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When the particle-to-target radius ratio R and the inverse Peclet number 1/P are small, particle capture by interception and diffusion by cylinders at low Reynolds numbers may be described ...

In this study, nine non linear growth curve models were used to determine the goodness of fit by the body weight measurements of the total number of 178 partridges(Alectoris chukar), 93 females, and 85 males, respectively. The R2(coefficients of determination) values for the total partridges, females and males in Brody, Gompertz, Logistic, von Bertalanffy, asymptote regression,exponential, Monomolecular, Richards and Weibull-type were 0.985, 0.980 and 0.984, 0.997, 0.998 and 0.998, 0.996, 0.999 and 0.999, 0.995, 0.995 and 0.996, 0.985, 0.980 and 0.984, 0.891, 0.871 and 0.892, 0.985, 0.980 and 0.984, 0.997, 0.999 and 0.999, 0.997, 0.999 and 0.999, respectively. The R2 values for Gompertz, Logistic, von Bertalanffy, Richards and Weibull-type were >0.99, while the exponential (

A variable updater based on the modified gradient projection (MGP) method is proposed for topology optimization. Both static and dynamic problems are considered and formulated using the solid isotropic microstructure (or material) with penalty method. Based on Rosen's gradient projection method, the search direction is obtained by projecting the gradient vector (sensitivity) to the volume constraint plane. Fixed step length is used to guarantee a high convergence rate, and then the iterative solutions are revised to satisfy the upper and lower boundaries. A gradual projecting strategy is suggested to reduce grey elements. Static and dynamic numerical examples are tested to verify the characteristics of the MGP method. The results show that compared with the optimality criterion method and method of moving asymptotes, the convergence rate and computational efficiency of the MGP method are much higher, while the boundaries of the optimal structures are much clearer and the objective function value i...

The study investigated learners’ mathematical discourse on the hyperbola from a commognitive perspective, and focused on algebraic, graphic, and numeric representations of the hyperbola. Task-based...

A data set of ventral-aspect insect radar cross-sections (RCSs) and polarization patterns, measured at X band (9.4 GHz, linear polarization) in laboratory rigs, has been collated from a number of sources. The data have been analysed to identify relationships between RCS parameters (one representing size and two the polarization-pattern shape) and the insects’ masses and morphological dimensions and forms. An improved mass-estimation relationship, with appropriate asymptotes for very small and very large insects, is presented. This relationship draws only on the RCS size parameter and it is shown that incorporating one or both of the RCS shape parameters provides little additional benefit. Small insects have polarization-pattern shapes that fall within a relatively limited region of the range of parameter values allowed by electromagnetic scattering theory. Larger insects have shapes that extend beyond this region, following a broad trajectory as size and mass increases; at masses above ~0.6 g, the pattern becomes ‘perpendicular’, with maxima when the E-field is orthogonal to the body axis rather than parallel to it. RCS shape can be used to infer morphological form for small insects (

We study some spectral properties of the solutions to generalized thermoelastic systems under Lord–Shulman, Green–Lindsay, and Green–Naghdi of type-II models. First, we prove that the linear operator of each model has compact resolvent and generates a C0−semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum-determined growth condition holds. Therefore, if the imaginary axis is not an asymptote of the spectrum, we prove that the energy of each model decays exponentially to a rate determined explicitly by the physical parameters. Finally, some simulations are given for each model to support our results.

We consider the symmetric solutions to the Young–Laplace equation, and its extensions past vertical points. We provide a classification of all symmetric solutions using certain families of parameters. This classification produces a unified approach to fluid interfaces in capillary tubes, sessile and pendent drops, liquid bridges, as well as exterior and annular capillary surfaces. The generating curves for symmetric solutions have asymptotes for large arclengths, and the behavior of these asymptotes is analyzed.

Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points.

To keep the spatially averaged temperature and thermal stress of gas turbine blades and guide vanes within a permissible level, the present research concentrates on the optimization of the internal cooling passages in a guide vane. The main purpose is to search for the most optimal sizes, distributions, and shapes of internal cooling channels located in a guide vane. Cylindrical cooling passages and newly built passages shaped by Bezier curves are both considered in this investigation. In order to maintain the shapes of the cooling channels within the scale of the vane profile, a new technique is suggested to discretize the vane into the components, and then the outline of the passages is built based on the components. The optimization of sizes, locations, and shapes of the cooling passages is solved as a single-objective problem using a gradient-based optimization algorithm, i.e., the globally convergent method of moving asymptotes (GCMMA). The optimized result displays a substantial reduction in...

