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Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

This paper presents some models of exchange rate with jumps, namely jump diffusion exchange rate models. Jump diffusion models are quite common in computational and theoretical finance. It is known that exchange rates sometimes exhibit jumps during some time periods. Therefore, it is important to take into account the presence of these jumps in exchange rate modeling in general. However, even the simplest jump diffusion model introduces some analytical difficulty in terms of finding a solution to the model. The models we analyze in this paper make use of Approximation Theory in order to come up with closed form solutions to the underlying variables. This approach leads to the branch of differential equations called functional differential equations and more specifically the so-called delay differential equations. Our approach leads to a second order delay differential equation. Though, in principle, these types of functional differential equations can be solved analytically in some cases, the task, in general, is quite enormous. We circumvent this technical difficulty by deriving an approximate solution using a power series expansion of the second order. Therefore, we derive a complete solution to the models and also investigate the model's predictions of the exchange rate. We introduce two jump diffusion models. The first model examines the case where there are jumps with a constant magnitude. The second model considers the case of jumps of different sizes. These are relatively simpler cases to be analyzed. We will present some computational aspects in terms of the difficulty often encountered in estimating these types of models. The difficulty increases for the type of exchange rate models being considered in this paper. Taking advantage of the specification of the models we have estimated the parameters using a two-step M-estimation strategy that combines full information maximum likelihood estimation in the first step and the simulated method of moments in the second step. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets are advancements of the intuitionistic fuzzy sets and overcome their limitations. In this paper, we exploit the concept of full congruence relation of Pythagorean fuzzy sets and define the lower and upper approximations of Pythagorean fuzzy set. Using the concept of approximations of Pythagorean fuzzy set we introduce the concept of rough Pythagorean fuzzy set. [ABSTRACT FROM AUTHOR]

This paper presents a novel arrangement of Routh table array for deriving an approximate model of a higher orderz-domain uncertain system. The demand for this computation is to procure a lower order model which is easy to be exercised in comparison to their original large scale systems. Additionally, the derived model should preserve fewer dynamic characteristic of the comprehensive higher order systems. The mentioned new arrangement is achieved from the arena of different combinations of numerator and denominator polynomials. The combinations are validated by their practice over the conventional example from the literature. This precise blend is then applied to a real-time system for its rational acceptability. Both the models play a significant role in establishing the algorithm. Besides this, the limitation encountered during the foundation course of the arrangement is also taken into consideration. The paper also offers a future scope for fellow researchers. [ABSTRACT FROM AUTHOR]

Nowadays, supplier selection process, a multicriteria decisionmaking problem, has become one of the most indispensable parts for every purchasing sector for the improvement of performances of business operations. Most of the literatures in this field have considered only the opinion of decision-makers. But in fact, each company has its own opinion about the suppliers. The purpose of this paper is to select the best supplier by integrating the opinions of both decision- makers and company's stake holders. In this literature, these opinions are taken as fuzzy soft sets. These two fuzzy soft sets are then integrated by the rough approximation theory. The attributes in this literature are taken in the form of linguistic variable. At the end of this paper, a case study is given to illustrate the proposed method for selecting the best supplier. [ABSTRACT FROM AUTHOR]

The difficulties associated with parameter estimation for phase-type approximations of empirical data distributions in queue modelling are well known. While significant progress has been achieved in improving such approximations, difficulties in parameter estimation still limit the extent to which queue modelling is applied in practice. This paper presents a simplified technique for approximating empirical data in service system simulations, based on the specialised Cox phase-type distribution. When utilised in simulation modelling of a service system, the specialised Cox distribution is shown to provide improved approximations to the combined waiting and service time distribution without the need for complex parameter estimation techniques. This approach should enable much greater flexibility in the application of queue modelling to service systems. [ABSTRACT FROM AUTHOR]

This paper presents an advance of the investigation in progress on the variation of the level of spatial concentration of economic activity and of the per capita income in the regions of the European Union (EU) and its impact on regional disparities. The first part seeks to place the academic debate on the state of affairs; the second part seeks to provide an approximation to the empirical analysis by studying the uneven impact of the economic crisis on the territory of the EU. The third part aims to provide the main conclusions of the study and some considerations of economic policy among which we highlight the proposal of a Regional Potential Index. [ABSTRACT FROM AUTHOR]

