primal dual distance bounds of linear codes with application to cryptography let n d dperp denote the minimum length n of a linear code c with d and dperp where d is the minimum hamming distance of c and dperp is the minimum hamming distance of cperp in this correspondence we show lower bounds and an upper bound on n d dperp further for small values of d and dperp we determine n d dperp and give a generator matrix of the optimum linear code this problem is directly related to the design method of cryptographic boolean functions suggested by kurosawa et al

a general piecewise necessity regression analysis based on linear programming abstract in possibilistic regression analysis proposed by tanaka and ishibuchi 1992 linear programming lp formulation of necessity analysis has no feasible solution under the enormous variation of the given data this work proposes a general piecewise necessity regression analysis based on lp rather than a non linear interval model that they recommended to obtain the necessity area of the given data in addition to maintaining a linear property the proposed method prevents the necessity analysis from having no feasible solution the problematic univariate example and a multivariate example with respect to different number of change points are demonstrated by the general piecewise necessity regression the proposed method characteristic is that according to data distribution practitioners can specify the number and the positions of change points the proposed method maintains the linear interval model and the order of necessity regression function does not need to be determined

axisymmetric vibration of a circular plate with double linear variable thickness abstract the rayleigh ritz method has been employed to study the axisymmetric transverse vibration of a circular plate with two different linear variations in thickness one in the central core and the other in the outer annular region the boundary has been taken either clamped or simply supported results for linearly varying thickness and uniform thickness have been obtained as special cases and are compared with those available in the literature the effects of the various parameters on the frequencies mode shapes and the nodal radii have been examined through extensive numerical results given in the form of graphs and tables

a characterization of hermite polynomials we show that for any orthogonal polynomials p x o satisfying a spectral type differential equation of order n 2 n ln y x x y i x 2 y x i i pn x 0 must be essentially hermite polynomials if and only if the leading coefficient en x is a nonzero constant

reduction to least squares estimates in multiple fuzzy regression analysis in this paper we deal with the problem of least squares multiple regression with fuzzy data the regression coefficients are assumed to be real crisp a formula for solving the regression coefficients in one variable models is derived if each independent variable is effective i e its corresponding regression coefficient is nonzero the multiple regression problem can be replaced with a 0 1 programming problem its optimal solution is easily computed finally we also propose effective algorithms to compute the regression coefficients in a general case

aperiodic propagation criteria for boolean functions we characterise the aperiodic autocorrelation for a boolean function f and define the aperiodic propagation criteria apc of degree l and order q we establish the strong similarity between apc and the extended propagation criteria as defined by preneel et al in 1991 although the criteria are not identical we also show how aperiodic autocorrelation can be related to the first derivative of f we further propose the metric apc distance and show that quantum error correcting codes are natural candidates for boolean functions with favourable apc distance

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

further examination of fuzzy linear regression abstract fuzzy linear regression was originally introduced by tanaka et al 1982 sakawa and yano 1992 expanded fuzzy linear regression by introducing a method that allows fuzzy independent variables as well as a fuzzy dependent variable the purpose of this paper is to examine the strengths and weaknesses of this formulation suggest possible improvements and discuss fundamental questions about fuzzy linear regression

a spectral characterization of correlation immune combining functions it is shown that a boolean combining function f x of n variables is mth order correlation immune if and only if its walsh transform f omega vanishes for all omega with hamming weight between 1 and m inclusive this result is used to extend slightly siegenthaler s ieee trans comput vol c 34 pp 81 85 jan 1985 characterization of the algebraic normal form of correlation immune combining functions

fuzzy least absolutes regression using shape preserving operations the purpose of this study is to introduce a new fuzzy regression model based on the least absolutes method the fuzzy simple and fuzzy multivariate regression models with fuzzy input fuzzy output are considered in which the coefficients of the models are themselves fuzzy the proposed method is based on a new metric on the space of lr fuzzy numbers fuzzy arithmetic operations are based on the weakest triangular norm t w which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication the results of comparative studies and numerical examples indicate that using the similarity measure criterion as well as a predictive ability index the proposed method has a better performance than the least squares method especially when the data set includes some outlier data point s

