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The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution. [ABSTRACT FROM AUTHOR]

Anaerobic lagoons remove organic matter in the absence of oxygen and must be designed considering facultative or aerated lagoons, to continue with the treatment and at the same time re-oxygenate the wastewater. The purpose of this document is to determine two graphs to calculate the elimination of fecal coliforms in anaerobic lagoons. An application example is included with the traditional method adopted by the Instituto Mexicano de Tecnología del Agua y la Comisión Nacional del Agua, later the graphs previously prepared are used. The results show the same values calculated with the traditional criteria. [ABSTRACT FROM AUTHOR]

Introduction: Sesame is one of the oldest crops and probably the oldest oilseed in the world. In most regions, the landrace and local masses of sesame are used. To increase production and yield, the production of modified cultivars for different agricultural climates is extremely important. Material and Methods: Seven genotypes included Isfahan, Sirjan, Fars, Oltan, Jiroft, Sabzevar, TS-3 and 21 hybrids that were obtained from them were studied in the research farm of the Faculty of Agriculture of the University of Birjand under the drought stress conditions during 2015-2018. The experiment was conducted in a randomized complete block design with three replications as a 7 × 7 one-way diallel. In this study, several traits were measured. These traits were including plant height, height to the first fruiting capsule, number of capsules per plant, number of sub-branches, number of leaves, leaf length, number of seeds per capsule, capsule length, capsule weight, capsule width, days to 50% and 90% flowering, days to physiological maturity, thousand seed weight, oil percentage, protein percentage, amount of chlorophyll a, chlorophyll b, total chlorophyll, biological yield, economic yield and harvest index. Results: The investigation of the adequacy of the additive-dominance model showed that the model was sufficient in the traits including plant height, capsule length, capsule weight, number of leaves, number of sub-branches, number of capsules per plant, economic yield, biological yield, days to 50 flowering, days to 90% flowering and days to physiological maturity, and therefore diallel analysis was done on these traits. Hayman's variance analysis showed that were significant component a (additive effects of genes) in all traits and component b (dominant effects of genes) in all traits except plant height. Also, were significant the component b1 (mean dominance effects) in most traits except plant height, number of auxiliary branches, number of capsules and seed yield, the component b2 (other dominance deviation due to the parents) in most traits except plant height, number of auxiliary branches and number of capsules, and the component b3 (residual dominance variation) in all traits except plant height. The investigation of genetic parameters showed significant additive genetic component (D) and dominanant genetic components (H1 and H2) in most traits. Also were significant the component F (average covariance of additive and dominance effects) and the component h2 (the overall dominance effect of heterozygous loci) in half of the traits. The average degree of dominance (√ (H1/D)) in different traits was observed as additive, incomplete, and over dominance. In all characteristics, except capsule weight, the ratio of genes with positive and negative effects (H2/(4H1)) was not equal to 0.25; therefore, in all traits, increasing and decreasing genes did not have symmetrical distribution among parents. The ratio of dominant and recessive genes in parents ((√(4DH1)+F)/(√(4DH1)-F)) was more than unity in most of the traits, so there was an uneven distribution of dominant and recessive genes in most of the traits. The number of dominant gene groups (h2/H2) was obtained from 0 to 2.04; therefore, all traits were controlled by one or two gene blocks. Broad sense (hb 2) and narrow sense (hn 2) heritability were high in all traits. Conclusion: In the traits studied, the type of action of genes controlling the traits, the ratio of dominant and recessive genes, the ratio of genes with increasing and decreasing effects, additive effects and dominance were variable and were different in most of the traits. Generally, most traits were controlled by genes with additive and dominant effects. The high heritability estimate indicates the promising news of the studied genetic materials in future studies. Therefore, among these materials, better genotypes can be selected for the climatic conditions of Birjand, so that it can be further investigated in the future. [ABSTRACT FROM AUTHOR]

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]

The incessant overcrowding of the space around the Earth with new operative satellites is a critical issue in the Space Traffic Management (STM) framework, especially in last years with the beginning of the new space economy. The operative life of the active satellites is seriously endangered by the numerous uncontrolled objects, i.e., the space debris, which populate the outer space. The consequence of an impact between these objects may be catastrophic, as proved by the events in the recent past. In this context, the in-orbit explosions both of dismissed satellites and rockets stages are one of the main causes of space debris generation. For this reason, a suitable observation and detection strategy of the fragments generated by these events is necessary, e.g., by means of optical systems. In this work, the Sapienza Space Systems and Space Surveillance Laboratory (S5Lab) shows the results, by means of a graphical method, of the short-term analysis of the in-orbit explosions that involved the third stage of the Russian rocket FREGAT-SB and the fragmentation of the military Chinese satellite YUNHAI 1–02. In order to approach the study of a fragmentation event, an observation strategy and an analysis method have been developed. The research of fragments was focused on the orbital plane leading to estimation of fragments' number and their distribution. The measurements obtained through the images were analyzed in order to understand if the objects present in the images are either included in the North American Aerospace Defense Command (NORAD) catalogue or not. The unknowns could be fragments. The next analysis follows the hypothesis of the isotropic explosion confined only on the tangential impulses. In first approximation, only semi-major axis and eccentricity change due to the impulse. Therefore, it is possible to generate a new Two-Line Elements (TLE) for each fragment leading to an association between the impulses and the affected TLEs. A new, simple, and fast analysis method was developed, specifically to improve the impulse association. It consists in a graphical method where it is possible to see the distribution of the fragments with respect to the original body using the angular distance trend between them. [ABSTRACT FROM AUTHOR]