In this paper we consider the problem of modelling the stage–discharge relationship by curve fitting using the least squares method. Our basic idea is to present new models which are more flexible and have the ability to model phenomena with increasing or unchanging carrying capacity. The new models present a generalization of some sigmoid smooth models commonly used in practice. They are characterized by a curvilinear asymptote and may have several inflection points. The use of these models on six real datasets collected from the US Geological Survey’s website proves their performance and their ability to model hydrological phenomena. Editor D. Koutsoyiannis; Associate editor S. Yue

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.

In this work we consider a class of generalized piecewise smooth maps, proposed in the study of engineering models. It is a class of one-dimensional discontinuous maps, with a linear branch and a nonlinear one, characterized by a power function with a term x−γ and a vertical asymptote. The bifurcation structures occurring in the family of maps are classified according to the invertibility or non-invertibility of the map, depending on the parameters characterizing the two branches. When the map is non-invertible we prove the persistence of chaos. In particular, the existence of robust unbounded chaotic attractors. The parameter space is characterized by intermingled regions of attracting cycles born by smooth fold bifurcations, issuing from codimension-two bifurcation points. The main result is related to the description of the relationship between two types of bifurcations, smooth fold bifurcations and border collision bifurcations (BCBs). We describe the particular role of codimension-two bifurcation poi...

Large-span prestressed concrete bridges are sensitive to concrete creep which has a profound effect on bridge safety and serviceability. In this study, 3D computational simulations based on different concrete creep and shrinkage models are employed to investigate the long-term deformation of a prestressed concrete bridge. An improved rate-type algorithm powered by the continuous spectrum method and exponential algorithm is utilised to enhance the computational accuracy and efficiency. The asymptotic behaviours of the deflection and shortening at the main cantilever tip are captured. Compared to deflection, the asymptotic slope of the shortening curve is more systematically correlated with the asymptotic trend of creep models containing logarithmic time functions and this close correlation can be established at a relatively young age after construction. Thus, it can be used to realistically predict long-term deformation, as well as approximate the governing parameters in the compliance functions. Sensitivity studies based on Latin hypercube sampling are employed to explore the scatter band of the deflection and shortening due to material randomness, prestress fluctuation and environmental variations. Its effect on the correlation between deformation and creep asymptote is comprehensively examined. Furthermore, the influence of individual tendons on the deflection is probed based on the sensitivity investigation.

A simple theoretical model, validated against available numerical and experimental data in the literature, is presented to predict the effects of crosswind on the performance of natural draft dry cooling towers. The intersection of asymptote method, along with scale analysis, is used to find a closed-form solution for the airflow rate at the tower exit for given crosswind speeds. The total heat rejected under a windy condition is then calculated based on the air mass flow rate at the tower exit. This theoretical model allows for parametric studies and can generate accurate data. Interestingly, the model results, expected to be accurate within an order of magnitude, are more accurate than anticipated when compared to available experimental and numerical data in the literature. In fact, the maximum relative error is observed to be 15% when current theoretical predictions are compared to available experimental data. The results of this study will be useful for future work on the development of air-cooled con...

This article presents a mathematical model for sizing optimization of undamped trusses subjected to dynamic loading leading to fatigue. The combined effect of static and dynamic loading, at steady state, is considered. An optimization model, whose objective is the maximization of the safety factor of these trusses, is developed. A new quantity (equivalent fatigue strain energy) combining the effects of static and dynamic stresses is presented. This quantity is used as a global measure of the proximity of fatigue failure. Therefore, the equivalent fatigue strain energy is minimized, and this seems to give a good value for the maximal equivalent static stress. This assumption is verified through two simple examples. The method of moving asymptotes is used in the optimization of trusses. The applicability of the proposed approach is demonstrated through two numerical examples; a 10-bar truss with different loading cases and a helicopter tail subjected to dynamic loading.

We present a smooth function that can be used as regression curve for modeling growth phenomena requiring an increasing curvilinear concave asymptote. This model is obtained as the product of a concave asymptotic curve and the exponential model. In addition to its increasing character with a curvilinear asymptote, including horizontal or linear increasing asymptote, the resulting model provides curves with a single inflection point. Numerical examples are presented.

