on the existence of nodal domains for elliptic differential operators we prove that the selfadjoint elliptic differential equation 1 has rectangular nodal domains if the quadratic form of the equation takes on negative values the existence of nodal domains is closely connected with the position of the smallest point of the spectrum of the corresponding selfadjoint operator friedrichs extension if the smallest point of a second order selfadjoint differential operator with dirichlet boundary conditions is an eigenvalue then this eigenvalue is strictly increasing when the possibly unbounded domain where the coefficients of the differential operator are denned is shrinking theorem 4

on bootstrap iteration for coverage correction in confidence intervals abstract iterated bootstrap procedures may be used to reduce error in many statistical problems we discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n 1 2 in one sided intervals but of order n 1 in two sided intervals explicit formulas are provided for the dominant term in coverage error after iteration in each case these results are used to compare various iterated bootstrap intervals and to assess the effect of bootstrap iteration on other indicators of interval performance such as position of critical points and length of interval we show that for one sided intervals the coverage correction algorithm yields critical points that are second order correct this is not the case for two sided intervals where second order correctness is not crucial in obtaining high order coverage accuracy we also show that the asymptotic mean increase in length between the original and cove

an efficient coding system for long source sequences the elias source coding scheme is modified to permit a source sequence of practically unlimited length to be coded as a single codeword using arithmetic of only limited precision the result is shown to be a nonblock arithmetic code of the first in first out fifo type source symbols are decoded in the same order as they were encoded codeword lengths which are near optimum for the specified statistical properties of the source can be achieved explicit encoding and decoding algorithms are provided which effectively implement the coding scheme applications to data compression and cryptography are suggested

bootstrap confidence bands for shrinkage estimators empirical application of shrinkage estimators has been limited by the inability to estimate confidence intervals we investigate confidence band estimators based on edgeworth expansions and bootstrapping our monte carlo results suggest that both efron s bias correction method with acceleration and the simple percentile bootstrap methods generate reasonable confidence bands approximations based on edgeworth expansions performed poorly we then use the percentile method with a single bootstrap to generate bands for predictions of gnp growth rates from a leading indicators model our study shows that simple percentile bootstrap confidence bands perform well enough to support empirical applications of shrinkage estimators

applications of universal context modeling to lossless compression of gray scale images inspired by theoretical results on universal modeling a general framework for sequential modeling of gray scale images is proposed and applied to lossless compression the model is based on stochastic complexity considerations and is implemented with a tree structure it is efficiently estimated by a modification of the universal algorithm context several variants of the algorithm are described the sequential lossless compression schemes obtained when the context modeler is used with an arithmetic coder are tested with a representative set of gray scale images the compression ratios are compared with those obtained with state of the art algorithms available in the literature with the results of the comparison consistently favoring the proposed approach

reversible intraframe compression of medical images the performance of several reversible intraframe compression methods is compared by applying them to angiographic and magnetic resonance mr images reversible data compression involves two consecutive steps decorrelation and coding the result of the decorrelation step is presented in terms of entropy because huffman coding generally approximates these entropy measures within a few percent coding has not been investigated separately it appears that a hierarchical decorrelation method based on interpolation hint outperforms all other methods considered the compression ratio is around 3 for angiographic images of 8 9 b pixel but is considerably less for mr images whose noise level is substantially higher

oscillation criteria for pde with p laplacian via the riccati technique abstract the conditions on the function c x r n r are derived which ensure that the pde div u p 2 u c x u p 2u 0 p 1 is oscillatory i e belongs to the closure of the set of zeros of every solution defined on the domain x r n x 1 the main tool is the riccati technique combined with suitable a priori bounds

double bootstrap for shrinkage estimators computer intensive bootstrap methods are potentially problematic when applied to biased estimators similar to ridge regression because biased estimators may lack a pivot we propose a modification for efron s bias corrected percentiles and suggest an approximate pivoting transformation for ridge regression we indicate practical aspects of beran s double bootstrap designed specifically for situations where there is nonnormality and a lack of a pivot econometric applications to estimating consumption functions a simulation with multicollinear data and new graphical tools are included

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

integral inequalities and second order linear oscillation on the interval 0 a u 0 below by a solution we mean a non trivial solution a solution is oscillatory if it has an infinite number of zeros numerous oscillation criteria are known and diversified approaches have proved fruitful among these is the use of the associated riccati equation although the theory of differential and integral inequalities has been used by some investigators see e g hartman 4 71 the authors believe that it has not been fully exploited the non oscillation of 1 1 is equivalent to the existence of a solution of the associated riccati equation on a half line thus one technique of proving oscillation is to show that any solution of the riccati equation diverges to i co at a finite point the theory of differential and integral inequalities comes in handy in the estimation of the growth of such a solution below we describe some known results that are relevant to results established in this paper although these are stated here for the case i co in the rest of the paper we consider both cases a 0 and a 00 it is well known that if q is large in the mean then 1 1 is oscillatory a typical example of such a criterion is due to fite leighton and wintner if