general fuzzy piecewise regression analysis with automatic change point detection yu et al fuzzy sets and systems 105 1999 429 performed general piecewise necessity regression analysis based on linear programming lp to obtain the necessity area their method is the same as that according to data distribution even if the data are irregular practitioners must specify the number and the positions of change points however as the sample size increases the number of change points increases and the piecewise linear interval model also becomes complex therefore this work devises general fuzzy piecewise regression analysis with automatic change point detection to simultaneously obtain the fuzzy regression model and the positions of change points fuzzy piecewise possibility and necessity regression models are employed when the function behaves differently in different parts of the range of crisp input variables as stated the above problem can be formulated as a mixed integer programming problem the proposed fuzzy piecewise regression method has three advantages a previously specifying the number of change points then the positions of change points and the fuzzy piecewise regression model are obtained simultaneously b it is more robust than conventional fuzzy regression the conventional regression is sensitive to outliers in contrast utilizing piecewise concept the proposed method can deal with outliers by automatically segmenting the data c by employing the mixed integer programming the solution is the global optimal rather than local optimal solution for illustrating more detail two numerical examples are shown in this paper by using the proposed method the fuzzy piecewise regression model with detecting change points can be derived simultaneously

use of characteristic orthogonal polynomials in two dimensions for transverse vibration of elliptic and circular plates with variable thickness abstract free flexural vibrations of elliptic and circular plates with variable thickness have been studied by using characteristic orthogonal polynomials satisfying the essential boundary conditions and the rayleigh ritz method two types of variable thickness have been considered in the first case it varies linearly or quadratically parallel to the major axis in the second case it is taken to be the same along concentric ellipses but varies linearly or quadratically as we move from one ellipse to another the results for a circular plate with variable thickness follow as a special case computations have been carried out for clamped simply supported and free boundary comparison has been made with known results in special cases

vibrations of a cantilever tapered beam with varying section properties and carrying a mass at the free end abstract the free vibration frequencies of a beam composed of two tapered beam sections with different physical characteristics with a mass at its end can be determined by using either the exact procedure for which purpose the solution to the problem can be expressed using bessel functions or the approximate rayleigh ritz treatment with the assumption of orthogonal polynomials as test functions the results and the numerical comparison between the two methods are provided in diagrams and tables the effect of different materials on vibrations modes is also provided

fuzzy least squares linear regression analysis for fuzzy input output data a fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment most fuzzy regression models are considered to be fuzzy outputs and parameters but non fuzzy crisp inputs in general there are two approaches in the analysis of fuzzy regression models linear programming based methods and fuzzy least squares methods in 1992 sakawa and yano considered fuzzy linear regression models with fuzzy outputs fuzzy parameters and also fuzzy inputs they formulated multiobjective programming methods for the model estimation along with a linear programming based approach in this paper two estimation methods along with a fuzzy least squares approach are proposed these proposed methods can be effectively used for the parameter estimation comparisons are also made between them

linear regression analysis for fuzzy input and output data using the extension principle abstract the method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed the membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators in order to obtain the membership value of any given value taken from the fuzzy least squares estimator optimization problems have to be solved we also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data

a variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy fuzzy regression models have been applied to operational research or applications such as forecasting some of previous studies on fuzzy regression analysis obtain crisp regression coefficients for eliminating the problem of increasing spreads for the estimated fuzzy responses as the magnitude of the independent variable increases however they still cannot cope with the situation of decreasing or variable spreads this paper proposes a three phase method to construct the fuzzy regression model with variable spreads to resolve this problem in the first phase on the basis of the extension principle the membership functions of the least squares estimates of regression coefficients are constructed to conserve completely the fuzziness of observations in the second phase then they are defuzzified by the center of gravity method to obtain crisp regression coefficients in the third phase the error terms of the proposed model are determined by setting each estimated spread equals its corresponding observed spread furthermore the mamdani fuzzy inference system is adopted for improving the accuracy of its forecasts compared to the previous studies the results from five examples and an application example of japanese house prices show that the proposed fuzzy linear regression model has higher explanatory power and forecasting performance