A new algorithm is proposed for topology optimization based on a fluid dynamics analogy. It possesses characteristics similar to most well-known methods, such as the Evolutionary Structural Optimization (ESO)/Bidirectional Evolutionary Structural Optimization (BESO) method due to Xie and Steven (1993, “A Simple Evolutionary Procedure for Structural Optimisation.” Computers and Structures 49 (5): 885–896.), which works with discrete values, and the Solid Isotropic Material with Penalization (SIMP) method due to Bendsoe (1989, “Optimal Shape Design as aMaterial Distribution Problem.” Structural Optimization 1 (4): 193–202.) and Zhou and Rozvany (1991, “The COCAlgorithm–Part II: Topological, Geometry and Generalized Shape Optimization.” Computer Methods in Applied Mechanics and Engineering 89 (1–3): 309–336.) (using Optimality Criterion (OC) or Method of Moving Asymptotes (MMA)), which works with intermediate values, as it is able to work both with discrete and intermediate densities, but always yields a sol...

Binary response models are often applied in dose–response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the ‘separated data’ issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose–response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.

Tree height–diameter relationship can be used as an important input component in forest growth and yield models, and description of stand dynamics. Five nonlinear growth functions were fitted to tree height–diameter data of a 21-year-old Gmelina arborea plantation in Ibadan, Nigeria. The data consisted of three sets obtained in 2004, 2008 and 2011 for total tree height and diameter at breast height (DBH). According to the model statistics, the five growth functions fitted the data equally well, but resulted in different asymptote estimates. Modified exponential fit was observed to give the best fit for the three data sets based on least square error, coefficient of determination and significance. The predicted values follow the same nonlinear pattern and formed close to the line of best fit without much outlier. The result of this study revealed that the ability of DBH in determining height is not strong enough based on the model's goodness of fit and the model's ability for predictive purposes. Hence, mo...

The method of testing pour points of pure substances and multicomponent hydrocarbon mixtures basing on the analyses of the path lengths of passing of equal volumes of substances along the tracking grooves on the refrigerated sloping metallic panel has been presented. Repeatability of the method makes up ±0.3°C, which surpasses the repeatability of testing pour points by the known international standards (ASTM D5853-95, ASTM D97-09, ISO 3016, GOST 20287-91) 5–7 times. Operability of the method has been shown on the example of testing pour points of hexadecane, octadecane, and paraffinic oil. It has been established that experimental curve plotted in coordinates (length of sample passing path − temperature), can be presented by the sum of two terms, the first of which is described by hyperbola with asymptote at temperature, equal to the pour point of the sample, which actually corresponds to the flow regime, and the second term is described by the parabola of variable exponent and the contribution to drop r...

Following the extended two-material density penalization scheme, a stress-based topology optimization method for the layout design of prestressed concrete structures is proposed. The Drucker–Prager yield criterion is used to predict the asymmetrical strength failure of concrete. The prestress is considered by making a reasonable assumption on the prestressing orientation in each element and adding an additional load vector to the structural equilibrium function. The proposed optimization model is thus formulated as to minimize the reinforcement material volume under Drucker–Prager yield constraints on elemental concrete local stresses. In order to give a reasonable definition of concrete local stress and prevent the stress singularity phenomenon, the local stress interpolation function and the ϵ -relaxation technique are adopted. The topology optimization problem is solved using the method of moving asymptotes combined with an active set strategy. Numerical examples are given to show the efficiency of the...

Three types of effects sizes for DIF are described in this exposition: log of the odds-ratio (differences in log-odds), differences in probability-correct, and proportion of variance accounted for. Using these indices involves conceptualizing the degree of DIF in different ways. This integrative review discusses how these measures are impacted in different ways by item difficulty, item discrimination, and item lower asymptote. For example, for a fixed discrimination, the difference in probabilities decreases as the difference between the item difficulty and the mean ability increases. Under the same conditions, the log of the odds-ratio remains constant if the lower asymptote is zero. A non-zero lower asymptote decreases the absolute value of the probability difference symmetrically for easy and hard items, but it decreases the absolute value of the log-odds difference much more for difficult items. Thus, one cannot set a criterion for defining a large effect size in one metric and find a corresponding cr...