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

eigenvalues below the essential spectra of singular elliptic operators on developpe une nouvelle technique pour determiner si le nombre de valeurs propres au dessous du spectre essentiel d un operateur elliptique singulier est fini on donne une methode pour etablir des bornes inferieures au plus petit point du spectre essentiel en fonction du comportement des coefficients et du poids pres des singularites

bootstrapping improved estimators for linear regression models abstract since stein 1955 proved that the least squares ls estimator for the linear regression model is inadmissible and james and stein 1961 demonstrated a superior estimator under squared error loss a number of better estimators have been proposed one reason these estimators have not been used in empirical work is that it is difficult to derive their sampling distributions this study shows that nonparametric bootstrapping provides good estimates of the sampling distribution of mundlak s 1981 restricted principal components estimator and a new stein rule estimator which shrinks mundlak s towards ls a monte carlo study of the bootstrap is performed for a range of increasingly collinear designs with 100 observations and 10 regressors using a squared error loss function the stein rule estimator performed much better than ls over most of the designs the nonparametric bootstrap generated reasonable estimates of the estimator s risk as well as standard errors of the individual components

near lossless image compression minimum entropy constrained error dpcm a near lossless image compression scheme is presented it is essentially a differential pulse code modulation dpcm system with a mechanism incorporated to minimize the entropy of the quantized prediction error sequence with a near lossless criterion of no more than a d gray level error for each pixel where d is a small nonnegative integer trellises describing all allowable quantized prediction error sequences are constructed a set of contexts is defined for the conditioning prediction error model and an algorithm that produces minimum entropy conditioned on the contexts is presented finally experimental results are given

integral averages and oscillation criteria for half linear partial differential equation the technique of weighted integral averages known in the oscillation theory of ordinary differential equations is extended to the half linear partial differential equation e div email protected email protected p email protected u c x u p 2u 0 p 1 this technique is used to obtain new oscillation criteria for e on the unbounded domains

oscillation of the half linear pde in general exterior domains the variational approach abstract in the paper a variational technique is used to show how to derive new oscillation criteria for the half linear partial differential equation via the oscillation criteria for the ordinary half linear differential equation in contrast to the results usually found in the literature general types of unbounded domains can be considered

the use of contextual information in the reversible compression of medical images the authors investigate the use of conditioning events or contexts in improving the performances of known compression methods by building a source model with multiple contexts to code the decorrelated pixels three methods for reversible compression namely dpcm differential pulse code modulation wht walsh hadamard transform and hint hierarchical interpolation employing respectively predictive decorrelation transform decorrelation and multiresolution decorrelation are considered it is shown that the performance of these methods can be enhanced significantly sometimes even up to 40 by using contexts the enhanced dpcm method is found to perform the best for mr and ut ultrasound medical images the enhanced wht method is found to be the best for x ray images the source models used in the enhanced models employ several hundred contexts

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

an application of integral inequality to second order nonlinear oscillation abstract a simple result concerning integral inequalities enables us to give an alternative proof of waltman s theorem lim t t 0 a s ds implies oscillation of the second order nonlinear equation y t a t f y t 0 to prove an analog of wintner s theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations assuming that lim t t 0 a s ds exists and to give an alternative proof and to extend a result of butler an often used condition on the coefficient a t is given a more familiar equivalent form and an oscillation criterion involving this condition is established

note on wong s paper using the method of interval integral average we establish some new oscillation criteria which improve the oscillation criteria due to james s w wong

interval criteria for oscillation of second order nonlinear neutral differential equations some new oscillation criteria are established in this paper for the second order nonlinear neutral delay differential equation r t x t p t x t q t f x t 0 where and are nonnegative constants r p q c t0 r and f c r r these results are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results about neutral and delay differential equations in particular several examples that dwell upon the sharp conditions of our results are also included

on the connection between schrodinger and dirichlet forms relations between schrodinger forms associated with schrodinger operators in l2 dnx rn open n 1 and the corresponding dirichlet forms are investigated various concrete examples are presented

oscillation and nonoscillation of hill s equation with periodic damping we prove new results on the oscillation and nonoscillation of the hill s equation with periodic damping y p t y q t y 0 t 0 where p t and q t are continuous and periodic the results show that the equation y sint y cost y 0 is nonoscillatory whilst the equation y cost y sint y 0 is oscillatory

on the robustness of shrinkage predictors in regression to differences between past and future data on etudie la robustesse des predicteurs de copas 1983 vis a vis des ecarts a la distribution

universal modeling and coding the problems arising in the modeling and coding of strings for compression purposes are discussed the notion of an information source that simplifies and sharpens the traditional one is axiomatized and adaptive and nonadaptive models are defined with a measure of complexity assigned to the models a fundamental theorem is proved which states that models that use any kind of alphabet extension are inferior to the best models using no alphabet extensions at all a general class of so called first in first out fifo arithmetic codes is described which require no alphabet extension devices and which therefore can be used in conjunction with the best models because the coding parameters are the probabilities that define the model their design is easy and the application of the code is straightforward even with adaptively changing source models