fuzzy regression models using the least squares method based on the concept of distance fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment in order to increase the explanatory performance of the model the least squares method is applied to determine the numeric coefficients based on the concept of distance unlike most existing approaches the numeric coefficients in the proposed model can have negative values the proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few alpha cuts the proposed approach is not limited to triangular fuzzy numbers it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods comparisons with existing methods show that based on the total estimation error using the mean squared error and kim and bishu s criterion the explanatory performance of the proposed model is satisfactory

balanced symmetric functions over hbox gf p under mild conditions on n p we give a lower bound on the number of n variable balanced symmetric polynomials over finite fields gf p where p is a prime number the existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound furthermore we prove that x 2t 2t 1lscr 1 are balanced and conjecture that these are the only balanced symmetric polynomials over gf 2 where x d n sigma1lesi 1 i 2 hellip i d lesnxi 1xi 2hellipxi d

least squares estimates in fuzzy regression analysis abstract regression is a very powerful methodology for forecasting which is considered as an essential component of successful or applications in this paper an idea stemmed from the classical least squares is proposed to handle fuzzy observations in regression analysis based on the extension principle the membership function of the sum of squared errors is constructed the fuzzy sum of squared errors is a function of the regression coefficients to be determined which can be minimized via a nonlinear program formulated under the structure of the chen klein method for ranking fuzzy numbers to illustrate how the proposed method is applied three cases one crisp input fuzzy output one fuzzy input fuzzy output and one non triangular fuzzy observations are exemplified the results show that the least squares method of this paper is able to determine the regression coefficients with better explanatory power most important it works for all types of fuzzy observations not restricted to the triangular one

a mathematical programming approach to fuzzy linear regression analysis most of previous studies on fuzzy regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude which is not suitable for general cases in this paper fuzzy linear regression models with fuzzy crisp output fuzzy crisp input are considered and an estimated method along with a mathematical programming based approach is proposed the advantages of the proposed approach are simplicity in programming and computation and minimum difference of total spread between observed and estimated values

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

modifications of patterson wiedemann functions for cryptographic applications three basic properties of boolean functions to be useful for cryptographic purposes are balancedness high algebraic degree and high nonlinearity in addition strict avalanche criteria and propagation characteristics are required for design of s boxes we introduce methods to modify the patterson wiedemann 19983 1990 and bent functions to achieve the above cryptographic properties in the process we are able to answer some open questions about boolean functions

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

theoretical choice of the optimal threshold for possibilistic linear model with noisy input based on possibility concepts various possibilistic linear models plms have been proposed and their pivotal role in fuzzy modeling and associated applications has been established when adopting plms one has to adopt an appropriate threshold lambda value however choosing such a value is by no means trivial and is still an open theoretical issue in this paper we propose a solution by first extending the plm to its regularized version i e a regularized plm rplm such that its generalization capability can be enhanced the rplm is then formulated as a maximum a posteriori map framework which facilitates the determination of the theoretically optimal threshold value for the rplm with noisy input our mathematical derivations reveal the approximately inversely proportional relationship between the threshold and the standard deviation of gaussian noisy input this is also confirmed by the simulation results this finding is very helpful for the practical applications of both plms and rplms