Structures with low thermal directional expansion and high stiffness have wide applications where dimensional stability is required when subject to large temperature change or thermal gradient, e.g. the supporting structure of a space camera and many other types of aero-spatial equipment. This article develops a new bi-objective structural topology optimization formulation which aims at design of structures composed of two materials with differing Young's modulus and thermal expansion coefficients to achieve low thermal directional expansion and high stiffness. A three-phase topology optimization technique is adopted to optimize the structures. Black and white (0/1) designs are obtained by using the volume-preserving Heaviside filter and GCMMA method (globally convergent version of the method of moving asymptotes). Three structural examples are shown to illustrate how the structural supports, temperature variation and the weight factors affect the material distribution and the objectives.

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

A modified version of the method of moving asymptotes is proposed based on the spectral parameter used in the updating of a key parameter of the model. The second-order information present in the spectral parameter is thus included in the model functions that define the rational approximations. Numerical experiments indicate that the idea is promising in the sense that the cost-benefit of computing the spectral parameter is worth it for reducing the total effort of the algorithm when compared with the original version.

An empirical correlation for free convection in a double-glazed window with an enclosed Venetian blind is developed. The correlation makes use of an existing model from the literature (called the reduced slat length model) for the pure conduction asymptote. Published experimental data for night-time conditions (i.e. with no solar irradiation) are used to characterize the average Nusselt number at higher Rayleigh numbers. The asymptote blending method of Churchill and Usagi is used to combine these results into an empirical correlation that spans the full range of variables for which experimental data are currently available. The correlation is applicable to all common fill gases, and predicts the effects of Rayleigh number, slat angle and blind-to-enclosure width ratio on the average Nusselt number. The use of the correlation to predict the U-value of this complex fenestration is demonstrated. The results compare well with published measurements.

We present a teaching approach to uniform continuity on unbounded intervals which, hopefully, may help to meet the following pedagogical objectives:To provide students with efficient and simple criteria to decide whether a continuous function is also uniformly continuous; To provide students with skill to recognize graphically significant classes of both uniformly and nonuniformly continuous functions. Assembling some well-known facts and refining the resulting statement, we establish a useful asymptotic coincidence test for the uniform continuity on unbounded intervals. That test is the core of the present note and yields an easily applicable technique. In particular, one of its immediate consequences is the elementary fact that continuity and existence of horizontal or oblique asymptotes imply uniform continuity.

The competition–density (C–D) effect for non-self-thinning Populus deltoides and Populus × euramericana plantations from 3 to 9 years was analyzed using the reciprocal equation of the C–D effect. The C–D effect was well described by the reciprocal equation, and with the progress of time the C–D curve, on logarithmic coordinates, of the P. × euramericana plantations shifted upward faster than that of the P. deltoides plantations. With increasing physical time t, the biological time τ, i.e. the integral from zero to t of the coefficient of growth λ(t) in the general logistic curve with respect to t, increased rapidly during early growth stages and the increases in τ gradually became slow during later growth stages. This trend was more evident in the P. deltoides plantations than in the P. × euramericana plantations. The coefficients A and B included in the reciprocal equation were calculated at each growth stage. With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level. On the other hand, the coefficient B, the reciprocal of which means the asymptote of mean stem volume at a given growth stage, decreased exponentially and tended to be close to zero with increasing τ. The λ(t) decreased with increasing stand age, whereas the final yield Y(t) defined as W(t) ρ, where W(t) is the asymptote of w in the general logistic growth curve, increased gradually with increasing stand age. The differences in coefficients A, B, and λ(t) between the two species were reported.

International audience; Standard parametric specifications of Cumulative Prospect theory (CPT) can explain why agents bet on longshots at actuarially unfair odds. However the standard specification of CPT cannot explain why people might bet on more favored outcomes, where by construction the greatest volume of money is bet. This paper outlines a parametric specification than can consistently explain gambling over all outcomes. In particular we assume that the value function is bounded from above and below and that the degree of loss aversion experienced by the agent is smaller for small-stake gambles (as a proportion of wealth) than usually assumed in CPT. There are a number of new implications of this specification. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability for a given stake will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum.

No one bird survey technique is perfect. Either the assumptions made by a technique are difficult to meet in the field, or there are biases due to the observer, the birds themselves, the landscape, or the nature of the habitat. These include survey effort, time of day, time of year, edge effects, vegetation structure, and variation in detectability functions. Biases in methodologies are only a problem if they are systematic with respect to the variables that are being tested. If, however, biases are randomly distributed with respect to the variables under consideration, they cannot affect a positive result, although a negative result may occur because of the noise they may introduce into the analysis. Therefore, it is crucial to determine and minimise biases in any study. We use extensive line transect census data from a study of the effects of habitat fragmentation on forest birds in Nigeria to illustrate the range of possible biases and their effects, and then how these may be accounted for. Asymptote a...