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

interval oscillation of second order half linear functional differential equations by using an inequality due to hardy littlewood and polya and averaging functions new interval oscillation criteria are established for the half linear functional differential equationr t y t a 1y t q t y t t a 1y t t 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results extend and improve some previous oscillation criteria and handle the cases which are not covered by known results and implies that the delay t t t t does not effect the oscillation where t 0 is a constant in particular several examples that dwell upon the sharp conditions of our results are also included

forecasting turning points in international output growth rates using bayesian exponentially weighted autoregression time varying parameter and pooling techniques abstract in this paper two variants of an autoregressive leading indicator arli model are employed to forecast turning points in the growth rates of 18 countries annual real output for the years 1974 1986 bayesian predictive densities have been employed to compute probabilities of downturns and upturns and they have been employed in a bayesian decision theoretic framework to obtain optimal turning point forecasts various versions of the arli model with and without pooling of data across countries produced about 70 to 80 percent correct forecasts for 158 turning points time varying parameter models performed slightly better than others the performance of the arli models in forecasting turning points is shown to be considerably better than that of four naive methods of forecasting turning points

oscillation criteria of nehari type for sturm liouville operators and elliptic differential operators of second order and the lower spectrum on etablit des criteres suffisants d oscillation de type nehari pour l equation differentielle u q t u t 0 0 t avec et sans restriction de signe sur q t on etend ces resultats aux equations de sturm liouville et aux equations elliptiques d ordre 2

fuzzy logic based matching pursuits for lossless predictive coding of still images this paper presents an application of fuzzy logic techniques to the reversible compression of grayscale images with reference to a spatial differential pulse code modulation dpcm scheme prediction may be accomplished in a space varying fashion either as adaptive i e with predictors recalculated at each pixel or as classified in which image blocks or pixels are labeled in a number of classes for which fitting predictors are calculated here an original tradeoff is proposed a space varying linear regression prediction is obtained through fuzzy logic techniques as a problem of matching pursuit in which a predictor different for every pixel is obtained as an expansion in series of a finite number of prototype nonorthogonal predictors that are calculated in a fuzzy fashion as well to enhance entropy coding the spatial prediction is followed by context based statistical modeling of prediction errors a thorough comparison with the most advanced methods in the literature as well as an investigation of performance trends and computing times to work parameters highlight the advantages of the proposed fuzzy approach to data compression

kamenev type and interval oscillation criteria for second order linear differential equations on a measure chain abstract we establish kamenev type criteria and interval criteria for oscillation of the second order scalar differential equation p t x t q t x t 0 on a measure chain our results cover those for differential equations and provide new oscillation criteria for difference equations several examples are given to show the significance of the results

on certain riccati integral equations and second order linear oscillation are closely related is well known many important results in the oscillation theory of 1 1 are in fact established by studying either 1 2 or 1 3 recent studies suggest that a great deal can still be said about 1 2 and l 3 thus leading to new results on 1 1 see 7 91 particularly useful in these studies is the theory of differential and integral inequalities the present work further supports this view point in this paper we first give a comparison theorem section 2 theorem 1 for riccati integral equations of the form 1 3 involving monotonic rearrangements of the function q t ji q s ds as a corollary we establish an extension of the well known oscillation criteria of hille s 6 to more general potentials section 3 theorem 4 in section 4 we elaborate on a method of hartman to derive a comparison type result involving the square of the integral j h q s ds and then deduce a lyapunov type inequality for disfocality the preliminaries will be introduced in the appropriate sections 315 0022 247x 82 020315 16 02 00 o

linear transformation and oscillation criteria for hamiltonian systems abstract using a linear transformation similar to the kummer transformation some new oscillation criteria for linear hamiltonian systems are established these results generalize and improve the oscillation criteria due to i s kumari and s umanaheswaram i sowjaya kumari s umanaheswaram oscillation criteria for linear matrix hamiltonian systems j differential equations 165 2000 174 198 q yang et al q yang r mathsen s zhu oscillation theorems for self adjoint matrix hamiltonian systems j differential equations 190 2003 306 329 and s chen and z zheng shaozhu chen zhaowen zheng oscillation criteria of yan type for linear hamiltonian systems comput math appl 46 2003 855 862 these criteria also unify many of known criteria in literature and simplify the proofs

integral averaging technique for the interval oscillation criteria of certain second order nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line they generalize and improve some known results examples are also given to illustrate the importance of our results

interval criteria for oscillation of certain matrix differential systems by employing a generalized riccati technique and an averaging technique interval oscillation criteria are established for the second order matrix differential system of the form p t y q t y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are presented in the form of a high degree of generality handle the cases which are not covered by known criteria and can be applied to extreme cases such as limt 1 t0tq s ds in particular several interesting examples that dwell upon the importance of our results are included