The feud between Robert Hooke and Isaac Newton, over whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits, the celebrated Proposition 1, Theorem 1 of the Principia , has remained ongoing among their respective supporters, even after 300 years. The drama has escalated in recent decades, with a claim that Hooke may have used the same method and obtained an elliptical orbit for a linear force, a feat that some considered Newton never did for the inverse-square force. Modern understanding of Newton's graphical method as a symplectic integrator can now shed light on whether this claim is creditable. [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]

Preventing and alleviating heat stress remain an enormous challenge in dairy farming. Although enhanced air distribution techniques have been developed and deployed in many barns, ventilation alone is no longer sufficient even in regions with historically mild climates. There is an increasing need for cooling of the intake fresh air. Evaporative cooling is a cost-effective sustainable technique used in many applications, including livestock farming. This paper presents a graphical method for preliminary evaluation of evaporative cooling as a viable and effective solution. Thermodynamic principles are combined with models for heat transfer in dairy cattle to develop a set of criteria on the psychrometric chart. The proposed method is demonstrated for a naturally ventilated dairy barn located in the continental central European climate and in two locations with hot climates, a semi-arid/Mediterranean and a humid subtropical climate. • Thermoregulation models combined with thermodynamic principles. • Limits for effectiveness of evaporative cooling derived. • Developed criteria mapped onto psychrometric chart. • A graphical method to assess effectiveness of evaporative cooling proposed. • Proposed method demonstrated for sample barn in Europe. [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]

Aims To demonstrate a novel method for presenting and exploring data in systematic reviews of the alcohol literature. Methods Harvest plots are a graphical method for displaying data on the overall pattern of evidence from a systematic review. They can display the direction of effects and risk of bias within studies for multiple outcomes in a single graphical chart. Using data from our previous meta-analysis on the association between personality disorder and alcohol treatment outcome, we extended the application of harvest plots by developing an interactive online harvest plot application. Results Studies included in the review were heterogeneous in design. There were many different primary outcomes, and similar outcomes were often defined differently across studies. The interactive harvest plot allows readers to explore trends in the data across multiple outcomes, including the impact of within-study bias and year of publication. In contrast, meta-analysis on the same data was hampered by a lack of consistency in the way outcomes were measured, and incomplete reporting of effect sizes and their variance. This meant many studies included in the systematic review could not be meta-analysed. Conclusions Interactive harvest plots are a novel graphical method to present data from systematic reviews. They can supplement or even replace meta-analysis when the studies included in a systematic review use heterogeneous designs and measures, as is often the case in the alcohol literature. [ABSTRACT FROM AUTHOR]

A graphical method developed for the construction of structure contours for inclined planar surfaces has been extended to curved or folded surfaces with cylindrical geometries and horizontal axes. These structure contours can be used to constrain the outcrop trace of a folded contact on a geological map. The extended method requires, as a minimum, a field of orientation data and the map position of a single elevation on the contact under investigation. The method utilises orientation data collected on and around a partially mapped trace of a folded contact to constrain the outcrop trace throughout a geological map. The method uses a vertical cross-section that is parallel to the profile plane of any folds present. Crest, trough and hinge points identified in the cross-section can be projected on to the geological map in their correct positions and elevations. Similarly, structure contours on fold axial surfaces can be projected on to the geological map and the contours used to locate the axial traces of cylindrical folds with horizontal axes. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of pauses detection in English speech signals. The aim of the current study is to create a new method of speech pauses detection that has no drawbacks other algorithms suffer from. The analysis of it suggests the opportunity to use the graphical method in real-time applications. The article provides a new vision and a new solution of pauses detection problem. The result of the study - the graphical method - may be applied to real-time signal processing, text-to-speech synthesis or used to enrich knowledge about the specified problems. [ABSTRACT FROM AUTHOR]

Industrial sectors are improving their energy efficiency and increasing their share of renewables for heating and cooling demands by using lower emission technologies. One specific approach to help achieve these targets is the integration of heat pumps (HPs) in industrial processes. However, due to the temporal variation of the heating and cooling requirements in non-continuous processes, the integration of HP is challenging. In this paper, a structured method for the design of HP integration is proposed. The method implements an engineer-centred workflow that extends the concept of the Indirect Source Sink Profile (ISSP) to HP integration. For this purpose, an adapted Grand Composite Curve is derived from the ISSP. This ensures correct HP integration across the pinch while maintaining the temperature lift of the HP small. The proposed workflow is applied to a demonstration case study and a case study from industry. In both cases, the resulting system with integrated HP enables the elimination of hot utility demand and significantly reduces cold utility demands. The static paybacks of the proposed solutions are in the range of 4.5 to 5 year. [ABSTRACT FROM AUTHOR]