In this paper we study the Riesz basis property of serially connected Timoshenko beams with joint and boundary feedback controls. Suppose that the left end of the whole beam is clamped and the right end is free. At intermediate nodes, the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous. The collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system. We prove that the operator determined by the closed loop system has compact resolvent and generates a C 0 semigroup in an appropriate Hilbert space. We also show that there is a sequence of the generalized eigenvectors of the operator that forms a Riesz basis with parentheses. Hence the spectrum determined growth condition holds. Therefore if the imaginary axis is not an asymptote of the spectrum, then the closed loop system is exponentially stable. Finally, we give a conclusion remark to explain that our result can be applied not ...

This paper derives simple computer-aid design (CAD) formulas of the components of the equivalent circuit of square spiral inductors on a microstrip substrate. The circuit components are the main inductor, its capacitors to ground, and resistance. The formulas are simple synthetic asymptotes constructed from duality and analytical moment method, and give clear physical insights. Compared with IE3D, a commercial software by Zeland, the errors of |S 11| and |S 21| are generally less than 2%.

A hybrid algorithm for solving structural topology optimization problems is presented. This hybrid algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This hybrid algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value during the optimization. This hybrid algorithm has improved calculation efficiency and accelerated convergence when compared with the MMA or MGCMMA algorithm, which is demonstrated with three examples.

This paper introduces a new method for curve smoothing which is specific for isobathymetric line generalization. Isobaths are modeled with B-spline curves that can maintain the smooth feature of the curves. Smoothing is performed by keeping the curve points always on the deepest side of the original curve so that the result is consistent with the safety constraint. It is done by using a snake model in which the constraints and the smoothness are expressed via external and internal energies defined from the curve derivatives. The advantage of the model is that the deformation is done by minimizing the system energy and, by tuning the parameters during the process, convergence towards a valid solution is ensured. Results from real case studies are presented.

In this article, the problem of the optimal design of simply supported columns under loadings controlled by displacements is investigated. It seeks a cross-sectional area, varying along the axis of the column, which leads to the maximal axial displacement caused by compression before the structure buckles. The uni-modal and bi-modal problems are considered. The optimal solutions for different constraints of minimal and maximal cross-sectional area and various elastic foundations are presented in this article. The results are obtained by solving an analytical formulation of the optimization problem and by using numerical optimization methods, namely the method of moving asymptotes and the simulated annealing method.

The poly-Weibull model is a general family which arise on competing risk scenarios when there is no direct information about which risk was responsible for the failure. Its advantage over the single-Weibull model is to allow not only constant, increasing or decreasing hazard curves with zero or non zero asymptotes, but also nonmonotones ones, including bathtub-shaped. In this paper we consider the non-identifiability problem, which arises when the shape parameters of a poly-Weibull model are close. Theoretical calculation of the information and correlation matrixes are used to assess when a poly-Weibull model is likely to be feasible. From the practical point of view, a graphical method, based on the total-time-on-test plot and its simulated envelop, is considered for detecting when a poly-Weibull model is likely to be identifiable. We also provide a general framework for constructing hypothesis tests for non-identifiability by using parametric bootstrap-based methods. We set up a simulation stud...

Data from vertebrate microsites are important in paleoecological reconstructions, but their usefulness has been limited because of undemonstrated repeatability of sampling data and the time- and labor-intensive nature of their retrieval. Re-examination of a previously studied vertebrate microsite revealed that repeatable diversity and abundance data are obtainable using a controlled sorting methodology. It was found that a curve fitted to a plot of empirical diversity vs. sampling frequency will tend toward an asymptote as sampling frequency increases, indicating that the likelihood of discovery of new taxa having a major impact upon a paleoecological interpretation is diminishing. Rarefaction analysis was applied to the data obtained, and the rarefaction curve provided support for the behavior of the empirical diversity curve. It was also found that as sampling frequency increases, rank orders of relative abundance stabilize among the most common taxa in the sample, indicating that the likelihoo...

This study presents an asymptotic matching method, the logarithmic matching. It states that for a complicated nonlinear problem or an experimental curve, if one can find two asymptotes, in extreme ...

