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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]

A great circle route (GCR) is the shortest route on a spherical earth model. Do we have a visual diagram to handle the shortest route? In this paper, a graphical method (GM) is proposed to solve the GCR problems based on the celestial meridian diagram (CMD) in celestial navigation. Unlike developed algebraic methods, the GM is a geometric method. Appling computer software to graph, the GM does not use any equations but is as accurate as using algebraic methods. In addition, the GM, which emphasizes the rotational surface, can depict a GCR and judge its benefit. [ABSTRACT FROM AUTHOR]

Abstract: Following specification of all variables of interest as well as their interrelationships, the validity of an ecological model (or of any of its components) is often tested by analysis of variance (ANOVA)-based procedures, either through experimentation, ‘screening’ of predictors, or simulation. To this end, the linear model diagram (LMD) is introduced as a graphical method for the display of factor relationships in ANOVA balanced complete designs. As an analysis-oriented diagram, hence in contrast with layout-oriented diagrams useful for the allocation of experimental units to factor levels (or vice versa), the purpose of the LMD is to streamline specification of a design''s underlying linear model. This contains all available information about each observation and its correct specification is essential for computing reliable ANOVA error terms. In the LMD, factor relationships, especially higher order interactions in complex fully factorial or nested/factorial designs, are more effectively visualised than in the other existing analysis-oriented diagrams. Further, by assigning a unique label to a design, including those sharing an otherwise identical linear model, the LMD provides the ecologist with a graphic ‘shorthand’ that streamlines the statistical analysis of an experiment as well as may help clarify terminological inconsistencies. [Copyright &y& Elsevier]

Background: Derivative based a-priori structural identifiability analyses of mathematical models can offer valuable insight into the identifiability of model parameters. However, these analyses are only capable of a binary confirmation of the mathematical distinction of parameters and a positive outcome can begin to lose relevance when measurement error is introduced. This article presents an integral based method that allows the observation of the identifiability of models with two-parameters in the presence of assay error. Methods: The method measures the distinction of the integral formulations of the parameter coefficients at the proposed sampling times. It can thus predict the susceptibility of the parameters to the effects of measurement error. The method is tested in-silico with Monte Carlo analyses of a number of insulin sensitivity test applications. Results: The method successfully captured the analogous nature of identifiability observed in Monte Carlo analyses of a number of cases including protocol alterations, parameter changes and differences in participant behaviour. However, due to the numerical nature of the analyses, prediction was not perfect in all cases. Conclusions: Thus although the current method has valuable and significant capabilities in terms of study or test protocol design, additional developments would further strengthen the predictive capability of the method. Finally, the method captures the experimental reality that sampling error and timing can negate assumed parameter identifiability and that identifiability is a continuous rather than discrete phenomenon. [ABSTRACT FROM AUTHOR]

Azeotropic distillation as an early and important special distillation process is commonly used in laboratory and industry. It can be used for separating the mixture with close boiling point or forming azeotrope. This paper tries to provide a review on azeotropic distillation for general readers, focusing on entrainer selection and mathematical models. Since the 1950s, along with extractive distillation, azeotropic distillation has gained a wide attention. Like extractive distillation, the entrainer, i.e., the third component added to the system, is also the core of azeotropic distillation. In the process design and synthesis, the graphical method (in most cases refer to as triangular diagram) is often employed. But it is better to take on the results from graphical method as the initial values of rigorous equilibrium (EQ) stage/non-equilibrium (NEQ) stage models. One outstanding characteristic of the EQ/NEQ stage models different from extractive distillation and catalytic distillation is to describe phase split for heterogeneous azeotropic distillation. In general, the operation process is very sensitive to some parameters in the case of more than one azeotrope formed, and thus the phenomenon of multiple steady states (MSS) tends to appear. [ABSTRACT FROM AUTHOR]