Research on graphical methods of reasoning has made enormous progress since the pioneering work of Wigmore in the early 20th century and its later rediscovery in the 1980s. While the usefulness of graphical methods for student training and research is widely acknowledged, their use by judges remains marginal, if not non-existent, even though this was Wigmore's objective. This article explores the difficulties that graphical methods of reasoning must overcome if they are to be integrated into the practice of the courts, at a time when courts are faced with ever more pressing imperatives of efficiency. The research is based on a partnership with the French School of Magistrates (Ecole Nationale de la Magistrature) and is informed by training courses given to magistrates on the basis of real cases, during which the authors proposed that they implement what we have called the Orderly Method of Evidence Analysis. Although the research confirms the value of graphical methods in promoting rigour in evidential reasoning, it also reaffirms the already clearly identified limits related to their complexity and time-consuming nature. The article also points out the difficulties that still need to be overcome in order to operationalise graphical methods of evidential reasoning, and the difficulties encountered by these methods in avoiding judgment bias. [ABSTRACT FROM AUTHOR]

The ecological niche sensu Hutchinson is defined as the set of environmental conditions allowing a species to grow, maintain, and reproduce. This conception of the niche, which is assimilated to a p‐dimensional hypervolume, with p representing all environmental variables, has been widely applied in ecology. However, displaying the niche hypervolume has proved challenging when more than three environmental dimensions are considered simultaneously. We propose a simple method (implemented in the specieschrom R package) that displays the full multidimensionality of the ecological niche of a species into a two‐dimensional space by means of a graphic we call species chromatogram. This method gives a graphical summary of the niche by representing together abundance gradients with respect to all environmental variables. A chromatogram enables niche optimums and breaths to be rapidly quantified, and when several chromatograms are examined (one per species), rapid comparisons can be made. From our chromatograms, we proposed a procedure that quantifies niche optimum and breadth as well as niche overlapping (index D) and the identification of the most discriminant combination of environmental variables. We apply these analyses on eight planktonic species collected by the Continuous Plankton Recorder (CPR) survey in the North Atlantic Ocean using 10 environmental variables. We display their full multidimensional niches and quantify their niche optimums and breadths along each dimension. We also compare our index D with other indices by means of hypervolume and dynRB R packages. By catching the full complexity of the niche, species chromatograms allow many different niche properties to be rapidly assessed and compared among species from niche optimums and breadths to the identification of the most relevant environmental parameters and the degree of niche overlapping among species. Species chromatograms may be seen as species' fingerprint and may also allow a better identification of the mechanisms involved in species assembly. [ABSTRACT FROM AUTHOR]

Equilibrium climate sensitivity (ECS) is defined as the change in the global mean surface air temperature due to the doubling or quadrupling of CO2 in a climate model simulation. This metric is used to determine the uncertainty in future climate projections, and therefore, the impact of model changes on ECS is of large interest to the climate modeling community. In this paper, we propose a new graphical method, which is an extension of Gregory's linear regression method, to represent the impact of model changes on ECS, climate forcing, and climate feedbacks in a single diagram. Using this visualization method, one can (a) quantify whether the model or process change amplifies, reduces, or has no impact on global warming, (b) evaluate the percentage changes in ECS, climate forcing, and climate feedbacks, and (c) quantify the ranges of the uncertainties in the estimated changes. We demonstrate this method using an example of climate sensitivity simulations with and without interactive chemistry. This method can be useful for multimodel assessments where the response of multiple models for the same model experiment (e.g., usage of interactive chemistry compared with the prescribed chemistry as shown here) can be assessed simultaneously, which is otherwise difficult to compare and comprehend. We also demonstrate how this method can be used to examine the spread in ECS, climate forcing, and climate feedbacks with respect to the multimodel mean (or one benchmark model) for multimodel frameworks such as Coupled Model Intercomparison Project Phase 5 or for different ensemble members in a large ensemble of simulations conducted using a single model. [ABSTRACT FROM AUTHOR]

We propose a powerful graphical method for evaluating the natural complex frequencies and amplitudes of the layered structures for their electromagnetic characterization. Its advantage is to show a pattern of the location of the natural complex frequencies so that it would be possible to examine how they can move for a possible error in the measurement system. The method is validated by a two-layered structure by comparing the natural complex frequencies and amplitudes computed by the proposed method and the inverse Fourier transform. It has been applied to monitor the effect of noise in a measurement system. [ABSTRACT FROM AUTHOR]

Heat exchanger networks (HENs) play a significant role in the energy conservation of any process industry. The HENs are used to maximize heat recovery by exchanging heat between hot and cold process streams. Therefore, the optimum design of HENs is extremely important to reach the maximum efficiency of energy systems. Many graphical methods have been developed during the last four decades for synthesizing of heat exchanger networks (HENs). However, most of these methods have only been evaluated for retrofitting design of HENs. In the grassroots design situation, these methods are often complicated and tedious. This paper introduces a new and simple graphical approach for HEN grassroots design. The new approach based on a single graph called Supply-Target Diagram (STD). The ST-D is formulated by plotting supply temperatures versus target temperatures of streams. Streams matching can easily be applied in the ST-D and splitting of streams is clearly visualized and evaluated. A case study is used to illustrate the application of the new graphical method for grassroots design of HENs. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) funicular structures can be easily generated and controlled by means of simple geometric constructions. These geometric constructions derive from reciprocal relationships between the form and force diagrams of a structure, which form the basis of graphic statics. Unlike in 2D space, in 3D space, similar geometric constructions cannot always be established for the design of three‐dimensional (3D) funicular structures. In some specific cases though, purely geometric procedures requiring no numerical approximations can be defined. In particular, this contribution explores the geometric transformation of 2D funicular structures as a means to graphically generate 3D funicular structures in equilibrium with coplanar loads. A fully graphical method for the construction of such pairs of 3D skew funiculars in equilibrium with coplanar loads and with control over the position of the supports is presented. It is based on geometrical linear relationships between the original and the transformed structures. Ultimately, it is shown how such pairs of 3D skew funiculars can be applied to the design of bridge and roof structures for instance. [ABSTRACT FROM AUTHOR]