a fuzzy linear regression model with better explanatory power previous studies on fuzzy linear regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude which is not suitable for general cases this paper proposes a two stage approach to construct the fuzzy linear regression model in the first stage the fuzzy observations are defuzzified so that the traditional least squares method can be applied to find a crisp regression line showing the general trend of the data in the second stage the error term of the fuzzy regression model which represents the fuzziness of the data in a general sense is determined to give the regression model the best explanatory power for the data the results from two examples one with crisp data and the other with fuzzy data for the independent variable indicate that the two stage method proposed in this paper has better performance than the previous studies

vibration in the two principal planes of a non uniform beam of rectangular cross section one side of which varies as the square root of the axial co ordinate abstract the transverse vibration of a type of slender beam of continuously varying rectangular cross section is considered in this paper one side of the cross section is constant while the other side is proportional to the square root of the axial co ordinate it is assumed that the beam dimensions are such that application of the euler bernoulli theory of bending is valid thus the vibration in the two principal planes will be uncoupled the two mode shape equations are fourth order linear differential equations with variable coefficients and with regular singularity analytical solutions of the two mode shape equations are derived based on the method of frobenius combinations of ideal clamped pinned sliding and free boundary conditions are considered the sharp end of a complete beam cannot sustain a bending moment or shearing force and hence must always remain free the large end may be clamped pinned sliding or free the frequency equations for a complete beam is the determinant of a 2 2 matrix equated to zero for a truncated beam any combinations of the four boundary conditions is possible and the frequency equations are the determinant of a 4 4 matrix equated to zero the first three dimensionless natural frequencies for vibration in the two principal planes are tabulated for 16 combinations of the four boundary conditions and truncation factors from 0 05 to 0 7 to preserve the accuracy of the frequencies to six figures the results are presented in tabular form it is hoped that they will serve as benchmarks

fuzzy linear regression analysis a multi objective programming approach fuzzy regression analysis is an extension of the classical regression analysis that is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment fuzzy regression has been criticized because it is sensitive to outliers it does not allow all data points to influence the estimated parameters and the spread of the estimated values become wider as more data are included in the model in this paper we develop a multi objective fuzzy linear regression model to overcome the above shortcomings

some algebraic properties of weakly non interactive fuzzy numbers abstract this study focuses on the concept of sup t norm convulution a generalized version of zadeh s extension principle the authors treat the algebraic structure of fuzzy arithmetic based on the sup t norm convolution and especially show some new properties comparing them with those of the conventional fuzzy arithmetic based on sup min convolution

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

sturm liouville equation for free vibration of a tube in tube tall building the equation for free vibration of a tube in tube tall building which is obtained by considering an influence coefficient due to the shear lag effect and using the equivalent closed tube method is proved strictly to be the fourth order sturm liouville differential equation and a formulation for calculating natural frequencies of the structure is obtained directly in comparison with other numerical and experimental results the frequencies found from the proposed method are quite satisfactory for practical use and are simple to calculate

a revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals conventional fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets however some limitations still exist this paper deals with a revisited approach for possibilistic fuzzy regression methods indeed a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property moreover this model output can have any kind of spread tendency in this framework the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution the potential of the proposed method with regard to the conventional approach is illustrated by simulation examples

multiobjective fuzzy regression with central tendency and possibilistic properties a multiobjective fuzzy regression model mofr is developed this mofr model combines central tendency and possibilistic properties of statistical and fuzzy regressions and overcomes several shortcomings of these two approaches a new class of distance measure for two intervals that takes into account all the points in both intervals is introduced the methodology is illustrated by numerical examples