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity fl ow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids. [ABSTRACT FROM AUTHOR]

We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is provided by a microarray experiment comparing healthy with sick subjects' expression levels for thousands of genes. This paper concerns the accuracy of summary statistics for the collection of normal variates, such as their empirical cdf or a false discovery rate statistic. It seems like we must estimate an N by N correlation matrix, N the number of cases, but our main result shows that this is not necessary: good accuracy approximations can be based on the root mean square correlation over all N ⋅ ( N − 1)/2 pairs, a quantity often easily estimated. A second result shows that z-values closely follow normal distributions even under nonnull conditions, supporting application of the main theorem. Practical application of the theory is illustrated for a large leukemia microarray study. [ABSTRACT FROM AUTHOR]

Copyright of Hydrological Sciences Journal/Journal des Sciences Hydrologiques is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a discretization technique for particle dynamics equation based on piecewise continuous approximations of the solution. The growth terms are re-solved using a Discontinuous Galerkin approach, and the coagulation by a collocation approach. The method fits in the general framework recently proposed by the author. The discontinuous approximation allows better representations of distributions with sharp peaks. Numerical tests reveal that accurate solutions can be obtained with a very small number of size bins. An efficient software package AeroSolve which implements the proposed algorithms was developed. [ABSTRACT FROM AUTHOR]

In this paper, we have proved the degree of approximation of functions belonging to L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series at x = 0. The aim of this paper is to concentrate on the approximation properties of the functions in L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series associated with the function f. [ABSTRACT FROM AUTHOR]

In this paper, we develop a perturbed reactive-based neighbourhood search algorithm for the expanding constraint multiple-choice knapsack problem. It combines reactive tabu search with some specific neighbourhood search strategies to approximately solve the problem. The tests were conducted on randomly generated instances and executed in comparable benchmark scenarios to those of the literature. The results outperform those of the Cplex solver and demonstrate the high quality of the two approach versions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiphase support vector regression (mp-SVR) technique to approximate a true relationship for the case where the effect of input on output changes abruptly at some break-points. A new formulation for mp-SVR is presented to allow such structural changes in regression function. And then, we present a new hybrid-encoding scheme in genetic algorithms to select the best combination of the kernel functions and to determine both break-points and hyperparameters of mp-SVR. The proposed method has a major advantage over the conventional ones that different kernel functions can be possibly adapted to different regions of the data domain. Computational results in two examples including a real-life data demonstrate its capability in capturing the local characteristics of the data more effectively. Consequently, the mp-SVR has a high potential value in a wide range of applications for function approximations. [ABSTRACT FROM AUTHOR]

A mixture distribution approach to modelling demand during lead time in a continuous-review inventory model is described. Using this approach, both lead time and demand per unit time can follow state-dependent distributions. By using mixtures of truncated exponentials functions to approximate these distributions, mixture distributions that can be easily manipulated in closed form can be constructed as the marginal distributions for lead time and demand per unit time. These are then used to approximate the mixture of compound distributions for demand during lead time. The technique is illustrated by first applying it to a 'normal-gamma' inventory problem, then by modelling a problem with empirical distributions for lead time and demand per unit time. [ABSTRACT FROM AUTHOR]

The response surface metamodel is a useful sequential methodology for approximating the relationship between the input variables and the output response in computer simulation. Several strategies have been proposed to increase the accuracy of the estimation of the metamodel. In the current paper, we introduce an effective pseudo-random number (PRN) assignment strategy with Box-Behnken design to construct a more accurate second-order polynomial metamodel to estimate the network reliability of a complex system. The results obtained from the simulation approach show that the reduction in maximum absolute relative error between the response surface approximation and the actual reliability function is 35.63% after the PRN assignment strategy is applied. [ABSTRACT FROM AUTHOR]

In a general k-level uncapacitated facility location problem (k-GLUFLP), we are given a set of demand points, denoted by D, where clients are located. Facilities have to be located at a given set of potential sites, which is denoted by F in order to serve the clients. Each client needs to be served by a chain of k different facilities. The problem is to determine some sites of F to be set up and to find an assignment of each client to a chain of k facilities so that the sum of the setup costs and the shipping costs is minimized. In this paper, for a fixed k, an approximation algorithm within a factor of 3 of the optimum cost is presented for k-GLUFLP under the assumption that the shipping costs satisfy the properties of metric space. In addition, when no fixed cost is charged for setting up the facilities and k=2, we show that the problem is strong NP-complete and the constant approximation factor is further sharpen to be 3/2 by a simple algorithm. Furthermore, it is shown that this ratio analysis is tight. [ABSTRACT FROM AUTHOR]