Increasing effort of solar power integration to the grid could be accelerated towards sustainability goal. However, high PV penetration ratio (PVR) in turn critically reduces system frequency response performance of an existing power system due to reduction of on‐line rotating generators. Besides intrinsic system inertia, system RC plays a vital role in dynamically securing the power system operation subject to large PV disturbances. This study proposes a graphical method to determine critical values of system RC requirement with respect to the anticipated PVR and PV ramp‐down rate of disturbance; both of which should be forecastable, in practice, in each operating time interval. Impact of PVR on dynamic performance of a power system, through the effective time‐varying of system inertia and governor response characteristic has been examined. The results of the analyses on graphical display will be useful for system operators to prepare enough system RC, economically well in‐advance through Unit Commitment program, to ensure system dynamic security, complying with the N‐1 contingency constraint. In addition, the proposed graphical display can reveal whether the curtailment of aggregated PV's output generation is necessary for that time interval. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

• Method proposed for diluted (constant velocity) and isothermal cases. • Adsorption breakthrough curves are integrated to capacity curves. • Capacity curves allow to obtain adsorbed quantities in equilibrium with intermediate zones. • Equilibria were obtained from breakthrough curves of alcohols on all-silica beta zeolite. • Two, instead of one, equilibrium points could be obtained from one breakthrough curve. Adsorption mixture equilibrium data remains challenging to obtain. An established technique is the adsorption breakthrough experiment where the final adsorbed capacities are determined. A graphical method to obtain adsorbed amounts from the intermediate plateaus in the breakthrough curves is proposed in this work. The method is proposed for isothermal, diluted breakthrough tests. Via an integrated capacity curve, the intermediate regions can be extrapolated to extract additional equilibrium points beyond the final state without the need for a multicomponent model. If the column is preloaded, the extra equilibrium points can correspond to multicomponent mixtures as multiple species can have non-zero intermediate concentration plateaus. The method is demonstrated on various simulated examples and then applied on breakthrough data from non-preloaded and preloaded columns of all-silica beta zeolite for diluted methanol/ethanol and diluted ethanol/isobutanol mixtures. [ABSTRACT FROM AUTHOR]

Introduction : Teen crash involvement is usually higher than other age groups, and they are typically overrepresented in car crashes. To infer teen drivers' understanding of crash potentials (factors that are associated with crash occurrence), two sources of data are generally used: retrospective data and prospective data. Retrospective data sources contain historical crash data, which have limitations in determining teen drivers' knowledge of crash potentials. Prospective data sources, like surveys, have more potential to minimize the research gap. Prior studies have shown that teen drivers are more likely to be involved in crashes during their early driving years. Thus, there is a benefit in examining how teen drivers' understanding of crash potentials change during their transition through licensing stages (i.e., no licensure to unrestricted licensure). Method : This study used a large set of teen driver survey data (a dataset from approximately 88,000 respondents) of Texas teens to answer the research question. Researchers provided rankings of the crash potentials by gender and licensure stages using a multivariate graphical method named taxicab correspondence analysis (TCA). Results : The findings show that driving behavior and understanding of crash potentials differ among teens based upon various licensing stages. Practical applications: Findings from this study can help government authorities to refine policies of teen driver licensing and implement potential countermeasures for safety improvement. • This study used a comprehensive survey data to determine the patterns of associated factors in teen driving risks. • This study used a robust survey interpretation tool Taxicab Correspondence Analysis (TCA) to perform the analysis. • Findings show the necessity of education and training of teen drivers. [ABSTRACT FROM AUTHOR]

This paper proposes a simple and fast method to obtain the aeroelastic response of a square cylinder following different modelling approaches underpinned by a novel graphical technique that establishes abstract relationships between different key physical parameters involved in the mathematical models. The method is applied to the analysis of three important aeroelastic problems in the crosswind response of a square cylinder, including the transverse galloping defined with a quasi-steady model, the vortex-induced vibration (VIV) using a nonlinear oscillator model, and the VIV-galloping interaction following a combined effects model. The results demonstrate that the proposed analytical method simplifies the analysis and it is able to capture most of the complex aeroelastic crosswind behaviors of a square bluff body. • A graphical method to obtain the aeroelastic response of a square cylinder following different modelling approaches is proposed. • Compared with conventional analytical methods, the new analytical method has advantages of simplicity and effectiveness. • The graphical analytical method is successfully applied to the study of transverse galloping, VIV and their potential interaction. [ABSTRACT FROM AUTHOR]