Generalized functions, in particular the Heaviside unit step H(t) and the Dirac delta impulse δ(t), are valuable teaching tools in many contexts of electric circuits. However, engineering undergraduate courses and textbooks normally cover only an introduction to these functions along with their basic properties, without tackling the rigorous mathematical framework of the theory of distributions. In this work, the Heaviside function is used to represent a square wave signal f(t), and the Dirac function appears when the derivative is calculated. The steps for obtaining f'(t) compare a graphical method with analytical procedures that employ the chain rule. The topic is further extended with the presentation of a theorem and a proposed corollary related to the study of the chain rule applied to general functions involving H(t) and δ(t). Thus, the work provides an appropriate mathematical support for the intuitive graphical method of analysis, which is very familiar in engineering practice. [ABSTRACT FROM AUTHOR]

The transient characteristics of proton exchange membrane water electrolysis for hydrogen production are crucial for the study of the load control and durability of the electrolyzer under the fluctuating conditions of renewable energy sources. In this study, a dynamic model of the electrolyzer is established based on various equivalence theories used to describe the transient characteristics of the electrolyzer during operation. Differential-equation-based transient models of the R C (resistance and capacitance) equivalent circuit and the equivalent controlled current source, their advantages and disadvantages, and their typical transient response spectra are presented. Among these, the graphical method based on the polarization curve is recommended because it has the advantages of intuitive and simple expression and can help researchers precisely and efficiently predict the response form and time of current or voltage using various control methods. The transient characteristics of the shutdown process reflect electrochemical processes similar to those of fuel cells in the electrolyzer during the OCV (open circuit voltage) period. The performance of the transient process is related to the structure of the electrolyzer and the operating conditions of the measurement. Low-voltage sustenance with manual intervention following shutdown may have a positive effect on the durability of the electrolyzer. • The transient characteristics of load regulation and shutdown are described. • Mathematical models based on differential equations are reviewed and summarized. • Different control methods are compared using the graphical method. • The 'voltage sustaining' after shutdown is measured and explained. [ABSTRACT FROM AUTHOR]

The lifetimes of polar optical phonons are known to affect both the electrical and thermal performances of gallium nitride (GaN) based devices. Hence, understanding the dynamical behavior of these phonons in GaN is integral to the elucidation of carrier drift velocities, hot phonon effects, and temperature localization in these nitride semiconductors. To investigate this dynamic behavior, temperature dependent phonon lifetimes were acquired through utilization of the linewidth of the Raman response for GaN samples having various doping types and concentrations. The temperature dependent lifetimes of the four examined phonon modes were then correlated with the Klemens decay model modified to account for four-phonon processes to deduce the decomposition of the zone center phonons. A graphical method that maps this decomposition in the high symmetry directions of the Brillouin zone is also presented. From the variation in lifetime with free carrier concentration, dominant scattering mechanisms are subsequently found for each of four different phonon modes. It is observed that the phonon-carrier interaction directly determines the lifetimes of the polar optical A1 and E1(LO) modes, while the transverse modes into which these longitudinal phonons decay are independent of this interplay. These results indicate that temperature localization likely arises due to the continual emission and reabsorption between the LO phonon modes and the free carriers rather than the persistence of lattice/carrier interaction throughout the entirety of the energy cascade. [ABSTRACT FROM AUTHOR]

Introducing purification devicesinto hydrogen systems can enhancethe extent of hydrogen reuse. The economic performance of a purificationdevice depends on its appropriate placement within a hydrogen system.This work presents an improved version of a previously published graphicalmethod for integrating purification processes in hydrogen systems.A mathematical method is deduced for calculating the maximum hydrogenutility savings potential of a hydrogen system with purification reuse.The improved graphical method is able to handle the constraints ofconcentration and flow rate of a purification process when targetingthe maximum hydrogen utility savings. The proposed method can be usedfor analyzing purification processes with any feed concentration.The graphical method is tested on two case studies. [ABSTRACT FROM AUTHOR]