The coalescence-redispersion (CRD) model is examined in the fast chemistry limit for the single bimolecular reaction A + B → R and the series parallel reactions A + B → R; B + R → S occurring in a plug flow reactor with unmixed feed streams. For the single bimolecular reaction it is shown that in this limit the CRD model is asymptotically equivalent to the 3E fast closure as t → 0. For the series parallel reactions the CRD model predictions tend to be bracketed by the 3E slow and fast closure formulations. Representative results are presented for the variance decay of the individual reactants, and it is seen that even in the fast reaction limit where mixing is controlling, the shape of the feed stream PDFs has negligible influence on the progress of the reaction.

An efficient numerical-analytical approach is developed to calculate spatial mixed-potential Green's functions for sheet currents placed over a cylindrical circular metal rod with a dielectric substrate. The approach is based on a special annihilation technique, which allows performing the Inverse Fourier Transform in a very effective way. This technique includes numerical-analytical extraction and inversion of cases of 'bad behaviour' of the spectral Green's functions, due to slowly decaying asymptotes and poles. As a result the spatial Green's functions are represented in a form in which the contribution of the source singularity and the surface waves is given by separate terms.

This paper derives simple CAD formulas of microstrips, coplanar waveguides (CPW) without and with a backing ground plane. Both analysis and design formulas, in pairs, of the three lines, can be derived from just one technique: the synthetic asymptote. This novel asymptotic technique ensures a maximum error of 4% or less with no limits on the possible parameter values. The technique also shows that a combination of the first two pairs of formulas of the above actually forms the third pair of formulas in a bootstrapping succession. It is possible to get smaller errors than above with formulas including a series of artificial coefficients. This is not done so as to maintain the simplicity of the formulas and to emphasize the insights to the interrelations between the different lines over full ranges of parameter values. Physical insights, such as the microstrip and CPW combining into the CPW with conductor backing, are very helpful in the initial design choices and estimates in an RF circuit. They are lackin...

1. Growth patterns of male ducks from 4 lines (lines A, B, C and D) selected for market weight were analysed and compared to growth patterns of ducks in the respective line 7 generations earlier. Growth curves were analysed using procedures derived from the Weibull sigmoidal function and the linear-linear relative growth rate model and simple allometry. 2. The ducks were fed ad libitum under 24-h lighting throughout the experiment. At weekly intervals from the time of hatch through 70 d of age, 16 ducks from each line were killed to determine body, carcase, breast-muscle, leg and thigh-muscle, and abdominal fat weights. 3. Line A was the heaviest line, followed by line B, line C and line D. However, body weight, carcase weight and breast-muscle weight at 49 d of age were not significantly different between lines A and B. After 7 generations of selection, the breast-muscle yield was increased to >19% and the abdominal fat percent was reduced to

We explore several alternative formal models of working memory capacity limits and of the effect of ageing on these capacity limits. Three models test variations of resource accounts, one assumes a fixed number of free slots in working memory, one is based on decay and processing speed, one attributes capacity limits to interference, and one to crosstalk between associations of content and context representations. The models are evaluated by fitting them to time–accuracy functions of 16 young and 17 old adults working on a numerical memory-updating task under varied memory-load conditions. With increasing complexity (i.e., memory load), both asymptotic accuracy and the rate of approach to the asymptote decreased. Old adults reached lower asymptotes with the more complex tasks, and had generally slower rates. The interference model and the decay model fit the individual time–accuracy functions reasonably well, whereas the other models failed to account for the data. Within the interference model, age effec...

The experimentally-measured pressure-volume relationship for the human intracranial system is a nonlinear ‘S-shaped’ curve with two pressure plateaus, a point of inflection, and a vertical asymptote at high pressures where all capacity for volume compensation is lost. In lumped-parameter mathematical models of the intracranial system, local compliance parameters relate volume adjustments to dynamic changes in pressure differences between adjacent model subunits. This work explores the relationship between the forms used for local model compliances and the calculated global pressure-volume relationship. It is shown that the experimentally-measured global relationship can be recovered using physiologically motivated expressions for the local compliances at the interfaces between the venous-cerebrospinal fluid (CSF) subunits and arterial-CSF subunits in the model. Establishment of a consistent link between local model compliances and the physiological bulk pressure-volume relationship is essential if lumped-...