The powerful image analysis and statistical capabilities of computers can effectively solve problems such as insufficient precision in clastic rock particle size measurements and the heavy workload during the process. The MATLAB programming language was employed to process the samples of the Zhoutian Formation in the Upper Cretaceous of the Huichang Basin through techniques such as grayscale transformation, binarization, adaptive median filtering, and color annotation, accurately measuring their grain size parameters. The results indicate the following. The average grain size obtained using MATLAB,s direct calculation method and the graphical method are 4. 008φ and 3. 103φ, respectively. The standard deviations are 0. 8φ and 0. 803φ, the skewness values are - 0. 195φ and - 0. 041φ, and the kurtosis values are 0. 911φ and 0. 916φ. The standard deviation and kurtosis errors are small, allowing for mutual substitution between the two calculation methods, while the standard deviation and skewness errors are relatively large, making them unsuitable for mutual substitution. Both MATLAB,s direct calculation method and microscopic rock mineral identification indicate a relatively poor roundness of the Zhoutian Formation as a whole, with angular to sub-angular clastic particles. The sedimentary environment discrimination formula reflects the formation of the Zhoutian Formation in a fluvial depositional environment, consistent with the geological background and microscopic observation results. Through the MATLAB programming language, it is possible to accurately identify particle outlines and calculate various parameters in clastic rocks, providing great convenience for sediment grain size research, eliminating subjective interference, and improving work efficiency [ABSTRACT FROM AUTHOR]

One of the impacts of harmonic resonances in wind parks is to overload wind park components. The process of identifying a problematic component may be time-consuming due to the number of scenarios and different components (capacitors, transformers, cables and generators) that must be analyzed. In this context, this paper develops a first-screening approach to narrow down the number of scenarios that must be studied in detail. It first identifies that the capacitor bank is the most critical component. Then, it uses the operating limits of the capacitor bank and the harmonic distortions measured at the wind park entrance to obtain a chart that maps the problematic operating conditions of the park. Detailed investigations are needed only if the wind park condition is in specific regions of the chart. The proposed chart is attractive for practical applications as it is obtained with a simple equation, without the need to run any computer simulation, and can be consulted with few information from the wind park that is readily available to engineers. [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]

The Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement (GUM) provides the framework for evaluating measurement uncertainty. The preferred GUM approach for addressing bias assumes that all systematic errors are identified and corrected at an early stage in the measurement process. We review some procedures for treating uncorrected bias and its inclusion into an overall uncertainty statement. When bias and its uncertainty are recognised as metrological states independent of scatter in the test results, the uncertainty of the reference and uncertainty of the bias can be equated. The net standard uncertainty of a test result is the root-sum-square of the standard uncertainty of the bias and the standard uncertainty of measurements on the test. Since an incomplete and therefore potentially erroneous formula is often used for estimating bias standard uncertainty, we propose an alternative calculation. We next propose a graphical method using a simple algorithm that quantifies the discrepancy between the results of a test measurement and the corresponding reference value, in terms of the percentage overlap of two probability density functions. We propose that bias should be corrected wherever possible and we illustrate this approach using the graphical method. Even though this review is focused principally on analytical chemistry and medical laboratory applications, much of the discussion is applicable to all areas of metrology. • Review of procedures for including uncorrected bias in an uncertainty statement. • Definition of bias, equality of uncertainty of bias and uncertainty of reference. • Net uncertainty of test method in terms of bias uncertainty and scatter of results. • Consistency with GUM equations for including uncorrected bias in an uncertainty. • Overlap of reference and test PDFs before bias correction measures concordance. [ABSTRACT FROM AUTHOR]

10.1119/10.0001299.1 In introductory physics courses, simple arguments based on traveling waves on a string are used to relate the frequency of standing waves to boundary conditions, e.g., the fixed ends of the string. Here, we extend that approach to two-dimensional waves such as the oscillations of a rectangular membrane with edges fixed at the boundary. This results in a graphical method that uses only simple geometry and is suitable for explaining two-dimensional standing-wave oscillations to non-science majors, e.g., in a physics of sound and music class. [ABSTRACT FROM AUTHOR]

Abstract Humidification–dehumidification (HDH) technology is an innovative desalination technology which has received considerable attention from researchers in recent years. In this study, the effects of mass flow rate ratio and pinch point temperature difference (PPTD) on the energy consumption of the HDH system are investigated by pinch analysis. A new parameter, pinch point heat capacity rate ratio (PHCR), is introduced to normalise the optimum point for energy consumption. It is found that the specific energy consumption of the system is minimised when the PHCR of the dehumidifier equals to unity. The value of GIR can be achieved 3.978 when the PHCR of dehumidifier equals to unity, at the inlet temperature of the solution in the humidifier equals to 65 °C and PPTD of the humidifier and dehumidifier equals to 1 °C. Based on this discovery, the regression equations are used to predict the optimum value of the mass flow rate ratio at different operating parameters. Combining the regression equations with the evaporation rate contour plots, an efficient graphical method is proposed for the determination of optimum operating parameters of the HDH system. It can be used to determine the operating parameters efficiently according to the performance requirements of the system. Highlights • A graphical method determining the optimum operating parameters is proposed. • PHCR is introduced to normalise the optimum point for energy consumption. • GIR and GOR are minimised when the PHCR of dehumidifier is equal to unity. • The relation of HRR and GIR is only related to the air states in the humidifier. • Regression functions can predict optimal value of mass flow rate ratio accurately. [ABSTRACT FROM AUTHOR]

Graphical method in physics education is accessible, visual and informative. The author presents new methodical approach for its applying in order to study uniformly accelerated motion. It is connected with applying the Internet resource Volfram Mathematica Online and its graphical opportunities. It is considered solving graphical problems. Methodology for extracting information from kinematic graphs is presented. This approach fortifies theory and practice of the physics education with new ideas for forming qualitative knowledge, graphical skills and logical thinking. [ABSTRACT FROM AUTHOR]

Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph, which is referred to herein as a "bin plot," is the IRT equivalent of a scatterplot for linear regression. Bin plots display a conventional IRT trace line (with ability on the horizontal axis and probability correct on the vertical axis). Students are binned according to how well they performed on the entire test, and the proportion of students in each bin who answered the focal question correctly is displayed on the graph as points above or below the trace line. With this arrangement, the difference between each point and the trace line is the residual for the bin. Confidence intervals can be added to the observed proportions in order to display uncertainty. Computer simulations were used to test four alternative ways for binning students. These simulations showed that binning students according to number of questions they answered correctly on the entire test works best. Simulations also showed confidence intervals for bin plots had coverage probabilities close to nominal values for common testing scenarios, but that there are scenarios in which confidence intervals had inflated error rates. [ABSTRACT FROM AUTHOR]

GGE biplot technique is one of the appropriate methods for investigating the genotype–environment interaction. An experiment was conducted to examine and evaluate the stability and adaptability of grain yield of 12 sunflower genotypes using the randomized complete block design (RCBD) with three replications in five regions including Karaj, Birjand, Firooz‐Abad, Kashmar, and Arak within two agricultural years. Analysis of variance indicated that the effect of location, year, location × year, genotype, and genotype × location was significant at 1% probability level. Results of biplot analysis showed that the first and second principle components accounted 50.6% and 22.8%, respectively, and in total 73.4% of grain yield variance. In this study, genotype, location, year, year × location, genotype × location, genotype × year, and genotype × year × location explained 2.75%, 17.36%, 5.47%, 17%, 10.8%, 1.04%, and 7.48% of total variance, respectively. Investigating the polygon view led to the identification of three top genotypes and also three mega‐environment. The first mega‐environment included Karaj, Birjand, and Kashmar. The second was Arak, and the third was Firooz‐Abad. To study the kernel yield and stability of genotypes simultaneously, average coordinate view of environments was used and it was determined that genotype Zaria with the highest grain yield has high yield stability also. Ranking the cultivars based on the ideal genotype introduced the genotype Zaria as the best genotype. The highest grain yield belonged to Zaria cultivar at 3.34 t/ha followed by Favorite with 3.23 t/ha. Results obtained from ranking the environments based on the ideal environment introduced Kashmar and Birjand regions as the best environments. Examining the biplot figure for testing environments correlation confirms the positive correlation among Karaj, Birjand, and Kashmar. Correlation between Karaj with Arak, Karaj with Firooz‐Abad, and Arak with Firooz‐Abad was negative. Arak and Firooz‐Abad were highly discriminating and representative and would be used to identification of superior genotypes. [ABSTRACT FROM AUTHOR]

The most critical point of gear design is bending stress which occurs on trochoid region of the gear. The high bending stress on trochoid region of the gear causes the tooth failure and the fatigue life of gear reduces. For this reason, bending stress must have lower magnitude as much as possible. In this study, to calculate bending stress, graphical method is proposed. It is based on DIN3990 and searches critical point in every point of trochoid region. First of all, for standard gear, stress is calculated with using the DIN 3990 standard and graphical method. Besides finite element analysis is used for validation of method. After validation, bending stresses are investigated for different gear parameters with finite element analysis and graphical method. It is evaluated that rack cutter tip radius is the most effective parameter on root stress. When increasing tip radius of rack cutter, the value of bending stress decreases 30%. It is seen that graphic method could be used with high reliability in gear stress analysis especially for gears with especially non-standard parameters. [ABSTRACT FROM AUTHOR]

Gears are the most important machine elements that have been used for centuries. It is used in many applications in several industries with many advantages such as higher load carrying capacity, longer service life, constant velocity ratio and reliability etc. For these reasons, it is significant that gears have to be designed and analyzed precisely. The most critical point of gear design is bending stress which occurs on trochoid region of the gear. The high bending stress on trochoid region of the gear causes the tooth failure and the fatigue life of gear reduces. For this reason, bending stress must have lower magnitude as much as possible. In this study, to calculate bending stress, graphical method is proposed. It is based on DIN3990 and searches critical point in every point of trochoid region. First of all, for standard gear, stress is calculated with using the DIN 3990 standard and graphical method. Besides finite element analysis is used for validation of method. After validation, bending stresses are investigated for different gear parameters with finite element analysis and graphical method. It is evaluated that rack cutter tip radius is the most effective parameter on root stress. When increasing tip radius of rack cutter, the value of bending stress decreases 30%. It is seen that graphic method could be used with high reliability in gear stress analysis especially for gears with especially non-standard parameters. [ABSTRACT FROM AUTHOR]

Stress and deformation analysis of a cavity in an infinite/finite medium is a fundamental applied mechanics problem of interest in multiple physics and engineering disciplines. This paper develops a complete semianalytical solution for the cylindrical cavity expansion in nonassociated Mohr–Coulomb materials, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single material point at the cavity wall). The novelty of the new solution framework lies not only in the relaxation of the stringent intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but also in the comprehensive consideration of nonhydrostatic initial stress conditions via arbitrary values of K0 (the coefficient of earth pressure at rest defined as the ratio between the horizontal and vertical initial stresses). The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during cavity expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K0 being covered. Some selected results are presented for the calculated cavity pressure-expansion curve and limit cavity pressure through an example analysis. The definitive semianalytical solution proposed will be not only substantially advancing the current state of knowledge on the fundamental cavity expansion theory, but also able to serve as a unique benchmark for truly verifying the correctness and capability of the classical cornered Mohr–Coulomb constitutive model built in commercial finite element programs. [ABSTRACT FROM AUTHOR]