Based on Fick’s diffusion law, mathematical model for specimens with simple shapes such as slab, sphere and cylinder are developed for condensed-solvent debinding process of powder injection molding. A graphical method is introduced to forecast the debinding process using the established model while complicated calculation could be avoided. Experiments are carried out to verify the mathematical model and graphical method, and the results are very close to those calculated from the up-mentioned model and method. [Copyright &y& Elsevier]

In this contribution we introduced a novel graphical method to compare protein sequences. By mapping a protein sequence into 3D space based on codons and physicochemical properties of 20 amino acids, we are able to get a unique P -vector from the 3D curve. This approach is consistent with wobble theory of amino acids. We compute the distance between sequences by their P -vectors to measure similarities/dissimilarities among protein sequences. Finally, we use our method to analyze four datasets and get better results compared with previous approaches. [ABSTRACT FROM AUTHOR]

There is an increased controversy regarding when the actual silane deposition process takes place, whether or not the silane solution should be left for a longer time before the silanization, so that a maximum concentration of hydroxil groups is achieved. The proposed method uses a specifically designed electrochemical cell to monitor the behaviour of the silane solution during hydrolisation process versus time. The main characteristic parameters are reunited into a goal function (the temperature influence is also taken into account) used for supplying the maximum coordinates, graphical method or from the first derivative. The results may be used further for the silane deposition process, so that the best possible coating is obtained. [ABSTRACT FROM AUTHOR]

This paper describes a semiparametric method for estimating a generic probability distribution using a basis expansion in. We express the given distribution as a monotonic transformation of the Gaussian cumulative distribution function, expanded in a basis of Hermite polynomials. The coefficients in the basis expansion are functionals of the quantile function, and can be consistently estimated to give a smooth estimate of the transformation function. For situations in which the estimated function is not monotone, a projection approach is used to adjust the estimated transformation function to guarantee monotonicity. Two applications are presented which focus on the analysis of model residuals. The first is a data example which uses the residuals from the 2012 Small Area Income and Poverty Estimates model. The Hermite estimation method is applied to these residuals as a graphical method for detection of departures from normality and to construct credible intervals. The second example analyses residuals from time series models for the purpose of estimating the variance of the mean and median and comparing the results to the AR-sieve. This paper concludes with a set of numerical examples to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Blocking Contours are a graphical method. By means of this technique, the gear designer obtains the values of the correction coefficients, which meets the undercutting geometric constraints, contact ratio, interference and teeth pointing. This paper presents a mathematical model that allows non-interactive construction of blocking contour in the field of cylindrical external gears with asymmetric teeth. For this purpose, the equations defining the mentioned restrictions are modified and it is set the sequence in which they should be calculated. This makes possible the analytical use of the limits of blocking contour for establishing the dependence between the geometric parameters of these transmissions, thereby facilitating synthesis work. [ABSTRACT FROM AUTHOR]

New heat recovery and power targeting models have been developed to evaluate and improve site-wide heat recovery and distribution, and cogeneration systematically. Previous graphical methods for utility system targeting have been proposed based on the assumption of only steam latent heat in the utility system. In this work, a practical graphical approach based on extended site composite curves to quantify site steam targeting has been proposed to provide realistic utility targeting methods, allowing for BFW (boiler feedwater) preheating and steam superheating in steam generation, and steam desuperheating for process heating. Condensate heat recovery from steam usage has also included in the graphical method. A new cogeneration targeting model has been developed including practical limits such as steam mains superheat and turbine exhaust dryness. These new realistic energy and power targeting methods improve the accuracy of the targeting, and overcome the shortcomings of previous targets. [ABSTRACT FROM AUTHOR]

This paper discusses the effect of temperature polarization in Vacuum Membrane Distillation (VMD). The main motivation for using VMD in this work is that this module configuration is much simpler and more suitable for this kind of investigation than the other MD configurations such as Direct Contact Membrane Distillation (DCMD). The coupling between heat and mass transfer mechanisms at the feed-membrane interface is presented from a theoretical point of view. In addition, a new simple graphical method and a mathematical model for determining VMD flux are presented. The two methods used in evaluating the extent of temperature polarization effect on water vapor flux (flux sensitivity factors and temperature polarization coefficient (TPC)) are also analyzed and compared. The effect of integrating a heat recovery system in a large scale module on the TPC coefficient has also been studied and presented in this paper. [ABSTRACT FROM AUTHOR]