In this paper, we model and solve the network interdiction problem of minimizing the maximum flow through a network from a given source node to a terminus node, while incorporating different forms of superadditive synergy effects of the resources applied to the arcs in the network. Within this context, we examine linear, concave, and convex-concave synergy relationships, illustrate their relative effect on optimal solution characteristics, and accordingly develop and test effective solution procedures for the underlying problems. For a concave synergy relationship, which yields a convex programme, we propose an inner-linearization procedure that significantly outperforms the competitive commercial solver SBB by improving the quality of solutions found by the latter by 6.2% (within a time limit of 1800 CPU s), while saving 84.5% of the required computational effort. For general non-concave synergy relationships, we develop an outer-approximation-based heuristic that achieves solutions of objective value 0.20% better than the commercial global optimization software BARON, with a 99.3% reduction in computational effort for the subset of test problems for which BARON could identify a feasible solution within the set time limit. [ABSTRACT FROM AUTHOR]

This paper describes an application of revenue management techniques and policies in the field of logistics and distribution. In particular, the problem of transportation operators, who offer products for hire, is considered. A product is a truck of a given capacity, which can be rented for one or several time periods, throughout a multi-period planning horizon. The logistic operator can satisfy the demand of a given product with trucks with a capacity greater than that initially required, that is an 'upgrade' can take place. In this context, the logistic operator has to decide whether to accept or reject a request and which type of truck should be used to address it. For this purpose, a dynamic programming (DP) formulation of the problem under consideration is devised. The 'course of dimensionality' leads to the necessity of introducing different mathematical programming models to represent the problem. The mathematical models we presented are an extension of the well-known approximations for the DP of traditional network capacity management analysis. Based on these models and exploiting revenue management concepts, primal and dual acceptance policies are developed and compared in a computational study. [ABSTRACT FROM AUTHOR]

In this paper, we consider the unbounded parallel-batch scheduling with rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and processed in batches on a machine. The processing time of a batch is defined as the longest processing time of the jobs contained in it. Four problems are considered: (1) to minimize the sum of the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs; (2) to minimize the total completion time of the accepted jobs subject to an upper bound on the total rejection penalty of the rejected jobs; (3) to minimize the total rejection penalty of the rejected jobs subject to an upper bound on the total completion time of the accepted jobs; (4) to find the set of all the Pareto optimal schedules. We provide a polynomial-time algorithm for the first problem. Furthermore, we show that all the other three problems are binary NP-hard and present a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for them. [ABSTRACT FROM AUTHOR]

The Thompson metric provides key geometric insights in the study of non-linear matrix equations and in many optimization problems. However, knowing that an approximate solution is within d T units, in the Thompson metric, of the actual solution provides little insight into how good the approximation is as a matrix or vector approximation. That is, bounding the Thompson metric between an approximate and accurate solution to a problem does not provide obvious bounds either for the spectral or the Frobenius norm, both Schatten norms, of the difference between the approximation and accurate solution. This paper reports such an upper bound, namely that ∥ X − Y ∥ p ≤ 2 1 p e d − 1 e d max ∥ X ∥ p , ∥ Y ∥ p where ⋅ p denotes the Schatten p-norm and d denotes the Thompson metric between X and Y. Furthermore, a more geometric proof leads to a slightly better bound in the case of the Frobenius norm, ∥ X − Y ∥ 2 ≤ e d − 1 e 2 d + 1 ∥ X ∥ 2 2 + ∥ Y ∥ 2 2 ≤ 2 1 2 e d − 1 e 2 d + 1 max ∥ X ∥ p , ∥ Y ∥ p . [ABSTRACT FROM AUTHOR]

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample sizes. The test statistics can be relatively easily computed using the package , or similar MATLAB software. Application of the tests is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model, the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace, estimation of the optimal subspace, and estimation of the regression kernel. [ABSTRACT FROM AUTHOR]