• A graphical technique for visualising CO 2 emissions reduction. • CO 2 emissions reduction procedure for multi-product plants. • CO 2 emissions of shared and dedicated facilities are analysed. • Different strategies for CO 2 emissions reduction are proposed. Carbon dioxide emissions reduction has been a common trend for many industrial processes in recent years. However, few analytical tools have been developed for visualising CO 2 emissions reduction and supporting decisions at the enterprise level. A graphical technique known as Carbon Emission Composite Curves was developed previously, but was limited to the production of single product. In this work, the CO 2 emissions reduction procedure is focused and extended to multi-product plants, in which CO 2 emissions of shared and dedicated facilities of the production line are analysed. For cases where the carbon intensity of shared facilities is higher than that of the dedicated facilities, CO 2 emissions reduction should focus on the shared facilities, before efforts are put forward for the dedicated facilities. In contrast, when the carbon intensity of dedicated facilities is higher than that of the shared facilities, it is necessary to explore ways to reduce CO 2 emissions of the dedicated facilities. Two case studies are used to illustrate the procedure. [ABSTRACT FROM AUTHOR]

An intuitive method is presented for detecting pseudosymmetries in Z′ > 1 cases as a complement to well‐proven strategies already available in the literature. It is based in the simple idea that the mid‐points between equivalent atoms in symmetrically related molecules are disposed according to simple well‐known patterns, which are easily recognizable by optical inspection. A number of Z′ = 4 cases in the literature are analyzed, which allows some of the potentialities of the method to be revealed. [ABSTRACT FROM AUTHOR]

Purpose: Dynamic 18F‐FDG PET allows quantitative estimation of cerebral glucose metabolism both at the regional and local (voxel) level. Although sensitive to noise and highly computationally expensive, nonlinear least‐squares (NLS) optimization stands as the reference approach for the estimation of the kinetic model parameters. Nevertheless, faster techniques, including linear least‐squares (LLS) and Patlak graphical method, have been proposed to deal with high resolution noisy data, representing a more adaptable solution for routine clinical implementation. Former research investigating the relative performance of the available algorithms lack precise evaluation of kinetic parameter estimates under realistic acquisition conditions. Methods: The present study aims at the systematic comparison of the feasibility and pertinence of kinetic modeling of dynamic cerebral 18F‐FDG PET using NLS, LLS, and Patlak method, based on numerical simulations and patient data. Numerical simulations were used to study the bias and variance of K1 and Ki parameters estimation under representative noise levels. Patient data allowed to assess the concordance between the three methods at the regional and voxel scale, and to evaluate the robustness of the estimations with respect to patient head motion. Results and Conclusions: Our findings indicate that at the regional level NLS and LLS provide kinetic parameter estimates (K1 and Ki) with similar bias and variance characteristics (K1 bias ± relative standard deviation [RSD] 0.0 ± 5.1% and 0.1% ± 4.9% for NLS and LLS respectively, Ki bias ± RSD 0.1% ± 4.5% and −0.7% ± 4.4% for NLS and LLS respectively). NLS estimates appear, however, to be slightly less sensitive to patient motion. At the voxel level, provided that patient motion is negligible or corrected, LLS offers an appealing alternative solution for local K1 mapping. It yields K1 estimates that are highly correlated, with high correlation with NLS values (Pearson's r = 0.95 on actual data) within computations times less than two orders of magnitude lower. Last, Patlak method appears as the most robust and accurate technique for the estimation of Ki values at the regional and voxel scale, with or without head motion. It provides low bias/low variance Ki quantification (bias ± RSD −1.5 ± 9.5% and −4.1 ± 19.7% for Patlak and NLS respectively) as well as smooth parametric images suitable for visual assessment. [ABSTRACT FROM AUTHOR]

In the Principia, Book 1, Proposition 1, Newton gave a geometrical proof of angular momentum conservation for central forces. A geometrical construction associated with this proof provides a very efficient graphical method to obtain approximate orbital curves for such forces that can be traced with a ruler and a pencil. Newton's geometrical construction also satisfies a discrete form of energy conservation and it is time reversal invariant. An algorithm corresponding to this construction provides an efficient and stable numerical method to integrate the equations of motion of classical mechanics. In the past, this algorithm has been rediscovered several times without recognizing its connection to Newton's geometrical construction. [ABSTRACT FROM AUTHOR]

Summary: Lowering CO2 emissions has become one of the key drivers behind the process intensification and modification in current chemical process industries. Here, we proposed a graphical method that features simultaneous correlation between CO2 emission reduction, fuel switching, energy saving, investment cost, carbon credit, and payback time. Such CO2 emission reduction can be obtained by fuel switching and/or retrofitting of the heat exchanger network. We illustrate the applications of this graphical method to the crude oil preheating train that uses furnace and the palm oil refinery that uses steam boiler. In crude oil preheat train case, for example, 55% emission reduction target can be achieved at an approximately 1.15 year of payback time from the alignment of fuel switching and energy saving. Further reduction in payback time from 1.15 to 0.91 years can be obtained by adding carbon credit contribution scheme into such alignment. This illustrates the flexibility of our graphical method to provide simple and convenient way for evaluating the technical and economic variable relationship for decision‐making. [ABSTRACT FROM AUTHOR]