Helical groove geometry has important influence on the performance of end mills. It is the hardest and most time-consuming grinding process in end mill manufacture. This paper reports a graphical analysis method to obtain the structure parameters and geometric shapes of helical grooves with the known wheel geometry and position. Mathematical models are presented to describe the wheel geometry and position (including orientation and location) in space. A family of wheel surfaces is calculated and a scattered point set in the cross section plane is deduced according to the grinding path. Finally, an original algorithm for the cross sectional outline profile identification is given using graphical method. To verify this method, a calculation program programmed using MATLAB programming is developed. This study provides a fundamental understanding for the groove grinding process, based on this, the influence of different grinding process parameters on groove geometry (including radial rake angle, groove width and core radius) is discussed. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this work is to show how the modeling of an electromechanical system can be addressed using the energy-based graphical modeling technique named “Power-Oriented Graphs” (POG). Differences and analogies of POG against Bond Graphs modeling technique are discussed. The paper presents the POG dynamic model of an automatic corking machine for threaded plastic caps: the system is composed by two electric motors moving a ball screw/spline that realizes the linear/rotary motion necessary to screw a plastic cap on a bottle. First an extended POG model is presented, together with the equivalent Bond Graph model, then some proper congruent state space transformations and a POG-based graphical method are introduced to transform and reduce the system dynamic model. Simulation and experimental results are finally presented and compared. [Copyright &y& Elsevier]

A data set {X1, X2,...Xn} comes from a counting process in many of maintenance, repair and replacement problems commonly includes systematical changes. Systematical changes in the data set indicate a trend which suggests that {X1, X2,...Xn}are not identically distributed. In this case renewal process cannot be used as a model. In modelling of a data set the existence of a trend has to be searched firstly. A simple way to detect a trend is to apply a graphical method. In this study the cumulative number of failures versus the cumulative time plot, estimating the rate of occurrence of failures in successive time periods plot, Nelson-Aalen plot and the total time on test plot will be described and evaluated on three real data sets. [ABSTRACT FROM AUTHOR]

A graphicalmethod for evaluating the Langmuir favorable adsorption is proposedin this work. The conditional Langmuir constant (KLN), a newparameter related to the Langmuir equilibrium constant (KL), can be used to predict the shapes of Langmuir favorableadsorption isotherms. On the dimensionless Langmuir isotherm diagram,all the Langmuir favorable adsorptions (0 < RL< 1) are further divided into three subgroups: favorableadsorption, very favorable adsorption, and highly favorable or pseudoirreversibleadsorption, with two critical Langmuir constants (KLN1and KLN2) as the demarcation point. The feasibility of the method is demonstratedby analyzing 14 adsorption systems. The graphical method is effectiveand intuitional, and can be used for the favorable evaluation of anyLangmuir isotherms. This method shows the advantage that the parameter KLNdoes not depend on the initial adsorbate concentration (co) over RLmethod. [ABSTRACT FROM AUTHOR]

We present an approach for quantitative trait locus (QTL) mapping, termed as 'lineage-specific QTL mapping', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops the idea of bivariate polar plots as a method for source detection and characterisation. Bivariate polar plots provide a graphical method for showing the joint wind speed, wind direction dependence of air pollutant concentrations. Bivariate polar plots provide an effective graphical means of discriminating different source types and characteristics. In the current work we apply k-means clustering techniques directly to bivariate polar plots to identify and group similar features. The technique is analogous to clustering applied to back trajectories at the regional scale. When applied to data from a monitoring site with high source complexity it is shown that the technique is able to identify important clusters in ambient monitoring data that additional analysis shows to exhibit different source characteristics. Importantly, this paper links identified clusters to known emission characteristics to confirm the inferences made in the analysis. The approaches developed should have wide application to the analysis of air pollution monitoring data and have been made freely available as part of the openair R package. [Copyright &y& Elsevier]

