/5 machine tool is studied experimentally. [ABSTRACT FROM AUTHOR]

Background: Reservoir bank collapse in loess areas may lead to the siltation of reservoir and bank retreat. Therefore, the study of reservoir bank collapse has practical significance. Almost of the bank collapse width prediction method were based on the classical graphical method which do not consider the process of bank collapse. But practice shows that this method can overestimate the width of bank collapse. Meanwhile, there are few studies specifically focused on the collapse of loess bank slopes. Methods: To improve the prediction method of loss bank collapse width, the influence of water depth, dry density and bank slope angle on loess bank collapse was studied by physical modelling. The bank collapse width and the morphology of the bank slope were recorded during the experiment. Results: The bank collapse width increases with the increase of water depth, increases with the increase of slope angle, and decreases with the increase of dry density. The modeling process shows that the loess bank collapse occurs firstly underwater, the erosion niche will be formed underwater, and then the above water slope is damaged. This process is repeated until the underwater accumulation slope reaches the stable state, and then bank collapse stops. After the bank collapse, the above water slope is polyline, while the underwater slope is curved. When the slope angle is less than 27°, the bank collapse will not occur, and when the slope angle is between 27° and 40°, the bank collapse type is abrasion type. When the slope angle is greater than 40°, the bank collapse type is dumping type or shear type. Based on this, the improved balanced alluvial accumulation approach was proposed, which considers the mechanical equilibrium of above water bank slope and the morphology of underwater slope. The new method can reflect the stage characteristics of loess bank collapse, which is more reasonable than the empirical graphical method. Conclusions: The experimental results indicate that when predicting the width of loess bank collapse, it is necessary to combine the bank collapse width and process of bank collapse. The relevant conclusions have a certain role in exploring the mechanism of loess bank collapse and bank collapse prediction methods. [ABSTRACT FROM AUTHOR]

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Copyright of Acta physica Academiae Scientiarum Hungaricae is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)