Copyright of Hydrological Sciences Journal/Journal des Sciences Hydrologiques is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The use of multiscale statistics, that is, the simultaneous inference about various stretches of data via multiple localized statistics, is a natural and popular method for inference about, for example, local qualitative characteristics of a regression function, a density, or its hazard rate. We focus on the problem of providing simultaneous confidence statements for the existence of local increases and decreases of a density and address several statistical and computational issues concerning such multiscale statistics. We first review the benefits of employing scale-dependent critical values for multiscale statistics and then derive an approximation scheme that results in a fast algorithm while preserving statistical optimality properties. The main contribution is a methodology for calibrating multiscale statistics that does not require a case-by-case derivation of its specific form. We show that in the above density context the methodology possesses statistical optimality properties and allows for a fast algorithm. We illustrate the methodology with two further examples: a multiscale statistic introduced by Gijbels and Heckman for inference about a hazard rate and local rank tests introduced by Dumbgen for inference in nonparametric regression. Code for the density application is available as the R package modehunt on CRAN. Additional code to compute critical values, reproduce the hazard rate and local rank example and the plots in the paper as well as datasets containing simulation results and an appendix with all the proofs of the theorems are available online as supplemental material. [ABSTRACT FROM AUTHOR]

With the number of wireless smart devices growing rapidly due to the constant technological advances and product availability, significant effort has been put into optimizing their functioning to achieve the best possible performance. Using a wireless device usually implies them having an integrated power supply, and often without a possibility of recharging it. To mitigate the devices running out of power too soon, there is a myriad of developed approaches. One of the approaches is to use a low-consumption data exchange protocol, such as Zigbee that relies on the short-range devices to construct a wireless personal area network and use it to relay messages. To route packages through the network, the Zigbee protocol uses the ad-hoc on-demand distant vector routing protocol. In this paper, we analyse two new versions of a modified ad-hoc on-demand distant vector routing protocol that define routes by maximizing a route quality measure based upon aggregated link quality approximations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new diagnosing technique for chronic kidney disease by using Artificial Neural Network (ANN). Where, the required data for the computational health-care system is collected from various hospitals at Jazan region, Saudi Arabia. Furthermore, in order to prove the convergence of this method, a ridge function is used in the hidden layer as a basis for the neurons. The technique applied for different number of neurons, and in each case a least square error is provided for choosing the best possible approximation. [ABSTRACT FROM AUTHOR]

This paper presents simple criteria which can be used to select which of the three members of the Johnson System of distributions should be used for fitting a set of data. The paper also presents elementary formulas for estimating the parameters for each of the members of the family. Thus, many obstacles to the use of the Johnson System are resolved. [ABSTRACT FROM AUTHOR]

In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein-Gordon and sine-Gordon equations. To present the present method's effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective. [ABSTRACT FROM AUTHOR]

In this paper, an optimal error estimate for system of parabolic quasi-variational inequalities related to stochastic control problems is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L∞-asymptotic behavior in maximum norm is proved using the semiimplicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolution and discrete regularity. [ABSTRACT FROM AUTHOR]

Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the W(Lr, ξ(t))-class by (..., pn, qn)(E, s)-product summability means of a Fourier series. The result obtained here, generalizes several known theorems. [ABSTRACT FROM AUTHOR]

In this work, we generated more topologies based on similarity relation for an information system and we found lower and upper approximations. This paper discussed two approaches for determining accuracy with Yao's method and Pawlak's method of qualitative data. From both ideas, it is seen that due to the uncertainty and vagueness of qualitative data, we get many topologies on one or two attributes. We determined the accuracies by the new method; this method showed the difference between one or two attributes. This method is clarified by application. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the Kantorovich-type Bernstein operators based on q-integers and get a Bohman-Korovkin-type approximation theorem of these operators. We also compute the rate of convergence using the first modulus of smoothness. [ABSTRACT FROM AUTHOR]

In this paper the optimal homotopy asymptotic method (OHAM) is employed to obtain approximate analytical solution of n th order ð n P 2 Þ linear fuzzy initial value problems (FIVPs). The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on n th linear FIVPs and comparisons of the exact solution that were made with numerical results showed the effectiveness and accuracy of this method. ª 2015 University of Bahrain. Publishing services by Elsevier B.V. [ABSTRACT FROM AUTHOR]