The problem of pumps connected in parallel can be easily solved by means of graphical method, but it becomes very time consuming when dealing with multiple scenarios. An analytical approach offers the possibility of implementing a software program that can significantly reduce this time and also adds further features. The mathematical algorithm used is dealing with a nonlinear equitation system and with polynomial fitting functions. A very special issue that is addressed in this paper is about the errors given by the very small values of flow rates. Since the algorithms assume that every physical measure is expressed in SI units, then the unitless values of flow rates are at least 10-3 magnitude order compared to other values (pump head for example). This in turn leads to very poor fitting polynomials and the end results are far from the truth. The key for solving this particular issue resides in constructing the inverse functions of H(Q). Once the algorithms were sort out, they were implemented in LabVIEW in order to create a software application. This final product offers both accuracy of the calculations and user friendly interface. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon–nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the -box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon–nucleon potential, are discussed in detail, and the results of numerical applications for the -shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on the -box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations. [Copyright &y& Elsevier]

In terms of its soluble precursors, the coagulation proteome varies quantitatively among apparently healthy individuals. The significance of this variability remains obscure, in part because it is the backdrop against which the hemostatic consequences of more dramatic composition differences are studied. In this study we have defined the consequences of normal range variation of components of the coagulation proteome by using a mechanism-based computational approach that translates coagulation factor concentration data into a representation of an individual's thrombin generation potential. A novel graphical method is used to integrate standard measures that characterize thrombin generation in both empirical and computational models (e.g max rate, max level, total thrombin, time to 2 nM thrombin ("clot time")) to visualize how normal range variation in coagulation factors results in unique thrombin generation phenotypes. Unique ensembles of the 8 coagulation factors encompassing the limits of normal range variation were used as initial conditions for the computational modeling, each ensemble representing "an individual" in a theoretical healthy population. These "individuals" with unremarkable proteome composition was then compared to actual normal and "abnormal" individuals, i.e. factor ensembles measured in apparently healthy individuals, actual coagulopathic individuals or artificially constructed factor ensembles representing individuals with specific factor deficiencies. A sensitivity analysis was performed to rank either individual factors or all possible pairs of factors in terms of their contribution to the overall distribution of thrombin generation phenotypes. Key findings of these analyses include: normal range variation of coagulation factors yields thrombin generation phenotypes indistinguishable from individuals with some, but not all, coagulopathies examined; coordinate variation of certain pairs of factors within their normal ranges disproportionately results in extreme thrombin generation phenotypes, implying that measurement of a smaller set of factors may be sufficient to identify individuals with aberrant thrombin generation potential despite normal coagulation proteome composition. [ABSTRACT FROM AUTHOR]

This study presents a simple approach to estimate the capacity of combined heat and power (CHP) units suitable for installation in high heat-to-power ratio (HPR) buildings when excess electricity cannot be sold back to the grid. The two different methods used in this approach, a graphical method and a simple equation, are capable of predicting the optimum capacity to within 7% and 15%, respectively, of the methods presented in previous studies. In particular, the simple equation has the advantage of selecting the optimum capacity using the base and peak of the demand power load. The two easy-to-use methods can be used with any building, region, and energy-price structure that satisfies the conditions considered in this study, and will be of great use to future CHP owners. [Copyright &y& Elsevier]

Abstract: Competition theory has developed separately for direct competition and for exploitative competition. However, the combined effects of the two types of competition on species coexistence remain unclear. To examine how intraspecific and interspecific direct competition contributes to the coexistence of species competing for a single resource, we constructed a chemostat-type resource competition model. With general functions for intraspecific and interspecific direct competition, we derived necessary and sufficient conditions (except for a critical case that rarely occurs in a biological sense) that determine the number of stably coexisting species. From these conditions, we found that the number of coexisting species is determined just by the invasibility of each species into subcommunities with a smaller number of species. In addition, using a combination of rigorous mathematical theory and a simple graphical method, we can demonstrate how the stronger intraspecific direct competition facilitates species invasion, leading to a larger number of coexisting species. [ABSTRACT FROM AUTHOR]