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

multiobjective fuzzy linear regression analysis for fuzzy input output data abstract fuzzy linear regression models where both input data and output data are fuzzy numbers are introduced by using three indices for equalities between fuzzy numbers by considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model three types of multiobjective programming problems for obtaining fuzzy linear regression models are formulated corresponding to the three indices then a linear programming based interactive decision making method to derive the satisficing solution of the decision maker for the formulated multiobjective programming problems is developed a numerical example demonstrates the appropriateness and efficiency of the proposed method

fuzzy linear regression using rank transform method in regression analysis the rank transform rt method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers in this paper we construct a so called level fuzzy regression model based on the resolution identity theorem and apply rt method to this model fuzzy regression models with crisp input fuzzy output and fuzzy input fuzzy output are investigated to show the effectiveness of the proposed method to compare its effectiveness with existing methods we introduce a new performance measure in addition we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers

fuzzy nonlinear regression analysis using a random weight network modeling a fuzzy in fuzzy out system where both inputs and outputs are uncertain is of practical and theoretical importance fuzzy nonlinear regression fnr is one of the approaches used most widely to model such systems in this study we propose the use of a random weight network rwn to develop a fnr model called fnrrwn where both the inputs and outputs are triangular fuzzy numbers unlike existing fnr models based on back propagation bp and radial basis function rbf networks fnrrwn does not require iterative adjustment of the network weights and biases instead the input layer weights and hidden layer biases of fnrrwn are selected randomly the output layer weights for fnrrwn are calculated analytically based on a derived updating rule which aims to minimize the integrated squared error between cut sets that correspond to the predicted fuzzy outputs and target fuzzy outputs respectively in fnrrwn the integrated squared error is solved approximately by riemann integral theory the experimental results show that the proposed fnrrwn method can effectively approximate a fuzzy in fuzzy out system fnrrwn obtains better prediction accuracy in a lower computational time compared with existing fnr models based on bp and rbf networks

vibration frequencies of a rotating tapered beam with end mass abstract the natural frequencies of vibration of a rotating tapered beam with tip mass are investigated explicit expressions for the finite element mass and stiffness matrices are derived by using a consistent mass formulation the beam is assumed to be linearly tapered in two planes the generalized eigenvalue problem is defined and numerical solutions are generated for a wide range of rotational speed and tip mass variations both fixed and hinged end conditions are considered comparisons are made whenever possible with exact solutions and numerical results available in the literature the results display high accuracy when compared with the exact solutions

robust fuzzy regression analysis in this paper we propose a robust fuzzy linear regression model based on the least median squares weighted least squares lms wls estimation procedure the proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions we also define suitable goodness of fit indices useful to evaluate the performances of the proposed model the effectiveness of our model in reducing the outliers influence is shown by using applicative examples based both on simulated and real data and by a simulation study

dynamics of transversely vibrating beams using four engineering theories abstract in this paper the full development and analysis of four models for the transversely vibrating uniform beam are presented the four theories are the euler bernoulli rayleigh shear and timoshenko first a brief history of the development of each beam model is presented second the equation of motion for each model and the expressions for boundary conditions are obtained using hamilton s variational principle third the frequency equations are obtained for four sets of end conditions free free clamped clamped hinged hinged and clamped free the roots of the frequency equations are presented in terms of normalized wave numbers the normalized wave numbers for the other six sets of end conditions are obtained using the analysis of symmetric and antisymmetric modes fourth the orthogonality conditions of the eigenfunctions or mode shape and the procedure to obtain the forced response using the method of eigenfunction expansion is presented finally a numerical example is shown for a non slender beam to signify the differences among the four beam models

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

on cryptographic propagation criteria for boolean functions we determine the functions on gf 2 n which satisfy the propagation criterion of degree n 2 pc n 2 we study subsequently the propagation criterion of degree and order k and its extended version epc we determine those boolean functions on gf 2 n which satisfy pc of order k n 2 we show that none of them satisfies epc of the same order we finally give a general construction of nonquadratic functions satisfying epc of order k this construction uses the existence of nonlinear systematic codes with good minimum distances and dual distances e g kerdock codes and preparata codes

on cryptographic properties of the cosets of r 1 m we introduce a new approach for the study of weight distributions of cosets of the reed muller code of order 1 our approach is based on the method introduced by kasami 1968 using pless 1963 identities by interpreting some equations we obtain a necessary condition for a coset to have a high minimum weight most notably we are able to distinguish such cosets which have three weights only we then apply our results to the problem of the nonlinearity of boolean functions we particularly study the links between this criterion and the propagation characteristics of a function