A cost-effective approach to the solution of 2D Navier-Stokes equations for incompressible fluid flow problems is presented. The aim is to reach a good compromise between numerical properties and computational efficiency. In order to achieve the set goal, the nonlinear convective terms are approximated by means of characteristics and spatial approximations of equal order are performed by polynomials of degree two. In this way, the computational kernels are reduced to elliptic ones for which solution very efficient techniques are available. The time-advancing is afforded by a fractional step method combined with a stabilization technique suitably simplified, so that the inf-sup condition is easily overcome. The algebraic systems generated by the new technique are solved by an iterative solver (Bi-CGSTAB), preconditioned by means of a suitable Schwarz additive scalable preconditioner. The properties of the new method have been confirmed from the comparison among the results obtained by it, and those obtained from other methods in the solution of some well known test problems. The obtained results, both in terms of accuracy and computational efficiency, make realistic the possibility to extend the method to 3D problems and to develop a multidomain approach. [ABSTRACT FROM AUTHOR]

Most inventory management systems at hospital departments are characterised by lost sales, periodic reviews with short lead times, and limited storage capacity. We develop two types of exact models that deal with all these characteristics. In a capacity model, the service level is maximised subject to a capacity restriction, and in a service model the required capacity is minimised subject to a service level restriction. We also formulate approximation models applicable for any lost-sales inventory system (cost objective, no lead time restrictions etc). For the capacity model, we develop a simple inventory rule to set the reorder levels and order quantities. Numerical results for this inventory rule show an average deviation of 1% from the optimal service levels. We also embed the single-item models in a multi-item system. Furthermore, we compare the performance of fixed order size replenishment policies and (R, s, 5) policies. [ABSTRACT FROM AUTHOR]

Copyright of Automatika: Journal for Control, Measurement, Electronics, Computing & Communications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Stochastic perturbation methods can be applied to problems for which either the objective function is represented analytically, or the objective function is the result of a simulation experiment. The Simultaneous Perturbation Stochastic Approximation (SPSA) method has the advantage over similar methods of requiring only two measurements at each iteration of the search. This feature makes SPSA attractive for robust parameter design (RPD) problems where some factors affect the variance of the response(s) of interest. In this paper, the feasibility of SPSA as a RPD optimizer is presented, first when the objective function is known, and then when the objective function is estimated by means of a discrete-event simulation. [ABSTRACT FROM AUTHOR]

This paper presents an approximation model for the retailer replenishment lead-times in a two-echelon distribution system, and discusses its implementation for safety stock optimization in a one-warehouse and N-identical retailers system. The model assumes normality of demand and nominal lead times. It takes into account not only the averages of these parameters but also their variances. This approximation model is first tested on a two-echelon, one-warehouse and N-identical retailers system using discrete event simulation. It is then applied to optimize the safety stock in a two-echelon distribution system of a European market leader in the production and distribution of air conditioning equipment. Results of this implementation are analysed and discussed in detail. [ABSTRACT FROM AUTHOR]

Copyright of Automatika: Journal for Control, Measurement, Electronics, Computing & Communications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article argues that if the Jordan curve theorem is false, then there is a solution to the utility graph puzzle. By the graph approximation theorem, there is a solution to the utility graph puzzle in which edges are horizontal and vertical segments, each of integral length. This graph can be described as a rectagon with three diagonals. By the Jordan curve theorem for rectagons, every diagonal lies in the interior or exterior region formed by the rectagon. By the pigeon-hole principle, at least two of the three diagonals traverse the same region.

This paper is focused on the exact calculation of the cycle service level for a generalized periodic review system accepting any discrete demand with a known probability function and any cycle service target. Previously, it was necessary to modify the definition of the cycle service level metric (also known as non stock out probability) so that it could be applied to these cases. The purpose of the proposed (R, S) system is to handle simultaneously fast-moving items, slow-moving items and intermittent or sporadic demand items any of them with high, medium or low cycle service targets. [ABSTRACT FROM AUTHOR]

It is well known that a local search method, a widely used approach for solving the permutation flow shop scheduling problem, can easily be trapped at a local optimum. In this paper, we propose two escape-from-trap procedures to move away from local optima. Computational experiments carried out on a standard set of instances show that this heuristic algorithm generally outperforms an effective approximation algorithm. [ABSTRACT FROM AUTHOR]