Quantitative analysis of solid-state processes from isothermal microcalorimetric data is straightforward if data for the total process have been recorded and problematic (in the more likely case) when they have not. Data are usually plotted as a function of fraction reacted (α); for calorimetric data, this requires knowledge of the total heat change (Q) upon completion of the process. Determination of Qis difficult in cases where the process is fast (initial data missing) or slow (final data missing). Here we introduce several mathematical methods that allow the direct calculation of Qby selection of data points when only partial data are present, based on analysis with the Pérez-Maqueda model. All methods in addition allow direct determination of the reaction mechanism descriptors mand nand from this the rate constant, k. The validity of the methods is tested with the use of simulated calorimetric data, and we introduce a graphical method for generating solid-state power−time data. The methods are then applied to the crystallization of indomethacin from a glass. All methods correctly recovered the total reaction enthalpy (16.6 J) and suggested that the crystallization followed an Avrami model. The rate constants for crystallization were determined to be 3.98 × 10−6, 4.13 × 10−6, and 3.98 × 10−6s−1with methods 1, 2, and 3, respectively. [ABSTRACT FROM AUTHOR]

Abstract: Malalignment may contribute to early prosthesis failure through point loading and premature polyethylene wear. Femoral resection requires for distal planar resection contingent upon correct rotation and coronal alignment. Using a standard model, we have examined the influence of differing femoral entry points and rotations upon final femoral component positioning. A graphical method and navigation system independently quantified the individual and combined impact of these variables, in 3 planes. Nine permutations were assessed with reference to neutral rotation and a central entry point. The graphical results were corroborated by the navigation analyses. We found that external rotation and a superolateral entry point introduced the greatest error in final component positioning. We have identified a safe envelope for femoral rod positioning and recommend that the rotational alignment is determined before distal bone resection. [ABSTRACT FROM AUTHOR]

An alternative graphical method, called the SSR plot, is proposed for use with a multiple regression model. The new method uses the fact that the sum of squares for regression (SSR) of two explanatory variables can be partitioned into the SSR of one variable and the increment in SSR due to the addition of the second variable. The SSR plot represents each explanatory variable as a vector in a half circle. Our proposed SSR plot explains that the explanatory variables corresponding to the vectors located closer to the horizontal axis have stronger effects on the response variable. Furthermore, for a regression model with two explanatory variables, the magnitude of the angle between two vectors can be used to identify suppression. [ABSTRACT FROM AUTHOR]

Abstract: The Pareto-positive stable (PPS) distribution is introduced as a new model for describing city size data in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data, where zero and unimodality are possible, and the classical Pareto and Zipf distributions are included as a particular case. Expressions for the shape, moments and other descriptive probabilistic measures are given. Estimation methods are discussed and a simple graphical method for studying the adequacy of the data to model is given. Finally, we consider city size data for Spain for several different years. The new distribution is compared with three classical models: Pareto, lognormal and Tsallis distributions. In all the data sets considered, the PPS distribution outperforms the fits of these three previous distributions. [Copyright &y& Elsevier]

Abstract: Reverse osmosis (RO) is increasingly used as a separation technique in chemical and environmental engineering for the removal of organics and organic pollutants present in waste water. Treatment of organics by RO is dependent on many factors and hence developing a viable RO system involves extensive pilot-plant studies. The removal of an organic compound, namely dimethyl phenol, using a polyamide membrane was investigated in this study. Experiments were conducted on a laboratory-scale spiral-wound RO module. The permeate concentrations and rejection coefficient values were measured for various transmembrane pressures and feed concentrations. A maximum rejection of 97% was observed. A mathematical model was developed for the RO module assuming a solution–diffusion mechanism for solute and solvent transport through the membrane and considering the concentration and pressure to be uniform on both permeate and retentate sides. The model has four parameters. A graphical method for estimating the model parameters was proposed. The model and the estimated parameter values were validated with the experimental data. The model was able to predict the permeate concentration within an error of 19% and rejection within 2% error. [Copyright &y& Elsevier]