determination of crack location in beams using natural frequencies abstract in this paper we describe a numerical method for determining the location of a crack in a beam of varying depth when the lowest three natural frequencies of the cracked beam are known the crack is modelled as a rotational spring and graphs of spring stiffness versus crack location are plotted for each natural frequency the point of intersection of the three curves gives the location of the crack earlier work in this area involved the use of the frobenius technique for solving the governing differential equation analytically and then using a semi numerical approach to obtain the crack location in this work we use the finite element approach to solve the same problem the beam is modelled using beam elements and the inverse problem of finding the spring stiffness given the natural frequency is shown to be related to the problem of a rank one modification of an eigenvalue problem examples outlining the accuracy and ease of using this method are shown the results are compared with those from semi analytical approaches the biggest advantage of this method is the generality in the approach different boundary conditions and variations in the depth of the beam can be easily modelled

insight of a fuzzy regression model fuzzy regression a nonparametric method can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise and variables are interacting in an uncertain qualitative and fuzzy way thus it may have considerably practical applications in many management and engineering problems but there is still lack of proper interpretation about fuzzy regression in this paper we provide an insight into regression intervals so that regression interval analysis data type analysis and variable selections can be analytically performed numerical examples are provided for illustration

free vibration analysis of rotating beams by a variable order finite element method the free vibration of rotating beams is analyzed by means of a finite element method of variable order this method entails displacement functions that are a complete power series of a variable number of terms the terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and additionally displacements at certain points within the element the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series numerical results are presented for uniform beams with zero and nonzero hub radii tapered beams and a nonuniform beam with discontinuities since the present method reduces to a conventional beam finite element method for a cubic displacement function the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom indeed essentially exact eigenvalues and eigenvectors are obtained with this technique which is far more rapidly convergent than other approaches in the literature

fuzzy linear regression analysis for fuzzy input output data using shape preserving operations abstract in this paper we have presented a new method to evaluate fuzzy linear regression models based on tanaka s approach where both input data and output data are fuzzy numbers using t w based fuzzy arithmetic operations this method simplifies the computation of fuzzy arithmetic operations general linear program is applied to derive the solutions we also prove scale independent property of our models and discuss the effects of outliers

nonparametric kernel estimation based on fuzzy random variables this paper extends the classical nonparametric curve fitting methods for fuzzy random variables the study was conducted in two parts 1 fuzzy density estimation and 2 nonparametric regression the classical nonparametric density estimation was first developed based on the kernel method for a given fuzzy random sample at crisp and or fuzzy point based on crisp or fuzzy bandwidth the classical bandwidth selection was also extended when the underlying population was normal with known or unknown fuzzy variance moreover the classical nonparametric kernel based regression model with crisp and or input or output is extended whenever a given bandwidth is a crisp or fuzzy number the cross validation procedure for selecting the optimal value of the crisp smoothing parameter is also extended to fit the proposed nonparametric regression model the large sample properties of the proposed fuzzy estimators were also investigated by some theorems several numerical examples including that of real life data are used to illustrate the proposed methods in curve fitting estimation with crisp and or fuzzy information moreover the proposed methods were examined in comparison with some other existing methods and their effectiveness were clarified via some numerical examples and simulation studies both theatrical and numerical results indicated that the nonparametric curve fitting methods significantly reduced the sum of square errors as well as the spreads of the fuzzy curve fitting estimation

transverse vibrations of a linearly tapered cantilever beam with constraining springs abstract the free vibrations of a linearly tapered cantilever beam elastically constrained at an arbitrary position along the length of the beam have been investigated using the bernoulli euler equation the beam has a rectangular cross section with equal taper in the horizontal and vertical planes and the constraint is a translational spring the characteristic determinant is derived in terms of dimensionless spring constant and the eigenfrequencies are determined using a straight search and bisection method the results are presented in tabular and graphical form