Paired comparison is a very popular method for establishing the relative importance of n objects, when they cannot be directly rated. The challenge faced by the pairwise comparison method stems from some missing properties in its associated matrix. In this paper, we focus on the following general problem: given a non-reciprocal and inconsistent matrix computing intransitivities, what is its associated ranking (defined by importance values)? We propose to use inconsistencies as a source of information for obtaining importance values. For this purpose, a methodology with a decomposition and aggregation phase is proposed. Interval Goal Programming will be a useful tool for implementing the aggregation process defined in the second phase. [ABSTRACT FROM AUTHOR]

Impingement of grinding fluid deep into grinding zone is a challenge due to presence of air layer around the grinding wheel. This paper presents experimental observation on air boundary layer formed around a rotating grinding wheel, a rexine-cloth covered grinding wheel and a solid disc. The effect of porous and rough grinding wheel surface towards strengthening air boundary layer has been studied. Modelling has been done to estimate variation of air pressure within this boundary layer. Out of three different methods of extrapolation done, the most suitable one is suggested. Results obtained using three different wheels are compared. A scraper board is also employed to observe reduction of air pressure. Higher value of air pressure is noted in case of bare grinding wheel than that in other conditions. Use of scraper board along with rexine-covered wheel is found to reduce air pressure to a large extent such that it becomes close to air pressure noted around the solid wheel. It shows the beneficial effect of using scraper board and rexine-pasted wheel to suppress air layer effectively. Correspondingly, grinding fluid is expected to reach deep into the grinding zone thereby rendering better control of grinding temperature, and hence, better grinding performance. [ABSTRACT FROM PUBLISHER]

In a graphical procedure for comparing k treatment means in a one-way ANOVA, one displays uncertainty intervals around the sample means and judges any pair to be significantly different if and only if their uncertainty intervals do not overlap. A graphical procedure is a Multiple Comparison Procedure (MCP) if and only if it controls the experimentwise error rate. In this paper we consider some new graphical MCP's for the unbalanced one-way ANOVA design. These procedures are based on different approximations to the Tukey-Kramer (TK) procedure (e.g., Kramer 1956). As such, they constitute alternatives to Gabriel (1978) (and its modification by Andrews, Snee, and Sarner 1980), which is based on approximating a less efficient MCP (the GT2 of Hochberg 1974). Two of the four procedures considered here are based on best and simple upper bounds to all the confidence-interval lengths of the TK method and hence must be conservative. The other two procedures are based on approximations (here too we have the best vs. the simple procedure), but simulations were used to find that their true experimentwise error rates are less than the nominal ones; that is, these procedures are still on the conservative side. The choice of a particular procedure will depend then on the relative importance of simplicity, efficiency, and the security of having a controlled experimentwise error rate. [ABSTRACT FROM AUTHOR]

This article is an expository paper to demonstrate the usefulness of Pearson curves in density estimation especially for those unaware of this early development in statistics. It is shown how to fit the curves and how very good approximate percentage points can be obtained for intractable distributions when the first four moments (or three moments and one endpoint) are known exactly (not estimated from sample data). The effectiveness of this method in density estimation is illustrated in three somewhat disparate contexts and reference is given to others. In general, the Pearson curves give an excellent approximation to the long tail of a distribution, the tail-most often needed in practical work. [ABSTRACT FROM AUTHOR]

Most of the literature on survey sampling deals with a single stratifying variable. In this paper an attempt is made to study the effect of using two stratifying variables. We present an approximation to the variance of the study variable under the assumption of a linear regression on the two stratifying variables. This approximation depends only on the number of strata, the simultaneous density of the stratifying variables, and the correlations between the study variable and each of the stratifying variables. The results indicate that in many practical situations the gain from using two stratifying variables over one is nontrivial. [ABSTRACT FROM AUTHOR]

This paper investigates the distribution-free outer confidence interval for the quantile interval introduced by Wilks. Besides exact expressions and a recurrence formula some bounds are derived for the probability of correct coverage of the quantile interval which improve bounds known up to now, and which are tested in several examples. Asymptotic approximations are discussed and applications of the developed methods to other statistics based on order statistics are indicated. [ABSTRACT FROM AUTHOR]