Regression diagnostics and lack-of-fit tests mainly focus on linear--linear regression models. When the design points are distributed on the circumference of a circle, difficulties arise as there is no natural starting point or origin. Most classical lack-of-fit tests require an arbitrarily chosen origin, but different choices may result in different conclusions. We propose a graphical diagnostic tool and a closely related lack-of-fit test, which does not require a natural starting point. The method is based on regional residuals which are defined on arcs of the circle. The graphical method formally locates and visualizes subsets of poorly fitting observations on the circle. A data example from the food technology is used to point out the before-mentioned problems with conventional lack-of-fit tests and to illustrate the strength of the methodology based on regional residuals in detecting and localizing departures from the no-effect hypothesis. A small simulation study shows a good performance of the regional residual test in case of both global and local deviations from the null model. Finally, the ideas are extended to the case of more than one predictor variable. [ABSTRACT FROM AUTHOR]

Based on graphical method, this paper proposed the necessary condition of zero liquid discharge (ZLD) and optimized the corresponding regenerated water flowrate and regeneration concentration for single contaminant water system with fixed mass load. As far as the water system without water loss is concerned, ZLD can be accomplished when the post-regeneration concentration is not higher than the minimum limiting inlet concentration of all the operations. Moreover, considering the water system with water loss, the formulations for calculating the optimal targets (the optimal regenerated water flowrate and the optimal regeneration concentration) for ZLD are deduced. The maximum post-regeneration concentration for ZLD is defined. If the post-regeneration concentration is not higher than it, ZLD is feasible. The optimal zero discharge water network is constructed with a given post-regeneration concentration. [ABSTRACT FROM AUTHOR]

The article discusses the mathematical solutions to Jug problem in the secondary mathematics education in the U.S. The problem is classified into two types: classic Jug problem and modified Jug problem. According to the author, Jug problems can be analyzed through the use of algebraic representation and algebraic counting argument, as well as graphical method. He concludes that the solvability of a Jug problem depends on the number of jugs needed to create is multiple of the greatest common divisor of the jug sizes.

A random effects model using two levels of hierarchical nesting has been applied to the calculation of a likelihood ratio as a solution to the problem of comparison between two sets of replicated multivariate continuous observations where it is unknown whether the sets of measurements shared a common origin. Replicate measurements from a population of such measurements allow the calculation of both within-group and between-group variances/covariances. The within-group distribution has been modelled assuming a Normal distribution, and the between-group distribution has been modelled using a kernel density estimation procedure. A graphical method of estimating the dependency structure among the variables has been used to reduce this highly multivariate problem to several problems of lower dimension. The approach was tested using a database comprising measurements of eight major elements from each of four fragments from each of 200 glass objects and found to perform well compared with previous approaches, achieving a 15.2% false-positive rate, and a 5.5% false-negative rate. The modelling was then applied to two examples of casework in which glass found at the scene of the criminal activity has been compared with that found in association with a suspect. [ABSTRACT FROM AUTHOR]

In digitally controlled dc-dc converters with a single voltage feedback loop, the two quantizers, namely the analog-to-digital (A/D) converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of dc solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. Based on the generalized describing function method, the amplitude and offset-dependent gain model of a quantizer is applied to derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with AID, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical model of iontophoretic transdermal drug delivery was applied to study the effects of physical parameters on the cumulative amount of amitriptyline HCl collected. A graphical method, based on an analytical solution of the system, was first used to estimate the drug diffusion coefficient in the membrane and its surface concentration in the absence of an electric potential difference. These initial values were improved by using an orthogonal collocation-based non-linear regression routine written in Mathematica (Wolfram Research Inc.). Assuming that the diffusion coefficient did not change, the surface concentration of the drug, following transdermal iontophoresis, was evaluated by a similar technique. Two case studies are presented. The first one, taken from the literature, verifies the validity of the procedure. The second case study is based on laboratory experiments using transport amitriptyline HCl across cadaver skin. Excellent agreement was observed between experimental and predicted values. The results support previous findings that the increase in the iontophoretic transdermal delivery of some drugs is mainly due to a rise in the surface concentration of the drug. [Copyright &y& Elsevier]