properties of certain fuzzy linear regression methods abstract fuzzy linear regression was originally introduced by tanaka uejima and asai ieee trans systems man cybern 12 1982 903 907 in subsequent years several different approaches to fuzzy linear regression have been proposed the purpose of this paper is to review and examine some of these formulations to discuss their strengths and weaknesses relative to each other and to suggest possible improvements in addition we compare and contrast these methods to the method of ordinary least squares regression

dependency between degree of fit and input noise in fuzzy linear regression using non symmetric fuzzy triangular coefficients fuzzy linear regression flr model can be thought of as a fuzzy variation of classical linear regression model it has been widely studied and applied in diverse fields when noise exists in data it is a very meaningful topic to reveal the dependency between the parameter h i e the threshold value used to measure degree of fit in flr model and the input noise in this paper the flr model is first extended to its regularized version i e regularized fuzzy linear regression rflr model so as to enhance its generalization capability then rflr model is explained as the corresponding equivalent maximum a posteriori map problem finally the general dependency relationship that the parameter h with noisy input should follow is derived particular attention is paid to the regression model using non symmetric fuzzy triangular coefficients it turns out that with the existence of typical gaussian noisy input the parameter h is inversely proportional to the input noise our experimental results here also confirm this theoretical claim obviously this theoretical result will be helpful to make a good choice for the parameter h and to apply flr techniques effectively in practical applications

a direct solution for the transverse vibration of euler bernoulli wedge and cone beams abstract a number of publications have appeared on the transverse vibration of complete and truncated wedge and cone beams the mode shape equations are linear differential equations with regular singularity the natural frequencies of complete beams are found in several publications for truncated beams several numerical solutions have been proposed and the natural frequencies documented in most cases for cantilever wedge and cone beams clamped at the large end analytical solutions of the mode shape equations have been derived based on bessel functions only in one publication are the natural frequencies tabulated for nine combinations of clamped pinned and free boundary conditions but the accuracy of the frequencies is limited to two figures after the decimal point for the fundamental frequency and the higher mode frequencies are rounded to integers the results are not suitable for judging the quality of the various approximate methods in this paper a direct solution of the mode shape equation is presented the sliding boundary condition is also considered and the first three dimensionless natural frequencies computed for 16 combinations of the boundary conditions are tabulated for values of truncation factors from 0 05 to 0 7 the tabulated results are benchmarks and frequencies for truncation factors not in the tables may be interpolated to within 0 1 accuracy

an enhanced fuzzy linear regression model with more flexible spreads one of the deficiencies of previous fuzzy linear regression models is that with the increase of the magnitudes of independent variables the spreads of estimated fuzzy dependent variables are increasing even though the spreads of observed dependent variables actually decrease or remain unchanged some solutions have been proposed to solve this spreads increasing problem however those solutions still cannot model a decreasing trend in the spreads of the observed dependent variables as the magnitudes of the independent variables increase in this paper we propose an enhanced fuzzy linear regression model model flr f s in which the spreads of the estimated dependent variables are able to fit the spreads of the observed dependent variables no matter the spreads of the observed dependent variables are increased decreased or unchanged as the magnitudes and spreads of the independent variables change four numerical examples are used to demonstrate the effectiveness of model flr f s

a simple method for computation of fuzzy linear regression we propose a new method for computation of fuzzy regression that is simple and gives good solutions we consider two cases first when only the dependent variable is fuzzy our approach is given and is compared with those suggested in the literature secondly when both dependent and independent variables are fuzzy our approach is extended and compared with those given in the literature in each case a simple example is used to compare the competing approaches

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

numerical methods for higher order sturm liouville problems we review some numerical methods for self adjoint and non self adjoint boundary eigenvalue problems