Genetic variation in the height growth curves was investigated by analyzing data from three clonal trials of sugi (Crytomeria japonica D. Don) in Kyushu. Average height of twelve clones measured at each of five years until 30 years of age were fitted to the Chapman-Richards function with two parameters model. Clonal variation in the two parameters (an upper asymptote and a rate of growth parameter) was statistically significant across the tests, indicating that height growth pattern is under genetic control. The type of growth curve was clearly classified with the two parameters and agreed with the empirical classifications of the growth habit of local varieties. The rate of growth parameter was correlated with total height up to 20 years of age, while the upper asymptote was correlated only with the last ten years’ increment from 21 to 30 years where the clonal repeatability was decreasing. This indicates that a clonal selection for long rotation management system would not be reliable unless the height is measured accurately with more advanced devices or it is adjusted by the current increment of diameter.

The authors demonstrated the empirical relationship between Cohen's chi-square effect size, w, and differential item functioning (DIF), defined as group differences in item response theory (IRT) item difficulty. In Experiment 1, in which the lower asymptote was 0, the authors argued that Cohen's designation of small, medium, and large effects connotes reasonably well for that definition of DIF. In Experiment 2, the lower asymptote of the item response function was raised from 0 to 0.2 and the item discrimination parameter was held to 1.0. Doing so admitted non-crossing nonuniform DIF to the model, violating an underlying assumption of the Mantel–Haenszel procedure that the odds ratio is constant across studied levels of the matching criterion. Smaller difficulty parameter difference resulted, which produced larger effects with an inflation in effect size of about 15%. In Experiment 3, the authors used the 1-parameter logistic model to examine the effect that group differences in the matching crit...

A bulk acoustic wave (BAW) impedance sensor has been applied to rapid determination of in vitro concentrations of cefotaxime sodium. The method based on the growth frequency curve of Proteus Morganii, inhibited by cefotaxime sodium, is continuously monitored by using a BAW impedance sensor. The growth kinetic parameter, e.g. asymptote or maximum frequency shift (AF, Hz), estimated by fitting a modified Gompertz model to the growth frequency curve, is proportional to the logarithm of antibiotic concentration. The proposed method exhibits a favourable response to 0.25 – 20.0 μg mL−1 cefotaxime sodium with a detection limit of 0.03 μg mL−1, and the recoveries range from 97.3 to 107.5% (n=9). The results are in good agreement with those obtained by the conventional disk diffusion test (DDT) method. The effects of temperature and pH on the determination are discussed and in vitro susceptibility to cefotaxime of the genus Proteus has been investigated in detail. On leave from Department of Mathematics,...

In 2 experiments, time-accuracy curves were derived for recall and recognition from episodic memory for both young and older adults. In Experiment 1, time-accuracy functions were estimated for free list recall and list recall cued by rhyme words or semantic associations for 13 young and 13 older participants. In Experiment 2, time-accuracy functions were estimated for recognition of word lists with or without distractor items and with or without articulatory suppression for 29 young and 30 older participants. In both studies, age differences were found in the asymptote (i.e., the maximum level of performance attainable) and in the rate of approach toward the asymptote (i.e., the steepness of the curve). These two parameters were only modestly correlated. In Experiment 2, it was found that 89% of the age-related variance in the rate of approach and 62% of the age-related variance in the asymptote was explained by perceptual speed. The data point at the existence of 2 distinct effects of aging on episodic memory, namely a dynamic effect (growing slower) and an asymptotic effect (growing less accurate). The absence of Age x Condition interactions in the age-related parameters in either experiment points at the rather general nature of both aging effects.

There are several well-known growth models (Monod, Moser, Tessier and Contois) often viewed as no difference except data fitting. With frequency response analysis, it is shown that periodic operation is suitable to differentiate these models. Estimation of system parameters by this method is also discussed. Additionally, the vertical distance between the intersection of two asymptotes and amplitude ratio curve in Bode diagram is found to be always log (√2) for a constant yield factor case.

Two-dimensional weight function theory is extended in this paper so as to compute stress intensity factors for inhomogeneous anisotropic elastic solids with notches and cracks. Elasticity constants have an arbitrary angular dependence around the notch (crack) tip. Particular crack and inhomogeneity geometries are analysed including interface cracks in anisotropic bimaterials. Specimens of finite size and arbitrary geometry, with both forces and dislocations present, are considered. Weight functions for forces and dislocations are treated equally by means of a six-dimensional real form representation. Following the Bueckner concepts of regular and fundamental fields, it is suggested that the fundamental field asymptote should be derived explicitly close to the tip, and then the reciprocity theorem for the evaluation of the stress intensity factors should be applied.