The problem of gradient focusing for concentrating trace analytes is considered. Variation of buffer viscosity, conductivity, and possibly also the ζ-potential results in a focusing point where the electrophoretic velocity is balanced by the electroosmotic flow (EOF) and where the sample concentrates. The axial inhomogeneity also results in an induced pressure gradient that alters the EOF profile and therefore causes Taylor dispersion. The coupled hydrodynamics and transport problem leading to the achievement of a steady state is studied in the context of the lubrication approximation: all variations in the axial direction take place over a length scale very much larger than the characteristic channel width. A single length scale σm and a single time scale τ is found to completely determine the dynamics of the evolution close to the focusing point. Using appropriate scaled variables, the time evolution of the concentration profile near equilibrium can be described by an inhomogeneous advection diffusion equation that is free of all parameters. Explicit formulas are deduced for the location of the peak centroid and its width as a function of time. A simple graphical method is proposed for optimizing the performance of the system when some tunable external parameters are available. [ABSTRACT FROM AUTHOR]

Infectious diseases present ecological and public health challenges that can be addressed with mathematical models. Certain pathogens, however, including the emerging West Nile virus (WN) in North America, exhibit a complex seasonal ecology that is not readily analysed with standard epidemiological methods. We develop a single-season susceptible-infectious-removed (SIR) model of WN cross-infection between birds and mosquitoes, incorporating specific features unique to WN ecology. We obtain the disease reproduction number, R0, and show that mosquito control decreases, but bird control increases, the chance of an outbreak. We provide a simple new analytical and graphical method for determining, from standard public health indicators, necessary mosquito control levels. We extend this method to a seasonally variable mosquito population and outline a multi-year model framework. The model's numerical simulations predict disease levels that are consistent with independent data. [ABSTRACT FROM AUTHOR]

Several studies have shown cycles in the vote for political parties in American presidential elections, raising the question of whether cycles are unique to two-party systems. This study extends the investigation of cycles to parliamentary elections in several countries that have multiple political parties: Japan, Germany, Norway, and Canada. Phase-space analysis, a graphical method, is used to show that these countries have a variety of cyclic voting patterns in the distribution of votes among their political parties. Voting cycles may be associated with significant changes in the political party system and with stability of the government. Voting in presidential elections in Alabama is shown to have some characteristics of chaotic change, which is an extreme form of cyclic behavior. The possibility of chaos in voting behavior raises important research issues. [ABSTRACT FROM AUTHOR]

The paper describes a simple mathematical model of the behaviour of buses, on a relatively frequent service, after one has arrived at a stop at a time different from that scheduled. The model is similar to that used in some earlier papers on the pairing of buses, but derives a different objective function. Results are presented in terms of parameters relating to the scheduled headway (h) and the size of the initial deviation from it (hd), the usual time spent by a bus at a stop, and the ratio (k) of the passenger arrival rate to the boarding rate. A graphical method was employed to find P, the number of the stop at which the first two buses form a pair. For the typical values of parameters used the relationship P = 1/6dk was deduced which, although no generality is claimed, can be used to set operational limits so that the bunching of buses does not occur. Limitations of the model are discussed. [ABSTRACT FROM AUTHOR]

Focuses on the use of spin orbit coupling in understanding electronic states and the electronic structure of atoms. Description of the electronic states using boxes-and-arrows graphical method; Application of the method to LS-coupling scheme.