In this work we recover and update a graphical method introduced by Prof. Pierre Lucie (1917 - 1985) in the study of image formation by thin lens. The method is associated by us with the modern technologies of information and communication through a PheT simulation that allows the visualization of image formation and the acquisition of the conjugated points. We also make use of the dynamical geometry software GeoGebra to analyze the data and obtain Gaus's equation for conjugated points. A class-oriented procedure for the teaching of image formation by thin lens was prepared and applied at the high-school level. Results indicate that this updated graphical method may be potentially significant. [ABSTRACT FROM AUTHOR]

Gears are the most important machine elements that have been used for centuries. It is used in many applications in several industries with many advantages such as higher load carrying capacity, longer service life, constant velocity ratio and reliability etc. For these reasons, it is significant that gears have to be designed and analyzed precisely. The most critical point of gear design is bending stress which occurs on trochoid region of the gear. The high bending stress on trochoid region of the gear causes the tooth failure and the fatigue life of gear reduces. For this reason, bending stress must have lower magnitude as much as possible. In this study, to calculate bending stress, graphical method is proposed. It is based on DIN3990 and searches critical point in every point of trochoid region. First of all, for standard gear, stress is calculated with using the DIN 3990 standard and graphical method. Besides finite element analysis is used for validation of method. After validation, bending stresses are investigated for different gear parameters with finite element analysis and graphical method. It is evaluated that rack cutter tip radius is the most effective parameter on root stress. When increasing tip radius of rack cutter, the value of bending stress decreases 30%. It is seen that graphic method could be used with high reliability in gear stress analysis especially for gears with especially non-standard parameters. [ABSTRACT FROM AUTHOR]

Summary: This paper concentrates on the robust stabilization of fractional‐order plant suffering from general interval uncertainties by using fractional‐order controllers. General interval uncertainties mean that the coefficients and orders of the denominator and nominator of the fractional‐order plant are all uncertain and lie in specified intervals. Two main contributions are presented, as follows. (i) Based on a graphical method, a necessary and sufficient criterion is proposed for the stabilization of the general interval fractional‐order plant. By adopting some well‐defined multivalue functions, the proposed method can explicitly construct the nonconvex boundary of the value set of the fractional system. (ii) Two alternative methods are presented to improve the computational efficiency of the stabilization test. Based on a newly developed redundancy elimination technique, the first method can avoid computing and plotting many segments, which are in the interior of the value set of the fractional system. The second method utilizes a novel convex polygon bounding approach. It can efficiently construct a convex polygon to bound the nonconvex value set of the general interval fractional system. Examples are followed to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Numerous studies on heat integration have made significant progress in reducing external thermal energy in chemical plants. However, the notion of work exchange between high- and low-pressure streams to reduce the costly mechanical energy has not been fully explored. In this paper, an upgraded graphical method is proposed for the synthesis of direct work exchanger networks (WEN) using direct work exchangers under any operating conditions, such as isothermal, isentropic, and polytropic. In this method, the improved composite curves of work sources and work sinks are plotted in the pressure index (μ) versus work (W) diagram. On the basis of thermodynamic and numerical analysis, two improved linear-approximation auxiliary lines for every work sink are presented to assist identifying the feasible match. Several matching rules are proposed to accurately identify the feasible matches between work sinks and work sources. From the proposed method, the maximum amount of mechanical energy recovery, the minimum amount of the external utility, as well as the corresponding network design can be determined. Two examples are presented, and the results prove the correctness and generality of the developed method for synthesizing direct WEN. [ABSTRACT FROM AUTHOR]

A surge in a centrifugal compressor can cause critical damage to the compressor, resulting in large repair costs, so one of the most important considerations in the design of compressor systems is to prevent a surge. However, conventional methods to size recycle valves in anti-surge systems are limited in that the valve characteristics and time delay cannot be quantitatively considered. This paper suggested a short-cut graphical method to easily size the recycle valves in an anti-surge system by considering the valve characteristics, including the dead time, actuation time, and opening types. Dynamic simulations were carried out to verify the resulting size of the valves, and the results of the simulation showed that a surge could be avoided effectively and economically. [ABSTRACT FROM AUTHOR]

We present a new seed dormancy classification scheme for the non-deep level of the class physiological dormancy ( PD), which contains six types. Non-deep PD is divided into two sublevels: one for seeds that exhibit a dormancy continuum (types 1, 2 and 3) and the other for those that do not exhibit a dormancy continuum (types 4, 5 and 6). Analysis of previous studies showed that different types of non-deep PD also can be identified using a graphical method. Seeds with a dormancy (D) ↔ conditional dormancy ( CD) ↔ non-dormancy ( ND) cycle have a low germination percentage in the early stages of CD, and during dormancy loss the germination capacity increases. However, seeds with a CD/ ND ( i.e. D→ CD↔ ND) cycle germinate to a high percentage at a narrow range of temperatures in the early stages of CD. Cardinal temperatures for seeds with either a D/ ND or a CD/ ND cycle change during dormancy loss: the ceiling temperature increases in seeds with Type 1, the base temperature decreases in seeds with Type 2 and the base and ceiling temperatures decrease and increase, respectively, in seeds with Type 3. Criteria for distinguishing the six types of non-deep PD and models of the temperature functions of seeds with types 1, 2 and 3 with both types of dormancy cycles are presented. The relevancy of our results to modelling the timing of weed seedling emergence is briefly discussed. [ABSTRACT FROM AUTHOR]